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Assembling stiffness matrices represents a significant cost in many finite element computations. We address the question of optimizing the evaluation of these matrices. By finding redundant computations, we are able to significantly reduce…
We address the problem of clustering a set of points in $\mathbb{R}^d$ with axis-parallel clusters. Previous exact approaches to this problem are mostly based on integer programming formulations and can only solve to optimality instances of…
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For…
Aiming at the study of critical phenomena in the presence of boundaries with a non-trivial shape we discuss how lattices with an adaptive lattice spacing can be implemented. Since the parameters of the Hamiltonian transform non-trivially…
The $3$SUM-Indexing problem was introduced as a data structure version of the $3$SUM problem, with the goal of proving strong conditional lower bounds for static data structures via reductions. Ideally, the conjectured hardness of…
Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…
While the SLIM approach obtained high ranking-accuracy in many experiments in the literature, it is also known for its high computational cost of learning its parameters from data. For this reason, we focus in this paper on variants of…
In topology optimization, the treatment of stress constraints for very large scale problems has so far not been tractable due to the failure of robust agglomeration methods, i.e. their inability to accurately handle the locality of the…
This work proposes a novel adaptive linearized alternating direction multiplier method (LADMM) to convex optimization, which improves the convergence rate of the LADMM-based algorithm by adjusting step-size iteratively.The innovation of…
We present a sub-matrix update algorithm for the continuous-time auxiliary field method that allows the simulation of large lattice and impurity problems. The algorithm takes optimal advantage of modern CPU architectures by consistently…
It has become standard for empirical studies to conduct inference robust to cluster dependence and heterogeneity. With a small number of clusters, the normal approximation for the $t$-statistics of regression coefficients may be poor. This…
Using off-lattice noise reduction it is possible to estimate the asymptotic properties of diffusion-limited aggregation clusters grown in three dimensions with greater accuracy than would otherwise be possible. The fractal dimension of…
In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces $L^{2}(\mu)$, with $\mu$ a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix to the…
We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints, the optimization…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
We study two practically important cases of model based clustering using Gaussian Mixture Models: (1) when there is misspecification and (2) on high dimensional data, in the light of recent advances in Gradient Descent (GD) based…
Test-time compute scaling, the practice of spending extra computation during inference via repeated sampling, search, or extended reasoning, has become a powerful lever for improving large language model performance. Yet deploying these…
In this paper we present a novel iterative multiphase clustering technique for efficiently clustering high dimensional data points. For this purpose we implement clustering feature (CF) tree on a real data set and a Gaussian density…
The extraction of inhomogeneous 3-dimensional densities around tagged solutes from molecular simulations is known to have a very high computational cost because this is traditionally performed by collecting histograms, with each discrete…
Particle swarm optimization is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The approach of particle swarms is an example for…