Definition of the determinant of Euclidean Dirac operator in the nontrivial sector of gauge fields suffers from an inherent ambiguity. The popular Osterwalder-Schrader (OS) recipe for the conjugate Dirac field leads to the option of a vanishing determinant. We propose a novel representation for the conjugate field which depends linearly on the Dirac field and yields a nonvanishing determinant i...

Separation of independent sources using independent component analysis (ICA) requires prior knowledge of the number of independent sources. Performing ICA when the number of recordings is greater than the number of sources can give erroneous results. To improve the quality of separation, the most suitable recordings have to be identified before performing ICA. Techniques employed to estimate su...

We study the necessary and sufficient conditions on Abelianizable first class constraints. The necessary condition is derived from topological considerations on the structure of gauge group. The sufficient condition is obtained by applying the theorem of implicit function in calculus and studying the local structure of gauge orbits. Since the sufficient condition is necessary for existence of p...

We prove that if φ : R × R → R, d ≥ 2, is a homogeneous function, smooth away from the origin and having nonzero Monge–Ampere determinant away from the origin, then R#{(n,m) ∈ Z × Z : |n|, |m| ≤ CR;R ≤ φ(n,m) ≤ R+ δ} . max{R 2 d+1 , Rδ}. This is a variable coefficient version of a result proved by Lettington, 2010, extending a previous result by Andrews, 1963, showing that if B ⊂ R, d ≥ 2, is a...

Liquidity, the ease of trading an asset, strongly varies between di erent sizes of stock positions. We analyze this aspect using the Xetra Liquidity Measure (XLM), which calculates daily, weighted spread for impatient traders transacting against the limit order book. For this measure, we have data for 160 German stocks over 5.5 years, which allows us a representative analysis of the order-size ...

We study properties of a generalization of the Mahler measure to elements in group rings, in terms of the Lück-Fuglede-Kadison determinant. Our main focus is the variation of the Mahler measure when the base group is changed. In particular, we study how to obtain the Mahler measure over an infinite group as limit of Mahler measures over finite groups, for example, in the classical case of the f...

The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of a weight q per connected component of meander translates into a bilinear form on the algebra, with a Gram matrix encoding the fine structure of meander numbers. Here, we calculate the associated Gram deter...

Abstract: Based on a computational procedure for determining the functional derivative with respect to the density of any antisymmetric N-particle wave function for a non-interacting system that leads to the density, we devise a test as to whether or not a wave function known to lead to a given density corresponds to a solution of a Schrödinger equation for some potential. We examine explicitly...

Using techniques from hopping expansion we identically map the lattice Schwinger model with Wilson fermions to a model of oriented loops on the lattice. This is done by first computing the explicit form of the fermion determinant in the external field. Subsequent integration of the gauge fields renders a sum over all loop configurations with simple Gaussian weights depending on the number of pl...

While many studies have found that perceived usefulness—an extrinsic motivator—is the strongest determinant of using utilitarian systems, others have found that it is less important than perceived enjoyment—an intrinsic motivator—in predicting hedonic system usage. In light of these interesting but mixed findings, our research applies the motivation theory to investigate the effects of extrinsi...