Transverse Takahashi Identities and Their Implications for Gauge Independent Dynamical Chiral Symmetry Breaking

In this article, we employ transverse Takahashi identities to impose valuable non-perturbative constraints on the transverse part of the fermion-photon vertex in terms of new form factors, the so called $Y_i$ functions. We show that the implementation of these identities is crucial in ensuring the correct local gauge transformation of the fermion propagator and its multiplicative renormalizability. Our construction incorporates the correct symmetry properties of the $Y_i$ under charge conjugation operation as well as their well-known one-loop expansion in the asymptotic configuration of incoming and outgoing momenta. Furthermore, we make an explicit analysis of various existing constructions of this vertex against the demands of transverse Takahashi identities and the previously established key features of quantum electrodynamics, such as gauge invariance of the critical coupling above which chiral symmetry is dynamically broken. We construct a simple example in its quenched version and compute the mass function as we vary the coupling strength and also calculate the corresponding anomalous dimensions $\gamma_m$. There is an excellent fit to the Miransky scalling law and we find $\gamma_m=1$ rather naturally in accordance with some earlier results in literature, using arguments based on Cornwall-Jackiw-Tomboulis effective potential technique. Moreover, we numerically confirm the gauge invariance of this critical coupling.Comment: 16 pages, 4 figure

The impact of groundwater drawdown and vacuum pressure on sinkhole development. Physical laboratory models

A considerable proportion of the damaging sinkholes worldwide correspond to human-induced subsidence events related to groundwater withdrawal and the associated water-table decline (e.g. aquifer overexploitation, dewatering for mining). Buoyancy loss in pre-existing cavity roofs is generally claimed to be the main underlying physical mechanism. It has been also postulated that rapid water-table drawdowns may create a vacuum effect in the subsurface and contribute to enhance sinkhole activity in karstic terrains with a low effective porosity cover. Our laboratory physical model explores the role played by vacuum pressure induced water-table drops with different magnitudes and rates on sinkhole development, simulating an invariable mantled karst comprising cavernous bedrock and a low-permeability cover. The multiple tests performed include real-time monitoring of the water level drawdown (magnitude, duration, rate), the negative air pressures in the bedrock cavity and the cover, and several features of the subsidence phenomena (deformation style, size, magnitude, rate). The main findings derived from the test results include: (1) Vacuum pressure may trigger the development of cover collapse sinkholes in areas with low-permeability covers. (2) Different water-table decline patterns (magnitude, duration, rate) may result in different subsidence styles or rheological behaviours: sagging versus collapse. (3) Ground fissuring, frequently related to extension at the margin of sagging depressions, may cancel or significantly diminish the vacuum effect. (4) An overall direct relationship between the water-table decline rate and the subsidence rate. Some possible strategies are proposed to ameliorate the adverse effect of the negative air pressure on sinkhole hazard, which most probably has a local impact restricted by the concurrence of rapid water drawdowns and low-permeability covers

Time After Time: Notes on Delays In Spiking Neural P Systems

Spiking Neural P systems, SNP systems for short, are biologically inspired computing devices based on how neurons perform computations. SNP systems use only one type of symbol, the spike, in the computations. Information is encoded in the time differences of spikes or the multiplicity of spikes produced at certain times. SNP systems with delays (associated with rules) and those without delays are two of several Turing complete SNP system variants in literature. In this work we investigate how restricted forms of SNP systems with delays can be simulated by SNP systems without delays. We show the simulations for the following spike routing constructs: sequential, iteration, join, and split.Comment: 11 pages, 9 figures, 4 lemmas, 1 theorem, preprint of Workshop on Computation: Theory and Practice 2012 at DLSU, Manila together with UP Diliman, DLSU, Tokyo Institute of Technology, and Osaka universit

A Low-Complexity and Asymptotically Optimal Coding Strategy for Gaussian Vector Sources

In this paper, we present a low-complexity coding strategy to encode (compress) finite-length data blocks of Gaussian vector sources. We show that for large enough data blocks of a Gaussian asymptotically wide sense stationary (AWSS) vector source, the rate of the coding strategy tends to the lowest possible rate. Besides being a low-complexity strategy it does not require the knowledge of the correlation matrix of such data blocks. We also show that this coding strategy is appropriate to encode the most relevant Gaussian vector sources, namely, wide sense stationary (WSS), moving average (MA), autoregressive (AR), and ARMA vector sources

On the asymptotic optimality of a low-complexity coding strategy for WSS, MA, and AR vector sources

In this paper, we study the asymptotic optimality of a low-complexity coding strategy for Gaussian vector sources. Specifically, we study the convergence speed of the rate of such a coding strategy when it is used to encode the most relevant vector sources, namely wide sense stationary (WSS), moving average (MA), and autoregressive (AR) vector sources. We also study how the coding strategy considered performs when it is used to encode perturbed versions of those relevant sources. More precisely, we give a sufficient condition for such perturbed versions so that the convergence speed of the rate remains unaltered

Quantum measurements and delays in scattering by zero-range potentials

Eisenbud-Wigner-Smith delay and the Larmor time give different estimates for the duration of a quantum scattering event. The difference is most pronounced in the case where de-Broglie wavelength is large compared to the size of the scatterer. We use the methods of quantum measurement theory to analyse both approaches, and to decide which one of them, if any, describes the duration a particle spends in the region which contains the scattering potential. The cases of transmission, reflection and three-dimensional elastic scattering are discussed in some detail