Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space

We find lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form T(u) = - \int_{\rr^d} K(x,y) (u(y)-u(x)) \, dy. Here we consider a kernel $K(x,y)=\psi (y-a(x))+\psi(x-a(y))$ where $\psi$ is a bounded, nonnegative function supported in the unit ball and $a$ means a diffeomorphism on \rr^d. A simple example being a linear function $a(x)= Ax$. The upper and lower bounds that we obtain are given in terms of the Jacobian of $a$ and the integral of $\psi$. Indeed, in the linear case $a(x) = Ax$ we obtain an explicit expression for the first eigenvalue in the whole \rr^d and it is positive when the the determinant of the matrix $A$ is different from one. As an application of our results, we observe that, when the first eigenvalue is positive, there is an exponential decay for the solutions to the associated evolution problem. As a tool to obtain the result, we also study the behaviour of the principal eigenvalue of the nonlocal Dirichlet problem in the ball $B_R$ and prove that it converges to the first eigenvalue in the whole space as $R\to \infty$

Decay estimates for nonlinear nonlocal diffusion problems in the whole space

In this paper we obtain bounds for the decay rate in the L^r (\rr^d)-norm for the solutions to a nonlocal and nolinear evolution equation, namely, u_t(x,t) = \int_{\rr^d} K(x,y) |u(y,t)- u(x,t)|^{p-2} (u(y,t)- u(x,t)) \, dy, with x \in \rr^d, $t>0$. Here we consider a kernel $K(x,y)$ of the form $K(x,y)=\psi (y-a(x))+\psi(x-a(y))$, where $\psi$ is a bounded, nonnegative function supported in the unit ball and $a$ is a linear function $a(x)= Ax$. To obtain the decay rates we derive lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form T(u) = - \int_{\rr^d} K(x,y) |u(y)-u(x)|^{p-2} (u(y)-u(x)) \, dy, with $1 \leq p < \infty$. The upper and lower bounds that we obtain are sharp and provide an explicit expression for the first eigenvalue in the whole \rr^d: \lambda_{1,p} (\rr^d) = 2(\int_{\rr^d} \psi (z) \, dz)|\frac{1}{|\det{A}|^{1/p}} -1|^p. Moreover, we deal with the $p=\infty$ eigenvalue problem studying the limit as $p \to \infty$ of $\lambda_{1,p}^{1/p}$

AI delivers Michaelis constants as fuel for genome-scale metabolic models

Michaelis constants (Km) are essential to predict the catalytic rate of enzymes, but are not widely available. A new study in PLOS Biology uses artificial intelligence (AI) to accurately predict Km on a proteome-wide scale, paving the way for dynamic, genome-wide modeling of metabolism

Application of photoluminescence and electroluminescence techniques to the characterization of intermediate band solar cells

The intermediatebandsolarcell (IBSC) is a photovoltaic device with a theoretical conversion efficiency limit of 63.2%. In recent years many attempts have been made to fabricate an intermediateband material which behaves as the theory states. One characteristic feature of an IBSC is its luminescence spectrum. In this work the temperature dependence of the photoluminescence (PL) and electroluminescence (EL) spectra of InAs/GaAs QD-IBSCs together with their reference cell have been studied. It is shown that EL measurements provide more reliable information about the behaviour of the IB material inside the IBSC structure than PL measurements. At low temperatures, the EL spectra are consistent with the quasi-Fermi level splits described by the IBSC model, whereas at room temperature they are not. This result is in agreement with previously reported analysis of the quantum efficiency of the solarcell

On-disk coronal rain

Small and elongated, cool and dense blob-like structures are being reported with high resolution telescopes in physically different regions throughout the solar atmosphere. Their detection and the understanding of their formation, morphology and thermodynamical characteristics can provide important information on their hosting environment, especially concerning the magnetic field, whose understanding constitutes a major problem in solar physics. An example of such blobs is coronal rain, a phenomenon of thermal non- equilibrium observed in active region loops, which consists of cool and dense chromospheric blobs falling along loop-like paths from coronal heights. So far, only off-limb coronal rain has been observed and few reports on the phenomenon exist. In the present work, several datasets of on-disk H{\alpha} observations with the CRisp Imaging SpectroPolarimeter (CRISP) at the Swedish 1-m Solar Telescope (SST) are analyzed. A special family of on-disk blobs is selected for each dataset and a statistical analysis is carried out on their dynamics, morphology and temperatures. All characteristics present distributions which are very similar to reported coronal rain statistics. We discuss possible interpretations considering other similar blob-like structures reported so far and show that a coronal rain interpretation is the most likely one. Their chromospheric nature and the projection effects (which eliminate all direct possibility of height estimation) on one side, and their small sizes, fast dynamics, and especially, their faint character (offering low contrast with the background intensity) on the other side, are found as the main causes for the absence until now of the detection of this on-disk coronal rain counterpart.Comment: 18 pages, 10 figures. Accepted for Solar Physic

An essential role of acetylcholine-glutamate synergy at habenular synapses in nicotine dependence

A great deal of interest has been focused recently on the habenula and its critical role in aversion, negative-reward and drug dependence. Using a conditional mouse model of the ACh-synthesizing enzyme choline acetyltransferase (Chat), we report that local elimination of acetylcholine (ACh) in medial habenula (MHb) neurons alters glutamate corelease and presynaptic facilitation. Electron microscopy and immuno-isolation analyses revealed colocalization of ACh and glutamate vesicular transporters in synaptic vesicles (SVs) in the central IPN. Glutamate reuptake in SVs prepared from the IPN was increased by ACh, indicating vesicular synergy. Mice lacking CHAT in habenular neurons were insensitive to nicotine-conditioned reward and withdrawal. These data demonstrate that ACh controls the quantal size and release frequency of glutamate at habenular synapses, and suggest that the synergistic functions of ACh and glutamate may be generally important for modulation of cholinergic circuit function and behavior

Suppression of peripheral pain by blockade of voltage-gated calcium 2.2 channels in nociceptors induces RANKL and impairs recovery from inflammatory arthritis in a mouse model

Objective: A hallmark of rheumatoid arthritis (RA) is the chronic pain that accompanies the inflammation and joint deformation. Patients with RA rate pain relief with highest priority, however, few studies have addressed the efficacy and safety of therapies directed specifically towards pain pathways. The conotoxin MVIIA (Prialt/Ziconotide) is used in humans to alleviate persistent pain syndromes because it specifically blocks the CaV 2.2 voltage-gated calcium channel, which mediates the release of neurotransmitters and proinflammatory mediators from peripheral nociceptor nerve terminals. The purpose of this study was to investigate whether block of CaV 2.2 can suppress arthritic pain, and to examine the progression of induced arthritis during persistent CaV 2.2 blockade. Methods: Transgenic mice (Tg-MVIIA) expressing a membrane-tethered form of the {Omega}-conotoxin MVIIA, under the control of a nociceptor-specific gene, were employed. These mice were subjected to unilateral induction of joint inflammation using the Antigen- and Collagen-Induced Arthritis (ACIA) model. Results: We observed that CaV 2.2-blockade mediated by t-MVIIA effectively suppressed arthritis-induced pain; however, in contrast to their wild-type littermates, which ultimately regained use of their injured joint as inflammation subsides, Tg-MVIIA mice showed continued inflammation with an up-regulation of the osteoclast activator RANKL and concomitant joint and bone destruction. Conclusion: Altogether, our results indicate that alleviation of peripheral pain by blockade of CaV 2.2- mediated calcium influx and signaling in nociceptor sensory neurons, impairs recovery from induced arthritis and point to the potentially devastating effects of using CaV 2.2 channel blockers as analgesics during inflammation

Adults with higher social anxiety show avoidant gaze behaviour in a real-world social setting: A mobile eye tracking study.

Attentional biases are a core characteristic of social anxiety (SA). However, research has yielded conflicting findings and failed to investigate these biases in real, face-to-face social situations. Therefore, this study examined attentional biases in SA by measuring participants' eye gaze within a novel eye-tracking paradigm during a real-life social situation. Student participants (N = 30) took part in what they thought was a visual search study, when a confederate posing as another participant entered the room. Whilst all participants avoided looking at the confederate, those with higher SA fixated for a shorter duration during their first fixation on him, and executed fewer fixations and saccades overall as well as exhibiting a shorter scanpath. These findings are indicative of additional avoidance in the higher SA participants. In contrast to previous experimental work, we found no evidence of social hypervigilance or hyperscanning in high SA individuals. The results indicate that in unstructured social settings, avoidance rather than vigilance predominates, especially in those with higher SA