Convex Combinatorial Optimization

We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications

A Sealed-Bid Auction that Matches the English Auction

This paper analyzes a two-stage sealed-bid auction that is frequently employed in privatization, takeover, and merger and acquisition contests. This auction format yields the same expected revenue as the open ascending (English) auction, yet is less susceptible to preemptive bidding and collusion.Auctions

Field measurements of a swell band, shore normal, flux divergence reversal

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2011Throughout this thesis we will discuss the theoretical background and empirical observation of a swell band shore normal flux divergence reversal. Specifically, we will demonstrate the existence and persistence of the energy flux divergence reversal in the nearshore region of Atchafalaya Bay, Gulf of Mexico, across storms during the March through April 2010 deployment. We will show that the swell band offshore component of energy flux is rather insignificant during the periods of interest, and as such we will neglect it during the ensuing analysis. The data presented will verify that the greatest flux divergence reversal is seen with winds from the East to Southeast, which is consistent with theories which suggest shoreward energy flux as well as estuarine sediment transport and resuspension prior to passage of a cold front. Employing the results of theoretical calculations and numerical modeling we will confirm that a plausible explanation for this phenomena can be found in situations where temporally varying wind input may locally balance or overpower bottom induced dissipation, which may also contravene the hypothesis that dissipation need increase shoreward due to nonlinear wave-wave interactions and maturation of the spectrum. Lastly, we will verify that the data presented is consistent with other measures collected during the same deployment in the Atchafalaya Bay during March - April 2010

Effects of atomic interactions on Quantum Accelerator Modes

We consider the influence of the inclusion of interatomic interactions on the delta-kicked accelerator model. Our analysis concerns in particular quantum accelerator modes, namely quantum ballistic transport near quantal resonances. The atomic interaction is modelled by a Gross-Pitaevskii cubic nonlinearity, and we address both attractive (focusing) and repulsive (defocusing) cases. The most remarkable effect is enhancement or damping of the accelerator modes, depending on the sign of the nonlinear parameter. We provide arguments showing that the effect persists beyond mean-field description, and lies within the experimentally accessible parameter range.Comment: 4 pages, 6 figure

Relative systoles of relative-essential 2-complexes

We prove a systolic inequality for the phi-relative 1-systole of a phi-essential 2-complex, where phi is a homomorphism from the fundamental group of the complex, to a finitely presented group G. Indeed we show that universally for any phi-essential Riemannian 2-complex, and any G, the area of X is bounded below by 1/8 of sys(X,phi)^2. Combining our results with a method of Larry Guth, we obtain new quantitative results for certain 3-manifolds: in particular for Sigma the Poincare homology sphere, we have sys(Sigma)^3 < 24 vol(Sigma).Comment: 20 pages, to appear in Algebraic and Geometric Topolog

Neutron Stars with a Stable, Light Supersymmetric Baryon

If a light gluino exists, the lightest gluino-containing baryon, the \OSO, is a possible candidate for self-interacting dark matter. In this scenario, the simplest explanation for the observed ratio $\Omega_{dm}/\Omega_b \approx 6-10$ is that $m_{S^0} \sim 900$\MeVcs; this is not at present excluded by particle physics. Such an \OSO could be present in neutron stars, with hyperon formation serving as an intermediate stage. We calculate equilibrium compositions and equation of state for high density matter with the \OSO, and find that for a wide range of parameters the properties of neutron stars with the \OSO are consistent with observations. In particular, the maximum mass of a nonrotating star is $1.7-1.8 M_\odot$, and the presence of the \OSO is helpful in reconciling observed cooling rates with hyperon formation.Comment: ApJL submitted, 4 pages, using emulateapj (very very minor changes to match published versio

The Localization Length of Stationary States in the Nonlinear Schreodinger Equation

For the nonlinear Schreodinger equation (NLSE), in presence of disorder, exponentially localized stationary states are found. In the present Letter it is demonstrated analytically that the localization length is typically independent of the strength of the nonlinearity and is identical to the one found for the corresponding linear equation. The analysis makes use of the correspondence between the stationary NLSE and the Langevin equation as well as of the resulting Fokker-Planck equation. The calculations are performed for the ``white noise'' random potential and an exact expression for the exponential growth of the eigenstates is obtained analytically. It is argued that the main conclusions are robust

Cosmic-ray induced destruction of CO in star-forming galaxies

We explore the effects of the expected higher cosmic ray (CR) ionization rates $\zeta_{\rm CR}$ on the abundances of carbon monoxide (CO), atomic carbon (C), and ionized carbon (C$^+$) in the H$_2$ clouds of star-forming galaxies. The study of Bisbas et al. (2015) is expanded by: a) using realistic inhomogeneous Giant Molecular Cloud (GMC) structures, b) a detailed chemical analysis behind the CR-induced destruction of CO, and c) exploring the thermal state of CR-irradiated molecular gas. CRs permeating the interstellar medium with $\zeta_{\rm CR}$$\gtrsim 10\times$(Galactic) are found to significantly reduce the [CO]/[H$_2$] abundance ratios throughout the mass of a GMC. CO rotational line imaging will then show much clumpier structures than the actual ones. For $\zeta_{\rm CR}$$\gtrsim 100\times$(Galactic) this bias becomes severe, limiting the utility of CO lines for recovering structural and dynamical characteristics of H$_2$-rich galaxies throughout the Universe, including many of the so-called Main Sequence (MS) galaxies where the bulk of cosmic star formation occurs. Both C$^+$ and C abundances increase with rising $\zeta_{\rm CR}$, with C remaining the most abundant of the two throughout H$_2$ clouds, when $\zeta_{\rm CR}\sim (1-100)\times$(Galactic). C$^+$ starts to dominate for $\zeta_{\rm CR}$$\gtrsim 10^3\times$(Galactic). The thermal state of the gas in the inner and denser regions of GMCs is invariant with $T_{\rm gas}\sim 10\,{\rm K}$ for $\zeta_{\rm CR}\sim (1-10)\times$(Galactic). For $\zeta_{\rm CR}$$\sim 10^3\times$(Galactic) this is no longer the case and $T_{\rm gas}\sim 30-50\,{\rm K}$ are reached. Finally we identify OH as the key species whose $T_{\rm gas}-$sensitive abundance could mitigate the destruction of CO at high temperatures.Comment: 17 pages, 12 figures, accepted by Ap

Bed-parallel slip : Identifying missing displacement in mass transport deposits

RW was supported by the Israel Science Foundation (ISF grant No. 868/17). SM acknowledges the Israel Science Foundation (ISF grant No. 1645/19). TL acknowledges the Israeli government GSI DS project 40706.Peer reviewedPostprin

On Some Positivity Properties of the Interquark Potential in QCD

We prove that the Fourier transform of the exponential e^{-\b V(R)} of the {\bf static} interquark potential in QCD is positive. It has been shown by Eliott Lieb some time ago that this property allows in the same limit of static spin independent potential proving certain mass relation between baryons with different quark flavors.Comment: 6 pages, latex with one postscript figur