Explicit and Exact Solutions to a Kolmogorov-Petrovskii-Piskunov Equation

Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ans\"atze. By a Cole-Hopf transformation, this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear equation and further two solutions to describe nonlinear interaction of traveling waves are generated. B\"acklund transformations of the linear form and some special cases are considered.Comment: 14pages, Latex, to appear in Intern. J. Nonlinear Mechanics, the original latex file is not complet

Monotone traveling wavefronts of the KPP-Fisher delayed equation

In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002) initiated the study of the positive wavefronts in the delayed Kolmogorov-Petrovskii-Piskunov-Fisher equation. Since then, this model has become one of the most popular objects in the studies of traveling waves for the monostable delayed reaction-diffusion equations. In this paper, we give a complete solution to the problem of existence and uniqueness of monotone waves in the KPP-Fisher equation. We show that each monotone traveling wave can be found via an iteration procedure. The proposed approach is based on the use of special monotone integral operators (which are different from the usual Wu-Zou operator) and appropriate upper and lower solutions associated to them. The analysis of the asymptotic expansions of the eventual traveling fronts at infinity is another key ingredient of our approach.Comment: 25 pages, 2 figures, submitte

Association between HLA Class I and Class II Alleles and the Outcome of West Nile Virus Infection: An Exploratory Study

BACKGROUND: West Nile virus (WNV) infection is asymptomatic in most individuals, with a minority developing symptoms ranging from WNV fever to serious neuroinvasive disease. This study investigated the impact of host HLA on the outcome of WNV disease. METHODS: A cohort of 210 non-Hispanic mostly white WNV(+) subjects from Canada and the U.S. were typed for HLA-A, B, C, DP, DQ, and DR. The study subjects were divided into three WNV infection outcome groups: asymptomatic (AS), symptomatic (S), and neuroinvasive disease (ND). Allele frequency distribution was compared pair-wise between the AS, S, and ND groups using χ2 and Fisher's exact tests and P values were corrected for multiple comparisons (Pc). Allele frequencies were compared between the groups and the North American population (NA) used as a control group. Logistic regression analysis was used to evaluate the potential synergistic effect of age and HLA allele phenotype on disease outcome. RESULTS: The alleles HLA-A*68, C*08 and DQB*05 were more frequently associated with severe outcomes (ND vs. AS, P(A*68) = 0.013/Pc = 0.26, P(C*08) = 0.0075/Pc = 0.064, and P(DQB1*05) = 0.029/Pc = 0.68), However the apparent DQB1*05 association was driven by age. The alleles HLA-B*40 and C*03 were more frequently associated with asymptomatic outcome (AS vs. S, P(B*40) = 0.021/Pc = 0.58 and AS vs. ND P(C*03) = 0.039/Pc = 0.64) and their frequencies were lower within WNV(+) subjects with neuroinvasive disease than within the North American population (NA vs. S, P(B*40) = 0.029 and NA vs. ND, P(C*03) = 0.032). CONCLUSIONS: Host HLA may be associated with the outcome of WNV disease; HLA-A*68 and C*08 might function as "susceptible" alleles, whereas HLA-B*40 and C*03 might function as "protective" alleles

Molecular profiling and combinatorial activity of CCT068127: a potent CDK2 and CDK9 inhibitor

Deregulation of the cyclin-dependent kinases (CDKs) has been implicated in the pathogenesis of multiple cancer types. Consequently, CDKs have garnered intense interest as therapeutic targets for the treatment of cancer. We describe herein the molecular and cellular effects of CCT068127, a novel inhibitor of CDK2 and CDK9. Optimised from the purine template of seliciclib, CCT068127 exhibits greater potency and selectivity against purified CDK2 and CDK9 and superior antiproliferative activity against human colon cancer and melanoma cell lines. X-ray crystallography studies reveal that hydrogen bonding with the DFG motif of CDK2 is the likely mechanism of greater enzymatic potency. Commensurate with inhibition of CDK activity, CCT068127 treatment results in decreased retinoblastoma protein (RB) phosphorylation, reduced phosphorylation of RNA polymerase II and induction of cell cycle arrest and apoptosis. The transcriptional signature of CCT068127 shows greatest similarity to other small molecule CDK and also HDAC inhibitors. CCT068127 caused a dramatic loss in expression of DUSP6 phosphatase, alongside elevated ERK phosphorylation and activation of MAPK pathway target genes. MCL1 protein levels are rapidly decreased by CCT068127 treatment and this associates with synergistic antiproliferative activity after combined treatment with CCT068127 and ABT263, a BCL2-family inhibitor. These findings support the rational combination of this series of CDK2/9 inhibitors and BCL2 family inhibitors for the treatment of human cancer

Rare region effects at classical, quantum, and non-equilibrium phase transitions

Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. In generic classical equilibrium systems, they lead to an essential singularity, the so-called Griffiths singularity, of the free energy in the vicinity of the phase transition. Stronger effects can be observed at zero-temperature quantum phase transitions, at nonequilibrium phase transitions, and in systems with correlated disorder. In some cases, rare regions can actually completely destroy the sharp phase transition by smearing. This topical review presents a unifying framework for rare region effects at weakly disordered classical, quantum, and nonequilibrium phase transitions based on the effective dimensionality of the rare regions. Explicit examples include disordered classical Ising and Heisenberg models, insulating and metallic random quantum magnets, and the disordered contact process.Comment: Topical review, 68 pages, 14 figures, final version as publishe

Quasi-Neutral theory of epidemic outbreaks

Some epidemics have been empirically observed to exhibit outbreaks of all possible sizes, i.e., to be scalefree or scale-invariant. Different explanations for this finding have been put forward; among them there is a model for "accidental pathogens" which leads to power-law distributed outbreaks without apparent need of parameter fine tuning. This model has been claimed to be related to self-organized criticality, and its critical properties have been conjectured to be related to directed percolation. Instead, we show that this is a (quasi) neutral model, analogous to those used in Population Genetics and Ecology, with the same critical behavior as the voter-model, i.e. the theory of accidental pathogens is a (quasi)-neutral theory. This analogy allows us to explain all the system phenomenology, including generic scale invariance and the associated scaling exponents, in a parsimonious and simple way.Comment: 13 pages, 6 figures Accepted for publication in PLoS ONE the text have been modified in orden to improve the figure's resolutio

Breast imaging technology: Recent advances in imaging endogenous or transferred gene expression utilizing radionuclide technologies in living subjects - applications to breast cancer

A variety of imaging technologies is being investigated as tools for studying gene expression in living subjects. Two technologies that use radiolabeled isotopes are single photon emission computed tomography (SPECT) and positron emission tomography (PET). A relatively high sensitivity, a full quantitative tomographic capability, and the ability to extend small animal imaging assays directly into human applications characterize radionuclide approaches. Various radiolabeled probes (tracers) can be synthesized to target specific molecules present in breast cancer cells. These include antibodies or ligands to target cell surface receptors, substrates for intracellular enzymes, antisense oligodeoxynucleotide probes for targeting mRNA, probes for targeting intracellular receptors, and probes for genes transferred into the cell. We briefly discuss each of these imaging approaches and focus in detail on imaging reporter genes. In a PET reporter gene system for in vivo reporter gene imaging, the protein products of the reporter genes sequester positron emitting reporter probes. PET subsequently measures the PET reporter gene dependent sequestration of the PET reporter probe in living animals. We describe and review reporter gene approaches using the herpes simplex type 1 virus thymidine kinase and the dopamine type 2 receptor genes. Application of the reporter gene approach to animal models for breast cancer is discussed. Prospects for future applications of the transgene imaging technology in human gene therapy are also discussed. Both SPECT and PET provide unique opportunities to study animal models of breast cancer with direct application to human imaging. Continued development of new technology, probes and assays should help in the better understanding of basic breast cancer biology and in the improved management of breast cancer patients

Defining the critical hurdles in cancer immunotherapy

Scientific discoveries that provide strong evidence of antitumor effects in preclinical models often encounter significant delays before being tested in patients with cancer. While some of these delays have a scientific basis, others do not. We need to do better. Innovative strategies need to move into early stage clinical trials as quickly as it is safe, and if successful, these therapies should efficiently obtain regulatory approval and widespread clinical application. In late 2009 and 2010 the Society for Immunotherapy of Cancer (SITC), convened an "Immunotherapy Summit" with representatives from immunotherapy organizations representing Europe, Japan, China and North America to discuss collaborations to improve development and delivery of cancer immunotherapy. One of the concepts raised by SITC and defined as critical by all parties was the need to identify hurdles that impede effective translation of cancer immunotherapy. With consensus on these hurdles, international working groups could be developed to make recommendations vetted by the participating organizations. These recommendations could then be considered by regulatory bodies, governmental and private funding agencies, pharmaceutical companies and academic institutions to facilitate changes necessary to accelerate clinical translation of novel immune-based cancer therapies. The critical hurdles identified by representatives of the collaborating organizations, now organized as the World Immunotherapy Council, are presented and discussed in this report. Some of the identified hurdles impede all investigators; others hinder investigators only in certain regions or institutions or are more relevant to specific types of immunotherapy or first-in-humans studies. Each of these hurdles can significantly delay clinical translation of promising advances in immunotherapy yet if overcome, have the potential to improve outcomes of patients with cancer

The nonperturbative functional renormalization group and its applications

The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for viable ultraviolet completions in fundamental physics. It provides us with a natural framework to study theoretical models where degrees of freedom are correlated over long distances and that may exhibit very distinct behavior on different energy scales. The nonperturbative functional renormalization-group (FRG) approach is a modern implementation of Wilson's RG, which allows one to set up nonperturbative approximation schemes that go beyond the standard perturbative RG approaches. The FRG is based on an exact functional flow equation of a coarse-grained effective action (or Gibbs free energy in the language of statistical mechanics). We review the main approximation schemes that are commonly used to solve this flow equation and discuss applications in equilibrium and out-of-equilibrium statistical physics, quantum many-particle systems, high-energy physics and quantum gravity.Comment: v2) Review article, 93 pages + bibliography, 35 figure