Related papers: Some application of difference equations in Crypto…
While it is known that there is at most a polynomial separation between quantum query complexity and the polynomial degree for total functions, the precise relationship between the two is not clear for partial functions. In this paper, we…
We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…
In this expository article we present an overview of the current state-of-the-art in post-quantum group-based cryptography. We describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic…
These are some notes on the basic properties of algebraic K-theory and G-theory of derived algebraic spaces and stacks, and the theory of fundamental classes in this setting.
Two well studied invariants of a complex projective variety are the unit Euclidean distance degree and the generic Euclidean distance degree. These numbers give a measure of the algebraic complexity for "nearest" point problems of the…
We show some classes of higher order partial difference equations admitting a zero-curvature representation and generalizing lattice potential KdV equation. We construct integrable hierarchies which, as we suppose, yield generalized…
The Lie algebraic integrability test is applied to the problem of classification of integrable Klein-Gordon type equations on quad-graphs. The list of equations passing the test is presented containing several well-known integrable models.…
In this article, we consider the Christoffel transformations for skew-orthogonal polynomials and partial-skew-orthogonal polynomials. We demonstrate that the Christoffel transformations can act as spectral problems for discrete integrable…
We propose to apply several gradient estimation techniques to enable the differentiation of programs with discrete randomness in High Energy Physics. Such programs are common in High Energy Physics due to the presence of branching processes…
A new integration scheme, combining the stability and the precision of usual pseudo-spectral codes with the locality of finite differences methods, is introduced. It turns out to be particularly suitable for the study of front and…
The $\epsilon$-approximate degree $deg_\epsilon(f)$ of a Boolean function $f$ is the least degree of a real-valued polynomial that approximates $f$ pointwise to error $\epsilon$. The approximate degree of $f$ is at least $k$ iff there…
We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…
The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector…
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…
Using the data schemes developed by Arrondo-Sols-Speiser, we give a rigorous definition of algebraic differential equations on the complex projective space $P^n$. For an algebraic subvariety $S \subseteq P^n$, we present an explicit formula…
A large number of quantum location verification protocols have been proposed. All existing protocols in this field are based on symmetric cryptography where verifiers and the prover use the same secret key. The prover obtains secret key…
It is shown that under reasonable assumptions a Drake-style equation can be obtained for the probability that our universe is the result of a deliberate simulation. Evaluating loose bounds for certain terms in the equation shows that the…
Recently, the invention of quantum computers was so revolutionary that they bring transformative challenges in a variety of fields, especially for the traditional cryptographic blockchain, and it may become a real thread for most of the…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
In this paper, we continue to study the sharing value problems for higher order derivatives of meromorphic functions with its linear difference and $q$-difference operators. Some of our results generalize and improve the results of…