Related papers: $\epsilon$-factors for Gauss-Manin determinants
A general formula for bound-continuous transition form factors is derived. It is shown that these form factors can be represented in the form of finite sum of terms with simple analytical structure.
Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent…
We present the new expressions for the formfactors of local operators for the XX - quantum spin chain as a Cauchy determinants. Using the known functional form of the correlator at large distances we propose the new expression for the…
We give a new combinatorial explanation for well-known relations between determinants and traces of matrix powers. Such relations can be used to obtain polynomial-time and poly-logarithmic space algorithms for the determinant. Our new…
We study the transition form factors (TFFs) of axial-vector mesons in the context of currently available experimental data, including new constraints from $e^+ e^- \to f_1(1285) \pi^+ \pi^-$ that imply stringent limits on the high-energy…
We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [Lemma…
This paper introduces a causation coefficient which is defined in terms of probabilistic causal models. This coefficient is suggested as the natural causal analogue of the Pearson correlation coefficient and permits comparing causation and…
The availability of a reliable bound on an integral involving the square of the modulus of a form factor on the unitarity cut allows one to constrain the form factor at points inside the analyticity domain and its shape parameters, and also…
The paper is devoted to differential geometric invariants determining a Frenet curve in up to a direct similarity These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then,…
Several graph decompositions that factorize the determinant of the adjacency matrix isolate a K\H{o}nig-Egerv\'ary part, such as the SD--KE decomposition and the critical independence decomposition of Larson. This suggests that the study of…
We study the geometry of determinant line bundles associated to Dirac operators on compact odd dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the…
We define a certain Hecke theoretic notion of family of smooth admissible representations of $GL_n(F)$, or of products of such groups, where $F$ is a nonarchimedean local field of characteristic zero. While this notion of family is rather…
We compute to all loop orders correlation function of four heavy BPS operators in $\mathcal{N}$= 4 SYM with special polarisations considered recently by Frank Coronado. Our main result is an expression for the octagon form factor as…
We give a complete factorization of the invariant factors of resultant matrices built from birational parameterizations of rational plane curves in terms of the singular points of the curve and their multiplicity graph. This allows us to…
We investigate families of graphs and graphons (graph limits) that are defined by a finite number of prescribed subgraph densities. Our main focus is the case when the family contains only one element, i.e., a unique structure is forced by…
We define transgressions of arbitrary order, with respect to families of unit-vector fields indexed by a polytope, for the Pfaffian of metric connections for semi-Riemannian metrics on vector bundles. We apply this formula to compute the…
We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition…
Girth-regular graphs with equal girth, regular degree and chromatic index are studied for the determination of 1-factorizations with each 1-factor intersecting every girth cycle. Applications to hamiltonian decomposability and to…
We present new expressions of form factors of the XXZ model which satisfy Smirnov's three axioms. These new form factors are obtained by acting the affine quantum group $U_q (\hat{\frak s \frak l_2})$ to the known ones obtained in our…
In this paper, we define deformed Schouten-Van Kampen connections which are metric connections and compute sub-Riemannian limits of Gaussian curvature for a Euclidean C2-smooth surface associated to deformed Schouten-Van Kampen connections…