Large-N multi-matrix loop equations are formulated as quadratic difference equations in concatenation of gluon correlations. Though non-linear, they involve highest rank correlations linearly. They are underdetermined in many cases. Additional linear equations for gluon correlations, associated to symmetries of action and measure are found. Loop equations aren’t differential equations as they i...

Modeling the flow curves of materials at elevated temperatures is the first step in mathematical simulation of the hot deformation processes of them. In this work a comparative study was provided to examine the capability of three different constitutive equations in modeling the hot deformation flow curves of AZ91 magnesium alloy. For this, the Arrhenius equation with strain dependent constants...

A Poisson algebra is a commutative algebra with a Lie bracket {, } satisfying the Leibniz rule. Such algebras appear in classical mechanics. Namely, functions on the phase space form a Poisson algebra, and Hamilton’s equation of motion is df dt = {f, H}, where H is the Hamiltonian (energy) function. Moreover, the transition from classical to quantum mechanics can be understood in terms of defor...

We study differentiable mixed-moment models (full zeroth and first moment, half higher moments) for a Fokker-Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of full-moment minimum entropy MN models. Realizability theory for these modification of mixed moments is derived for second order. Numerical tests are performed wi...

Abstract. To achieve sparse parametrizations that allows intuitive analysis, we aim to represent deformation with a basis containing interpretable elements, and we wish to use elements that have the description capacity to represent the deformation compactly. To accomplish this, we introduce in this paper higher-order momentum distributions in the LDDMM registration framework. While the zeroth ...

Zeroth-order (derivative-free) optimization attracts a lot of attention in machine learning, because explicit gradient calculations may be computationally expensive or infeasible. To handle large scale problems both in volume and dimension, recently asynchronous doubly stochastic zeroth-order algorithms were proposed. The convergence rate of existing asynchronous doubly stochastic zeroth order ...

The equations of parallel transport for a non-linear connection on phase space are examined. It is shown that, for a free-particle Lagrangian, the connection term first-order in momentum reproduces the geodesic equation of General Relativity and the term zeroth-order in the momentum reproduces the Lorentz electromagnetic force law. Hence from one mathematical expression, a non-linear parallel t...

We consider the problem of optimizing a high-dimensional convex function using stochastic zeroth-order queries. Under sparsity assumptions on the gradients or function values, we present two algorithms: a successive component/feature selection algorithm and a noisy mirror descent algorithm using Lasso gradient estimates, and show that both algorithms have convergence rates that depend only loga...

The distributed-tubes model of hepatic elimination is extended to include intermixing between sinusoids, resulting in the formulation of a new, interconnected-tubes model. The new model is analysed for the simple case of two interconnected tubes, where an exact solution is obtained. For the case of many strongly-interconnected tubes, it is shown that a zeroth-order approximation leads to the co...