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31.
The multi-transshipment problem is NP-hard already for two commodities over bipartite networks. Nonetheless, using our recent
theory of n-fold integer programming and extensions developed herein, we are able to establish the polynomial time solvability of the
problem in two broad situations. First, for any fixed number of commodities and number of suppliers, we solve the problem
over bipartite networks with variable number of consumers in polynomial time. This is very natural in operations research
applications where few facilities serve many customers. Second, for every fixed network, we solve the problem with variable
number of commodities in polynomial time. 相似文献
32.
Even the most regular stick-slip frictional sliding is always stochastic, with irregularity in both the intervals between slip events and the sizes of the associated stress drops. Applying small-amplitude oscillations to the shear force, we show, experimentally and theoretically, that the stick-slip periods synchronize. We further show that this phase locking is related to the inhibition of slow rupture modes which forces a transition to fast rupture, providing a possible mechanism for observed remote triggering of earthquakes. Such manipulation of collective modes may be generally relevant to extended nonlinear systems driven near to criticality. 相似文献
33.
Ronhovde P Chakrabarty S Hu D Sahu M Sahu KK Kelton KF Mauro NA Nussinov Z 《The European physical journal. E, Soft matter》2011,34(9):105
We elaborate on a general method that we recently introduced for characterizing the “natural” structures in complex physical
systems via multi-scale network analysis. The method is based on “community detection” wherein interacting particles are partitioned into an “ideal
gas” of optimally decoupled groups of particles. Specifically, we construct a set of network representations (“replicas”)
of the physical system based on interatomic potentials and apply a multiscale clustering (“multiresolution community detection”)
analysis using information-based correlations among the replicas. Replicas may i) be different representations of an identical
static system, ii) embody dynamics by considering replicas to be time separated snapshots of the system (with a tunable time
separation), or iii) encode general correlations when different replicas correspond to different representations of the entire
history of the system as it evolves in space-time. Inputs for our method are the inter-particle potentials or experimentally
measured two (or higher order) particle correlations. We apply our method to computer simulations of a binary Kob-Andersen
Lennard-Jones system in a mixture ratio of A80B20 , a ternary model system with components “A”, “B”, and “C” in ratios of A88B7C5 (as in Al88Y7Fe5 , and to atomic coordinates in a Zr80Pt20 system as gleaned by reverse Monte Carlo analysis of experimentally determined structure factors. We identify the dominant
structures (disjoint or overlapping) and general length scales by analyzing extrema of the information theory measures. We
speculate on possible links between i) physical transitions or crossovers and ii) changes in structures found by this method
as well as phase transitions associated with the computational complexity of the community detection problem. We also briefly
consider continuum approaches and discuss rigidity and the shear penetration depth in amorphous systems; this latter length
scale increases as the system becomes progressively rigid. 相似文献
34.
Using mutually modulated cross-gain modulation, Stokes optical frequency changes are converted into modulation phase changes with high sensitivity. In the slow-light transition regime, we demonstrate kilohertz sensitivity to the Stokes optical carrier frequency. The sensitivity is inversely proportional to the modulation frequency of the pump and Stokes beams. 相似文献
35.
By varying the absorption coefficient and width of an intralipid-India ink solution in a quasi-one-dimensional experiment, we investigate the transition between the ballistic and the diffusive regimes. The medium's attenuation coefficient changes abruptly between two different values within a single mean free path. This problem is analyzed both experimentally and theoretically, and it is demonstrated that the transition location depends on the scattering coefficient as well as on the measuring solid angle. 相似文献
36.
We provide a complexity classification of four variants of robust integer programming when the underlying Graver basis is given. We discuss applications to robust multicommodity flows and multiway statistical table problems, and describe an effective parametrization of robust integer programming. 相似文献
37.
Multilingual text compression exploits the existence of the same text in several languages to compress the second and subsequent copies by reference to the first. This is done based on bilingual text alignment, a mapping of words and phrases in one text to their semantic equivalents in the translation. A new multilingual text compression scheme is suggested, which improves over an immediate generalization of bilingual algorithms. The idea is to store the necessary markup data within the source language text; the incurred compression loss due to this overhead is smaller than the savings in the compressed target language texts, for a large enough number of the latter. Experimental results are presented for a parallel corpus in six languages extracted from the EUR-Lex website of the European Union. These results show the superiority of the new algorithm as a function of the number of languages. 相似文献
38.
39.
Shmuel Rosset 《Israel Journal of Mathematics》1991,73(3):257-279
The Baer invariants Γ
n
(G) of a group are central extensions of the elementsγ
n
(G) of the lower central series. We show that the inclusionsγ
n
+1 ⊂γ
n
can be lifted to functor morphisms Γ
n+1→Γ
n
and a canonical Lie algebra, analogous to Lazard’s Lie algebra, can be constructed which is explicitly computable. This is
applied in various ways. 相似文献
40.
Erik Guentner Nigel Higson Shmuel Weinberger 《Publications Mathématiques de L'IHéS》2005,101(1):243-268
Let K be a field. We show that every countable subgroup of GL(n,K) is uniformly embeddable in a Hilbert space. This implies that Novikov’s higher signature conjecture holds for these groups. We also show that every countable subgroup of GL(2,K) admits a proper, affine isometric action on a Hilbert space. This implies that the Baum-Connes conjecture holds for these groups. Finally, we show that every subgroup of GL(n,K) is exact, in the sense of C*-algebra theory. 相似文献