We discuss boundary conditions for conformal field theories that preserve the boundary Poincaré invariance. As in the bulk field theories, a question arises whether boundary scale invariance leads to boundary conformal invariance. With unitarity, Cardy’s condition of vanishing momentum flow is necessary for the boundary conformal invariance, but it is not sufficient in general. We show both a p...

This report deals with translation invariance of convolutional neural networks (CNNs) for automatic target recognition (ATR) from synthetic aperture radar (SAR) imagery. In particular, the translation invariance of CNNs for SAR ATR represents the robustness against misalignment of target chips extracted from SAR images. To understand the translation invariance of the CNNs, we trained CNNs which...

In Computable Analysis each computable function is continuous and computably invariant , i.e. it maps computable points to computable points. On the other hand, discontinuity is a suucient condition for non-computability, but a discontinuous function might still be computably invariant. We investigate algebraic conditions which guarantee that a discon-tinuous function is suuciently discontinuou...

‎In this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎We also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.

Data often have a nested, multilevel structure, for example when data are collected from children in classrooms. This kind of data complicate the evaluation of reliability and measurement invariance, because several properties can be evaluated at both the individual level and the cluster level, as well as across levels. For example, cross-level invariance implies equal factor loadings across le...

data envelopment analysis (dea) models with interval inputs and outputs have been rarely discussed in dea literature. this paper, using the enhanced russell measurement proposes an extended model which permits the presence of interval scale variables which can take both negative and positive values. the model is compared with most well-known dea models of which include the ccr model, the bcc mo...

BACKGROUND Nutrition is one of the major determinants of successful aging. The Satisfaction with Food-related Life (SWFL) scale measures a person's overall assessment regarding their food and eating habits. The SWFL scale has been used in older adult samples across different countries in Europe, Asia and America, however, there are no studies that have evaluated the cross-cultural measurement i...