Related papers: A class of digit extraction BBP-type formulas in g…
This work gives an explicit construction of a family of error correcting codes for the binary deletion channel and for the Poisson repeat channel. In the binary deletion channel with parameter $p$ (BDC$_p$) every bit is deleted…
We construct explicit bases of simple modules and Bernstein-Gelfand-Gelfand (BGG) resolutions of all simple modules of the (graded) Temperley-Lieb algebra of type B over a field of characteristic zero.
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
We use the notion of Borel generators to give alternative methods for computing standard invariants, such as associated primes, Hilbert series, and Betti numbers, of Borel ideals. Because there are generally few Borel generators relative to…
In a multi-base representation of an integer (in contrast to, for example, the binary or decimal representation) the base (or radix) is replaced by products of powers of single bases. The resulting numeral system has desirable properties…
We obtain the expected asymptotic formula for the number of primes $p<N=2^n$ with $r$ prescribed (arbitrarly placed) binary digits, provided $r<cn$ for a suitable constant $c>0$. This result improves on our earlier result where $r$ was…
Distributions on integers are ubiquitous in probabilistic modeling but remain challenging for many of today's probabilistic programming languages (PPLs). The core challenge comes from discrete structure: many of today's PPL inference…
The main aim of this paper is to further develop the multiple-correction method that formulated in our previous works~\cite{CXY, Cao}. As its applications, we establish a kind of hybrid-type finite continued fraction approximations related…
An algorithm for computing /pi(N) is presented.It is shown that using a symmetry of natural numbers we can easily compute /pi(N).This method relies on the fact that counting the number of odd composites not exceeding N suffices to calculate…
Binary logic programs can be obtained from ordinary logic programs by a binarizing transformation. In most cases, binary programs obtained this way are less efficient than the original programs. (Demoen, 1992) showed an interesting example…
We show that for every homogeneous polynomial of degree $d$, if it has determinantal complexity at most $s$, then it can be computed by a homogeneous algebraic branching program (ABP) of size at most $O(d^5s)$. Moreover, we show that for…
In previous work, the first author developed an algorithm for the computation of Hilbert modular forms. In this paper, we extend this to all totally real number fields of even degree and nontrivial class group. Using the algorithm over…
A method is developed for calculating effective sums of divergent series. This approach is a variant of the self-similar approximation theory. The novelty here is in using an algebraic transformation with a power providing the maximal…
In this paper we construct a combinatorial algorithm of resolution of singularities for binomial ideals, over a field of arbitrary characteristic. This algorithm is applied to any binomial ideal. This means ideals generated by binomial…
We establish a sharp estimate for a minimal number of binary digits (bits) needed to represent all bounded total generalized variation functions taking values in a general totally bounded metric space $(E,\rho)$ up to an accuracy of…
We investigate exponential sums over singular binary quartic forms, proving an explicit formula for the finite field Fourier transform of this set. Our formula shares much in common with analogous formulas proved previously for other vector…
Probabilistic programming languages (PPLs) are expressive means for creating and reasoning about probabilistic models. Unfortunately hybrid probabilistic programs, involving both continuous and discrete structures, are not well supported by…
Multiplicative inverse is a crucial operation in public key cryptography, and been widely used in cryptography. Public key cryptography has given rise to such a need, in which we need to generate a related public and private pair of…
For non-negative integers $k\leq n$, we prove a combinatorial identity for the $p$-binomial coefficient $\binom{n}{k}_p$ based on abelian p-groups. A purely combinatorial proof of this identity is not known. While proving this identity, for…
A determined algorithm is presented for solving the rSUM problem for any natural r with a sub-quadratic assessment of time complexity in some cases. In terms of an amount of memory used the obtained algorithm is the nlog^3(n) order. The…