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In this talk, we first briefly review history of the geometric singular perturbation theory, then talk about the traveling pulses for a diffusive Rosenzweig MacArthur model. We show the existence of t...
In this talk, we first consider convex optimization whose smooth components have a locally Lipschitz continuous gradient and propose a first-order method for finding an epsilon-KKT solution. We then c...
Utilizing approximation algorithm, there has been a large quantity of work on optimization for submodular functions since the 1970s. As a variant, $k$-submodular function appears in many fields to mat...
We derive upper and lower a posteriori estimates for the maximum norm error in nite element solutions of monotone semi-linear equations. The estimates hold for Lagrange elements of any xed order, n...
We consider the least angle regression and forward stagewise algorithms for solving penalized least squares regression problems. In Efron,Hastie, Johnstone & Tibshirani (2004) it is proved that the le...
We also study a condition under which the coefficient paths of the lasso are monotone, and hence the different algorithms coincide. Finally, we compare the lasso and forward stagewise pro...
Some new examples of K-monotone couples of the type (X, X(w)), where X is a symmetric space on [0, 1] and w is a weight on [0, 1], are presented. Based on the property of the w-decomposability of a sy...
Abstract: In this article, we study the notion of genus expansion in the Harish-Chandra-Itzykson-Zuber matrix model. We prove that, under suitable hypotheses, each Taylor coefficient of the HCIZ free ...
Abstract: We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if each of its partial derivatives keep...
Abstract: Motivated by results for the HCIZ integral in Part I of this paper, we study the structure of monotone Hurwitz numbers, which are a desymmetrized version of classical Hurwitz numbers. We pro...
Abstract: We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An ...
We prove the Conley conjecture for negative monotone, closed symplectic manifolds, i.e., the existence of infinitely many periodic orbits for Hamiltonian diffeomorphisms of such manifolds.
Inspired by the theory of analysis on fractals, we construct an example of a continuous, monotone function on an interval, which has vanishing derivatives on a dense set and infinite derivatives on an...
Cauchy's condensation test allows to determine the convergence of a monotone series by looking at a weighted subseries that only involves terms of the original series indexed by the powers of two. It ...
We show by example that there is a Cayley graph and two invariant random subgraphs $X$ and $Y$ of it such that there exists a monotone coupling between them in the sense that $X \subset Y$ but no suc...

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