Related papers: Minimizing storage in implementations of the overl…
We consider the problem of minimizing a smooth, Lipschitz, convex function over a compact, convex set using sub-zeroth-order oracles: an oracle that outputs the sign of the directional derivative for a given point and a given direction, an…
In a capacitated directed graph, it is known that the set of all min-cuts forms a distributive lattice [1], [2]. Here, we describe this lattice as a regular predicate whose forbidden elements can be advanced in constant parallel time after…
Bitmap indexes must be compressed to reduce input/output costs and minimize CPU usage. To accelerate logical operations (AND, OR, XOR) over bitmaps, we use techniques based on run-length encoding (RLE), such as Word-Aligned Hybrid (WAH)…
Widely used Lagrangian numerical codes that compute the physical interaction with neighbouring resolution elements (particles), duplicate the calculation of the interaction between pairs of particles. We developed an algorithm that reduces…
In recent years, processing in memory (PIM) based mixedsignal designs have been proposed as energy- and area-efficient solutions with ultra high throughput to accelerate DNN computations. However, PIM designs are sensitive to imperfections…
Motion planning is the soul of robot decision making. Classical planning algorithms like graph search and reaction-based algorithms face challenges in cases of dense and dynamic obstacles. Deep learning algorithms generate suboptimal…
I derive the overlap Dirac operator starting from the overlap formalism, discuss the numerical hurdles in dealing with this operator and present ways to overcome them.
A linear-scaling algorithm is presented for computing the Hartree-Fock (HF) exchange matrix using concentric atomic density fitting. The algorithm utilizes the stronger distance dependence of the three-center electron repulsion integrals…
We consider the two-dimensional Dirac operator with Lorentz-scalar $\delta$-shell interactions on each edge of a star-graph. An orthogonal decomposition is performed which shows such an operator is unitarily equivalent to an orthogonal sum…
Hierarchical matrices provide a highly memory-efficient way of storing dense linear operators arising, for example, from boundary element methods, particularly when stored in the H^2 format. In such data-sparse representations, iterative…
Many parallel algorithms use at least linear auxiliary space in the size of the input to enable computations to be done independently without conflicts. Unfortunately, this extra space can be prohibitive for memory-limited machines,…
Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian circumvents this problem. We show that the modified…
We consider stopping criteria that balance algebraic and discretization errors for the conjugate gradient algorithm applied to high-order finite element discretizations of Poisson problems. Firstly, we introduce a new stopping criterion…
We introduce a data distribution scheme for $\mathcal{H}$-matrices and a distributed-memory algorithm for $\mathcal{H}$-matrix-vector multiplication. Our data distribution scheme avoids an expensive $\Omega(P^2)$ scheduling procedure used…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
With lowrank approximation the storage requirements for dense data are reduced down to linear complexity and with the addition of hierarchy this also works for data without global lowrank properties. However, the lowrank factors itself are…
Recent studies of the topological properties of a general class of lattice Dirac operators are reported. This is based on a specific algebraic realization of the Ginsparg-Wilson relation in the form…
We have constructed the lowest few eigenvectors of the staggered Dirac operator on SU(3) gauge configurations, both quenched and dynamical. We use these modes to study the topological charge and to construct approximate hadronic…
Euclidean space hadronic correlators are computed in quenched QCD at small quark mass using truncations of quark propagators which include or exclude low eigenvalue eigenmodes of the Dirac operator. High modes provide the dominant…
Block-structured integer linear programs (ILPs) play an important role in various application fields. We address $n$-fold ILPs where the matrix $\mathcal{A}$ has a specific structure, i.e., where the blocks in the lower part of…