Well-posedness for a class of nonlinear degenerate parabolic equations

In this paper we obtain well-posedness for a class of semilinear weakly degenerate reaction-diffusion systems with Robin boundary conditions. This result is obtained through a Gagliardo-Nirenberg interpolation inequality and some embedding results for weighted Sobolev spaces

Effects of Synaptic and Myelin Plasticity on Learning in a Network of Kuramoto Phase Oscillators

Models of learning typically focus on synaptic plasticity. However, learning is the result of both synaptic and myelin plasticity. Specifically, synaptic changes often co-occur and interact with myelin changes, leading to complex dynamic interactions between these processes. Here, we investigate the implications of these interactions for the coupling behavior of a system of Kuramoto oscillators. To that end, we construct a fully connected, one-dimensional ring network of phase oscillators whose coupling strength (reflecting synaptic strength) as well as conduction velocity (reflecting myelination) are each regulated by a Hebbian learning rule. We evaluate the behavior of the system in terms of structural (pairwise connection strength and conduction velocity) and functional connectivity (local and global synchronization behavior). We find that for conditions in which a system limited to synaptic plasticity develops two distinct clusters both structurally and functionally, additional adaptive myelination allows for functional communication across these structural clusters. Hence, dynamic conduction velocity permits the functional integration of structurally segregated clusters. Our results confirm that network states following learning may be different when myelin plasticity is considered in addition to synaptic plasticity, pointing towards the relevance of integrating both factors in computational models of learning.Comment: 39 pages, 15 figures This work is submitted in Chaos: An Interdisciplinary Journal of Nonlinear Scienc

Fluid Flows of Mixed Regimes in Porous Media

In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are usually treated separately in literature. To study complex flows when all three regimes may be present in different portions of a same domain, we use a single equation of motion to unify them. Several scenarios and models are then considered for slightly compressible fluids. A nonlinear parabolic equation for the pressure is derived, which is degenerate when the pressure gradient is either small or large. We estimate the pressure and its gradient for all time in terms of initial and boundary data. We also obtain their particular bounds for large time which depend on the asymptotic behavior of the boundary data but not on the initial one. Moreover, the continuous dependence of the solutions on initial and boundary data, and the structural stability for the equation are established.Comment: 33 page

On a Cahn--Hilliard--Darcy system for tumour growth with solution dependent source terms

We study the existence of weak solutions to a mixture model for tumour growth that consists of a Cahn--Hilliard--Darcy system coupled with an elliptic reaction-diffusion equation. The Darcy law gives rise to an elliptic equation for the pressure that is coupled to the convective Cahn--Hilliard equation through convective and source terms. Both Dirichlet and Robin boundary conditions are considered for the pressure variable, which allows for the source terms to be dependent on the solution variables.Comment: 18 pages, changed proof from fixed point argument to Galerkin approximatio

Existence of Ricci flows of incomplete surfaces

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.Comment: 20 pages; updated to reflect galley proof correction

Rhodopsin Expression Level Affects Rod Outer Segment Morphology and Photoresponse Kinetics

Background: The retinal rod outer segment is a sensory cilium that is specialized for the conversion of light into an electrical signal. Within the cilium, up to several thousand membranous disks contain as many as a billion copies of rhodopsin for efficient photon capture. Disks are continually turned over, requiring the daily synthesis of a prodigious amount of rhodopsin. To promote axial diffusion in the aqueous cytoplasm, the disks have one or more incisures. Across vertebrates, the range of disk diameters spans an order of magnitude, and the number and length of the incisures vary considerably, but the mechanisms controlling disk architecture are not well understood. The finding that transgenic mice overexpressing rhodopsin have enlarged disks lacking an incisure prompted us to test whether lowered rhodopsin levels constrain disk assembly. Methodology/Principal Findings: The structure and function of rods from hemizygous rhodopsin knockout (R+/−) mice with decreased rhodopsin expression were analyzed by transmission electron microscopy and single cell recording. R+/− rods were structurally altered in three ways: disk shape changed from circular to elliptical, disk surface area decreased, and the single incisure lengthened to divide the disk into two sections. Photocurrent responses to flashes recovered more rapidly than normal. A spatially resolved model of phototransduction indicated that changes in the packing densities of rhodopsin and other transduction proteins were responsible. The decrease in aqueous outer segment volume and the lengthened incisure had only minor effects on photon response amplitude and kinetics. Conclusions/Significance: Rhodopsin availability limits disk assembly and outer segment girth in normal rods. The incisure may buffer the supply of structural proteins needed to form larger disks. Decreased rhodopsin level accelerated photoresponse kinetics by increasing the rates of molecular collisions on the membrane. Faster responses, together with fewer rhodopsins, combine to lower overall sensitivity of R+/− rods to light

The Determination of Titan Gravity Field from Doppler Tracking of the Cassini Spacecraft

In its tour of the Saturnian system, the spacecraft Cassini is carrying out measurements of the gravity field of Titan, whose knowledge is crucial for constraining the internal structure of the satellite. In the five flybys devoted to gravity science, the spacecraft is tracked in X (8.4 GHz) and Ka band (32.5 GHz) from the antennas of NASA's Deep Space Network. The use of a dual frequency downlink is used to mitigate the effects of interplanetary plasma, the largest noise source affecting Doppler measurements. Variations in the wet path delay are effectively compensated by means of advanced water vapor radiometers placed close to the ground antennas. The first three flybys occurred on February 27, 2006, December 28, 2006, and June 29, 2007. Two additional flybys are planned in July 2008 and May 2010. This paper presents the estimation of the mass and quadrupole field of Titan from the first two flybys, carried out by the Cassini Radio Science Team using a short arc orbit determination. The data from the two flybys are first independently fit using a dynamical model of the spacecraft and the bodies of the Saturnian system, and then combined in a multi-arc solution. Under the assumption that the higher degree harmonics are negligible, the estimated values of the gravity parameters from the combined, multi-arc solution are GM = 8978.1337 +/- 0.0025 km(exp 3) / s(exp 2), J (sub 2) = (2.7221 +/- 0.0185) 10 (exp -5) and C (sub 22) = (1.1159 +/- 0.0040) 10 (exp -5) The excellent agreement (within 1.7 sigma) of the results from the two flybys further increases the confidence in the solution and provides an a posteriori validation of the dynamical model

Riesz potentials and nonlinear parabolic equations

The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation. Heat kernels type estimates persist in the nonlinear cas

Six-month mortality rates are lower in patients with an acute coronary syndrome treated with the combination of clopidogrel and a statin than in patients treated with either therapy alone: An analysis from the global registry of acute coronary events

La remunta la podem data de l'any 1928, aproximadament.Primer pla d'un edifici d'habitages, inicialment de planta baixa i pis, en què es remunten tres plantes en la part de la parcel·la que forma xamfrà a tres carrers. La remunta forma un volum molt potent que revalora estèticament l'edifici

Improved catalytic activity of ruthenium–arene complexes in the reduction of NAD+

A series of neutral Ru-II half-sandwich complexes of the type [(eta(6)-arene)Ru(N,N')Cl] where the arene is para-cymene (p-cym), hexamethylbenzene (hmb), biphenyl (bip), or benzene (bn) and N,N' is N-(2-aminoethyl) -4-(trifluoromethyl)benzenesulfonamide (TfEn), N-(2-aminoethyl)-4-toluenesulfonamide (TsEn), or N-(2-aminoethyl)-methylenesulfonamide (MsEn) were synthesized and characterized. X-ray crystal structures of [(p-cym)Ru(MsEn)Cl] (1), [(hmb)Ru(TsEn)Cl] (5), [(hmb)Ru(TfEn)Cl] (6), [(bip)Ru(MsEn)Cl] (7), and [(bip)Ru(TsEn)Cl] (8) have been determined. The complexes can regioselectively catalyze the transfer hydrogenation of NAD(+) to give 1,4-NADH in the presence of formate. The turnover frequencies (TOF) when the arene is varied decrease in the order bn > bip > p-cym > hmb for complexes with the same N,N' chelating ligand. The TOF decreased with variation in the N,N' chelating ligand in the order TfEn > TsEn > MsEn for a given arene. [(bn)Ru(TfEn)Cl] (12) was the most active, with a TOP of 10.4 h(-1). The effects of NAD(+) and formate concentration on the reaction rates were determined for [(p-cym)Ru(TsEn)Cl] (2). Isotope studies implicated the formation of [(arene)Ru(N,N')(H)] as the rate-limiting step. The coordination of formate and subsequent CO2 elimination to generate the hydride were modeled computationally by density functional theory (DFT). CO2 elimination occurs via a two-step process with the coordinated formate first twisting to present its hydrogen toward the metal center. The computed barriers for CO2 release for arene = benzene follow the order MsEn > TsEn > TfEn, and for the Ms En system the barrier followed bn < hmb, both consistent with the observed rates. The effect of methanol on transfer hydrogenation rates in aqueous solution was investigated. A study of pH dependence of the reaction in D2O gave the optimum pH* as 7.2 with a TOF of 1.58 h(-1) for 2. The series of compounds reported here show an improvement in the catalytic activity by an order of magnitude compared to the ethylenediamine analogues