Is a Higgs Vacuum Instability Fatal for High-Scale Inflation?

We study the inflationary evolution of a scalar field $h$ with an unstable potential for the case where the Hubble parameter $H$ during inflation is larger than the instability scale $\Lambda_I$ of the potential. Quantum fluctuations in the field of size $\delta h \sim \frac{H}{2 \pi}$ imply that the unstable part of the potential is sampled during inflation. We investigate the evolution of these fluctuations to the unstable regime, and in particular whether they generate cosmological defects or even terminate inflation. We apply the results of a toy scalar model to the case of the Standard Model (SM) Higgs boson, whose quartic evolves to negative values at high scales, and extend previous analyses of Higgs dynamics during inflation utilizing statistical methods to a perturbative and fully gauge-invariant formulation. We show that the dynamics are controlled by the renormalization group-improved quartic coupling $\lambda(\mu)$ evaluated at a scale $\mu = H$, such that Higgs fluctuations are enhanced by the instability if $H > \Lambda_I$. Even if $H > \Lambda_I$, the instability in the SM Higgs potential does not end inflation; instead the universe slowly sloughs off crunching patches of space that never come to dominate the evolution. As inflation proceeds past 50 $e$-folds, a significant proportion of patches exit inflation in the unstable vacuum, and as much as 1% of the spacetime can rapidly evolve to a defect. Depending on the nature of these defects, however, the resulting universe could still be compatible with ours.Comment: 31 pages, 3 figures; v2: references added, journal versio

Summary Based Structures with Improved Sublinear Recovery for Compressed Sensing

We introduce a new class of measurement matrices for compressed sensing, using low order summaries over binary sequences of a given length. We prove recovery guarantees for three reconstruction algorithms using the proposed measurements, including $\ell_1$ minimization and two combinatorial methods. In particular, one of the algorithms recovers $k$-sparse vectors of length $N$ in sublinear time $\text{poly}(k\log{N})$, and requires at most $\Omega(k\log{N}\log\log{N})$ measurements. The empirical oversampling constant of the algorithm is significantly better than existing sublinear recovery algorithms such as Chaining Pursuit and Sudocodes. In particular, for $10^3\leq N\leq 10^8$ and $k=100$, the oversampling factor is between 3 to 8. We provide preliminary insight into how the proposed constructions, and the fast recovery scheme can be used in a number of practical applications such as market basket analysis, and real time compressed sensing implementation

On the modeling of low-Reynolds-number turbulence

A full Reynolds-stress closure that is capable of describing the flow all the way to the wall was formulated for turbulent flow through circular pipe. Since viscosity does not appear explicitly in the pressure redistribution terms, conventional high-number models for these terms are found to be applicable. However, the models for turbulent diffusion and viscous dissipation have to be modified to account for viscous diffusion near a wall. Two redistribution and two diffusion models are investigated for their effects on the model calculations. Wall correction to pressure redistribution modeling is also examined. Diffusion effects on calculated turbulent properties are further investigated by simplifying the transport equations to algebraic equations for Reynolds stress. Two approximations are explored. These are the equilibrium and nonequilibrium turbulence assumptions. Finally, the two-equation closure is also used to calculate the flow in question and the results compared with all the other model calculations. Fully developed pipe flows at two moderate Reynolds numbers are used to validate these model calculations

Impact of acquisition channels on customer equity, The

Customer equity (CE henceforth) is a powerful new paradigm to evaluate the firm's value and to optimally allocate marketing resources. This paper is focused on the relationship between customer acquisition and CE. The authors attempt to answer the following four questions: 1) how should customer acquisition channels be categorized to make them meaningful to managers and academics?; 2) how do we measure the effects of different acquisition channels on the firm's performance?; 3) how do we disentangle short-run effect and long-run effects?, and 4) how should the manager allocate a limited budget among the acquisition channels so as to maximize customer equity? The authors first propose a way of categorizing customer acquisition channels according to their level of contact and intrusiveness. A vector-autoregressive (VAR) model is used to examine the dynamics of acquisition channels and the firm's performance, and an empirical illustration on a surviving Internet company is provided. The results show that each cohort (i.e., customers from different acquisition channels) has different short-run and long-run effects on the firm's performance by the subsequent login and purchasing behavior. Building on previous research on optimal resource allocation, the authors develop a Marketing Decision Support System (MDSS) to help managers allocate the acquisition budget among different channels with the objective of maximizing customer equity. The consequences of naively maximizing the short-term profit and not accounting for differences in the margin contribution of different cohorts are illustrated.customer equity; customer acquisition; VAR; long-run modeling;

General Relativistic Description of the Observed Galaxy Power Spectrum: Do We Understand What We Measure?

We extend the general relativistic description of galaxy clustering developed in Yoo, Fitzpatrick, and Zaldarriaga (2009). For the first time we provide a fully general relativistic description of the observed matter power spectrum and the observed galaxy power spectrum with the linear bias ansatz. It is significantly different from the standard Newtonian description on large scales and especially its measurements on large scales can be misinterpreted as the detection of the primordial non-Gaussianity even in the absence thereof. The key difference in the observed galaxy power spectrum arises from the real-space matter fluctuation defined as the matter fluctuation at the hypersurface of the observed redshift. As opposed to the standard description, the shape of the observed galaxy power spectrum evolves in redshift, providing additional cosmological information. While the systematic errors in the standard Newtonian description are negligible in the current galaxy surveys at low redshift, correct general relativistic description is essential for understanding the galaxy power spectrum measurements on large scales in future surveys with redshift depth z>3. We discuss ways to improve the detection significance in the current galaxy surveys and comment on applications of our general relativistic formalism in future surveys.Comment: accepted for publication in Physical Review

Cool-associated Tyrosine-phosphorylated Protein 1 Is Required for the Anchorage-independent Growth of Cervical Carcinoma Cells by Binding Paxillin and Promoting AKT Activation.

Cool-associated tyrosine-phosphorylated protein 1 (Cat-1) is a signaling scaffold as well as an ADP-ribosylation factor-GTPase-activating protein. Although best known for its role in cell migration, we recently showed that the ability of Cat-1 to bind paxillin, a major constituent of focal complexes, is also essential for the anchorage-independent growth of HeLa cervical carcinoma cells. Here we set out to learn more about the underlying mechanism by which Cat-paxillin interactions mediate this effect. We show that knocking down paxillin expression in HeLa cells promotes their ability to form colonies in soft agar, whereas ectopically expressing paxillin in these cells inhibits this transformed growth phenotype. Although knocking down Cat-1 prevents HeLa cells from forming colonies in soft agar, when paxillin is knocked down together with Cat-1, the cells are again able to undergo anchorage-independent growth. These results suggest that the requirement of Cat-1 for this hallmark of cellular transformation is coupled to its ability to bind paxillin and abrogate its actions as a negative regulator of anchorage-independent growth. We further show that knocking down Cat-1 expression in HeLa cells leads to a reduction in Akt activation, which can be reversed by knocking down paxillin. Moreover, expression of constitutively active forms of Akt1 and Akt2 restores the anchorage-independent growth capability of HeLa cells depleted of Cat-1 expression. Together, these findings highlight a novel mechanism whereby interactions between Cat-1 and its binding partner paxillin are necessary to ensure sufficient Akt activation so that cancer cells are able to grow under anchorage-independent conditions