Self-similar disk packings as model spatial scale-free networks

The network of contacts in space-filling disk packings, such as the Apollonian packing, are examined. These networks provide an interesting example of spatial scale-free networks, where the topology reflects the broad distribution of disk areas. A wide variety of topological and spatial properties of these systems are characterized. Their potential as models for networks of connected minima on energy landscapes is discussed.Comment: 13 pages, 12 figures; some bugs fixed and further discussion of higher-dimensional packing

Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions

We evaluate the virial coefficients B_k for k<=10 for hard spheres in dimensions D=2,...,8. Virial coefficients with k even are found to be negative when D>=5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D>=5. Further analysis provides evidence that negative virial coefficients will be seen for some k>10 for D=4, and there is a distinct possibility that negative virial coefficients will also eventually occur for D=3.Comment: 33 pages, 12 figure

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. IV. Chromatic polynomial with cyclic boundary conditions

We study the chromatic polynomial P_G(q) for m \times n square- and triangular-lattice strips of widths 2\leq m \leq 8 with cyclic boundary conditions. This polynomial gives the zero-temperature limit of the partition function for the antiferromagnetic q-state Potts model defined on the lattice G. We show how to construct the transfer matrix in the Fortuin--Kasteleyn representation for such lattices and obtain the accumulation sets of chromatic zeros in the complex q-plane in the limit n\to\infty. We find that the different phases that appear in this model can be characterized by a topological parameter. We also compute the bulk and surface free energies and the central charge.Comment: 55 pages (LaTeX2e). Includes tex file, three sty files, and 22 Postscript figures. Also included are Mathematica files transfer4_sq.m and transfer4_tri.m. Journal versio

Persistently modified h-channels after complex febrile seizures convert the seizure-induced enhancement of inhibition to hyperexcitability.

Febrile seizures are the most common type of developmental seizures, affecting up to 5% of children. Experimental complex febrile seizures involving the immature rat hippocampus led to a persistent lowering of seizure threshold despite an upregulation of inhibition. Here we provide a mechanistic resolution to this paradox by showing that, in the hippocampus of rats that had febrile seizures, the long-lasting enhancement of the widely expressed intrinsic membrane conductance Ih converts the potentiated synaptic inhibition to hyperexcitability in a frequency-dependent manner. The altered gain of this molecular inhibition-excitation converter reveals a new mechanism for controlling the balance of excitation-inhibition in the limbic system. In addition, here we show for the first time that h-channels are modified in a human neurological disease paradigm

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Analysis of two methods of isometric muscle contractions during the anti-G straining maneuver

This study investigated the difference in Mean Arterial Pressure (MAP) and Cardiac Output (CO) between two methods of isometric muscle contractions during the Anti-G Straining Maneuver (AGSM). 12 subjects (ages 18 to 38 yrs, height 176.8 +/- 7.4 cm, body mass 78.8 +/- 15.6 kg, percent body fat 14.3 +/- 6.6%) participated in the study. The study was a one-way within-subject design with test conditions counterbalanced. Two methods of isometric muscle contractions lasting 30 seconds each were assessed; an isometric push contraction and an isometric muscle tensing contraction. The dependent parameters were MAP and CO. The average MAP during the push contraction was 123 mmHg, SD +/- 11 and for tense was 118 mmHg, SD +/- 8. CO was 7.6 L/min, SD +/- 1.6 for push and 7.9 L/min, SD +/- 2.0 for tense method. Dependent t-tests revealed t(11) = 1.517, p = 0.157 for MAP and t(11) = 0.875, p = 0.400 for CO. This study demonstrated that the two methods of isometric muscle contractions were not statistically different with regards to MAP and CO. Therefore, both forms of isometric contractions may be potentially useful when performing the muscle contraction portion of the AGSM

The role of inflammation in epilepsy.

Epilepsy is the third most common chronic brain disorder, and is characterized by an enduring predisposition to generate seizures. Despite progress in pharmacological and surgical treatments of epilepsy, relatively little is known about the processes leading to the generation of individual seizures, and about the mechanisms whereby a healthy brain is rendered epileptic. These gaps in our knowledge hamper the development of better preventive treatments and cures for the approximately 30% of epilepsy cases that prove resistant to current therapies. Here, we focus on the rapidly growing body of evidence that supports the involvement of inflammatory mediators-released by brain cells and peripheral immune cells-in both the origin of individual seizures and the epileptogenic process. We first describe aspects of brain inflammation and immunity, before exploring the evidence from clinical and experimental studies for a relationship between inflammation and epilepsy. Subsequently, we discuss how seizures cause inflammation, and whether such inflammation, in turn, influences the occurrence and severity of seizures, and seizure-related neuronal death. Further insight into the complex role of inflammation in the generation and exacerbation of epilepsy should yield new molecular targets for the design of antiepileptic drugs, which might not only inhibit the symptoms of this disorder, but also prevent or abrogate disease pathogenesis