Density of the domain of doubly nonlinear operators in L1L^1

The aim of this paper is to provide sufficient conditions implying that the effective domain $D(A\phi)$ of an $m$-accretive operator $A\phi$ in $L^1$ is dense in $L^1$. Here, $A\phi$ refers to the composition $A\circ \phi$ in $L^1$ of the part $A=(\partial\mathcal{E})_{\vert L^{1\cap \infty}}$ in $L^{1\cap\infty}\times L^{1\cap\infty}$ of the subgradient $\partial\mathcal{E}$ in $L^2$ of a convex, proper, lower semicontinuous functional $\mathcal{E}$ on $L^2$ and a continuous, strictly increasing function $\phi$ on the real line $\mathbb{R}$. To illustrate the role of the sufficient conditions, we apply our main result to the class of doubly nonlinear operators $A\phi$, where $A$ is a classical Leray-Lions operator

A doubly nonlinear fractional diffusive equation

This thesis focuses on the `doubly nonlinear fractional diffusive equation', a doubly nonlinear nonlocal parabolic initial boundary value problem driven by the fractional p-Laplacian equipped with homogeneous Dirichlet boundary conditions on a domain in Euclidean space and composed with a power-like function. We also include a Lipschitz perturbation and a forcing term depending on space and time. We first generalize the nonlinear term u^m, replacing this by a continuous, strictly increasing function. Here we establish well-posedness in L1 in the sense of mild solutions and a comparison principle. For domains with finite measure and with restricted initial data we obtain that mild solutions of the inhomogeneous evolution problem are strong and distributional. We then consider the power-like case where we obtain further regularity properties. In particular, we have an Ll-L∞ regularizing effect for mild solutions (and therefore also for strong solutions), also known as ultracontractivity. We further obtain derivative and energy estimates for this problem. Using these, we extend the previous strong regularity result to obtain strong distributional solutions on general open domains with initial data in L1. Moreover, we prove local and global Hölder continuity results in restricted cases as well as a comparison principle that yields extinction in finite time of mild solutions to the homogeneous evolution equation. We finally restrict to the doubly nonlinear fractional diffusive equation without forcing terms, where we investigate self-similarity properties and, in particular, the asymptotic behaviour of solutions for large times. The main result in this case is the existence of Barenblatt solutions. However, in finding these we also prove an Aleksandrov symmetry principle for solutions and estimate solutions by global bounding functions which are integrable in space

Off the Beaten Track: Laterally Weighted Motion Planning for Local Obstacle Avoidance

We extend the behaviour of generic sample-based motion planners to support obstacle avoidance during long-range path following by introducing a new edge-cost metric paired with a curvilinear planning space. The resulting planner generates naturally smooth paths that avoid local obstacles while minimizing lateral path deviation to best exploit prior terrain knowledge from the reference path. In this adaptation, we explore the nuances of planning in the curvilinear configuration space and describe a mechanism for natural singularity handling to improve generality. We then shift our focus to the trajectory generation problem, proposing a novel Model Predictive Control (MPC) architecture to best exploit our path planner for improved obstacle avoidance. Through rigorous field robotics trials over 5 km, we compare our approach to the more common direct path-tracking MPC method and discuss the promise of these techniques for reliable long-term autonomous operations.Comment: 15 pages, 21 Figures, 3 Tables. Manuscript was submitted to IEEE Transactions on Robotics on September 17th, 202

Is Alpha-Synuclein Loss-of-Function a Contributor to Parkinsonian Pathology? Evidence from Non-human Primates

Accumulation of alpha-synuclein (α-syn) in Lewy bodies and neurites of midbrain dopamine neurons is diagnostic for Parkinson’s disease (PD), leading to the proposal that PD is a toxic gain-of-function synucleinopathy. Here we discuss the alternative viewpoint that α-syn displacement from synapses by misfolding and aggregation results in a toxic loss-of-function. In support of this hypothesis we provide evidence from our pilot study demonstrating that knockdown of endogenous α-syn in dopamine neurons of nonhuman primates reproduces the pattern of nigrostriatal degeneration characteristic of PD

Neutral Solar Wind Generated by Lunar Exospheric Dust at the Terminator

We calculate the flux of neutral solar wind observed on the lunar surface at the terminator due to solar wind protons penetrating exospheric dust grains with (1) radii greater than 0.1 microns and (2) radii greater than 0.01 microns. For grains with radii larger than 0.1 microns, the ratio of the neutral solar wind flux produced by exospheric dust to the incident ionized solar wind flux is estimated to be about 10^-4-10^-3 for solar wind speeds in excess of 800 km/s, but much lower (less than 10^-5) at average to slow solar wind speeds. However, when the smaller grain sizes are considered, this ratio is estimated to be greater than 10^-5 at all speeds, and at speeds in excess of 700 km/s reaches about 10^-3. These neutral solar wind fluxes are easily measurable with current low energy neutral atom instrumentation. Observations of neutral solar wind from the surface of the Moon would provide independent information on the distribution of very small dust grains in the lunar exosphere that would complement and constrain optical measurements at ultraviolet and visible wavelengths.Comment: in press in J. Geophys. Re

Quantitative Top-Down Proteomics of SILAC Labeled Human Embryonic Stem Cells

Human embryonic stem cells (hESCs) are self-renewing pluripotent cells with relevance to treatment of numerous medical conditions. However, a global understanding of the role of the hESC proteome in maintaining pluripotency or triggering differentiation is still largely lacking. The emergence of top-down proteomics has facilitated the identification and characterization of intact protein forms that are not readily apparent in bottom-up studies. Combined with metabolic labeling techniques such as stable isotope labeling by amino acids in cell culture (SILAC), quantitative comparison of intact protein expression under differing experimental conditions is possible. Herein, quantitative top-down proteomics of hESCs is demonstrated using the SILAC method and nano-flow reverse phase chromatography directly coupled to a linear-ion-trap Fourier transform ion cyclotron resonance mass spectrometer (nLC-LTQ-FT-ICR-MS). In this study, which to the best of our knowledge represents the first top-down analysis of hESCs, we have confidently identified 11 proteins by accurate intact mass, MS/MS, and amino acid counting facilitated by SILAC labeling. Although quantification is challenging due to the incorporation of multiple labeled amino acids (i.e., lysine and arginine) and arginine to proline conversion, we are able to quantitatively account for these phenomena using a mathematical model

The Lunar Dust Pendulum

Shadowed regions on the lunar surface acquire a negative potential. In particular, shadowed craters can have a negative potential with respect to the surrounding lunar regolith in sunlight, especially near the terminator regions. Here we analyze the motion of a positively charged lnnar dust grain in the presence of a shadowed crater at a negative potential in vacuum. Previous models describing the transport of charged lunar dust close to the surface have typically been limited to one-dimensional motion in the vertical direction, e.g. electrostatic levitation; however. the electric fields in the vicinity of shadowed craters will also have significant components in the horizontal directions. We propose a model that includes both the horizontal and vertical motion of charged dust grains near shadowed craters. We show that the dust grains execute oscillatory trajectories and present an expression for the period of oscillation drawing an analogy to the motion of a pendulum

Using Actual Financial Accounting Information To Conduct Financial Ratio Analysis: The Case Of Motorola

In this paper, we demonstrate the use of actual financial data for financial ratio analysis.  We construct a financial and industry analysis for Motorola Corporation.  The objective is to show students exactly how to compute ratios for an actual company.  This paper demonstrates the difficulties in applying the principles of financial ratio analysis when the data are not homogeneous, as is the case in textbook examples.  We use Motorola as an example because the firm has several segments, two of which account for the majority of sales and represent two industries (semi-conductor and communications) that have different characteristics.  The case illustrates the complexity of financial analysis