A Probabilistic Approach to Generalized Zeckendorf Decompositions

Generalized Zeckendorf decompositions are expansions of integers as sums of elements of solutions to recurrence relations. The simplest cases are base-$b$ expansions, and the standard Zeckendorf decomposition uses the Fibonacci sequence. The expansions are finite sequences of nonnegative integer coefficients (satisfying certain technical conditions to guarantee uniqueness of the decomposition) and which can be viewed as analogs of sequences of variable-length words made from some fixed alphabet. In this paper we present a new approach and construction for uniform measures on expansions, identifying them as the distribution of a Markov chain conditioned not to hit a set. This gives a unified approach that allows us to easily recover results on the expansions from analogous results for Markov chains, and in this paper we focus on laws of large numbers, central limit theorems for sums of digits, and statements on gaps (zeros) in expansions. We expect the approach to prove useful in other similar contexts.Comment: Version 1.0, 25 pages. Keywords: Zeckendorf decompositions, positive linear recurrence relations, distribution of gaps, longest gap, Markov processe

Towards an analysis of shear suspension flows using radial basis functions

In this paper, radial basis functions are utilised for numerical prediction of the bulk properties of particulate suspensions under simple shear conditions. The suspending fluid is Newtonian and the suspended particles are rigid. Results obtained are compared well with those based on finite elements in the literature

Identifying Governance Best Practices in Systems-of-Systems Acquisition

Disclaimer: The views represented in this report are those of the authors and do not reflect the official policy position of the Navy, the Department of Defense, or the federal government.Excerpt from the Proceedings of the Tenth Annual Acquisition Research Symposium System of Systems ManagementThe research presented in this report was supported by the Acquisition Research Program of the Graduate School of Business & Public Policy at the Naval Postgraduate School. To request defense acquisition research, to become a research sponsor, or to print additional copies of reports, please contact any of the staff listed on the Acquisition Research Program website (www.acquisitionresearch.net).Prepared for the Naval Postgraduate School, Monterey, CA 93943.Approved for public release; distribution is unlimited

Cholinergic modulation of epileptiform activity in the developing rat neocortex

The effects of carbachol on picrotoxin-induced epileptiform activity and membrane properties of neurons in the developing rat neocortex were examined in an in vitro slice preparation. Intracellular recordings were obtained in layer II–III neurons of slices prepared from rats 9–21 days of age. Epileptiform activity in 9- to 14-day-olds consisted of a sharply rising, sustained (10–30 s) membrane depolarization with superimposed action potentials. Bath application of carbachol (5–50 μM) raised the threshold for evoking epileptiform activity but, when such responses were evoked, their underlying depolarizations were increased in amplitude. Orthodromic stimulation in slices from 15- to 21-day-old animals evoked a prolonged epileptiform burst response that triggered an episode of spreading depression (SD). Carbachol reduced epileptiform responses and suppressed the occurrence of SD. It did not significantly affect the resting membrane potential or the height of the action potential but decreased the rheobase current needed to evoke an action potential and increased the input resistance. All effects of carbachol were antagonized by atropine (1 μM). These results indicate that carbachol has both pre- and postsynaptic effects in the developing neocortex and can significantly modulate neuronal excitability in the immature nervous system

Efficient Symmetry Reduction and the Use of State Symmetries for Symbolic Model Checking

One technique to reduce the state-space explosion problem in temporal logic model checking is symmetry reduction. The combination of symmetry reduction and symbolic model checking by using BDDs suffered a long time from the prohibitively large BDD for the orbit relation. Dynamic symmetry reduction calculates representatives of equivalence classes of states dynamically and thus avoids the construction of the orbit relation. In this paper, we present a new efficient model checking algorithm based on dynamic symmetry reduction. Our experiments show that the algorithm is very fast and allows the verification of larger systems. We additionally implemented the use of state symmetries for symbolic symmetry reduction. To our knowledge we are the first who investigated state symmetries in combination with BDD based symbolic model checking

Improving BDD Based Symbolic Model Checking with Isomorphism Exploiting Transition Relations

Symbolic model checking by using BDDs has greatly improved the applicability of model checking. Nevertheless, BDD based symbolic model checking can still be very memory and time consuming. One main reason is the complex transition relation of systems. Sometimes, it is even not possible to generate the transition relation, due to its exhaustive memory requirements. To diminish this problem, the use of partitioned transition relations has been proposed. However, there are still systems which can not be verified at all. Furthermore, if the granularity of the partitions is too fine, the time required for verification may increase. In this paper we target the symbolic verification of asynchronous concurrent systems. For such systems we present an approach which uses similarities in the transition relation to get further memory reductions and runtime improvements. By applying our approach, even the verification of systems with an previously intractable transition relation becomes feasible.Comment: In Proceedings GandALF 2011, arXiv:1106.081

Galanin Receptor 1 Deletion Exacerbates Hippocampal Neuronal Loss after Systemic Kainate Administration in Mice

Galanin is a neuropeptide with a wide distribution in the central and peripheral nervous systems and whose physiological effects are mediated through three G protein-coupled receptor subtypes, GalR1, GalR2, and GalR3. Several lines of evidence indicate that galanin, as well as activation of the GalR1 receptor, is a potent and effective modulator of neuronal excitability in the hippocampus.In order to test more formally the potential influence of GalR1 on seizure-induced excitotoxic cell death, we conducted functional complementation tests in which transgenic mice that exhibit decreased expression of the GalR1 candidate mRNA underwent kainate-induced status epilepticus to determine if the quantitative trait of susceptibility to seizure-induced cell death is determined by the activity of GalR1. In the present study, we report that reduction of GalR1 mRNA via null mutation or injection of the GalR1 antagonist, galantide, prior to kainate-induced status epilepticus induces hippocampal damage in a mouse strain known to be highly resistant to kainate-induced neuronal injury. Wild-type and GalR1 knockout mice were subjected to systemic kainate administration. Seven days later, Nissl and NeuN immune- staining demonstrated that hippocampal cell death was significantly increased in GalR1 knockout strains and in animals injected with the GalR1 antagonist. Compared to GalR1-expressing mice, GalR1-deficient mice had significantly larger hippocampal lesions after status epilepticus.Our results suggest that a reduction of GalR1 expression in the C57BL/6J mouse strain renders them susceptible to excitotoxic injury following systemic kainate administration. From these results, GalR1 protein emerges as a new molecular target that may have a potential therapeutic value in modulating seizure-induced cell death

Refuting the challenges of the developmental shift of polarity of GABA actions: GABA more exciting than ever!

During brain development, there is a progressive reduction of intracellular chloride associated with a shift in GABA polarity: GABA depolarizes and occasionally excites immature neurons, subsequently hyperpolarizing them at later stages of development. This sequence, which has been observed in a wide range of animal species, brain structures and preparations, is thought to play an important role in activity-dependent formation and modulation of functional circuits. This sequence has also been considerably reinforced recently with new data pointing to an evolutionary preserved rule. In a recent 'Hypothesis and Theory Article', the excitatory action of GABA in early brain development is suggested to be "an experimental artefact" (Bregestovski and Bernard, 2012). The authors suggest that the excitatory action of GABA is due to an inadequate/insufficient energy supply in glucose-perfused slices and/or to the damage produced by the slicing procedure. However, these observations have been repeatedly contradicted by many groups and are inconsistent with a large body of evidence including the fact that the developmental shift is neither restricted to slices nor to rodents. We summarize the overwhelming evidence in support of both excitatory GABA during development, and the implications this has in developmental neurobiology. \ua9 2012 Ben-ari, Woodin, Sernagor, Cancedda, Vinay, Rivera,Legendre, Luhmann, Bordey, Wenner, Fukuda, Pol, Jean-luc and Cherubini

Bumetanide for autism: more eye contact, less amygdala activation.

We recently showed that constraining eye contact leads to exaggerated increase of amygdala activation in autism. Here, in a proof of concept pilot study, we demonstrate that administration of bumetanide (a NKCC1 chloride importer antagonist that restores GABAergic inhibition) normalizes the level of amygdala activation during constrained eye contact with dynamic emotional face stimuli in autism. In addition, eye-tracking data reveal that bumetanide administration increases the time spent in spontaneous eye gaze during in a free-viewing mode of the same face stimuli. In keeping with clinical trials, our data support the Excitatory/Inhibitory dysfunction hypothesis in autism, and indicate that bumetanide may improve specific aspects of social processing in autism. Future double-blind placebo controlled studies with larger cohorts of participants will help clarify the mechanisms of bumetanide action in autism

Assessing architectural evolution: A case study

This is the post-print version of the Article. The official published can be accessed from the link below - Copyright @ 2011 SpringerThis paper proposes to use a historical perspective on generic laws, principles, and guidelines, like Lehman’s software evolution laws and Martin’s design principles, in order to achieve a multi-faceted process and structural assessment of a system’s architectural evolution. We present a simple structural model with associated historical metrics and visualizations that could form part of an architect’s dashboard. We perform such an assessment for the Eclipse SDK, as a case study of a large, complex, and long-lived system for which sustained effective architectural evolution is paramount. The twofold aim of checking generic principles on a well-know system is, on the one hand, to see whether there are certain lessons that could be learned for best practice of architectural evolution, and on the other hand to get more insights about the applicability of such principles. We find that while the Eclipse SDK does follow several of the laws and principles, there are some deviations, and we discuss areas of architectural improvement and limitations of the assessment approach