ShantanuT01/DACTYL-Pretraining huggingface dataset:
We explore the spin and charge properties of electrons in wurtzite semiconductor nanowires where radial and axial confinement leads to tubular or ring-shaped quantum structures. Accounting for spin-orbit interaction induced by the wurtzite lattice as well as a radial potential gradient, we analytically derive the corresponding low-dimensional Hamiltonians. It is demonstrated that the resulting tubular spin-orbit Hamiltonian allows to construct spin states that are persistent in time and robust against disorder. We find that these special scenarios are characterized by distinctive features in the optical conductivity spectrum, which enable an unambiguous experimental verification. In both types of quantum structures, we discuss the dependence of the occurring persistent charge and spin currents on an axial magnetic field and Fermi energy which show clear fingerprints of the electronic subband structure. Here, the spin-preserving symmetries become manifest in the vanishing of certain spin current tensor components. Our analytic description relates the distinctive features of the optical conductivity and persistent currents to bandstructure characteristics which allows to deduce spin-orbit coefficients and other band parameters from measurements.
A seminal result due to Wall states that if $x$ is normal to a given base $b$ then so is $rx+s$ for any rational numbers $r,s$ with $r\neq 0$. We show that a stronger result is true for normality with respect to the continued fraction expansion. In particular, suppose $a,b,c,d\in \mathbb{Z}$ with $ad-bc\neq 0$. Then if $x$ is continued fraction normal, so is $(ax+b)/(cx+d)$.
We prove that the cohomology jump loci in the space of rank one local systems over a smooth quasi-projective variety are finite unions of torsion translates of subtori. The main ingredients are a recent result of Dimca-Papadima, some techniques introduced by Simpson, together with properties of the moduli space of logarithmic connections constructed by Nitsure and Simpson.
The present paper is dedicated to the global well-posedness for the 3D inhomogeneous incompressible Navier-Stokes equations, in critical Besov spaces without smallness assumption on the variation of the density. We aim at extending the work by Abidi, Gui and Zhang (Arch. Ration. Mech. Anal. 204 (1):189--230, 2012, and J. Math. Pures Appl. 100 (1):166--203, 2013) to a more lower regularity index about the initial velocity. The key to that improvement is a new a priori estimate for an elliptic equation with nonconstant coefficients in Besov spaces which have the same degree as $L^2$ in $\mathbb{R}^3$. Finally, we also generalize our well-posedness result to the inhomogeneous incompressible MHD equations.
We report X-ray observations of two galaxy clusters Abell 1555 and Abell 1558 with Suzaku, which are included in a large scale filamentary structure and a supercluster, to search for non-thermal emission driven by shocks produced in structure formation. These two clusters are detected by Suzaku/XIS for the first time in the X-ray band of 0.5-7 keV. No significant flux is detected by HXD in the energy band of 13-40 keV, and upper limits are reported. From the analysis of the XIS data, we find that the spectrum of A1555 is fit by a thermal plus power-law model, significantly better than a single-temperature pure thermal spectrum. If this power-law component is due to inverse-Compton scattering, the fraction of total baryon energy imparted to non-thermal electrons is consistent with the typical value inferred from the observation of other clusters. However, other scenarios (e.g., under lying AGNs, multi-temperature thermal models) cannot be excluded and further investigation of this system is desired. Basic physical properties of A1555 (e.g., total mass) are also reported.
Atomic and electronic structures of phosphorene nanoribbons are studied within density functional theory. These novel materials present different physical phenomena expected in two very different physical systems: one dimensional metallic chains and semiconductor surfaces. While `rugged' nanoribbons are semiconducting in their layer-terminnated structures, pure `linear' and `zigzag' nanoribbons are metallic due to metallic edge states. Linear nanoribbons undergo edge reconstruction and zigzag nanoribbons beyond a certain width undergo Peierls transition leading to opening of a band gap in the electronic structure and lowering of total energy. Mixed nanoribbons with linear and zigzag edges on the two sides turn out to be a curious case that display both edge reconstruction and Peierls transition simultaneously. Most phosphoeren nanoribbons turn out to be semiconductors having important implications for their application.
The goal of metric learning is to learn a function that maps samples to a lower-dimensional space where similar samples lie closer than dissimilar ones. Particularly, deep metric learning utilizes neural networks to learn such a mapping. Most approaches rely on losses that only take the relations between pairs or triplets of samples into account, which either belong to the same class or two different classes. However, these methods do not explore the embedding space in its entirety. To this end, we propose an approach based on message passing networks that takes all the relations in a mini-batch into account. We refine embedding vectors by exchanging messages among all samples in a given batch allowing the training process to be aware of its overall structure. Since not all samples are equally important to predict a decision boundary, we use an attention mechanism during message passing to allow samples to weigh the importance of each neighbor accordingly. We achieve state-of-the-art results on clustering and image retrieval on the CUB-200-2011, Cars196, Stanford Online Products, and In-Shop Clothes datasets. To facilitate further research, we make available the code and the models at https://github.com/dvl-tum/intra_batch_connections.
1 identify a correspondence between the various spherical harmonic modes of massless 11 dimensional fields propagating on the $AdS_{4/7}$ in an $AdS_{4/7} \times S^{7\4}$ compactification of M theory, and the corresponding operators, primary under the conformal group, on the world volume of $M_2,M_5$ branes. This is achieved by matching representations of the superconformal algebra on the two sides of the correspondence.
BiVO3F is a promising material used in solar energy conversion systems. Here, we first report the calculated structural, electronic, and surface reaction properties using PBE and hybrid density functionals. We found it is a direct band gap semiconductor, and the calculated band gap is consistent with experimental value only using the hybrid density functional with a fraction of Hartree Fock (HF) exchange {\alpha}=0.1. The (001) surface is the most stable surface among all the low index (001), (010), and (100) surfaces. There are V and Bi sites exposed on (001) surface which can serves as activity sites. That is quite different from BiVO4 where only Bi sties can be taken as surface reaction sites. The OER intermediates OH* and OOH* prefer to form a bridge structure on both V and Bi sites. This makes the first proton removal step is very easy, but the O-O bond is difficult to form which leads the overpotential of OER is very high. Our work plays a guide principle to design the high efficiency photocatalysis and photoanodes based on BiVO3F.
We studied the structural, magnetic and transport properties of LaAlO3/EuTiO3/SrTiO3 heterostructures grown by Pulsed Laser Deposition. The samples have been characterized in-situ by electron diffraction and scanning probe mi-croscopy and ex-situ by transport measurements and x-ray absorption spectroscopy. LaAlO3/EuTiO3/SrTiO3 films show a ferromagnetic transition at T<7.5 K, related to the ordering of Eu2+ spins, even in samples characterized by just two EuTiO3 unit cells. A finite metallic conductivity is observed only in the case of samples composed by one or two EuTiO3 unit cells and, simultaneously, by a LaAlO3 thickness equal or above 4 unit cells. The role of ferromagnetic EuTiO3 on the transport properties of delta-doped LaAlO3/EuTiO3/SrTiO3 is critically discussed.
Learning to rank has recently emerged as an attractive technique to train deep convolutional neural networks for various computer vision tasks. Pairwise ranking, in particular, has been successful in multi-label image classification, achieving state-of-the-art results on various benchmarks. However, most existing approaches use the hinge loss to train their models, which is non-smooth and thus is difficult to optimize especially with deep networks. Furthermore, they employ simple heuristics, such as top-k or thresholding, to determine which labels to include in the output from a ranked list of labels, which limits their use in the real-world setting. In this work, we propose two techniques to improve pairwise ranking based multi-label image classification: (1) we propose a novel loss function for pairwise ranking, which is smooth everywhere and thus is easier to optimize; and (2) we incorporate a label decision module into the model, estimating the optimal confidence thresholds for each visual concept. We provide theoretical analyses of our loss function in the Bayes consistency and risk minimization framework, and show its benefit over existing pairwise ranking formulations. We demonstrate the effectiveness of our approach on three large-scale datasets, VOC2007, NUS-WIDE and MS-COCO, achieving the best reported results in the literature.
We give a method for constructing Kummer covers with many points over finite fields.
The Cauchy problem is considered for the scalar wave equation in the Schwarzschild geometry. Using an integral spectral representation we derive the exact decay rate for solutions of the Cauchy problem with spherical symmetric initial data, which is smooth and compactly supported outside the event horizon.
The width of the broad emission lines in quasars is commonly characterized either by the full-width-at-half-maximum (FWHM) or the square root of the second moment of the line profile ($\sigma_{\rm line}$), and used as an indicator of the virial velocity of the broad-line region (BLR) in the estimation of black hole (BH) mass. We measure FWHM and $\sigma_{\rm line}$ for H$\alpha$, H$\beta$ and Mg II broad lines in both the mean and root-mean-square (rms) spectra of a large sample of quasars from the Sloan Digital Sky Survey Reverberation Mapping (SDSS-RM) project. We introduce a new quantitative recipe to measure $\sigma_{\rm line}$ that is reproducible, less susceptible to noise and blending in the wings, and scales with the intrinsic width of the line. We compare the four definitions of line width (FWHM and $\sigma_{\rm line}$ in mean and rms spectra, respectively) for each of the three broad lines and among different lines. There are strong correlations among different width definitions for each line, providing justification for using the line width measured in single-epoch spectroscopy as a virial velocity indicator. There are also strong correlations among different lines, suggesting alternative lines to H$\beta$ can be used to estimate virial BH masses. We further investigate the correlations between virial BH masses using different line width definitions and the stellar velocity dispersion of the host galaxies, and the dependence of line shape (characterized by the ratio FWHM/$\sigma_{\rm line}$) on physical properties of the quasar. Our results provide further evidence that FWHM is more sensitive to the orientation of a flattened BLR geometry than $\sigma_{\rm line}$, but the overall comparison between the virial BH mass and host stellar velocity dispersion does not provide conclusive evidence that one particular width definition is significantly better than the others.
The present Cosmic Microwave Background (CMB) temperature and polarization anisotropy data is consistent with not only a power law scalar primordial power spectrum (PPS) with a small running but also with the scalar PPS having very sharp features. This has motivated inflationary models with such sharp features. Recently, even the possibility of having nulls in the power spectrum (at certain scales) has been considered. The existence of these nulls has been shown in linear perturbation theory. What shall be the effect of higher order corrections on such nulls? Inspired by this question, we attempt to calculate quantum radiative corrections to the Fourier transform of the two-point function in a toy field theory and address the issue of how these corrections to the power spectrum behave in models in which the tree-level power spectrum has a sharp dip (but not a null). In particular, we consider the possibility of the relative enhancement of radiative corrections in a model in which the tree-level spectrum goes through a dip in power at a certain scale. The mode functions of the field (whose power spectrum is to be evaluated) are chosen such that they undergo the kind of dynamics that leads to a sharp dip in the tree level power spectrum. Next we consider the situation in which this field has quartic self interactions and find one loop correction in a suitably chosen renormalization scheme. We thus attempt to answer the following key question in the context of this toy model (which is as important in the realistic case): in the chosen renormalization scheme, can quantum radiative corrections get enhanced relative to tree-level power spectrum at scales at which sharp dips appear in the tree-level spectrum?
Semantic segmentation of eyes has long been a vital pre-processing step in many biometric applications. Majority of the works focus only on high resolution eye images, while little has been done to segment the eyes from low quality images in the wild. However, this is a particularly interesting and meaningful topic, as eyes play a crucial role in conveying the emotional state and mental well-being of a person. In this work, we take two steps toward solving this problem: (1) We collect and annotate a challenging eye segmentation dataset containing 8882 eye patches from 4461 facial images of different resolutions, illumination conditions and head poses; (2) We develop a novel eye segmentation method, Shape Constrained Network (SCN), that incorporates shape prior into the segmentation network training procedure. Specifically, we learn the shape prior from our dataset using VAE-GAN, and leverage the pre-trained encoder and discriminator to regularise the training of SegNet. To improve the accuracy and quality of predicted masks, we replace the loss of SegNet with three new losses: Intersection-over-Union (IoU) loss, shape discriminator loss and shape embedding loss. Extensive experiments shows that our method outperforms state-of-the-art segmentation and landmark detection methods in terms of mean IoU (mIoU) accuracy and the quality of segmentation masks. The eye segmentation database is available at https://www.dropbox.com/s/yvveouvxsvti08x/Eye_Segmentation_Database.zip?dl=0.
We have detected the CO(6-5), CO(7-6), and [CI] 370 micron lines from the nuclear region of NGC 891 with our submillimeter grating spectrometer ZEUS on the CSO. These lines provide constraints on photodissociation region (PDR) and shock models that have been invoked to explain the H_2 S(0), S(1), and S(2) lines observed with Spitzer. We analyze our data together with the H_2 lines, CO(3-2), and IR continuum from the literature using a combined PDR/shock model. We find that the mid-J CO originates almost entirely from shock-excited warm molecular gas; contributions from PDRs are negligible. Also, almost all the H_2 S(2) and half of the S(1) line is predicted to emerge from shocks. Shocks with a pre-shock density of 2x10^4 cm^-3 and velocities of 10 km/s and 20 km/s for C-shocks and J-shocks, respectively, provide the best fit. In contrast, the [CI] line emission arises exclusively from the PDR component, which is best parameterized by a density of 3.2x10^3 cm^-3 and a FUV field of G_o = 100 for both PDR/shock-type combinations. Our mid-J CO observations show that turbulence is a very important heating source in molecular clouds, even in normal quiescent galaxies. The most likely energy sources for the shocks are supernovae or outflows from YSOs. The energetics of these shock sources favor C-shock excitation of the lines.
This paper studies the behaviour of the empirical eigenvalue distribution of large random matrices W_N W_N* where W_N is a ML x N matrix, whose M block lines of dimensions L x N are mutually independent Hankel matrices constructed from complex Gaussian correlated stationary random sequences. In the asymptotic regime where M \rightarrow \infty, N \rightarrow +\infty and ML/N \rightarrow c > 0, it is shown using the Stieltjes transform approach that the empirical eigenvalue distribution of W_N W_N* has a deterministic behaviour which is characterized.
The Pariser-Parr-Pople model of pi-conjugated electrons is solved by the density matrix renormalization group method for the light emitting polymer, poly(para-phenylene vinylene). The energies of the primary excited states are calculated. When solid state screening is incorporated into the model parameters there is excellent agreement between theory and experiment, enabling an identification of the origin of the key spectroscopic features.
We show the existence of Fano resonances in the context of near-field radiative heat transfer, which enable the strong suppression and enhancement of the spectral heat flux at specific wavelengths. This is demonstrated by making use of the plasmon-phonon coupling in a symmetric nano cavity composed by a polaritonic material coated with a metallic layer, in which each side of the cavity is kept at different temperatures. The strong hybridization of the plasmonic and phononic modes sustained by the multilayer structure is determined by the matching of their polarization. This leads to the opening of a thermal band gap, where heat transfer in the coupled system is inhibited for all wave vectors and for wavelengths at which the individual constituents are thermally transmissive.
The low-lying eigenstates of a system of two electrons confined within a two-dimensional quantum dot with a hard polygonal boundary are obtained by means of exact diagonalization. The transition from a weakly correlated charge distribution for small dots to a strongly correlated "Wigner molecule" for large dots is studied, and the behaviour at the crossover is determined. In sufficiently large dots, a recently proposed mapping to an effective charge-spin model is investigated, and is found to produce the correct ordering of the energy levels and to give a good first approximation to the size of the level spacings. We conclude that this approach is a valuable method to obtain the low energy spectrum of few-electron quantum dots.
We present analytic proofs of the properties of four particle states in the g9/2 shell which have seniority v=4 and angular momentum I=4 or 6.We show in particular that the number of pairs with angular momentum I is equal to one for these states.
Most large galaxies host supermassive black holes in their nuclei and are subject to mergers, which can produce a supermassive black hole binary (SMBHB), and hence periodic signatures due to orbital motion. We report unique periodic radio flux density variations in the blazar PKS~2131$-$021, which strongly suggest an SMBHB with an orbital separation of $\sim 0.001-0.01$ pc. Our 45.1-year radio light curve shows two epochs of strong sinusoidal variation with the same period and phase to within $<2\%$ and $\sim 10\%$, respectively, straddling a 20-year period when this variation was absent. Our simulated light curves accurately reproduce the ``red noise'' of this object, and Lomb-Scargle, weighted wavelet Z-transform, and least-squares sine wave analyses demonstrate conclusively, at the $4.6\sigma$ significance level, that the periodicity in this object is not due to random fluctuations in flux density. The observed period translates to $2.082\pm 0.003$ years in the rest frame at the $z=1.285$ redshift of PKS~2131$-$021. The periodic variation in PKS~2131$-$021 is remarkably sinusoidal. We present a model in which orbital motion, combined with the strong Doppler boosting of the approaching relativistic jet, produces a sine-wave modulation in the flux density which easily fits the observations. Given the rapidly-developing field of gravitational wave experiments with pulsar timing arrays, closer counterparts to PKS~2131$-$021 and searches using the techniques we have developed are strongly motivated. These results constitute a compelling demonstration that the phenomenology, not the theory, must provide the lead in this field.
We propose a kind of Bak-Sneppen dynamics as a general optimization technique to treat magnetic systems. The resulting dynamics shows self-organized criticality with power law scaling of the spatial and temporal correlations. An alternative method of the extremal optimization is also analyzed here. We provided a numerical confirmation that, for any possible value of its free parameter $\tau$, the extremal optimization dynamics exhibits a non-critical behavior with an infinite spatial range and exponential decay of the avalanches. Using the chiral clock model as our test system, we compare the efficiency of the two dynamics with regard to their abilities to find the system's ground state.
In one-loop string effective action, we study a generality of non-singular cosmological solutions found in the isotropic and homogeneous case. We discuss Bianchi I and IX type spacetimes. We find that nonsingular solutions still exist in Bianchi I model around nonsingular flat Friedmann solutions. On the other hand, we cannot find any nonsingular solutions in Bianchi IX model. Non-existence of nonsingular Bianchi IX universe may be consistent with the analysis by Kawai, Sakagami and Soda, i.e. the tensor mode perturbations against nonsingular flat Friedmann universe are unstable, because Bianchi IX model can be regarded as a closed Friedmann universe with a single gravitational wave. So based on these facts, we may conclude the nonsingular universe is found in isotropic case is generally unstable, a singularity avoidance may not work in the present model.
The space of Siegel cuspforms of degree $2$ of weight $3$ with respect to the congruence subgroup $\G_2(2,4,8)$ was studied by van Geemen and van Straten in Math. computation. {\bf 61} (1993). They showed the space is generated by six-tuple products of Igusa $\th$-constants, and all of them are Hecke eigenforms. They gave conjecture on the explicit description of the Andrianov $L$-functions. In J. Number Theory. {\bf 125} (2007), we proved some conjectures by showing that some products are obtained by the Yoshida lift, a construction of Siegel eigenforms. But, other products are not obtained by the Yoshida lift, and our technique did not work. In this paper, we give proof for such products. As a consequence, we determine automorphic representations of O(6), and give Hermitian modular forms of SU(2,2) of weight $4$. Further, we give non-holomorphic differential threeforms on the Siegel threefold with respect to $\G_2(2,4,8)$.