We establish a connection between the concept of distinguishability of quantum states and the concept of continuity in geometric symmetry. For this purpose, we employ the continuous symmetry measure and the nuclear wave functions of a molecule, and evaluate the physical effects of deviation from geometric symmetry. We apply this tool in presenting a unified approach to assigning symmetry number...

1. Abstract Structural topology optimization often leads to slender structures which are sensitive to geometric imperfections such as the misplacement of material. A robust approach is therefore presented in order to take into account material misplacement in topology optimization problems. A probabilistic approach to robust optimization is followed. Spatially varying geometric imperfections ar...

In this contribution we introduce a model quality measure called Modal Coherence Indicators which gives a complement to traditional model validation techniques. The indicators are derived by a geometric comparison of the model induced observability and controllability matrices with the data induced ones using a common description basis.

The modeling of the historical architecture can be characterized by different levels geometric development, more or less advanced, which correspond to values deviation between real object and its three-dimensional representation. aim paper is a critical study geometry (LoG) that architectural elements model have in relation efforts required achieve them objectives. More specifically, contributi...

In this paper (based on my tutorial in Utrecht) I want to discuss some themes from contemporary model theory, mainly originating in stability theory and classification theory, and point out some mathematical implications. Model theory has become largely the study of definable sets (or the category of definable sets and functions) in given structures, as well as the study of interpretability and...

Current neutrino oscillation data from solar, atmospheric, and reactor experiments are consistent with the neutrino mixing matrix elements taking values sin θ12 = 1/3, sin θ23 = 1/2, and sin 2 θ13 = 0. We present a class of renormalizable gauge models which realize such a geometric mixing pattern naturally. These models, which are based on the non–Abelian discrete symmetry A4, place significant...

Contrasting “geometric fitting”, for which the noise level is taken as the asymptotic variable, with “statistical inference”, for which the number of observations is taken as the asymptotic variable, we give a new definition of the “geometric AIC” and the “geometric MDL” as the counterparts of Akaike’s AIC and Rissanen’s MDL. We discuss various theoretical and practical problems that emerge fro...

This paper presents a design approach for a magnetic sensor module to detect mover position using the proper orthogonal decomposition-dynamic mode decomposition (POD-DMD)-based nonlinear parametric model order reduction (PMOR). The parameterization of the sensor module is achieved by using the multipolar moment matching method. Several geometric variables of the sensor module are considered whi...

Abstract 1: CMAQ is a numerical air quality model which gives concentration of various air pollutants at several different scales. Our main interest is to model the conditional distribution of high resolution output (96 by 96 in space,576 hours) given low resolution output (24 by 24 in space, 576 hours). By a Haar Wavelet Packet Transform of high resolution output for each hour, we naturally li...