We present new results for the Frank-Wolfe method (also known as the conditional gradient method). We derive computational guarantees for arbitrary step-size sequences, which are then applied to various step-size rules, including simple averaging and constant step-sizes. We also develop step-size rules and computational guarantees that depend naturally on the warm-start quality of the initial (...

Methods of estimating the difference between exact and approximate solutions are considered for boundary-value problems in spaces of solenoidal functions. The estimates obtained apply to any functions in the energy space of the respective problem, and their computation requires solving only finite-dimensional problems. In the paper, two different methods are considered: one involves variational...

The symbiotic branching model describes the evolution of two interacting populations and if started with complementary Heaviside functions, the interface where both populations are present remains compact. In this paper, we show tightness of the diffusively rescaled solutions and thus provide a first step towards a scaling limit for the interface. The crucial estimate involves a mixed fourth mo...

Gauging is a general procedure for mapping quantum many-body system with global symmetry to one local gauge symmetry. We consider generalized gauging map that does not enforce at all lattice sites, and show it an isometry on the full input space including charged sectors. apply this convert global-symmetric bulk systems of holographic codes gauge-symmetric systems, vice versa, while preserving ...

“T-fold” backgrounds are generically-nongeometric compactifications of string theory, described by T fibrations over a base N with transition functions in the perturbative T-duality group. We review Hull’s doubled torus formalism, which geometrizes these backgrounds, and use the formalism to constrain the D-brane spectrum (to leading order in gs and α ) on T fibrations over S with O(n, n;Z) mon...

Within the generalized thermostatistics of Tsallis, we propose for the spin-1⁄2 Ising ferromagnet a transmissivity variable which extends that defined by Tsallis and Levy for thermal magnetic systems. By using this generalized transmissivity as well as duality arguments, we calculate the q-dependence of the critical temperature corresponding to the square lattice, where q is the entropic index ...

Inspired by previous work on the constraints that duality imposes on beta functions of spin models, we propose a consistency condition between those functions and RG flows at different points in coupling constant space. We show that this consistency holds for a non self-dual model which admits an exact RG flow, but that it is violated when the RG flow is only approximate. We discuss the use of ...

the purpose of this paper is to obtain necessary and suffcient conditionsfor existence approximate fixed point on geraghty-contraction. in this paper,denitions of approximate -pair fixed point for two maps tα , sα and theirdiameters are given in a metric space.

We present new results for the conditional gradient method (also known as the Frank-Wolfe method). We derive computational guarantees for arbitrary step-size sequences, which are then applied to various step-size rules, including simple averaging and constant step-sizes. We also develop step-size rules and computational guarantees that depend naturally on the warm-start quality of the initial (...