A contact process with a semi-infected state on the complete graph

In this paper, we are concerned with a contact process with a semi-infected state on the complete graph C_n with n vertices. Our model is a special case of a general model introduced by Schinazi in 2003. In our model, each vertex is in one of three states, namely, “healthy,” “semi-infected,” or “fully-infected.” Only fully-infected vertices can infect others. A healthy vertex becomes semi-infected when being infected while a semi-infected vertex becomes fully-infected when being further infected. Each (semi- and fully-) infected vertex becomes healthy at constant rate. Our main result shows a phase transition for the waiting time until extinction of the fully-infected vertices. Conditioned on all the vertices are fully-infected when t = 0, we show that fully-infected vertices survive for exp?{O(n)} units of time when the infection rate λ > 4 while they die out in O(log?n) units of time when λ < 4.     

Joint impact of nodes-mobility and channel estimation error on the performance of two-way relay systems

This paper presents the performance analysis of a two-way relay system with nodes-mobility (NM) and channel estimation errors (CEE) under time-varying Rayleigh fading. Herein, analog network coding protocol is employed at the relay node. All the participating nodes are half-duplex and equipped with single-antenna devices. Specifically, we utilize first-order Markovian model to characterize the impact of NM in the channel. Along with the NM, we also consider that the CEE may exist in practical scenarios, where nodes require to estimate the channel state information. By incorporating these factors, we first derive the instantaneous end-to-end (e2e) signal-to-noise ratios (SNRs) at two source nodes. Then, we obtain the exact closed-form expressions for distribution and density functions of the two e2e SNRs. After that, we derive the accurate expressions of various performance metrics, viz., sum-bit error rate, overall outage probability, and ergodic sum-rate. Further, to attain more insights into the considered system, we deduce the asymptotic behavior of these performance metrics. Finally, numerical and Monte-Carlo simulation results are provided to validate our theoretical analysis and to illustrate the impact of NM and CEE on the performance measures of the considered system.     

A new class of multi-wavelet bases: V-system

The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite number of continuous and discontinuous functions. The V-system has interesting properties, such as orthogonality, symmetry, completeness and short compact support. It is shown in this paper that the V-system is essentially a special multi-wavelet basis. As a result, some basic properties of the V-system are established through the well-developed theory of multi-wavelets. From this point of view, more other V-systems are constructed.     

Gauss’ law of error revisited in the framework of Sharma-Taneja-Mittal information measure

We reformulate the Gauss’ law of error in presence of correlations which are taken into account by means of a deformed product arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an asymptotic power-law behavior.      

Super-symmetric informationally complete measurements

Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is intimately connected with the geometry of the quantum state space and also has profound implications for foundational studies. Here we explore those SICs that are most symmetric according to a natural criterion and show that all of them are covariant with respect to the Heisenberg–Weyl groups, which are characterized by the discrete analog of the canonical commutation relation. Moreover, their symmetry groups are subgroups of the Clifford groups. In particular, we prove that the SIC in dimension 2, the Hesse SIC in dimension 3, and the set of Hoggar lines in dimension 8 are the only three SICs up to unitary equivalence whose symmetry groups act transitively on pairs of SIC projectors. Our work not only provides valuable insight about SICs, Heisenberg–Weyl groups, and Clifford groups, but also offers a new approach and perspective for studying many other discrete symmetric structures behind finite state quantum mechanics, such as mutually unbiased bases and discrete Wigner functions.     

The Wigner–Yanase information can increase under phase sensitive incoherent operations

We found that the Wigner-Yanase skew information, which has been recently proposed as a measure of coherence in Girolami (2014), can increase under a class of operations which may be interpreted as incoherent following the framework of Baumgratz et al., while being phase sensitive.     

Integrated Access to Genomic and Other Bioinformation: An Essential Ingredient of the Drug Discovery Process

Abstract

Due to the high rate of data production and the need of researchers to have rapid access to new data, public databases have become the major medium through which genome mapping and sequencing data as well as macromolecular structural data are published. There are now more than 250 databases of biomolecular, structural, genetic, or phenotypic data, many of which are doubling in size annually. These databases, many of which were created and are maintained by experimentalists for their own research use, provide valuable collections of organized, validated data. However, the very number and diversity of databases now make efficient data resource discovery as important as effective data resource use. Existing autonomous biological databases contain related data which are more valuable when interconnected than when isolated. Political and scientific realities dictate that these databases will be built by different teams, in different locations, for different purposes, and using different data models and supporting DBMSs. As a consequence, connecting the related data they contain is not straightforward. Experience with existing biological databases indicates that it is possible to form useful queries across these databases, but that doing so usually requires expertise in the semantic structure of each source database. Advancing to the next level of integration among biological information resources poses significant technical and sociological challenges.     

Avoiding problems with hydrogen misplacement in reporting crystal structures

Intermolecular hydrogen bonding is an integral part of many crystal structures. Hydrogen bonding sometimes results in one‐, two‐ or three‐dimensional supramolecular assemblies, a common feature of which is positional disorder of H atoms related to space‐group symmetry. Yet some reported structures fail to include all possible donor–acceptor close contacts, or to seek H‐atom electron densities associated with apparent D—H...A trios, while some H‐atom positions violate principles of chemistry or crystal physics. Modern diffraction equipment and sophisticated computing systems provide high‐quality data; thus, failure to characterize and report fully an accurate, complete and physically correct hydrogen‐bonding model should not be acceptable. We illustrate the relevant issues with three published examples in the hope of slowing the proliferation of these problems, with the scientifically desirable goal of improving the accuracy of crystallographic models while also providing improved search keys for information retrieval.     

Channel capacities via p-summing norms

In this paper we show how the metric theory of tensor products developed by Grothendieck perfectly fits in the study of channel capacities, a central topic in Shannon's information theory. Furthermore, in the last years Shannon's theory has been fully generalized to the quantum setting, and revealed qualitatively new phenomena in comparison. In this paper we consider the classical capacity of quantum channels with restricted assisted entanglement. These capacities include the classical capacity and the unlimited entanglement-assisted classical capacity of a quantum channel. Our approach to restricted capacities is based on tools from functional analysis, and in particular the notion of p  -summing maps going back to Grothendieck's work. Pisier's noncommutative vector-valued _Lp$L_p$ spaces allow us to establish the new connection between functional analysis and information theory in the quantum setting.     

The reduced expressions in a Coxeter system with a strictly complete Coxeter graph

Let (W,S)$(W,S)$ be a Coxeter system with a strictly complete Coxeter graph. The present paper concerns the set Red(z)$\mathrm{Red}(z)$ of all reduced expressions for any z∈W$z\in W$. By associating each bc-expression to a certain symbol, we describe the set Red(z)$\mathrm{Red}(z)$ and compute its cardinal |Red(z)|$|\mathrm{Red}(z)|$ in terms of symbols. An explicit formula for |Red(z)|$|\mathrm{Red}(z)|$ is deduced, where the Fibonacci numbers play a crucial role.