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In the projective space $\mathrm{PG}(3,q)$, we consider the orbits of lines under the stabilizer group of the twisted cubic. In the literature, lines of $\mathrm{PG}(3,q)$ are partitioned into classes, each of which is a union of line orbits. In this paper, all classes of lines consisting of a unique orbit are found. For the remaining line types, with one exception, it is proved that they consist exactly of two or three orbits; sizes and structures of these orbits are determined. Also, the subgroups of the stabilizer group of the twisted cubic fixing lines of the orbits are obtained. Problems which remain open for one type of lines are formulated and, for $5\le q\le37$ and $q=64$, a solution is provided., Comment: 6 pages, 21 references. arXiv admin note: text overlap with arXiv:2103.11248

The growth of transition metal dichalcogenide (TMDC) alloys provides an opportunity to experimentally access information elucidating how optical properties change with gradual substitutions in the lattice compared with their pure compositions. In this work, we performed growths of alloyed crystals with stoichiometric compositions between pure forms of NbSe2 and WSe2, followed by an optical analysis of those alloys by utilizing Raman spectroscopy and spectroscopic ellipsometry.

During the DESY summer student program 2021, young scientists from more than 13 different countries worked together, connecting from remote, to provide computer codes within the Rivet framework for 19 HERA measurements. Most of these measurements were originally available within the HZTool package, but no longer accessible for modern analysis packages such as Rivet. The temporary RivetHZTool interface was used to validate most of the new Rivet plugins., Comment: Part of the DESY summerstudent program 2021 (DESYsummer2021)

The azimuthal correlation, $\Delta \phi_{12}$, of high transverse momentum jets in pp collisions at $\sqrt{s}=13$ TeV is studied by applying PB-TMD distributions to NLO calculations via MCatNLO together with the PB-TMD parton shower. A very good description of the cross section as a function of $\Delta \phi_{12}$ is observed. In the back-to-back region of $\Delta \phi_{12} \to \pi$, a very good agreement is observed with the PB-TMD Set 2 distributions while significant deviations are obtained with the PB-TMD Set 1 distributions. Set 1 uses the evolution scale while Set 2 uses transverse momentum as an argument in $\alpha_s$, and the above observation therefore confirms the importance of an appropriate soft-gluon coupling in angular ordered parton evolution. The total uncertainties of the predictions are dominated by the scale uncertainties of the matrix element, while the uncertainties coming from the PB-TMDs and the corresponding PB-TMD shower are very small. The $\Delta \phi_{12}$ measurements are also compared with predictions using MCatNLO together PYTHIA8, illustrating the importance of details of the parton shower evolution., Comment: 15 pages, 8 Figures

Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive performance and reduced memory consumption. However, they can remain brittle with respect to input adversarial perturbations. This paper proposes a theoretical and computational framework for robustness verification of implicit neural networks; our framework blends together mixed monotone systems theory and contraction theory. First, given an implicit neural network, we introduce a related embedded network and show that, given an $\ell_\infty$-norm box constraint on the input, the embedded network provides an $\ell_\infty$-norm box overapproximation for the output of the given network. Second, using $\ell_{\infty}$-matrix measures, we propose sufficient conditions for well-posedness of both the original and embedded system and design an iterative algorithm to compute the $\ell_{\infty}$-norm box robustness margins for reachability and classification problems. Third, of independent value, we propose a novel relative classifier variable that leads to tighter bounds on the certified adversarial robustness in classification problems. Finally, we perform numerical simulations on a Non-Euclidean Monotone Operator Network (NEMON) trained on the MNIST dataset. In these simulations, we compare the accuracy and run time of our mixed monotone contractive approach with the existing robustness verification approaches in the literature for estimating the certified adversarial robustness.

The Skinned Multi-Person Linear (SMPL) model can represent a human body by mapping pose and shape parameters to body meshes. This has been shown to facilitate inferring 3D human pose and shape from images via different learning models. However, not all pose and shape parameter values yield physically-plausible or even realistic body meshes. In other words, SMPL is under-constrained and may thus lead to invalid results when used to reconstruct humans from images, either by directly optimizing its parameters, or by learning a mapping from the image to these parameters. In this paper, we therefore learn a prior that restricts the SMPL parameters to values that produce realistic poses via adversarial training. We show that our learned prior covers the diversity of the real-data distribution, facilitates optimization for 3D reconstruction from 2D keypoints, and yields better pose estimates when used for regression from images. We found that the prior based on spherical distribution gets the best results. Furthermore, in all these tasks, it outperforms the state-of-the-art VAE-based approach to constraining the SMPL parameters.

The fast luminescence component of barium fluoride (BaF$_2$) crystals with a subnanosecond decay time can find wide application in particle physics and nuclear physics. However, the slow luminescence component with the 630~ns decay time could cause pile-up signals at a high rate environment. Doping of BaF$_2$ crystals with rare earth elements suppresses the slow emission component, but at the same time the radiation hardness of the crystals deteriorates. This work presents the results of studying crystal samples, both pure BaF$_2$ and those doped with yttrium in a proportion of 1at.\%Y, 3at.\%Y and 5at.\%Y, irradiated with a fast neutron fluence of about 2.3$\times$10$^{14}$~n/cm$^2$. Their light output and decay kinetics were measured before and after irradiation. It is found that the light output loss of a pure BaF$_2$ crystal after irradiation is about 7\%, and the light output loss of yttrium doped samples after irradiation is about two times higher. The measurement results demonstrate that after irradiation the fast component of each sample has a relative light output loss 2-3\% larger than the slow one.

Given the importance of incorporating various superconducting materials to device fabrication or substrate development, studying the interface for possible interactions is warranted. In this work, NbN films sputter-deposited on 4H-SiC were heat-treated at 1400 C and 1870 C and were examined with transmission electron microscopy to assess whether the interfacial interactions undergo temperature-dependent behavior. We report the diffusion of NbN into the SiC substrate and the formation of NbN nanocrystallites therein during the 1400 C treatment. After the 1870 C treatment, tiered porosity and the formation of voids are observed, likely due to catalytic reactions between the two materials and accelerated by the stresses induced by the differences in the materials' coefficients of thermal expansion. Lastly, Raman spectroscopy is employed to gain an understanding of the interface lattices' optical responses.

Low power consumption in both static and dynamic modes of operation is a key requirement in modern, highly scaled nanoelectronics. Tunneling field-effect transistors (TFETs) that exploit direct band-to-band tunneling of charges and exhibit steep sub-threshold slope (SS) transfer characteristics are an attractive option in this regard. However, current generation of Si and III-V heterojunction based TFETs while suffer from low ON current density and ON/OFF current ratios for < 60 mV/dec operation. Semiconducting two-dimensional (2D) layers have recently renewed enthusiasm in novel device design for TFETs not only because of their atomically-thin bodies that favor superior electrostatic control but the same feature also favors higher ON current density and consequently high ON/OFF ratio. Here, we demonstrate gate-tunable heterojunction diodes (triodes) fabricated from InSe/Si 2D/3D van der Waals heterostructures, with a minimum subthreshold swing (SS) as low as 6.4 mV/dec and an SS average of 30 mV/dec over 4 decades of current. Further, the devices show a large current on/off ratio of approximately 10^6 and on-state current density of 0.3 uA/um at a drain bias of -1V. Our work opens new avenues for 2D semiconductors for 3D hetero-integration with Si to achieve ultra-low power logic devices., Comment: 5 figures and supporting information

Layered materials enable the assembly of a new class of heterostructures where lattice-matching is no longer a requirement. Interfaces in these heterostructures therefore become a fertile ground for unexplored physics as dissimilar phenomena can be coupled via proximity effects. In this article we identify an unexpected photoluminescence (PL) peak when MoSe$_2$ interacts with TiSe$_2$. A series of temperature-dependent and spatially-resolved PL measurements reveal this peak is unique to the TiSe$_2$-MoSe$_2$ interface, higher in energy compared to the neutral exciton, and exhibits exciton-like characteristics. The feature disappears at the TiSe$_2$ charge density wave transition, suggesting that the density wave plays an important role in the formation of this new exciton. We present several plausible scenarios regarding the origin of this peak that individually capture some aspects of our observations, but cannot fully explain this feature. These results therefore represent a fresh challenge for the theoretical community and provide a fascinating way to engineer excitons through interactions with charge density waves.

Critical questions in dynamical neuroscience and machine learning are related to the study of continuous-time neural networks and their stability, robustness, and computational efficiency. These properties can be simultaneously established via a contraction analysis. This paper develops a comprehensive non-Euclidean contraction theory for continuous-time neural networks. Specifically, we provide novel sufficient conditions for the contractivity of general classes of continuous-time neural networks including Hopfield, firing rate, Persidskii, Lur'e, and other neural networks with respect to the non-Euclidean $\ell_1/\ell_\infty$ norms. These sufficient conditions are based upon linear programming or, in some special cases, establishing the Hurwitzness of a particular Metzler matrix. To prove these sufficient conditions, we develop novel results on non-Euclidean logarithmic norms and a novel necessary and sufficient condition for contractivity of systems with locally Lipschitz dynamics. For each model, we apply our theoretical results to compute the optimal contraction rate and corresponding weighted non-Euclidean norm with respect to which the neural network is contracting.

The design of fixed point algorithms is at the heart of monotone operator theory, convex analysis, and of many modern optimization problems arising in machine learning and control. This tutorial reviews recent advances in understanding the relationship between Demidovich conditions, one-sided Lipschitz conditions, and contractivity theorems. We review the standard contraction theory on Euclidean spaces as well as little-known results for Riemannian manifolds. Special emphasis is placed on the setting of non-Euclidean norms and the recently introduced weak pairings for the $\ell_1$ and $\ell_\infty$ norms. We highlight recent results on explicit and implicit fixed point schemes for non-Euclidean contracting systems., Comment: Paper in the invited tutorial session "Contraction Theory for Machine Learning" at 60th IEEE Conference on Decision and Control, 2021

The exotic properties of two-dimensional (2D) materials and 2D heterostructures, built by forming heterogeneous multi-layered stacks, have been widely explored across a number of subject matters following the goal to invent, design, and improve applications enabled by 2D materials. To successfully harvest these unique properties effectively and increase the yield of manufacturing 2D material-based devices for achieving reliable and repeatable results is the current challenge. The scientific community has introduced various experimental transfer systems explained in detail for exfoliated 2D materials, however, the field lacks statistical analysis and the capability of producing a transfer technique enabling; i) high transfer precision and yield, ii) cross-contamination free transfer, iii) multi-substrate transfer, and iv) rapid prototyping without wet chemistry. Here we introduce a novel 2D material deterministic transfer system and experimentally show its high accuracy, reliability, repeatability, and non-contaminating transfer features by demonstrating fabrication of 2D material-based optoelectronic devices featuring novel device physics and unique functionality. Such rapid and material-near prototyping capability can accelerate not only layered material science in discovery but also engineering innovations.

The length function $\ell_q(r,R)$ is the smallest length of a $ q $-ary linear code with codimension (redundancy) $r$ and covering radius $R$. In this work, new upper bounds on $\ell_q(tR+1,R)$ are obtained in the following forms: \begin{equation*} \begin{split} &(a)~\ell_q(r,R)\le cq^{(r-R)/R}\cdot\sqrt[R]{\ln q},~ R\ge3,~r=tR+1,~t\ge1, &\phantom{(a)~} q\text{ is an arbitrary prime power},~c\text{ is independent of }q. \end{split} \end{equation*} \begin{equation*} \begin{split} &(b)~\ell_q(r,R)< 3.43Rq^{(r-R)/R}\cdot\sqrt[R]{\ln q},~ R\ge3,~r=tR+1,~t\ge1, &\phantom{(b)~} q\text{ is an arbitrary prime power},~q\text{ is large enough}. \end{split} \end{equation*} In the literature, for $q=(q')^R$ with $q'$ a prime power, smaller upper bounds are known; however, when $q$ is an arbitrary prime power, the bounds of this paper are better than the known ones. For $t=1$, we use a one-to-one correspondence between $[n,n-(R+1)]_qR$ codes and $(R-1)$-saturating $n$-sets in the projective space $\mathrm{PG}(R,q)$. A new construction of such saturating sets providing sets of small size is proposed. Then the $[n,n-(R+1)]_qR$ codes, obtained by geometrical methods, are taken as the starting ones in the lift-constructions (so-called "$q^m$-concatenating constructions") for covering codes to obtain infinite families of codes with growing codimension $r=tR+1$, $t\ge1$., Comment: 31 pages, 55 references, 1 figure; the text is edited, the results are slightly improved, 3 new references are added, title is changed

Photodetectors converting light signals into detectable photocurrents are ubiquitously in use today. To improve the compactness and performance of next-generation devices and systems, low dimensional materials provide rich physics to engineering the light matter interaction. Photodetectors based on two dimensional (2D) material van der Waals heterostructures have shown high responsivity and compact integration capability, mainly in the visible range due to their intrinsic bandgap. The spectral region of near-infrared (NIR) is technologically important featuring many data communication and sensing applications. While some initial NIR 2D material-based detectors have emerged, demonstrating doping junction based 2D material photodetectors with the capability to harness the charge separation photovoltaic effect are yet outstanding. Here, we demonstrate a 2D p-n van der Waals heterojunction photodetector constructed by vertically stacking p type and n type few layer indium selenide (InSe) 2D flakes. This heterojunction charge separation based photodetector shows a three fold enhancement in responsivity at near infrared spectral region (980 nm) as compared to a photoconductor detector based on p or n only doped regions, respectively. We show, that this junction device exhibits self-powered photodetection operation and hence enables few pA-low dark currents, which is about 4 orders of magnitude more efficient than state of the art foundry based devices., Comment: 12 pages, 5 figures