Related papers: Generalized immediate exchange models and their sy…
We calculate the time-evolution of a discrete-time fragmentation process in which clusters of particles break up and reassemble and move stochastically with size-dependent rates. In the continuous-time limit the process turns into the…
Generalization and invariance are two essential properties of any machine learning model. Generalization captures a model's ability to classify unseen data while invariance measures consistency of model predictions on transformations of the…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse…
It is proved that almost every interval exchange transformation given by the symmetric permutation 1->m, 2->m-1,..., m-1->2, m->1, where m>1 is an odd number, is disjoint from ELF systems. The notion of ELF systems was introduced to express…
We consider the edge-based compartmental models for epidemic spread developed in Part I. We show conditions under which simpler models may be substituted for more detailed models, and in so doing we define a hierarchy of epidemic models. In…
Neuromorphic devices, with their distinct advantages in energy efficiency and parallel processing, are pivotal in advancing artificial intelligence applications. Among these devices, memristive transistors have attracted significant…
We propose Energy-based generator matching (EGM), a modality-agnostic approach to train generative models from energy functions in the absence of data. Extending the recently proposed generator matching, EGM enables training of arbitrary…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
Entanglement of multipartite systems is studied based on exchange symmetry under the permutation group S_N. With the observation that symmetric property under the exchange of two constituent states and their separability are intimately…
We show by a surprisingly simple argument that the exchangeability condition, which is key to the exchangeable pair approach in Stein's method for distributional approximation, can be omitted in many standard settings. This is achieved by…
We give a general definition of gauge mediated supersymmetry breaking which encompasses all the known gauge mediation models. In particular, it includes both models with messengers as well as direct mediation models. A formalism for…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
We analyze a general class of reversible aggregate-reorganization processes. These processes are shown to exhibit globally attracting equilibrium distributions, which are \textit{universal}, i.e. identical for large classes of models.…
The eigenstate thermalization hypothesis (ETH) posits how isolated quantum many-body systems thermalize, assuming that individual eigenstates at the same energy density have identical expectation values of local observables in the limit of…
Analytical models for common envelope evolution (CEE), particularly the energy formalism, are used in binary population synthesis to predict post-CEE configurations. This formalism is based on an efficiency parameter alpha, which relates…
In order to better fit real-world datasets, studying asymmetric distribution is of great interest. In this work, we derive several mathematical properties of a general class of asymmetric distributions with positive support which shows up…
In this work, we define the notion of unimodular random measured metric spaces as a common generalization of various other notions. This includes the discrete cases like unimodular graphs and stationary point processes, as well as the…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…