相关论文: Efficient construction of contact coordinates for …
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
We investigate constrained quantum motion on curves and surfaces using connection factorization methods. We show that Laplace operators admit an exact half-connection factorization generated by connection one-forms. The first-order part of…
Recent research on accelerated gradient methods of use in optimization has demonstrated that these methods can be derived as discretizations of dynamical systems. This, in turn, has provided a basis for more systematic investigations,…
This paper studies distributed algorithms for the extended monotropic optimization problem, which is a general convex optimization problem with a certain separable structure. The considered objective function is the sum of local convex…
Nielsen, et al. [1, 2] proposed a view of quantum computation where determining optimal algorithms is equivalent to extremizing a geodesic length or cost functional. This view of optimization is highly suggestive of an action principle of…
Self-organizing maps (SOM) are widely used for their topology preservation property: neighboring input vectors are quantified (or classified) either on the same location or on neighbor ones on a predefined grid. SOM are also widely used for…
Our study of Goursat distributions originates new types of $k$-contact distributions and Lie systems with applications. In particular, families of generators for Goursat distributions on $\mathbb{R}^4, \mathbb{R}^5$ and $\mathbb{R}^6$ give…
For an embedded conformal hypersurface with boundary, we construct critical order local invariants and their canonically associated differential operators. These are obtained holographically in a construction that uses a singular Yamabe…
We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bond-bond…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
Let $M^3 \subset \mathbb{C}^2$ be a $\mathcal{C}^\omega$ Levi nondegenerate hypersurface. In the literature, Cartan-Moser chains are detected from rather advanced considerations: either from the construction of a Cartan connection…
We extend the construction of GAG codes to the case of evaluation codes. We estimate the minimum distance of these extended evaluation codes and we describe the connection to the one-point GAG codes.
We derive a general expression for the streaming term in radiative transport equa- tions and other transport problems when formulated in curvilinear coordinates, emphasizing coordinate systems adapted to the geometry of the domain and the…
High-efficient direct numerical methods are currently in demand for optimization procedures in the fields of both conventional diffractive and metasurface optics. With a view of extending the scope of application of the previously proposed…
We propose a sharp and conservative 3D numerical method for simulating moving contact lines on complex geometries, developed within a coupled geometric Volume-of-Fluid (VOF) and embedded boundary framework. The first major contribution is a…
Coordinate descent methods have considerable impact in global optimization because global (or, at least, almost global) minimization is affordable for low-dimensional problems. Coordinate descent methods with high-order regularized models…
A number of prototypical optimization problems in multi-agent systems (e.g., task allocation and network load-sharing) exhibit a highly local structure: that is, each agent's decision variables are only directly coupled to few other agent's…
In this article I propose a new method for reducing a co-oriented contact manifold M equipped with an action of a Lie group G by contact transformations. With a certain regularity and integrality assumption the contact quotient $M_\mu$ at…
This papers studies multi-agent (convex and \emph{nonconvex}) optimization over static digraphs. We propose a general distributed \emph{asynchronous} algorithmic framework whereby i) agents can update their local variables as well as…
In this chapter we show that chordal structure can be used to devise efficient optimization methods for many common model predictive control problems. The chordal structure is used both for computing search directions efficiently as well as…