Altering integration of network models

Abstract

Systems and methods of increasing integration within a network, including: providing the network including a plurality of nodes including at least one of a neutral stimulus node, an unconditioned stimulus node, and a response node; testing the network to evaluate a pre-training level of associative memory comprising comparing a first response at the response node to stimulation of the neutral stimulus node to a second response at the response node to a stimulation of the unconditioned stimulus node; training the network including applying coordinated stimulation of the neutral stimulus node and the unconditioned stimulus node to elicit a response at the response node; and determining a set of stimuli to alter the integration within the network based on the evaluated level of associative memory.

Description

Tufts T002885Quarles 166118.01571ALTERING INTEGRATION OF NETWORK MODELSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Application No. 63 / 728,018, filed on December 4, 2024, and U.S. Provisional Application No. 63 / 755,699, filed on February 7, 2025, all of which are incorporated herein by reference in its entirety for all purposes.BACKGROUND

[0002] Gene Regulatory Network (GRN) models represent sets of elements that regulate each other’s activity based on a functional connectivity map. These networks can be used to explore various areas in biomedicine, developmental biology, synthetic biology, and swarm robotics, and are a special case of a more general and ubiquitous phenomenon: molecular pathway or other subsystems whose interactions are describable by coupled equations. Here, GRNs are used as a system to explore emergent properties, particularly integrated, distributed memory and the ways in which learning and system coherence influence each other. Methods and systems described herein provide a new framework to alter a system’s integrated coherence.SUMMARY

[0003] Disclosed herein are methods and systems for altering integration within a network. In various embodiments, the methods and systems may include one or more of the following.

[0004] In one embodiment, a method of increasing integration within a network is disclosed. In some embodiments, the method includes: providing the network including a plurality of nodes including at least one of a neutral stimulus node, an unconditioned stimulus node, and a response node; testing the network to evaluate a pre-training level of associative memory, including comparing a first response at the response node to stimulation of the neutral stimulus node to a second response at the response node to stimulation of the unconditioned stimulus node; training the network including applying coordinated stimulation of the conditioned stimulus node and the unconditioned stimulus node to elicit a response at the response node; evaluating a post-training level of associative memory by applying stimulation of the neutral stimulus node and observing a1QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 post-training response at the response node, in which, if the neutral stimulus node elicits a posttraining response at the response node above a threshold, the neutral stimulus node becomes a conditioned stimulus node; and determining a set of stimuli to alter the integration within the network based on the evaluated level of associative memory.BRIEF DESCRIPTION OF THE DRAWINGS

[0005] FIGS. 1A-1B show schematics of learning in gene regulatory networks (GRNs). FIG. 1A shows Pavlovian conditioning and applications to gene regulatory networks. The standard paradigm is that the Conditioned Stimulus (CS) is initially neutral in that it does not elicit a Response (R), while an Unconditioned Stimulus (UCS) does. Some systems, like dogs, eventually show a response to the CS after it has been presented together with the UCS (forming an association between those stimuli). The same paradigm has been used with GRNs and pathways, by mapping the CS, UCS, and R roles to specific nodes in the network and stimulating them by transiently raising their activity level (for example, by increasing their expression via a chemical ligand). Associative memory requires a degree of integration within the network, and here we explore the hypothesis that associative conditioning reifies the learning agent by increasing its emergent integration metrics (schematized by the dog progressively becoming more of a unified, centralized agent and less a collection of cells). FIG. IB shows associative conditioning in simulated gene regulatory networks; simulation time is on the x-axis, while gene expression levels are on the y-axis. During the train phase, we pair a UCS and CS stimuli to regulate a response R. If associative conditioning has taken place, we observe the CS alone (i.e., with no UCS stimulation) regulates R. In the schematic, we illustrate stimulation / regulation as upticks of the expression levels over a baseline value; in reality, gene expression can have a quantitatively different shape, but the principle remains the same. Used with permission from Biswas et al., 2022.

[0006] FIGS. 2A-2B show biological network with memory exhibit increase of causal emergence during training, and do so more than random networks. FIG. 2A shows error bars for the percent change in causal emergence from before to after training for biological and random networks; each point corresponds to one circuit of one network. Biological networks are2QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 significantly more causally emergent after training. FIG. 2B shows bars for the percent of those networks that have memory and those that, if they have memory, show an increase in causal emergence after training. Associative training results in increased causal emergence among almost all networks with memory.

[0007] FIGS. 3A-3C show change in causal emergence is not correlated with established structure, function, and activity metrics for networks. Kendall’s rank correlation coefficient between percent change in causal emergence and network structure properties (FIG. 3A), function properties (FIG. 3B), and activity, measured as first-derivative of the state variables (FIG. 3C). Our causal emergence metric captures an aspect that neither established network properties nor mere activity encompass: how GRNs react to training.

[0008] FIGS. 4A-4E show GRNs exhibit distinct patterns of causal emergence with respect to the effects of training. Panels show five sample causal emergence trajectories of the automatically discovered behaviors. Each row represents one GRN. Stimulation of the CS happens every 500 seconds. Each behavior represents trajectories sharing a specific and distinct temporal pattern during the text phase: homing (FIG. 4A), inflating (FIG. 4B), deflating (FIG. 4C), spiky (FIG. 4D), and steppy (FIG. 4E).

[0009] FIG. 5 shows effects of training on causal emergence occur in five distinct types. t-SNE embedding in 2D of the behavior descriptors for the test trajectories, colored by behavior “species” as classified by the k-means unsupervised learning algorithm; each point corresponds to the test phase for one circuit of one network. The behaviors segregate well into distinct clusters. “Homing” is clustered in the top left portion of the graph; “spiky” is clustered in the top right portion of the graph; “inflating” is clustered in an extended shape in the bottom right portion of the graph; “deflating” is clustered in the bottom center of the graph; “steppy” is shown in a small cluster in the center of the graph.

[0010] FIGS. 6A-6E show different behaviors characterized by different distributions of the descriptors. Histograms for the seven descriptors (one per row) and the five automatically discovered behaviors: homing (FIG. 6A), inflating (FIG. 6B), deflating (FIG. 6C), spiky (FIG. 6D), and steppy (FIG. 6E).3QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571

[0011] FIGS. 7A-7D show relationships between behavior class and the biological nature of each network. Two-way table of relative occurrences of behaviors for circuits (ways in which emergence changes upon training) for each taxon (FIG. 7A) and gene ontology (FIG. 7C); columns sum to one. Two-way table of average percent causal emergence change from before to after training for each taxon (FIG. 7B) and gene ontology (FIG. 7D); it includes the margins. Some cells are marked as “N / A” because not every taxon or gene ontology is represented for a given behavior. The occurrence of behavior is related to taxa and gene ontologies.

[0012] FIG. 8 shows a schematic of a method for increasing integration within a network.

[0013] FIG. 9 shows a schematic of a computer system.DETAILED DESCRIPTION

[0014] In accordance with some embodiments of the disclosed subject matter, mechanisms (which can include, for example, systems and methods) for increasing integration in a network are provided.

[0015] Described herein are methods and systems providing a foundation for altering (e.g., increasing or decreasing) integration (e.g., integrated coherence) of a network. In particular, meta-heuristic search algorithms (e.g., evolutionary algorithms) can be used to search for network interventions that maximize or minimize integration. The methods and systems apply to any network that is modeled as coupled equations. As described below, learning is used to alter a network’s integrated coherence (e.g., the extent to which the network functions as a unit is greater that the sum of its parts, and the extent to which the network functions as a unit has memory and pursues goals individual parts of the network do not). This can be viewed as an “agency spiral” between learning and integration; by specific types of training stimuli, it is possible to control to coherence of a system. This can be used to augment artificial intelligence and virtual governors in many other systems, from biological pathways to autonomy in networks such as power grids, financial structures, or others.

[0016] In some embodiments, systems and methods for increasing integration within a network are provided. A network can refer to a network of elements (e.g., nodes) that regulate each4QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 other’s function. The nodes may be connected by edges, and the edges may determine how the nodes interact. For instance, nodes may activate or inhibit function in another node.

[0017] In some embodiments, a network may be a gene regulatory network (GRN). GRNs may correspond to a biological network. In some embodiments, nodes in a GRN correspond to proteins or nucleic acids, and edges represent how the proteins and nucleic acids are known to interact.

[0018] In some embodiments, GRNs correspond to biochemical pathways, metabolic pathways, catabolic pathways, physiological pathways, transcriptional pathways, signaling pathways, cell differentiation, developmental (morphogenetic), regenerative, cancer-related, immune, or circadian pathways. GRNs may also correspond to evolutionary or developmental biology. GRNs may also correspond to stem cell differentiation.

[0019] In some embodiments, GRNs correspond to systems that are not biological systems. For instance, GRNs can correspond to swarm robotics, in which each node in a GRN corresponds to an individual robot, and the network corresponds to the collective or swarm behavior of the robots. In economics, each node of a GRN corresponds to a functional unit (e.g., a community, a market, a consumer class) and the network corresponds to the collective interactions within an economy. In the physical sciences, nodes correspond to bodies (e.g., celestial bodies) and the network corresponds to the gravitational and electromagnetic forces the bodies exert on one another. The methods described herein could further be used for systems such as traffic networks, information / communication networks, power grids, resource distribution networks (water, energy, etc.), logistics inside warehouses, and logistics more broadly distribution of materials across distance.

[0020] A GRN may be governed by a set of differential equations. In some embodiments, a GRN is governed by linear partial differential equations. In some embodiments, the network is governed by ordinary differential equations (ODEs), in which case the GRN may be referred to as an ODE GRN. ODEs impose rules that govern how the network is modeled. In some embodiments, the ODE imposes rules such that the network is modeled according to chemical rate laws. This enforces that the GRN is modeled as a continuous-time dynamical system. GRNs may be modeled over a time series (e.g., over the course of time steps; a step may refer to a5QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 nanosecond, millisecond, second, etc., over which the network is simulated). In some embodiments, the network is governed by a Boolean network which simplifies gene expression into binary states (on / off, or present / absent). In some embodiments, the network is governed by a stochastic differential equation which accounts for randomness in genetic expression, or a Bayesian network which represents probabilistic relationships and dependences between genes.

[0021] The nodes in a network include neutral stimulus nodes, unconditioned stimulus nodes, and response nodes. A neutral stimulus node has the ability to deliver a stimulus to the response node, but the stimulus does not initially elicit a response at the response node. An unconditioned stimulus may stimulate the response node and elicit a response at the response node. “Eliciting a response” refers to changing the activity at the response node. For instance, up-regulating or down-regulating activity at the response node may be elicited responses.

[0022] In some embodiments, a network is “relaxed” prior to any testing or training. “Relaxing” a network refers to simulating the behavior of the network without applying any stimulus to the network. This allows the network to settle into a steady state, and provides baseline behavior to which a trained network may be compared. In some embodiments, a network goes through relaxation phases in between other phases (e.g., testing, training, or evaluating).

[0023] In some embodiments, a network is tested to evaluate a pre-training level of associative memory. A neutral stimulus node in the network is stimulated, and the response (or lack thereof) at the response node is recorded. An unconditioned stimulus node is then stimulated, and a second response at the response node is recorded. In some embodiments, the network is subject to a relaxing phase after testing the network.

[0024] A network may be trained by applying coordinated stimulation of the neutral stimulation node and the unconditioned stimulation node. In some embodiments, the coordinated stimulation may refer to stimulating both nodes at the same time. In some embodiments, the coordinated stimulation may refer to a specific time variation between the stimulation of the neutral stimulation and the unconditioned stimulation (e.g., applying stimulation to the neutral node five time-steps prior to applying stimulation to the unconditioned node). In some embodiments, the network is subject to a relaxing phase after training the network.6QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571

[0025] A network may be evaluated post-training to assess the level of associative memory in the network. For instance, a stimulus may be applied to only the neutral stimulus node, and a response at the response node may be observed or recorded. In some embodiments, the training step conditions the network to respond to the neutral stimulus node. If, after training, a neutral stimulus node is applied to the response node and elicits a response from the response node, the neutral stimulus node becomes a conditioned stimulus node. In some embodiments, the elicited response must be above a certain threshold for a neutral stimulus node to become a conditioned stimulus node. “Evaluating” the network can also be referred to as “re-testing” the network.

[0026] A “trained” or “conditioned” network refers to a network that has been through a training process. The trained or conditioned network can exhibit behavior that is different from its behavior from prior to training (e.g., different from its behavior during the testing phase). If training is unsuccessful, the network behavior is the same as prior to training (e.g., the same as its behavior during the testing phase).

[0027] In some embodiments, “associative memory” refers to how trained or conditioned a network is. Associative memory is analogous to Pavlovian conditioning. In some embodiments, “associative memory” refers to the ability to generate a conditioned node from a neutral node. There are many mechanisms to assess and quantify associative memory. Different forms of memory and learning may be assessed to describe and evaluate the system.

[0028] GRNs or networks are generally made up of many more than three nodes; thus, a single network may contain multiple unconditioned stimulus nodes, multiple neutral nodes, and multiple response nodes. After training, a fraction of the neutral nodes may become conditioned nodes. GRNs can be analyzed by “triplets” of nodes (e.g., one unconditioned stimulus node, one neutral node, one response node). A triplet of nodes may also be referred to as a circuit.

[0029] GRNs can be further evaluated to investigate the effect of having more than one source variable. This can be evaluated by using Partial Information Decomposition, or other similar methods.

[0030] In some embodiments, the method further includes determining a set of stimuli to alter the integration within the network. “A set of stimuli” may refer to stimulus of a specific selection of nodes, or a specific time variation of stimulating one or more nodes. “Alter the integration”7QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 within the network refers to increasing or decreasing integration of the network. Decreasing integration of the network may be useful in applications where it is undesirable for the system to be too integrated or have autonomy.

[0031] A causal emergence of the network may be determined. In some embodiments, a causal emergence of the network may be determined based on the post-training activity of the network (e.g., the post-training associative memory). In some embodiments, causal emergence can be computed on any history (e.g., a specific state of the network at a given time in the simulation) of the network’s behavior. Determining the causal emergence over multiple histories of the network may be particularly useful to raise or lower the integration of a system regardless of a “training,”

[0032] Determining a causal emergence can include using Integrated Information Decomposition. Integrated Information Decomposition may be a multidimensional decomposition, which captures informational dependencies of a system. Emergence capacity may be decomposed into downward causation, and causal decoupling. Downward causation refers to the amount of information that the whole predicts about the future of individual single components. Causal decoupling refers to the amount of information that the whole predicts about the future of the whole.

[0033] After training and evaluating a network, it is possible to classify the behavior of the network. To do so, the behavior may be characterized by behavior descriptors. In some embodiments, the behavior descriptors may be selected from trend, monotonicity, flatness, number of peaks, average distance among peaks, average difference in causal emergence, or range. Behavior may be characterized by one or more of the listed behavior descriptors. Other such behavior descriptors are possible.

[0034] In some embodiments, GRNs can be clustered based on similar behaviors. For instance, multiple test trajectories can be generated from a trained GRN. Based on the clustering, the trajectories may be grouped into “species” that share similar behavior. Clustering methods may include k-means clustering, Gaussian mixture model clustering, centroid-based clustering, spectral clustering, or other suitable clustering methods.8QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571

[0035] In some embodiments, studying a GRN may be used to develop or suggest a therapy or treatment for a disease. For instance, a GRN may be used to investigate a biological network known to be affiliated with a disease. Applied stimuli could correspond to administering a specific therapy. By investigating the adaptive learning and causal emergence possible in the system, treatment plans may be developed. For instance, studying the GRN may suggest a dose schedule that would improve response to a drug. Or, a GRN may suggest that a system is susceptible to associative learning; this opens up possibilities to suggest initially giving a subject a drug and an inert or harmless stimulus, and eventually switching to just the placebo and still expect a response to the inert stimulus. The inert stimulus may refer to a placebo, a harmless drug, or a non-drug stimulus such as a vibration electric pulse, etc. that cells can perceive. In some embodiments, the methods may be used to raise or lower the integration of some body system (e.g., cells, tissues bioelectric networks, biochemical networks, etc.) which will then affect how that system resists, holds on to, or implements disease states.

[0036] The methods and systems describes herein can be applied to a variety of systems, including but not limited to swarm robotics, computer / information networks, distributed control and monitoring systems (e.g., drone flocks, environmental sensor / effector technology, etc.), biobots (e.g., bots built from biological systems), or hybrots (e.g., hybrid bots built from a combination of biological systems and non-biological systems, or more generally built from a combination of different systems). In some embodiments, the methods and systems described herein may be used to detect points of failure of a network, and identify remedy interventions to the network. This can help prevent failures and identify the best remedies for failures in a network. In some embodiments, the methods and systems described herein may be used to controls the level of integration of the system or the level of autonomy of a system such as an artificial system.

[0037] EXAMPLES

[0038] The following examples are meant to be illustrative and should not be seen as limiting.

[0039] Introduction

[0040] We investigate how the properties of active components enable the emergence of a high- level, integrated decision-making entity. This focus bears on issues in ecology, psychiatry, swarm9QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 robotics, and developmental biology. In a sense, all intelligence is collective intelligence because even human minds supervene on a collection of cells which are themselves active agents. One practical way to define integrated emergent systems is by the fact that they have goals, memories, preferences, and problem-solving capabilities that their parts do not have. For example, while individual cells solve problems in metabolic, physiological, and transcriptional spaces, what makes an embryo more than a collection of cells is the alignment of cellular activity toward a specific outcome in anatomical morphospace. Here, we focus on one aspect of emergent agency: integrated, distributed memory.

[0041] When a rat learns to press a lever to receive a reward, the cells at the paw touch the lever, those in the gut receive the delicious food - no individual cell has both experiences. The “rat” is the owner of the associative memory that none of its parts can have. This ability to bind together individual experiences of their parts is a hallmark of emergent agents. The rat can do associative learning because it has the right causal architecture (implemented by the nervous system) to integrate information across space and time within its body. However, this ability is not unique to brainy animals - various kinds of problem-solving and learning occur in single cells because biology fundamentally exploits a multi-scale competency architecture in which the molecular components within a cell are likewise integrated to provide system-level context-sensitive responses.

[0042] Regardless of specific material implementation, certain functional topologies exhibit high emergent integration. In recent years, quantitative methods have been developed to measure a degree to which a system is more than its parts and possesses higher levels of organization that do causal work distinct from its lowest level mechanisms. This now enables a study of the relationship between minimal cognition and collective intelligence. A degree of integration among parts is required for any amount of cognitive function, such as learning. Here, we explore whether the process of learning can increase integration within a system. For instance, we investigate whether training a system can rectify and strengthen the existence of it as a unified, emergent, and virtual governor.

[0043] To study this question in a most minimal model system, in which all the components are well-defined, deterministic, and transparent, we chose Gene Regulatory Networks. GRN models10QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 represent sets of gene products that up- or down-regulate each other’s activity based on a given functional connectivity map. These networks are very important topics in biomedicine, evolutionary developmental biology, and synthetic biology. It is essential to be able to not only predict their behaviors, but also to induce desired dynamics for interventions in regenerative medicine and bioengineering. These networks are well-recognized to have emergent properties, yet their control remains challenging. We recently showed that such networks can be trained - by providing stimuli on chosen nodes and reading out responses on other nodes, well-known paradigms from behavioral and cognitive science can be used to predicably change future responses as a function of experience. Biological networks show several different kinds of learning, including Pavlovian conditioning. Thus, we sought to measure emergent integration in these networks before, during, and after training, to determine what effect the induction of memory has on the network as a coherent agent.

[0044] To quantify this property, we took advantage of tools from neuroscience, where several measures of “integrated information” have been proposed to explain how the activity of individual neurons gives rise to a unified emergent mind. Different flavors of integrated information have been applied to study information dynamics in, among the others, natural evolution, genetic information flow, and biological and artificial neural systems. We adopt the framework of Integrated Information Decomposition (ID) to specifically define a measure of causal emergence: it quantifies to what extent the whole system provides information about the future evolution that cannot be inferred by any of its individual components, or, in other words, the extent to which the system behaves as a collective whole. Intuitively, the higher causal emergence, the stronger the integration (or inseparability) of a collective of components. <blD provides a rigorous framework to study causal emergence in a variety of different systems, from Conway’s game of life to human and primate neural dynamics, including for the comatose and the brain-injured.

[0045] Here, we analyze in silico simulations showing how causal emergence increases in response to associative training in specific GRNs, characterize the GRNs’ integration behaviors, and uncover a relationship between this phenomenon and the underlying biology (phylogeny and gene ontology of specific networks.)11QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571

[0046] Results

[0047] We adopted the recent framework of Integrated Information Decomposition <bID, an established approach to quantify causal emergence, in the dynamics of 29 GRNs (described as DDEs) from the BioModels database, before and after training the networks for an associative memory task. We assessed how learning strengthens causal emergence in basal biological systems like regulatory networks, and how this resulted in qualitatively different patterns of behavior of the GRNs and related to the biology (phylogeny and gene ontology) of the networks.

[0048] We illustrate how associative memory works in FIGS. 1A-1B. For each network, we pretested every triplet of its nodes (a circuit in which we assign nodes to the roles of unconditioned stimulus (UCS), a neutral stimulus (NS), and a response (R)) to determine whether it passed the test for associative memory; similarly to Pavlovian conditioning in animals. We did so by: ensuring that stimulating the UCS alone triggers an increase in R, ensuring that stimulating the NS alone does not trigger R, and then: 1) “relaxing” the network in the initial phase; 2) stimulating both unconditioned and neutral stimuli during the subsequent training phase; 3) verifying that after the paired exposure, stimulation of the neutral stimulus alone regulated the response (see Materials and Methods). Out of all the circuits, 808 (among 19 networks) passed this pretest and we considered these for all subsequent analyses.

[0049] We then applied the <bID compute causal emergence on the genes’ expression signals, exploiting it as an exhaustive measurement of all the ways a macroscopic (i.e., whole network) feature could affect the future of any parts of the network (including the network itself).Intuitively, this definition quantifies the degree to which the whole system influences the future in a way not discernible by considering the parts only (schematized by the dog of FIG. 1 A progressively becoming more of a unified, centralized agent and less a collection of cells). Causal emergence is a numerical quantity measured in natural units of information; the higher it is, the more “emergent” the system is, in the sense that the more the “macro” beats the “micro” in explaining how the system dynamics.

[0050] Emergence increases after training

[0051] We set out to study how causal emergence changes before and after training GRNs for associative memory, and specifically to test the conjecture that the experience of learning an12QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 associative task raises the causal integration of the system. Because we also wanted to know whether biological networks have any unique properties in this regard, we constructed a set of 140 random networks as controls, by the established gene circuit method (see Materials and Methods), which involves to randomizing the topology and connection strengths of these pseudo-biological networks with different random seeds. We computed the average percent change in causal emergence from before to after “training” with paired stimuli (FIG. 2A), where each point corresponds to one circuit of one network for biological and random. We also plotted in FIG. 2B the ratio of biological GRNs that had any associative memory and witnessed an increase in causal emergence from before to after “training" in most networks.

[0052] In total, causal emergence was strengthened in 17 out of 19 networks. The change amounted, on average, to a 128.32±81.31% increase from before to after training, meaning more than a two-and-a-half-fold increase. This result was significant (p<0.001) with the Wilcoxon signed-rank test for paired data, meaning that the two samples of before and after training came from statistically different distributions, confirming that training for associative memory increased causal emergence for most of the networks studied. Random networks had an average change of 56.25±51.40% and the difference with biological networks was significant (p<0.001). Instead, random networks had higher levels of absolute causal emergence before training. In other words, random networks started with higher emergence but did not increase it, while biological networks started with lower emergence but increased it with experience.

[0053] Previous network structure and function classifications do not capture emergence

[0054] We next sought to test whether our Off) results captured new information about these networks that could not be derived with other previously existing metrics. To this end, we characterized the GRNs along existing structural and functional metrics. For all the circuits with memory, we computed established properties from network theory (in-degree, out-degree, betweenness centrality, PageRank, and HITS scores) for the structure and from dynamical systems literature (sample entropy, Lyapunov exponents, correlation dimension, detrended fluctuation analysis, and generalized Hurst exponent) for the function. We found no significant or only weak correlation with the change in causal emergence (FIGS. 3A 3B). These findings reveal13QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 that our experimental protocol uncovers new information that existing classifications of networks do not capture: how training GRNs affects causal emergence.

[0055] We next tested whether <bID corresponds to mere network “activity” (i.e., checking that periods of low integration did not merely correspond to quiescent periods of low signaling). We characterized overall network “activity” as the first derivative of the ODE state variables and found no correlation with percent change in causal emergence (FIG. 3C), revealing that causal emergence is not the same as network activity. If, for example, causal emergence spikes up, it is not an artifact of increased network activity. Similarly, if causal emergence drops, it is not attributable is a drop in signaling among nodes.

[0056] Automatic classification of emergence trajectories into behaviors finds five “species”

[0057] We observed several different ways in which integration of a network changed due to the training phase (FIGS. 4A-4E). We wondered if the effects of training on integration across networks were highly diverse (forming a smooth space of possible effects of training), or, whether there would be discrete categories of effects which define a kind of “species” with respect to how GRNs’ causal emergence affected training. We first described each test phase causal emergence trajectory using behavioral descriptors; alternatively, we could have extracted learned features through a neural network, but these would have been less interpretable. We settled on seven descriptors we found (after manual search) to be, at the same time, the most expressive (in terms of quality of the classification) and compact: trend, monotonicity, flatness, number of peaks, average distance among peaks, average difference among peaks, and range (see Materials and Methods for detailed procedure).

[0058] We applied k-means, an established unsupervised learning technique, to automatically classify the extracted behavioral descriptors from each test phase of the circuits that have memory. This technique revealed discrete clusters in terms of the behavior descriptors (how emergence changes due to training), in effect classifying networks into “species” of individuals that exhibited similar effects of training upon their integrated emergence. We tuned the number of species to be the optimal one according to the Silhouette coefficient of quality of a clustering. We found five optimal “species” of behavior and nicknamed them homing, inflating, deflating, spiky, and steppy after their characteristics (see next section). We plotted the t-SNE embedding14QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 in 2D of the descriptors of each test phase trajectory, colored by the assigned behavior, in FIG. 5. We found that behaviors corresponded to an almost perfect separation in the t-SNE embedding, with some overlapping around the intersection of the five behaviors. The Silhouette coefficient of 0.5 indicates a good partitioning, that is significantly different from random assignment (in which case the coefficient would be 0). We report the value counts per species in Table 1. This analysis showed that the species distribution was uneven, with a slight plurality of homing individuals and steppy being the rarest of all species among the GRNs that have memory.

[0059] Table 1 : Number of memory circuits per behavior class. Breakdown by behavior of the number of GRN circuits with memory. Behavior distribution is uneven, with a plurality of homing individuals and a rarity of steppy individuals.15QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571

[0060] Finally, we tested whether different circuits within the same network have different behaviors or consistently fall into one; in other words, we tested whether the same network can have multiple different “personalities” with respect to housing circuits that respond differently to training. We performed a chi-squared test for independence between the network identifier and its behavior label, which revealed (p<0.001) that circuits belonging to the same network preferentially adopted one species of behavior.

[0061] Visualization of the five behaviors reveals relevant patterns

[0062] We then set out to study how the five types of behaviors differed. We plotted five sample trajectories for each behavior in FIGS. 4A-4E, where the x-axis corresponds to simulated time. Each behavior represented trajectories sharing a distinct pattern, as if the GRN agents were adopting a specific behavior in the emergence space. Homing trajectories frequently oscillated around their mean, as if the GRN was “numb”. Inflating individuals had an overall positive trend, as the name suggests, as if training made them more and more emergent, whereas the opposite is true for inflating individuals. The spiky behavior consisted of a few periodic, extreme bursts of emergence that left the trend unchanged in the long-term. Finally, steppy was about having a few prolonged (not short, like inflating) bursts of emergence as if they were strides.

[0063] The descriptor histograms in FIGS. 6A-6E illustrate the effects of training on emergence. They show, for example, how homing individuals were non-monotonous and flat; spiky individuals were also flat but had, on average, more distanced peaks and a larger range; finally, deflating individuals were more negatively monotonous whereas inflating ones had positively monotonic effects on causal emergence.

[0064] Behaviors differ by phylogeny and gene ontology

[0065] Having seen that the integrated nature of biological networks displayed different responses to training, we wondered if these classes corresponded to distinct biology (phylogeny and gene ontology of the network). We explored whether networks belonging to different types of processes or species exhibit different responses with respect to how much they are reified by the associative conditioning. We extracted this information directly from the BioModels website and visualized the results in FIGS. 7A-7D with heatmaps. FIG. 7A shows the relative occurrence (i.e., all the behaviors sum to 1) of the five automatically classified behaviors by phylogeny16QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571(FIG. 7A and FIG. 7B) and gene ontology (FIG. 7C and FIG. 7D). Some cells are marked with “N / A” because not every behavior is represented in every phylogeny or gene ontology. From the tables, we see that there existed a relationship between phylogeny (or gene ontology) and behavior occurrence. For example, lower vertebrates (which mostly included Xenopus laevis) have the highest diversity, followed by insects and plants, whereas mammals showed the least. Slime molds broke down similarly to mammals, but it was hard to draw conclusions from that comparison because only one network fell under this taxon (from Physarum polycephalum), but we still included its results for completeness. When looking at gene ontology, the MAPK cascade and the mitotic cell cycle were the most diverse, and stem cell differentiation the least. Similarly to slime molds, some gene ontologies (the far-red right signaling in P. polycephalum and the sucrose biosynthetic process in Saccharum officinarum) were represented by only one network, but we included their results for completeness, even though few inferences could be made.

[0066] A similar result was revealed analyzing the average (across the circuits) percent change in causal emergence from before to after training in FIG. 7B, which includes the margins. Plants showed the greatest increase in emergence and insects the greatest decrease, while also having the highest behavior diversity (FIG. 7A). On the other axis, the sucrose biosynthetic process showed the greatest increase in causal emergence and the regulation of the circadian rhythm showed the greatest decrease. We performed a chi-squared test for independence in two-way tables for all the tables of FIGS. 7A-7D and found the results to be significant, confirming our hypothesis that the specific ways in which causal emergence is potentiated by learning correlates with specific phylogeny and gene ontology of the networks.

[0067] Discussion

[0068] Here we show that re-engineering its hardware architecture (physical topology) is not required to accomplish this. Using an in silico model of a minimal agent, we find that training it for associative memory can increase its integrated causal power. This demonstrates another surprising result: the relationship between causal integration and learning is bi-directional - associative conditioning experiences tend to potentiate the collectivity of networks.

[0069] We have shown that this holds for a specific type of system, ODE GRNs, which has relevance to the mechanisms implementing high level cognition in animals, both at the17QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 evolutionary and individual behavioral scale. Our work was motivated by two considerations. The first is aimed at the nascent field of diverse intelligence and unconventional cognition, seeking to understand the dynamics necessary and sufficient for the emergence of integrated selves on a scale from the most minimal matter to human metacognition and beyond. The second is a roadmap toward new ways to manipulate biological matter for biomedical and bioengineering applications, that moves beyond rewiring biochemical details toward the programming, communicating with, and motivating living tissues toward desired system-level outcomes.

[0070] Network theory and dynamical systems theory provide metrics to analyze networks, including computational models of GRNs. These existing tools allow the inference of biological pathways from data, as well as algorithms for predicting how they will respond to new inputs. While very useful, advances are limited by the assumption that structure fully explains function: a view of molecular pathways as mechanical machines inevitably focuses attention on the hardware and approaches to modify it such as CRISPR, protein engineering, and the editing of promoters to create novel connections between them. However, network rewiring is hard and time-consuming, with many challenges for the synthetic biologist or the designer of gene therapies. Recent research has shown that GRNs can demonstrate a variety of unanticipated behaviors, such as associative memory - and that such behavior arises from changes in the signaling within a specific network rather than changes in its wiring; moreover, that approaches from behavioral science can lead to new discoveries about their dynamics. Thus, we seek to expand the transfer of concepts from neuroscience (such as measures of integration) to novel substrates. We found a surprising result, in which training reifies the causal potency of a distributed system.

[0071] Training a biological network for associative memory increases causal emergence by 128.32%, on average, meaning an almost two-and-a-half factor. This does not happen for every network: some GRNs remain as they were natively, before their training, while others (the vast majority) adapt based on what they experience. Borrowing an analogy from circuit components, some GRNs behave like resistors (which function the same regardless of their history or the frequency of the incoming signal), while others like memristors (which have a high degree of hysteresis and are also frequency-dependent). Interestingly, the specific way in which causal18QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 emergence rises after training is similar within the various circuits of a given network, suggesting that a network has a consistent “personality” with respect to how stimulation of its various input nodes affects its integrated nature.

[0072] This increased causal emergence contrasts dramatically with what we observed in random networks, which have an average increase of only 56.25%. This result suggests that evolution may have selected biological networks to be more responsive to training in a way that is not reducible to random network dynamics. In other words, unlike some generic network properties that hold for all networks, these have been (directly or indirectly) reinforced by the processes of life. There was no correlation between causal emergence and mere GRN activity, meaning that our findings cannot be derived from established metrics on networks. This result is in line with studies on integration information and psychedelics, which have shown that “how much activity” in the brain does not correlate well with conscious experience.

[0073] We automatically categorized causal emergence trajectories into behaviors and investigated how the behavior depends on the biology of the network, in particular, phylogeny and gene ontology. As expected, there is a dependence between the two, with different phylogenies and gene ontologies preferentially adopting different behaviors. However, we found no relationship between evolutionary history and behavior. Mammals and slime molds are, respectively, the least and one of the most ancient taxa in our study, yet they share low levels of diversity and relatively higher levels of increase in causal emergence. Plants (an ancient taxon) and insects (a less ancient taxon) have, respectively, the greatest positive and negative change of causal emergence. In the future, we will investigate what happens when considering a wider repertoire of ontologies for each phylogeny. Crucially, there is also no relationship between “intelligence” when measured as number of neurons (if any) and the effects of training on integration. Mammals (which, in our study, mostly consist of human GRNs) are dominated by plants (that do not even have a nervous system) in terms of causal emergence change, and slime molds (having the most primitive nervous systems) dominate insects. Subsequent research may identify other biological parameters that map more tightly to the different classes of response that we found in these GRNs (but what we know already is that popular ways to categorize networks are not sufficient to capture the dynamics we observed).19QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571

[0074] The relationship between causal emergence and gene ontology also deserves mention. The MAPK cascade is not only the most diverse ontology here, but it also corresponds to an almost doubling of causal emergence after training. This finding is relevant considering that, in addition to regulating response to a wide array of stimuli and being found in most eukaryotes, it pre-organizes pathway segments so that they respond faster and stronger to subsequent stimuli — that is, that they form new memories more readily. Similarly, the mitotic cell cycle (the second most diverse ontology) also plays a key role in the reproduction of every cell in the organism. On the other hand, the regulation of the circadian rhythm results in the greatest negative change in emergence after training, contrary to what happens with most ontologies. One possible reason is that the circadian GRNs are not persuadable, or, in other words, hold to their priors more strongly, but it is hard to draw conclusions in the absence of more experiments. In general, our intuitions are limited by the subset of networks analyzed and would be stronger if tested on a larger and more diverse pool of GRNs, consisting of, for example, phylogenies not considered so far in this work. It is a limitation of this area of inquiry that biologically accurate, fully parameterized network models are not plentiful.

[0075] There are essential areas for future work. The first concerns the need to test these ideas in real cells. ODEs are a convenient formalism to study continuous-time GRNs, but it is possible they provide spurious behaviors (within certain parameter ranges) that may not map to observable phenotypes. The main reason for this is that our ODEs model GRNs that operate in isolation and do not consider the biological noise and interactions coming from the intracellular matrix (future work will model the matrix as an environment for receiving and sending feedback to GRNs). Future work will also consider how causal emergence differs across other dimensions like, for example, the age of the host (i.e., GRNs in uteri, middle-aged adults, and elderly patients). An intriguing hypothesis is also that cancer networks may react differently than tissue networks to training. Such insights would then inform biomedical control for the development of more efficacious drugs with fewer side effects. We have previously suggested that taking advantage of the decision-making, problem-solving, and other competencies of living material, such as by understanding how experiences affect its causality as an integrated whole distinct from the collection of parts, will lead to a much different therapeutic landscape.20QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571

[0076] Three other areas offer immediate opportunities for further investigation. First is evolution. Significant work has looked at the interplay between intelligence and evolvability. Simulations and in vitro experiments could now look at the effects of learning-induced potentiation of integrated agency on the evolutionary process. Second, the study of the phylogenetic and ontogenetic origins of Selfhood and integrated minds may be enriched by a better understanding of relevant dynamics not tied to a specific neural basis. Third, an expanded survey of training modes (besides associative conditioning), and subject matter (pathways, and other networks in biological and technological systems) should be examined for these dynamics.

[0077] Questions about the capabilities of living matter, and the applicability of tools from computational and cognitive sciences outside the neural domain, form the basis of an exciting emerging field that encompasses efforts to understand basal cognition, diverse intelligence, active matter, and unconventional computing. We suspect it is likely that the ability to modulate integrated emergent agency by specific training experiences (that do not require physical rewiring) will have implications for not only evolutionary biology and but also for engineering efforts involving biological, engineered, and hybrid agents.

[0078] Materials and Methods

[0079] Biological models and simulation

[0080] We curated a dataset of 29 peer-reviewed biological network models from the BioModels open database encompassing all the strata of life (from bacteria to humans), the same adopted in. Each model describes a GRN whose nodes are proteins, metabolites, or genes (the species of a network) and whose edges are mutual reactions. Each network is modeled over time according to chemical rate law Ordinary Differential Equations (ODEs), and so each one is a continuous-time dynamical system. Species take values on a continuous domain (like protein concentrations or gene expression levels). We relied on the SBMLtoODEjax Python library, which parses System Biology Markup Language (SBML) specification files into JAX programs. We then simulated each model in AutoDiscJAX (github.com / flowersteam / autodiscjax), which is not only written in the highly efficient and compute-optimized JAX language but also enables interventions on GRNs like applying stimuli. For all experiments, simulations were integrated with the fourthorder Runge-Kutta method using a step size of 0.01.21QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571

[0081] Random models

[0082] We built a set of 140 (5 different seeds per biological model) random networks by the gene circuit method, as in Biswas et al., 2022. For each biological network, we created 5 different random networks by sampling - with different random seeds - the parameters (e.g., connection strengths, initial concentrations, and constants) from a uniform distribution U(0, 1), where we set the bounds to be consistent with the empirical distribution of parameters in the biological models. So, we created a total of 140 random networks. These models had the same distribution of topology and network theoretic properties (in-degree, out-degree, betweenness centrality, PageRank, HITS scores) as the biological models they are built from, but since connection strengths could effectively approach zero, we also randomized the topology.

[0083] Memory evaluation

[0084] Of the types of memory identified in, here we focused on associative memory, since it most emphasizes the need for a network to integrate experiences across different nodes, and because it is the most interesting clinically (offering the possibility of associating powerful but toxic drugs with “placebo” triggers). Associative memory is analogous to Pavlovian training in animals; we present an illustration in FIG. 1A, with the corresponding training schedule for our ODE GRNs in FIG. IB. Associative memory involves a triplet of nodes (a circuit): a target response R, an unconditioned stimulus UCS that regulates R, and a neutral stimulus NS that does not. We first “relaxed” the GRN to allow it to settle on a steady state and have a baseline for its pre-training behavior (relaxation phase) by simulating it for ts time steps without any stimuli. We then trained it by stimulating UCS and NS simultaneously (training phase) for another ts time steps. If, finally, stimulation of NS only regulated (testing phase) for other ts time steps, we said the network had “learned” to associate UCS with NS, turning NS into a conditioned stimulus CS. After preliminary experiments, we found ts=250,000 (2500 seconds of simulated time) to be sufficient for all the networks to settle on steady values.

[0085] For each network, we tested every possible triplet of nodes for associative memory. Since biological entities take on continuous values in ODE networks, we can either up-stimulate (increase the value to some extent) or down- stimulate (decrease the value up to some extent) for a specific species. Similarly, stimulation can up-regulate or down-regulate R, depending on22QB1166118.01571199770098.1Tufts T002885Quarles 166118.01571 whether stimulation increases or decreases its value. Following Abramson et al., we up- stimulated and down-stimulated by setting the quantity of a stimulus ST to emaxSTx100 and eminSI7100 respectively, where emaxSTand eminSTwere the maximum and the minimum values the species attained. We called R up-regulated if the mean value during testing was at least twice that during relaxation, and down-regulated if it was no more than half. In line with Abramson et al., we found these values for stimulation and regulation to result in associative learning in our network and simulate the delivery of real-world drugs.

[0086] Stimulation through the delivery of real-world drugs did not take place in one persistent bout, but in several time-delayed dispensations. For this reason, we applied stimulation in pulses: we partitioned the phase (whether training or testing) into five equally sized time intervals and alternated between applying the stimulus (e.g., at the first, third, and fifth intervals) and not applying it. When a stimulus was not applied, the species followed their intrinsic dynamics as dictated by the network; in the Results, we verify that this pulsed stimulation was not correlated with causal emergence and, thus, could not explain alone the increase in emergence after training.

[0087] Of all the triplets of the 29 biological networks considered the 808 that passed the pretest belonged to 19 networks (more than half). We considered these circuits for all the analyses and visualizations.

[0088] Data preprocessing

[0089] We applied the following preprocessing steps from Blackiston et al., 2024, to highlight underlying structures in the GRN simulation data and allow for more meaningful inferences. For each simulated ODE trajectory, we performed global signal regression by regressing out the mean at each time step across the species to filter out global artifacts; these could be of biological significance, but, when computing information flows, we are interested in changes from the baseline and not global trends. Second, we removed autocorrelation. Indeed, biological signals are known to be autocorrelated which could inflate pairwise dependencies between time series by reducing the effective degrees of freedom. We followed the approach of and performed the following steps, independently for each species: we computed the linear least-squares23QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 regression between time t -1 and t, computed the predicted values at time given the regression results, and finally obtained the residuals as our preprocessed signal.

[0090] Information theory and Partial Information Decomposition

[0091] Information theory, originally introduced to study the transmission capacity of communication channels, has over the years emerged as a principled language to evaluate dependencies in complex systems, including biological. The basic object of study is Shannon’s entropy:

[0092] Where the summation is over the support of X, and it quantifies the amount of uncertainty about a random variable X. We can then define for a process consisting of a “source” variable X and a “target” variable Y the mutual information as the uncertainty that is left on Y after observing X, i.e., how much information observing X discloses about Y.

[0093] Next, we investigate the effect of having more than one source variable, as having more than one source variable is common in complex regulatory networks. For a finer grained understanding of information, we must consider all the different ways information flows across a system. Intuitively, let us consider the case of stereoscopic vision in humans: with one eye open, we perceive a unique set of visual features for each, and also redundant features both of our eyes capture, but, finally, depth perception, which can only be captured if both eyes are open simultaneously, corresponds to synergistic information. The seminal work on Partial Information Decomposition (PID) provides a framework to parcel out mutual information into various information atoms (redundant, unique, and synergistic).

[0094] Mutual information and PID, by themselves, are instantaneous measures of integration; they fail to capture the temporal and causal aspects of information dependencies up to and including all future time steps, a crucial aspect for dynamical systems that evolve over time, like our models of biological regulation.

[0095] Causal emergence and Integrated Information Decomposition24QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571

[0096] We investigated how associative learning impacts the causal emergence of a system, meant as the ability of a whole to influence the future of its parts. Several operationalizations to quantify the integration of a system have blossomed, like the various 0 measures, with groundbreaking results in neuroscience. Still, they are unidimensional and so tend to behave inconsistently. We pursue a multidimensional decomposition and relied on the recent framework of Integrated Information Decomposition GID, which is a finer decomposition of the PID and captures all informational dependencies of a system in space (macro- and micro-scale) and time (instantaneous up to and including all future time steps). According to general assumptions outlined in Rosas et al., 2020, a system’s capacity to display emergence depends on how much information the whole provides about the future evolution that cannot be inferred by any subset of parts. The OLD formal apparatus then tells us that we can decompose emergence capacity as the sum of two terms:

[0097] 1. Downward causation: the amount information that the whole predicts about the future of the single components;

[0098] 2. Causal decoupling: the amount of information that the whole predicts about the future of the whole. This definition previously appeared to quantify the reduction in emergence capacity between healthy and brain injured patients; we chose it as our measure of causal emergence in biological systems since it considers all types of influences the whole can have on the future of a system.

[0099] Gaussian Information Theory

[0100] Our models are continuous-valued biological dynamical systems, while information theory was originally defined for discrete random variables. We used the continuous generalization of Shannon’s entropy, the differential entropy:

[0101] Where the integral is over the support of X. This generalization is, in general, hard to compute because it requires estimating p(x). But, if we assume that p\left(x\right) is distributed25QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 as a Gaussian, we can leverage closed-form estimators for the entropy and, as a result, all the other information measures. Indeed, the bivariate mutual information (in natural units) becomes: ln(l — p2) / ( , r) =2

[0102] Where p is the Pearson correlation coefficient between X and Y. While the Gaussian hypothesis is limiting in the general case, for our specific data we observed precisely standard Gaussians (according to statistical tests) after preprocessing.

[0103] Most practical computations of causal emergence converge on the same simple form for Gaussian continuous variables, that we adopted here. We first computed the lag-1 mutual information matrix among all pairs of nodes in the system using the equation above. Since we cannot handle systems with several elements because of the combinatorics involved, we reduced the dimensionality by the Minimum Information Bipartition (MIB). The MIB bisects the system in two components by approximating the bisection through the Fiedler vector (the eigenvector of the graph Laplacian corresponding to the smallest non-zero eigenvalue). After bisecting the graph with the Fiedler vector, we averaged within each component and compared the dynamics of the two parts to the whole. In essence, we sliced a watermelon along its longest axis and measured the extent to which the average number of seeds in one half predicted the average number of seeds in the other. Finally, we solved a linear system of equations relating the mutual information to the atoms the ID is decomposed in.

[0104] Behavior descriptors

[0105] We extracted seven descriptors from each causal emergence trajectory, to be fed to an unsupervised learning pipeline for automatic classification into behaviors. The descriptors are:

[0106] 1. Trend: the slope of the least squares fit of the trajectory. A positive slope indicates an increasing trend, while a negative slope indicates a decreasing trend.

[0107] 2. Monotonicity: the Kendall’s tau coefficient between the trajectory and the sequence of its time stamps. Kendall’s tau is a standard statistic to measure ordinal association between two quantities and, in our case, it is the highest for a perfectly monotonically increasing trajectory,26QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 and the lowest for a perfectly monotonically decreasing one, with values around zero corresponding to the trajectory fluctuating independently of the time axis.

[0108] 3. Flatness: how flat the trajectory is and does not locally deviate from the mean. We divided the trajectory into consecutive intervals and approximated the trajectory with the mean over each interval. We computed flatness as the r-squared coefficient of this approximation: the higher the coefficient, the better fit are the local means, meaning the trajectory was locally flat (though jumps may have existed in correspondence of the interval boundaries). After preliminary experiments, we found an interval size of 100 to correctly capture the intuition behind flatness of a trajectory.

[0109] 4. Number of peaks: the number of local minima and maxima of the trajectory. To detect the maxima of a trajectory, we searched the time step list for values that are higher than the values neighboring them, and, to exclude weak maxima, filtered out those that were not equal to the maximum over a centered window of size 100 to correctly capture the intuition behind a peak. To detect the local minima, we repeat the same procedure but for values that are smaller.

[0110] 5. Average distance among peaks: the average distance among all the peaks from 4) (or 0 if there were none).

[0111] 6. Average difference among peaks: the average difference in causal emergence value of the peaks from 4) (or 0 if there were none).

[0112] 7. Range: the difference in causal emergence value between the maximum and the minimum peaks.

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[0190] Illustrative Embodiments of Methods and Systems Described Herein

[0191] FIG. 8 shows an example process 800 to alter integration within a network. At step 802, a network is provided. The network may include at least one of a neutral stimulus node, an unconditioned stimulus node, and a response node. At step 804, the network may be testing to evaluate a pre-training level of associative memory. This may include comparing a first response to stimulation of the neutral stimulus node at the response node, and a second response to stimulation of the unconditioned stimulus node at the response node. At step 806, the network is trained. Training the network may include applying coordinated stimulation of the neutral stimulus node and the unconditioned stimulus node to elicit a response at the response node. At step 808, the network may be evaluated for a post-training level of associative memory. This may include applying stimulation of the neutral stimulus node alone and observing a post-training response at the response node. If the neutral stimulus node elicits a post-training response from the response node, the neutral stimulus node may be considered a conditioned response node. At step 810, a set of stimuli to alter the integration within the network is determined based on the evaluated level of associated memory.

[0192] In FIG. 9, an example 900 of a system (e.g., a data processing system) for increasing integration in a network with some embodiments of the disclosed subject matter is shown.

[0193] In some embodiments, computing device 904 and / or server 916 can be any suitable computing device or combination of devices, such as a desktop computer, a laptop computer, a smartphone, a tablet computer, a wearable computer, a server computer, a virtual machine being executed by a physical computing device, etc. As described herein, system 900 can present information about the integration within a network to a user.

[0194] In some embodiments, communication network 902 can be any suitable communication network or combination of communication networks. In some embodiments, communication network 902 can be any suitable communication network or combination of communication networks. For example, communication network 902 can include a Wi-Fi network (which can34QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 include one or more wireless routers, one or more switches, etc.), a peer-to-peer network (e.g., a Bluetooth network), a cellular network (e.g., a 4G network, a 5G network, etc., complying with any suitable standard, such as CDMA, GSM, LTE, LTE Advanced, WiMAX, etc.), a wired network, etc. In some embodiments, communication network 902 can be a local area network, a wide area network, a public network (e.g., the Internet), a private or semi-private network (e.g., a corporate or university intranet), any other suitable type of network, or any suitable combination of networks. Communications links shown in FIG. 9 can each be any suitable communications link or combination of communications links, such as wired links, fiber optic links, Wi-Fi links, Bluetooth links, cellular links, etc.

[0195] FIG. 9 additionally shows an example of hardware that can be used to implement computing device 904 and server 916 in accordance with some embodiments of the disclosed subject matter. In some embodiments, computing device 904 can be used to execute one or more set of instructions to identify a behavioral catalog. In other embodiments, computing device 904 can be used to identify therapeutic interventions. In still other embodiments, computing device 904 can be used to determine a set of stimuli to alter the integration within the network based on the evaluated level of associative memory.

[0196] As shown in FIG. 9, computing device 904 can include one or more hardware processor 906, one or more displays 908, one or more inputs 910, one or more communications 912, and / or memory 914. In some embodiments, processor 906 can be any suitable hardware processor or combination of processors, such as central processing unit, a graphics processing unit, etc. In some embodiments, display 908 can include any suitable display devices, such as a computer monitor, a touchscreen, a television, etc. In some embodiments, inputs 910 can include any suitable input device and / or sensors that can be used to receive user input, such as a keyboard, a mouse, a touchscreen, a microphone, etc.

[0197] In some embodiments, communication systems 912 can include any suitable hardware, firmware, and / or software for communicating information over communication network 902 and / or any other suitable communication networks. For example, communications systems 912 can include one or more transceivers, one or more communication chips and / or chip sets, etc. In a more particular example, communications systems 912 can include hardware, firmware and / or35QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 software that can be used to establish a Wi-Fi connection, a Bluetooth connection, a cellular connection, an Ethernet connection, etc.

[0198] In some embodiments, memory 914 can include any suitable storage device or devices that can be used to store instructions, values, etc., that can be used, for example, by processor 906 to present content using display 908, to communicate with server 916 via communications system(s) 912, etc.

[0199] Memory 914 can include any suitable volatile memory, non-volatile memory, storage, or any suitable combination thereof. For example, memory 914 can include RAM, ROM, EEPROM, one or more flash drives, one or more hard disks, one or more solid state drives, one or more optical drives, etc. In some embodiments, memory 914 can have encoded thereon a computer program for controlling operation of computing device 904. In such embodiments, processor 906 can execute at least a portion of the computer program to present content (e.g., images, user interfaces, graphics, tables, etc.), receive content from server 916, transmit information to server 916, etc.

[0200] In some embodiments, server 916 can include a processor 918, a display 920, one or more inputs 922, one or more communications systems 924, and / or memory 926. In some embodiments, processor 918 can be any suitable hardware processor or combination of processors, such as a central processing unit, a graphics processing unit, etc. In some embodiments, display 920 can include any suitable display devices, such as a computer monitor, a touchscreen, a television, etc. In some embodiments, inputs 922 can include any suitable input devices and / or sensors that can be used to receive user input, such as a keyboard, a mouse, a touchscreen, a microphone, etc.

[0201] In some embodiments, communications systems 924 can include any suitable hardware, firmware, and / or software for communicating information over communication network 902 and / or any other suitable communication networks. For example, communications systems 924 can include one or more transceivers, one or more communication chips and / or chip sets, etc. In a more particular example, communications systems 924 can include hardware, firmware and / or software that can be used to establish a Wi-Fi connection, a Bluetooth connection, a cellular connection, an Ethernet connection, etc.36QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571

[0202] In some embodiments, memory 926 can include any suitable storage device or devices that can be used to store instructions, values, etc., that can be used, for example, by processor 918 to present content using display 920, to communicate with one or more computing devices 904, etc. Memory 926 can include any suitable volatile memory, non-volatile memory, storage, or any suitable combination thereof. For example, memory 926 can include RAM, ROM, EEPROM, one or more flash drives, one or more hard disks, one or more solid state drives, one or more optical drives, etc. In some embodiments, memory 926 can have encoded thereon a server program for controlling operation of server 916. In such embodiments, processor 918 can execute at least a portion of the server program to transmit information and / or content (e.g., results of testing, training, or evaluating the network, or determining a set of stimuli, a user interface, etc.) to one or more computing devices 904, receive information and / or content from one or more computing devices 904, receive instructions from one or more devices (e.g., a personal computer, a laptop computer, a tablet computer, a smartphone, etc ), etc.

[0203] In some embodiments, any suitable computer readable media can be used for storing instructions for performing the functions and / or processes described herein. For example, in some embodiments, computer readable media can be transitory or non-transitory. For example, non-transitory computer readable media can include media such as magnetic media (such as hard disks, floppy disks, etc.), optical media (such as compact discs, digital video discs, Blu-ray discs, etc.), semiconductor media (such as RAM, Flash memory, electrically programmable read only memory (EPROM), electrically erasable programmable read only memory (EEPROM), etc.), any suitable media that is not fleeting or devoid of any semblance of permanence during transmission, and / or any suitable tangible media. As another example, transitory computer readable media can include signals on networks, in wires, conductors, optical fibers, circuits, or any suitable media that is fleeting and devoid of any semblance of permanence during transmission, and / or any suitable intangible media.

[0204] A number of references to patent and non-patent documents are made throughout the publication, each of which is herein incorporated by reference in its entirety.

[0205] Thus, while the invention has been described above in connection with particular embodiments and examples, the invention is not necessarily so limited, and that numerous other37QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 embodiments, examples, uses, modifications and departures from the embodiments, examples and uses are intended to be encompassed by the claims attached hereto.38QB\166118.01571\99770098.1

Claims

Tufts T002885Quarles 166118.01571CLAIMSWhat is claimed is:1 . A method of altering integration within a network, comprising: providing the network comprising a plurality of nodes including at least one of a neutral stimulus node, an unconditioned stimulus node, and a response node; testing the network to evaluate a pre-training level of associative memory comprising comparing a first response at the response node to stimulation of the neutral stimulus node to a second response at the response node to stimulation of the unconditioned stimulus node; training the network, comprising applying coordinated stimulation of the neutral stimulus node and the unconditioned stimulus node to elicit a response at the response node; evaluating a post-training level of associative memory, comprising applying stimulation of the neutral stimulus node and observing a post-training response at the response node, wherein, if the neutral stimulus node elicits a post-training response at the response node above a threshold, the neutral stimulus node becomes a conditioned response node; and determining a set of stimuli to alter the integration within the network based on the evaluated level of associative memory.

2. The method of claim 1, further comprising a relaxing phase after testing the network and after training the network, during which no stimulus is applied to the network.

3. The method of claim 1, further comprising determining a causal emergence of the network based on the post-training level of associative memory.39QB\166118.01571\99770098.1Tufts T002885Quarles 166118.015714. The method of claim 3, wherein determining the causal emergence of the network comprises using integrated information decomposition to decompose the causal emergence into multiple properties.

5. The method of claim 4, wherein the multiple properties comprise at least one of downward causation or causal decoupling.

6. The method of claim 1, further comprising classifying a post-training behavior of the network.

7. The method of claim 6, wherein classifying the post-training behavior comprises analyzing the behavior for behavior descriptors, the behavior descriptors comprising at least one of trend, monotonicity, flatness, number of peaks, average distance among peaks, average difference in causal emergence, or range.

8. The method of claim 1, wherein evaluating a post-trained level of associative memory comprises evaluating every unique combination of the at least one neutral stimulus node, unconditioned stimulus node, and response node.

9. The method of claim 1, wherein the network comprises a gene regulatory network (GRN).

10. The method of claim 9, wherein the GRN comprises a biological GRN.40QB\166118.01571\99770098.1Tufts T002885Quarles 166118.0157111. The method of claim 10, wherein the biological GRN corresponds to at least one of a biochemical pathway, metabolic pathway, catabolic pathway, physiological pathway, transcriptional pathway, signaling pathway, cell differentiation, or circadian pathway.

12. The method of claim 9, wherein the GRN corresponds to swarm robotics.

13. The method of claim 1, wherein the method further comprises using the evaluated posttraining associative memory and determined causal emergence to recommend a treatment for a disease.

14. The method of claim 13, wherein the recommended treatment comprises a suggested dose schedule.

15. A system for altering integration within a network, comprising: a processor in communication with a memory, the memory having stored thereon a set of instructions which, when executed by the processor, cause the processor to: provide the network comprising a plurality of nodes including at least one of a neutral stimulus node, an unconditioned stimulus node, and a response node; test the network to evaluate a pre-training level of associative memory comprising comparing a first response at the response node to stimulation of the neutral stimulus node to a second response at the response node to stimulation of the unconditioned stimulus node; train the network, comprising applying coordinated stimulation of the neutral stimulus node and the unconditioned stimulus node to elicit a response at the response node;41QB\166118.01571\99770098.1Tufts T002885Quarles 166118.01571 evaluate a post-training level of associative memory, comprising applying stimulation of the neutral stimulus node and observing a post-training response at the response node, wherein, if the neutral stimulus node elicits a post-training response at the response node above a threshold, the neutral stimulus node becomes a conditioned response node; and determine a set of stimuli to alter the integration within the network based on the evaluated level of associative memory.

16. The system of claim 15, further comprising a causing the processor to execute a relaxing phase after testing the network and after training the network, during which no stimulus is applied to the network.

17. The system of claim 15, wherein the instructions further cause the processor to: determine a causal emergence of the network based on the post-training level of associative memory.

18. The system of claim 16, wherein determining the causal emergence of the network comprises using integrated information decomposition to decompose the causal emergence into multiple properties.

19. The method of claim 18, wherein the multiple properties comprise at least one of downward causation or causal decoupling.

20. The system of claim 15, further comprising classifying a post-training behavior of the network.42QB\166118.01571\99770098.1Tufts T002885Quarles 166118.0157121. The system of claim 20, wherein classifying the post-training behavior comprises analyzing the behavior for behavior descriptors, the behavior descriptors comprising at least one of trend, monotonicity, flatness, number of peaks, average distance among peaks, average difference in causal emergence, or range.

22. The system of claim 15, wherein evaluating a post-trained level of associative memory comprises evaluating every unique combination of the at least one neutral stimulus node, unconditioned stimulus node, and response node.

23. The system of claim 15, wherein the network comprises a gene regulatory network (GRN).

24. The system of claim 23, wherein the GRN comprises a biological GRN.

25. The system of claim 24, wherein the biological GRN corresponds to at least one of biochemical pathways, metabolic pathways, catabolic pathways, physiological pathways, transcriptional pathways, signaling pathways, cell differentiation, or circadian pathways.

26. The method of claim 23, wherein the GRN corresponds to swarm robotics.

27. The system of claim 15, wherein the system further comprises using the evaluated posttraining associative memory and determined causal emergence to recommend a treatment for a disease.43QB\166118.01571\99770098.1Tufts T002885Quarles 166118.0157128. The system of claim 15, wherein the recommended treatment comprises a suggested dose schedule.44QB\166118.01571\99770098.1

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