ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study topological phase transitions in one dimensional (1-D) Rashba nanowire under a spatially varying Zeeman field when coupled to an $s$-wave superconductor substrate. We show that this system supports both Majorana bound states (MBS) and fractionally charged bound states (FBS) of Jackiw-Rebbi type. By disassembling Zeeman Hamiltonian into multiple helical components, we find that each helical component is relating to a corresponding topological region, characterized by the emergence of MBS. FBS arises in the overlapping gapped area created by any two helical components with topologically differing configuration, analogous to those formed at the knot in SSH model. We then develop a general criteria for the occurrence conditions of MBS and FBS. Our results suggest that systems with large Rashba spin orbit couple amplitude or in presence of weak Zeeman fields favor MBS, and otherwise FBS are more favorable. In the end, we demonstrate that spin components of zero energy bound states in topological phases are polarized in the plane perpendicular to Rashba vector, and the polarization oscillates with the variance of phases of the Zeeman field.
We determine the Lyapunov spectrum and stable manifolds of some stochastic flows on the Poincar\'e group associated to Dudley's relativistic processes.
Unlike conventional frame-based sensors, event-based visual sensors output information through spikes at a high temporal resolution. By only encoding changes in pixel intensity, they showcase a low-power consuming, low-latency approach to visual information sensing. To use this information for higher sensory tasks like object recognition and tracking, an essential simplification step is the extraction and learning of features. An ideal feature descriptor must be robust to changes involving (i) local transformations and (ii) re-appearances of a local event pattern. To that end, we propose a novel spatiotemporal feature representation learning algorithm based on slow feature analysis (SFA). Using SFA, smoothly changing linear projections are learnt which are robust to local visual transformations. In order to determine if the features can learn to be invariant to various visual transformations, feature point tracking tasks are used for evaluation. Extensive experiments across two datasets demonstrate the adaptability of the spatiotemporal feature learner to translation, scaling and rotational transformations of the feature points. More importantly, we find that the obtained feature representations are able to exploit the high temporal resolution of such event-based cameras in generating better feature tracks.
A decay rate asymmetry of the top quark is discussed within the framework of the supersymmetric standard model. Although new sources of CP violation in this model are severely constrained from the electric dipole moments of the neutron and the electron, there is a possibility that a top squark has a mass of around 100 GeV and CP violation in its interaction with a top quark is unsuppressed. Then partial widths could be different between the decays $t\to bW^+$ and $\bar t\to \bar bW^-$. The magnitude of this CP asymmetry can be of order $10^{-3}$, which may be detectable in the near future.
The understanding of pulsar radio emission demands a close look at all regions of the huge parameter space present for pulsar observations. In this review we concentrate on the space given by the range of observed pulse periods, spanning four orders of magnitude. A comparative study of the emission properties of millisecond pulsars and normal pulsars, both at radio and high energy frequencies, promises to shed light on the still poorly understood emission theory.
Our first very wide survey of the supercritical phase diagram and its key properties reveals a universal interrelation between dynamics and thermodynamics and an unambiguous transition between liquidlike and gaslike states. This is seen in the master plot showing a collapse of the data representing the dependence of specific heat on key dynamical parameters in the system for many different paths on the phase diagram. As a result, the observed transition is path-independent. We call it a "c"-transition due to the "c"-shaped curve parameterizing the dependence of the specific heat on key dynamical parameters. The "c"-transition has a fixed inversion point and provides a new structure to the phase diagram, operating deep in the supercritical state (up to at least 2000 times the critical pressure and 50 times the critical temperature). The data collapse and path independence as well as the existence of a special inversion point on the phase diagram are indicative of either of a sharp crossover or a new phase transition in the deeply supercritical state.
The soldering procedure has been for the first time generalized to the case of spin-3/2 fermionic theories. We have demonstrated that the fermionic part of the so called "New Topologically Massive Supergravity" theory, which is of third order in derivatives, can be soldered in order to obtain a fourth order dublet model analogue to the linearized version of the New Massive Gravity theory, while the soldering of two second order self-dual models give us a theory similar to the linearized version of the Einstein-Hilbert-Fierz-Pauli theory.
The recent observation by CDF collaboration has disclosed a modification in the mass of the $W$ boson. In this regard we show that this modification in the mass of the $W$ boson can be well explained in the background of a 6-dimensional warped geometry model, where the double warping is associated with the two extra spatial dimensions. We consider that all the Standard Model fields are residing in the bulk, where the bulk Higgs field gives rise to the spontaneous symmetry breaking in the 6-dimensional spacetime. Allowing a little hierarchy between the two moduli we exactly obtain the observed mass for the $W$ boson, which is identified as the lowest lying Kaluza-Klein mass mode of the bulk $W$ boson on the $(3+1)$ dimensional visible brane. The essential feature of the 5-dimensional Randall-Sundrum scenario such as the resolution of the gauge hierarchy problem without introducing any intermediate scale between the Planck and the TeV scale, remains intact.
An increasing number of methods for background subtraction use Robust PCA to identify sparse foreground objects. While many algorithms use the L1-norm as a convex relaxation of the ideal sparsifying function, we approach the problem with a smoothed Lp-norm and present pROST, a method for robust online subspace tracking. The algorithm is based on alternating minimization on manifolds. Implemented on a graphics processing unit it achieves realtime performance. Experimental results on a state-of-the-art benchmark for background subtraction on real-world video data indicate that the method succeeds at a broad variety of background subtraction scenarios, and it outperforms competing approaches when video quality is deteriorated by camera jitter.
Lock polynomials and lock Kohnert tableaux are natural analogues to key polynomials and key Kohnert tableaux, respectively. In this paper, we compare lock polynomials to the much-studied key polynomials and show that the difference of a key polynomial and lock polynomial for the same composition is monomial positive. We also examine the conditions for which key and lock polynomials are symmetric or quasisymmetric. We accomplish these goals combinatorially using key Kohnert tableaux and lock Kohnert tableaux. In particular, for the difference of a key minus a lock, we focus on the behavior of crystal operators on Kohnert tableaux. The Type A Demazure crystal can be realized on the vertex set of key Kohnert tableaux, and we show with an explicit combinatorial definition that a similar crystal-like structure exists on the vertex set of lock Kohnert tableaux. Finally, we construct an injective, weight-preserving map from lock Kohnert tableaux to key Kohnert tableaux that intertwines the crystal operators.
Giant stellar clumps are ubiquitous in high-redshift galaxies. They are thought to play an important role in the build-up of galactic bulges and as diagnostics of star formation feedback in galactic discs. Hubble Space Telescope (HST) blank field imaging surveys have estimated that these clumps have masses up to 10$^{9.5}$ M$_{\odot}$ and linear sizes larger than ~1 kpc. Recently, gravitational lensing has also been used to get higher spatial resolution. However, both recent lensed observations and models suggest that the clumps properties may be overestimated by the limited resolution of standard imaging techniques. A definitive proof of this observational bias is nevertheless still missing. Here we investigate directly the effect of resolution on clump properties by analysing multiple gravitationally-lensed images of the same galaxy at different spatial resolutions, down to 30 pc. We show that the typical mass and size of giant clumps, generally observed at $\sim$1 kpc resolution in high-redshift galaxies, are systematically overestimated. The high spatial resolution data, only enabled by strong gravitational lensing using currently available facilities, support smaller scales of clump formation by fragmentation of the galactic gas disk via gravitational instabilities.
In this paper, we consider the initial boundary value problem for the three-dimensional viscous primitive equations of large-scale moist atmosphere which are used to describe the turbulent behavior of long-term weather prediction and climate changes. First, we obtain the existence and uniqueness of global strong solutions of the problem. Second, by studying the long-time behavior of strong solutions, we construct a (weak) universal attractor which captures all the trajectories.
A nonlocal dispersive-optical-model analysis has been carried out for neutrons and protons in $^{208}$Pb. Elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, the charge distribution, and the binding energy have been fitted to extract the neutron and proton self-energies both above and below the Fermi energy. From the single-particle propagator derived from these self-energies, we have determined the charge and matter distributions in $^{208}$Pb. The predicted spectroscopic factors are consistent with results from the $(e,e'p)$ reaction and inelastic-electron-scattering data to very high spin states. Sensible results for the high-momentum content of neutrons and protons are obtained with protons appearing more correlated, in agreement with experiment and \textit{ab initio} calculations of asymmetric matter. A neutron skin of $0.25\pm0.05$ fm is deduced. An analysis of several nuclei leads to the conclusion that finite-size effects play a non-negligible role in the formation of the neutron skin in finite nuclei.
The response of a single InGaAs quantum dot, embedded in a miniaturized charge-tunable device, to an applied GHz bandwidth electrical pulse is investigated via its optical response. Quantum dot response times of 1.0 \pm 0.1 ns are characterized via several different measurement techniques, demonstrating GHz bandwidth electrical control. Furthermore a novel optical detection technique based on resonant electron-hole pair generation in the hybridization region is used to map fully the voltage pulse experienced by the quantum dot, showing in this case a simple exponential rise.
Deep learning methods have proven to outperform traditional computer vision methods in various areas of image processing. However, the application of deep learning in industrial surface defect detection systems is challenging due to the insufficient amount of training data, the expensive data generation process, the small size, and the rare occurrence of surface defects. From literature and a polymer products manufacturing use case, we identify design requirements which reflect the aforementioned challenges. Addressing these, we conceptualize design principles and features informed by deep learning research. Finally, we instantiate and evaluate the gained design knowledge in the form of actionable guidelines and strategies based on an industrial surface defect detection use case. This article, therefore, contributes to academia as well as practice by (1) systematically identifying challenges for the industrial application of deep learning-based surface defect detection, (2) strategies to overcome these, and (3) an experimental case study assessing the strategies' applicability and usefulness.
Asteroseismology, i.e. the study of the internal structures of stars via their global oscillations, is a valuable tool to obtain stellar parameters such as mass, radius, surface gravity and mean density. These parameters can be obtained using certain scaling relations which are based on an asymptotic approximation. Usually the observed oscillation parameters are assumed to follow these scaling relations. Recently, it has been questioned whether this is a valid approach, i.e., whether the order of the observed oscillation modes are high enough to be approximated with an asymptotic theory. In this work we use stellar models to investigate whether the differences between observable oscillation parameters and their asymptotic estimates are indeed significant. We compute the asymptotic values directly from the stellar models and derive the observable values from adiabatic pulsation calculations of the same models. We find that the extent to which the atmosphere is included in the models is a key parameter. Considering a larger extension of the atmosphere beyond the photosphere reduces the difference between the asymptotic and observable values of the large frequency separation. Therefore, we conclude that the currently suggested discrepancies in the scaling relations might have been overestimated. Hence, based on the results presented here we believe that the suggestions of Mosser et al. (2013) should not be followed without careful consideration.
We show that the decomposition of caesium lead halide perovskite nanocrystals under continuous X-ray illumination depends on the surface ligand. For oleic acid/oleylamine, we observe a fast decay accompanied by the formation of elemental lead and halogen. Upon surface functionalization with a metal porphyrin derivate, the decay is markedly slower and involves the disproportionation of lead to Pb0 and Pb3+. In both cases, the decomposition is preceded by a contraction of the atomic lattice, which appears to initiate the decay. We find that the metal porphyrin derivative induces a strong surface dipole on the nanocrystals, which we hold responsible for the altered and slower decomposition pathway. These results are important for application of lead halide perovskite nanocrystals in X-ray scintillators.
Let $\mathcal{F}$ be an antichain of finite subsets of $\mathbb{N}$. How quickly can the quantities $|\mathcal{F}\cap 2^{[n]}|$ grow as $n\to\infty$? We show that for any sequence $(f_n)_{n\ge n_0}$ of positive integers satisfying $\sum_{n=n_0}^\infty f_n/2^n \le 1/4$, $f_{n_0}=1$ and $f_n\le f_{n+1}\le 2f_n$, there exists an infinite antichain $\mathcal{F}$ of finite subsets of $\mathbb{N}$ such that $|\mathcal{F}\cap 2^{[n]}| \geq f_n$ for all $n\ge n_0$. It follows that for any $\varepsilon>0$ there exists an antichain $\mathcal{F}\subseteq 2^\mathbb{N}$ such that $$\liminf_{n \to \infty} |\mathcal{F}\cap 2^{[n]}| \cdot \left(\frac{2^n}{n\log^{1+\varepsilon} n}\right)^{-1} > 0.$$ This resolves a problem of Sudakov, Tomon and Wagner in a strong form, and is essentially tight.
PbCuTe2O6 is a rare example of a spin liquid candidate featuring a three dimensional magnetic lattice. Strong geometric frustration arises from the dominant antiferromagnetic interaction which generates a hyperkagome network of Cu2+ ions although additional interactions enhance the magnetic lattice connectivity. Through a combination of magnetization measurements and local probe investigation by NMR and muSR down to 20 mK, we provide a robust evidence for the absence of magnetic freezing in the ground state. The local spin susceptibility probed by the NMR shift hardly deviates from the macroscopic one down to 1 K pointing to a homogeneous magnetic system with a low defect concentration. The saturation of the NMR shift and the sublinear power law temperature (T) evolution of the 1/T1 NMR relaxation rate at low T point to a non-singlet ground state favoring a gapless fermionic description of the magnetic excitations. Below 1 K a pronounced slowing down of the spin dynamics is witnessed, which may signal a reconstruction of spinon Fermi surface. Nonetheless, the compound remains in a fluctuating spin liquid state down to the lowest temperature of the present investigation.
This note presents a short, transparent proof of the theorem that every Euclidean quadratic form over a normed integral domain is an Aubry-Davenport-Cassels form. The theorem, as formulated in the note, allows besides quadratic terms also linear and constant terms, imposes no restrictions on the characteristic of the integral domain, and makes no unnecessary assumptions about the norm.
We derive a product formula for the multiple stochastic integrals with respect to Levy process. The idea is to use exponential vectors and the polarization technique which greatly simplify the argument.
We discuss a model for non-linear quantum evolution based on the idea of time displaced entanglement, produced by taking one member of an entangled pair on a round trip at relativistic speeds, thus inducing a time-shift between the pair. We show that decoherence of the entangled pair is predicted. For non-maximal entanglement this then implies the ability to induce a non-unitary, non-linear quantum evolution. Although exhibiting unusual characteristics, we show that these evolutions cannot be dismissed on the basis of entropic or causal arguments.
A simple and direct, based on the equations of motion, derivation of the variational principle and effective actions for a spherical charged dust shell in general relativity is offered. This principle is based on the relativistic version of the D{\AE}Alembert principle of virtual displacements and leads to the effective actions for the shell, which describe the shell from the point of view of the exterior or interior stationary observers. Herewith, sides of the shell are considered independently, in the coordinates of the interior or exterior region of the shell. Canonical variables for a charged dust shell are built. It is shown that the conditions of isometry of the sides of the shell lead to the Hamiltonian constraint on these interior and exterior dynamical systems. Special cases of the \^ohollow\"o and \^oscreening\"o shells are briefly considered, as well as a family of the concentric charged dust shells.
In 1986 Harer and Zagier computed a certain matrix integral to determine an influential closed-form formula for the number of (orientable) one-face maps on n vertices colored from N colors. Kerov (1997) provided a proof which computed the same matrix integral differently, which gave an interpretation of these numbers as also counting the number of placements of non-attacking rooks on Young diagrams. Bernardi (2010) provided a bijective proof of this formula by putting one-face maps in bijection with tree-rooted maps, which are orientable maps with a designated spanning tree. In the first part of the paper, we explore the connection between these rook placements and tree-rooted maps by developing a bijection between these objects. Rook placements on Young diagrams have a q-analogue due to Garsia and Remmel (1986). In the second part of the paper, we propose a statistic on rook placements that leads to a conjectured identity which is a q-analogue of part of the Harer-Zagier formula. This identity is also expressed in terms of moments of orthogonal polynomials which are rescaling of q-Hermite polynomials. We then use these moments to give a recurrence for the proposed q-analogue.
The tree-level flavour-changing neutral currents in the two-Higgs-doublet models can be suppressed by protecting the breaking of either flavour or flavour-blind symmetries, but only the first choice, implemented by the application of the Minimal Flavour Violation hypothesis, is stable under quantum corrections. Moreover, a two-Higgs-doublet model with Minimal Flavour Violation enriched with flavour-blind phases can explain the anomalies recently found in the Delta F = 2 transitions, namely the large CP-violating phase in B_s mixing and the tension between epsilon_K and S_\psi_K.
A cyclic $n$-gonal surface is a compact Riemann surface $X$ of genus $g\geq 2$ admitting a cyclic group of conformal automorphisms $C$ of order $n$ such that the quotient space $X/C$ has genus 0. In this paper, we provide an overview of ongoing research into automorphism groups of cyclic $n$-gonal surfaces. Much of the paper is expository or will appear in forthcoming papers, so proofs are usually omitted. Numerous explicit examples are presented illustrating the computational methods currently being used to study these surfaces.
Most stars will experience episodes of substantial mass loss at some point in their lives. For very massive stars, mass loss dominates their evolution, although the mass loss rates are not known exactly, particularly once the star has left the main sequence. Direct observations of the stellar winds of massive stars can give information on the current mass-loss rates, while studies of the ring nebulae and HI shells that surround many Wolf-Rayet (WR) and luminous blue variable (LBV) stars provide information on the previous mass-loss history. The evolution of the most massive stars, (M > 25 solar masses), essentially follows the sequence O star to LBV or red supergiant (RSG) to WR star to supernova. For stars of mass less than 25 solar masses there is no final WR stage. During the main sequence and WR stages, the mass loss takes the form of highly supersonic stellar winds, which blow bubbles in the interstellar and circumstellar medium. In this way, the mechanical luminosity of the stellar wind is converted into kinetic energy of the swept-up ambient material, which is important for the dynamics of the interstellar medium. In this review article, analytic and numerical models are used to describe the hydrodynamics and energetics of wind-blown bubbles. A brief review of observations of bubbles is given, and the degree to which theory is supported by observations is discussed.
This paper addresses saddle-shaped solutions to the semilinear equation $L_K u = f(u)$ in $\mathbb{R}^{2m}$, where $L_K$ is a linear elliptic integro-differential operator with a radially symmetric kernel $K$, and $f$ is of Allen-Cahn type. Saddle-shaped solutions are doubly radial, odd with respect to the Simons cone $\{(x', x'') \in \mathbb{R}^m \times \mathbb{R}^m \, : \, |x'| = |x''|\}$, and vanish only in this set.   We establish the uniqueness and the asymptotic behavior of the saddle-shaped solution. For this, we prove a Liouville type result, the one-dimensional symmetry of positive solutions to semilinear problems in a half-space, and maximum principles in "narrow" sets. The existence of the solution was already proved in part I of this work.
We have investigated the low frequency (f) flicker (also called 1/f) noise of single-layer graphene devices on h-BN (placed on SiO2/Si) along with those on SiO2/Si. We observe that the devices fabricated on h-BN have on average one order of magnitude lower noise amplitude compared with devices fabricated on SiO2/Si. We associate this noise reduction to the lower densities of impurities and trap sites in h-BN than in SiO2. Furthermore, the gate voltage dependent noise amplitude shows a broad maximum at Dirac point for devices on h-BN, in contrast to the M-shaped behavior showing a minimum at Dirac point for devices on SiO2, consistent with the reduced charge inhomogeneity (puddles) for graphene on h-BN. This study demonstrates that the use of h-BN as a substrate or dielectric can be a simple and efficient noise reduction technique valuable for electronic applications of graphene and other nanomaterials.