A note on the fractional perimeter and interpolation

We present the fractional perimeter as a set-function interpolation between the Lebesgue measure and the perimeter in the sense of De Giorgi. Our motivation comes from a new fractional Boxing inequality that relates the fractional perimeter and the Hausdorff content and implies several known inequalities involving the Gagliardo seminorm of the Sobolev spaces $W^{\alpha, 1}$ of order $0 < \alpha < 1$

Unlikely Estimates of the Ex Ante Real Interest Rate: Another Dismal Performance from the Dismal Science1

The ex ante real rate of interest is one of the most important concepts in economics and finance. Because the universally-used Fisher theory of interest requires positive ex ante real interest rates, empirical estimates of the ex ante real interest rate derived from the Fisher theory of interest should also be positive. Unfortunately, virtually all estimates of the ex ante real interest rate published in economic journals and textbooks or used in macroeconomic models and policy discussions for the past 35 years contain negative values for extended time periods and, thus, are theoretically flawed. Moreover, the procedures generally used to estimate ex ante real interest rates were shown to produce biased estimates of the ex ante real rate over 30 years ago. In this article, we document this puzzling chasm between the Fisherian theory that mandates positive ex ante real interest rates and the practice of macroeconomists who generate and use ex ante real interest rate estimates that violate this theory. We explore the reasons that this problem exists and assess some alternative approaches for estimating the ex ante real interest rate to determine whether they might resolve this problem.ex ante real interest rate, Fisher theory of interest, biased real interest rate estimates

Applications of Partial Supersymmetry

I examine quantum mechanical Hamiltonians with partial supersymmetry, and explore two main applications. First, I analyze a theory with a logarithmic spectrum, and show how to use partial supersymmetry to reveal the underlying structure of this theory. This method reveals an intriguing equivalence between two formulations of this theory, one of which is one-dimensional, and the other of which is infinite-dimensional. Second, I demonstrate the use of partial supersymmetry as a tool to obtain the asymptotic energy levels in non-relativistic quantum mechanics in an exceptionally easy way. In the end, I discuss possible extensions of this work, including the possible connections between partial supersymmetry and renormalization group arguments.Comment: 11 pages, harvmac, no figures; typo corrected in identifying info on title pag

Stable periodic waves in coupled Kuramoto-Sivashinsky - Korteweg-de Vries equations

Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky - Korteweg-de Vries (KS-KdV) equation, which is linearly coupled to an extra linear dissipative equation. The model describes, e.g., a two-layer liquid film flowing down an inclined plane. It has been recently shown that the system supports stable solitary pulses. We demonstrate that a perturbation analysis, based on the balance equation for the field momentum, predicts the existence of stable cnoidal waves (CnWs) in the same system. It is found that the mean value U of the wave field u in the main subsystem, but not the mean value of the extra field, affects the stability of the periodic waves. Three different areas can be distinguished inside the stability region in the parameter plane (L,U), where L is the wave's period. In these areas, stable are, respectively, CnWs with positive velocity, constant solutions, and CnWs with negative velocity. Multistability, i.e., the coexistence of several attractors, including the waves with several maxima per period, appears at large value of L. The analytical predictions are completely confirmed by direct simulations. Stable waves are also found numerically in the limit of vanishing dispersion, when the KS-KdV equation goes over into the KS one.Comment: a latex text file and 16 eps files with figures. Journal of the Physical Society of Japan, in pres

Gut microbiome diversity and high-fibre intake are related to lower long-term weight gain

BACKGROUND: Cross-sectional studies suggest that the microbes in the human gut have a role in obesity by influencing the human body's ability to extract and store calories. The aim of this study was to assess if there is a correlation between change in body weight over time and gut microbiome composition. METHODS: We analysed 16S ribosomal RNA gene sequence data derived from the faecal samples of 1632 healthy females from TwinsUK to investigate the association between gut microbiome measured cross-sectionally and longitudinal weight gain (adjusted for caloric intake and baseline body mass index). Dietary fibre intake was investigated as a possible modifier. RESULTS: Less than half of the variation in long-term weight change was found to be heritable (h2=0.41 (0.31, 0.47)). Gut microbiota diversity was negatively associated with long-term weight gain, whereas it was positively correlated with fibre intake. Nine bacterial operational taxonomic units (OTUs) were significantly associated with weight gain after adjusting for covariates, family relatedness and multiple testing (false discovery rate <0.05). OTUs associated with lower long-term weight gain included those assigned to Ruminococcaceae (associated in mice with improved energy metabolism) and Lachnospiraceae. A Bacterioides species OTU was associated with increased risk of weight gain but this appears to be driven by its correlation with lower levels of diversity. CONCLUSIONS: High gut microbiome diversity, high-fibre intake and OTUs implicated in animal models of improved energy metabolism are all correlated with lower term weight gain in humans independently of calorie intake and other confounders

Evidence for a nuclear compartment of transcription and splicing located at chromosome domain boundaries

The nuclear topography of splicing snRNPs, mRNA transcripts and chromosome domains in various mammalian cell types are described. The visualization of splicing snRNPs, defined by the Sm antigen, and coiled bodies, revealed distinctly different distribution patterns in these cell types. Heat shock experiments confirmed that the distribution patterns also depend on physiological parameters. Using a combination of fluorescencein situ hybridization and immunodetection protocols, individual chromosome domains were visualized simultaneously with the Sm antigen or the transcript of an integrated human papilloma virus genome. Three-dimensional analysis of fluorescence-stained target regions was performed by confocal laser scanning microscopy. RNA transcripts and components of the splicing machinery were found to be generally excluded from the interior of the territories occupied by the individual chromosomes. Based on these findings we present a model for the functional compartmentalization of the cell nucleus. According to this model the space between chromosome domains, including the surface areas of these domains, defines a three-dimensional network-like compartment, termed the interchromosome domain (ICD) compartment, in which transcription and splicing of mRNA occurs