Related papers: Dirac optimal reduction
This paper is devoted to the understanding of regularisation process in the shape optimization approach to the so-called Dirichlet inverse obstacle problem for elliptic operators. More precisely, we study two different regularisations of…
The infinite reduction of couplings is a tool to consistently renormalize a wide class of non-renormalizable theories with a reduced, eventually finite, set of independent couplings, and classify the non-renormalizable interactions. Several…
The article is about a "desingularization principle" common to various canonical desingularization algorithms in characteristic zero, and the roles played by the exceptional divisors in the underlying local construction. We compare…
We present a reduction procedure for gauge theories based on quotienting out the kernel of the presymplectic form in configuration-velocity space. Local expressions for a basis of this kernel are obtained using phase space procedures; the…
In this article, we introduce symplectic reduction in the framework of nonrational toric geometry. When we specialize to the rational case, we get symplectic reduction for the action of a general, not necessarily closed, Lie subgroup of the…
There is still a lot of confusion about "optimal" sharing in the lambda calculus, and its actual efficiency. In this article, we shall try to clarify some of these issues.
The quest for regular models of arithmetic surfaces allows different viewpoints and approaches: using valuations or a covering by charts. In this article, we sketch both approaches and then show in a concrete example, how surprisingly…
We present general reduction procedures for Courant, Dirac and generalized complex structures, in particular when a group of symmetries is acting. We do so by taking the graded symplectic viewpoint on Courant algebroids and carrying out…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
In the distributed optimization problem for a multi-agent system, each agent knows a local function and must find a minimizer of the sum of all agents' local functions by performing a combination of local gradient evaluations and…
We establish a result which states that regularizing an inverse problem with the gauge of a convex set $C$ yields solutions which are linear combinations of a few extreme points or elements of the extreme rays of $C$. These can be…
This paper provides a new algorithm for solving inverse problems, based on the minimization of the $L^2$ norm and on the control of the Total Variation. It consists in relaxing the role of the Total Variation in the classical Total…
The idea of reduction of couplings in renormalizable theories will be presented and then will be applied in Particle Physics models. Reduced couplings appeared as functions of a primary one, compatible with the renormalization group…
This paper focuses on investigating the optimal actuator location for achieving minimum norm controls in the context of approximate controllability for degenerate parabolic equations. We propose a formulation of the optimization problem…
We give a purely algebraic treatment of reduction theory for connections over the formal punctured disc. Our proofs apply to arbitrary connected linear algebraic groups over an algebraically closed field of characteristic 0. We also state…
We develop elliptic regularity theory for Dirac operators in a very general framework: we consider Dirac operators linear over $C^*$-algebras, on noncompact manifolds, and in families which are not necessarily locally trivial fibre bundles.
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
This paper proposes a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalised discrete algebraic Riccati equation. In…
Trace norm regularization is a widely used approach for learning low rank matrices. A standard optimization strategy is based on formulating the problem as one of low rank matrix factorization which, however, leads to a non-convex problem.…
Dropout is a regularization technique widely used in training artificial neural networks to mitigate overfitting. It consists of dynamically deactivating subsets of the network during training to promote more robust representations. Despite…