We investigate what can be learned from multi-point correlations of stochastic particle trajectories, i.e., correlations that relate the particle position at multiple points in time. One such observable was recently introduced as the Mean Back Relaxation [1]. We discuss its properties and the information that can be obtained from it, as, e.g., regards time reversal symmetry [2,3]. We exemplify...
I will discuss paradigmatic examples of a tracer trapped in a harmonic potential and coupled to nonequilibrium baths: In particular, the tracer equation of motion and its relaxation function, for which this equation is averaged under an initial tracer position. For equilibrium, the tracer-bath force on average vanishes, a well known consequence of Boltzmann statistics. If tracer and bath are...
Recent pioneering experiments on non-Markovian dynamics done, e.g., for active matter have demonstrated that our theoretical understanding of this challenging yet hot topic is rather incomplete and there is a wealth of phenomena still awaiting discovery. It is related to the fact that typically for simplification the Markovian approximation is employed and as a consequence the memory is...
Collective behavior of animals is a fascinating example of self-organization in biology. This phenomenon is believed to provide several advantages to individuals, such as facilitating exchange of social information, promoting accurate collective decisions, or affording protection from predators. It has been theorized that animal collectives should operate in a special parameter region close to...
Nonequilibrium complex systems often exhibit a hierarchical structure of different dynamics on different time scales. The statistical nature of spatiotemporal fluctuations relevant to the dynamics is known to be of central importance for treating a wide class of such systems. Maximum entropy principle has been the crux for describing the fluctuation distribution in the literature, beyond the...
The heat exchange fluctuation theorem (XFT) by Jarzynski and Wojcik [Phys. Rev. Lett. 92, 230602 (2004)] addresses the setting where two systems with different temperatures are brought in thermal contact at time $t=0$ and then disconnected at later time $\tau$. The theorem asserts that the probability of an anomalous heat flux (from cold to hot), while nonzero, is exponentially smaller than...
As developing tissues grow in size and undergo morphogenetic changes, their material properties may be altered. Such changes result from tension dynamics at cell contacts or cellular jamming. Yet, in many cases, the cellular mechanisms controlling the physical state of growing tissues are unclear. We found that at early developmental stages, the tissue in the developing mouse spinal cord...
Inspired by dense contractile tissues, where cells are subject to periodic deformation, we will formulate a generic hydrodynamic theory of confluent pulsating liquids. Combining mechanical and phenomenological arguments, we will postulate that the mechanochemical feedback between the local phase, which describes how cells deform due to autonomous driving, and the local density can be described...
Spinning objects moving through air or liquids experience a Magnus force, a phenomenon widely exploited in ball sports and significant in various scientific and engineering applications. Opposed to large objects where Magnus forces are strong, they are only weak at small scales and eventually vanish for overdamped micron-sized particles in simple liquids. Here we demonstrate an about...
The nucleation and growth theory, described by the Avrami equation (also called Johnson–Mehl–Avrami–Kolmogorov equation), and usually used to describe crystallization and nucleation processes in condensed matter physics, was applied to cancer physics as Avrami-Dobrzyński Model. This approach assumes the transforming system as a DNA chain including many oncogenic mutations. Finally, the...
The Thermodynamic Uncertainty Relation (TUR) establishes a fundamental trade-off between the cost of driving a system and the precision of its output. While TUR has been proven for discrete systems and overdamped Brownian motion, TUR violations for more general dynamics have been recently demonstrated using elaborate models based on underdamped dynamics. In our study, we present simple models...
Surfactant molecules, above a critical concentration in solution, are able to spontaneously self-assemble to form aggregates. One of these aggregates are micelles, which are used in many field of sciences and industry. In an aqueous environment, due to the amphiphilic nature of the surfactants, the micelles in the core have a hydrophobic part. Micelles comes into contact with the aqueous...
Correlation matrix estimation from functional magnetic resonance (fMRI) data presents a major challenge for a multitude of reasons, including non-stationarity of the signal and low temporal resolution, resulting in the number of variables (locations from which the signal is sampled) exceeding the number of time points. The Pearson correlation matrix is most commonly used, but likely...
Almost universally, individual agents in collectives of active particles require time to examine their surroundings and form an appropriate response. Examples of when perception and actuation delays significantly affect system dynamics can be found in living organisms, robotic collectives, communication networks, and cellular processes like biopolymer assembly and migration. Still,...
We consider an open (Brownian) classical harmonic oscillator in contact with a non-Markovian thermal bath and described by a generalized Langevin equation. When the bath's spectrum has a finite upper cutoff frequency, the oscillator may have ergodic and nonergodic configurations. In ergodic configurations (when exist, they correspond to lower oscillator frequencies) the oscillator...
According to the well-known biophysical Single Hit Target Model, DNA chain damage, caused for instance by ionizing radiation, is purely random in nature. This presentation demonstrates that such radiation-induced DNA damage is associated with an increase in system entropy, which is characteristic of purely stochastic processes. However, it turns out that not all changes in the DNA region...
We present a new set of Turing patterns based on the superposition of multiple waves. Turing patterns are well known solutions to a set of reaction-diffusion equations. Such patterns have been studied in the context of embryo development, chemical reactions, nonlinear optics, ecology and random walks, to name a few. The main feature of systems giving rise to Turing patterns is that a stable...
Escape kinetics of a stochastic process can be influenced by imposing stochastic resetting, a protocol of starting anew. We study the escape kinetics from a finite interval restricted by two absorbing boundaries in the presence of heavy-tailed, Lévy type, $\alpha$-stable noise. We find that the width of the domain where resetting is beneficial depends on the value of the stability index...
The phase of tissue and its transitions are critical phenomena during development. The Active Vertex Model is a well-known approach for studying tissue mechanical properties. In this model, the tissue is represented as a collection of polygonal cells, with forces applied to the vertices, leading to cell dynamics and rearrangement. This model includes passive forces representing the competition...
We discuss the dynamics of major genetic forces that shape evolution of cancer cells, using mathematics of stochastic processes. A range of biological examples will serve to illustrate the methodology, including leukemias and other hematological syndromes as well as solid neoplasia, such as lung, breast and bladder cancers. The latter example will help illustrate the notion of the field...
The recent expansion of single-cell sequencing technologies has enabled simultaneous genome-wide measurements of multiple modalities in the same single cell. The potential to jointly profile such modalities as gene expression, chromatin accessibility, proteins, or multiple histone modifications at single-cell resolution represents a compelling opportunity to study biological processes at...
The radiation adaptive response (or radioadaptiation) effect is a biophysical and radiobiological phenomenon responsible for e.g. the enhancement of repair processes, cell cycle and apoptosis regulation or enhancement of antioxidant production in cells / organisms irradiatied by low doses and low dose-rates of ionising radiation. Here we propose a comprehensive and complete theoretical model...
We present analytical results for the distribution of first passage times of random walks (RWs) on random regular graphs (RRGs) [1]. RRGs are random networks, consisting of $N$ nodes, in which all the nodes are of the same degree $c \ge 3$ and the connections are random and uncorrelated. Starting from a random initial node $i$ at time $t=0$, at each time step $t \ge 1$ an RW hops into a...
The diffusion of particles with passage times significantly slower than regular Brownian motion is observed in various systems, such as amorphous materials, living cells and rheology. This behavior is typically attributed to trapping or waiting times that are scale-free and uncorrelated. Our work demonstrates that correlated waiting times, termed quenched disorder, can redefine our...
The celebrated ``standard'' $q$-state (color) Potts model, where the ferromagnetic interaction is between nearest-neighboring spins on the square lattice, is known to change its temperature-driven phase transition, from continuous to discontinuous, at some critical integer $q_c = 4$ [1,2,3]. Renormalization group theory suggests that this result should hold for other lattices or interaction...
We develop a hypothesis that the dynamics of equilibrium systems at criticality have their dynamics constricted to a fractal subspace. We relate the correlation fractal dimension associated with this subspace to the Fisher critical exponent controlling the singularity associated with the correlation function. This fractal subspace is different from that which is associated with the order...
We explore the critical properties of the recently discovered finite-time dynamical phase transition in the non-equilibrium relaxation of Ising magnets. The transition is characterized by a sudden switch in the relaxation dynamics and occurs at a sharp critical time. While previous works have focused either on mean-field interactions or on investigating the properties of the critical time, we...
Anomalous diffusion is often observed in complex environments which are inherently heterogeneous. This is expected in biological media, where variability often applies to the traced particles themselves as well as their immediate surroundings, which is theorised to locally affect their motions through transient associations. As a result, the dynamics can be non-ergodic and the description of...
More than a decade ago, I. Goychuk reported on a universal behavior of subdiffusive motion (as described by the generalized Langevin equation) in a one-dimensional bounded periodic potential [1], where the numerical findings show that the long-time behavior of the mean squared displacement is not influenced by the potential, so that the behavior in the potential, under homogenization, is the...
Active fluctuations are detected in a growing number of systems due to self-propulsion mechanisms or collisions with active environment. They drive the system far from equilibrium and can induce phenomena which at equilibrium states are forbidden by e.g. fluctuation-dissipation relations and detailed balance symmetry. Recently a paradoxical effect has been briefly communicated in which a free...
The precision of currents in Markov networks is bounded by dissipation via the so-called thermodynamic uncertainty relation (TUR) [1]. In our work [2], we demonstrate a similar inequality that bounds the precision of the static current response to perturbations of kinetic barriers. Perturbations of such type, which affect only the system kinetics but not the thermodynamic forces, are highly...
I will discuss real-space condensation in the balls-in-box model (also known as the urn model, backgammon model, or random allocation model). I will then briefly present a classification of phase transitions related to condensation and discuss the critical behavior of the model, as well as the singularities of the thermodynamic potential and Rényi entropy associated with the phase transition.
We consider the Price model for an evolving network, i.e., a growing graph, in which, in every iteration, we add a new vertex and join its edges to the existing vertices based on a mixture of the preferential attachment rule and the purely accidental component. We derive the models' expected vertex degrees and show that they coincide with the order statistics from the Pareto type-2...
In many biological systems and various artificial materials that map them, particles pass through nanopores and nanochannels.
Artificial single nanopores are attracting increasing attention due to their potential use in nanofluidics, sensor technology, and information processing.
In this type of research, experiments focus on properties that affect the mobility of a molecule traveling...
We studied equilibrium systems composed of wedge-shaped monodisperse molecules using hard-particle Monte Carlo simulations. Each model molecule was made up of six colinear tangent spheres with linearly decreasing diameters. Thus, the shape was unequivocally described by a single parameter $d$: the ratio of the smallest and largest diameters of the spheres. The phases of the systems were...
