Related papers: Most abundant isotope peaks and efficient selectio…
The theoretical computation of isotopic distribution of compounds is crucial in many important applications of mass spectrometry, especially as machine precision grows. A considerable amount of good tools have been created in the last…
Selection and sorting the Cartesian sum, $X+Y$, are classic and important problems. Here, a new algorithm is presented, which generates the top $k$ values of the form $X_i+Y_j$. The algorithm relies only on median-of-medians and is simple…
We describe a maximum entropy approach for computing volumes and counting integer points in polyhedra. To estimate the number of points from a particular set X in R^n in a polyhedron P in R^n, by solving a certain entropy maximization…
The layer-ordered heap (LOH) is a simple, recently proposed data structure used in optimal selection on $X+Y$, thealgorithm with the best known runtime for selection on $X_1+X_2+\cdots+X_m$, and the fastest method in practice for computing…
In this paper we find exact formulas for the numbers of partitions and compositions of an element into $m$ parts over a finite field, i.e. we find the number of nonzero solutions of the equation $x_1+x_2+...+x_m=z$ over a finite field when…
A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…
The isotopic composition, for example, 14C/12C, 13C/12C, 2H/1H, 15N/14N and 18O/16O, of the elements of matter is heterogeneous. It is ruled by physical, chemical and biological mechanisms. Isotopes can be employed to follow the fate of…
For systems of polynomial equations, we study the problem of computing the Newton polytope of their eliminants. As was shown by Esterov and Khovanskii, such Newton polytopes are mixed fiber polytopes of the Newton polytopes of the input…
We show that there are infinitely many primes of the form $X^2+(Y^2+1)^2$ and $X^2+(Y^3+Z^3)^2$. This extends the work of Friedlander and Iwaniec showing that there are infinitely many primes of the form $X^2+Y^4$. More precisely,…
We propose a new method for determination of element abundances in stellar atmospheres aimed for the automatic processing of high-quality stellar spectra. The pan-spectral method is based on weighted cumulative line-widths Q of studied…
Selection on $X_1+X_2+\cdots + X_m$ is an important problem with many applications in areas such as max-convolution, max-product Bayesian inference, calculating most probable isotopes, and computing non-parametric test statistics, among…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
Any given density matrix can be represented as an infinite number of ensembles of pure states. This leads to the natural question of how to uniquely select one out of the many, apparently equally suitable, possibilities. Following Jaynes'…
The knowledge of isotopic and elemental abundances of the pristine solar system material provides a fundamental test of galactic chemical evolution models, while the composition of the solar photosphere is a reference pattern to understand…
We consider the mass-dependent aggregation process (k+1)X -> X, given a fixed number of unit mass particles in the initial state. One cluster is chosen proportional to its mass and is merged into one either with k-neighbors in one…
We provide formulas and algorithms for computing the excess numbers of certain ideals. The solution for monomial ideals is given by the mixed volumes of certain polytopes. These results enable us to design specific homotopies for numerical…
We give the first sorting algorithm with bounds in terms of higher-order entropies: let $S$ be a sequence of length $m$ containing $n$ distinct elements and let (H_\ell (S)) be the $\ell$th-order empirical entropy of $S$, with (n^{\ell + 1}…
In this paper we consider $m$ ($m \geq 1$)conjunctions of Max-atoms that is atoms of the form $\max(z,y) + r \geq x$, where the offset $r$ is a real constant and $x,y,z$ are variables. We show that the Max-atom problem (MAP) belongs to…
In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…
We present an ab initio method of calculation of isotope shift and relativistic shift in atoms with a few valence electrons. It is based on an energy calculation involving combination of the configuration interaction method and many-body…