Related papers: Critical branching processes in digital memcomputi…

Avalanches of electrochemical activity in brain networks have been empirically reported to obey scale-invariant behavior --characterized by power-law distributions up to some upper cut-off-- both in vitro and in vivo. Elucidating whether…

Reservoir computing is a machine learning paradigm that uses a structure called a reservoir, which has nonlinearities and short-term memory. In recent years, reservoir computing has expanded to new functions such as the autonomous…

Power laws and distributions with heavy tails are common features of many experimentally studied complex systems, like the distribution of the sizes of earthquakes and solar flares, or the duration of neuronal avalanches in the brain.…

Diffusion and flow matching approaches to generative modeling have shown promise in domains where the state space is continuous, such as image generation or protein folding & design, and discrete, exemplified by diffusion large language…

We use a discrete-time formulation to study the asymmetric avalanche process [Phys. Rev. Lett. vol. 87, 084301 (2001)] on a finite ring and obtain an exact expression for the average avalanche size of particles as a function of toppling…

We study a simple model for a neuron function in a collective brain system. The neural network is composed of uncorrelated random scale-free network for eliminating the degree correlation of dynamical processes. The interaction of neurons…

We study the abelian sandpile model on a random binary tree. Using a transfer matrix approach introduced by Dhar & Majumdar, we prove exponential decay of correlations, and in a small supercritical region (i.e., where the branching process…

Metric learning is a fundamental problem in computer vision whereby a model is trained to learn a semantically useful embedding space via ranking losses. Traditionally, the effectiveness of a ranking loss depends on the minibatch size, and…

Memcomputing is a novel computing paradigm beyond the von-Neumann one. Its digital version is designed for the efficient solution of combinatorial optimization problems, which emerge in various fields of science and technology. Previously,…

Unsupervised machine learning methods are used to identify structural changes using the melting point transition in classical molecular dynamics simulations as an example application of the approach. Dimensionality reduction and clustering…

Cumulative probability models (CPMs) are a robust alternative to linear models for continuous outcomes. However, they are not feasible for very large datasets due to elevated running time and memory usage, which depend on the sample size,…

Let $\left\{ Z_{n},n=0,1,2,...\right\} $ be a critical branching process in random environment and let $\left\{ S_{n},n=0,1,2,...\right\} $ be its associated random walk. It is known that if the increments of this random walk belong…

Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with…

Digital memcomputing machines (DMMs) are non-linear dynamical systems designed so that their equilibrium points are solutions of the Boolean problem they solve. In a previous work [Chaos 27, 023107 (2017)] it was argued that when DMMs…

The branch-and-bound algorithm based on decision diagrams introduced by Bergman et al. in 2016 is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width…

This paper demonstrates a new regeneration processes technology making use of positive stable distributions. We study the asymptotic behavior of branching processes with a randomly controlled migration component. Using the new method, we…

Machine learning opens new avenues for modelling correlated materials. Quantum embedding approaches, such as the dynamical mean-field theory (DMFT), provide corrections to first-principles calculations for strongly correlated materials,…

Process mining has become one of the best programs that can outline the event logs of production processes in visualized detail. We have addressed the important problem that easily occurs in the industrial process called Bottleneck. The…

Markov Chain Monte Carlo (MCMC) algorithms are essential tools in computational statistics for sampling from unnormalised probability distributions, but can be fragile when targeting high-dimensional, multimodal, or complex target…

Criticality is a behavioral state in dynamical systems that is known to present the highest computation capabilities, i.e., information transmission, storage, and modification. Therefore, such systems are ideal candidates as a substrate for…