arXiv subjects

Mor Nitzan

Publications and source records attributed to Mor Nitzan.

15 recordsLinked to original sources

arXiv2025

Fitness and Overfitness: Implicit Regularization in Evolutionary Dynamics

A common assumption in evolutionary thought is that adaptation drives an increase in biological complexity. However, the rules governing evolution of complexity appear more nuanced. Evolution is deeply connected to learning, where complexity is much better understood, with established results on optimal complexity appropriate for a given learning task. In this work, we suggest a mathematical framework for studying the relationship between evolved organismal complexity and enviroenmntal complexity by leveraging a mathematical isomorphism between evolutionary dynamics and learning theory. Namely, between the replicator equation and sequential Bayesian learning, with evolving types corresponding to competing hypotheses and fitness in a given environment to likelihood of observed evidence. In Bayesian learning, implicit regularization prevents overfitting and drives the inference of hypotheses whose complexity matches the learning challenge. We show how these results naturally carry over to the evolutionary setting, where they are interpreted as organism complexity evolving to match the complexity of the environment, with too complex or too simple organisms suffering from \textit{overfitness} and \textit{underfitness}, respectively. Other aspects, peculiar to evolution and not to learning, reveal additional trends. One such trend is that frequently changing environments decrease selected complexity, a result with potential implications to both evolution and learning. Together, our results suggest that the balance between over-adaptation to transient environmental features, and insufficient flexiblity in responding to environmental challenges, drives the emergence of optimal complexity, reflecting environmental structure. This framework offers new ways of thinking about biological complexity, suggesting new potential causes for it to increase or decrease in different environments.

q-bio.PE↗

arXiv2025

Enhancing Swarms Durability to Threats via Graph Signal Processing and GNN-based Generative Modeling

Swarms, such as schools of fish or drone formations, are prevalent in both natural and engineered systems. While previous works have focused on the social interactions within swarms, the role of external perturbations--such as environmental changes, predators, or communication breakdowns--in affecting swarm stability is not fully understood. Our study addresses this gap by modeling swarms as graphs and applying graph signal processing techniques to analyze perturbations as signals on these graphs. By examining predation, we uncover a "detectability-durability trade-off", demonstrating a tension between a swarm's ability to evade detection and its resilience to predation, once detected. We provide theoretical and empirical evidence for this trade-off, explicitly tying it to properties of the swarm's spatial configuration. Toward task-specific optimized swarms, we introduce SwaGen, a graph neural network-based generative model. We apply SwaGen to resilient swarm generation by defining a task-specific loss function, optimizing the contradicting trade-off terms simultaneously.With this, SwaGen reveals novel spatial configurations, optimizing the trade-off at both ends. Applying the model can guide the design of robust artificial swarms and deepen our understanding of natural swarm dynamics.

q-bio.QM↗

arXiv2025

Characterizing Nonlinear Dynamics via Smooth Prototype Equivalences

Characterizing the long term behavior of dynamical systems given limited measurements is a common challenge throughout the physical and biological sciences. This is a challenging task due to the sparsity and noise inherent to empirical observations, as well as the variability of possible long-term dynamics. We address this by introducing smooth prototype equivalences (SPE), a framework for matching sparse observations to prototypical behaviors using invertible neural networks which model smooth phase space deformations. SPE can localize the invariant sets describing long-term behavior of the observed dynamics through the learned mapping from prototype space to data space. Furthermore, SPE can classify dynamical regimes by comparing the data residual of the deformed measurements to prototype dynamics. Our method outperforms existing techniques in the classification of oscillatory systems and can efficiently identify invariant structures like limit cycles and fixed points in an equation-free manner, even when only a small, noisy subset of the phase space is observed. SPE further reveals driving genes in synthetic oscillators such as the repressilator regulatory circuit, and traces cyclic biological processes like the cell cycle trajectory directly from experimental high-dimensional single-cell gene expression data.

cs.LG↗

arXiv2024

TRENDy: Temporal Regression of Effective Nonlinear Dynamics

Spatiotemporal dynamics pervade the natural sciences, from the morphogen dynamics underlying patterning in animal pigmentation to the protein waves controlling cell division. A central challenge lies in understanding how controllable parameters induce qualitative changes in system behavior called bifurcations. This endeavor is particularly difficult in realistic settings where governing partial differential equations (PDEs) are unknown and data is limited and noisy. To address this challenge, we propose TRENDy (Temporal Regression of Effective Nonlinear Dynamics), an equation-free approach to learning low-dimensional, predictive models of spatiotemporal dynamics. TRENDy first maps input data to a low-dimensional space of effective dynamics through a cascade of multiscale filtering operations. Our key insight is the recognition that these effective dynamics can be fit by a neural ordinary differential equation (NODE) having the same parameter space as the input PDE. The preceding filtering operations strongly regularize the phase space of the NODE, making TRENDy significantly more robust to noise compared to existing methods. We train TRENDy to predict the effective dynamics of synthetic and real data representing dynamics from across the physical and life sciences. We then demonstrate how we can automatically locate both Turing and Hopf bifurcations in unseen regions of parameter space. We finally apply our method to the analysis of spatial patterning of the ocellated lizard through development. We found that TRENDy's predicted effective state not only accurately predicts spatial changes over time but also identifies distinct pattern features unique to different anatomical regions, such as the tail, neck, and body--an insight that highlights the potential influence of surface geometry on reaction-diffusion mechanisms and their role in driving spatially varying pattern dynamics.

nlin.PS↗

arXiv2023

Let's do the time-warp-attend: Learning topological invariants of dynamical systems

Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing methods predict oncoming catastrophes in individual systems but are primarily time-series-based and struggle both to categorize qualitative dynamical regimes across diverse systems and to generalize to real data. To address this challenge, we propose a data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries based on the extraction of topologically invariant features. We focus on the paradigmatic case of the supercritical Hopf bifurcation, which is used to model periodic dynamics across a wide range of applications. Our convolutional attention method is trained with data augmentations that encourage the learning of topological invariants which can be used to detect bifurcation boundaries in unseen systems and to design models of biological systems like oscillatory gene regulatory networks. We further demonstrate our method's use in analyzing real data by recovering distinct proliferation and differentiation dynamics along pancreatic endocrinogenesis trajectory in gene expression space based on single-cell data. Our method provides valuable insights into the qualitative, long-term behavior of a wide range of dynamical systems, and can detect bifurcations or catastrophic transitions in large-scale physical and biological systems.

cs.LG↗

arXiv2022

Phase2vec: Dynamical systems embedding with a physics-informed convolutional network

Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or incompressible. Predicting these classes from data remains an essential open challenge in computational physics at which existing time-series classification methods struggle. Here, we propose, \texttt{phase2vec}, an embedding method that learns high-quality, physically-meaningful representations of 2D dynamical systems without supervision. Our embeddings are produced by a convolutional backbone that extracts geometric features from flow data and minimizes a physically-informed vector field reconstruction loss. In an auxiliary training period, embeddings are optimized so that they robustly encode the equations of unseen data over and above the performance of a per-equation fitting method. The trained architecture can not only predict the equations of unseen data, but also, crucially, learns embeddings that respect the underlying semantics of the embedded physical systems. We validate the quality of learned embeddings investigating the extent to which physical categories of input data can be decoded from embeddings compared to standard blackbox classifiers and state-of-the-art time series classification techniques. We find that our embeddings encode important physical properties of the underlying data, including the stability of fixed points, conservation of energy, and the incompressibility of flows, with greater fidelity than competing methods. We finally apply our embeddings to the analysis of meteorological data, showing we can detect climatically meaningful features. Collectively, our results demonstrate the viability of embedding approaches for the discovery of dynamical features in physical systems.

cs.LG↗

arXiv2020

Optimizing testing policies for detecting COVID-19 outbreaks

The COVID-19 pandemic poses challenges for continuing economic activity while reducing health risks. While these challenges can be mitigated through testing, testing budget is often limited. Here we study how institutions, such as nursing homes, should utilize a fixed test budget for early detection of an outbreak. Using an extended network-SEIR model, we show that given a certain budget of tests, it is generally better to test smaller subgroups of the population frequently than to test larger groups but less frequently. The numerical results are consistent with an analytical expression we derive for the size of the outbreak at detection in an exponential spread model. Our work provides a simple guideline for institutions: distribute your total tests over several batches instead of using them all at once. We expect that in the appropriate scenarios, this easy-to-implement policy recommendation will lead to earlier detection and better mitigation of local COVID-19 outbreaks.

physics.soc-ph↗

arXiv2019

Unified framework for modeling multivariate distributions in biological sequences

Revealing the functional sites of biological sequences, such as evolutionary conserved, structurally interacting or co-evolving protein sites, is a fundamental, and yet challenging task. Different frameworks and models were developed to approach this challenge, including Position-Specific Scoring Matrices, Markov Random Fields, Multivariate Gaussian models and most recently Autoencoders. Each of these methods has certain advantages, and while they have generated a set of insights for better biological predictions, these have been restricted to the corresponding methods and were difficult to translate to the complementary domains. Here we propose a unified framework for the above-mentioned models, that allows for interpretable transformations between the different methods and naturally incorporates the advantages and insight gained individually in the different communities. We show how, by using the unified framework, we are able to achieve state-of-the-art performance for protein structure prediction, while enhancing interpretability of the prediction process.

q-bio.QM↗

arXiv2018

Statistical Optimal Transport via Factored Couplings

We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical counterparts, our method promotes couplings with low transport rank, a new structural assumption that is similar to the nonnegative rank of a matrix. Regularizing based on this assumption leads to drastic improvements on high-dimensional data for various tasks, including domain adaptation in single-cell RNA sequencing data. These findings are supported by a theoretical analysis that indicates that the transport rank is key in overcoming the curse of dimensionality inherent to data-driven optimal transport.

stat.ML↗

arXiv2018

Model-free inference of direct network interactions from nonlinear collective dynamics

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.

physics.soc-ph↗

arXiv2018

Revealing physical interaction networks from statistics of collective dynamics

Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of detail often not available. We exploit changes in invariant measures, in particular distributions of sampled states of the system in response to driving signals, and use compressed sensing to reveal physical interaction networks. Dynamical observations following driving suffice to infer physical connectivity even if they are temporally disordered, are acquired at large sampling intervals, and stem from different experiments. Testing various nonlinear dynamic processes emerging on artificial and real network topologies indicates high reconstruction quality for existence as well as type of interactions. These results advance our ability to reveal physical interaction networks in complex synthetic and natural systems.

physics.soc-ph↗

arXiv2017

Flexible Level-1 Consensus Ensuring Stable Social Choice: Analysis and Algorithms

Level-1 Consensus is a property of a preference-profile. Intuitively, it means that there exists a preference relation which induces an ordering of all other preferences such that frequent preferences are those that are more similar to it. This is a desirable property, since it enhances the stability of social choice by guaranteeing that there exists a Condorcet winner and it is elected by all scoring rules. In this paper, we present an algorithm for checking whether a given preference profile exhibits level-1 consensus. We apply this algorithm to a large number of preference profiles, both real and randomly-generated, and find that level-1 consensus is very improbable. We support these empirical findings theoretically, by showing that, under the impartial culture assumption, the probability of level-1 consensus approaches zero when the number of individuals approaches infinity. Motivated by these observations, we show that the level-1 consensus property can be weakened while retaining its stability implications. We call this weaker property Flexible Consensus. We show, both empirically and theoretically, that it is considerably more probable than the original level-1 consensus. In particular, under the impartial culture assumption, the probability for Flexible Consensus converges to a positive number when the number of individuals approaches infinity.

cs.GT↗

arXiv2016

Distance distribution in configuration model networks

We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical simulations for networks with degenerate, binomial and power-law degree distributions. The mean, mode and variance of the distribution of shortest path lengths are also evaluated. These results provide expressions for central measures and dispersion measures of the distribution of shortest path lengths in terms of moments of the degree distribution, illuminating the connection between the two distributions.

cond-mat.dis-nn↗

arXiv2015

Analytical results for the distribution of shortest path lengths in random networks

We present two complementary analytical approaches for calculating the distribution of shortest path lengths in Erdos-Rényi networks, based on recursion equations for the shells around a reference node and for the paths originating from it. The results are in agreement with numerical simulations for a broad range of network sizes and connectivities. The average and standard deviation of the distribution are also obtained. In the case that the mean degree scales as $N^α$ with the network size, the distribution becomes extremely narrow in the asymptotic limit, namely almost all pairs of nodes are equidistant, at distance $d=\lfloor 1/α\rfloor$ from each other. The distribution of shortest path lengths between nodes of degree $m$ and the rest of the network is calculated. Its average is shown to be a monotonically decreasing function of $m$, providing an interesting relation between a local property and a global property of the network. The methodology presented here can be applied to more general classes of networks.

cond-mat.dis-nn↗

arXiv2014

Stochastic analysis of bistability in coherent mixed feedback loops combining transcriptional and post-transcriptional regulations

Mixed feedback loops combining transcriptional and post-transcriptional regulations are common in cellular regulatory networks. They consist of two genes, encoding a transcription factor and a small non-coding RNA (sRNA), which mutually regulate each other's expression. We present a theoretical and numerical study of coherent mixed feedback loops of this type, in which both regulations are negative. Under suitable conditions, these feedback loops are expected to exhibit bistability, namely two stable states, one dominated by the transcriptional repressor and the other dominated by the sRNA. We use deterministic methods based on rate equation models, in order to identify the range of parameters in which bistability takes place. However, the deterministic models do not account for the finite lifetimes of the bistable states and the spontaneous, fluctuation-driven transitions between them. Therefore, we use stochastic methods to calculate the average lifetimes of the two states. It is found that these lifetimes strongly depend on rate coefficients such as the transcription rates of the transcriptional repressor and the sRNA. In particular, we show that the fraction of time the system spends in the sRNA dominated state follows a monotonically decreasing sigmoid function of the transcriptional repressor transcription rate. The biological relevance of these results is discussed in the context of such mixed feedback loops in {\it Escherichia coli}.

q-bio.MN↗