Invariant and polynomial identities for higher rank matrices

We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct discriminants and the determinant as the discriminant of order $d$, where $d$ is the dimension of the matrix. The characteristic polynomials and the Cayley--Hamilton theorem for higher rank matrices are obtained there from

Universal field equations for metric-affine theories of gravity

We show that almost all metric--affine theories of gravity yield Einstein equations with a non--null cosmological constant $\Lambda$. Under certain circumstances and for any dimension, it is also possible to incorporate a Weyl vector field $W_\mu$ and therefore the presence of an anisotropy. The viability of these field equations is discussed in view of recent astrophysical observations.Comment: 13 pages. This is a copy of the published paper. We are posting it here because of the increasing interest in f(R) theories of gravit

Keeping Promises: Municipal communities struggle to fulfill promises to narrow the digital divide with Municipal Community Wireless Networks

Some public elites assert that the digital divide is a serious social problem and that governments must intervene by affording wireless solutions to improve this social ill.  Few studies, however, examine the relationship between the claims-making activities around such interventions, specifically in reference to closing the digital divide, and the perceptions of the actual impact of those initiatives on this divide.  We bring together two data sets.  The first dataset is from a previous study examining the public rhetoric surrounding these initiatives vis-à-vis the digital divide.  The latter is part of a much larger study on the network’s impact on the divide.  We conclude that these networks are necessary but insufficient in bridging the gap

Phylogenetic analyses reveal a new old introduced red algal species in Europe

The detection of invasive species is commonly challenging in marine environments, often related with the insufficient taxonomic knowledge of the local diversity. Using DNA sequences in diversity surveys and their phylogenetic analysis can assist us to clarify the native or introduced origin of some species. We applied this approach to study the red algae Aphanocladia stichidiosa. It was originally described in the Mediterranean (1955), later recorded in Portugal (1960), the Canary Islands (1986), the northwestern Spain (1990) and the Azores (2012). Unexpectedly, our diversity surveys in Australia revealed its presence in Victoria in 2015, finding that European and Australian specimens had identical DNA sequences (rbcL gene) and suggesting that it is introduced in one of the regions. Phylogenetic analysis resolved A. stichidiosa in a highly supported clade with species restricted to the southern hemisphere, mainly from Australia. Accordingly, we conclude that A. stichidiosa is native from Australia, although it has never been recorded there before, and that it represents a relatively old introduction in Europe. In both native and introduced regions, it is frequent in algal turfs, a type of assemblage composed by a carpet of small, morphologically similar species whose identification is often difficult. The type of growth of this species explains the absence of previous records in Australia, where the number of taxonomists studying this assemblage is lower than in Europe. Sequential reports of A. stichidiosa in different European regions suggest that it is expanding its distribution, as well as its abundance is increasing. The invasive character of this species needs to be determined yet, and its small size should not lead to underestimate its potential harmfulness. In the current context, in which kelp forests are globally declining and algal turfs are expanding, this species might play a relevant role in the transformation of the European marine ecosystems

When Protests go Virtual: How Organizing Social Protest in Virtual Worlds Changes the Nature of Organizing

In this paper, we introduce a case study of social protest that has occurred in the virtual world Second Life. This case is a labor strike that occurred against IBM by Italian employees and a large European labor union. We begin with identifying the four key elements in the protest organizing process: Identifying Supporters, Organizing and Establishing Hierarchy, Getting the Word Out, and Building Solidarity/Establishing Social Networks. Next, we briefly examine how non-virtual technologies have changed the protest organizing process. Finally, we present our case data and illustrate how moving a protest to a fully virtual environment changes the organizing process. We conclude by asserting that three aspects fundamentally change protest organizing: entertainment, costs, and culture

S-matrix poles and the second virial coefficient

For cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S-matrix is meromorphic. We can express it in terms of its poles, and then calculate the quantum mechanical second virial coefficient of a neutral gas. Here, we take another look at this approach, and discuss the feasibility, attraction and problems of the method. Among concerns are the rate of convergence of the 'pole' expansion and the physical significance of the 'higher' poles.Comment: 20 pages, 8 tables, submitted to J. Mol. Phy

Mesoscopic Model for Free Energy Landscape Analysis of DNA sequences

A mesoscopic model which allows us to identify and quantify the strength of binding sites in DNA sequences is proposed. The model is based on the Peyrard-Bishop-Dauxois model for the DNA chain coupled to a Brownian particle which explores the sequence interacting more importantly with open base pairs of the DNA chain. We apply the model to promoter sequences of different organisms. The free energy landscape obtained for these promoters shows a complex structure that is strongly connected to their biological behavior. The analysis method used is able to quantify free energy differences of sites within genome sequences.Comment: 7 pages, 5 figures, 1 tabl

On the geometry of four qubit invariants

The geometry of four-qubit entanglement is investigated. We replace some of the polynomial invariants for four-qubits introduced recently by new ones of direct geometrical meaning. It is shown that these invariants describe four points, six lines and four planes in complex projective space ${\bf CP}^3$. For the generic entanglement class of stochastic local operations and classical communication they take a very simple form related to the elementary symmetric polynomials in four complex variables. Moreover, their magnitudes are entanglement monotones that fit nicely into the geometric set of $n$-qubit ones related to Grassmannians of $l$-planes found recently. We also show that in terms of these invariants the hyperdeterminant of order 24 in the four-qubit amplitudes takes a more instructive form than the previously published expressions available in the literature. Finally in order to understand two, three and four-qubit entanglement in geometric terms we propose a unified setting based on ${\bf CP}^3$ furnished with a fixed quadric.Comment: 19 page