Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

GENERICITY OF NONDEGENERATE GEODESICS WITH GENERAL BOUNDARY CONDITIONS

Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of L. Biliotti, M. A. Javaloyes and P. Piccione [6] for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P subset of M x M that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal Delta subset of M x M. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C(k)-generic are given.

Financial time series analysis : Chaos and neurodynamics approach

This work aims at combining the Chaos theory postulates and Artificial Neural Networks classification and predictive capability, in the field of financial time series prediction. Chaos theory, provides valuable qualitative and quantitative tools to decide on the predictability of a chaotic system. Quantitative measurements based on Chaos theory, are used, to decide a-priori whether a time series, or a portion of a time series is predictable, while Chaos theory based qualitative tools are used to provide further observations and analysis on the predictability, in cases where measurements provide negative answers. Phase space reconstruction is achieved by time delay embedding resulting in multiple embedded vectors. The cognitive approach suggested, is inspired by the capability of some chartists to predict the direction of an index by looking at the price time series. Thus, in this work, the calculation of the embedding dimension and the separation, in Takens‘ embedding theorem for phase space reconstruction, is not limited to False Nearest Neighbor, Differential Entropy or other specific method, rather, this work is interested in all embedding dimensions and separations that are regarded as different ways of looking at a time series by different chartists, based on their expectations. Prior to the prediction, the embedded vectors of the phase space are classified with Fuzzy-ART, then, for each class a back propagation Neural Network is trained to predict the last element of each vector, whereas all previous elements of a vector are used as features.

Decompositions of finite projective planes

We consider decompositions of finite projective planes into copies of a particular structure. Our main theorem provides a connection between the existence of a proper projective subplane and the existence of a decomposition into sets of collinear points. Based on this result, we develop a connection between the existence of a projective subplane in a plane II and that of a hitting set in the dual of II.

Combinatorial aspects of jump codes

We develop an approach to jump codes concentrating on their combinatorial and symmetry properties. The main result is a generalization of a theorem previously proved in the context of isodual codes. We show that several previously constructed jump codes are instances of this theorem.

Fred: An approach to generating real, correct, reusable programs from proofs

In this paper we describe our system for automatically extracting "correct" programs from proofs using a development of the Curry-Howard process. Although program extraction has been developed by many authors, our system has a number of novel features designed to make it very easy to use and as close as possible to ordinary mathematical terminology and practice. These features include 1. the use of Henkin's technique to reduce higher-order logic to many-sorted (first-order) logic; 2. the free use of new rules for induction subject to certain conditions; 3. the extensive use of previously programmed (total, recursive) functions; 4. the use of templates to make the reasoning much closer to normal mathematical proofs and 5. a conceptual distinction between the computational type theory (for representing programs)and the logical type theory (for reasoning about programs). As an example of our system we give a constructive proof of the well known theorem that every graph of even parity, which is non-trivial in the sense that it does not consist of isolated vertices, has a cycle. Given such a graph as input, the extracted program produces a cycle as promised.

Protocols between programs and proofs

In this paper we describe a new protocol that we call the Curry-Howard protocol between a theory and the programs extracted from it. This protocol leads to the expansion of the theory and the production of more powerful programs. The methodology we use for automatically extracting “correct” programs from proofs is a development of the well-known Curry-Howard process. Program extraction has been developed by many authors, but our presentation is ultimately aimed at a practical, usable system and has a number of novel features. These include 1. a very simple and natural mimicking of ordinary mathematical practice and likewise the use of established computer programs when we obtain programs from formal proofs, and 2. a conceptual distinction between programs on the one hand, and proofs of theorems that yield programs on the other. An implementation of our methodology is the Fred system. As an example of our protocol we describe a constructive proof of the well-known theorem that every graph of even parity can be decomposed into a list of disjoint cycles. Given such a graph as input, the extracted program produces a list of the (non-trivial) disjoint cycles as promised.

Quantified Interference: Information Theory and Information Flow

The paper investigates which of Shannon’s measures (entropy, conditional entropy, mutual information) is the right one for the task of quantifying information flow in a programming language. We examine earlier relevant contributions from Denning, McLean and Gray and we propose and motivate a specific quantitative definition of information flow. We prove results relating equivalence relations, interference of program variables, independence of random variables and the flow of confidential information. Finally, we show how, in our setting, Shannon’s Perfect Secrecy theorem provides a sufficient condition to determine whether a program leaks confidential information.

A scale-model room as a practical teaching experiment

A practical experiment is described which was used to help university students increase their understanding of the effect of construction methods and window design on passive solar heating and electrical heating. A number of one tenth scale model rooms were constructed by students and sited out-of-doors in the late autumn. The models were fabricated to mimic available commercial construction techniques with careful consideration being given to window size and placement for solar access. Each model had a thermostatically controlled electric heating element. The temperatures and electricity use of the models were recorded using data-loggers over a two week period. The performances of the models based on energy consumption and internal temperature were compared with each other and with predictions based upon thermal mass and R-values. Examples of questions used by students to facilitate this process are included. The effect of scaling on thermal properties was analysed using Buckingham’s p-theorem.

Leontief paradox and the role of factor intensity measurement

In contrast with the prediction of the Heckscher-Ohlin (HO) theorem, Leontief (1953) found that the capital-labor ratio embodied in the US exports is smaller than the capital-labor ratio embodied in the US competitive import replacements. In Leontief's analysis, the measured factor content of US imports is computed based on the assumption that all countries are using the US factor intensity techniques. This paper relaxes all assumption of identical factor intensity techniques. It uses an inferring method to infer the factor intensity techniques of different countries based on international relative factor price differences. With the inferred differentiated factor intensity techniques , the Leontief paradox is re-investigated and is found to be either disappeared or eased.

Che Vuoi? Politico-philosophical remarks on Leo Strauss' Spinoza

Rumors surrounding the Hebraic-American classical philosopher Leo Strauss’ supposed influence on leading neoconservative politicians and commentators make reconsidering Leo Strauss’ thought and legacy a philosophical task of the first political importance today. A host of articles have appeared by students and (more recently) books by Stephen Smith (2006), Heinrich Meier (2006) and Catherine and Michael Zuckert (2006). This essay is proffered as a critical contribution, by a non-Straussian student, to this literature. Its methodology and justification is to return to and reconsider Strauss’ earliest works, on the ‘political theology’ of Benedict de Spinoza. The paper argues two theses. The first is that the popular depiction of Strauss as an esoteric Nietzschean hiding behind a ‘noble’ classical or theological veneer importantly misses the mark. The second is that Strauss’ early work shows his proximity, via Jacobi, to the Heideggerian disclosure of the groundless grounds of philosophical reason, given which one must extra-rationally choose reason over faith. One striking implication of this argument, in the contemporary political climate, is to underscore the unlikely convergence between the philosophical sources of neoconservative and the ‘post-structuralist’ thought associated with much of the intellectual left in France and the Anglophone world. Yet in contrast to the widespread image of Strauss, I argue that the mature Strauss’ continuing commitment to this decisionistic framework is in fact most clear is his ‘exoteric,’ public statements on religion – i.e. it is not the ‘esoteric’ purloined letter Strauss’ critics seek out. The reason for Strauss’ continuing public advocacy of the impossibility of reason’s disproving faith, I propose, highlights the primarily political (versus philosophical) nature of this turn: in Strauss’ conservative acceptance of the political necessity of religion for social order, framed in terms of a revised commitment to the ‘medieval’ (versus modern) enlightenment of Maimonides and Farabi.

Mining inconsistent secure messages toward analyzing security protocols

Traditional approaches such as theorem proving and model checking have been successfully used to analyze security protocols. Ideally, they assume the data communication is reliable and require the user to predetermine authentication goals. However, missing and inconsistent data have been greatly ignored, and the increasingly complicated security protocol makes it difficult to predefine such goals. This paper presents a novel approach to analyze security protocols using association rule mining. It is able to not only validate the reliability of transactions but also discover potential correlations between secure messages. The algorithm and experiment demonstrate that our approaches are useful and promising.

Democracy, global transitions, and education : using speculative fictions as thought experiments in anticipatory critical inquiry

The purpose of a thought experiment, as the term was used by quantum and relativity physicists in the early part of the twentieth century, was not prediction (as is the goal of classical experimental science), but more defensible representations of present 'realities'. Indeed, one of the best-known examples of a thought experiment ('Schrodinger's cat') demonstrates the impossibility of prediction at the quantum level. Speculative fictions, from Mary Shelley's Frankenstein to the Star Wars saga, can be read as socio-technical thought experiments that can help us to apprehend and comprehend present 'realities' and uncertainties, and to anticipate and critique possible futures. In this paper I will demonstrate how two examples of popular speculative fictions, Frank Herbert's Dune (1965) and Ursula Le Guin's The Telling (2000), can be read as thought experiments that describe problematic aspects of contemporary social and cultural transformations. I will argue that critical and deconstructive readings of these novels can help us to produce anticipatory critiques of possible ways in which democratic institutions are being transformed by globalisation. I will conclude by considering the implications of such anticipatory critiques for generating questions, problems and issues in educational inquiry and for choosing appropriate methodologies for investigating them.

3D haptic needle insertion simulator utilising an agent based spherical voxel model

This paper describes a technique for the real-time modeling of deformable tissue. Specifically geared towards needle insertion simulation, the low computational requirements of the model enable highly accurate haptic feedback to a user without introducing noticeable time delay or buzzing generally associated with haptic surgery simulation. Using a spherical voxel array combined with aspects of computational geometry and agent communication and interaction principals, the model is capable of providing haptic update rates of over 1000Hz with real-time visual feedback. Iterating through over 1000 voxels per millisecond to determine collision and haptic response while making use of Vieta’s Theorem for extraneous force culling.