Search results for "quantitative"
showing 10 items of 2409 documents
Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants
2020
We provide a quantitative lower bound to the Cheeger constant of a set $\Omega$ in both the Euclidean and the Gaussian settings in terms of suitable asymmetry indexes. We provide examples which show that these quantitative estimates are sharp.
Characteristics of neuronal systems in the visual cortex
1987
The coupling complexity of cortical areas makes it very difficult to analyse them experimentally. Studies of model systems provide the possibility of adapting the analysis to the available data base and elaborating the fundamental properties that depend on the structure of the system. We propose a model system of variable complexity that is spatially two-dimensional and time-dependent, uses feedback for iteration and smoothing, includes the mapping of the cortical networks and can be nonlinear as the case requires. Combining such elementary systems on the basis of neuroanatomical findings enables us to simulate cortical mappings and to interpret neurophysiological data. The decisive factor …
High-speed exhaustive 3-locus interaction epistasis analysis on FPGAs
2015
Abstract Epistasis, the interaction between genes, has become a major topic in molecular and quantitative genetics. It is believed that these interactions play a significant role in genetic variations causing complex diseases. Several algorithms have been employed to detect pairwise interactions in genome-wide association studies (GWAS) but revealing higher order interactions remains a computationally challenging task. State of the art tools are not able to perform exhaustive search for all three-locus interactions in reasonable time even for relatively small input datasets. In this paper we present how a hardware-assisted design can solve this problem and provide fast, efficient and exhaus…
Wavefront invasion for a chemotaxis model of Multiple Sclerosis
2016
In this work we study wavefront propagation for a chemotaxis reaction-diffusion system describing the demyelination in Multiple Sclerosis. Through a weakly non linear analysis, we obtain the Ginzburg–Landau equation governing the evolution of the amplitude of the pattern. We validate the analytical findings through numerical simulations. We show the existence of traveling wavefronts connecting two different steady solutions of the equations. The proposed model reproduces the progression of the disease as a wave: for values of the chemotactic parameter below threshold, the wave leaves behind a homogeneous plaque of apoptotic oligodendrocytes. For values of the chemotactic coefficient above t…
On operads, bimodules and analytic functors
2017
We develop further the theory of operads and analytic functors. In particular, we introduce a bicategory that has operads as 0-cells, operad bimodules as 1-cells and operad bimodule maps as 2-cells, and prove that this bicategory is cartesian closed. In order to obtain this result, we extend the theory of distributors and the formal theory of monads.
Nonlinear elliptic equations involving the p-Laplacian with mixed Dirichlet-Neumann boundary conditions
2019
In this paper, a nonlinear differential problem involving the \(p\)-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results.
A Quantitative Analysis of Metrics on Rn with Almost Constant Positive Scalar Curvature, with Applications to Fast Diffusion Flows
2017
We prove a quantitative structure theorem for metrics on $\mathbf{R}^n$ that are conformal to the flat metric, have almost constant positive scalar curvature, and cannot concentrate more than one bubble. As an application of our result, we show a quantitative rate of convergence in relative entropy for a fast diffusion equation in $\mathbf{R}^n$ related to the Yamabe flow.
Donnan phenomena in membranes with charge due to ion adsorption. Effects of the interaction between adsorbed charged groups
1993
A physical model for the modified Donnan phenomenon associated with ion adsorption on localized membrane sites is presented. This model accounts for the dependence of the concentration of adsorbed ions on electrolyte concentration and pH as it is influenced by the electrostatic interaction between adsorbed ions. The equilibrium thermodynamic concepts employed are based on the Donnan formalism for the ion equilibria between membrane and solution, and the Bragg–Williams approximation for an adsorption isotherm that incorported interaction between adsorbed ions. Our results include the concentration of charged groups in the membrane, the pH of the membrane phase solution, and the Donnan potent…
Non-hermitian operator modelling of basic cancer cell dynamics
2018
We propose a dynamical system of tumor cells proliferation based on operatorial methods. The approach we propose is quantum-like: we use ladder and number operators to describe healthy and tumor cells birth and death, and the evolution is ruled by a non-hermitian Hamiltonian which includes, in a non reversible way, the basic biological mechanisms we consider for the system. We show that this approach is rather efficient in describing some processes of the cells. We further add some medical treatment, described by adding a suitable term in the Hamiltonian, which controls and limits the growth of tumor cells, and we propose an optimal approach to stop, and reverse, this growth.
Mechanism of Anesthetic Action: Oxygen Pathway Perturbation Hypothesis
2001
Although more than 150 years have past since the discovery of general anesthetics, how they precisely work remains a mystery. We propose a novel unitary mechanism of general anesthesia verifiable by experiments. In the proposed mechanism, general anesthetics perturb oxygen pathways in both membranes and oxygen-utilizing proteins such that the availabilities of oxygen to its sites of utilization are reduced which in turn triggers cascading cellular responses through oxygen-sensing mechanisms resulting in general anesthesia. Despite the general assumption that cell membranes are readily permeable to oxygen, exiting publications indicate that these membranes are plausible oxygen transport barr…