Related papers: The phase transition in random catalytic sets
A new point of view about the deep origin of thermodynamic phase transitions is sketched. The main idea is to link the appearance of phase transitions to some major topology change of suitable submanifolds of phase space instead of linking…
A cyclically dominating three-species ecosystem, modeled within the framework of rock-paper-scissor game, is studied in presence of natural death and an effect of the environment. The environmental impact is parameterized along with the…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
We investigate species-rich mathematical models of ecosystems. While much of the existing literature focuses on the properties of equilibrium fixed points, persistent dynamics (e.g., limit cycles or chaos) have also been observed, both in…
Autocatalytic sets are sets of entities that mutually catalyse each other's production through chemical reactions from a basic food source. Recently, the reflexively autocatalytic and food generated theory has introduced a formal definition…
A numerical method based on Matrix Product Formalism is proposed to study the phase transitions and shock formation in the Asymmetric Simple Exclusion Process with open boundaries and parallel dynamics. By working in a canonical ensemble,…
Despite the striking successes of deep neural networks trained with gradient-based optimization, these methods differ fundamentally from their biological counterparts. This gap raises key questions about how nature achieves robust,…
We investigate the formation of stable ecological networks where many species share the same resource. We show that such stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of…
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…
Boundary conditions may change the phase diagram of non-equilibrium statistical systems like the one-dimensional asymmetric simple exclusion process with and without particle number conservation. Using the quantum Hamiltonian approach, the…
We study a class of two-stage stochastic programs in which the second stage includes a set of components with uncertain capacity, and the expression for the distribution function of the uncertain capacity includes first-stage variables.…
In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism…
It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing theory provides a rather complete picture…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
We investigate a quadratic dynamical system known as nonlinear recombinations. This system models the evolution of a probability measure over the Boolean cube, converging to the stationary state obtained as the product of the initial…
We investigate the dynamics following sudden quenches across quantum critical points belonging to different universality classes. Specifically, we use matrix product state methods to study the quantum Ising chain in the presence of two…
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
Dynamical phase transitions are defined through non-analyticities of the survival probability of an out-of-equilibrium time-evolving state at certain critical times. They ensue from zeros of the corresponding survival amplitude. By…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
Discontinuous transitions have received considerable interest due to the uncovering that many phenomena such as catastrophic changes, epidemic outbreaks and synchronization present a behavior signed by abrupt (macroscopic) changes (instead…