Let H be an n-generated numerical semigroup such that its tangent cone grmK[H] is defined by quadratic relations. We show that if n < 5 then grmK[H] is CohenMacaulay, and for n = 5 we explicitly describe the semigroups H such that grmK[H] is not Cohen-Macaulay. As an application we show that if the field K is algebraically closed and of characteristic different from two, and n 6 5 then grmK[H] ...

We say that a system of functions is hodograph diminishing if the tangent directions of the curve are contained in the cone generated by the sides of the control polygon. We characterize such systems and conclude that Bézier curves, B-spline curves and, more generally, curves generated by totally positive bases are hodograph diminishing. A characterization is also found for rational curves. Hod...

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation, and noisy matrix completion. We propose computationally feasible convex programs for statistical inference including estimation, confidence interv...

With the aid of some novel complementarity constraint quali cations, we derive some simpli ed primal-dual characterizations of a B-stationary point for a mathematical program with complementarity constraints (MPEC). The approach is based on a locally equivalent piecewise formulation of such a program near a feasible point. The simpli ed results, which rely heavily on a careful dissection and im...

Yves Bouligand's analysis of the organizations of biological materials in relation to those of liquid crystals enabled the development of the idea that physical forces exerting their actions under strong spatial constraints determine the structures and morphologies of these materials. The different levels of organization in collagen have preoccupied him for a long time. We present here our rece...

We prove a conjecture by Kreiman and Lakshmibai on a combinatorial description of multiplicities of points on Schubert varieties in Graßmannians in terms of certain sets of reflections in the corresponding Weyl group. The proof is accomplished by relating these sets of reflections to the author’s previous combinatorial interpretation of these multiplicities in terms of non-intersecting lattice ...

Eigenvalues of a potential dynamical system with damping forces that are described by an indefinite real symmetric matrix can behave as those of a Hamiltonian system when gain and loss are in a perfect balance. This happens when the indefinitely damped system obeys parity-time ( ) symmetry. How do pure imaginary eigenvalues of a stable -symmetric indefinitely damped system behave when variation...

We extend an efficient cone beam transform inversion formula, proposed earlier by one of the authors for helices, to a general class of curves. The conditions that describe the class are very natural. Curves C are smooth, without self-intersections, have positive curvature and torsion, do not bend too much, and do not admit lines which are tangent to C at one point and intersect C at another po...

A Richardson variety X α in the Orthogonal Grassmannian is defined to be the intersection of a Schubert variety X in the Orthogonal Grassmannian and an opposite Schubert variety X α therein. We give an explicit description of the initial ideal (with respect to certain conveniently chosen term order) for the ideal of the tangent cone at any T-fixed point of X α , thus generalizing a result of Ra...

For complex parameters a, c, we consider the Hénon mapping Ha,c : C → C, given by (x, y) 7→ (x + c−ay, x), and its Julia set, J . In this paper, we describe a rigorous computer program for attempting to construct a cone field in the tangent bundle over J , which is preserved by DH, and a continuous norm in which DH (and DH) uniformly expands the cones (and their complements). We show a conseque...