Linear resolutions of powers and products

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi deformation

Betti numbers for numerical semigroup rings

We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra and Applications (V. Ene, E. Miller Eds.

Quark-Gluon Plasma/Black Hole duality from Gauge/Gravity Correspondence

The Quark-Gluon Plasma (QGP) is the QCD phase of matter expected to be formed at small proper-times in the collision of heavy-ions at high energy. Experimental observations seem to favor a strongly coupled QCD plasma with the hydrodynamic properties of a quasi-perfect fluid, i.e. rapid thermalization (or isotropization) and small viscosity. The theoretical investigation of such properties is not obvious, due to the the strong coupling. The Gauge/Gravity correspondence provides a stimulating framework to explore the strong coupling regime of gauge theories using the dual string description. After a brief introduction to Gauge/Gravity duality, and among various existing studies, we focus on challenging problems of QGP hydrodynamics, such as viscosity and thermalization, in terms of gravitational duals of both the static and relativistically evolving plasma. We show how a Black Hole geometry arises naturally from the dual properties of a nearly perfect fluid and explore the lessons and prospects one may draw for actual heavy ion collisions from the Gauge/Gravity duality approach.Comment: 6 pages, 4 figures, invited talk at the EPS HEP 2007 Conference, Manchester (UK), and at the ``Deuxiemes rencontres PQG-France'', Etretat (2007); reference adde

String Tensions and Three Dimensional Confining Gauge Theories

In the context of gauge/gravity duality, we try to understand better the proposed duality between the fractional D2-brane supergravity solutions of (Nucl. Phys. B 606 (2001) 18, hep-th/0101096) and a confining 2+1 dimensional gauge theory. Based on the similarities between this fractional D2-brane solution and D3-brane supergravity solutions with more firmly established gauge theory duals, we conjecture that a confining q-string in the 2+1 dimensional gauge theory is dual to a wrapped D4-brane. In particular, the D4-brane looks like a string in the gauge theory directions but wraps a S**3 in S**4 in the transverse geometry. For one of the supergravity solutions, we find a near quadratic scaling law for the tension: $T \sim q (N-q)$. Based on the tension, we conjecture that the gauge theory dual is SU(N) far in the infrared. We also conjecture that a quadratic or near quadratic scaling is a generic feature of confining 2+1 dimensional SU(N) gauge theories.Comment: 23 pages, 2 figure

Production of human recombinant proapolipoprotein A-I in Escherichia coli: purification and biochemical characterization

A human liver cDNA library was used to isolate a clone coding for apolipoprotein A-I (Apo A-I). The clone carries the sequence for the prepeptide (18 amino acids), the propeptide (6 amino acids), and the mature protein (243 amino acids). A coding cassette for the proapo A-I molecule was reconstructed by fusing synthetic sequences, chosen to optimize expression and specifying the amino-terminal methionine and amino acids -6 to +14, to a large fragment of the cDNA coding for amino acids 15-243. The module was expressed in pOTS-Nco, an Escherichia coli expression vector carrying the regulatable X P^ promoter, leading to the production of proapolipoprotein A-I at up to 10% of total soluble proteins. The recombinant polypeptide was purified and characterized in terms of apparent molecular mass, isoelectric point, and by both chemical and enzymatic peptide mapping. In addition, it was assayed in vitro for the stimulation of the enzyme lecithin: cholesterol acyltransferase. The data show for the first time that proapo A-I can be produced efficiently in E. coli as a stable and undegraded protein having physical and functional properties indistinguishable from those of the natural product

Stochastic String Motion Above and Below the World Sheet Horizon

We study the stochastic motion of a relativistic trailing string in black hole AdS_5. The classical string solution develops a world-sheet horizon and we determine the associated Hawking radiation spectrum. The emitted radiation causes fluctuations on the string both above and below the world-sheet horizon. In contrast to standard black hole physics, the fluctuations below the horizon are causally connected with the boundary of AdS. We derive a bulk stochastic equation of motion for the dual string and use the AdS/CFT correspondence to determine the evolution a fast heavy quark in the strongly coupled $\N=4$ plasma. We find that the kinetic mass of the quark decreases by $\Delta M=-\sqrt{\gamma \lambda}T/2$ while the correlation time of world sheet fluctuations increases by $\sqrt{\gamma}$.Comment: 27 pages, 5 figures; v2 final version, small changes, references adde

Sound-Induced Flash Illusion is Resistant to Feedback Training

A single flash accompanied by two auditory beeps tends to be perceived as two flashes (Shams et al. Nature 408:788, 2000, Cogn Brain Res 14:147–152, 2002). This phenomenon is known as ‘sound-induced flash illusion.’ Previous neuroimaging studies have shown that this illusion is correlated with modulation of activity in early visual cortical areas (Arden et al. Vision Res 43(23):2469–2478, 2003; Bhattacharya et al. NeuroReport 13:1727–1730, 2002; Shams et al. NeuroReport 12(17):3849–3852, 2001, Neurosci Lett 378(2):76–81, 2005; Watkins et al. Neuroimage 31:1247–1256, 2006, Neuroimage 37:572–578, 2007; Mishra et al. J Neurosci 27(15):4120–4131, 2007). We examined how robust the illusion is by testing whether the frequency of the illusion can be reduced by providing feedback. We found that the sound-induced flash illusion was resistant to feedback training, except when the amount of monetary reward was made dependent on accuracy in performance. However, even in the latter case the participants reported that they still perceived illusory two flashes even though they correctly reported single flash. Moreover, the feedback training effect seemed to disappear once the participants were no longer provided with feedback suggesting a short-lived refinement of discrimination between illusory and physical double flashes rather than vanishing of the illusory percept. These findings indicate that the effect of sound on the perceptual representation of visual stimuli is strong and robust to feedback training, and provide further evidence against decision factors accounting for the sound-induced flash illusion

Mouse models of preterm birth: Suggested assessment and reporting guidelines

Preterm birth affects approximately 1 out of every 10 births in the United States, leading to high rates of mortality and long-term negative health consequences. To investigate the mechanisms leading to preterm birth so as to develop prevention strategies, researchers have developed numerous mouse models of preterm birth. However, the lack of standard definitions for preterm birth in mice limits our field\u27s ability to compare models and make inferences about preterm birth in humans. In this review, we discuss numerous mouse preterm birth models, propose guidelines for experiments and reporting, and suggest markers that can be used to assess whether pups are premature or mature. We argue that adoption of these recommendations will enhance the utility of mice as models for preterm birth

Surprising Connections Between General Relativity and Condensed Matter

This brief review is intended to introduce gravitational physicists to recent developments in which general relativity is being used to describe certain aspects of condensed matter systems, e.g., superconductivity.Comment: 14 pages; based on talk given at GR1

Lectures on hydrodynamic fluctuations in relativistic theories

These are pedagogical lecture notes on hydrodynamic fluctuations in normal relativistic fluids. The lectures discuss correlation functions of conserved densities in thermal equilibrium, interactions of the hydrodynamic modes, an effective action for viscous fluids, and the breakdown of the derivative expansion in hydrodynamics.Comment: 55 pages. Based on lectures given at the Seattle INT Summer School on Applications of String Theory in July 201