Theory of Computation of Multidimensional Entropy with an Application to the Monomer-Dimer Problem

We outline the most recent theory for the computation of the exponential growth rate of the number of configurations on a multi-dimensional grid. As an application we compute the monomer-dimer constant for the 2-dimensional grid to 8 decimal digits, agreeing with the heuristic computations of Baxter, and for the 3-dimensional grid with an error smaller than 1.35%.Comment: 35 pages, one pstricks and two eps figures, submitte

Flavor Gauge Models Below the Fermi Scale

The mass and weak interaction eigenstates for the quarks of the third generation are very well aligned, an empirical fact for which the Standard Model offers no explanation. We explore the possibility that this alignment is due to an additional gauge symmetry in the third generation. Specifically, we construct and analyze an explicit, renormalizable model with a gauge boson, $X$, corresponding to the $B-L$ symmetry of the third family. Having a relatively light (in the MeV to multi-GeV range), flavor-nonuniversal gauge boson results in a variety of constraints from different sources. By systematically analyzing 20 different constraints, we identify the most sensitive probes: kaon, $B^+$, $D^+$ and Upsilon decays, $D-\bar{D}^0$ mixing, atomic parity violation, and neutrino scattering and oscillations. For the new gauge coupling $g_X$ in the range $(10^{-2} - 10^{-4})$ the model is shown to be consistent with the data. Possible ways of testing the model in $b$ physics, top and $Z$ decays, direct collider production and neutrino oscillation experiments, where one can observe nonstandard matter effects, are outlined. The choice of leptons to carry the new force is ambiguous, resulting in additional phenomenological implications, such as non-universality in semileptonic bottom decays. The proposed framework provides interesting connections between neutrino oscillations, flavor and collider physics.Comment: 44 pages, 7 figures, 3 tables; B physics constraints and references added, conclusions unchange

Impact of aging on the auditory system and related cognitive functions: A narrative review

Age-related hearing loss (ARHL), presbycusis, is a chronic health condition that affects approximately one-third of the world’s population. The peripheral and central hearing alterations associated with age-related hearing loss have a profound impact on perception of verbal and non-verbal auditory stimuli. The high prevalence of hearing loss in the older adults corresponds to the increased frequency of dementia in this population. Therefore, researchers have focused their attention on age-related central effects that occur independent of the peripheral hearing loss as well as central effects of peripheral hearing loss and its association with cognitive decline and dementia. Here we review the current evidence for the age-related changes of the peripheral and central auditory system and the relationship between hearing loss and pathological cognitive decline and dementia. Furthermore, there is a paucity of evidence on the relationship between ARHL and established biomarkers of Alzheimer’s disease, as the most common cause of dementia. Such studies are critical to be able to consider any causal relationship between dementia and ARHL. While this narrative review will examine the pathophysiological alterations in both the peripheral and central auditory system and its clinical implications, the question remains unanswered whether hearing loss causes cognitive impairment or vice versa

Regular subgraphs of almost regular graphs

AbstractSuppose every vertex of a graph G has degree k or k + 1 and at least one vertex has degree k + 1. It is shown that if k ≥ 2q − 2 and q is a prime power then G contains a q-regular subgraph (and hence an r-regular subgraph for all r < q, r ≡ q (mod 2)). It is also proved that every simple graph with maximal degree Δ ≥ 2q − 2 and average degree d > ((2q − 2)(2q − 1))(Δ + 1), where q is a prime power, contains a q-regular subgraph (and hence an r-regular subgraph for all r < q, r ≡ q (mod 2)). These results follow from Chevalley's and Olson's theorems on congruences

The polytope of dual degree partitions

AbstractWe determine the extreme points and facets of the convex hull of all dual degree partitions of simple graphs on n vertices. (This problem was raised in the Laplace Energy group of the Workshop Spectra of Families of Matrices described by Graphs, Digraphs, and Sign Patterns held at the American Institute of Mathematics Research Conference Center on October 23–27, 2006 [R. Brualdi, Leslie Hogben, Brian Shader, AIM Workshop – Spectra of Families of Matrices Described by Graphs, Digraphs, and Sign Patterns, Final Report: Mathematical Results, November 17, 2006].

Membrane Type 1 Matrix Metalloproteinase Regulates Monocyte Migration and Collagen Destruction in Tuberculosis

Tuberculosis (TB) remains a global pandemic and drug resistance is rising. Multicellular granuloma formation is the pathological hallmark of Mycobacterium tuberculosis infection. The membrane type 1 matrix metalloproteinase (MT1-MMP or MMP-14) is a collagenase that is key in leukocyte migration and collagen destruction. In patients with TB, induced sputum MT1-MMP mRNA levels were increased 5.1-fold compared with matched controls and correlated positively with extent of lung infiltration on chest radiographs (r = 0.483; p &lt; 0.05). M. tuberculosis infection of primary human monocytes increased MT1-MMP surface expression 31.7-fold and gene expression 24.5-fold. M. tuberculosis-infected monocytes degraded collagen matrix in an MT1-MMP-dependent manner, and MT1-MMP neutralization decreased collagen degradation by 73%. In human TB granulomas, MT1-MMP immunoreactivity was observed in macrophages throughout the granuloma. Monocyte-monocyte networks caused a 17.5-fold increase in MT1-MMP surface expression dependent on p38 MAPK and G protein-coupled receptor-dependent signaling. Monocytes migrating toward agarose beads impregnated with conditioned media from M. tuberculosis-infected monocytes expressed MT1-MMP. Neutralization of MT1-MMP activity decreased this M. tuberculosis network-dependent monocyte migration by 44%. Taken together, we demonstrate that MT1-MMP is central to two key elements of TB pathogenesis, causing collagen degradation and regulating monocyte migration

Extension of Ekman (1905) wind-driven transport theory to the <i>β</i> plane

The seminal Ekman (1905) f-plane theory of wind-driven transport at the ocean surface is extended to the β plane by substituting the pseudo-angular momentum for the zonal velocity in the Lagrangian equation. When the β term is added, the equations become nonlinear, which greatly complicates the analysis. Though rotation relates the momentum equations in the zonal and the meridional directions, the transformation to pseudo-angular momentum greatly simplifies the longitudinal dynamics, which yields a clear description of the meridional dynamics in terms of a slow drift compounded by fast oscillations; this can then be applied to describe the motion in the zonal direction. Both analytical expressions and numerical calculations highlight the critical role of the Equator in determining the trajectories of water columns forced by eastward-directed (in the Northern Hemisphere) wind stress even when the water columns are initiated far from the Equator. Our results demonstrate that the averaged motion in the zonal direction depends on the amplitude of the meridional oscillations and is independent of the direction of the wind stress. The zonal drift is determined by a balance between the initial conditions and the magnitude of the wind stress, so it can be as large as the mean meridional motion; i.e., the averaged flow direction is not necessarily perpendicular to the wind direction.</p

Seiberg Duality and e+ e- Experiments

Seiberg duality in supersymmetric gauge theories is the claim that two different theories describe the same physics in the infrared limit. However, one cannot easily work out physical quantities in strongly coupled theories and hence it has been difficult to compare the physics of the electric and magnetic theories. In order to gain more insight into the equivalence of two theories, we study the ``e+ e-'' cross sections into ``hadrons'' for both theories in the superconformal window. We describe a technique which allows us to compute the cross sections exactly in the infrared limit. They are indeed equal in the low-energy limit and the equality is guaranteed because of the anomaly matching condition. The ultraviolet behavior of the total ``e+ e-'' cross section is different for the two theories. We comment on proposed non-supersymmetric dualities. We also analyze the agreement of the ``\gamma\gamma'' and ``WW'' scattering amplitudes in both theories, and in particular try to understand if their equivalence can be explained by the anomaly matching condition.Comment: 24 pages, 2 figures, uses psfi

Bounds on the Magnetic Fields in the Radiative Zone of the Sun

We discuss bounds on the strength of the magnetic fields that could be buried in the radiative zone of the Sun. The field profiles and decay times are computed for all axisymmetric toroidal Ohmic decay eigenmodes with lifetimes exceeding the age of the Sun. The measurements of the solar oblateness yield a bound <~ 7 MG on the strength of the field. A comparable bound is expected to come from the analysis of the splitting of the solar oscillation frequencies. The theoretical analysis of the double diffusive instability also yields a similar bound. The oblateness measurements at their present level of sensitivity are therefore not expected to measure a toroidal field contribution.Comment: 15 pages, 6 figure