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Monte Carlo rendering algorithms are widely used to produce photorealistic computer graphics images. However, these algorithms need to sample a substantial amount of rays per pixel to enable proper global illumination and thus require an…

Residual networks are an Euler discretization of solutions to Ordinary Differential Equations (ODE). This paper explores a deeper relationship between Transformer and numerical ODE methods. We first show that a residual block of layers in…

Multidimensional Retiming is one of the most important optimization techniques to improve timing parameters of nested loops. It consists in exploring the iterative and recursive structures of loops to redistribute computation nodes on cycle…

Minimal-residual methods for PDEs with a residual in a dual space are non-trivial to guarantee stability. We present a minimal-residual finite element method in which the solution space is a standard finite element space, but neural…

Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with encodability criteria. There exists a bunch…

Benchmarking is a common practice in software engineering to assess the qualities and performance of software variants, coming from multiple competing systems or from configurations of the same system. Benchmarks are used notably to compare…

Geographical information systems are ideal candidates for the application of parallel programming techniques, mainly because they usually handle large data sets. To help us deal with complex calculations over such data sets, we investigated…

This paper addresses the density based multi-sensor cooperative fusion using random finite set (RFS) type multi-object densities (MODs). Existing fusion methods use scalar weights to characterize the relative information confidence among…

We consider the problem of sampling $n$ numbers from the range $\{1,\ldots,N\}$ without replacement on modern architectures. The main result is a simple divide-and-conquer scheme that makes sequential algorithms more cache efficient and…

A numerical irreducible decomposition for a polynomial system provides representations for the irreducible factors of all positive dimensional solution sets of the system, separated from its isolated solutions. Homotopy continuation methods…

The reflection superposition phenomenon is complex and widely distributed in the real world, which derives various simplified linear and nonlinear formulations of the problem. In this paper, based on the investigation of the weaknesses of…

Neural network-based methods for solving differential equations have been gaining traction. They work by improving the differential equation residuals of a neural network on a sample of points in each iteration. However, most of them employ…

Existing Neural Radiance Fields (NeRF) methods suffer from the existence of reflective objects, often resulting in blurry or distorted rendering. Instead of calculating a single radiance field, we propose a multi-space neural radiance field…

Although Recurrent Neural Network (RNN) has been a powerful tool for modeling sequential data, its performance is inadequate when processing sequences with multiple patterns. In this paper, we address this challenge by introducing a novel…

Capsule Networks (CapsNets) is a machine learning architecture proposed to overcome some of the shortcomings of convolutional neural networks (CNNs). However, CapsNets have mainly outperformed CNNs in datasets where images are small and/or…

Mixture models are flexible tools in density estimation and classification problems. Bayesian estimation of such models typically relies on sampling from the posterior distribution using Markov chain Monte Carlo. Label switching arises…

A new O(N) algorithm based on a recursion method, in which the computational effort is proportional to the number of atoms N, is presented for calculating the inverse of an overlap matrix which is needed in electronic structure calculations…

Model fusion seeks to combine independently trained neural networks into a single model without retraining, but is complicated by representational divergence arising from permutation invariance, random initialization, and heterogeneous…

A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…

We describe a new parallel implementation, mplrs, of the vertex enumeration code lrs that uses the MPI parallel environment and can be run on a network of computers. The implementation makes use of a C wrapper that essentially uses the…