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Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…
3D printing has revolutionized the manufacturing of volumetric components and structures in many areas. Different technologies have been developed including light-induced techniques based on the photopolymerization of liquid resins. In…
Partial Unit Memory (PUM) codes are a special class of convolutional codes, which are often constructed by means of block codes. Decoding of PUM codes may take advantage of existing decoders for the block code. The Dettmar--Sorger algorithm…
This article describes algorithms for the hybrid parallelization and SIMD vectorization of molecular dynamics simulations with short-range forces. The parallelization method combines domain decomposition with a thread-based parallelization…
Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of modern computations. The efficiency of its performance depends on various factors, in particular vectorization, data movement and arithmetic…
A new fast algorithm for clustering and classification of large collections of text documents is introduced. The new algorithm employs the bipartite graph that realizes the word-document matrix of the collection. Namely, the modularity of…
Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…
The Vampire automated theorem prover is extended to output machine-checkable proofs in the Dedukti concrete syntax for the LambdaPi-calculus modulo. This significantly reduces the trusted computing base, and in principle eases proof…
We develop algorithms for inner approximating the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and…
Submodular optimization is a special class of combinatorial optimization arising in several machine learning problems, but also in cooperative control of complex systems. In this paper, we consider agents in an asynchronous, unreliable and…
The singular value decomposition (SVD) of large-scale matrices is a key tool in data analytics and scientific computing. The rapid growth in the size of matrices further increases the need for developing efficient large-scale SVD…
In this paper we present a hardware-oriented algorithm for constant matrix-vector product calculating, when the all elements of vector and matrix are complex numbers. The proposed algorithm versus the naive method of analogous calculations…
In this paper, we discuss the generation of symbols (and alphabets) based on specific user requirements (medium, priorities, type of information that needs to be conveyed). A framework for the generation of alphabets is proposed, and its…
Procedural materials, represented as functional node graphs, are ubiquitous in computer graphics for photorealistic material appearance design. They allow users to perform intuitive and precise editing to achieve desired visual appearances.…
We overview numerous algorithms in computational $D$-module theory together with the theoretical background as well as the implementation in the computer algebra system \textsc{Singular}. We discuss new approaches to the computation of…
We present a modular analysis program written in Python devoted to the estimation of autocorrelation times for Monte Carlo simulations by means of the $\Gamma$-method algorithm. We give a brief review of this method and describe the main…
Designers increasingly rely on procedural generation for automatic generation of content in various industries. These techniques require extensive knowledge of the desired content, and about how to actually implement such procedural…
This paper introduces the Modular Neural Computer (MNC), a memory-augmented neural architecture for exact algorithmic computation on variable-length inputs. The model combines an external associative memory of scalar cells, explicit read…
We represent vector bundles over a regular algebraic curve as pairs of lattices over the maximal orders of its function field and we give polynomial time algorithms for several tasks: computing determinants of vector bundles, kernels and…
Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations…