Related papers: Formalizing Pfaffian in bounded arithmetic
We propose reductions to quantified Boolean formulas (QBF) as a new approach to showing fixed-parameter linear algorithms for problems parameterized by treewidth. We demonstrate the feasibility of this approach by giving new algorithms for…
I discuss algorithms for the evaluation of Feynman integrals. These algorithms are based on Hopf algebras and evaluate the Feynman integral to (multiple) polylogarithms.
The explicit computation of amplitudes for fermionic Gaussian pure states in arbitrary Pauli bases is a long-standing challenge in quantum many-body physics, with significant implications for quantum tomography, experimental studies, and…
This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…
Holographic algorithms, alternatively known as Pfaffian circuits, have received a great deal of attention for giving polynomial-time algorithms of $\#\mathsf{P}$-hard problems. Much work has been done to determine the extent of what this…
In this paper we revisit a result due to Franz Rellich on smoothness of solutions of parametrized linear systems. With this result as a starting point, we obtain finer smoothness results in an elementary fashion and propose an efficient…
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…
In analogy to the definition of the lambda-determinant, we define a one-parameter deformation of the Dodgson condensation formula for Pfaffians. We prove that the resulting rational function is a polynomial with weights given by the…
We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.
This paper is the first in the series devoted to evaluation of the partition function in statistical models on graphs with loops in terms of the Berezin/fermion integrals. The paper focuses on a representation of the determinant of a square…
This short note describes the connection between strong minimality of the differential equation satisfied by an complex analytic function and the real and imaginary parts of the function being Pfaffian. This connection combined with a…
In this paper we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation of such problems, including their well-posedness and…
With reference to a baseline parametrization, we explore highly efficient fractional factorial designs for inference on the main effects and, perhaps, some interactions. Our tools include approximate theory together with certain carefully…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that hold at each location of a given affine program (i.e., a program having only non-deterministic (as opposed to conditional) branching and all of whose…
We introduce a version of Farber's topological complexity suitable for investigating mechanical systems whose configuration spaces exhibit symmetries. Our invariant has vastly different properties to the previous approaches of Colman-Grant,…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…
In this note known formulas for the product of Toeplitz operators are revisited in the context of their applications to the study of Fredholmness, boundedness of Toeplitz products, and the Berezin-Toeplitz quantization. A few open problems…
We describe an algorithm that, given a k-tuple of permutations representing the monodromy of a rational map, constructs an arbitrarily precise floating-point complex approximation of that map. We then explain how it has been used to study a…