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We use Levy processes to generate joint prior distributions, and therefore penalty functions, for a location parameter as p grows large. This generalizes the class of local-global shrinkage rules based on scale mixtures of normals,…
Deformed generalized gauge groups, whch were created from physical considerations and made it possible to clarify some long-standing problems in physics, such as the problem of motion and the problem of the energy of the gravitational…
Series-parallel networks are a class of graphs on which many NP-hard problems have tractable solutions. In this paper, we examine performance measures on leader-follower consensus on series-parallel networks. We show that a distributed…
The Altarelli-Parisi-Lipatov equations for the parton distribution functions are rederived using the dynamical renormalization group approach to quantum kinetics. This method systematically treats the ln Q^2 corrections that arises in…
This is a survey of several exciting recent results in which techniques originating in the area known as additive combinatorics have been applied to give results in other areas, such as group theory, number theory and theoretical computer…
There has been substantial work studying consensus problems for which there is a single common final state, although there are many real-world complex networks for which the complete consensus may be undesirable. More recently, the concept…
Convergence of non-uniform spherical averages is obtained for measure-preserving actions of free groups. This result generalizes theorems of Grigorichuk, Nevo and Stein [in particular, a simpler proof of the Nevo-Stein theorem about uniform…
We describe a new method to formulate classical Lagrangian mechanics on a finite-dimensional Lie group. This new approach is much more pedagogical than many previous treatments of the subject, and it directly introduces students to…
We propose new abstract and unified perspectives on a range of scheduling and graph coloring problems with general min-sum objectives. Specifically, we consider various problems where the objective function is the weighted sum of completion…
The field theoretic renormalization group is applied to a simple model of random walk on a rough fluctuating surface. We consider the Fokker--Planck equation for a particle in a uniform gravitational field. The surface is modelled by the…
The hypercontractive inequality is a fundamental result in analysis, with many applications throughout discrete mathematics, theoretical computer science, combinatorics and more. So far, variants of this inequality have been proved mainly…
We consider the group lasso penalty for the linear model. We note that the standard algorithm for solving the problem assumes that the model matrices in each group are orthonormal. Here we consider a more general penalty that blends the…
Given a free and proper action of a groupoid on a Fell bundle (over another groupoid), we give an equivalence between the semidirect-product and the generalized-fixed-point Fell bundles, generalizing an earlier result where the action was…
This paper presents a series of general results about the optimal estimation of physical transformations in a given symmetry group. In particular, it is shown how the different symmetries of the problem determine different properties of the…
We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of…
We develop new sub-optimality bounds for gradient descent (GD) that depend on the conditioning of the objective along the path of optimization rather than on global, worst-case constants. Key to our proofs is directional smoothness, a…
In the heavy quark limit of QCD, using the Operator Product Expansion and the non-forward amplitude, as proposed by Nikolai Uraltsev, we formulate sum rules that generalize Bjorken and Uraltsev sum rules. We recover the Uraltsev lower bound…
Using the machinery of smooth scaling and coarse-graining of observables, developed recently in the context of so-called fluctuation operators (originally developed by Verbeure et al), we extend this approach to a rigorous renormalisation…
A survey of finite group actions on symplectic 4-manifolds is given with a special emphasis on results and questions concerning smooth or symplectic classification of group actions, group actions and exotic smooth structures, and…
In his $1994$ survey, Kleinert defined formally and formulated the problem to obtain unit theorems for unit groups of orders in a semisimple algebra $A$. If $A$ is a group algebra $FG$, it boils down to classifying all finite groups $G$…