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This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process (PP's) models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon…
Decompositions of networks are useful not only for structural exploration. They also have implications and use in analysis and computational solution of processes (such as the Ising model, percolation, SIR model) running on a given network.…
A class of random discrete distributions $P$ is introduced by means of a recursive splitting of unity. Assuming supercritical branching, we show that for partitions induced by sampling from such $P$ a power growth of the number of blocks is…
The observation of light super-partners from a supersymmetric extension to the Standard Model is an intensely sought-after experimental outcome, providing an explanation for the stabilization of the electroweak scale and indicating the…
We propose a hole decomposition scheme to exactly solve a class of spin-1 quantum Ising models with transverse or longitudinal single-ion anisotropy. In this scheme, the spin-1 model is mapped onto a family of the $S=1/2$ transverse Ising…
In the sandpile model, vertices of a graph are allocated grains of sand. At each unit of time, a grain is added to a randomly chosen vertex. If that causes its number of grains to exceed its degree, that vertex is called unstable, and…
The Self-Similar Secondary Infall Model (SSIM) is modified to simulate a merger event. The model encompass spherical versions of tidal stripping and dynamical friction that agrees with the Syer & White merger paradigm's behaviour. The SSIM…
The iterative method of Sinkhorn allows, starting from an arbitrary real matrix with non-negative entries, to find a so-called 'scaled matrix' which is doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and with all…
We study the Abelian sandpile model (ASM), a process where grains of sand are placed on a graph's vertices. When the number of grains on a vertex is at least its degree, one grain is distributed to each neighboring vertex. This model has…
Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the…
The rapid adoption of synthetic data for training Large Language Models (LLMs) has introduced the technical challenge of "model collapse"-a degenerative process where recursive training on model-generated content leads to a contraction of…
We show that the hierarchical model at finite volume has a symmetry group which can be decomposed into rotations and translations as the familiar Poincar\'e groups. Using these symmetries, we show that the intricate sums appearing in the…
The reconstruction of interaction networks between random events is a critical problem arising from statistical physics and politics, sociology, biology, psychology, and beyond. The Ising model lays the foundation for this reconstruction…
Spontaneous self-assembly in molecular systems is a fundamental route to both biological and engineered soft matter. Simple micellisation, emulsion formation, and polymer mixing principles are well understood. However, the principles behind…
Recursive Bayesian filters have been widely deployed in structural system identification where output-only filters are of higher practicality. Unfortunately, the estimation obtained by instantaneous system inversion via filters can be…
We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm…
We introduce a new class of growth models, with a surface restructuring mechanism in which impinging particles may dislodge suspended particles, previously aggregated on the same column in the deposit. The flux of these particles is…
In recent years, we have established the iteration theory of the index for symplectic matrix paths and applied it to periodic solution problems of nonlinear Hamiltonian systems. This paper is a survey on these results.
Parametric human body models are foundational to human reconstruction, animation, and simulation, yet they remain mutually incompatible: SMPL, SMPL-X, MHR, Anny, and related models each diverge in mesh topology, skeletal structure, shape…
We generalize the well known formulation of the susceptibles, infected, susceptibles (SIS) spatial epidemics with creation and annihilation operators to the reinfection model including recovered which can be reinfected, the SIRI model,…