Field theory in superfluid 3He: What are the lessons for particle physics, gravity, and high-temperature superconductivity?

There are several classes of homogeneous Fermi systems that are characterized by the topology of the energy spectrum of fermionic quasiparticles: (i) gapless systems with a Fermi surface, (ii) systems with a gap in their spectrum, (iii) gapless systems with topologically stable point nodes (Fermi points), and (iv) gapless systems with topologically unstable lines of nodes (Fermi lines). Superfluid 3He-A and electroweak vacuum belong to the universality class 3. The fermionic quasiparticles (particles) in this class are chiral: they are left-handed or right-handed. The collective bosonic modes of systems of class 3 are the effective gauge and gravitational fields. The great advantage of superfluid 3He-A is that we can perform experiments by using this condensed matter and thereby simulate many phenomena in high energy physics, including axial anomaly, baryoproduction, and magnetogenesis. 3He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. With 3He-A one can simulate event horizons, Hawking radiation, rotating vacuum, etc. High-temperature superconductors are believed to belong to class 4. They have gapless fermionic quasiparticles with a “relativistic” spectrum close to gap nodes, which allows application of ideas developed for superfluid 3He-A.

Forming classes by stimulus frequency: Behavior and theory

Visual classification is the way we relate to different images in our environment as if they were the same, while relating differently to other collections of stimuli (e.g., human vs. animal faces). It is still not clear, however, how the brain forms such classes, especially when introduced with new or changing environments. To isolate a perception-based mechanism underlying class representation, we studied unsupervised classification of an incoming stream of simple images. Classification patterns were clearly affected by stimulus frequency distribution, although subjects were unaware of this distribution. There was a common bias to locate class centers near the most frequent stimuli and their boundaries near the least frequent stimuli. Responses were also faster for more frequent stimuli. Using a minimal, biologically based neural-network model, we demonstrate that a simple, self-organizing representation mechanism based on overlapping tuning curves and slow Hebbian learning suffices to ensure classification. Combined behavioral and theoretical results predict large tuning overlap, implicating posterior infero-temporal cortex as a possible site of classification.

Groups, information theory, and Einstein's likelihood principle

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.

Diversity for Texts Builds in Language L(MT): Indexes Based in Theory of Information

If one has a distribution of words (SLUNs or CLUNS) in a text written in language L(MT), and is adjusted one of the mathematical expressions of distribution that exists in the mathematical literature, some parameter of the elected expression it can be considered as a measure of the diversity. But because the adjustment is not always perfect as usual measure; it is preferable to select an index that doesn't postulate a regularity of distribution expressible for a simple formula. The problem can be approachable statistically, without having special interest for the organization of the text. It can serve as index any monotonous function that has a minimum value when all their elements belong to the same class, that is to say, all the individuals belong to oneself symbol, and a maximum value when each element belongs to a different class, that is to say, each individual is of a different symbol. It should also gather certain conditions like they are: to be not very sensitive to the extension of the text and being invariant to certain number of operations of selection in the text. These operations can be theoretically random. The expressions that offer more advantages are those coming from the theory of the information of Shannon-Weaver. Based on them, the authors develop a theoretical study for indexes of diversity to be applied in texts built in modeling language L(MT), although anything impedes that they can be applied to texts written in natural languages.

What is truth? an essay in the theory of knowledge,

"Published on the foundation established in memory of James Wesley Cooper of the class of 1865, Yale college."

A class of translation lattices.

"CU-2-62-NSF G19022-M."

Theory of mind and relational complexity

Cognitive complexity and control theory and relational complexity theory attribute developmental changes in theory of mind (TOM) to complexity. In 3 studies, 3-, 4-, and 5-year-olds performed TOM tasks (false belief, appearance-reality), less complex connections (Level 1 perspective-taking) tasks, and transformations tasks (understanding the effects of location changes and colored filters) with content similar to TOM. There were also predictor tasks at binary-relational and ternary-relational complexity levels, with different content. Consistent with complexity theories: (a) connections and transformations were easier and mastered earlier than TOM; (b) predictor tasks accounted for more than 80% of age-related variance in TOM; and (c) ternary-relational items accounted for TOM variance, before and after controlling for age and binary-relational items. Prediction did not require hierarchically structured predictor tasks.

A new class of critical sets in Latin squares

Previously the process of finding critical sets in Latin squares has been inside cumbersome by the complexity and number of Latin trades that, must be constructed. In this paper we develop a theory of Latin trades that yields more transparent constructions. We use these Latin trades to find a new class of critical sets for Latin squares which are a product of the Latin square of order 2 with a. back circulant Latin square of odd order.

Embedding a restricted class of partial K-4-designs

Given a partial K-4-design (X, P), if x is an element of X is a vertex which occurs in exactly one block of P, then call x a free vertex. In this paper, a technique is described for obtaining a cubic embedding of any partial K-4-design with the property that every block in the partial design contains at least two free vertices.

A class of self-stabilizing MCA learning algorithms

In this letter, we propose a class of self-stabilizing learning algorithms for minor component analysis (MCA), which includes a few well-known MCA learning algorithms. Self-stabilizing means that the sign of the weight vector length change is independent of the presented input vector. For these algorithms, rigorous global convergence proof is given and the convergence rate is also discussed. By combining the positive properties of these algorithms, a new learning algorithm is proposed which can improve the performance. Simulations are employed to confirm our theoretical results.

Compositional class refinement in object-Z

Object-Z allows coupling constraints between classes which, on the one hand, facilitate specification at a high level of abstraction, but, on the other hand, make class refinement non-compositional. The consequence of this is that refinement is not practical for large Systems. This paper overcomes this limitation by introducing a methodology for compositional class refinement in Object-Z. The key step is an equivalence transformation of an arbitrary Object-Z specification to one in which introduced constraints prohibit non-compositional refinements. The methodology also allows the constraints which couple classes to be refined yielding an unrestricted approach to compositional class refinement.

Interactive data in financial reporting:the construction of the non-professional investor

The Securities and Exchange Commission (SEC) in the United States and in particular its immediately past chairman, Christopher Cox, has been actively promoting an upgrade of the EDGAR system of disseminating filings. The new generation of information provision has been dubbed by Chairman Cox, "Interactive Data" (SEC, 2006). In October this year the Office of Interactive Disclosure was created(http://www.sec.gov/news/press/2007/2007-213.htm). The focus of this paper is to examine the way in which the non-professional investor has been constructed by various actors. We examine the manner in which Interactive Data has been sold as the panacea for financial market 'irregularities' by the SEC and others. The academic literature shows almost no evidence of researching non-professional investors in any real sense (Young, 2006). Both this literature and the behaviour of representatives of institutions such as the SEC and FSA appears to find it convenient to construct this class of investor in a particular form and to speak for them. We theorise the activities of the SEC and its chairman in particular over a period of about three years, both following and prior to the 'credit crunch'. Our approach is to examine a selection of the policy documents released by the SEC and other interested parties and the statements made by some of the policy makers and regulators central to the programme to advance the socio-technical project that is constituted by Interactive Data. We adopt insights from ANT and more particularly the sociology of translation (Callon, 1986; Latour, 1987, 2005; Law, 1996, 2002; Law & Singleton, 2005) to show how individuals and regulators have acted as spokespersons for this malleable class of investor. We theorise the processes of accountability to investors and others and in so doing reveal the regulatory bodies taking the regulated for granted. The possible implications of technological developments in digital reporting have been identified also by the CEO's of the six biggest audit firms in a discussion document on the role of accounting information and audit in the future of global capital markets (DiPiazza et al., 2006). The potential for digital reporting enabled through XBRL to "revolutionize the entire company reporting model" (p.16) is discussed and they conclude that the new model "should be driven by the wants of investors and other users of company information,..." (p.17; emphasis in the original). Here rather than examine the somewhat illusive and vexing question of whether adding interactive functionality to 'traditional' reports can achieve the benefits claimed for nonprofessional investors we wish to consider the rhetorical and discursive moves in which the SEC and others have engaged to present such developments as providing clearer reporting and accountability standards and serving the interests of this constructed and largely unknown group - the non-professional investor.

Problems and Theorems in the Theory of Multiplier Sequences

The purpose of this paper is (1) to highlight some recent and heretofore unpublished results in the theory of multiplier sequences and (2) to survey some open problems in this area of research. For the sake of clarity of exposition, we have grouped the problems in three subsections, although several of the problems are interrelated. For the reader’s convenience, we have included the pertinent definitions, cited references and related results, and in several instances, elucidated the problems by examples.

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

Understanding the labour–environmental relationship in Britain, 1967–2011:a new narrative using political opportunity structure and coalition theory

Orthodox depictions of a fraught labour–environmental relationship privileging class, ideological and programmatic differences are problematised by newly quantified evidence of British unions' pro-environmental policy-making since 1967. The following narrative blends widely accepted accounts of the fortunes of both movements with an evaluation of Britain's shifting political opportunity structure and coalition theory to identify an alternative range of constraints and opportunities influencing the propensity and capacity of both movements to interact effectively, culminating recently in unions' emergence as environmental actors in their own right.