Sasakian metric as a Ricci soliton and related results

We prove the following results: (i) A Sasakian metric as a non-trivial Ricci soliton is null $\eta$-Einstein, and expanding. Such a characterization permits to identify the Sasakian metric on the Heisenberg group $\mathcal{H}^{2n+1}$ as an explicit example of (non-trivial) Ricci soliton of such type. (ii) If an $\eta$-Einstein contact metric manifold $M$ has a vector field $V$ leaving the structure tensor and the scalar curvature invariant, then either $V$ is an infinitesimal automorphism, or $M$ is $D$-homothetically fixed $K$-contact.Comment: Non

Sasakian Manifolds with Purely Transversal Bach Tensor

We show that a (2n + 1)-dimensional Sasakian manifold (M, g) with a purely transversal Bach tensor has constant scalar curvature ≥2n(2n+1), equality holding if and only if (M, g) is Einstein. For dimension 3, M is locally isometric to the unit sphere S3. For dimension 5, if in addition (M, g) is complete, then it has positive Ricci curvature and is compact with finite fundamental group π1(M)

Contact Hypersurfaces of a Bochner-Kaehler Manifold

We have studied contact metric hypersurfaces of a Bochner-Kaehler manifold and obtained the following two results: (1) A contact metric constant mean curvature (C M C) hypersurface of a Bochner-Kaehler manifold is a (k, µ)-contact manifold, and (2) If M is a compact contact metric C M C hypersurface of a Bochner-Kaehler manifold with a conformal vector field V that is neither tangential nor normal anywhere, then it is totally umbilical and Sasakian, and under certain conditions on V , is isometric to a unit sphere

Double-phase transition and giant positive magnetoresistance in the quasi-skutterudite Gd3_3Ir4_4Sn13_{13}

The magnetic, thermodynamic and electrical/thermal transport properties of the caged-structure quasi-skutterudite Gd$_3$Ir$_4$Sn$_{13}$ are re-investigated. The magnetization $M(T)$, specific heat $C_p(T)$ and the resistivity $\rho(T)$ reveal a double-phase transition -- at $T_{N1}\sim$ 10~K and at $T_{N2}\sim$ 8.8~K -- which was not observed in the previous report on this compound. The antiferromagnetic transition is also visible in the thermal transport data, thereby suggesting a close connection between the electronic and lattice degrees of freedom in this Sn-based quasi-skutterudite. The temperature dependence of $\rho(T)$ is analyzed in terms of a power-law for resistivity pertinent to Fermi liquid picture. Giant, positive magnetoresistance (MR) $\approx$ 80$\%$ is observed in Gd$_3$Ir$_4$Sn$_{13}$ at 2~K with the application of 9~T. The giant MR and the double magnetic transition can be attributed to the quasi-cages and layered antiferromagnetic structure of Gd$_3$Ir$_4$Sn$_{13}$ vulnerable to structural distortions and/or dipolar or spin-reorientation effects. The giant value of MR observed in this class of 3:4:13 type alloys, especially in a Gd-compound, is the highlight of this work.Comment: 20 pages single column, 7 figures, 1 table; Accepted to J. Appl. Phys., 201

Recent progress in piezotronic sensors based on one-dimensional zinc oxide nanostructures and its regularly ordered arrays: from design to application

Piezotronic sensors and self-powered gadgets are highly sought-after for flexible, wearable, and intelligent electronics for their applications in cutting-edge healthcare and human-machine interfaces. With the advantages of a well-known piezoelectric effect, excellent mechanical properties, and emerging nanotechnology applications, one-dimensional (1D) ZnO nanostructures organized in the form of a regular array have been regarded as one of the most promising inorganic active materials for piezotronics. This report intends to review the recent developments of 1D ZnO nanostructure arrays for multifunctional piezotronic sensors. Prior to discussing rational design and fabrication approaches for piezotronic devices in precisely controlled dimensions, well-established synthesis methods for high-quality and well-controlled 1D ZnO nanostructures are addressed. The challenges associated with the well-aligned, site-specific synthesis of 1D ZnO nanostructures, development trends of piezotronic devices, advantages of an ordered array of 1D ZnO in device performances, exploring new sensing mechanisms, incorporating new functionalities by constructing heterostructures, the development of novel flexible device integration technology, the deployment of novel synergistic strategies in piezotronic device performances, and potential multifunctional applications are covered. A brief evaluation of the end products, such as small-scale miniaturized unconventional power sources in sensors, high-resolution image sensors, and personalized healthcare medical devices, is also included. The paper is summarized towards the conclusion by outlining the present difficulties and promising future directions. This study will provide guidance for future research directions in 1D ZnO nanostructure-based piezotronics, which will hasten the development of multifunctional devices, sensors, chips for human-machine interfaces, displays, and self-powered systems

Enhancing Visual Domain Adaptation with Source Preparation

Robotic Perception in diverse domains such as low-light scenarios, where new modalities like thermal imaging and specialized night-vision sensors are increasingly employed, remains a challenge. Largely, this is due to the limited availability of labeled data. Existing Domain Adaptation (DA) techniques, while promising to leverage labels from existing well-lit RGB images, fail to consider the characteristics of the source domain itself. We holistically account for this factor by proposing Source Preparation (SP), a method to mitigate source domain biases. Our Almost Unsupervised Domain Adaptation (AUDA) framework, a label-efficient semi-supervised approach for robotic scenarios -- employs Source Preparation (SP), Unsupervised Domain Adaptation (UDA) and Supervised Alignment (SA) from limited labeled data. We introduce CityIntensified, a novel dataset comprising temporally aligned image pairs captured from a high-sensitivity camera and an intensifier camera for semantic segmentation and object detection in low-light settings. We demonstrate the effectiveness of our method in semantic segmentation, with experiments showing that SP enhances UDA across a range of visual domains, with improvements up to 40.64% in mIoU over baseline, while making target models more robust to real-world shifts within the target domain. We show that AUDA is a label-efficient framework for effective DA, significantly improving target domain performance with only tens of labeled samples from the target domain

Spatio-temporal models of infectious disease with high rates of asymptomatic transmission

The surprisingly mercurial Covid-19 pandemic has highlighted the need to not only accelerate research on infectious disease, but to also study them using novel techniques and perspectives. A major contributor to the dificulty of containing the current pandemic is due to the highly asymptomatic nature of the disease. In this investigation, we develop a modeling framework to study the spatio-temporal evolution of diseases with high rates of asymptomatic transmission, and we apply this framework to a hypothetical country with mathematically tractable geography; namely, square counties uniformly organized into a rectangle. We first derive a model for the temporal dynamics of susceptible, infected, and recovered populations, which is applied at the county level. Next we use likelihood-based parameter estimation to derive temporally varying disease transmission parameters on the state-wide level. While these two methods give us some spatial structure and show the effects of behavioral and policy changes, they miss the evolution of hot zones that have caused significant difficulties in resource allocation during the current pandemic. It is evident that the distribution of cases will not be stagnantly based on the population density, as with many other diseases, but will continuously evolve. We model this as a diffusive process where the diffusivity is spatially varying based on the population distribution, and temporally varying based on the current number of simulated asymptomatic cases. With this final addition coupled to the SIR model with temporally varying transmission parameters, we capture the evolution of \hot zones in our hypothetical setup