Showing papers on "Antisymmetry published in 2017"

Translation invariance and antisymmetry in the theory of the nucleon optical model

Abstract: The first step in any formalism that aims to connect a many-nucleon theory of nucleon-nucleus scattering and the concept of an optical model potential in the sense pioneered by Feshbach is to explain what is meant by the optical model wave function. By definition, this is a function of a single space coordinate plus a set of single-nucleon internal variables. This article gives a critique of the definition as it is frequently expressed in second quantization language and suggests a new definition which is more consistent with the requirements of antisymmetry and translational invariance. A modification of the time-dependent Green's function formalism is suggested.

Embedding Knowledge Graphs Based on Transitivity and Antisymmetry of Rules

Abstract: Representation learning of knowledge graphs encodes entities and relation types into a continuous low-dimensional vector space, learns embeddings of entities and relation types. Most existing methods only concentrate on knowledge triples, ignoring logic rules which contain rich background knowledge. Although there has been some work aiming at leveraging both knowledge triples and logic rules, they ignore the transitivity and antisymmetry of logic rules. In this paper, we propose a novel approach to learn knowledge representations with entities and ordered relations in knowledges and logic rules. The key idea is to integrate knowledge triples and logic rules, and approximately order the relation types in logic rules to utilize the transitivity and antisymmetry of logic rules. All entries of the embeddings of relation types are constrained to be non-negative. We translate the general constrained optimization problem into an unconstrained optimization problem to solve the non-negative matrix factorization. Experimental results show that our model significantly outperforms other baselines on knowledge graph completion task. It indicates that our model is capable of capturing the transitivity and antisymmetry information, which is significant when learning embeddings of knowledge graphs.

A Note on Huave Morpheme Ordering: Local Dislocation or Generalized U20?

Abstract: This chapter pursues the question whether postsyntactic reordering is a necessary component of UG (as in DM), or (can)not (be) (as in Antisymmetry). A typology of morpheme ordering is developed based on the typology of word order patterns characterized by (Greenberg’s) Universal 20 (U20), modeled by Cinque (Linguistic inquiry 36: 315–332, 2005), and since shown to characterize the typology of word orders in other syntactic domains. Under a syntactic antisymmetry account, morpheme orders are expected to track the syntactic U20 patterns. In syntactic theories without Antisymmetry and with head movement, no such expectations hold, and postsyntactic morpheme reordering must be assumed, If postsyntactic reordering is not available in UG, morpheme orders that have been argued to require postsyntactic reordering in DM should fall within the allowable U20 typology. This chapter looks at a puzzling morpheme order paradigm from Huave, argued by Embick and Noyer (2007), to require postsyntactic local dislocation. It shows that a local dislocation account is ill-motivated, regardless of antisymmetry. This puzzling paradigm turns out to be unremarkable, given the expected U20 syntactic typology. This chapter further develops and tests the antisymmetric U20 account for Huave, and shows that the morpheme alternations can be captured successfully without any need for postsyntactic reordering. It has the advantage of relating specific morpho-syntactic problems to general syntactic configurations, and is shown to extend to capture morpheme order variation within varieties of Huave.

A simple finite-difference scheme for handling topography with the first-order wave equation

Abstract: One approach to incorporate topography in seismic finite-difference codes is a local modification of the difference operators near the free surface. An earlier paper described an approach for modelling irregular boundaries in a constant-density acoustic finite-difference code, based on the second-order formulation of the wave equation that only involves the pressure. Here, a similar method is considered for the first-order formulation in terms of pressure and particle velocity, using a staggered finite-difference discretization both in space and in time. In one space dimension, the boundary conditions consist in imposing antisymmetry for the pressure and symmetry for particle velocity components. For the pressure, this means that the solution values as well as all even derivatives up to a certain order are zero on the boundary. For the particle velocity, all odd derivatives are zero. In 2D, the 1-D assumption is used along each coordinate direction, with antisymmetry for the pressure along the coordinate and symmetry for the particle velocity component parallel to that coordinate direction. Since the symmetry or antisymmetry should hold along the direction normal to the boundary rather than along the coordinate directions, this generates an additional numerical error on top of the time stepping errors and the errors due to the interior spatial discretization. Numerical experiments in 2D and 3D nevertheless produce acceptable results

Symmetry and antisymmetry properties of optimal solutions to regression problems

Abstract: Besides requiring a good fit of the learned model to the empirical data, machine learning problems usually require such a model to satisfy additional constraints. Their satisfaction can be either imposed a-priori, or checked a-posteriori, once the optimal solution to the learning problem has been determined. In this framework, it is proved in the paper that the optimal solutions to several batch and online regression problems (specifically, the Ordinary Least Squares, Tikhonov regularization, and Kalman filtering problems) satisfy, under certain conditions, either symmetry or antisymmetry constraints, where the symmetry/antisymmetry is defined with respect to a suitable transformation of the data. Computational issues related to the obtained theoretical results (i.e., reduction of the dimensions of the matrices involved in the computations of the optimal solutions) are also described. The results, which are validated numerically, have potential application in machine-learning problems such as pairwise binary classification, learning of preference relations, and learning the weights associated with the directed arcs of a graph under symmetry/antisymmetry constraints.

Proposed physical explanation for the electron spin and related antisymmetry

Abstract: We offer a possible physical explanation for the origin of the electron spin and the related antisymmetry of the wave function for a two-electron system, in the framework of nonrelativistic quantum mechanics as provided by linear stochastic electrodynamics. A consideration of the separate coupling of the electron to circularly polarized modes of the random electromagnetic vacuum field, allows to disclose the spin angular momentum and the associated magnetic moment with a $g$-factor 2, and to establish the connection with the usual operator formalism. The spin operator turns out to be the generator of internal rotations, in the corresponding coordinate representation. In a bipartite system, the distinction between exchange of particle coordinates (which include the internal rotation angle) and exchange of states becomes crucial. Following the analysis of the respective symmetry properties, the electrons are shown to couple in antiphase to the same vacuum field modes. This finding, encoded in the antisymmetry of the wave function, provides a physical rationale for the Pauli principle. The extension of our results to a multipartite system is briefly discussed.

Physical basis for the electron spin and antisymmetry: A first-principles explanation

Abstract: We present a possible physical explanation for the origin of both the electron spin and the related antisymmetry of the wave function, in the framework of (nonrelativistic) quantum mechanics as provided by linear stochastic electrodynamics. A separate consideration of the coupling of the electron with circularly polarized modes of the electromagnetic vac- uum, taken as a real fluctuating field, allows to disclose the spin angular momentum and the associated magnetic moment with a g-factor 2, and to establish the connection with the usual operator formalism. Further, in a bipartite system the electrons are shown to couple in antiphase to the same vacuum field modes. This finding, encoded in the antisymmetry of the wave function, provides a physical rationale for the Pauli principle. The extension of our results to a multipartite system is briefly discussed.

Antisymmetry of solutions for some weighted elliptic problems

Abstract: This article concerns the antisymmetry, uniqueness, and monotonicity properties of solutions to some elliptic functionals involving weights and a double well potential. In the one-dimensional case, we introduce the continuous odd rearrangement of an increasing function and we show that it decreases the energy functional when the weights satisfy a certain convexity-type hypothesis. This leads to the antisymmetry or oddness of increasing solutions (and not only of minimizers). We also prove a uniqueness result (which leads to antisymmetry) where a convexity-type condition by Berestycki and Nirenberg on the weights is improved to a monotonicity condition. In addition, we provide with a large class of problems where antisymmetry does not hold. Finally, some rather partial extensions in higher dimensions are also given.