ShantanuT01/DACTYL-Pretraining huggingface dataset:
A diffusion process associated with the real sub-Laplacian $\Delta_b$, the real part of the complex Kohn-Spencer laplacian $\square_b$, on a strictly pseudoconvex CR manifold is constructed via the Eells-Elworthy-Malliavin method by taking advantage of the metric connection due to Tanaka-Webster. Using the diffusion process and the Malliavin calculus, the heat kernel and the Dirichlet problem for $\Delta_b$ are studied in a probabilistic manner. Moreover, distributions of stochastic line integrals along the diffusion process will be investigated.
We highlight recent advances in the theory, materials fabrication, and experimental characterization of strongly correlated and topological states in [111] oriented transition metal oxide thin films and heterostructures, which are notoriously difficult to realize compared to their [001] oriented counterparts. We focus on two classes of complex oxides, with the chemical formula ABO3 and A2B2O7, where the B sites are occupied by an open-shell transition metal ion with a local moment, and the A sites are typically a rare earth. The [111] oriented quasi-two-dimensional lattices derived from these parent compound lattices can exhibit peculiar geometries and symmetries, namely, a buckled honeycomb lattice, as well as kagome and triangular lattices. These lattice motifs form the basis for emergent strongly correlated and topological states expressed in exotic magnetism, various forms of orbital ordering, topological insulators, topological semimetals, quantum anomalous Hall insulators, and quantum spin liquids. For transition metal ions with high atomic number, spin-orbit coupling plays a significant role and may give rise to additional topological features in the electronic band structure and in the spectrum of magnetic excitations. We conclude the Perspective by articulating open challenges and opportunities in this actively developing field.
A topologically ordered phase on a torus possesses degenerate ground states that transform nontrivially under the modular transformations of the torus, generated by Dehn twists. Representation of modular transformations on the ground states (modular matrices) characterizes the topological order. We show that the modular matrices can be numerically measured as the non-Abelian Berry phase of adiabatic deformations of the lattice model placed on a torus. We apply this method to the example of a gauged $p_x+i p_y$ superconductor, and show that the result is consistent with the topological quantum field theory descriptions.
The Cygnus Cocoon region is a complex region containing an OB star cluster that is prominent in the TeV energy range. Located in this region is 3HWC J2031+415, a significant TeV gamma-ray source whose emission is possibly associated with 2 components, the Cygnus OB2 star cluster and a pulsar wind nebula (PWN). In this work, several modelling methods are presented to best describe the emission. These models disentangle emission believed to be from the Cocoon and isolate the component emitted by the probable PWN. I will present several spectral models to describe the emission of the probable PWN using the latest data set from the High-Altitude Water Cherenkov (HAWC) observatory. Furthermore, I will present an energy morphology study of the PWN component of 3HWC J2031+415 in distinct energy bands.
We consider recurrence versus transience for models of random walks on domains of $\mathbb{Z}^d$, in which monotone interaction enforces domain growth as a result of visits by the walk (or probes it sent), to the neighborhood of domain boundary.
Spin fluctuation in LiV2O4 is revisited by examining the earlier result of muon spin rotation/ relaxation measurements. Instead of a relationship for the localized electron limit, one for itinerant electron systems between muon depolarization rate and spin fluctuation rate ({\nu}_D) is employed to re-analyze data, which reveals that {\nu}D varies linearly with temperature ({\nu}_D {\propto} T) over a range 10^8-10^{12} /s for 0.02 {\le} T < 102 K. Such a linear-T behavior as well as the magnitude of {\nu}_D is fully consistent with that of the magnetic relaxation rate previously observed by inelastic neutron scattering (INS), demonstrating that {\mu}SR and INS have a common time window over the fluctuation spectrum. The linear-T dependence of {\nu}_D is understood as a specific feature predicted by a Hubbard model for intersecting one-dimensional (1D) chains. This quasi-1D character, which is co-existent with enhanced uniform susceptibility at low temperatures, supports the scenario of 1D-to-3D crossover for the microscopic origin of heavy-fermion behavior in LiV2O4.
An important task when processing sensor data is to distinguish relevant from irrelevant data. This paper describes a method for an iterative singular value decomposition that maintains a model of the background via singular vectors spanning a subspace of the image space, thus providing a way to determine the amount of new information contained in an incoming frame. We update the singular vectors spanning the background space in a computationally efficient manner and provide the ability to perform block-wise updates, leading to a fast and robust adaptive SVD computation. The effects of those two properties and the success of the overall method to perform a state of the art background subtraction are shown in both qualitative and quantitative evaluations.
In this paper we propose an approach to perform semantic segmentation of 3D point cloud data by importing the geographic information from a 2D GIS layer (OpenStreetMap). The proposed automatic procedure identifies meaningful units such as buildings and adjusts their locations to achieve best fit between the GIS polygonal perimeters and the point cloud. Our processing pipeline is presented and illustrated by segmenting point cloud data of Trinity College Dublin (Ireland) campus constructed from optical imagery collected by a drone.
Writer identification from musical score documents is a challenging task due to its inherent problem of overlapping of musical symbols with staff lines. Most of the existing works in the literature of writer identification in musical score documents were performed after a preprocessing stage of staff lines removal. In this paper we propose a novel writer identification framework in musical documents without removing staff lines from documents. In our approach, Hidden Markov Model has been used to model the writing style of the writers without removing staff lines. The sliding window features are extracted from musical score lines and they are used to build writer specific HMM models. Given a query musical sheet, writer specific confidence for each musical line is returned by each writer specific model using a loglikelihood score. Next, a loglikelihood score in page level is computed by weighted combination of these scores from the corresponding line images of the page. A novel Factor Analysis based feature selection technique is applied in sliding window features to reduce the noise appearing from staff lines which proves efficiency in writer identification performance.In our framework we have also proposed a novel score line detection approach in musical sheet using HMM. The experiment has been performed in CVC-MUSCIMA dataset and the results obtained that the proposed approach is efficient for score line detection and writer identification without removing staff lines. To get the idea of computation time of our method, detail analysis of execution time is also provided.
We prove a duality theorem for the $p$-adic etale motivic cohomology of a variety $U$ which is the complement of a divisor on a smooth projective variety over $\F_p$. This extends the duality theorems of Milne and Jannsen-Saito-Zhao. The duality introduces a filtration on $H^1_{\etl}(U, {\Q}/{\Z})$. We identify this filtration to the classically known Matsuda filtration when the reduced part of the divisor is smooth. We prove a reciprocity theorem for the idele class groups with modulus introduced by Kerz-Zhao and Rulling-Saito. As an application, we derive the failure of Nisnevich descent for Chow groups with modulus.
We study a class of one-dimensional interacting particle systems with random boundaries as a microscopic model for Stefan's melting and freezing problem. We prove that under diffusive rescaling these particle systems exhibit a hydrodynamic behavior described by the solution of a Cauchy--Stefan problem.
Feedback from supernovae is essential to understanding the self-regulation of star formation in galaxies. However, the efficacy of the process in a cosmological context remains unclear due to excessive radiative losses during the shock propagation. To better understand the impact of SN explosions on the evolution of galaxies, we perform a suite of high-resolution (12 pc), zoom-in cosmological simulations of a Milky Way-like galaxy at z=3 with adaptive mesh refinement. We find that SN explosions can efficiently regulate star formation, leading to the stellar mass and metallicity consistent with the observed mass-metallicity relation and stellar mass-halo mass relation at z~3. This is achieved by making three important changes to the classical feedback scheme: i) the different phases of SN blast waves are modelled directly by injecting radial momentum expected at each stage, ii) the realistic time delay of SNe, commencing at as early as 3 Myr, is required to disperse very dense gas before a runaway collapse sets in at the galaxy centre via mergers of gas clumps, and iii) a non-uniform density distribution of the ISM is taken into account below the computational grid scale for the cell in which SN explodes. The last condition is motivated by the fact that our simulations still do not resolve the detailed structure of a turbulent ISM in which the fast outflows can propagate along low-density channels. The simulated galaxy with the SN feedback model shows strong outflows, which carry approximately ten times larger mass than star formation rate, as well as smoothly rising circular velocity. Other feedback models that do not meet the three conditions form too many stars, producing a peaked rotation curve. Our results suggest that understanding the structure of the turbulent ISM may be crucial to assess the role of SN and other feedback processes in galaxy formation theory.
We update our previous work on an analysis of the electroweak data by including new and partly preliminary data available up to the 1996 summer conferences. The new results on the Z partial decay widths into b and c hadrons now offer a consistent interpretation of all data in the minimal standard model. The value extracted for the strong interaction coupling constant \alpha_s(mZ) agrees well with determinations in other areas. New constraints on the universal parameters S, T and U are obtained from the updated measurements. No signal of new physics is found in the S,T,U analysis once the SM contributions with mt \sim 175GeV and those of not a too heavy Higgs boson are accounted for. The naive QCD-like technicolor model is now ruled out at the 99%CL even for the minimal model with SU(2)_{TC}. In the absence of a significant new physics effect in the electroweak observables, constraints on masses of the top quark, mt, and Higgs boson, mH, are derived as a function of \alpha_s and the QED effective coupling $\bar{\alpha}(m_Z^2)$. The preferred range of mH depends rather strongly on the actual value of mt: mH<360 GeV for mt=170GeV, while mH>130GeV for mt=180GeV at 95%CL. Prospects due to forthcoming improved measurements of asymmetries, the mass of the weak boson W mW, mt and $\bar{\alpha}(m_Z^2)$ are discussed. Anticipating uncertainties of 0.00020 for $\sbar^2(m_Z^2)$, 20MeV for mW, and 2GeV for mt, the new physics contributions to the S,T,U parameters will be constrained more severely, and, within the SM, the logarithm of the Higgs mass can be constrained to about +-0.35. The better constraints on S,T,U and on mH within the minimal SM should be accompanied with matching precision in $\bar{\alpha}(m_Z^2)$.
Using the quantum field theory approach developed in Phys. Rev. D. 93, 045002 (2016), we consider particle scattering and vacuum instability in the so-called L-constant electric field, which is a constant electric field confined between two capacitor plates separated by a finite distance L. We obtain and analyze special sets of stationary solutions of the Dirac and Klein-Gordon equations with the L-constant electric field. Then, we represent probabilities of particle scattering and characteristics of the vacuum instability (related to pair creation) in terms of the introduced solutions. From exact formulas, we derive asymptotic expressions for the differential mean numbers, for the total mean number of created particles, and for the vacuum-to-vacuum transition probability. Using the equivalence principle, we demonstrate that the distributions of particles created by the L-constant electric field and the gravitational field of a black hole have a similar thermal structure.
The kinematics and stellar populations of the low-mass nearby S0 galaxy NGC 5102 are studied from integral field spectra taken with the Multi-Unit Spectroscopic Explorer (MUSE). The kinematic maps reveal for the first time that NGC 5102 has the characteristic 2 sigma peaks indicative of galaxies with counter-rotating discs. This interpretation is quantitatively confirmed by fitting two kinematic components to the observed spectra. Through stellar population analysis we confirm the known young stellar population in the centre and find steep age and metallicity gradients. We construct axisymmetric Jeans anisotropic models of the stellar dynamics to investigate the initial mass function (IMF) and the dark matter halo of the galaxy. The models show that this galaxy is quite different from all galaxies previously studied with a similar approach: even within the half-light radius, it cannot be approximated with the self-consistent mass-follows-light assumption. Including an NFW dark matter halo, we need a heavy IMF and a dark matter fraction of 0.37+-0.04 within a sphere of one effective radius to describe the stellar kinematics. The more general model with a free slope of the dark matter halo shows that slope and IMF are degenerate, but indicates that a light weight IMF (Chabrier-like) and a higher dark matter fraction, with a steeper (contracted) halo, fit the data better. Regardless of the assumptions about the halo profile, we measure the slope of the total mass density to be -1.75+-0.04. This is shallower than the slope of -2 of an isothermal halo and shallower than published slopes for more massive early type galaxies.
Several quantum critical compounds have been argued to have multiple instabilities towards orders with distinct dynamical exponents. We present an analysis of a quantum multicritical point in an itinerant magnet with competition between ferro- and antiferromagnetic order, modelled using Hertz-Millis theory. We perform a one-loop renormalization group treatment of this action in the presence of two dynamical exponents. In two and in three dimensions, when both incipient orders are quantum critical, we find that the specific heat, thermal expansion and Gr\"{u}neisen parameter obey the same power laws as those expected for a single ferromagnetic quantum critical point. The antiferromagnetic correlation length and boundary of the antiferromagnetic ordered phase are suppressed by the dangerously irrelevant interactions with quantum critical ferromagnetic fluctuations. We find no difference between a quantum bicritical point and a quantum tetracritical point. Our results are compared with experiments on NbFe$_2$.
The interaction of optically excited excitons in atomically thin semiconductors with residual doping densities leads to many-body effects which are continuously tunable by external gate voltages. Here, we develop a fully microscopic theory to describe the doping-dependent manipulation of the excitonic properties in atomically thin transition metal dichalcogenides. In particular, we establish a diagonalization approach for the Schr\"odinger equation which characterizes the interaction of a virtual exciton with the Fermi sea of dopants. Solving this many-body Schr\"odinger equation provides access to trions as well as a continuum of scattering states. The dynamics of coupled excitons, trions, and scattering continua is subsequently described by Heisenberg equations of motion including mean-field contributions and correlation effects due to the interaction of excitons with trions and scattering continuum states. Our calculations for optical excitation close to the band edge reveal the influence of doping on the exciton resonances in combination with the simultaneous identification of not only ground-, but also excited-, state trion resonances.
We analyze long-cadence Kepler K2 observations of AR Sco from 2014, along with survey photometry obtained between 2005 and 2016 by the Catalina Real-Time Sky Survey and the All-Sky Automated Survey for Supernovae. The K2 data show the orbital modulation to have been fairly stable during the 78 days of observations, but we detect aperiodic deviations from the average waveform with an amplitude of ~2% on a timescale of a few days. A comparison of the K2 data with the survey photometry reveals that the orbital waveform gradually changed between 2005 and 2010, with the orbital maximum shifting to earlier phases. We compare these photometric variations with proposed models of this unusual system.
Quantum algorithms require a universal set of gates that can be implemented in a physical system. For these, an optimal decomposition into a sequence of available operations is desired. Here, we present a method to find such sequences for a small-scale ion trap quantum information processor. We further adapt the method to state preparation and quantum algorithms with in-sequence measurements.
In this work, we investigate calcium titanate (CaTiO3 - CTO) using X-ray diffraction and Raman spectroscopy up to 60 and 55 GPa respectively. Both experiments show that the orthorhombic Pnma structure remains stable up to the highest pressures measured, in contradiction to ab-initio predictions. A fit of the compression data with a second-order Birch-Murnaghan equation of state yields a bulk modulus K0 of 181.0(6) GPa. The orthorhombic distortion is found to increase slightly with pressure, in agreement with previous experiments at lower pressures and the general rules for the evolution of perovskites under pressure. High-pressure polarized Raman spectra also enable us to clarify the Raman mode assignment of CTO and identify the modes corresponding to rigid rotation of the octahedra, A-cation shifts and Ti-O bond stretching. The Raman signature is then discussed in terms of compression mechanisms.
We study mild solutions to the Navier-Stokes equation on the $n$-dimensional hyperbolic space $\mathbb{H}^n$, $n \geq 2$. We use dispersive and smoothing estimates proved by Pierfelice on a class of complete Riemannian manifolds to extend the Fujita-Kato theory of mild solutions from $\mathbb{R}^n$ to $\mathbb{H}^n$. This includes well-posedness results for $L^n$ initial data and $L^n \cap L^p$ initial data for $1 < p < n$, global in time results for small initial data, and time decay results for the $L^n$ and $L^p$ norms of both $u$ and $\nabla u$. Due to the additional exponential time decay offered on $\mathbb{H}^n$, we are able to simplify the proofs of the $L^n$ and $L^p$ norm decay results as compared to the Euclidean setting. Additionally, we are able to show that mild solutions on $\mathbb{H}^n$ belong to a wider range of space-time $L^rL^q$ spaces than is known for Euclidean space, and that the $L^n$ norm of a global solution decays to zero as $t$ goes to infinity on $\mathbb{H}^n$, which was a question left open by Kato for $\mathbb{R}^n$, $n\geq 3$. As a necessary part of our work, we extend to $\mathbb{H}^n$ known facts in Euclidean space concerning the strong continuity and contractivity of the semigroup generated by the Laplacian. Also, we establish necessary boundedness and commutation properties for a certain projection operator in the setting of $\mathbb{H}^n$ using spectral theory. This work, together with Pierfelice's, contributes to providing a full Fujita-Kato theory on $\mathbb{H}^n$.
In Ziegler (2002), the second author presented a lower bound for the chromatic numbers of hypergraphs $\KG{r}{\pmb s}{\calS}$, "generalized $r$-uniform Kneser hypergraphs with intersection multiplicities $\pmb s$." It generalized previous lower bounds by Kriz (1992/2000) for the case ${\pmb s}=(1,...,1)$ without intersection multiplicities, and by Sarkaria (1990) for $\calS=\tbinom{[n]}k$. Here we discuss subtleties and difficulties that arise for intersection multiplicities $s_i>1$:   1. In the presence of intersection multiplicities, there are two different versions of a "Kneser hypergraph," depending on whether one admits hypergraph edges that are multisets rather than sets. We show that the chromatic numbers are substantially different for the two concepts of hypergraphs. The lower bounds of Sarkaria (1990) and Ziegler (2002) apply only to the multiset version.   2. The reductions to the case of prime $r$ in the proofs Sarkaria and by Ziegler work only if the intersection multiplicities are strictly smaller than the largest prime factor of $r$. Currently we have no valid proof for the lower bound result in the other cases.   We also show that all uniform hypergraphs without multiset edges can be represented as generalized Kneser hypergraphs.
Samarium hexaboride (SmB$_6$), a Kondo insulator with mixed valence, has recently attracted much attention as a possible host for correlated topological surface states. Here, we use a combination of x-ray absorption and reflectometry techniques, backed up with a theoretical model for the resonant $M_{4,5}$ absorption edge of Sm and photoemission data, to establish laterally averaged chemical and valence depth profiles at the surface of SmB$_6$.   We show that upon cleaving, the highly polar (001) surface of SmB$_6$ undergoes substantial chemical and valence reconstruction, resulting in boron termination and a Sm$^{3+}$ dominated sub-surface region. Whereas at room temperature, the reconstruction occurs on a time scale of less than two hours, it takes about 24 hours below 50 K. The boron termination is eventually established, irrespective of the initial termination. Our findings reconcile earlier depth resolved photoemission and scanning tunneling spectroscopy studies performed at different temperatures and are important for better control of polarity and, as a consequence, surface states in this system.
We develop a probabilistic approach to continuous-time finite state mean field games. Based on an alternative description of continuous-time Markov chain by means of semimartingale and the weak formulation of stochastic optimal control, our approach not only allows us to tackle the mean field of states and the mean field of control in the same time, but also extend the strategy set of players from Markov strategies to closed-loop strategies. We show the existence and uniqueness of Nash equilibrium for the mean field game, as well as how the equilibrium of mean field game consists of an approximative Nash equilibrium for the game with finite number of players under different assumptions of structure and regularity on the cost functions and transition rate between states.
We present a time-series Doppler imaging study of the K-subgiant component in the RS CVn-type binary system IL Hya (P orb=12.905 d). From re-processing the unique long-term spectroscopic dataset of 70 days taken in 1996/97, we perform a thorough cross-correlation analysis to derive surface differential rotation. As a result we get solar-type differential rotation with a shear value alpha of 0.05, in agreement with preliminary suggestions from previous attempts. A possible surface pattern of meridional circulation is also detected.