arXiv subjects

Steve Presse

Publications and source records attributed to Steve Presse.

9 recordsLinked to original sources

arXiv2025

Spatially Correlated Noise Induces Transitions from the Diffusive to Ballistic Regime in Fluids

We investigate the fluctuating incompressible Navier--Stokes equation driven by spatially correlated thermal noise characterized by a single length scale. This formulation is constructed to preserve thermal equilibrium through the fluctuation--dissipation relation (FDR), which enforces the same spatial correlation in the viscous diffusion term and therefore gives rise to nonlocal momentum transport. Numerical simulations of tracer diffusion in fluids governed by this formulation reveal that the mean-squared displacement (MSD) depends monotonically on the correlation length $\ell$ and the correlation strength $\beta$. Intuitively, increasing $\ell$ enhances MSD and induces the emergence of an early-time ballistic regime, as a larger correlation length slows momentum diffusion. Counterintuitively, decreasing $\beta$ also increases the MSD, since a weaker correlation strength also retards momentum diffusion, whereas smaller $\ell$ or larger $\beta$ suppresses the ballistic regime and leads to a diffusive behavior. The emergence or suppression of the ballistic regime stems from how spatial correlations, incorporated through the FDR to maintain equilibrium, alter the effective momentum transport across scales. Interestingly, we further show that the resulting nonlocal diffusion is reminiscent of the slow dynamics in glassy and other disordered systems.

physics.bio-ph↗

arXiv2024

Perspectives: Comparison of Deep Learning Segmentation Models on Biophysical and Biomedical Data

Deep learning based approaches are now widely used across biophysics to help automate a variety of tasks including image segmentation, feature selection, and deconvolution. However, the presence of multiple competing deep learning architectures, each with its own unique advantages and disadvantages, makes it challenging to select an architecture best suited for a specific application. As such, we present a comprehensive comparison of common models. Here, we focus on the task of segmentation assuming the typically small training dataset sizes available from biophysics experiments and compare the following four commonly used architectures: convolutional neural networks, U-Nets, vision transformers, and vision state space models. In doing so, we establish criteria for determining optimal conditions under which each model excels, thereby offering practical guidelines for researchers and practitioners in the field.

eess.IV↗

arXiv2024

Avoiding matrix exponentials for large transition rate matrices

Exact methods for exponentiation of matrices of dimension $N$ can be computationally expensive in terms of execution time ($N^{3}$) and memory requirements ($N^{2}$) not to mention numerical precision issues. A type of matrix often exponentiated in the sciences is the rate matrix. Here we explore five methods to exponentiate rate matrices some of which apply even more broadly to other matrix types. Three of the methods leverage a mathematical analogy between computing matrix elements of a matrix exponential and computing transition probabilities of a dynamical processes (technically a Markov jump process, MJP, typically simulated using Gillespie). In doing so, we identify a novel MJP-based method relying on restricting the number of "trajectory" jumps based on the magnitude of the matrix elements with favorable computational scaling. We then discuss this method's downstream implications on mixing properties of Monte Carlo posterior samplers. We also benchmark two other methods of matrix exponentiation valid for any matrix (beyond rate matrices and, more generally, positive definite matrices) related to solving differential equations: Runge-Kutta integrators and Krylov subspace methods. Under conditions where both the largest matrix element and the number of non-vanishing elements scale linearly with $N$ -- reasonable conditions for rate matrices often exponentiated -- computational time scaling with the most competitive methods (Krylov and one of the MJP-based methods) reduces to $N^2$ with total memory requirements of $N$.

physics.chem-ph↗

arXiv2022

Inferring potential landscapes from noisy trajectories

While particle trajectories encode information on their governing potentials, potentials can be challenging to robustly extract from trajectories. Measurement errors may corrupt a particle's position, and sparse sampling of the potential limits data in higher-energy regions such as barriers. We develop a Bayesian method to infer potentials of arbitrary shape alongside measurement noise. As an alternative to Gaussian process priors over potentials, we introduce structured kernel interpolation to the Natural Sciences which allows us to extend our analysis to large data sets. Our method is validated on 1D and 2D experimental trajectories for particles in a feedback trap.

physics.data-an↗

arXiv2019

Quantitative Kinetic Models from Intravital Microcopy: A Case Study Using Hepatic Transport

The liver performs critical physiological functions, including metabolizing and removing substances, such as toxins and drugs, from the bloodstream. Hepatotoxicity itself is intimately linked to abnormal hepatic transport and hepatotoxicity remains the primary reason drugs in development fail and approved drugs are withdrawn from the market. For this reason, we propose to analyze, across liver compartments, the transport kinetics of fluorescein-a fluorescent marker used as a proxy for drug molecules-using intravital microscopy data. To resolve the transport kinetics quantitatively from fluorescence data, we account for the effect that different liver compartments (with different chemical properties) have on fluorescein's emission rate. To do so, we develop ordinary differential equation transport models from the data where the kinetics are related to the observable fluorescence levels by "measurement parameters" that vary across different liver compartments. On account of the steep non-linearities in the kinetics and stochasticity inherent to the model, we infer kinetic and measurement parameters by generalizing the method of parameter cascades. For this application, the method of parameter cascades ensures fast and precise parameter estimates from noisy time traces.

physics.bio-ph↗

arXiv2017

ICON: an adaptation of infinite HMMs for time traces with drift

Bayesian nonparametric methods have recently transformed emerging areas within data science. One such promising method, the infinite hidden Markov model (iHMM), generalizes the HMM which itself has become a workhorse in single molecule data analysis. The iHMM goes beyond the HMM by self-consistently learning all parameters learned by the HMM in addition to learning the number of states without recourse to any model selection steps. Despite its generality, simple features (such as drift), common to single molecule time traces, result in an over-interpretation of drift and the introduction of artifact states. Here we present an adaptation of the iHMM that can treat data with drift originating from one or many traces (e.g. FRET). Our fully Bayesian method couples the iHMM to a continuous control process (drift) self-consistently learned while learning all other quantities determined by the iHMM (including state numbers). A key advantage of this method is that all traces -regardless of drift or states visited across traces- may now be treated on an equal footing thereby eliminating user-dependent trace selection (based on drift levels), pre-processing to remove drift and post-processing model selection on state number.

physics.data-an↗

arXiv2017

An introduction to infinite HMMs for single molecule data analysis

The hidden Markov model (HMM) has been a workhorse of single molecule data analysis and is now commonly used as a standalone tool in time series analysis or in conjunction with other analyses methods such as tracking. Here we provide a conceptual introduction to an important generalization of the HMM which is poised to have a deep impact across Biophysics: the infinite hidden Markov model (iHMM). As a modeling tool, iHMMs can analyze sequential data without a priori setting a specific number of states as required for the traditional (finite) HMM. While the current literature on the iHMM is primarily intended for audiences in Statistics, the idea is powerful and the iHMM's breadth in applicability outside Machine Learning and Data Science warrants a careful exposition. Here we explain the key ideas underlying the iHMM with a special emphasis on implementation and provide a description of a code we are making freely available. In a companion article, we provide an important extension of the iHMM to accommodate complications such as drift.

physics.data-an↗

arXiv2015

Simulated evolution of protein-protein interaction networks with realistic topology

We model the evolution of eukaryotic protein-protein interaction (PPI) networks. In our model, PPI networks evolve by two known biological mechanisms: (1) Gene duplication, which is followed by rapid diversification of duplicate interactions. (2) Neofunctionalization, in which a mutation leads to a new interaction with some other protein. Since many interactions are due to simple surface compatibility, we hypothesize there is an increased likelihood of interacting with other proteins in the target protein's neighborhood. We find good agreement of the model on 10 different network properties compared to high-confidence experimental PPI networks in yeast, fruit flies, and humans. Key findings are: (1) PPI networks evolve modular structures, with no need to invoke particular selection pressures. (2) Proteins in cells have on average about 6 degrees of separation, similar to some social networks, such as human-communication and actor networks. (3) Unlike social networks, which have a shrinking diameter (degree of maximum separation) over time, PPI networks are predicted to grow in diameter. (4) The model indicates that evolutionarily old proteins should have higher connectivities and be more centrally embedded in their networks. This suggests a way in which present-day proteomics data could provide insights into biological evolution.

q-bio.MN↗

arXiv2011

Markov processes follow from the principle of Maximum Caliber

Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible dynamical trajectories in a time-homogeneous process, then the only type of process that maximizes the path entropy, for any given singlet statistics, is a sequence of identical, independently distributed (i.i.d.) random variables, which is the simplest Markov process. If the data is in the form of sequentially pairwise statistics, then maximizing the caliber dictates that the process is Markovian with a uniform initial distribution. Furthermore, if an initial non-uniform dynamical distribution is known, or multiple trajectories are conditioned on an initial state, then the Markov process is still the only one that maximizes the caliber. Second, given a model, MaxCal can be used to compute the parameters of that model. We show that this procedure is equivalent to the maximum-likelihood method of inference in the theory of statistics.

cond-mat.stat-mech↗