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823
BOUNDS FOR THE CATALAN NUMBERS
, 1990
"... For the simple symmetric random walk on a two-dimensional lattice, it is well known (see, e.g., Feller [4], p. 361) that the probability of the origin begin revisited at the 2n th step is ..."
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For the simple symmetric random walk on a two-dimensional lattice, it is well known (see, e.g., Feller [4], p. 361) that the probability of the origin begin revisited at the 2n th step is
Schaftingen, The continuity of functions with N-th derivative measure
- Houston J. Math
"... Abstract. We study the continuity of functions u whose mixed derivative ∂1 · · · ∂Nu is a measure. If u ∈W 1,1(RN), then we prove that u is continu-ous. The same conclusion holds for u ∈ Wk,p(Q), with kp> N − 1, where Q denotes a cube in RN. The key step in the proof consists in showing that th ..."
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Cited by 1 (0 self)
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Abstract. We study the continuity of functions u whose mixed derivative ∂1 · · · ∂Nu is a measure. If u ∈W 1,1(RN), then we prove that u is continu-ous. The same conclusion holds for u ∈ Wk,p(Q), with kp> N − 1, where Q denotes a cube in RN. The key step in the proof consists in showing
BRANCHING RANDOM WALK WITH EXPONENTIALLY DECREASING STEPS, AND STOCHASTICALLY SELF-SIMILAR MEASURES
, 2007
"... Abstract. We consider a Branching Random Walk on R whose step size decreases by a fixed factor, 0 < λ < 1, with each turn. This process generates a random probability measure on R, that is, the limit of uniform distribution among the 2 n particles of the n-th step. We present an initial invest ..."
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Cited by 1 (0 self)
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Abstract. We consider a Branching Random Walk on R whose step size decreases by a fixed factor, 0 < λ < 1, with each turn. This process generates a random probability measure on R, that is, the limit of uniform distribution among the 2 n particles of the n-th step. We present an initial
On the Episode Duration Distribution Spanning Arbitrary States in Fixed-Policy Markov Decision Processes
, 2010
"... A method for obtaining a computationally efficient closed-form solution for the episode duration distribution in finite-horizon, fixed-policy Markov decision processes (MDP) is presented. The approach is based on finding the n th-step first visit probability mass function between any two states of a ..."
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A method for obtaining a computationally efficient closed-form solution for the episode duration distribution in finite-horizon, fixed-policy Markov decision processes (MDP) is presented. The approach is based on finding the n th-step first visit probability mass function between any two states
An algebraic version of a theorem of Kurihara
- Journal of Number Theory
"... Abstract. Let E/Q be an elliptic curve and let p be an odd supersingular prime for E. In this article, we study the simplest case of Iwasawa theory for elliptic curves, namely when E(Q) is finite, X(E/Q) has no p-torsion and the Tamagawa factors for E are all prime to p. Under these hypotheses, we p ..."
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Cited by 2 (0 self)
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prove that E(Qn) is finite and make precise statements about the size and structure of the p-power part of X(E/Qn). Here Qn is the n-th step in the cyclotomic Zp-extension of Q. 1.
An Approximate Max-Flow Min-Cut Theorem for Uniform Multicommodity Flow Problems with Applications to Approximation Algorithms
, 1989
"... In this paper, we consider a multicommodity flow problem where for each pair of vertices, (u,v), we are required to sendf half-units of commodity (uv) from u to v and f half-units of commodity (vu) from v to u without violating capacity constraints. Our main result is an algorithm for performing th9 ..."
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Cited by 246 (12 self)
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can prove that any n-node bounded degree graph, G, with minimum edge expansion h can be configured off-line to simulate any n-node bounded degree graph H in 0(log n/a)steps using constant size queues. By letting H be a universal network, we can then use G to simulate a PRAM on-line with elay 0(log2 n1
Randomized Distributed Algorithms as Markov Chains
- IN PROC. 15TH INT. CONF. ON DISTRIBUTED COMPUTING (DISC 2001), LNCS 2180
, 2001
"... Distributed randomized algorithms, when they operate under a memoryless scheduler, behave as finite Markov chains: the probability at n-th step to go from a configuration x to another one y is a constant p that depends on x and y only. By Markov theory, we thus know that, no matter where the algorit ..."
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Cited by 1 (0 self)
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Distributed randomized algorithms, when they operate under a memoryless scheduler, behave as finite Markov chains: the probability at n-th step to go from a configuration x to another one y is a constant p that depends on x and y only. By Markov theory, we thus know that, no matter where
Simulation of function Y = f (X) by means of random choices of increments ¢X and ¢Y (Method of Expectancies)
"... Abstract: In many mathematical models of growth phenomena, an elemental area ¢A is added to an object growing in the plane; in doing so, the perimeter of the object changes with the area. If ¢A is an elemental area (a square of sides equal to unity), it turns out that the changes of perimeter, ¢P; m ..."
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of increments ¢X and ¢Y chosen at random from a given set of possibilities for each of them. Thus, the purpose of this paper is the study of the algorithm Yn+1 = Yn +¢Y and Xn+1 = Xn +¢X at the n-th step of the growth of the function. Key words: expectancies, growth phenomena 1.
ðn 2 = log nÞ Speed-Up of TBR Heuristics for the Gene-Duplication Problem
"... Abstract—The gene-duplication problem is to infer a species supertree from gene trees that are confounded by complex histories of gene duplications. This problem is NP-complete and thus requires efficient and effective heuristics. Existing heuristics perform a stepwise search of the tree space, wher ..."
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Cited by 2 (1 self)
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, where each step is guided by an exact solution to an instance of a local search problem. We improve on the time complexity of the local search problem by a factor of n 2 = log n, where n is the size of the resulting species supertree. Typically, several thousand instances of the local search problem
Coil sensitivity encoding for fast MRI. In:
- Proceedings of the ISMRM 6th Annual Meeting,
, 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
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Cited by 193 (3 self)
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, must not exceed n C . In other words, the reduction factor is bound by the number of coils used. Note that n P does not need to be the same for all partial unfolding steps. Upon non-integer reduction the number of pixels actually superimposed may vary in the reduced FOV. Generally, the degree
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823
