Monotonicity and logarithmic convexity relating to the volume of the unit ball

Let $\Omega_n$ stand for the volume of the unit ball in $\mathbb{R}^n$ for $n\in\mathbb{N}$. In the present paper, we prove that the sequence $\Omega_{n}^{1/(n\ln n)}$ is logarithmically convex and that the sequence $\frac{\Omega_{n}^{1/(n\ln n)}}{\Omega_{n+1}^{1/[(n+1)\ln(n+1)]}}$ is strictly decreasing for $n\ge2$. In addition, some monotonic and concave properties of several functions relating to $\Omega_{n}$ are extended and generalized.Comment: 12 page

Multicanonical Recursions

The problem of calculating multicanonical parameters recursively is discussed. I describe in detail a computational implementation which has worked reasonably well in practice.Comment: 23 pages, latex, 4 postscript figures included (uuencoded Z-compressed .tar file created by uufiles), figure file corrected

Hydrodynamic attraction of swimming microorganisms by surfaces

Cells swimming in confined environments are attracted by surfaces. We measure the steady-state distribution of smooth-swimming bacteria (Escherichia coli) between two glass plates. In agreement with earlier studies, we find a strong increase of the cell concentration at the boundaries. We demonstrate theoretically that hydrodynamic interactions of the swimming cells with solid surfaces lead to their re-orientation in the direction parallel to the surfaces, as well as their attraction by the closest wall. A model is derived for the steady-state distribution of swimming cells, which compares favorably with our measurements. We exploit our data to estimate the flagellar propulsive force in swimming E. coli

Large deviations for ideal quantum systems

We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a subdomain of the container are described by a large deviation function related to the pressure of the system. That is, untypical densities occur with a probability exponentially small in the volume of the subdomain, with the coefficient in the exponent given by the appropriate thermodynamic potential. Furthermore, small fluctuations satisfy the central limit theorem.Comment: 28 pages, LaTeX 2

Cellular Proliferation of Equine Bone Marrow- and Adipose Tissue-Derived Mesenchymal Stem Cells Decline With Increasing Donor Age

Background: Bone marrow (BM)- and adipose tissue (AT)-derived mesenchymal stem cells (MSCs) are used increasingly for autologous cell therapy in equine practice to treat musculoskeletal and other injuries. Current recommendations often call for 10–100 million MSCs per treatment, necessitating the expansion of primary cells in culture prior to therapeutic use. Of concern, human and rodent studies have shown a decline of both MSC recovery from sampled tissue and in vitro proliferative capacity with increasing donor age. This may be problematic for applications of autologous cell-based therapies in the important equine demographic of older patients. Objectives: To investigate the effect of donor age on the cellular proliferation of equine BM- and AT-MSCs. Study Design: In vitro study. Methods: BM- and AT-MSCs and dermal fibroblasts (biological control) were harvested from horses in five different age groups (n = 4, N = 60); newborn (0 days), yearling (15–17 months), adult (5–8 years), middle-aged (12–18 years), and geriatric (≥ 22 years). Proliferation of the cells was tested using an EdU incorporation assay and steady state mRNA levels measured for targeted proliferation, aging, and senescence biomarkers. Results: The cellular proliferation of equine BM- and AT-MSCs declined significantly in the geriatric cohort relative to the younger age groups. Proliferation levels in the two MSC types were equally affected by donor age. Analysis of steady state mRNA levels showed an up-regulation in tumor suppressors, apoptotic genes, and multiple growth factors in MSCs from old horses, and a down-regulation of some pro-cycling genes with a few differences between cell types. Main Limitations: Potential age-dependent differences in cell function parameters relevant to cell-therapy application were not investigated. Conclusions: The cellular proliferation of equine BM- and AT-MSCs declined at advanced donor ages. High levels of in vitro proliferation were observed in both MSC types from horses in the age groups below 18 years of age

Long-term observations of the pulsars in 47 Tucanae. I. A study of four elusive binary systems

For the past couple of decades, the Parkes radio telescope has been regularly observing the millisecond pulsars in 47 Tucanae (47 Tuc). This long-term timing program was designed to address a wide range of scientific issues related to these pulsars and the globular cluster where they are located. In this paper, the first of a series, we address one of these objectives: the characterization of four previously known binary pulsars for which no precise orbital parameters were known, namely 47 Tuc P, V, W and X (pulsars 47 Tuc R and Y are discussed elsewhere). We determined the previously unknown orbital parameters of 47 Tuc V and X and greatly improved those of 47 Tuc P and W. For pulsars W and X we obtained, for the first time, full coherent timing solutions across the whole data span, which allowed a much more detailed characterization of these systems. 47 Tuc W, a well-known tight eclipsing binary pulsar, exhibits a large orbital period variability, as expected for a system of its class. 47 Tuc X turns out to be in a wide, extremely circular, 10.9-day long binary orbit and its position is ~3.8 arcmin away from the cluster center, more than three times the distance of any other pulsar in 47 Tuc. These characteristics make 47 Tuc X a very different object with respect to the other pulsars of the cluster.Comment: Accepted for publication by MNRAS, 18 pages, 11 figure

Dynamics of adaptive agents with asymmetric information

We apply path-integral techniques to study the dynamics of agent-based models with asymmetric information structures. In particular, we devise a batch version of a model proposed originally by Berg et al. [Quant. Fin. 1 (2001) 203], and convert the coupled multi-agent processes into an effective-agent problem from which the dynamical order parameters in ergodic regimes can be derived self-consistently together with the corresponding phase structure. Our dynamical study complements and extends the available static theory. Results are confirmed by numerical simulations.Comment: minor revision of text, accepted by JSTA

Combination of improved multibondic method and the Wang-Landau method

We propose a method for Monte Carlo simulation of statistical physical models with discretized energy. The method is based on several ideas including the cluster algorithm, the multicanonical Monte Carlo method and its acceleration proposed recently by Wang and Landau. As in the multibondic ensemble method proposed by Janke and Kappler, the present algorithm performs a random walk in the space of the bond population to yield the state density as a function of the bond number. A test on the Ising model shows that the number of Monte Carlo sweeps required of the present method for obtaining the density of state with a given accuracy is proportional to the system size, whereas it is proportional to the system size squared for other conventional methods. In addition, the new method shows a better performance than the original Wang-Landau method in measurement of physical quantities.Comment: 12 pages, 3 figure

A Multicanonical Molecular Dynamics Study on a Simple Bead-Spring Model for Protein Folding

We have performed a multicanonical molecular dynamics simulation on a simple model protein.We have studied a model protein composed of charged, hydrophobic, and neutral spherical bead monomers.Since the hydrophobic interaction is considered to significantly affect protein folding, we particularly focus on the competition between effects of the Coulomb interaction and the hydrophobic interaction. We found that the transition which occurs upon decreasing the temperature is markedly affected by the change in both parameters and forms of the hydrophobic potential function, and the transition changes from first order to second order, when the Coulomb interaction becomes weaker.Comment: 7 pages, 6 postscript figures, To appear in J.Phys.Soc.Jpn. Vol.70 No.