2,297,237 research outputs found

    Confidence Intervals

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    PowerPoint slides for Confidence Intervals. Examples are taken from the Medical Literatur

    Inter-spikes-intervals exponential and gamma distributions study of neuron firing rate for SVITE motor control model on FPGA

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    This paper presents a statistical study on a neuro-inspired spike-based implementation of the Vector-Integration-To-End-Point motor controller (SVITE) and compares its deterministic neuron-model stream of spikes with a proposed modification that converts the model, and thus the controller, in a Poisson like spike stream distribution. A set of hardware pseudo-random numbers generators, based on a Linear Feedback Shift Register (LFSR), have been introduced in the neuron-model so that they reach a closer biological neuron behavior. To validate the new neuron-model behavior a comparison between the Inter-Spikes-Interval empirical data and the Exponential and Gamma distributions has been carried out using the Kolmogorov–Smirnoff test. An in-hardware validation of the controller has been performed in a Spartan6 FPGA to drive directly with spikes DC motors from robotics to study the behavior and viability of the modified controller with random components. The results show that the original deterministic spikes distribution of the controller blocks can be swapped with Poisson distributions using 30-bit LFSRs. The comparative between the usable controlling signals such as the trajectory and the speed profile using a deterministic and the new controller show a standard deviation of 11.53 spikes/s and 3.86 spikes/s respectively. These rates do not affect our system because, within Pulse Frequency Modulation, in order to drive the motors, time length can be fixed to spread the spikes. Tuning this value, the slow rates could be filtered by the motor. Therefore, this SVITE neuro-inspired controller can be integrated within complex neuromorphic architectures with Poisson-like neurons

    MinMax-Profiles: A Unifying View of Common Intervals, Nested Common Intervals and Conserved Intervals of K Permutations

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    Common intervals of K permutations over the same set of n elements were firstly investigated by T. Uno and M.Yagiura (Algorithmica, 26:290:309, 2000), who proposed an efficient algorithm to find common intervals when K=2. Several particular classes of intervals have been defined since then, e.g. conserved intervals and nested common intervals, with applications mainly in genome comparison. Each such class, including common intervals, led to the development of a specific algorithmic approach for K=2, and - except for nested common intervals - for its extension to an arbitrary K. In this paper, we propose a common and efficient algorithmic framework for finding different types of common intervals in a set P of K permutations, with arbitrary K. Our generic algorithm is based on a global representation of the information stored in P, called the MinMax-profile of P, and an efficient data structure, called an LR-stack, that we introduce here. We show that common intervals (and their subclasses of irreducible common intervals and same-sign common intervals), nested common intervals (and their subclass of maximal nested common intervals) as well as conserved intervals (and their subclass of irreducible conserved intervals) may be obtained by appropriately setting the parameters of our algorithm in each case. All the resulting algorithms run in O(Kn+N)-time and need O(n) additional space, where N is the number of solutions. The algorithms for nested common intervals and maximal nested common intervals are new for K>2, in the sense that no other algorithm has been given so far to solve the problem with the same complexity, or better. The other algorithms are as efficient as the best known algorithms.Comment: 25 pages, 2 figure

    Coding rotations on intervals

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    We show that the coding of rotation by α\alpha on mm intervals with rationally independent lengths can be recoded over mm Sturmian words of angle α.\alpha. More precisely, for a given mm an universal automaton is constructed such that the edge indexed by the vector of values of the iith letter on each Sturmian word gives the value of the iith letter of the coding of rotation.Comment: LIAFA repor

    Involutions of real intervals

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    This paper shows a simple construction of the continuous involutions of real intervals in terms of the continuous even functions. We also study the smooth involutions defined by symmetric equations. Finally, we review some applications, in particular the characterization of the isochronous potentials by means of smooth involutions

    Primes in short intervals

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    Contrary to what would be predicted on the basis of Cram\'er's model concerning the distribution of prime numbers, we develop evidence that the distribution of ψ(x+H)−ψ(x)\psi(x+H)- \psi(x), for 0≀x≀N0\le x\le N, is approximately normal with mean ∌H\sim H and variance ∌Hlog⁥N/H\sim H\log N/H, when NΎ≀H≀N1−ήN^\delta \le H \le N^{1-\delta}.Comment: 29 page
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