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Me$_{3+\delta}$Ge, being a Weyl semimetal, shows a large anomalous Hall effect (AHE), which decreases slowly with an increase in $\delta$ from 0.1 to 0.4. However, AHE in this compound remains significantly large in the whole range of $\delta$ because of the robust nature of the topology of bands. To explore the possibility of tuning the anomalous transport effects in Weyl semimetals, we have studied the single-crystal hexagonal-(Mn$_{0.78}$Fe$_{0.22}$)$_3$Ge compound. Magnetization of this compound shows two magnetic transitions at 242 K ($T_{\text{N1}}$) and 120 K ($T_{\text{N2}}$). We observed that the AHE persists between $T_{\text{N2}}$ - $T_{\text{N1}}$ and vanishes below $T_{\text{N2}}$. Further, we performed single-crystal neutron diffraction experiments (using spherical neutron polarimetry and unpolarized neutron diffraction) to determine the magnetic structures of (Mn$_{0.78}$Fe$_{0.22}$)$_3$Ge at different temperatures. Our neutron diffraction results show that the sample possesses a collinear antiferromagnetic structure below $T_{\text{N2}}$. However, the magnetic structure of the sample remains noncollinear antiferromagnetic, the same as Mn$_3$Ge, between $T_{\text{N1}}$ to $T_{\text{N2}}$. The presence of AHE, and noncollinear magnetic structure in (Mn$_{0.78}$Fe$_{0.22}$)$_3$Ge, between $T_{\text{N1}}$ and $T_{\text{N2}}$, suggest the existence of Weyl points in this temperature regime. Below $T_{\text{N2}}$, AHE is absent, and the magnetic structure also changes to a collinear antiferromagnetic structure. These observations signify a strong link between the magnetic structure of the sample and AHE., Comment: Accepted in Physical Review B

Complete dissociation dynamics of low energy electron attachment to nitrogen dioxide around 8.5 eV resonance has been studied using a velocity map imaging (VMI) spectrometer. Besides the three prominent resonant peaks at around 1.4 eV, 3.1 eV, and 8.5 eV, we have found an additional small resonance at the higher energy tail of the 8.5 eV resonance. We have collected the momentum distribution data of O$^-$ ions at different incident electron energies around the 8.5 eV resonance along with the smaller additional resonant peak. A theoretical analysis of these resonances with the momentum imaging experimental data on dissociative electron attachment to nitrogen dioxide in the gas phase is used to provide a detailed picture of the molecular dissociation process.

Randomized smoothing (RS) is a well known certified defense against adversarial attacks, which creates a smoothed classifier by predicting the most likely class under random noise perturbations of inputs during inference. While initial work focused on robustness to $\ell_2$ norm perturbations using noise sampled from a Gaussian distribution, subsequent works have shown that different noise distributions can result in robustness to other $\ell_p$ norm bounds as well. In general, a specific noise distribution is optimal for defending against a given $\ell_p$ norm based attack. In this work, we aim to improve the certified adversarial robustness against multiple perturbation bounds simultaneously. Towards this, we firstly present a novel \textit{certification scheme}, that effectively combines the certificates obtained using different noise distributions to obtain optimal results against multiple perturbation bounds. We further propose a novel \textit{training noise distribution} along with a \textit{regularized training scheme} to improve the certification within both $\ell_1$ and $\ell_2$ perturbation norms simultaneously. Contrary to prior works, we compare the certified robustness of different training algorithms across the same natural (clean) accuracy, rather than across fixed noise levels used for training and certification. We also empirically invalidate the argument that training and certifying the classifier with the same amount of noise gives the best results. The proposed approach achieves improvements on the ACR (Average Certified Radius) metric across both $\ell_1$ and $\ell_2$ perturbation bounds.

We present a detailed multi-wavelength study of star formation in the dwarf galaxy NGC 4395 which hosts an active galactic nucleus (AGN). From our observations with the Ultra-Violet Imaging Telescope, we have compiled a catalogue of 284 star forming (SF) regions, out of which we could detect 120 SF regions in H$\alpha$ observations. Across the entire galaxy, we found the extinction corrected star formation rate (SFR) in the far ultra-violet (FUV) to range from 2.0 $\times$ 10$^{-5}$ M$_\odot$yr$^{-1}$ to 1.5 $\times$ 10$^{-2}$ M$_\odot$yr$^{-1}$ with a median of 3.0 $\times$ 10$^{-4}$ M$_\odot$yr$^{-1}$ and age to lie in the range of $\sim$ 1 to 98 Myr with a median of 14 Myr. In H$\alpha$ we found the SFR to range from 7.2 $\times$ 10$^{-6}$ M$_\odot$yr$^{-1}$ to 2.7 $\times$ 10$^{-2}$ M$_\odot$yr$^{-1}$ with a median of 1.7 $\times$ 10$^{-4}$ M$_\odot$yr$^{-1}$ and age to lie between 3 to 6 Myr with a median of 5 Myr. The stellar ages derived from H$\alpha$ show a gradual decline with galactocentric distance. We found three SF regions close to the center of NGC~4395 with high SFR both from H$\alpha$ and UV which could be attributed to feedback effects from the AGN. We also found six other SF regions in one of the spiral arms having higher SFR. These are very close to supernovae remnants which could have enhanced the SFR locally. We obtained a specific SFR (SFR per unit mass) for the whole galaxy 4.64 $\times$ 10$^{-10}$ yr$^{-1}$., Comment: 10 pages, 11 figures, Accepted for publication in ApJ

Human pose estimation (HPE) with convolutional neural networks (CNNs) for indoor monitoring is one of the major challenges in computer vision. In contrast to HPE in perspective views, an indoor monitoring system can consist of an omnidirectional camera with a field of view of 180{\deg} to detect the pose of a person with only one sensor per room. To recognize human pose, the detection of keypoints is an essential upstream step. In our work we propose a new dataset for training and evaluation of CNNs for the task of keypoint detection in omnidirectional images. The training dataset, THEODORE+, consists of 50,000 images and is created by a 3D rendering engine, where humans are randomly walking through an indoor environment. In a dynamically created 3D scene, persons move randomly with simultaneously moving omnidirectional camera to generate synthetic RGB images and 2D and 3D ground truth. For evaluation purposes, the real-world PoseFES dataset with two scenarios and 701 frames with up to eight persons per scene was captured and annotated. We propose four training paradigms to finetune or re-train two top-down models in MMPose and two bottom-up models in CenterNet on THEODORE+. Beside a qualitative evaluation we report quantitative results. Compared to a COCO pretrained baseline, we achieve significant improvements especially for top-view scenes on the PoseFES dataset. Our datasets can be found at https://www.tu-chemnitz.de/etit/dst/forschung/comp_vision/datasets/index.php.en.

In this paper we explore two intertwined issues. First, using primary data we examine the impact of asymmetric networks, built on rich relational information on several spheres of living, on access to workfare employment in rural India. We find that unidirectional relations, as opposed to reciprocal relations, and the concentration of such unidirectional relations increase access to workfare jobs. Further in-depth exploration provides evidence that patron-client relations are responsible for this differential access to such employment for rural households. Complementary to our empirical exercises, we construct and analyse a game-theoretical model supporting our findings.

Let $(G,w)$ be an undirected weighted graph. The group inverse of $(G,w)$ is the weighted graph with the adjacency matrix $A^{\#}$, where $A$ is the adjacency matrix of $(G,w)$. We study the group inverse of singular weighted trees. It is shown that if $(T,w)$ is a singular weighted tree, then $T^{\#}$ is again a tree, if and only if $T$ is a star tree, which in turn, holds if and only if $T^{\#}$ is graph isomorphic to $T$. A new class $\mathbb{T}$ of weighted trees, is introduced and studied here. It is shown that the group inverse of the adjacency matrix of a positively weighted tree in $\mathbb{T}$, is signature similar to a non-negative matrix., Comment: 16 pages, 3 figures