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Interpolative and CUR decompositions involve "natural bases" of row and column subsets, or skeletons, of a given matrix that approximately span its row and column spaces. These low-rank decompositions preserve properties such as sparsity or…

Proving program termination is key to guaranteeing absence of undesirable behaviour, such as hanging programs and even security vulnerabilities such as denial-of-service attacks. To make termination checks scale to large systems,…

We apply simple linear programming methods and an LP solver to refute a number of open conjectures in extremal combinatorics.

This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for…

This paper concerns a class of DC composite optimization problems which, as an extension of convex composite optimization problems and DC programs with nonsmooth components, often arises in robust factorization models of low-rank matrix…

We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…

This note is a response to [7] in which it is claimed that [13, Proposition 11] is false. We demonstrate here that this assertion in [7] is false, and is based on a misreading of the notion of set membership in [13, Proposition 11]. We…

This paper studies the problem of decomposing a low-rank matrix into a factor with binary entries, either from $\{\pm 1\}$ or from $\{0,1\}$, and an unconstrained factor. The research answers fundamental questions about the existence and…

ACLP is a system which combines abductive reasoning and constraint solving by integrating the frameworks of Abductive Logic Programming (ALP) and Constraint Logic Programming (CLP). It forms a general high-level knowledge representation…

This paper has been withdrawn by the author(s). The material contained in the paper will be published in a subtantially reorganized form, part of it is now included in math.QA/0510174

In this complementary note to [1] (arXiv:1501.05641), we provide an alternative proof for the factorial decay estimate of iterated integrals for geometric rough paths without using the neoclassical inequality. This note intends to aid the…

Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these…

We extend the results of Deligne and Illusie on liftings modulo $p^2$ and decompositions of the de Rham complex in several ways. We show that for a smooth scheme $X$ over a perfect field $k$ of characteristic $p>0$, the truncations of the…

In this paper we introduce a class of constraint logic programs such that their termination can be proved by using affine level mappings. We show that membership to this class is decidable in polynomial time.

We construct fast, structure-preserving iterations for computing the sign decomposition of a unitary matrix $A$ with no eigenvalues equal to $\pm i$. This decomposition factorizes $A$ as the product of an involutory matrix $S =…

Successive cancellation list (SCL) decoding algorithm is a powerful method that can help polar codes achieve excellent error-correcting performance. However, the current SCL algorithm and decoders are based on likelihood or log-likelihood…

The Iterative Filtering method is a technique developed recently for the decomposition and analysis of non-stationary and non-linear signals. In this work we propose two alternative formulations of the original algorithm which allows to…

Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been…

Using $E_8$ bundles, we construct some modular forms over $SL(2,{\bf Z})$, $\Gamma^0(2)$ and $\Gamma_0(2)$. By these modular forms, we get some new anomaly cancellation formulas of characteristic forms.

Simulation results illustrating the performance and complexity of the sequential successive cancellation decoding algorithm are presented for the case of polar subcodes with Arikan and large kernels, as well as for extended BCH\ codes.…