Lyapunov 1-forms for flows

In this paper we find conditions which guarantee that a given flow $\Phi$ on a compact metric space $X$ admits a Lyapunov one-form $\omega$ lying in a prescribed \v{C}ech cohomology class $\xi\in \check H^1(X;\R)$. These conditions are formulated in terms of the restriction of $\xi$ to the chain recurrent set of $\Phi$. The result of the paper may be viewed as a generalization of a well-known theorem of C. Conley about the existence of Lyapunov functions.Comment: 27 pages, 3 figures. This revised version incorporates a few minor improvement

Solutions of mKdV in classes of functions unbounded at infinity

In 1974 P. Lax introduced an algebro-analytic mechanism similar to the Lax L-A pair. Using it we prove global existence and uniqueness for solutions of the initial value problem for mKdV in classes of smooth functions which can be unbounded at infinity, and may even include functions which tend to infinity with respect to the space variable. Moreover, we establish the invariance of the spectrum and the unitary type of the Schr{\"o}dinger operator under the KdV flow and the invariance of the spectrum and the unitary type of the impedance operator under the mKdV flow for potentials in these classes.Comment: 35 pages, new results about spectra and eigenfunctions of Schr\"odinger operators added, new references adde

Isospectrality and heat content

We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with infinitely many components. Other planar examples have mixed Dirichlet and Neumann boundary conditions. We also consider Schr\"{o}dinger operators acting in $L^2[0,1]$ with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content.Comment: 18 page

Qualitative features of periodic solutions of KdV

In this paper we prove new qualitative features of solutions of KdV on the circle. The first result says that the Fourier coefficients of a solution of KdV in Sobolev space $H^N,\, N\geq 0$, admit a WKB type expansion up to first order with strongly oscillating phase factors defined in terms of the KdV frequencies. The second result provides estimates for the approximation of such a solution by trigonometric polynomials of sufficiently large degree

Genetic regulation of parasite infection: empirical evidence of the functional significance of an IL4 gene SNP on nematode infections in wild primates

Background Susceptibility to parasite infection affects fitness-related processes, such as mate choice and survival, yet its genetic regulation remains poorly understood. Interleukin-4 (IL4) plays a central role in the humoral immune defence against nematode parasite infections, inducing IgE switch and regulation of worm expulsion from the intestines. The evolutionary and functional significance of single nucleotide polymorphisms (SNPs) in IL4-genes is known, yet empirical information on the effect of IL4 SNPs on gastro-intestinal infections is lacking. Using samples from a population of wild red-fronted lemurs (Eulemur fulvus rufus, Primates: Lemuridae), from western Madagascar, we explored the association of IL4-gene promoter polymorphisms with nematode infections and investigated a possible functional role of the IL4 polymorphism on male reproductive success. Results Using sequence analyses of lemur DNA we detected a new SNP in the IL4 gene promoter area. Carriers of the genotype T/T showed higher nematode infection intensities than individuals of genotypes C/T and C/C. Genetic population analyses using data from more than 10 years, suggested higher reproductive success of T/T males than expected. Conclusions Our results suggest a regulatory effect of an IL4 gene promoter polymorphism on the intensity of parasite infections in a natural population of red-fronted lemurs, with a seemingly disadvantageous genotype represented in low frequencies. Long-term population analyses, however, point in the direction of a negative frequency-dependent association, giving a fitness advantage to the rare genotype. Due to low frequencies of the genotype in question conclusive evidence of a functional role of IL4 polymorphism cannot be drawn here; still, we suggest the use of IL4 polymorphism as a new molecular tool for quick assessment of individual genetic constitution with regard to nematode infection intensities, contributing to a better understanding of the actual components of the immune response that mediate protection against gastro-intestinal parasites

The Behavioral Ecology of the Tibetan Macaque

This open access book summarizes the multi-disciplinary results of one of China’s main primatological research projects on the endemic Tibetan macaque (Macaca thibetana), which had continued for over 30 years, but which had never been reported on systematically. Dedicated to this exceptional Old World monkey, this book makes the work of Chinese primatologists on the social behavior, cooperation, culture, cognition, group dynamics, and emerging technologies in primate research accessible to the international scientific community

On efficiency and localisation for the torsion function

We consider the torsion function for the Dirichlet Laplacian $-\Delta$, and for the Schr\"odinger operator $- \Delta + V$ on an open set $\Omega\subset \R^m$, with Lebesgue measure $0<|\Omega|<\infty$, with a real-valued, non-negative, measurable potential $V.$ We investigate the phenomena of vanishing efficiency and localisation, and large efficiency for the torsion function and the first Dirichlet eigenfunction.Comment: 34 pages, minor corrections and additions to v1 (May 2020

Retinoid receptors in ovarian cancer: expression and prognosis

Background: Ovarian cancer is frequently lethal despite aggressive multimodal therapy, and new therapies are therefore needed. Retinoids are potential candidate drugs: they prevent the development of ovarian carcinoma and enhance the efficacy of cytotoxic drugs in ovarian cancer cells. At present, little is known about the retinoid receptor expression in ovarian cancer. Patients and methods: The retinoid receptors comprise two classes, retinoic acid receptors (RARs) and retinoid X receptors (RXRs), each with three subclasses, α, β and γ. We investigated the expression of the subtypes RARα, RARγ, RXRα and RXRβ by immunohistochemistry in ovarian cancers of 80 patients, and assessed their prognostic significance. In addition, we quantified the expression of retinoid receptor mRNA using real-time PCR and correlated the results with clinical characteristics. Results: RARα and RXRβ were highly expressed in a majority of ovarian cancers, particularly in advanced stages. High expression of RARα was an independent negative prognostic factor of survival in addition to FIGO stage, age and p53 accumulation. The mRNA expression of retinoid receptors did not correlate with clinical properties of the tumors. Conclusions: Retinoic acid receptors are frequently and strongly expressed in epithelial ovarian cancer and may be indicators of an adverse prognosis. This study provides the molecular basis for the therapeutic use of retinoids in ovarian cance

Global Birkhoff coordinates for the periodic Toda lattice

In this paper we prove that the periodic Toda lattice admits globally defined Birkhoff coordinates.Comment: 32 page

Refuge sharing network predicts ectoparasite load in a lizard

Living in social groups facilitates cross-infection by parasites. However, empirical studies on indirect transmission within wildlife populations are scarce. We investigated whether asynchronous overnight refuge sharing among neighboring sleepy lizards, Tiliqua rugosa, facilitates indirect transmission of its ectoparasitic tick, Amblyomma limbatum. We fitted 18 neighboring lizards with GPS recorders, observed their overnight refuge use each night over 3 months, and counted their ticks every fortnight. We constructed a transmission network to estimate the cross-infection risk based on asynchronous refuge sharing frequencies among all lizards and the life history traits of the tick. Although self-infection was possible, the network provided a powerful predictor of measured tick loads. Highly connected lizards that frequently used their neighbors’ refuges were characterized by higher tick loads. Thus, indirect contact had a major influence on transmission pathways and parasite loads. Furthermore, lizards that used many different refuges had lower cross- and self-infection risks and lower tick loads than individuals that used relatively fewer refuges. Increasing the number of refuges used by a lizard may be an important defense mechanism against ectoparasite transmission in this species. Our study provides important empirical data to further understand how indirectly transmitted parasites move through host populations and influence individual parasite loads