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Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…
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In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…
The partition functions of ferromagnetic Ising models of square lattices in a finite magnetic field is deduced using topological considerations within a heuristic graph-theoretical approach. These equations are derived separately for low…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
We present three new complexity results for classes of planning problems with simple causal graphs. First, we describe a polynomial-time algorithm that uses macros to generate plans for the class 3S of planning problems with binary state…
A family of multispecies Ising models on generalized regular random graphs is investigated in the thermodynamic limit. The architecture is specified by class-dependent couplings and magnetic fields. We prove that the magnetizations,…
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Valiant introduced matchgate computation and holographic algorithms. A number of seemingly exponential time problems can be solved by this novel algorithmic paradigm in polynomial time. We show that, in a very strong sense, matchgate…
Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…
Compact and I/O-efficient data representations play an important role in efficient algorithm design, as memory bandwidth and latency can present a significant performance bottleneck, slowing the computation by orders of magnitude. While…
In a seminal paper (Weitz, 2006), Weitz gave a deterministic fully polynomial approximation scheme for count- ing exponentially weighted independent sets (equivalently, approximating the partition function of the hard-core model from…
In this paper we show a new way of constructing deterministic polynomial-time approximation algorithms for computing complex-valued evaluations of a large class of graph polynomials on bounded degree graphs. In particular, our approach…
Toric (or sparse) elimination theory is a framework developped during the last decades to exploit monomial structures in systems of Laurent polynomials. Roughly speaking, this amounts to computing in a \emph{semigroup algebra}, \emph{i.e.}…
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