Related papers: Quantifier Elimination for Normal Cone Computation…
We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end.…
We give formal normal forms for parabolic logarithmic transseries $f=z+\cdots \, $, with respect to parabolic logarithmic normalizations. Normalizations are given algorithmically, using fixed point theorems, as limits of Picard's sequences…
A Normalizing Flow computes a bijective mapping from an arbitrary distribution to a predefined (e.g. normal) distribution. Such a flow can be used to address different tasks, e.g. anomaly detection, once such a mapping has been learned. In…
We present a C program to compute by successive approximations the regular order reduction of a large class of ordinary differential equations, which includes evolution equations in electrodynamics and gravitation. The code may also find…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Quantum algorithms for computing classical nonlinear maps are widely known for toy problems but might not suit potential applications to realistic physics simulations. Here, we propose how to compute a general differentiable invertible…
Regular resolution is a refinement of the resolution proof system requiring that no variable be resolved on more than once along any path in the proof. It is known that there exist sequences of formulas that require exponential-size proofs…
For a possibly singular subset of a regular Poisson manifold we construct a deformation quantization of its algebra of Whitney functions. We then extend the construction of a deformation quantization to the case where the underlying set is…
We consider different Linear Combination of Unitaries (LCU) decompositions for molecular electronic structure Hamiltonians. Using these LCU decompositions for Hamiltonian simulation on a quantum computer, the main figure of merit is the…
Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varying the initial guess supplied to the solver. The central idea…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
This study proposes a cubic regularization of the Newton method for generating weakly efficient points of unconstrained vector optimization problems under no convexity assumption on the objective function. It is observed that at a given…
The present article is primarily a review of the projection-operator approach to quantize systems with constraints. We study the quantization of systems with general first- and second-class constraints from the point of view of…
We study a variant of Newton's algorithm applied to under-determined systems of non-smooth equations. The notion of regularity employed in our work is based on Newton differentiability, which generalizes semi-smoothness. The classic notion…
We give a sufficient condition for a model theoretic structure $B$ to 'inherit' quantifier elimination from another structure $A$. This yields an alternative proof of one of the main result from \cite{kle}, namely quantifier elimination for…
The paper is devoted to the problem of exact calculation of the norms in ideal spaces for monotone operators on the cones of functions with monotonicity properties. We implement a general approach to this problem that covers many concrete…
Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…
We give a quantifier elimination procedure for one-parametric Presburger arithmetic, the extension of Presburger arithmetic with the function $x \mapsto t \cdot x$, where $t$ is a fixed free variable ranging over the integers. This resolves…
Quantile normalisation is a popular normalisation method for data subject to unwanted variations such as images, speech, or genomic data. It applies a monotonic transformation to the feature values of each sample to ensure that after…
The paper is devoted to a new idea of simulation of accounting by quantum computing. We expose the actual accounting principles in a pure mathematics language. After that we simulated the accounting principles on quantum computers. We show…