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51.
Spectral compression by self-phase modulation of amplitude- and phase-shaped pulses is demonstrated as superior compared to pulses that have only been phase shaped. We synthesize linearly negatively chirped parabolic pulses, which we send through a nonlinear photonic crystal fiber, in which self-phase modulation compresses the spectrum of the pulses to within 20% of the Fourier transform limit. 相似文献
52.
Let fr(n,v,e) denote the maximum number of edges in an r-uniform hypergraph on n vertices, which does not contain e edges spanned by v vertices. Extending previous results of Ruzsa and Szemerédi and of Erdős, Frankl and R?dl, we partially resolve a problem
raised by Brown, Erdős and Sós in 1973, by showing that for any fixed 2≤k<r, we have
* Researchs upported in part by a USA-Israeli BSF grant, by the Israel Science Foundation and by the Hermann Minkowski Minerva
Center for Geometry at Tel Aviv University.
† This work forms part of the author's Ph.D. Thesis. Research supported by a Charles Clore Foundation Fellowship and an IBM
Ph.D. Fellowship. 相似文献
53.
The behavior of the random graph G(n,p) around the critical probability pc = is well understood. When p = (1 + O(n1/3))pc the components are roughly of size n2/3 and converge, when scaled by n?2/3, to excursion lengths of a Brownian motion with parabolic drift. In particular, in this regime, they are not concentrated. When p = (1 ‐ ?(n))pc with ?(n)n1/3 →∞ (the subcritical regime) the largest component is concentrated around 2??2 log(?3n). When p = (1 + ?(n))pc with ?(n)n1/3 →∞ (the supercritical regime), the largest component is concentrated around 2?n and a duality principle holds: other component sizes are distributed as in the subcritical regime. Itai Benjamini asked whether the same phenomenon occurs in a random d‐regular graph. Some results in this direction were obtained by (Pittel, Ann probab 36 (2008) 1359–1389). In this work, we give a complete affirmative answer, showing that the same limiting behavior (with suitable d dependent factors in the non‐critical regimes) extends to random d‐regular graphs. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010 相似文献
54.
We prove packing and counting theorems for arbitrarily oriented Hamilton cycles in (n, p) for nearly optimal p (up to a factor). In particular, we show that given t = (1 ? o(1))np Hamilton cycles C1,…,Ct, each of which is oriented arbitrarily, a digraph ~(n, p) w.h.p. contains edge disjoint copies of C1,…,Ct, provided . We also show that given an arbitrarily oriented n‐vertex cycle C, a random digraph ~(n, p) w.h.p. contains (1 ± o(1))n!pn copies of C, provided . 相似文献
55.
We study the problem of minimizing total latency in machine scheduling with deliveries, which is defined as follows. There is a set of n jobs to be processed by a single machine at a plant, where job Ji is associated with its processing time and a customer i located at location i to which the job is to be delivered. In addition, there is a single uncapacitated delivery vehicle available. All jobs (vehicle) are available for processing (delivery) at time 0. Our aim is to determine the sequence in which the jobs should be processed in the plant, the departure times of the vehicle from the plant, and the routing of the vehicle, so as to minimize the total latency (job delivery time). We present a 6e16.309691-approximation algorithm for the problem. 相似文献
56.
We consider the following Turán-type problem: given a fixed tournament H, what is the least integer t = t(n,H) so that adding t edges to any n-vertex tournament, results in a digraph containing a copy of H. Similarly, what is the least integer t = t(T n ,H) so that adding t edges to the n-vertex transitive tournament, results in a digraph containing a copy of H. Besides proving several results on these problems, our main contributions are the following:
相似文献
- Pach and Tardos conjectured that if M is an acyclic 0/1 matrix, then any n × n matrix with n(log n) O(1) entries equal to 1 contains the pattern M. We show that this conjecture is equivalent to the assertion that t(T n ,H) = n(log n) O(1) if and only if H belongs to a certain (natural) family of tournaments.
- We propose an approach for determining if t(n,H) = n(log n) O(1). This approach combines expansion in sparse graphs, together with certain structural characterizations of H-free tournaments. Our result opens the door for using structural graph theoretic tools in order to settle the Pach–Tardos conjecture.
57.
We propose a method, Temperature Integration, which allows an efficient calculation of free energy differences between two systems of interest, with the same degrees of freedom, which may have rough energy landscapes. The method is based on calculating, for each single system, the difference between the values of lnZ at two temperatures, using a Parallel Tempering procedure. If our two systems of interest have the same phase space volume, they have the same values of lnZ at high-T, and we can obtain the free energy difference between them, using the two single-system calculations described above. If the phase space volume of a system is known, our method can be used to calculate its absolute (versus relative) free energy as well. We apply our method and demonstrate its efficiency on a “toy model” of hard rods on a 1-dimensional ring. 相似文献
58.
We analyze Avoider–Enforcer games played on edge disjoint hypergraphs, providing an analog of the classic and well known game Box, due to Chvátal and Erd?s. We consider both strict and monotone versions of Avoider–Enforcer games, and for each version we give a sufficient condition to win for each player. We also present applications of our results to several general Avoider–Enforcer games. 相似文献
59.
Optical sectioning is performed by collecting the fluorescent emission of two-exciton states in colloidal quantum dots. The two-exciton state is created by two consecutive resonant absorption events, thus requiring unprecedented low excitation energy and peak powers as low as 10(5) W/cm(2). The depth resolution is shown to be equivalent to that of standard multiphoton microscopy, and it was found to deteriorate only slowly as saturation of the two-exciton state is approached, owing to signal contribution from higher excitonic states. 相似文献
60.