On Entanglement Measures: Discrete Phase Space and Inverter-Chain Link Viewpoint

In contrast to abstract statistical analyses in the literature, we present a concrete physical diagrammatic model of entanglement characterization and measure with its underlying discrete phase-space physics. This paper serves as a pedagogical treatment of this complex subject of entanglement measures. We review the important inherent concurrence property of entangled qubits, as well as underscore its emergent qubit behavior. From the discrete phase space point of view, concurrence translates to translation symmetry of entangled binary systems in some quantitative measure of entanglement. Although the focus is on bipartite system, the notion is readily extendable to multi-partite system of qubits, as can easily be deduced from the physical inverter-chain link model. A diagrammatic analysis of the entanglement of formation for any multi-partite qubit system is givenComment: 21 pages, 6 figure

Dynamics of Functional Phase Space Distribution in QFT: A Third Quantization and Dynamical Unification of QFT and CMP

We proposed a third quantization scheme to derive the quantum dynamics of the functional phase space distribution in quantum field theory (QFT). The derivation is straightforward and algorithmic. This readily yields the ballistic quantum transport equation of QFT distribution in (p,q)- functional phase space, not in ordinary position-momentum (p,q)-space. Our starting point is the general mixed space representation in QFT. The end result serves as a unification of the quantum superfield transport theory of condensed matter physics (CMP) and QFT. This is summarized in a Table of correspondence. This third quantization scheme may have significance in quantum fluctuation theory of systems with many degrees of freedom. It may have relevance to cosmology: gravity, multi-universes, and Yang-Mills theory.Comment: 24 pages, 0 figures. arXiv admin note: substantial text overlap with arXiv:2204.0769

Multiple solutions to the likelihood equations in the Behrens-Fisher problem

The Behrens-Fisher problem concerns testing the equality of the means of two normal populations with possibly different variances. The null hypothesis in this problem induces a statistical model for which the likelihood function may have more than one local maximum. We show that such multimodality contradicts the null hypothesis in the sense that if this hypothesis is true then the probability of multimodality converges to zero when both sample sizes tend to infinity. Additional results include a finite-sample bound on the probability of multimodality under the null and asymptotics for the probability of multimodality under the alternative

Data-Discriminants of Likelihood Equations

Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. The problem is to maximize the likelihood function with respect to given data on a statistical model. An algebraic approach to this problem is to solve a very structured parameterized polynomial system called likelihood equations. For general choices of data, the number of complex solutions to the likelihood equations is finite and called the ML-degree of the model. The only solutions to the likelihood equations that are statistically meaningful are the real/positive solutions. However, the number of real/positive solutions is not characterized by the ML-degree. We use discriminants to classify data according to the number of real/positive solutions of the likelihood equations. We call these discriminants data-discriminants (DD). We develop a probabilistic algorithm for computing DDs. Experimental results show that, for the benchmarks we have tried, the probabilistic algorithm is more efficient than the standard elimination algorithm. Based on the computational results, we discuss the real root classification problem for the 3 by 3 symmetric matrix~model.Comment: 2 table

Swimming pool deck as environmental reservoir of Fusarium

While investigations on fungal contamination of swimming pools usually focus on dermatophytes, data on other potentially pathogenic molds are scarce. Here, we report the investigation of fungal colonization of the deck surrounding a hospital physical therapy swimming pool. Five series of samples from 8 sites were collected over one year from the pool surroundings. Concomitantly, 58 patients using the swimming pool were examined and samples obtained from those with suspected onychomycosis. All surface samples were positive for fungi, with Fusarium the most frequently recovered from 22 of 27 samples of sites surrounding the pool. Among the outpatients evaluated, two presented with a mixed onychomycosis from which Fusarium and Trichophyton rubrum were isolated. The questions of possible acquisition from the swimming pool area must be considered in both cases as the ungual lesions had developed within the previous three months. This warrants further studies to better understand the epidemiology of potentially pathogenic molds in areas surrounding pools in order to adopt appropriate measures to avoid contamination. This is of particular importance within medical institutions, considering the potential role of Fusarium onychomycosis as a starting point for disseminated infections in immunocompromised patient

Charging effects in the ac conductance of a double barrier resonant tunneling structure

There have been many studies of the linear response ac conductance of a double barrier resonant tunneling structure (DBRTS). While these studies are important, they fail to self-consistently include the effect of time dependent charge density in the well. In this paper, we calculate the ac conductance by including the effect of time dependent charge density in the well in a self-consistent manner. The charge density in the well contributes to both the flow of displacement currents and the time dependent potential in the well. We find that including these effects can make a significant difference to the ac conductance and the total ac current is not equal to the average of non-selfconsitently calculated conduction currents in the two contacts, an often made assumption. This is illustrated by comparing the results obtained with and without the effect of the time dependent charge density included properly