CNN model for studying dynamics and travelling wave solutions of FitzHugh-Nagumo equation

AbstractIn this paper, a cellular neural network (CNN) model of FitzHugh–Nagumo equation is introduced. Dynamical behavior of this model is investigated using harmonic balance method. For the CNN model of FitzHugh–Nagumo equation, propagation of solitary waves have been proved

On the exponential stability of set-valued differential equations

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An oriented coincidence index for nonlinear Fredholm inclusions with nonconvex-valued perturbations

We suggest the construction of an oriented coincidence index for nonlinear Fredholm operators of zero index and approximable multivalued maps of compact and condensing type. We describe the main properties of this characteristic, including applications to coincidence points. An example arising in the study of a mixed system, consisting of a first-order implicit differential equation and a differential inclusion, is given

Early gut microbiota signature of aGvHD in children given allogeneic hematopoietic cell transplantation for hematological disorders

The onset of acute Graft-versus-Host Disease (aGvHD) has been correlated with the gut microbiota (GM) composition, but experimental observations are still few, mainly involving cohorts of adult patients. In the current scenario where fecal microbiota transplantation has been used as a pioneer therapeutic approach to treat steroid-refractory aGvHD, there is an urgent need to expand existing observational studies of the GM dynamics in Hematopoietic Stem Cell Transplantation (HSCT). Aim of the present study is to explore the GM trajectory in 36 pediatric HSCT recipients in relation to aGvHD onset

Analysis of shared common genetic risk between amyotrophic lateral sclerosis and epilepsy

Because hyper-excitability has been shown to be a shared pathophysiological mechanism, we used the latest and largest genome-wide studies in amyotrophic lateral sclerosis (n = 36,052) and epilepsy (n = 38,349) to determine genetic overlap between these conditions. First, we showed no significant genetic correlation, also when binned on minor allele frequency. Second, we confirmed the absence of polygenic overlap using genomic risk score analysis. Finally, we did not identify pleiotropic variants in meta-analyses of the 2 diseases. Our findings indicate that amyotrophic lateral sclerosis and epilepsy do not share common genetic risk, showing that hyper-excitability in both disorders has distinct origins

Genetic correlation between amyotrophic lateral sclerosis and schizophrenia

A. Palotie on työryhmän Schizophrenia Working Grp Psychiat jäsen.We have previously shown higher-than-expected rates of schizophrenia in relatives of patients with amyotrophic lateral sclerosis (ALS), suggesting an aetiological relationship between the diseases. Here, we investigate the genetic relationship between ALS and schizophrenia using genome-wide association study data from over 100,000 unique individuals. Using linkage disequilibrium score regression, we estimate the genetic correlation between ALS and schizophrenia to be 14.3% (7.05-21.6; P = 1 x 10(-4)) with schizophrenia polygenic risk scores explaining up to 0.12% of the variance in ALS (P = 8.4 x 10(-7)). A modest increase in comorbidity of ALS and schizophrenia is expected given these findings (odds ratio 1.08-1.26) but this would require very large studies to observe epidemiologically. We identify five potential novel ALS-associated loci using conditional false discovery rate analysis. It is likely that shared neurobiological mechanisms between these two disorders will engender novel hypotheses in future preclinical and clinical studies.Peer reviewe

On some properties of dissipative functional differential inclusions in a Banach space

For a semilinear functional differential inclusion of the form $$y'(t) \in Ay(t0+f(t, x_t)$$ satisfying a dissipativity condition in a separable Banach space we prove the existence of a periodic solution and a global compact attractor

Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)

The volume contains the texts of four courses, given by the authors at a summer school that sought to present the state of the art in the growing field of topological methods in the theory of o.d.e. (in finite and infinitedimension), and to provide a forum for discussion of the wide variety of mathematical tools which are involved. The topics covered range from the extensions of the Lefschetz fixed point and the fixed point index on ANR's, to the theory of parity of one-parameter families of Fredholm operators, and from the theory of coincidence degree for mappings on Banach spaces to homotopy methods for continuation principles. CONTENTS: P. Fitzpatrick: The parity as an invariant for detecting bifurcation of the zeroes of one parameter families of nonlinear Fredholm maps.- M. Martelli: Continuation principles and boundary value problems.- J. Mawhin: Topological degree and boundary value problems for nonlinear differential equations.- R.D. Nussbaum: The fixed point index and fixed point theorems

On boundary value problems for degenerate differential inclusions in Banach spaces

We consider the applications of the theory of condensing set-valued maps, the theory of set-valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in a reflexive Banach space. Further, these techniques are used to obtain the solvability of general boundary value problems for a given class of inclusions. Some particular cases including periodic problems are considered

An epidemiologically-based needds assessment of cancer survivors

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