Related papers: Computing Integer Sequences: Filtering vs Generati…
The paper exploits an isomorphism between the natural numbers N and a space U of periodic sequences of the roots of unity in constructing a recursive procedure for representing and computing the prime numbers. The nth wave number ${\bf…
Many scientific computing problems can be reduced to Matrix-Matrix Multiplications (MMM), making the General Matrix Multiply (GEMM) kernels in the Basic Linear Algebra Subroutine (BLAS) of interest to the high-performance computing…
We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output,…
Existing unsupervised hash learning is a kind of attribute-centered calculation. It may not accurately preserve the similarity between data. This leads to low down the performance of hash function learning. In this paper, a hash algorithm…
Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…
Since its birth as a new scientific body of knowledge in the late 1950s, computer programming has become a fundamental skill needed in many other disciplines. However, programming is not easy, it is prone to errors and code re-use is key…
Using specializations of unfold and fold on a generic tree data type we derive unranking and ranking functions providing natural number encodings for various Hereditarily Finite datatypes. In this context, we interpret unranking operations…
We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also…
Convolutional Neural Networks have achieved state-of-the-art performance on a wide range of tasks. Most benchmarks are led by ensembles of these powerful learners, but ensembling is typically treated as a post-hoc procedure implemented by…
Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences whose elements…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…
We count permutations avoiding a nonconsecutive instance of a two- or three-letter pattern, that is, the pattern may occur but only as consecutive entries in the permutation. Two-letter patterns give rise to the Fibonacci numbers. The…
In this paper, we enumerate two families of pattern-avoiding permutations: those avoiding the vincular pattern $2-41-3$, which we call semi-Baxter permutations, and those avoiding the vincular patterns $2-41-3$, $3-14-2$ and $3-41-2$, which…
Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents a significant computational challenge, motivating the development of machine learning-based…
In recent studies [1][13][12] Recurrent Neural Networks were used for generative processes and their surprising performance can be explained by their ability to create good predictions. In addition, data compression is also based on…
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…
Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…
In this paper we describe a deep learning--based probabilistic algorithm for integer factorisation. We use Lawrence's extension of Fermat's factorisation algorithm to reduce the integer factorisation problem to a binary classification…
In this paper, we present an~algorithm that computes funnels along trajectories of systems of ordinary differential equations. A funnel is a time-varying set of states containing the given trajectory, for which the evolution from within the…
Hashing methods aim to learn a set of hash functions which map the original features to compact binary codes with similarity preserving in the Hamming space. Hashing has proven a valuable tool for large-scale information retrieval. We…