Magnetic structure and phase diagram in a spin-chain system: Ca3_3Co2_2O6_6

The low-temperature structure of the frustrated spin-chain compound Ca$_3$Co$_2$O$_6$ is determined by the ground state of the 2D Ising model on the triangular lattice. At high-temperatures it transforms to the honeycomb magnetic structure. It is shown that the crossover between the two magnetic structures at 12 K arises from the entropy accumulated in the disordered chains. This interpretation is in an agreement with the experimental data. General rules for for the phase diagram of frustrated Ising chain compounds are formulated.Comment: 4 pages, 2 figure

Non-Perturbative U(1) Gauge Theory at Finite Temperature

For compact U(1) lattice gauge theory (LGT) we have performed a finite size scaling analysis on $N_{\tau} N_s^3$ lattices for $N_{\tau}$ fixed by extrapolating spatial volumes of size $N_s\le 18$ to $N_s\to\infty$. Within the numerical accuracy of the thus obtained fits we find for $N_{\tau}=4$, 5 and~6 second order critical exponents, which exhibit no obvious $N_{\tau}$ dependence. The exponents are consistent with 3d Gaussian values, but not with either first order transitions or the universality class of the 3d XY model. As the 3d Gaussian fixed point is known to be unstable, the scenario of a yet unidentified non-trivial fixed point close to the 3d Gaussian emerges as one of the possible explanations.Comment: Extended version after referee reports. 6 pages, 6 figure

Bankruptcy risk model and empirical tests

We analyze the size dependence and temporal stability of firm bankruptcy risk in the US economy by applying Zipf scaling techniques. We focus on a single risk factor-the debt-to-asset ratio R-in order to study the stability of the Zipf distribution of R over time. We find that the Zipf exponent increases during market crashes, implying that firms go bankrupt with larger values of R. Based on the Zipf analysis, we employ Bayes's theorem and relate the conditional probability that a bankrupt firm has a ratio R with the conditional probability of bankruptcy for a firm with a given R value. For 2,737 bankrupt firms, we demonstrate size dependence in assets change during the bankruptcy proceedings. Prepetition firm assets and petition firm assets follow Zipf distributions but with different exponents, meaning that firms with smaller assets adjust their assets more than firms with larger assets during the bankruptcy process. We compare bankrupt firms with nonbankrupt firms by analyzing the assets and liabilities of two large subsets of the US economy: 2,545 Nasdaq members and 1,680 New York Stock Exchange (NYSE) members. We find that both assets and liabilities follow a Pareto distribution. The finding is not a trivial consequence of the Zipf scaling relationship of firm size quantified by employees-although the market capitalization of Nasdaq stocks follows a Pareto distribution, the same distribution does not describe NYSE stocks. We propose a coupled Simon model that simultaneously evolves both assets and debt with the possibility of bankruptcy, and we also consider the possibility of firm mergers.Comment: 8 pages, 8 figure

Feminists really do count : the complexity of feminist methodologies

We are delighted to be presenting this special issue on the topic of feminism and quantitative methods. We believe that such an issue is exceptionally timely. This is not simply because of ongoing debates around quantification within the field of feminism and women‟s studies. It is also because of debates within the wider research community about the development of appropriate methodologies that take account of new technological and philosophical concerns and are fit-for-purpose for researching contemporary social, philosophical, cultural and global issues. Two areas serve as exemplars in this respect and both speak to these combined wider social science and specifically feminist methodological concerns. The first is the increasing concern amongst social scientists with how the complexity of social life can be captured and analysed. Within feminism, this can be seen in debates about intersectionality that recognise the concerns arising from multiple social positions/divisions and associated power issues. As Denis (2008: 688) comments in respect of intersectional analysis „The challenge of integrating multiple, concurrent, yet often contradictory social locations into analyses of power relations has been issued. Theorising to accomplish this end is evolving, and we are struggling to develop effective methodological tools in order to marry theorising with necessary complex analyses of empirical data.‟ Secondly, new techniques and new data sources are now coming on line. This includes work in the UK of the ESRC National Data Strategy which has been setting out the priorities for the development of research data resources both within and across the boundaries of the social sciences. This will facilitate historical, longitudinal, interdisciplinary and mixed methodological research. And it may be the case that these developments facilitate the achievement of a longstanding feminist aim not simply for interdisciplinarity but for transdisciplinarity in epistemological and methodological terms

Comparing and characterizing some constructions of canonical bases from Coxeter systems

The Iwahori-Hecke algebra $\mathcal{H}$ of a Coxeter system $(W,S)$ has a "standard basis" indexed by the elements of $W$ and a "bar involution" given by a certain antilinear map. Together, these form an example of what Webster calls a pre-canonical structure, relative to which the well-known Kazhdan-Lusztig basis of $\mathcal{H}$ is a canonical basis. Lusztig and Vogan have defined a representation of a modified Iwahori-Hecke algebra on the free $\mathbb{Z}[v,v^{-1}]$-module generated by the set of twisted involutions in $W$, and shown that this module has a unique pre-canonical structure satisfying a certain compatibility condition, which admits its own canonical basis which can be viewed as a generalization of the Kazhdan-Lusztig basis. One can modify the parameters defining Lusztig and Vogan's module to obtain other pre-canonical structures, each of which admits a unique canonical basis indexed by twisted involutions. We classify all of the pre-canonical structures which arise in this fashion, and explain the relationships between their resulting canonical bases. While some of these canonical bases are related in a trivial fashion to Lusztig and Vogan's construction, others appear to have no simple relation to what has been previously studied. Along the way, we also clarify the differences between Webster's notion of a canonical basis and the related concepts of an IC basis and a $P$-kernel.Comment: 32 pages; v2: additional discussion of relationship between canonical bases, IC bases, and P-kernels; v3: minor revisions; v4: a few corrections and updated references, final versio

Current-Controlled Negative Differential Resistance due to Joule Heating in TiO2

We show that Joule heating causes current-controlled negative differential resistance (CC-NDR) in TiO2 by constructing an analytical model of the voltage-current V(I) characteristic based on polaronic transport for Ohm's Law and Newton's Law of Cooling, and fitting this model to experimental data. This threshold switching is the 'soft breakdown' observed during electroforming of TiO2 and other transition-metal-oxide based memristors, as well as a precursor to 'ON' or 'SET' switching of unipolar memristors from their high to their low resistance states. The shape of the V(I) curve is a sensitive indicator of the nature of the polaronic conduction.Comment: 13 pages, 2 figure

Effective Invariant Theory of Permutation Groups using Representation Theory

Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner combinatorial description of the invariant ring.Comment: Draft version, the corrected full version is available at http://www.springer.com