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We give a {\em deterministic} algorithm for approximately computing the fraction of Boolean assignments that satisfy a degree-$2$ polynomial threshold function. Given a degree-2 input polynomial $p(x_1,\dots,x_n)$ and a parameter $\eps >…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
Perhaps surprisingly, it is possible to predict how long an algorithm will take to run on a previously unseen input, using machine learning techniques to build a model of the algorithm's runtime as a function of problem-specific instance…
Partitioned neural network functions are used to approximate the solution of partial differential equations. The problem domain is partitioned into non-overlapping subdomains and the partitioned neural network functions are defined on the…
Exactly computing the full output distribution of linear optical circuits remains a challenge, as existing methods are either time-efficient but memory-intensive or memory-efficient but slow. Moreover, any realistic simulation must account…
Time-varying vector fields produced by computational fluid dynamics simulations are often prohibitively large and pose challenges for accurate interactive analysis and exploration. To address these challenges, reduced Lagrangian…
We propose a setup for fractionally cointegrated time series which is formulated in terms of latent integrated and short-memory components. It accommodates nonstationary processes with different fractional orders and cointegration of…
In this paper, we develop a unified framework able to certify both exponential and subexponential convergence rates for a wide range of iterative first-order optimization algorithms. To this end, we construct a family of parameter-dependent…
Discriminative segmental models offer a way to incorporate flexible feature functions into speech recognition. However, their appeal has been limited by their computational requirements, due to the large number of possible segments to…
In engineering design, one often wishes to calculate the probability that the performance of a system is satisfactory under uncertainty. State of the art algorithms exist to solve this problem using active learning with Gaussian process…
In this paper an asymptotic expansion of the global error on the stepsize for partitioned linear multistep methods is proved. This provides a tool to analyse the behaviour of these integrators with respect to error growth with time and…
We develop a stochastic model for Lagrangian velocity as it is observed in experimental and numerical fully developed turbulent flows. We define it as the unique statistically stationary solution of a causal dynamics, given by a stochastic…
Matrix representations are a powerful tool for designing efficient algorithms for combinatorial optimization problems such as matching, and linear matroid intersection and parity. In this paper, we initiate the study of matrix…
In this paper we introduce a new methodology to determine an optimal coefficient of penalized functional regression. We assume the dependent, independent variables and the regression coefficients are functions of time and error dynamics…
We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Lochs theorem from 1964. Thus, we aimed to compare the efficiency by describing the rate at which the…
Many state-of-the-art algorithms for solving hard combinatorial problems in artificial intelligence (AI) include elements of stochasticity that lead to high variations in runtime, even for a fixed problem instance. Knowledge about the…
We develop a methodology to learn finitely generated random iterated function systems from time-series of partial observations using delay embeddings. We obtain a minimal model representation for the observed dynamics, using a hidden…
Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…
We propose a novel time-splitting scheme for a class of semilinear stochastic evolution equations driven by cylindrical fractional noise. The nonlinearity is decomposed as the sum of a one-sided, non-globally, Lipschitz continuous function,…
Computational fluid dynamics plays a key role in the design process across many industries. Recently, there has been increasing interest in data-driven methods, in order to exploit the large volume of data generated by such computations.…