Structured optimization problems are ubiquitous in fields like data science and engineering. The goal structured is using a prescribed set of points, called atoms, to build up solution that minimizes or maximizes given function. In the present paper, we want minimize black-box function over convex hull problem can be used model number real-world applications. We focus on whose solutions sparse,...

It is well known that, for context-free grammars, a leftmost derivation of a sentence univocally defines its syntactical tree; the construction of this tree consists of an iterative procedure during which two successive strings in the leftmost derivation are compared (see, e.g., [1, 2]). These -o r similar--properties do not hold for leftmost derivations in general phrase-structure grammars [3-...

We study the size distribution of spontaneous knots on semiflexible chains confined in square cross-section channels using Monte Carlo simulations. The most probable knot size, i.e. the metastable knot size, is found to vary nonmonotonically with the channel size. In the case of weak confinement, the metastable knot size is larger than the knot size in bulk because the segments within the knot ...

This paper focuses on modeling of a coupled magnetoelastic problem. The model for magnetostriction is developed for isotropic ferromagnetic materials commonly used in electrical machines. The constitutive equations of the model are written on the basis of the Helmholtz free energy in which the strain tensor and the magnetic flux density vector are chosen as the basic variables. Numerical soluti...

Periodic microphases universally emerge in systems for which short-range inter-particle attraction is frustrated by long-range repulsion. The morphological richness of these phases makes them desirable material targets, but our relatively coarse understanding of even simple models hinders controlling their assembly. We report here the solution of the equilibrium phase behavior of a microscopic ...

For pure SU(N) gauge theory without quarks ’t Hooft’s gauge invariant electric and magnetic fluxes [1] describe, respectively, the effect of a static fundamental color charge and a center monopole in a finite volume. The partition function of a certain amount of electric/magnetic flux yields the free energy of a static electric/magnetic charge with boundary conditions to imitate the presence of...

Treebanks are a valuable resource for the training of parsers that perform automatic annotation of unseen data. It has been shown that changes in the representation of linguistic annotation have an impact on the performance of a certain annotation task. We focus on the task of Topological Field Parsing for German using Probabilistic Context-Free Grammars in the present research. We investigate ...

It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a simpler proof of this result by using approximate solutions in the Parisi formula and give one example of application of differentiability to prove non self-averaging of the overlap outside of the...