On Uniqueness of Boundary Blow-up Solutions of a Class of Nonlinear Elliptic Equations

We study boundary blow-up solutions of semilinear elliptic equations $Lu=u_+^p$ with $p>1$, or $Lu=e^{au}$ with $a>0$, where $L$ is a second order elliptic operator with measurable coefficients. Several uniqueness theorems and an existence theorem are obtained.Comment: To appear in Comm. Partial Differential Equations; 10 page

Supersymmetry and the relationship between a class of singular potentials in arbitrary dimensions

The eigenvalues of the potentials $V_{1}(r)=\frac{A_{1}}{r}+\frac{A_{2}}{r^{2}}+\frac{A_{3}}{r^{3}}+\frac{A_{4 }}{r^{4}}$ and $V_{2}(r)=B_{1}r^{2}+\frac{B_{2}}{r^{2}}+\frac{B_{3}}{r^{4}}+\frac{B_{4}}{r^ {6}}$, and of the special cases of these potentials such as the Kratzer and Goldman-Krivchenkov potentials, are obtained in N-dimensional space. The explicit dependence of these potentials in higher-dimensional space is discussed, which have not been previously covered.Comment: 13 pages article in LaTEX (uses standard article.sty). Please check "http://www1.gantep.edu.tr/~ozer" for other studies of Nuclear Physics Group at University of Gaziante

The Impact of COVID-19 on Electroconvulsive Therapy: A Multisite, Retrospective Study from the Clinical Alliance and Research in Electroconvulsive Therapy and Related Treatments Network

Objectives The coronavirus disease 2019 (COVID-19) pandemic has led to reported change in electroconvulsive therapy (ECT) services worldwide. However, minimal data have been published demonstrating tangible changes across multiple ECT centers. This article aimed to examine changes in ECT patients and ECT service delivery during the pandemic. Methods We retrospectively assessed data collected on ECT patients within the Clinical Alliance and Research in Electroconvulsive Therapy and Related Treatments (CARE) Network during a 3-month period starting at the first COVID-19 restrictions in 2020 and compared data with predicted values based on the corresponding 3-month period in 2019. Mixed-effects repeated-measures analyses examined differences in the predicted and actual number of acute ECT courses started and the total number of acute ECT treatments given in 2020. Sociodemographic, clinical, treatment factors, and ECT service delivery factors were compared for 2020 and 2019. Results Four Australian and 1 Singaporean site participated in the study. There were no significant differences between the predicted and actual number of acute ECT courses and total number of acute ECT treatments administered in 2020. During 2020, there were statistically significant increases in the proportion of patients requiring ECT under substitute consent and receiving ECT for urgent reasons compared with 2019. Conclusions This multisite empirical study is among the first that supports anecdotal reports of changes in the triaging and delivery of ECT during COVID-19. Results suggest that ECT was prioritized for the most severely ill patients. Further data assessing the impacts of COVID-19 on ECT are needed

Symbolic Discovery of Optimization Algorithms

We present a method to formulate algorithm discovery as program search, and apply it to discover optimization algorithms for deep neural network training. We leverage efficient search techniques to explore an infinite and sparse program space. To bridge the large generalization gap between proxy and target tasks, we also introduce program selection and simplification strategies. Our method discovers a simple and effective optimization algorithm, $\textbf{Lion}$ (\textit{Evo\textbf{L}$ved S$\textbf{i}$gn M$\textbf{o}$me$\textbf{n}tum}). It is more memory-efficient than Adam as it only keeps track of the momentum. Different from adaptive optimizers, its update has the same magnitude for each parameter calculated through the sign operation. We compare Lion with widely used optimizers, such as Adam and Adafactor, for training a variety of models on different tasks. On image classification, Lion boosts the accuracy of ViT by up to 2% on ImageNet and saves up to 5x the pre-training compute on JFT. On vision-language contrastive learning, we achieve 88.3% $\textit{zero-shot}$ and 91.1% $\textit{fine-tuning}$ accuracy on ImageNet, surpassing the previous best results by 2% and 0.1%, respectively. On diffusion models, Lion outperforms Adam by achieving a better FID score and reducing the training compute by up to 2.3x. For autoregressive, masked language modeling, and fine-tuning, Lion exhibits a similar or better performance compared to Adam. Our analysis of Lion reveals that its performance gain grows with the training batch size. It also requires a smaller learning rate than Adam due to the larger norm of the update produced by the sign function. Additionally, we examine the limitations of Lion and identify scenarios where its improvements are small or not statistically significant. The implementation of Lion is publicly available.Comment: 30 pages, update the tuning instruction

Quantum Phase Transition in a Resonant Level Coupled to Interacting Leads

An interacting one-dimensional electron system, the Luttinger liquid, is distinct from the "conventional" Fermi liquids formed by interacting electrons in two and three dimensions. Some of its most spectacular properties are revealed in the process of electron tunneling: as a function of the applied bias or temperature the tunneling current demonstrates a non-trivial power-law suppression. Here, we create a system which emulates tunneling in a Luttinger liquid, by controlling the interaction of the tunneling electron with its environment. We further replace a single tunneling barrier with a double-barrier resonant level structure and investigate resonant tunneling between Luttinger liquids. For the first time, we observe perfect transparency of the resonant level embedded in the interacting environment, while the width of the resonance tends to zero. We argue that this unique behavior results from many-body physics of interacting electrons and signals the presence of a quantum phase transition (QPT). In our samples many parameters, including the interaction strength, can be precisely controlled; thus, we have created an attractive model system for studying quantum critical phenomena in general. Our work therefore has broadly reaching implications for understanding QPTs in more complex systems, such as cold atoms and strongly correlated bulk materials.Comment: 11 pages total (main text + supplementary

A frozen super-Earth orbiting a star at the bottom of the Main Sequence

We observed the microlensing event MOA-2007-BLG-192 at high angular resolution in JHKs with the NACO adaptive optics system on the VLT while the object was still amplified by a factor 1.23 and then at baseline 18 months later. We analyzed and calibrated the NACO photometry in the standard 2MASS system in order to accurately constrain the source and the lens star fluxes. We detect light from the host star of MOA-2007-BLG-192Lb, which significantly reduces the uncertainties in its char- acteristics as compared to earlier analyses. We find that MOA-2007-BLG-192L is most likely a very low mass late type M-dwarf (0.084 [+0.015] [-0.012] M\odot) at a distance of 660 [+100] [-70] pc orbited by a 3.2 [+5.2] [-1.8] M\oplus super-Earth at 0.66 [+0.51] [-0.22] AU. We then discuss the properties of this cold planetary system.Comment: published version A&A 540, A78 (2012) A&A, 10 pages, 7 Figure

Residual Kondo effect in quantum dot coupled to half-metallic ferromagnets

We study the Kondo effect in a quantum dot coupled to half-metallic ferromagnetic electrodes in the regime of strong on-dot correlations. Using the equation of motion technique for nonequilibrium Green functions in the slave boson representation we show that the Kondo effect is not completely suppressed for anti-parallel leads magnetization. In the parallel configuration there is no Kondo effect but there is an effect associated with elastic cotunneling which in turn leads to similar behavior of the local (on-dot) density of states (LDOS) as the usual Kondo effect. Namely, the LDOS shows the temperature dependent resonance at the Fermi energy which splits with the bias voltage and the magnetic field. Moreover, unlike for non-magnetic or not fully polarized ferromagnetic leads the only minority spin electrons can form such resonance in the density of states. However, this resonance cannot be observed directly in the transport measurements and we give some clues how to identify the effect in such systems.Comment: 15 pages, 8 figures, accepted for publication in J. Phys.: Condens. Mat

Octet magnetic moments and the Coleman-Glashow sum rule violation in the chiral quark model

Baryon octet magnetic moments when calculated within the chiral quark model, incorporating the orbital angular momentum as well as the quark sea contribution through the Cheng-Li mechanism, not only show improvement over the non relativistic quark model results but also gives a non zero value for the right hand side of Coleman-Glashow sum rule. When effects due to spin-spin forces between constituent quarks as well as `mass adjustments' due to confinement are added, it leads to an excellent fit for the case of p, \Sigma^+, \Xi^o and violation of Coleman-Glashow sum rule, whereas in almost all the other cases the results are within 5% of the data.Comment: 5 RevTeX pages, accepted for publication in PRD(Rapid Communication

Modulation of MicroRNA-194 and cell migration by HER2-targeting trastuzumab in breast cancer

Conceived and designed the experiments: XFL GAC RCB. Performed the experiments: XFL MIA WM RS MSN SZ. Analyzed the data: XFL SR. Contributed reagents/materials/analysis tools: YW GAC. Wrote the paper: XFL RCB.Trastuzumab, a humanized monoclonal antibody directed against the extracellular domain of the HER2 oncoprotein, can effectively target HER2-positive breast cancer through several mechanisms. Although the effects of trastuzumab on cancer cell proliferation, angiogenesis and apoptosis have been investigated in depth, the effect of trastuzumab on microRNA (miRNA) has not been extensively studied. We have performed miRNA microarray profiling before and after trastuzumab treatment in SKBr3 and BT474 human breast cancer cells that overexpress HER2. We found that trastuzumab treatment of SKBr3 cells significantly decreased five miRNAs and increased three others, whereas treatment of BT474 cells significantly decreased two miRNAs and increased nine. The only change in miRNA expression observed in both cell lines following trastuzumab treatment was upregulation of miRNA-194 (miR-194) that was further validated in vitro and in vivo. Forced expression of miR-194 in breast cancer cells that overexpress HER2 produced no effect on apoptosis, modest inhibition of proliferation, significant inhibition of cell migration/invasion in vitro and significant inhibition of xenograft growth in vivo. Conversely, knockdown of miR-194 promoted cell migration. Increased miR-194 expression markedly reduced levels of the cytoskeletal protein talin2 and specifically inhibited luciferase reporter activity of a talin2 wild-type 39-untranslated region, but not that of a mutant reporter, indicating that talin2 is a direct downstream target of miR-194. Trastuzumab treatment inhibited breast cancer cell migration and reduced talin2 expression in vitro and in vivo. Knockdown of talin2 inhibited cell migration/invasion. Knockdown of trastuzumab-induced miR-194 expression with a miR-194 inhibitor compromised trastuzumab-inhibited cell migration in HER2-overexpressing breast cancer cells. Consequently, trastuzumab treatment upregulates miR-194 expression and may exert its cell migration-inhibitory effect through miR-194-mediated downregulation of cytoskeleton protein talin2 in HER2-overexpressing human breast cancer cells.This work was supported by the Anne and Henry Zarrow Foundation, kind gifts from Stuart and Gaye Lynn Zarrow and from Mrs. Delores Wilkenfeld, the Laura and John Arnold Foundation, the RGK Foundation, and the MD Anderson NCI CCSG P30 CA16672. G.A.C. is supported as a Fellow at the University of Texas MD Anderson Research Trust, as a University of Texas System Regents Research Scholar and by the CLL Global Research Foundation