Publications

Synchronization among a group of active agents is ubiquitous in nature. Although synchronization based on direct interactions between agents described by the Kuramoto model is well understood, the other general mechanism based on indirect interactions among agents sharing limited resources are less known. Here, we propose a minimal thermodynamically consistent model for the altruistic resource-sharing (ARS) mechanism wherein resources are needed for an individual agent to advance but a more advanced agent has a lower competence to obtain resources. We show that while differential competence in ARS mechanism provides a negative feedback leading to synchronization it also breaks detailed balance and thus requires additional energy dissipation besides the cost of driving individual agents. By solving the model analytically, our study reveals a general trade-off relation between the total energy dissipation rate and the two key performance measures of the system: average speed and synchronization accuracy. For a fixed dissipation rate, there is a distinct speed-accuracy Pareto front traversed by the scarcity of resources: scarcer resources lead to slower speed but more accurate synchronization. Increasing energy dissipation eases this trade-off by pushing the speed-accuracy Pareto front outward. The connections of our work to realistic biological systems such as the KaiABC system in cyanobacterial circadian clock and other theoretical results based on thermodynamic uncertainty relation are also discussed.

Convergence analysis can characterize genetic elements underlying morphological adaptations. However, its performance on regulatory elements is limited due to their modular composition of transcription factor motifs, which have rapid turnover and experience different evolutionary pressures.

We introduce phyloConverge, a phylogenetic method that performs scalable, fine-grained local convergence analysis of genomic elements at flexible length scales. Using a benchmarking case of convergent subterranean mammal adaptation, phyloConverge identifies rate-accelerated conserved noncoding elements (CNEs) with high specificity and statistical robustness relative to competing methods. From CNE-level scoring, we detect the convergent regression of entire CNE units and highlight the contrast that subterranean-associated coding region regression is highly specific to ocular functions, whereas regulatory element regression is enriched for accompanying neuronal phenotypes and other developmental processes. From transcription factor motif-level scoring, we dissect elements into subregions with uneven convergence signals and demonstrate the modular adaptation of CNEs with high functional specificity. Finally, we demonstrate phyloConverge’s scalability to perform high-resolution convergence analysis genome-wide.

The brain encodes external stimuli through patterns of neural activity, forming internal representations of the world. Increasing experimental evidence showed that neural representations for a specific stimulus can change over time in a phenomenon called “representational drift” (RD). However, the underlying mechanisms for this widespread phenomenon remain poorly understood. Here, we study RD in the piriform cortex of the olfactory system with a realistic neural network model that incorporates two general mechanisms for synaptic weight dynamics operating at two well-separated timescales: spontaneous multiplicative fluctuations on a scale of days and spike-timing-dependent plasticity (STDP) effects on a scale of seconds. We show that the slow multiplicative fluctuations in synaptic sizes, which lead to a steady-state distribution of synaptic weights consistent with experiments, can induce RD effects that are in quantitative agreement with recent empirical evidence. Furthermore, our model reveals that the fast STDP learning dynamics during presentation of a given odor drives the system toward a low-dimensional representational manifold, which effectively reduces the dimensionality of synaptic weight fluctuations and thus suppresses RD. Specifically, our model explains why representations of already “learned” odors drift slower than unfamiliar ones, as well as the dependence of the drift rate with the frequency of stimulus presentation—both of which align with recent experimental data. The proposed model not only offers a simple explanation for the emergence of RD and its relation to learning in the piriform cortex, but also provides a general theoretical framework for studying representation dynamics in other neural systems.

The brain encodes external stimuli through patterns of neural activity, forming internal representations of the world. Increasing experimental evidence showed that neural representations for a specific stimulus can change over time in a phenomenon called “representational drift” (RD). However, the underlying mechanisms for this widespread phenomenon remain poorly understood. Here, we study RD in the piriform cortex of the olfactory system with a realistic neural network model that incorporates two general mechanisms for synaptic weight dynamics operating at two well-separated timescales: spontaneous multiplicative fluctuations on a scale of days and spike-timing-dependent plasticity (STDP) effects on a scale of seconds. We show that the slow multiplicative fluctuations in synaptic sizes, which lead to a steady-state distribution of synaptic weights consistent with experiments, can induce RD effects that are in quantitative agreement with recent empirical evidence. Furthermore, our model reveals that the fast STDP learning dynamics during presentation of a given odor drives the system toward a low-dimensional representational manifold, which effectively reduces the dimensionality of synaptic weight fluctuations and thus suppresses RD. Specifically, our model explains why representations of already “learned” odors drift slower than unfamiliar ones, as well as the dependence of the drift rate with the frequency of stimulus presentation—both of which align with recent experimental data. The proposed model not only offers a simple explanation for the emergence of RD and its relation to learning in the piriform cortex, but also provides a general theoretical framework for studying representation dynamics in other neural systems.

We study gradient flow on the multi-index regression problem for high-dimensional Gaussian data. Multi-index functions consist of a composition of an unknown low-rank linear projection and an arbitrary unknown, low-dimensional link function. As such, they constitute a natural template for feature learning in neural networks. We consider a two-timescale algorithm, whereby the low-dimensional link function is learnt with a non-parametric model infinitely faster than the subspace parametrizing the low-rank projection. By appropriately exploiting the matrix semigroup structure arising over the subspace correlation matrices, we establish global convergence of the resulting Grassmannian gradient flow dynamics, and provide a quantitative description of its associated “saddle-to-saddle” dynamics. Notably, the timescales associated with each saddle can be explicitly characterized in terms of an appropriate Hermite decomposition of the target link function.

We address the problem of predicting the next states of a dynamical system governed by unknown temporal partial differential equations (PDEs) using only a short trajectory. While standard transformers provide a natural blackbox solution to this task, the presence of a wellstructured evolution operator in the data suggests a more tailored and efficient approach. Specifically, when the PDE is fully known, classical numerical solvers can evolve the state accurately with only a few parameters. Building on this observation, we introduce DISCO, a model that uses a large hypernetwork to process a short trajectory and generate the parameters of a much smaller operator network, which then predicts the next states through time integration. Our framework decouples dynamics estimation — i.e., DISCovering an evolution Operator from a short trajectory — from state prediction — i.e., evolving this operator. Experiments show that pretraining our model on diverse physics datasets achieves state-of-the-art performance while requiring significantly fewer epochs. Moreover, it generalizes well to unseen initial conditions and remains competitive when fine-tuned on downstream tasks. The code will be made publicly available upon publication at https: //github.com/RudyMorel/DISCO.

Studies in Drosophila have contributed a great deal to our understanding of developmental mechanisms. Indeed, familiar names of critical signaling components, such as Hedgehog and Notch, have their origins in the readily identifiable morphological phenotypes of Drosophila. Most studies that led to the identification of these and many other highly conserved genes were based on the end-point phenotypes, such as the larval cuticle or the adult wing. Additional information can be extracted from longitudinal studies, which can reveal how the phenotypes emerge over time. Here we present the Fruit Fly Auxodrome, an experimental setup that enables monitoring and quantitative analysis of the entirety of development of 96 individually housed Drosophila from hatching to eclosion. The Auxodrome combines an inexpensive live imaging setup and a computer vision pipeline that provides access to a wide range of quantitative information, such as the times of hatching and pupation, as well as dynamic patterns of larval activity. We demonstrate the Auxodrome in action by recapitulating several previously reported features of wild-type development as well as developmental delay in a Drosophila model of a human disease. The scalability of the presented design makes it readily suitable for large-scale longitudinal studies in multiple developmental contexts.

Although canonical protein design has benefited from machine learning methods trained on databases of protein sequences and structures, synthetic heteropolymer design still relies heavily on physics-based methods. The Rosetta software, which provides diverse physics-based methods for designing sequences, exploring conformations, docking molecules, and performing analysis, has proven invaluable to this field. Nevertheless, Rosetta’s aging architecture, monolithic structure, non-open source code, and steep development learning curve are beginning to hinder new methods development. Here, we introduce the Masala software suite, a free, open-source set of C++ libraries intended to extend Rosetta and other software, and ultimately to be a successor to Rosetta. Masala is structured for modern computing hardware, and its build system automates the creation of application programming interface (API) layers, permitting Masala’s use as an extension library for existing software, including Rosetta. Masala features modular architecture in which it is easy for novice developers to add new plugin modules, which can be independently compiled and loaded at runtime, extending functionality of software linking Masala without source code alteration. Here, we describe implementation of Masala modules that accelerate protein and synthetic peptide design. We describe the implementation of Masala real-valued local optimizers and cost function network optimizers that can be used as drop-in replacements for Rosetta’s minimizer and packer when designing heteropolymers. We explore design-centric guidance terms for promoting desirable features, such as hydrogen bond networks, or discouraging undesirable features, such as unsatisfied buried hydrogen bond donors and acceptors, which we have re-implemented far more efficiently in Masala, providing up to two orders of magnitude of speedup in benchmarks. Finally, we discuss development goals for future versions of Masala.

Unraveling the phenotypic and genetic complexity of autism is extremely challenging yet critical for understanding the biology, inheritance, trajectory and clinical manifestations of the many forms of the condition. Using a generative mixture modeling approach, we leverage broad phenotypic data from a large cohort with matched genetics to identify robust, clinically relevant classes of autism and their patterns of core, associated and co-occurring traits, which we further validate and replicate in an independent cohort. We demonstrate that phenotypic and clinical outcomes correspond to genetic and molecular programs of common, de novo and inherited variation and further characterize distinct pathways disrupted by the sets of mutations in each class. Remarkably, we discover that class-specific differences in the developmental timing of affected genes align with clinical outcome differences. These analyses demonstrate the phenotypic complexity of children with autism, identify genetic programs underlying their heterogeneity, and suggest specific biological dysregulation patterns and mechanistic hypotheses.

We prove analytically that the two fundamental rheological equations for (elastic) disc suspensions and long flexible polymers, the so-called Oldroyd-A and -B models, respectively, predict the same flow and total stress fields in any planar incompressible flow. We illustrate this equivalence for creeping flow in a cross-slot channel and investigate differences arising from three-dimensional effects in a weakly elastic Taylor-Couette flow. Finally, we discuss implications for understanding elastic instabilities, controlling inertial turbulence, and deriving constitutive models for complex fluids.