4,172 research outputs found

    The transition temperature of the dilute interacting Bose gas for NN internal degrees of freedom

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    We calculate explicitly the variation δTc\delta T_c of the Bose-Einstein condensation temperature TcT_c induced by weak repulsive two-body interactions to leading order in the interaction strength. As shown earlier by general arguments, δTc/Tc\delta T_c/T_c is linear in the dimensionless product an1/3an^{1/3} to leading order, where nn is the density and aa the scattering length. This result is non-perturbative, and a direct perturbative calculation of the amplitude is impossible due to infrared divergences familiar from the study of the superfluid helium lambda transition. Therefore we introduce here another standard expansion scheme, generalizing the initial model which depends on one complex field to one depending on NN real fields, and calculating the temperature shift at leading order for large NN. The result is explicit and finite. The reliability of the result depends on the relevance of the large NN expansion to the situation N=2, which can in principle be checked by systematic higher order calculations. The large NN result agrees remarkably well with recent numerical simulations.Comment: 10 pages, Revtex, submitted to Europhysics Letter

    Private Matchings and Allocations

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    We consider a private variant of the classical allocation problem: given k goods and n agents with individual, private valuation functions over bundles of goods, how can we partition the goods amongst the agents to maximize social welfare? An important special case is when each agent desires at most one good, and specifies her (private) value for each good: in this case, the problem is exactly the maximum-weight matching problem in a bipartite graph. Private matching and allocation problems have not been considered in the differential privacy literature, and for good reason: they are plainly impossible to solve under differential privacy. Informally, the allocation must match agents to their preferred goods in order to maximize social welfare, but this preference is exactly what agents wish to hide. Therefore, we consider the problem under the relaxed constraint of joint differential privacy: for any agent i, no coalition of agents excluding i should be able to learn about the valuation function of agent i. In this setting, the full allocation is no longer published---instead, each agent is told what good to get. We first show that with a small number of identical copies of each good, it is possible to efficiently and accurately solve the maximum weight matching problem while guaranteeing joint differential privacy. We then consider the more general allocation problem, when bidder valuations satisfy the gross substitutes condition. Finally, we prove that the allocation problem cannot be solved to non-trivial accuracy under joint differential privacy without requiring multiple copies of each type of good.Comment: Journal version published in SIAM Journal on Computation; an extended abstract appeared in STOC 201

    Live-Learn Cal Poly: A New-Urbanist Vision for a More Livable and Sustainable Campus

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    Universities across the nation have begun a mixed-use initiative in an effort to densify campuses and diversify retail and housing choices to increase student residency on campus. The movement to model the built environment after traditional mixed-use urbanism has been shown to improve capital flow within the local submarket on campus, foster flexible learning environments to support student success, and reduce automobile dependency. In order to reflect Cal Poly’s Master Plan moving forward, this report intends to follow the guiding principles outlined in the Master Plan while proposing sustainable and efficient land use designs to accommodate future growth at Cal Poly

    Quantum phase transition in an atomic Bose gas near a Feshbach resonance

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    We study the quantum phase transition in an atomic Bose gas near a Feshbach resonance in terms of the renormalization group. This quantum phase transition is characterized by an Ising order parameter. We show that in the low temperature regime where the quantum fluctuations dominate the low-energy physics this phase transition is of first order because of the coupling between the Ising order parameter and the Goldstone mode existing in the bosonic superfluid. However, when the thermal fluctuations become important, the phase transition turns into the second order one, which belongs to the three-dimensional Ising universality class. We also calculate the damping rate of the collective mode in the phase with only a molecular Bose-Einstein condensate near the second-order transition line, which can serve as an experimental signature of the second-order transition.Comment: 8 pages, 2 figures, published version in Phys. Rev.

    FPT-Algorithms for the l-Matchoid Problem with Linear and Submodular Objectives

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    We design a fixed-parameter deterministic algorithm for computing a maximum weight feasible set under a â„“\ell-matchoid of rank kk, parameterized by â„“\ell and kk. Unlike previous work that presumes linear representativity of matroids, we consider the general oracle model. Our result, combined with the lower bounds of Lovasz, and Jensen and Korte, demonstrates a separation between the â„“\ell-matchoid and the matroid â„“\ell-parity problems in the setting of fixed-parameter tractability. Our algorithms are obtained by means of kernelization: we construct a small representative set which contains an optimal solution. Such a set gives us much flexibility in adapting to other settings, allowing us to optimize not only a linear function, but also several important submodular functions. It also helps to transform our algorithms into streaming algorithms. In the streaming setting, we show that we can find a feasible solution of value zz and the number of elements to be stored in memory depends only on zz and â„“\ell but totally independent of nn. This shows that it is possible to circumvent the recent space lower bound of Feldman et al., by parameterizing the solution value. This result, combined with existing lower bounds, also provides a new separation between the space and time complexity of maximizing an arbitrary submodular function and a coverage function in the value oracle model

    Typing tumors using pathways selected by somatic evolution.

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    Many recent efforts to analyze cancer genomes involve aggregation of mutations within reference maps of molecular pathways and protein networks. Here, we find these pathway studies are impeded by molecular interactions that are functionally irrelevant to cancer or the patient's tumor type, as these interactions diminish the contrast of driver pathways relative to individual frequently mutated genes. This problem can be addressed by creating stringent tumor-specific networks of biophysical protein interactions, identified by signatures of epistatic selection during tumor evolution. Using such an evolutionarily selected pathway (ESP) map, we analyze the major cancer genome atlases to derive a hierarchical classification of tumor subtypes linked to characteristic mutated pathways. These pathways are clinically prognostic and predictive, including the TP53-AXIN-ARHGEF17 combination in liver and CYLC2-STK11-STK11IP in lung cancer, which we validate in independent cohorts. This ESP framework substantially improves the definition of cancer pathways and subtypes from tumor genome data
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