Related papers: A note on lattice coverings
This paper provides a simplified proof for the existence of nested lattice codebooks allowing to achieve the capacity of the additive white Gaussian noise channel, as well as the optimal rate-distortion trade-off for a Gaussian source. The…
This short note, in part of expository nature, points out several new or recent consequences of a quite nice decomposition for positive semi-definite matrices.
A compact complex surface with positive definite intersection lattice is either the projective plane or a false projective plane. If the intersection lattice is negative definite, the surface is either a non-minimal secondary Kodaira…
In this notes we show how a problem regarding continued fractions of rational numbers, lead to several phenomena in number theory and dynamics, and eventually to the problem of shearing of divergent diagonal orbits in the space of adelic…
It is a study note detailing the connection between Boolean inverse monoids and ample groupoids.
The main problem considered in this paper is construction and theoretical study of efficient $n$-point coverings of a $d$-dimensional cube $[-1,1]^d$. Targeted values of $d$ are between 5 and 50; $n$ can be in hundreds or thousands and the…
The translation is not verbatim, many parts have been abbreviated and in some case alternative proofs were devised emphasizing intuition.
Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.
Some important problems in quantitative QCD will certainly yield to hard work and adequate investment of resources, others appear difficult but may be accessible, and still others will require essentially new ideas. Here I identify several…
It is shown that Darwiche and Pearl's postulates imply an interesting property, not noticed by the authors.
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
We investigated SU(3) lattice gauge theory with a fundamental and adjoint plaquette term in the action. The purpose is to test whether the choice of a negative adjoint coupling can reduce lattice artefacts and improve the scaling b…
Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and…
A brief overview of the QCD phase diagram at nonzero temperature and density is provided. It is explained why standard lattice QCD techniques are not immediately applicable for its determination, due to the sign problem. We then discuss a…
This small note contains some easy examples of quartic hypersurfaces that have finite-dimensional motive. As an illustration, we verify a conjecture of Voevodsky (concerning smash-equivalence) for some of these special quartics.
This paper gives an example of a non-arithmetic surface with marked length variety rigidity.
The electric resistance between two arbitrary nodes on any infinite lattice structure of resistors that is a periodic tiling of space is obtained. Our general approach is based on the lattice Green's function of the Laplacian matrix…
We study the Fourier transforms of indicator functions of some special high-dimensional finite type domains and obtain estimates of the associated lattice point discrepancy.
A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…
We prove some extensions of Andrews inequality.