Statistical Mechanics of 2+1 Gravity From Riemann Zeta Function and Alexander Polynomial:Exact Results

In the recent publication (Journal of Geometry and Physics,33(2000)23-102) we demonstrated that dynamics of 2+1 gravity can be described in terms of train tracks. Train tracks were introduced by Thurston in connection with description of dynamics of surface automorphisms. In this work we provide an example of utilization of general formalism developed earlier. The complete exact solution of the model problem describing equilibrium dynamics of train tracks on the punctured torus is obtained. Being guided by similarities between the dynamics of 2d liquid crystals and 2+1 gravity the partition function for gravity is mapped into that for the Farey spin chain. The Farey spin chain partition function, fortunately, is known exactly and has been thoroughly investigated recently. Accordingly, the transition between the pseudo-Anosov and the periodic dynamic regime (in Thurston's terminology) in the case of gravity is being reinterpreted in terms of phase transitions in the Farey spin chain whose partition function is just a ratio of two Riemann zeta functions. The mapping into the spin chain is facilitated by recognition of a special role of the Alexander polynomial for knots/links in study of dynamics of self homeomorphisms of surfaces. At the end of paper, using some facts from the theory of arithmetic hyperbolic 3-manifolds (initiated by Bianchi in 1892), we develop systematic extension of the obtained results to noncompact Riemannian surfaces of higher genus. Some of the obtained results are also useful for 3+1 gravity. In particular, using the theorem of Margulis, we provide new reasons for the black hole existence in the Universe: black holes make our Universe arithmetic. That is the discrete Lie groups of motion are arithmetic.Comment: 69 pages,11 figures. Journal of Geometry and Physics (in press

A new sequential covering strategy for inducing classification rules with ant colony algorithms

Ant colony optimization (ACO) algorithms have been successfully applied to discover a list of classification rules. In general, these algorithms follow a sequential covering strategy, where a single rule is discovered at each iteration of the algorithm in order to build a list of rules. The sequential covering strategy has the drawback of not coping with the problem of rule interaction, i.e., the outcome of a rule affects the rules that can be discovered subsequently since the search space is modified due to the removal of examples covered by previous rules. This paper proposes a new sequential covering strategy for ACO classification algorithms to mitigate the problem of rule interaction, where the order of the rules is implicitly encoded as pheromone values and the search is guided by the quality of a candidate list of rules. Our experiments using 18 publicly available data sets show that the predictive accuracy obtained by a new ACO classification algorithm implementing the proposed sequential covering strategy is statistically significantly higher than the predictive accuracy of state-of-the-art rule induction classification algorithms

Evolving Recursive Programs using Non-recursive Scaffolding

Genetic programming has proven capable of evolving solutions to a wide variety of problems. However, the successes have largely been with programs without iteration or recursion; evolving recursive programs has turned out to be particularly challenging. The main obstacle to evolving recursive programs seems to be that they are particularly fragile to the application of search operators: a small change in a correct recursive program generally produces a completely wrong program. In this paper, we present a simple and general method that allows us to pass back and forth from a recursive program to an associated non-recursive program. Finding a recursive program can be reduced to evolving non-recursive programs followed by converting the optimum non-recursive program found to the associated optimum recursive program. This avoids the fragility problem above, as evolution does not search the space of recursive programs. We present promising experimental results on a test-bed of recursive problems

Improving the predictive performance of SAFEL: A Situation-Aware FEar Learning model

In this paper, we optimize the predictive performance of a Situation-Aware FEar Learning model (SAFEL) by investigating the relationship between its parameters. SAFEL is a hybrid computational model based on the fear-learning system of the brain, which was developed to provide robots with the capability to predict threatening or undesirable situations based on temporal context. The main aim of this work is to improve SAFEL's emotional response. An emotional response coherent with environmental changes is essential not only for self-preservation and adaptation purposes, but also for improving the believability and interaction skills of companion robots. Experiments with a NAO humanoid robot show that adjusting the ratio between two parameters of SAFEL can significantly increase the predictive performance and reduce parameter settings

A Situation-Aware Fear Learning (SAFEL) Model for Robots

This work proposes a novel Situation-Aware FEar Learning (SAFEL) model for robots. SAFEL combines concepts of situation-aware expert systems with well-known neuroscientific findings on the brain fear-learning mechanism to allow companion robots to predict undesirable or threatening situations based on past experiences. One of the main objectives is to allow robots to learn complex temporal patterns of sensed environmental stimuli and create a representation of these patterns. This memory can be later associated with a negative or positive “emotion”, analogous to fear and confidence. Experiments with a real robot demonstrated SAFEL’s success in generating contextual fear conditioning behaviour with predictive capabilities based on situational information

Predicted aircraft effects on stratospheric ozone

The possibility that the current fleet of subsonic aircraft may already have caused detectable changes in both the troposphere and stratosphere has raised concerns about the impact of such operations on stratospheric ozone and climate. Recent interest in the operation of supersonic aircraft in the lower stratosphere has heightened such concerns. Previous assessments of impacts from proposed supersonic aircraft were based mostly on one-dimensional model results although a limited number of multidimensional models were used. In the past 15 years, our understanding of the processes that control the atmospheric concentrations of trace gases has changed dramatically. This better understanding was achieved through accumulation of kinetic data and field observations as well as development of new models. It would be beneficial to start examining the impact of subsonic aircraft to identify opportunities to study and validate the mechanisms that were proposed to explain the ozone responses. The two major concerns are the potential for a decrease in the column abundance of ozone leading to an increase in ultraviolet radiation at the ground, and redistribution of ozone in the lower stratosphere and upper troposphere leading to changes in the Earth's climate. Two-dimensional models were used extensively for ozone assessment studies, with a focus on responses to chlorine perturbations. There are problems specific to the aircraft issues that are not adequately addressed by the current models. This chapter reviews the current status of the research on aircraft impact on ozone with emphasis on immediate model improvements necessary for extending our understanding. The discussion will be limited to current and projected commercial aircraft that are equipped with air-breathing engines using conventional jet fuel. The impacts are discussed in terms of the anticipated fuel use at cruise altitude

Jouberin localizes to collecting ducts and interacts with nephrocystin-1

Joubert syndrome and related disorders are autosomal recessive multisystem diseases characterized by cerebellar vermis aplasia/hypoplasia, retinal degeneration and cystic kidney disease. There are five known genes; mutations of which give rise to a spectrum of renal cystic diseases the most common of which is nephronophthisis, a disorder characterized by early loss of urinary concentrating ability, renal fibrosis, corticomedullary cyst formation and renal failure. Many of the proteins encoded by these genes interact with one another and are located at adherens junctions or the primary cilia and or basal bodies. Here we characterize Jouberin, a multi-domain protein encoded by the AHI1 gene. Immunohistochemistry with a novel antibody showed that endogenous Jouberin is expressed in brain, kidney and HEK293 cells. In the kidney, Jouberin co-localized with aquaporin-2 in the collecting ducts. We show that Jouberin interacts with nephrocystin-1 as determined by yeast-2-hybrid system and this was confirmed by exogenous and endogenous co-immunoprecipitation in HEK293 cells. Jouberin is expressed at cell-cell junctions, primary cilia and basal body of mIMCD3 cells while a Jouberin-GFP construct localized to centrosomes in subconfluent and dividing MDCK cells. Our results suggest that Jouberin is a protein whose expression pattern supports both the adherens junction and the ciliary hypotheses for abnormalities leading to nephronophthisis

Synchronous dynamics of zooplankton competitors prevail in temperate lake ecosystems

Although competing species are expected to exhibit compensatory dynamics (negative temporal covariation), empirical work has demonstrated that competitive communities often exhibit synchronous dynamics (positive temporal covariation). This has led to the suggestion that environmental forcing dominates species dynamics; however, synchronous and compensatory dynamics may appear at different length scales and/or at different times, making it challenging to identify their relative importance. We compiled 58 long-term datasets of zooplankton abundance in north-temperate and sub-tropical lakes and used wavelet analysis to quantify general patterns in the times and scales at which synchronous/compensatory dynamics dominated zooplankton communities in different regions and across the entire dataset. Synchronous dynamics were far more prevalent at all scales and times and were ubiquitous at the annual scale. Although we found compensatory dynamics in approximately 14% of all combinations of time period/scale/lake, there were no consistent scales or time periods during which compensatory dynamics were apparent across different regions. Our results suggest that the processes driving compensatory dynamics may be local in their extent, while those generating synchronous dynamics operate at much larger scales. This highlights an important gap in our understanding of the interaction between environmental and biotic forces that structure communities