Related papers: On the number of populations of critical points of…

Estimating the score function (or other population-density-dependent functions) is a fundamental component of most generative models. However, such function estimation is computationally and statistically challenging. Can we avoid function…

We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors in the GL(3)-based quantum integrable…

We consider the nonconvex optimization problem associated with the decomposition of a real symmetric tensor into a sum of rank-one terms. Use is made of the rich symmetry structure to construct infinite families of critical points…

We study the algebraicity of the central critical values of twisted triple product $L$-functions associated to motivic Hilbert cusp forms over a totally real \'etale cubic algebra in the totally unbalanced case. The algebraicity is…

$k$-point crossover operators and their recombination sets are studied from different perspectives. We show that transit functions of $k$-point crossover generate, for all $k>1$, the same convexity as the interval function of the underlying…

The $k$-center problem is to choose a subset of size $k$ from a set of $n$ points such that the maximum distance from each point to its nearest center is minimized. Let $Q=\{Q_1,\ldots,Q_n\}$ be a set of polygons or segments in the…

The algebraicity of critical values of triple product $L$-functions in the balanced case was proved by Garrett and Harris, under the assumption that the critical points are on the right and away from center of the critical strip. The…

Let $U_q(\hat{\cal G})$ be an infinite-dimensional quantum affine Lie algebra. A family of central elements or Casimir invariants are constructed and their eigenvalues computed in any integrable irreducible highest weight representation.…

We consider an interacting particle process on a graph which, from a macroscopic point of view, looks like $\Z^d$ and, at a microscopic level, is a complete graph of degree $N$ (called a patch). There are two birth rates: an inter-patch one…

We develop a new method for representing Hilbert series based on the highest weight Dynkin labels of their underlying symmetry groups. The method draws on plethystic functions and character generating functions along with Weyl integration.…

Let $D$ be an open disk of radius $\le 1$ in $\mathbb C$, and let $(\epsilon_n)$ be a sequence of $\pm 1$. We prove that for every analytic function $f: D \to \mathbb C$ without zeros in $D$, there exists a unique sequence $(\alpha_n)$ of…

Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Statistically optimal procedures such as Tukey's median and other estimators based on depth…

A celebrated theorem of M. Heins says that up to post-composition with a M\"obius transformation, a finite Blaschke product is uniquely determined by its critical points. K. Dyakonov suggested that it may interesting to extend this result…

The weight multiplicities of finite dimensional simple Lie algebras can be computed individually using various methods. Still, it is hard to derive explicit closed formulas. Similarly, explicit closed formulas for the multiplicities of…

We define a filtration indexed by the integers on the tensor product of an integrable highest weight module and a loop module for a quantum affine algebra. We prove that the filtration is either trivial or strictly decreasing and give…

We construct irreducible modules V_{\alpha}, \alpha \in \C over W_3 algebra with c = -2 in terms of a free bosonic field. We prove that these modules exhaust all the irreducible modules of W_3 algebra with c = -2. Highest weights of modules…

A theorem of Feigin, Frenkel and Reshetikhin provides expressions for the eigenvalues of the higher Gaudin Hamiltonians on the Bethe vectors in terms of elements of the center of the affine vertex algebra at the critical level. In our…

We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…

Increasing attention is being focussed on the use of symmetry-adapted functions to describe magnetic structures, structural distortions, and incommensurate crystallography. Though the calculation of such functions is well developed,…

Let (X,[\omega]) be a compact Kaehler manifold with a fixed Kaehler class [\omega]. Let K_\omega be the set of all Kaehler metrics on X whose Kaehler class equals [\omega]. In this paper we investigate the critical points of the functional…