Peak deconvolution for chromatographic time series composite signals

Abstract

The present disclosure is directed to systems and methods for accessing and analyzing chromatographic time-series composite signals that include multiple signal distributions, deconvoluting the signal distributions, and correlating such deconvoluted signals with chemical constituents of various sample types, e.g., samples of a biopharmaceutical purification process.

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Provisional Patent Application No. 63 / 305,516, filed February 1, 2022, the contents of which are incorporated by reference in their entirety and to which priority is claimed.

[0002] FIELD OF THEINVENTION The present disclosure is directed to systems and methods for accessing and analyzing chromatographic time-series composite signals comprising multiple signal distributions, deconvoluting the signal distributions, and correlating such deconvoluted signals with chemical constituents of various sample types, e.g., biopharmaceutical purification process samples. [Background technology]

[0003] Introduction Rapid advances in cell biology and immunology have driven the demand for developing novel therapeutic recombinant proteins for various diseases, including cancer, cardiovascular and metabolic diseases. These biopharmaceuticals are generally produced by commercially available cell lines capable of expressing the product of interest. For example, Chinese Hamster Ovary (CHO) cells have been widely adapted to produce monoclonal antibodies.

[0004] The use of cell lines to express biopharmaceuticals has necessitated the development of robust purification processes to facilitate the separation and isolation of the biopharmaceutical from cells, cell debris, and culture media, as well as undesired variants of the biopharmaceutical itself. Typically, a sample of interest, e.g., a purified or partially purified biopharmaceutical sample, is composed of multiple chemical components, and the goal of any assay used to assess the purity of the sample is to determine the amount of each component in the sample. Such determinations are often expressed as compositional data, with the relative abundance of each chemical component as a percentage. To accurately quantify the number or chemical components and their relative abundance, most assays aim to detect the chemical components separately, either by physical separation of the chemical components (as in chromatography) or by physical separation of signals from different chemical components (as in spectroscopy). However, identifying the number of chemical components and their relative abundance when the analytical technique has insufficient resolution may involve subjective assumptions about the number of chemical components present, and is subject to the risk of systematic error. For example, one analyst may assume that a chromatographic peak is composed of three chemical components, while another may identify four. Furthermore, analysts' judgments regarding the starting and ending peak integration positions may vary. Finally, when there is a large overlap or convolution between the signals of different chemical components, it may be difficult or impossible to accurately determine the relative areas by traditional methods (e.g., vertical line integrals, tangent integrals, iterative peak fitting, etc.). Thus, a technique that can robustly deconvolute signals from poorly resolved chromatographic time series signals, allowing improved identification and quantification of sample components, would save considerable time and improve the accuracy and robustness of current strategies. Summary of the Invention

[0005] Overview of Certain Embodiments Provided herein are systems and methods for accessing and analyzing chromatographic time-series composite signals that include multiple signal distributions, deconvoluting the signal distributions, and correlating such deconvoluted signals with chemical constituents of various sample types, e.g., samples from a biopharmaceutical purification process.

[0006] To effectively deconvolute peaks of a chromatographic time series composite signal, certain signal processing systems disclosed herein can use mathematically and statistically robust methods to interpret the signal and determine the number of chemical components, their elution times, and their relative abundance. In contrast to conventional methods that attempt to deconvolute the raw signal, the signal processing systems disclosed herein, in certain embodiments, can instead convert the signal into a count distribution. Furthermore, the signal processing systems disclosed herein, in certain embodiments, can use a Dirichlet process algorithm or any related suitable algorithm. This feature can enable a mathematically and statistically robust, consistent, and objective method for deconvoluting and integrating overlapping chromatographic peaks without subject matter expert intervention / assumptions. The ability to deconvolute peaks with large overlaps can enable much more rapid development of analytical assays, or in some cases, the use of standard assays that are normally inappropriate due to peak overlaps. One limitation of chromatographic assays (e.g., high performance liquid chromatography) is that increasing flow rates (accelerated assays) frequently results in a decrease in chromatographic resolution, preventing users from accurately determining chemical components and the number of those components. The ability to accurately identify and quantify chemical components in accelerated assays can expand the range of applications in which chromatographic assays can be useful. By way of example and not limitation, faster chromatographic assays can be used in-line or online in benchtop or production-scale bioreactors or chromatography skids to monitor and / or control bioprocessing in real time. Knowing the true relative abundance of chemical components (e.g., product variants and process impurities) can also provide more accurate process knowledge and lead to improvements when developing mechanistic models.Although this disclosure describes processing particular signals by particular systems in particular manners, this disclosure contemplates processing any suitable signal by any suitable system in any suitable manner.

[0007] In certain embodiments, the signal processing system disclosed herein can access a chromatographic time series synthetic signal that includes a plurality of signal distributions. The chromatographic time series synthetic signal can be associated with a two-dimensional (2D) array. In certain embodiments, a first dimension of the 2D array can include a plurality of indexes, and a second dimension of the 2D array can include a plurality of response values ​​that respectively correspond to the plurality of indexes. The signal processing system can then select a plurality of candidate index-response pairs from the 2D array. The signal processing system can further convert the chromatographic time series synthetic signal into a one-dimensional (1D) array. In certain embodiments, converting can include the following steps: For each of the plurality of candidate index-response pairs, the signal processing system can generate an array segment that includes one or more array elements. The number of the one or more array elements can be determined based on the response values ​​of the candidate index-response pair. The one or more array elements can be generated by unpacking the candidate index-response pair based on the array decomposition. The signal processing system can then concatenate a plurality of array segments that correspond to the plurality of candidate index-response pairs to generate a 1D array. In certain embodiments, the signal processing system can then process the 1D array with a probability distribution realization algorithm to determine one or more of the mean, standard deviation, or relative area of ​​each of the multiple signal distributions, the exponential decay component parameter, or any parameter that defines each of the multiple signal distributions. The signal processing system can then individually identify each of the multiple signal distributions based on one or more of the mean, standard deviation, or relative area of ​​each of the multiple signal distributions, the exponential decay component parameter, or any parameter that defines each of the multiple signal distributions. In certain embodiments, the signal processing system can further correlate each identified signal distribution with a chemical component.

[0008] In certain embodiments, the signal processing system can generate a one-dimensional (1D) array including array elements. Each array element can embody a plurality of signal distributions corresponding to a plurality of chemical components. In certain embodiments, the signal processing system can process the 1D array using a probability distribution realization algorithm to determine one or more of the mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, exponential decay component parameters, or any parameter defining each of the plurality of signal distributions. The signal processing system can further identify at least one signal distribution corresponding to a chemical component from the plurality of signal distributions corresponding to the plurality of chemical components. [Brief description of the drawings]

[0009] [Figure 1] 1 shows an exemplary chromatographic time series composite signal. [Diagram 2] 1 illustrates an exemplary workflow of data transformation for a probability distribution realization algorithm. [Diagram 3] 1 illustrates an exemplary method for peak deconvolution. [Figure 4] 1 illustrates an exemplary method for identifying a signal distribution. [Diagram 5] 1 illustrates an example of a computing system. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] explanation In certain embodiments, the signal processing system disclosed herein can access a chromatographic time series composite signal that includes a plurality of signal distributions. Each signal distribution can correspond to a chemical component. In certain embodiments, each signal distribution can be any suitable probability distribution function. By way of example and not limitation, each signal distribution can be a Gaussian distribution or an exponentially modified Gaussian distribution. Two or more of the plurality of signal distributions can be convolved. In certain embodiments, the chromatographic time series composite signal can be associated with a two-dimensional (2D) array. A first dimension of the 2D array can include a plurality of indexes, and a second dimension of the 2D array can include a plurality of response values ​​that respectively correspond to the plurality of indexes. In certain embodiments, the signal processing system can select a plurality of candidate index-response pairs from the 2D array. Each candidate index-response pair can include an index from the plurality of indexes and its corresponding response value from the plurality of response values. The signal processing system can then select a range of time for converting the chromatographic time series composite signal into a one-dimensional (1D) array. In certain embodiments, the signal processing system can remove drift of the baseline associated with the chromatographic time series composite signal. The signal processing system can then determine one or more binning parameters associated with a plurality of virtual bins used to convert the chromatographic time series composite signal into a 1D array. By way of example and not limitation, the one or more binning parameters can include one or more of: a number of a plurality of virtual bins determined based on a signal distribution of the chromatographic time series composite signal; a position of each virtual bin determined based on the number of virtual bins; a reference height of each virtual bin proportional to a sum signal of a range associated with the virtual bin; or a width of each virtual bin determined based on the number of virtual bins. The signal processing system can also generate a scaled response value for each response value of the plurality of index-response pairs by multiplying the response value by a scaling factor. In certain embodiments, the signal processing system can further convert the chromatographic time series composite signal into a one-dimensional (1D) array. The converting can include the following steps.For each of the plurality of candidate index-response pairs, the signal processing system can first identify a corresponding virtual bin from the plurality of virtual bins of the candidate index-response pairs. The identified virtual bin can be associated with a range of indices. The signal processing system can secondly generate an array segment including one or more array elements. The number of the one or more array elements can be determined based on the response values ​​of the candidate index-response pairs. The one or more array elements can be generated by unpacking the candidate index-response pairs based on the array decomposition. The element values ​​of the one or more array elements can be determined based on the range of indices. The signal processing system can thirdly distribute the one or more array elements to the identified virtual bins based on a pseudo-random low discrepancy sequence. In a particular embodiment, the signal processing system can concatenate the plurality of array segments corresponding to the plurality of candidate index-response pairs to generate a 1D array. The signal processing system can then process the 1D array using a probability distribution realization algorithm to determine one or more of the mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, exponential decay component parameters, or any parameter defining each of the plurality of signal distributions. By way of example and not of limitation, the probability distribution realization algorithm can be based on a Dirichlet process. In certain embodiments, the signal processing system can determine the number of multiple signal distributions of the chromatographic time series composite signal based on maximizing a likelihood function associated with the probability distribution realization algorithm. The signal processing system can then individually identify each of the multiple signal distributions based on one or more of the mean, standard deviation, or relative area of ​​each of the multiple signal distributions, exponential decay component parameters, or any parameter that defines each of the multiple signal distributions. In certain embodiments, the signal processing system can further correlate each identified signal distribution with a chemical component. Although the present disclosure describes processing a specific signal by a specific system in a specific manner, the present disclosure contemplates processing any suitable signal by any suitable system in any suitable manner.

[0011] FIG. 1 illustrates an exemplary chromatographic time series synthetic signal 100. The chromatographic time series synthetic signal 100 can refer to a signal having multiple peaks that overlap with each other. The chromatographic time series synthetic signal 100 can have a parent distribution 110. In certain embodiments, the chromatographic time series synthetic signal 100 can include a mixture model that includes multiple probability distributions. Each probability distribution can correspond to a chemical component. The chemical component can refer to a composition of matter that one wishes to identify from the chromatographic time series synthetic signal 100. By way of example and not limitation, the mixture model can include a Gaussian mixture model, and each of the probability distributions can include a Gaussian distribution or an exponentially modified Gaussian distribution. The chromatographic time series synthetic signal 100 can be the result of multiple chromatographic signals corresponding to different chemical components being convolved with each other. In other words, two or more of the multiple signal distributions can be convolved, i.e., there are peaks that overlap with each other. By way of example and not limitation, there may be four chromatographic signals corresponding to the four chemical components in FIG. 1. Each of them may have a respective child signal distribution 120, namely, child distribution 120a, child distribution 120b, child distribution 120c, and child distribution 120d. A signal distribution may refer to the distribution of signals corresponding to a chemical component. These signals may have overlap or convolution between them. In FIG. 1, the peaks of the child distributions 120a-c of the corresponding signals may still be identifiable, which may make it relatively easy to deconvolute them. However, more often the overlap may be much larger. For example, the peaks of the two signals may overlap by more than 50%. As another much more difficult scenario, the peak of one of the signals may be completely under the other peak of another signal, e.g., child distribution 120d may be completely within child distribution 120b. When such large overlap or convolution exists between the signals of different chemical components, it may be difficult or impossible to accurately determine the individual relative areas by traditional methods (e.g., vertical line integrals, tangent integrals, iterative peak fitting, etc.).Moreover, in many cases the number of chemical components may be unknown, making it much more difficult to individually identify each signal distribution. Although this disclosure describes the signals of a particular chromatogram in a particular manner, this disclosure contemplates processing any suitable chromatogram in any suitable manner.

[0012] In certain embodiments, to effectively deconvolute the chromatographic time series composite signal 100, which includes overlapping or convoluted signals corresponding to different chemical components, as illustrated in FIG. 1, the signal processing system can process and analyze the composite signal as follows: Occasionally, drift may occur in the chromatographic time series composite signal 100. Drift may be a low-frequency signal variation occurring in the baseline of the chromatographic time series composite signal 100. By way of example and not limitation, if the process is run without any injection, a line with a negative or positive slope may be seen. In order to properly process the chromatographic time series composite signal 100, increases or decreases may need to be removed. Thus, the signal processing system can remove the drift in the baseline associated with the chromatographic time series composite signal 100. In certain embodiments, the signal processing system can remove the drift in the baseline using a baseline removal algorithm. By way of example and not limitation, the signal processing system can use an open source baseline removal library associated with the chromatogram processing software.

[0013] In a particular embodiment, the signal processing system can convert the chromatographic time series synthetic signal 100 into a 1D array. The chromatographic time series synthetic signal 100 can be composed of thousands of data points that can be represented by a 2D array. The 2D array can be considered as a representation of the chromatographic time series synthetic signal 100. A first dimension of the 2D array can include an index, and a second dimension of the 2D array can include a response value that corresponds to each index. That is, each data point can be associated with an index and a corresponding response value, e.g., (1,1), (2,5), (3,20), etc., where the first dimension corresponds to the index (e.g., time) and the second dimension corresponds to the response value. Since each data point of the chromatographic time series synthetic signal 100 has an index and a corresponding response value, the entire chromatographic time series synthetic signal can be represented as a 2D array such as [(0.5,1), (1,2), (1,5)...]. In certain embodiments, the signal processing system can select multiple candidate index-response pairs from the 2D array. This may be because the chromatographic time series synthetic signal 100 is a continuous signal, which means it can have an indefinite number of data points. It may be necessary to select some of them and distribute them into virtual bins. As an example, and not as a limitation, 1, 2, 3, 4, 5 data points can be selected for times 0 to 5. For each selected data point, it can have the form [time, response] defined as a candidate index-response pair. As another example, and not as a limitation, the indices of these candidate index-response pairs can be 1, 2, ..., 1000, where the difference between any two adjacent indices is 1.

[0014] In certain embodiments, the probability distribution realization algorithm (e.g., a Dirichlet process algorithm) can operate only on the position (i.e., index) data and does not need to use the response values ​​directly. To solve this problem, the signal processing system can first convert each response value into a data point with counts only. By way of example and not limitation, (1,1) can be converted to [1] and (2,5) can be converted to [2,2,2,2,2]. However, the data points cannot be left in this form as this would introduce spikes in the data and make it impossible to develop a reasonable distribution. To solve this problem, the signal processing system can distribute the data points into virtual bins as outlined below.

[0015] FIG. 2 illustrates an exemplary workflow 200 of data transformation for a probability distribution realization algorithm. In certain embodiments, the 1D array 210 can be derived from a two-dimensional (2D) array, and an element value for each array element of the 1D array can be derived from one of a plurality of response values ​​of the 2D array. In certain embodiments, the signal processing system can select a range of time for transforming the chromatographic time series synthetic signal 100 into the 1D array 210. By way of example and not by way of limitation, the range of time can be 0 to 1000 seconds. By way of another example and not by way of limitation, the range of time can be 10 seconds to 100 seconds. In certain embodiments, the selected range of time can cover a threshold percentage (e.g., 95%) of the chromatographic time series synthetic signal 100. The signal processing system can then determine one or more binning parameters associated with a plurality of virtual bins (e.g., virtual bins 220a to 220d in FIG. 2) used to transform the chromatographic time series synthetic signal 100 into the 1D array 210. A virtual bin 220 may refer to where a data point is distributed. In certain embodiments, the one or more binning parameters may include one or more of: a number of the plurality of virtual bins 220 determined based on the signal distribution of the chromatographic time series composite signal 100; a position of each virtual bin 220 determined based on the number of virtual bins 220; a base height of each virtual bin 220 proportional to the sum signal of the range associated with that virtual bin 220; or a width of each virtual bin 220 determined based on the number of virtual bins 220. Although the present disclosure describes a particular data point distribution and a particular virtual bin (e.g., a flat bin), the present disclosure contemplates any suitable data point distribution and virtual bin (e.g., non-flat or sloping). In certain embodiments, any data point distribution corresponding to the chromatographic time series composite signal 100 may be used. The closer the data point distribution is to the original chromatographic time series composite signal 100, the better the results may be. By way of example and not limitation, the data point distribution may be a trapezoidal distribution. Correspondingly, each virtual bin may be a trapezoidal bin based on the local gradient.As another example, and not by way of limitation, the distribution of data points may be a random distribution of points.

[0016] In certain embodiments, the signal processing system may need to define a width of each virtual bin 220 for data delivery. The width of each virtual bin 220 may be determined based on the number of response values ​​of the selected candidate index response pairs 230, the distance between the indexes of the candidate index response pairs 230, and the number of virtual bins 220. By way of example and not limitation, if there are 100 virtual bins 220 and 1000 response values, each spaced 1 second apart (i.e., the time span is 1000 seconds), each virtual bin 220 may have a width of 10 seconds. In certain embodiments, the number of virtual bins 220 may be any suitable number. In certain embodiments, the virtual bins 220 may be of equal width. In alternative embodiments, the virtual bins 220 may have different widths. In certain embodiments, the signal processing system may improve speed by determining the width based on the curvature of the chromatographic time series composite signal 100. By way of example and not limitation, a flat portion of the chromatographic time-series synthetic signal 100 may include a small number of virtual bins 220 , while a curved portion may include many virtual bins 220 .

[0017] In certain embodiments, the signal processing system can generate scaled response values ​​for each of the multiple index-response pairs of the 2D array by multiplying the response value by a scaling factor. In other words, the signal processing system can scale the count number of each virtual bin 220 to provide a useful resolution. If the resolution is too low, changes in the chromatographic time-series composite signal 100 may not be captured. By way of example and not of limitation, for two index response pairs (5, 15.8) and (6, 16.4), if the scaling factor is 1, both index response pairs may be converted to 16 counts at 5 and 16 counts at 6, since counts can only be integer values. However, such conversion may cause some information loss. If the scaling factor is significantly larger, the resolution may be significantly higher, but the deconvolution may take much longer. In particular, the more data points there are, the longer it will take to deconvolve. By way of example and not limitation, if the scaling factor is 1 million, the two index response pairs mentioned above can be converted to 15.8 million counts at 5 and 16.4 million counts at 6. As can be seen, the counts can be well defined, but the likelihood of convergence of 30 million data points during optimization of the probability distribution realization algorithm can be low. In a particular embodiment, the signal processing system can use an exemplary scaling factor of 1000. Thus, the signal processing system can identify any difference in the chromatographic time series composite signal 100 that is greater than 0.1% (1 / 1000).

[0018] In a particular embodiment, the signal processing system may identify a corresponding virtual bin 220 from the multiple virtual bins 220 for each candidate index-response pair 230. The identified virtual bin 220 may be associated with a range of indices. The signal processing system may then randomly generate one or more array elements to be included in the array segment. An element value of the one or more array elements may be determined based on the range of indices, and the number of the one or more array elements may be equal to the scaled response value associated with the candidate index-response pair 230. By way of example and not limitation, an index-response pair may be (1,1) 230a, where the first 1 corresponds to an index (e.g., time) and the second 1 corresponds to the scaled response value. The signal processing system may need to distribute this index-response pair 230a into virtual bins 220 with an index range [0.5,1.5]. Thus, the signal processing system may generate one array element (count) with a randomly generated element value, such as 1, to be included in the array segment 240a. As another example, and not by way of limitation, another index-response pair may be (2,5) 230b, where 2 corresponds to an index (e.g., time) and 5 corresponds to a scaled response value. The signal processing system may need to distribute this index-response pair 230b into virtual bins 220 having a range of indices [1.5,2.5]. Thus, the signal processing system may generate five array elements (counts) with randomly generated element values ​​such as 1.6, 1.9, 2, 2.3, and 2.4. The signal processing system may further distribute the counts around a center point of each virtual bin 220 (e.g., center points 250a-250d in FIG. 2). Continuing with the previous example, the location of the virtual bin 220 may be 2, the width may be 1, and the counts may be distributed from 1.5 to 2.5 (i.e., the range of indices) around the center point 250 of 2.In certain embodiments, the signal processing system can distribute one or more generated array elements to the identified virtual bins 220 based on a quasi-random low discrepancy sequence (e.g., a Sobol sequence), thereby ensuring that the array elements are well distributed across the virtual bins 220. Continuing with the previous example of array elements 1.6, 1.9, 2, 2.3, and 2.4, the resulting array segment can be [1.6, 2.4, 2.3, 1.9, 2] 240b. In certain embodiments, if a trapezoidal distribution is used as the distribution of data points, the signal processing system can still use a quasi-random low discrepancy sequence, but with only linear scaling from one side to the other.

[0019] In a particular embodiment, the signal processing system may perform the above-mentioned array segment generation for each of the plurality of candidate index-response pairs 230 by distributing them into each of the plurality of virtual bins 220. The signal processing system may further concatenate a plurality of array segments 240 corresponding to the plurality of candidate index-response pairs 230 to generate the 1D array 210.

[0020] In certain embodiments, the signal processing system can then input the 1D array 210 into a probability distribution realization algorithm. By way of example and not limitation, the probability distribution realization algorithm can be based on a Dirichlet process. The Dirichlet process algorithm can be used with Gaussian distributions. The Dirichlet process algorithm can also be used with exponentially modified Gaussian distributions, which can better represent chromatographic signals.

[0021] In certain embodiments, the Dirichlet process algorithm may not technically be able to find the number of distributions in the chromatographic time series composite signal 100. The number of distributions may be infinite, and the total area of ​​all of them may be 1. Infinite distributions may not be computationally possible, and if so, the output may not be useful. Instead, the signal processing system may define a maximum number of possible distributions (i.e., corresponding to chemical components) that are expected to be found in the feedstock. By way of example and not limitation, the maximum number may be set to 10, but may be completely flexible. If it is certain that there are five or fewer chemical components, the maximum number may be set to 5, 15, or any suitable number.

[0022] In a particular embodiment, the Dirichlet process algorithm cycles through all array elements of the input 1D array 210 and can either assign it to an existing distribution or create a new distribution for it. This cycle can be repeated until convergence, i.e., until the array element assignments do not change any more. After convergence, the weighting coefficients used to determine whether a new distribution is created can be changed in a Monte Carlo manner and the process can be repeated. This cycle can continue until the weighting coefficients converge, i.e., changing the weighting coefficients does not result in an improved fit to the data.

[0023] In certain embodiments, the signal processing system can determine the number of signal distributions of the chromatographic time-series composite signal 100 based on maximizing a likelihood function associated with a probability distribution realization algorithm. In certain embodiments, the number of chemical components may be unknown. However, the signal processing system can determine the number of chemical components based on the determined number of signal distributions, which may be a technical advantage of the embodiments disclosed herein over conventional methods.

[0024] Once the algorithm has converged, the signal processing system can identify a number of spectral data points assigned to each of a plurality of signal distributions associated with a plurality of chemical components for the ensemble of spectral data points. The signal processing system can further determine a relative area associated with each of the plurality of signal distributions based on the identified number of spectral data points assigned to that signal distribution. In certain embodiments, a cutoff can also be defined at which the "found" distributions can be ignored. By way of example and not limitation, if the scaling factor is 1000, the cutoff can be set to 0.1% of the total area. If the maximum number of chemical components is set to 5, the final result of the relative area of ​​each chemical component can be, for example, [0.7, 0.29, 0.009, 0.00006, 0.00004]. However, since the last two values ​​are below the cutoff, the signal processing system can determine the relative area as [0.7, 0.29, 0.009]. Note that since this result is no longer 1, the relative area can be rescaled. The new area can be calculated as [0.7, 0.29, 0.009] / total([0.7, 0.29, 0.009]) = [0.7007, 0.2903, 0.009].

[0025] In certain embodiments, along with the relative areas, the algorithm may also provide the mean, standard deviation, or relative area of ​​each signal distribution, exponential decay component parameters (e.g., in the case of an exponentially modified Gaussian distribution), or any suitable parameters defining each signal distribution, which may also be used to identify each signal distribution.

[0026] 3 illustrates an exemplary method 300 for peak deconvolution of a convolved chromatogram signal. The method may begin at step 310, where a signal processing system may access a chromatographic time-series synthetic signal 100 including a plurality of signal distributions, the chromatographic time-series synthetic signal 100 being associated with a two-dimensional (2D) array, a first dimension of the 2D array including a plurality of indexes, and a second dimension of the 2D array including a plurality of response values ​​corresponding to the plurality of indexes, respectively. At step 320, the signal processing system may select a plurality of candidate index-response pairs 230 from the 2D array. At step 330, the signal processing system may convert the chromatographic time-series synthetic signal 100 into a one-dimensional (1D) array 210. Converting may include the following substeps: In sub-step 330a, the signal processing system can generate an array segment 240 including one or more array elements for each of the plurality of candidate index response pairs 230, the number of the one or more array elements being determined based on the response values ​​of the candidate index response pairs 230, and the one or more array elements being generated by unpacking the candidate index response pairs 230 based on the array decomposition. In sub-step 330b, the signal processing system can concatenate the plurality of array segments 240 corresponding to the plurality of candidate index response pairs 230 to generate the 1D array 210. In step 340, the signal processing system can process the 1D array 210 using a probability distribution realization algorithm to determine one or more of the mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, exponential decay component parameters, or any parameter defining each of the plurality of signal distributions. In step 350, the signal processing system can individually identify each of the plurality of signal distributions based on one or more of the mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, exponential decay component parameters, or any parameter defining each of the plurality of signal distributions. In step 360, the signal processing system can correlate each identified signal distribution with a chemical component.Certain embodiments may repeat one or more steps of the method of FIG. 3, where appropriate. Although the present disclosure describes and illustrates certain steps of the method of FIG. 3 as occurring in a particular order, the present disclosure contemplates any suitable steps of the method of FIG. 3 occurring in any suitable order. Moreover, although the present disclosure describes and illustrates an exemplary method for peak deconvolution of a convoluted chromatogram signal that includes certain steps of the method of FIG. 3, the present disclosure contemplates any suitable method for peak deconvolution of a convoluted chromatogram signal that includes any suitable steps, which may include all, some, or none of the steps of the method of FIG. 3, where appropriate. Moreover, although the present disclosure describes and illustrates certain components, devices, or systems that perform certain steps of the method of FIG. 3, the present disclosure contemplates any suitable combination of any suitable components, devices, or systems that perform any suitable steps of the method of FIG. 3.

[0027] FIG. 4 illustrates an exemplary method 400 for identifying a signal distribution. The method may begin at step 410, where a signal processing system may generate a one-dimensional (1D) array 210 including array elements, each array element embodying a plurality of signal distributions corresponding to a plurality of chemical components. In step 420, the signal processing system may process the 1D array 210 with a probability distribution realization algorithm to determine one or more of the mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, exponential decay component parameters, or any parameter defining each of the plurality of signal distributions. In step 430, the signal processing system may identify at least one signal distribution corresponding to a chemical component from the plurality of signal distributions corresponding to the plurality of chemical components. Certain embodiments may repeat one or more steps of the method of FIG. 4, as appropriate. Although the present disclosure describes and illustrates certain steps of the method of FIG. 4 as occurring in a particular order, the present disclosure contemplates any suitable steps of the method of FIG. 4 occurring in any suitable order. Moreover, although this disclosure describes and illustrates an exemplary method for identifying a signal distribution that includes particular steps of the method of Figure 4, this disclosure contemplates any suitable method for identifying a signal distribution that includes any suitable steps, which may include all, some, or none of the steps of the method of Figure 4, as appropriate. Moreover, although this disclosure describes and illustrates particular components, devices, or systems that perform particular steps of the method of Figure 4, this disclosure contemplates any suitable combination of any suitable components, devices, or systems that perform any suitable steps of the method of Figure 4.

[0028] FIG. 5 illustrates an exemplary computer system 500. In certain embodiments, one or more computer systems 500 perform one or more steps of one or more methods described or illustrated herein. In certain embodiments, one or more computer systems 500 provide functionality described or illustrated herein. In certain embodiments, software running on one or more computer systems 500 performs one or more steps of one or more methods described or illustrated herein or provides functionality described or illustrated herein. Certain embodiments include one or more portions of one or more computer systems 500. In this specification, reference to a computer system may encompass a computing device, and vice versa, where appropriate. Moreover, reference to a computer system may encompass one or more computer systems, where appropriate.

[0029] The present disclosure contemplates any suitable number of computer systems 500. The present disclosure contemplates computer system 500 taking any suitable physical form. By way of example and not limitation, computer system 500 may be an embedded computer system, a system on a chip (SOC), a single board computer system (SBC) (e.g., a computer on module (COM) or system on module (SOM)), a desktop computer system, a laptop or notebook computer system, an interactive kiosk, a mainframe, a mesh of computer systems, a mobile phone, a personal digital assistant (PDA), a server, a tablet computer system, or a combination of two or more of these. Where appropriate, computer system 500 may be monolithic or distributed, including one or more computer systems 500, span multiple locations, span multiple machines, span multiple data centers, or be in a cloud that may include one or more cloud components in one or more networks. Where appropriate, one or more computer systems 500 may perform one or more steps of one or more methods described or illustrated herein without substantial spatial or temporal limitations. By way of example, and not by way of limitation, the one or more computer systems 500 may perform one or more steps of one or more methods described or illustrated herein in real time or in batch mode. The one or more computer systems 500 may perform one or more steps of one or more methods described or illustrated herein at different times or in different locations, where appropriate.

[0030] In a particular embodiment, computer system 500 includes a processor 502, memory 504, storage 506, input / output (I / O) interface 508, communications interface 510, and a bus 512. Although this disclosure describes and illustrates a particular computer system having a particular number of particular components in a particular arrangement, this disclosure contemplates any suitable computer system having any suitable number of any suitable components in any suitable arrangement.

[0031] In particular embodiments, the processor 502 includes hardware for executing instructions, such as those that make up a computer program. By way of example and not by way of limitation, to execute an instruction, the processor 502 may retrieve (or fetch) an instruction from an internal register, an internal cache, memory 504, or storage 506, decode and execute the instruction, and then write one or more results to an internal register, an internal cache, memory 504, or storage 506. In particular embodiments, the processor 502 may include one or more internal caches for data, instructions, or addresses. This disclosure contemplates the processor 502 including any suitable number of any suitable internal caches, where appropriate. By way of example and not by way of limitation, the processor 502 may include one or more instruction caches, one or more data caches, and one or more translation lookaside buffers (TLBs). Instructions in the instruction caches may be copies of instructions in memory 504 or storage 506, and the instruction caches may speed up the retrieval of those instructions by the processor 502. The data in the data cache may be a copy of data in memory 504 or storage 506 on which instructions executing in the processor 502 are to operate, results of previous instructions executed in the processor 502 for access by subsequent instructions executing in the processor 502 or for writing to memory 504 or storage 506, or other suitable data. The data cache may speed up read or write operations by the processor 502. The TLB may speed up virtual address translation for the processor 502. In particular embodiments, the processor 502 may include one or more internal registers for data, instructions, or addresses. This disclosure contemplates a processor 502 including any suitable number of any suitable internal registers, where appropriate. Where appropriate, the processor 502 may include one or more arithmetic logic units (ALUs), be a multi-core processor, or include one or more processors 502.Although this disclosure describes and illustrates a particular processor, this disclosure contemplates any suitable processor.

[0032] In a particular embodiment, memory 504 includes a main memory for storing instructions for processor 502 to execute or data for processor 502 to operate on. By way of example and not by way of limitation, computer system 500 may load instructions from storage 506 or another source (such as, for example, another computer system 500) into memory 504. Processor 502 may then load the instructions from memory 504 into an internal register or cache. To execute an instruction, processor 502 may retrieve the instruction from the internal register or cache and decode the instruction. During or after execution of an instruction, processor 502 may write one or more results (which may be intermediate or final results) to an internal register or cache. Processor 502 may then write one or more of those results to memory 504. In particular embodiments, the processor 502 executes instructions only from one or more internal registers or caches (as opposed to storage 506 or elsewhere) or from memory 504, and operates only on data from one or more internal registers or caches (as opposed to storage 506 or elsewhere) or from memory 504. One or more memory buses (each of which may include an address bus and a data bus) may couple the processor 502 to the memory 504. The bus 512 may include one or more memory buses, as described below. In particular embodiments, one or more memory management units (MMUs) are between the processor 502 and the memory 504 and facilitate accesses to the memory 504 requested by the processor 502. In particular embodiments, the memory 504 includes random access memory (RAM). The RAM may be volatile memory, where appropriate. The RAM may be dynamic RAM (DRAM) or static RAM (SRAM), where appropriate. Moreover, the RAM may be single-ported or multi-ported RAM, where appropriate. The present disclosure contemplates any suitable RAM. Memory 504 may include one or more memories 504, where appropriate. Although this disclosure describes and illustrates a particular memory, this disclosure contemplates any suitable memory.

[0033] In particular embodiments, storage 506 includes mass storage for data or instructions. By way of example and not limitation, storage 506 may include a hard disk drive (HDD), a floppy disk drive, a flash memory, an optical disk, a magneto-optical disk, a magnetic tape, or a universal serial bus (USB) drive, or a combination of two or more of these. Storage 506 may include removable or non-removable (or fixed) media, where appropriate. Storage 506 may be internal or external to computer system 500, where appropriate. In particular embodiments, storage 506 is a non-volatile solid-state memory. In particular embodiments, storage 506 includes read-only memory (ROM). Where appropriate, this ROM may be a mask program ROM, a programmable ROM (PROM), an erasable PROM (EPROM), an electrically erasable PROM (EEPROM), an electrically alterable ROM (EAROM), or a flash memory, or a combination of two or more of these. This disclosure contemplates mass storage 506 taking any suitable physical form. Storage 506 may include one or more storage control units that facilitate communications between processor 502 and storage 506, where appropriate. Storage 506 may include one or more storages 506, where appropriate. Although this disclosure describes and illustrates particular storage, this disclosure contemplates any suitable storage.

[0034] In certain embodiments, I / O interface 508 includes hardware, software, or both, providing one or more interfaces for communication between computer system 500 and one or more I / O devices. Computer system 500 may include one or more of these I / O devices, as appropriate. One or more of these I / O devices may enable communication between a person and computer system 500. By way of example and not by way of limitation, the I / O devices may include a keyboard, a keypad, a microphone, a monitor, a mouse, a printer, a scanner, a speaker, a still camera, a stylus, a tablet, a touch screen, a trackball, a video camera, another suitable I / O device, or a combination of two or more of these. The I / O devices may include one or more sensors. This disclosure contemplates any suitable I / O devices and any suitable I / O interfaces 508 therefor. As appropriate, I / O interface 508 may include one or more device or software drivers that enable processor 502 to drive one or more of these I / O devices. I / O interface 508 may include one or more I / O interfaces 508, where appropriate. Although this disclosure describes and illustrates a particular I / O interface, this disclosure contemplates any suitable I / O interface.

[0035] In particular embodiments, the communication interface 510 includes hardware, software, or both that provide one or more interfaces for communication (e.g., packet-based communication, etc.) between the computer system 500 and one or more other computer systems 500 or one or more networks. By way of example and not by way of limitation, the communication interface 510 may include a network interface controller (NIC) or network adapter for communicating with an Ethernet or other wire-based network, or a wireless NIC (WNIC) or wireless adapter for communicating with a wireless network, such as a WI-FI network. This disclosure contemplates any suitable network and any suitable communication interface 510 therefor. By way of example and not by way of limitation, the computer system 500 may communicate with one or more portions of an ad-hoc network, a personal area network (PAN), a local area network (LAN), a wide area network (WAN), a metropolitan area network (MAN), or the Internet, or a combination of two or more of these. One or more portions of one or more of these networks may be wired or wireless. By way of example, computer system 500 may communicate with a wireless PAN (WPAN) (such as, for example, a BLUETOOTH WPAN), a WI-FI network, a WI-MAX network, a cellular telephone network (such as, for example, a Global System for Mobile Communications (GSM) network), or other suitable wireless networks or a combination of two or more of these. Computer system 500 may include any suitable communications interface 510 for any of these networks, as appropriate. Communications interface 510 may include one or more communications interfaces 510, as appropriate. Although this disclosure describes and illustrates a particular communications interface, this disclosure contemplates any suitable communications interface.

[0036] In particular embodiments, bus 512 includes hardware, software, or both that couple components of computer system 500 together. By way of example, and not limitation, bus 512 may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), a HYPERTRANSPORT (HT) interconnect, an Industry Standard Architecture (ISA) bus, an INFINIBAND interconnect, a Low Pin Count (LPC) bus, a memory bus, a MicroChannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI Express (PCIe) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or another suitable bus or a combination of two or more of these. Bus 512 may include one or more buses 512, where appropriate. Although this disclosure describes and illustrates a particular bus, this disclosure contemplates any suitable bus or interconnect.

[0037] As used herein, one or more computer-readable non-transitory storage media may include, where appropriate, one or more semiconductor-based or other integrated circuits (ICs) (such as, for example, field programmable gate arrays (FPGAs) or application specific ICs (ASICs)), hard disk drives (HDDs), hybrid hard drives (HHDs), optical disks, optical disk drives (ODDs), magneto-optical disks, magneto-optical drives, floppy diskettes, floppy disk drives (FDDs), magnetic tapes, solid state drives (SSDs), RAM drives, SECURE DIGITAL cards or drives, any other suitable computer-readable non-transitory storage media, or any suitable combination of two or more of these. A computer-readable non-transitory storage medium may be volatile, non-volatile, or a combination of volatile and non-volatile, where appropriate.

[0038] In this specification, "or" is inclusive and not exclusive, unless otherwise clearly indicated or indicated by the context. Thus, in this specification, "A or / or B" means "A, B, or / and both" unless otherwise clearly indicated or indicated by the context. Moreover, "and" is both jointly and severally, unless otherwise clearly indicated or indicated by the context. Thus, in this specification, "A and / and B" means "A and / and B, jointly or severally," unless otherwise clearly indicated or indicated by the context.

[0039] Exemplary embodiments In certain embodiments, the disclosure provides a method, comprising: accessing, by one or more computing systems, a chromatographic time-series synthetic signal including a plurality of signal distributions, each signal distribution corresponding to a chemical component, two or more of the plurality of signal distributions being convolved, the chromatographic time-series synthetic signal being associated with a two-dimensional (2D) array, a first dimension of the 2D array including a plurality of indexes, a second dimension of the 2D array including a plurality of response values ​​each corresponding to the plurality of indexes, each signal distribution being a Gaussian distribution or an exponentially modified Gaussian distribution; selecting a plurality of candidate index-response pairs from the 2D array, each candidate index-response pair including an index from the plurality of indexes and its corresponding response value from the plurality of response values; selecting a range of time for converting the chromatographic time-series synthetic signal to a one-dimensional (1D) array; and removing a baseline drift associated with the chromatographic time-series synthetic signal. determining one or more binning parameters associated with a plurality of virtual bins used to convert the chromatographic time-series composite signal into a 1D array, the one or more binning parameters including one or more of: a number of a plurality of virtual bins determined based on a signal distribution of the chromatographic time-series composite signal, a position of each virtual bin determined based on the number of virtual bins, a base height of each virtual bin proportional to a sum signal of a range associated with the virtual bin, or a width of each virtual bin determined based on the number of virtual bins; generating a scaled response value for each response value of the plurality of index-response pairs by multiplying the response value by a scaling factor; and converting the chromatographic time-series composite signal into a 1D array, the converting including: for each of a plurality of candidate index-response pairs, identifying a corresponding virtual bin from the plurality of virtual bins of the candidate index-response pairs, the identified virtual bin being associated with a range of indexes;generating array segments including one or more array elements, the number of the one or more array elements being determined based on scaled response values ​​of the candidate index-response pairs, the one or more array elements being generated by unpacking the candidate index-response pairs based on an array decomposition, and element values ​​of the one or more array elements being determined based on a range of indexes; distributing the one or more array elements to the identified virtual bins based on a quasi-random low discrepancy sequence; and further comprising concatenating a plurality of array segments corresponding to the plurality of candidate index-response pairs to generate a 1D array; and determining the mean, standard deviation, and average of each of the plurality of signal distributions. or processing the 1D array with a probability distribution realization algorithm to determine one or more of a relative area, an exponential decay component parameter, or any parameter defining each of the plurality of signal distributions, the probability distribution realization algorithm being based on a Dirichlet process; determining a number of a plurality of signal distributions in the chromatographic time-series composite signal based on maximizing a likelihood function associated with the probability distribution realization algorithm; individually identifying each of the plurality of signal distributions based on a mean, a standard deviation, or one or more of a relative area, an exponential decay component parameter, or any parameter defining each of the plurality of signal distributions, and correlating each identified signal distribution with a chemical component.

[0040] In certain embodiments, the disclosure provides a method, comprising: accessing, by one or more computing systems, a chromatographic time-series synthetic signal comprising a plurality of signal distributions, the chromatographic time-series synthetic signal being associated with a two-dimensional (2D) array, a first dimension of the 2D array comprising a plurality of indexes, and a second dimension of the 2D array comprising a plurality of response values ​​respectively corresponding to the plurality of indexes; selecting a plurality of candidate index-response pairs from the 2D array; and converting the chromatographic time-series synthetic signal into a one-dimensional (1D) array, the converting comprising: generating, for each of the plurality of candidate index-response pairs, an array segment comprising one or more array elements, a number of the one or more array elements being determined based on the response values ​​of the candidate index-response pairs; the plurality of array elements are generated by unpacking candidate index-response pairs based on an array decomposition, the plurality of array segments corresponding to the plurality of candidate index-response pairs are concatenated to generate a 1D array, the plurality of array elements include a transform, the plurality of array elements include a transform, the plurality of array segments corresponding to the plurality of candidate index-response pairs are concatenated to generate a 1D array ...

[0041] In certain embodiments of the above-described methods, two or more of the multiple signal distributions are convolved.

[0042] In certain embodiments of the above-described method, the method further comprises selecting a range of time for converting the chromatographic time series composite signal into a 1D array.

[0043] In certain embodiments of the above-described method, the method further comprises removing baseline drift associated with the chromatographic time-series composite signal.

[0044] In certain embodiments of the method described above in (B), the method further includes determining one or more binning parameters associated with a plurality of virtual bins used to convert the chromatographic time-series composite signal into a 1D array, the one or more binning parameters including one or more of: a number of a plurality of virtual bins determined based on a signal distribution of the chromatographic time-series composite signal; a position of each virtual bin determined based on the number of virtual bins; a reference height of each virtual bin proportional to a sum signal of a range associated with the virtual bin; or a width of each virtual bin determined based on the number of virtual bins.

[0045] In certain embodiments of the above-described method, the method further includes generating a scaled response value for each response value of the plurality of index-response pairs of the 2D array by multiplying the response value by a scaling factor.

[0046] In certain embodiments of the above-described method, generating an array segment for each of a plurality of candidate index-response pairs includes identifying a corresponding virtual bin from a plurality of virtual bins of the candidate index-response pair, where the identified virtual bin is associated with a range of indexes; randomly generating one or more array elements to be included in the array segment, where an element value of the one or more array elements is determined based on the range of indexes, and a number of the one or more array elements is equivalent to a scaled response value associated with the candidate index-response pair; and distributing the one or more generated array elements to the identified virtual bins based on a quasi-random low discrepancy sequence.

[0047] In certain embodiments of the above-described method, the chromatographic time-series composite signal includes a mixture model that includes a plurality of probability distributions, each probability distribution corresponding to a chemical component.

[0048] In certain embodiments of the above-described method, the mixture model comprises a Gaussian mixture model, and each of the probability distributions comprises a Gaussian distribution or an exponentially modified Gaussian distribution.

[0049] In a particular embodiment of the above method, the probability distribution realization algorithm is based on a Dirichlet process.

[0050] In certain embodiments of the above-mentioned method, the method further includes determining a number of a plurality of signal distributions in the chromatographic time-series composite signal based on maximizing a likelihood function associated with the probability distribution realization algorithm.

[0051] In certain embodiments of the above-described methods, the number of the plurality of chemical components is unknown, and the method further includes determining the number of the plurality of chemical components based on the determined number of signal distributions.

[0052] In certain embodiments of the above-described methods, the method further includes identifying a number of spectral data points assigned to each of a plurality of signal distributions associated with the plurality of chemical components for the ensemble of spectral data points, and determining a relative area associated with each of the plurality of signal distributions based on the identified number of spectral data points assigned to that signal distribution.

[0053] In certain embodiments, the present disclosure is directed to a method including: generating, by one or more computing systems, a one-dimensional (1D) array including array elements, each array element embodying a plurality of signal distributions corresponding to a plurality of chemical components; processing the 1D array with a probability distribution realization algorithm to determine one or more of the mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, exponential decay component parameters, or any parameters defining each of the plurality of signal distributions; and identifying at least one signal distribution corresponding to the chemical component from the plurality of signal distributions corresponding to the plurality of chemical components.

[0054] In a particular embodiment of the above-described method, the 1D array is derived from a two-dimensional (2D) array, a first dimension of the 2D array includes a plurality of indexes, and a second dimension of the 2D array includes a plurality of response values ​​each corresponding to the plurality of indexes.

[0055] In certain embodiments of the above-described method, an element value for each array element of the 1D array is derived from one of a plurality of response values ​​of the 2D array.

[0056] In certain embodiments of the above-mentioned method, the method further includes selecting a plurality of candidate index-response pairs from the 2D array and generating a scaled response value for each of the plurality of index-response pairs of the 2D array by multiplying the response value by a scaling factor, and generating the 1D array includes generating an array segment including one or more array elements for each of the plurality of candidate index-response pairs, where the number of the one or more array elements is determined based on the response values ​​of the candidate index-response pairs, and the one or more array elements are generated by unpacking the candidate index-response pairs based on the array decomposition, and concatenating the plurality of array segments corresponding to the plurality of candidate index-response pairs to generate the 1D array.

[0057] In certain embodiments of the above-described method, generating an array segment for each of a plurality of candidate index-response pairs includes determining a virtual bin for the candidate index-response pair, where the determined virtual bin is associated with a range of indices; randomly generating one or more array elements to be included in the array segment, where an element value of the one or more array elements is determined based on the range of indices and the number of the one or more array elements is equivalent to a scaled response value associated with the candidate index-response pair; and distributing the one or more generated array elements to the determined virtual bin based on a pseudo-random low discrepancy sequence.

[0058] In certain embodiments of the above-described methods, the 2D array is associated with a chromatographic time-series composite signal comprising a plurality of signal distributions, each signal distribution corresponding to a chemical component, and two or more of the plurality of signal distributions are convolved.

[0059] In certain embodiments of the above-described methods, two or more of the multiple signal distributions are convolved.

[0060] In certain embodiments of the above-described method, each of the probability distributions comprises a Gaussian distribution or an exponentially modified Gaussian distribution.

[0061] In a particular embodiment of the above method, the probability distribution realization algorithm is based on a Dirichlet process.

[0062] In certain embodiments of the above-described method, the method further includes determining the number of the plurality of signal distributions based on maximizing a likelihood function associated with the probability distribution realization algorithm.

[0063] In certain embodiments of the above-described methods, when the number of the plurality of chemical components is unknown, the method further includes determining the number of the plurality of chemical components based on the determined number of signal distributions.

[0064] In certain embodiments of the above-described methods, the method further includes identifying a number of spectral data points assigned to the at least one signal distribution for the ensemble of spectral data points, and determining a relative area associated with the at least one signal distribution based on the identified number of spectral data points.

[0065] In certain embodiments, the disclosure provides one or more computer-readable non-transitory storage media embodying software that, when executed, includes accessing a chromatographic time-series synthetic signal comprising a plurality of signal distributions, the chromatographic time-series synthetic signal being associated with a two-dimensional (2D) array, a first dimension of the 2D array comprising a plurality of indexes, and a second dimension of the 2D array comprising a plurality of response values ​​each corresponding to the plurality of indexes; selecting a plurality of candidate index-response pairs from the 2D array; and converting the chromatographic time-series synthetic signal into a one-dimensional (1D) array, the converting generating, for each of the plurality of candidate index-response pairs, an array segment comprising one or more array elements, the number of the one or more array elements being based on the response values ​​of the candidate index-response pairs. the one or more array elements are generated by unpacking the candidate index-response pairs based on the array decomposition; and concatenating a plurality of array segments corresponding to the plurality of candidate index-response pairs to generate a 1D array; processing the 1D array with a probability distribution realization algorithm to determine one or more of a mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, an exponential decay component parameter, or any parameter defining each of the plurality of signal distributions; individually identifying each of the plurality of signal distributions based on one or more of a mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, an exponential decay component parameter, or any parameter defining each of the plurality of signal distributions; and correlating each identified signal distribution with a chemical component.

[0066] In certain embodiments of the above-described medium, two or more of the multiple signal distributions are convolved.

[0067] In certain embodiments of the above-described medium, the software, when executed, is further operable to select a time range for converting the chromatographic time series composite signal into a 1D array.

[0068] In certain embodiments of the above-described medium, the software, when executed, is further operable to remove baseline drift associated with the chromatographic time-series composite signal.

[0069] In certain embodiments of the above-mentioned media, the software, when executed, is further operable to determine one or more binning parameters associated with a plurality of virtual bins used to convert the chromatographic time-series composite signal into a 1D array, the one or more binning parameters including one or more of: a number of a plurality of virtual bins determined based on a signal distribution of the chromatographic time-series composite signal; a position of each virtual bin determined based on the number of virtual bins; a reference height of each virtual bin proportional to a sum signal of a range associated with that virtual bin; or a width of each virtual bin determined based on the number of virtual bins.

[0070] In certain embodiments of the above-described medium, the software, when executed, is further operable to generate a scaled response value for each response value of the plurality of index-response pairs of the 2D array by multiplying the response value by a scaling factor.

[0071] In a particular embodiment of the above-mentioned medium, generating an array segment for each of a plurality of candidate index-response pairs includes identifying a corresponding virtual bin from a plurality of virtual bins of the candidate index-response pair, where the identified virtual bin is associated with a range of indexes; randomly generating one or more array elements to be included in the array segment, where an element value of the one or more array elements is determined based on the range of indexes, and a number of the one or more array elements is equivalent to a scaled response value associated with the candidate index-response pair; and distributing the one or more generated array elements to the identified virtual bins based on a quasi-random low discrepancy sequence.

[0072] In certain embodiments of the above-described media, the chromatographic time-series composite signal includes a mixture model that includes a plurality of probability distributions, each probability distribution corresponding to a chemical component.

[0073] In a particular embodiment of the above-mentioned medium, the mixture model comprises a Gaussian mixture model, and each of the probability distributions comprises a Gaussian distribution or an exponentially modified Gaussian distribution.

[0074] In a particular embodiment of the above-mentioned medium, the probability distribution realization algorithm is based on a Dirichlet process.

[0075] In certain embodiments of the above-mentioned media, the software, when executed, is further operable to determine a number of multiple signal distributions in the chromatographic time-series composite signal based on maximizing a likelihood function associated with the probability distribution realization algorithm.

[0076] In certain embodiments of the above-described media, the number of the plurality of chemical components is unknown, and the software, when executed, is further operable to determine the number of the plurality of chemical components based on the number of determined signal distributions.

[0077] In certain embodiments of the above-described media, the software, when executed, is further operable to: identify a number of spectral data points assigned to each of a plurality of signal distributions associated with a plurality of chemical components for the ensemble of spectral data points; and determine a relative area associated with each of the plurality of signal distributions based on the identified number of spectral data points assigned to the signal distribution.

[0078] In a particular embodiment, the disclosure provides a system comprising one or more processors and a non-transitory memory coupled to the processor that includes instructions executable by the processor, the processor, when executing the instructions, includes accessing a chromatography time-series synthetic signal comprising a plurality of signal distributions, the chromatography time-series synthetic signal being associated with a two-dimensional (2D) array, a first dimension of the 2D array including a plurality of indexes, and a second dimension of the 2D array including a plurality of response values ​​respectively corresponding to the plurality of indexes; selecting a plurality of candidate index-response pairs from the 2D array; and converting the chromatography time-series synthetic signal into a one-dimensional (1D) array, the converting generating, for each of the plurality of candidate index-response pairs, an array segment including one or more array elements, the number of the one or more array elements being greater than or equal to the number of candidate indexes. generating array segments, where a response value of a candidate index-response pair is determined based on a response value of the candidate index-response pair, and one or more array elements are generated by unpacking the candidate index-response pairs based on the array decomposition; and concatenating a plurality of array segments corresponding to the plurality of candidate index-response pairs to generate a 1D array; processing the 1D array with a probability distribution realization algorithm to determine one or more of a mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, an exponential decay component parameter, or any parameter defining each of the plurality of signal distributions; individually identifying each of the plurality of signal distributions based on one or more of a mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, an exponential decay component parameter, or any parameter defining each of the plurality of signal distributions; and correlating each identified signal distribution with a chemical component.

[0079] In certain embodiments of the above-described systems, two or more of the multiple signal distributions are convolved.

[0080] In certain embodiments of the above-described system, the processor, when executing the instructions, is further operable to select a range of time for converting the chromatographic time-series composite signal into a 1D array.

[0081] In certain embodiments of the above-described system, the processor, when executing the instructions, is further operable to remove baseline drift associated with the chromatographic time-series composite signal.

[0082] In certain embodiments of the above-described system, the processor, when executing the instructions, is further operable to determine one or more binning parameters associated with a plurality of virtual bins used to convert the chromatographic time-series composite signal into a 1D array, the one or more binning parameters including one or more of: a number of a plurality of virtual bins determined based on a signal distribution of the chromatographic time-series composite signal; a position of each virtual bin determined based on the number of virtual bins; a reference height of each virtual bin proportional to a sum signal of a range associated with that virtual bin; or a width of each virtual bin determined based on the number of virtual bins.

[0083] In certain embodiments of the above-described system, the processor, when executing the instructions, is further operable to generate a scaled response value for each response value of a plurality of index-response pairs of the 2D array by multiplying the response value by a scaling factor.

[0084] In certain embodiments of the above-described system, generating an array segment for each of a plurality of candidate index-response pairs includes identifying a corresponding virtual bin from a plurality of virtual bins of the candidate index-response pair, where the identified virtual bin is associated with a range of indexes; randomly generating one or more array elements to be included in the array segment, where an element value of the one or more array elements is determined based on the range of indexes, and a number of the one or more array elements is equivalent to a scaled response value associated with the candidate index-response pair; and distributing the one or more generated array elements to the identified virtual bins based on a quasi-random low discrepancy sequence.

[0085] In certain embodiments of the above-described system, the chromatographic time-series composite signal includes a mixture model that includes a plurality of probability distributions, each probability distribution corresponding to a chemical component.

[0086] In certain embodiments of the above-described system, the mixture model comprises a Gaussian mixture model, and each of the probability distributions comprises a Gaussian distribution or an exponentially modified Gaussian distribution.

[0087] In a particular embodiment of the above-described system, the probability distribution realization algorithm is based on a Dirichlet process.

[0088] In certain embodiments of the above-described system, the processor, when executing the instructions, is further operable to determine a number of multiple signal distributions in the chromatographic time-series composite signal based on maximizing a likelihood function associated with the probability distribution realization algorithm.

[0089] In certain embodiments of the above-described system, the number of the plurality of chemical components is unknown, and the processor, when executing the instructions, is further operable to determine the number of the plurality of chemical components based on the number of determined signal distributions.

[0090] In certain embodiments of the above-described system, the processor, when executing the instructions, is further operable to identify a number of spectral data points assigned to each of a plurality of signal distributions associated with a plurality of chemical components for the ensemble of spectral data points, and to determine a relative area associated with each of the plurality of signal distributions based on the identified number of spectral data points assigned to the signal distribution.

[0091] The scope of the present disclosure encompasses all changes, substitutions, variations, modifications, and alterations to the exemplary embodiments described or illustrated herein that would be understood by a person skilled in the art. The scope of the present disclosure is not limited to the exemplary embodiments described or illustrated herein. Moreover, although the present disclosure has described and illustrated each embodiment herein as including certain components, elements, features, functions, operations, or steps, any of these embodiments may include any combination or permutation of any of the components, elements, features, functions, operations, or steps described or illustrated anywhere herein that would be understood by a person skilled in the art. Moreover, references in the appended claims to an apparatus or system, or an apparatus or system component, being adapted to, arranged to, capable to, configured to, enabled to, operable to, or operative to perform a particular function encompass that apparatus, system, component, or particular function thereof, so long as the apparatus, system, or component is so adapted, arranged, capable, configured, enabled, operable, or operative, regardless of whether the apparatus, system, component, or particular function thereof is activated, turned on, or unlocked. Additionally, although the present disclosure describes or illustrates particular embodiments as providing certain advantages, a particular embodiment may provide none of these advantages, some of these advantages, or all of these advantages.

Claims

1. 1. A method, comprising: Accessing a chromatographic time series composite signal comprising a plurality of signal distributions, comprising: Each signal distribution corresponds to a chemical component. two or more of the plurality of signal distributions are convolved; the chromatographic time-series composite signal is associated with a two-dimensional (2D) array, a first dimension of the 2D array including a plurality of indexes, and a second dimension of the 2D array including a plurality of response values ​​respectively corresponding to the plurality of indexes; accessing a chromatographic time series composite signal, each signal distribution being a Gaussian or an exponentially modified Gaussian; selecting a plurality of candidate index-response pairs from the 2D array, each candidate index-response pair including an index from the plurality of indexes and its corresponding response value from the plurality of response values; selecting a time range for converting the chromatographic time series composite signal into a one-dimensional (1D) array; removing baseline drift associated with the chromatographic time-series composite signal; determining one or more binning parameters associated with a number of virtual bins used to convert the chromatographic time series composite signal to the 1D array, the one or more binning parameters including one or more of: a number of the plurality of virtual bins determined based on a signal distribution of the chromatographic time series composite signal; a position of each virtual bin determined based on the number of virtual bins; a base height of each virtual bin proportional to a sum signal of a range associated with that virtual bin; or a width of each virtual bin determined based on the number of virtual bins; generating a scaled response value for the response value of each of the plurality of index-response pairs by multiplying the response value by a scaling factor; converting the chromatographic time series composite signal into the 1D array, said converting comprising: For each of the plurality of candidate index-response pairs, identifying a corresponding virtual bin from the plurality of virtual bins of the candidate index-response pairs, the identified virtual bin being associated with a range of indices; generating an array segment including one or more array elements, a number of the one or more array elements being determined based on the scaled response values ​​of the candidate index-response pairs, the one or more array elements being generated by unpacking the candidate index-response pairs based on an array decomposition, and element values ​​of the one or more array elements being determined based on a range of the indexes; Distributing the one or more array elements into the identified virtual bins based on a pseudo-random low discrepancy sequence; and and concatenating a plurality of said array segments corresponding to said plurality of candidate index-response pairs to generate said 1D array; converting the chromatographic time series composite signal into the 1D array; processing the 1D array with a probability distribution realization algorithm to determine one or more of a mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, an exponential decay component parameter, or any parameter defining each of the plurality of signal distributions, wherein the probability distribution realization algorithm is based on a Dirichlet process; determining a number of the plurality of signal distributions in the chromatographic time-series composite signal based on maximizing a likelihood function associated with the probability distribution realization algorithm; individually identifying each of the plurality of signal distributions based on one or more of the mean, the standard deviation, or the relative area of ​​each of the plurality of signal distributions, the exponential decay component parameter, or any parameter defining each of the plurality of signal distributions; Correlating each identified signal distribution with a chemical component; A method comprising:

2. 1. A method, comprising: accessing a chromatographic time-series synthetic signal comprising a plurality of signal distributions, the chromatographic time-series synthetic signal being associated with a two-dimensional (2D) array, a first dimension of the 2D array comprising a plurality of indexes, and a second dimension of the 2D array comprising a plurality of response values ​​each corresponding to the plurality of indexes; selecting a number of candidate index-response pairs from the 2D array; converting the chromatographic time series composite signal into a one-dimensional (1D) array, said converting comprising: generating an array segment including one or more array elements for each of the plurality of candidate index-response pairs, a number of the one or more array elements being determined based on the response values ​​of the candidate index-response pairs, the one or more array elements being generated by unpacking the candidate index-response pairs based on an array decomposition; concatenating a plurality of the array segments corresponding to the plurality of candidate index-response pairs to generate the 1D array; converting the chromatographic time series composite signal into a 1D array; processing the 1D array with a probability distribution realization algorithm to determine one or more of the mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, exponential decay component parameters, or any parameter defining each of the plurality of signal distributions; individually identifying each of the plurality of signal distributions based on one or more of the mean, the standard deviation, or the relative area of ​​each of the plurality of signal distributions, the exponential decay component parameter, or any parameter defining each of the plurality of signal distributions; Correlating each identified signal distribution with a chemical component; A method comprising:

3. The method of claim 2 , wherein two or more of the plurality of signal distributions are convolved.

4. The method of claim 2 , further comprising selecting a range of time for converting the chromatographic time series composite signal into the 1D array.

5. The method of claim 2 , further comprising removing baseline drift associated with the chromatographic time-series composite signal.

6. determining one or more binning parameters associated with a plurality of virtual bins used to convert the chromatographic time-series composite signal to the 1D array, the one or more binning parameters comprising: a number of the plurality of virtual bins determined based on a signal distribution of the chromatographic time series composite signal; a position of each virtual bin determined based on said number of virtual bins; a reference height for each virtual bin that is proportional to the sum signal for the range associated with that virtual bin, or a width of each virtual bin determined based on the number of virtual bins.

7. 7. The method of claim 6, further comprising generating a scaled response value for the response value of each of the plurality of index-response pairs of the 2D array by multiplying the response value by a scaling factor.

8. Generating the array segment for each of the plurality of candidate index-response pairs includes: identifying a corresponding virtual bin from the plurality of virtual bins of the candidate index-response pairs, the identified virtual bin being associated with a range of indices; randomly generating the one or more array elements to be included in the array segment, wherein element values ​​of the one or more array elements are determined based on the range of indices, and a number of the one or more array elements is equivalent to the scaled response values ​​associated with the candidate index-response pairs; Distributing the one or more generated array elements into the identified virtual bins based on a pseudo-random low discrepancy sequence. The method of claim 7, comprising:

9. The method of claim 2 , wherein the chromatographic time-series synthetic signal comprises a mixture model including a plurality of probability distributions, each probability distribution corresponding to a chemical component.

10. The method of claim 9 , wherein the mixture model comprises a Gaussian mixture model and each of the probability distributions comprises a Gaussian distribution or an exponentially modified Gaussian distribution.

11. The method of claim 10 , wherein the probability distribution realization algorithm is based on a Dirichlet process.

12. The method of claim 2 , further comprising determining a number of the plurality of signal distributions in the chromatographic time-series composite signal based on maximizing a likelihood function associated with the probability distribution realization algorithm.

13. The number of said plurality of chemical components is unknown, and said method further comprises: The method of claim 12 , further comprising determining the number of the plurality of chemical components based on the determined number of signal distributions.

14. identifying a number of spectral data points assigned to each of a plurality of signal distributions associated with a plurality of said chemical constituents for an ensemble of spectral data points; determining the relative area associated with each of the plurality of signal distributions based on a number of the identified spectral data points assigned to that signal distribution; The method of claim 2 , further comprising:

15. 1. A method, comprising: generating a one-dimensional (1D) array including array elements, each array element embodying a plurality of signal distributions corresponding to a plurality of chemical moieties; processing the 1D array with a probability distribution realization algorithm to determine one or more of the mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, exponential decay component parameters, or any parameter defining each of the plurality of signal distributions; identifying at least one signal distribution corresponding to a chemical component from the plurality of signal distributions corresponding to the plurality of chemical components; A method comprising:

16. 16. The method of claim 15, wherein the 1D array is derived from a two-dimensional (2D) array, a first dimension of the 2D array including a plurality of indexes, and a second dimension of the 2D array including a plurality of response values ​​corresponding respectively to the plurality of indexes.

17. The method of claim 16 , wherein an element value for each array element of the 1D array is derived from one of the plurality of response values ​​of the 2D array.

18. selecting a number of candidate index-response pairs from the 2D array; generating a scaled response value for the response value of each of the plurality of index-response pairs of the 2D array by multiplying the response value by a scaling factor; Further comprising: Generating the 1D array includes: generating an array segment including one or more array elements for each of the plurality of candidate index-response pairs, a number of the one or more array elements being determined based on the response values ​​of the candidate index-response pairs, the one or more array elements being generated by unpacking the candidate index-response pairs based on an array decomposition; concatenating a plurality of the array segments corresponding to the plurality of candidate index-response pairs to generate the 1D array; 17. The method of claim 16, comprising:

19. Generating the array segment for each of the plurality of candidate index-response pairs includes: determining virtual bins for the candidate index-response pairs, the determined virtual bins being associated with ranges of indices; randomly generating the one or more array elements to be included in the array segment, wherein element values ​​of the one or more array elements are determined based on the range of indices, and a number of the one or more array elements is equivalent to the scaled response values ​​associated with the candidate index-response pairs; 20. The method of claim 18, comprising distributing the one or more generated array elements into the determined virtual bins based on a pseudo-random low discrepancy sequence.

20. 17. The method of claim 16, wherein the 2D array is associated with a chromatographic time-series composite signal comprising the plurality of signal distributions, each signal distribution corresponding to a chemical component, and two or more of the plurality of signal distributions are convolved.

21. The method of claim 15 , wherein two or more of the multiple signal distributions are convolved.

22. The method of claim 15 , wherein each of the probability distributions comprises a Gaussian distribution or an exponentially modified Gaussian distribution.

23. The method of claim 15 , wherein the probability distribution realization algorithm is based on a Dirichlet process.

24. The method of claim 15 , further comprising determining the number of the plurality of signal distributions based on maximizing a likelihood function associated with the probability distribution realization algorithm.

25. The number of said plurality of chemical components is unknown, and said method further comprises:

24. The method of claim 23, further comprising determining the number of the plurality of chemical components based on a determined number of signal distributions.

26. identifying a number of spectral data points assigned to the at least one signal distribution for an ensemble of spectral data points; determining a relative area associated with the at least one signal distribution based on the number of identified spectral data points; The method of claim 15 further comprising:

27. One or more computer-readable non-transitory storage media embodying software that, when executed, accessing a chromatographic time-series synthetic signal comprising a plurality of signal distributions, the chromatographic time-series synthetic signal being associated with a two-dimensional (2D) array, a first dimension of the 2D array comprising a plurality of indexes, and a second dimension of the 2D array comprising a plurality of response values ​​respectively corresponding to the plurality of indexes; selecting a number of candidate index-response pairs from the 2D array; converting the chromatographic time series composite signal into a one-dimensional (1D) array, said converting comprising: generating an array segment including one or more array elements for each of the plurality of candidate index-response pairs, a number of the one or more array elements being determined based on the response values ​​of the candidate index-response pairs, the one or more array elements being generated by unpacking the candidate index-response pairs based on an array decomposition; concatenating a plurality of the array segments corresponding to the plurality of candidate index-response pairs to generate the 1D array; converting the chromatographic time series composite signal into a 1D array; processing the 1D array with a probability distribution realization algorithm to determine one or more of the mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, exponential decay component parameters, or any parameter defining each of the plurality of signal distributions; individually identifying each of the plurality of signal distributions based on one or more of the mean, the standard deviation, or the relative area of ​​each of the plurality of signal distributions, the exponential decay component parameter, or any parameter defining each of the plurality of signal distributions; Correlating each identified signal distribution with a chemical component; A medium operable to perform the steps of:

28. 30. The medium of claim 27, wherein two or more of the plurality of signal distributions are convoluted.

29. The software, when executed, 30. The medium of claim 27, further operable to select a range of time for converting the chromatographic time series composite signal into the 1D array.

30. The software, when executed, 30. The medium of claim 27, further operable to remove baseline drift associated with the chromatographic time-series composite signal.

31. The software, when executed, and further operable to determine one or more binning parameters associated with a plurality of virtual bins used to convert the chromatographic time-series composite signal to the 1D array, the one or more binning parameters comprising: a number of the plurality of virtual bins determined based on a signal distribution of the chromatographic time series composite signal; a position of each virtual bin determined based on said number of virtual bins; a reference height for each virtual bin that is proportional to the sum signal for the range associated with that virtual bin, or and a width of each virtual bin determined based on the number of virtual bins.

32. The software, when executed, 32. The medium of claim 31, further operable to generate a scaled response value for the response value of each of the plurality of index-response pairs of the 2D array by multiplying the response value by a scaling factor.

33. Generating the array segment for each of the plurality of candidate index-response pairs includes: identifying a corresponding virtual bin from the plurality of virtual bins of the candidate index-response pairs, the identified virtual bin being associated with a range of indices; randomly generating the one or more array elements to be included in the array segment, wherein element values ​​of the one or more array elements are determined based on the range of indices, and a number of the one or more array elements is equivalent to the scaled response values ​​associated with the candidate index-response pairs; Distributing the one or more generated array elements into the identified virtual bins based on a pseudo-random low discrepancy sequence. The medium of claim 32, comprising:

34. 30. The medium of claim 27, wherein the chromatographic time-series synthetic signal comprises a mixture model including a plurality of probability distributions, each probability distribution corresponding to a chemical component.

35. 35. The medium of claim 34, wherein the mixture model comprises a Gaussian mixture model and each of the probability distributions comprises a Gaussian distribution or an exponentially modified Gaussian distribution.

36. 36. The medium of claim 35, wherein the probability distribution realization algorithm is based on a Dirichlet process.

37. The software, when executed, 30. The medium of claim 27, further operable to determine a number of the plurality of signal distributions in the chromatographic time-series composite signal based on maximizing a likelihood function associated with the probability distribution realization algorithm.

38. The number of the plurality of chemical components is unknown, and the software, when executed, 40. The medium of claim 37, further operable to determine the number of the plurality of chemical components based on the determined number of signal distributions.

39. The software, when executed, identifying a number of spectral data points assigned to each of a plurality of signal distributions associated with a plurality of said chemical constituents for an ensemble of spectral data points; determining the relative area associated with each of the plurality of signal distributions based on a number of the identified spectral data points assigned to that signal distribution; 30. The medium of claim 27, further operable to execute:

40. 1. A system comprising one or more processors and a non-transitory memory coupled to the processors, the non-transitory memory including instructions executable by the processors, the processor, when executing the instructions, accessing a chromatographic time-series synthetic signal comprising a plurality of signal distributions, the chromatographic time-series synthetic signal being associated with a two-dimensional (2D) array, a first dimension of the 2D array comprising a plurality of indexes, and a second dimension of the 2D array comprising a plurality of response values ​​respectively corresponding to the plurality of indexes; selecting a number of candidate index-response pairs from the 2D array; converting the chromatographic time series composite signal into a one-dimensional (1D) array, said converting comprising: generating an array segment including one or more array elements for each of the plurality of candidate index-response pairs, a number of the one or more array elements being determined based on the response values ​​of the candidate index-response pairs, the one or more array elements being generated by unpacking the candidate index-response pairs based on an array decomposition; concatenating a plurality of the array segments corresponding to the plurality of candidate index-response pairs to generate the 1D array; converting the chromatographic time series composite signal into a 1D array; processing the 1D array with a probability distribution realization algorithm to determine one or more of the mean, standard deviation, or relative area of ​​each of the plurality of signal distributions, exponential decay component parameters, or any parameter defining each of the plurality of signal distributions; individually identifying each of the plurality of signal distributions based on one or more of the mean, the standard deviation, or the relative area of ​​each of the plurality of signal distributions, the exponential decay component parameter, or any parameter defining each of the plurality of signal distributions; Correlating each identified signal distribution with a chemical component; A system operable to execute the

41. 41. The system of claim 40, wherein two or more of the plurality of signal distributions are convolved.

42. The processor, when executing the instructions, 41. The system of claim 40, further operable to select a range of time for converting the chromatographic time series composite signal into the 1D array.

43. The processor, when executing the instructions, 41. The system of claim 40, further operable to remove baseline drift associated with the chromatographic time-series composite signal.

44. The processor, when executing the instructions, and further operable to determine one or more binning parameters associated with a plurality of virtual bins used to convert the chromatographic time-series composite signal to the 1D array, the one or more binning parameters comprising: a number of the plurality of virtual bins determined based on a signal distribution of the chromatographic time series composite signal; a position of each virtual bin determined based on said number of virtual bins; a reference height for each virtual bin that is proportional to the sum signal for the range associated with that virtual bin, or a width of each virtual bin determined based on the number of virtual bins.

45. The processor, when executing the instructions, 45. The system of claim 44, further operable to generate a scaled response value for the response value of each of the plurality of index-response pairs of the 2D array by multiplying the response value by a scaling factor.

46. Generating the array segment for each of the plurality of candidate index-response pairs includes: identifying a corresponding virtual bin from the plurality of virtual bins of the candidate index-response pairs, the identified virtual bin being associated with a range of indices; randomly generating the one or more array elements to be included in the array segment, wherein element values ​​of the one or more array elements are determined based on the range of indices, and a number of the one or more array elements is equivalent to the scaled response values ​​associated with the candidate index-response pairs; Distributing the one or more generated array elements into the identified virtual bins based on a pseudo-random low discrepancy sequence.

46. ​​The system of claim 45, comprising:

47. 41. The system of claim 40, wherein the chromatographic time-series synthetic signal comprises a mixture model including a plurality of probability distributions, each probability distribution corresponding to a chemical component.

48. 48. The system of claim 47, wherein the mixture model comprises a Gaussian mixture model and each of the probability distributions comprises a Gaussian distribution or an exponentially modified Gaussian distribution.

49. 49. The system of claim 48, wherein the probability distribution realization algorithm is based on a Dirichlet process.

50. The processor, when executing the instructions, 41. The system of claim 40, further operable to determine a number of the plurality of signal distributions in the chromatographic time-series composite signal based on maximizing a likelihood function associated with the probability distribution realization algorithm.

51. The number of the plurality of chemical components is unknown, and the processor, when executing the instructions, 51. The system of claim 50, further operable to determine the number of the plurality of chemical components based on the determined number of signal distributions.

52. The processor, when executing the instructions, identifying a number of spectral data points assigned to each of a plurality of signal distributions associated with a plurality of said chemical constituents for an ensemble of spectral data points; determining the relative area associated with each of the plurality of signal distributions based on a number of the identified spectral data points assigned to that signal distribution; 41. The system of claim 40, further operable to:

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