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We present a general method for constructing integrable stochastic processes, with two-step discrete time Floquet dynamics, from the transfer matrix formalism. The models can be interpreted as a discrete time parallel update. The method can…
We describe new methods for deciding the stability of switching systems. The methods build on two ideas previously appeared in the literature: the polytope norm iterative construction, and the lifting procedure. Moreover, the combination of…
We present a determinantal formula for the steady state probability of each state of the TASEP (Totally Asymmetric Simple Exclusion Process) with open boundaries, a 1D particle model that has been studied extensively and displays rich…
Recently it was shown by Nesterov (2011) that techniques form convex optimization can be used to successfully accelerate simple derivative-free randomized optimization methods. The appeal of those schemes lies in their low complexity, which…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
We consider any fixed $d\in\mathbb{Z}_{>0}$ number of second class particles in the asymmetric simple exclusion process (ASEP), constructed via a basic coupling of two ASEPs. We give the joint distribution of the positions of the second…
We introduce a family of discrete determinantal point processes related to orthogonal polynomials on the real line, with correlation kernels defined via spectral projections for the associated Jacobi matrices. For classical weights, we show…
Longitudinal or panel data can be represented as a matrix with rows indexed by units and columns indexed by time. We consider inferential questions associated with the missing data version of panel data induced by staggered adoption. We…
We find the formulas of the transition probabilities of the $N$-particle multi-species asymmetric simple exclusion processes (ASEP), and show that the transition probabilities are written as a determinant when the order of particles in the…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
Previous work of Ayyer, Martin, and Williams gave a probabilistic interpretation of the Macdonald polynomials $P_{\lambda}(x_1,\dots,x_n;1,t)$ at $q=1$ in terms of a Markov chain called the multispecies $t$-Push TASEP, a Markov chain…
We revisit a totally asymmetric simple exclusion process (TASEP) with open boundaries and a global constraint on the total number of particles [Adams, et. al. 2008 J. Stat. Mech. P06009]. In this model, the entry rate of particles into the…
We consider the asymmetric simple exclusion process (ASEP) on the integers in which the initial density at a site (the probability that it is occupied) is given by a periodic function on the positive integers. (When the function is constant…
Most popular word embedding techniques involve implicit or explicit factorization of a word co-occurrence based matrix into low rank factors. In this paper, we aim to generalize this trend by using numerical methods to factor higher-order…
Simulation-based inference has been popular for amortized Bayesian computation. It is typical to have more than one posterior approximation, from different inference algorithms, different architectures, or simply the randomness of…
The link between (super)-affine Lie algebras as Poisson brackets structures and integrable hierarchies provides both a classification and a tool for obtaining superintegrable hierarchies. The lack of a fully systematic procedure for…
We consider the dynamics of a single shock in a partially asymmetric simple exclusion process (PASEP) on a finite lattice with open boundaries in the sublattice-parallel updating scheme. We then construct the steady state of the system by…
A new algorithm, termed subspace evolution and transfer (SET), is proposed for solving the consistent matrix completion problem. In this setting, one is given a subset of the entries of a low-rank matrix, and asked to find one low-rank…
In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…
We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an…