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Jeffrey L Spielman 《Journal of multivariate analysis》1976,6(3):426-446
Let be a real separable Hilbert space; let X(t), t?[0, 1], be a separable, stochastically continuous, -valued stochastic process with independent increments. Then a decomposition of X(t) into a uniformly convergent sum of independent processes is found. In this decomposition one of the processes is Gaussian with continuous sample functions, and the remainder of the processes have sample functions whose discontinuities correspond to those of certain real-valued Poisson processes. The decomposition of X(t) leads to a Levy-Khintchine representation of the characteristic functional of X(t). In addition, the case when X(t) has finite variance is explored, and, as a consequence of the above decomposition, a Kolmogorov-type representation of the characteristic functional of X(t) is derived. 相似文献
14.
This paper communicates the impact of prospective teachers' learning of mathematics using novel curriculum materials in an innovative classroom setting. Two sections of a mathematics content course for prospective elementary teachers used different text materials and instructional approaches. The primary mathematical authorities were the instructor and text in the textbook section and the prospective teachers in the curriculum materials section. After one semester, teachers in the curriculum materials section (n= 34) placed significantly more importance on classroom group work and discussions, less on instructor lecture and explanation, and less on textbooks having practice problems, examples, and explanations. They valued student exploration over practice. In the textbook section (n= 19), there was little change in the teachers' beliefs, in which practice was valued over exploration. These results highlight the positive impact of experiences with innovative curriculum materials on prospective elementary teachers' beliefs about mathematics instruction. 相似文献
15.
Goldman N Satija I Nikolic P Bermudez A Martin-Delgado MA Lewenstein M Spielman IB 《Physical review letters》2010,105(25):255302
We lay out an experiment to realize time-reversal invariant topological insulators in alkali atomic gases. We introduce an original method to synthesize a gauge field in the near field of an atom chip, which effectively mimics the effects of spin-orbit coupling and produces quantum spin-Hall states. We also propose a feasible scheme to engineer sharp boundaries where the hallmark edge states are localized. Our multiband system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Because of their remarkable versatility, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing. 相似文献
16.
We perform a smoothed analysis of a termination phase for linear programming algorithms. By combining this analysis with
the smoothed analysis of Renegar's condition number by Dunagan, Spielman and Teng (http://arxiv.org/abs/cs.DS/0302011) we
show that the smoothed complexity of interior-point algorithms for linear programming is O(m
3
log(m/Σ)). In contrast, the best known bound on the worst-case complexity of linear programming is O(m
3 L), where L could be as large as m. We include an introduction to smoothed analysis and a tutorial on proof techniques that have been useful in smoothed analyses.
Received: December 10, 2002 / Accepted: April 28, 2003
Published online: June 5, 2003
Key words. smoothed analysis – linear programming – interior-point algorithms – condition numbers
Mathematics Subject Classification (1991): 90C05, 90C51, 68Q25 相似文献
17.
We give an elementary proof of a generalization of Bourgain and Tzafriri’s Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which it is well-invertible. Our proof gives the tightest known form of this result, is constructive, and provides a deterministic polynomial time algorithm for finding the desired subspace. 相似文献
18.
We perform a smoothed analysis of Renegar’s condition number for linear programming by analyzing the distribution of the distance
to ill-posedness of a linear program subject to a slight Gaussian perturbation. In particular, we show that for every n-by-d matrix Ā, n-vector
[`(\varvec b)]{\bar{\varvec b}}, and d-vector
[`(\varvec c)]{\bar{\varvec c}} satisfying
||[`(A)], [`(\varvec b)], [`(\varvec c)]||F £ 1{{||\bar{\bf A}, \bar{\varvec b}, \bar{\varvec c}||_F \leq 1}} and every σ ≤ 1,
EA,\varvec b,\varvec c [logC (A,\varvec b,\varvec c) = O (log(nd/s)),\mathop{\bf E}\limits_{\bf A,\varvec b,\varvec c }{{[\log C (\bf A,\varvec b,\varvec c)} = O (\log (nd/\sigma)),} 相似文献
19.
L.A. Tracy I.B. Spielman J.P. Eisenstein L.N. Pfeiffer K.W. West 《Physica E: Low-dimensional Systems and Nanostructures》2006,34(1-2):220
Via a resistively detected NMR technique, the nuclear spin–lattice relaxation time T1 of 71Ga has been measured in a GaAs/AlGaAs heterostructure containing two weakly coupled 2D electron systems (2DES) at low temperatures, each at Landau level filling . Incomplete electronic spin polarization, which has been reported previously for low density 2DESs at , should facilitate hyperfine-coupled nuclear spin relaxation owing to the presence of both electron spin states at the Fermi level. Composite fermion theory suggests a Korringa-law temperature dependence: T1T=constant is expected for temperatures . Our measurements show that for temperatures in the range , T1 rises less rapidly with falling temperature than this law predicts. This may suggest the existence of alternate nuclear spin relaxation mechanisms in this system. Also, our data allows for an estimate of the composite fermion mass. 相似文献
20.
We realize a single-band 2D Bose-Hubbard system with Rb atoms in an optical lattice and measure the condensate fraction as a function of lattice depth, crossing from the superfluid to the Mott-insulating phase. We quantitatively identify the location of the superfluid to normal transition by observing when the condensed fraction vanishes. Our measurement agrees with recent quantum Monte Carlo calculations for a finite-sized 2D system to within experimental uncertainty. 相似文献
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