ShantanuT01/DACTYL-Pretraining huggingface dataset:
Our aim is to clarify the relationship between Kudla's and Bruinier's Green functions attached to special cycles on Shimura varieties of orthogonal and unitary type. These functions play a key role in the arithmetic geometry of the special cycles in the context of Kudla's program.   In particular, we show that the generating series obtained by taking the differences of the two families of Green functions is a modular form with trivial holomorphic projection. Along the way, we construct a section of the Maass lowering operator for moderate growth modular forms valued in the Weil representation using a regularized theta lift, which may be of independent interest. We also consider arithmetic-geometric applications to integral models of U(n, 1) Shimura varieties.   Each family of Green functions gives rise to a formal arithmetic theta function, valued in an arithmetic Chow group, that is conjectured to be modular; our main result is the modularity of the difference of the two arithmetic theta functions. Finally, we relate the arithmetic heights of the special cycles to special derivatives of Eisenstein series, as predicted by Kudla's conjecture, and describe a refinement of a theorem of Bruinier-Howard-Yang on arithmetic intersections against CM points.
The paper presents two arithmetical versions of the Nyman-Beurling equivalence with the Riemann hypothesis, proved by classical, quasi elementary, number-theoretic methods, based on an integrated version of the classical combinatorial identity for Moebius numbers. These proofs also give insight into the troublesome phenomenon that many natural sequences of Beurling functions tending to the indicator function of (0,1) both pointwise and in L1 norm do not converge in L2 norm.
We discuss the nature of the velocity dispersion vs. size relation for molecular clouds. In particular, we add to previous observational results showing that the velocity dispersions in molecular clouds and cores are not purely functions of spatial scale but involve surface gas densities as well. We emphasize that hydrodynamic turbulence is required to produce the first condensations in the progenitor medium. However, as the cloud is forming, it also becomes bound, and gravitational accelerations dominate the motions. Energy conservation in this case implies $|E_g| \sim E_k$, in agreement with observational data, and providing an interpretation for two recent observational results: the scatter in the $\delta v-R$ plane, and the dependence of the velocity dispersion on the surface density ${\delta v^2/ R} \propto \Sigma$. We argue that the observational data are consistent with molecular clouds in a state of hierarchical gravitational collapse, i.e., developing local centers of collapse throughout the whole cloud while the cloud itself is collapsing, and making equilibrium unnecessary at all stages prior to the formation of actual stars. Finally, we discuss how this mechanism need not be in conflict with the observed star formation rate.
The evolution pattern of exceptional points is studied in a non-integrable limit of the complex-extended 3-level Richardson-Gaudin model. The appearance of a pseudo-diabolic point from the fusion of two exceptional points is demonstrated in the anti-hermitian limit of the model and studied in some details.
We study, both theoretically and experimentally, the occurrence of topological defects in polariton superfluids in the optical parametric oscillator (OPO) regime. We explain in terms of local supercurrents the deterministic behaviour of both onset and dynamics of spontaneous vortex-antivortex pairs generated by perturbing the system with a pulsed probe. Using a generalised Gross-Pitaevskii equation, including photonic disorder, pumping and decay, we elucidate the reason why topological defects form in couples and can be detected by direct visualizations in multi-shot OPO experiments.
Anisotropic magneto-transport measurements are reported on Fe1/4TaS2 single crystals grown by vapor transport. Both the magnetization and resistivity are extremely anisotropic, with the magnetic moments aligned parallel to the c crystallographic direction. Fe1/4TaS2 orders ferromagnetically below TC = 160 K and displays very sharp hysteresis loops in the ordered state for H||c. The corresponding magnetoresistance is negative, and it qualitatively reproduces the features observed in the M(H) data, by showing a sharp drop around the critical field Hs for the moment reversal. The magnetization switching time shows an unusual increase with increasing temperature. For field applied within the ab plane, the magnetization remains small and linear in field up to 5 T, and the magnetoresistance is positive and quadratic in field, with no visible hysteresis. The squareness of the H||c M(H) loops and the high critical field for the magnetization switch (Hs = 3.7 T at T = 2 K) allow us to classify Fe1/4TaS2 as a strong ferromagnet.
Eclipsing binary stars are rare and extremely valuable astrophysical laboratories that make possible precise determination of fundamental stellar parameters. Investigation of early-type chemically peculiar stars in eclipsing binaries provides important information for understanding the origin and evolutionary context of their anomalous surface chemistry. In this study we discuss observations of eclipse variability in six mercury-manganese (HgMn) stars monitored by the TESS satellite. These discoveries double the number of known eclipsing HgMn stars and yield several interesting objects requiring further study. In particular, we confirm eclipses in HD 72208, thereby establishing this object as the longest-period eclipsing HgMn star. Among five other eclipsing binaries, reported here for the first time, HD 36892 and HD 53004 stand out as eccentric systems showing heartbeat variability in addition to eclipses. The latter object has the highest eccentricity among eclipsing HgMn stars and also exhibits tidally induced oscillations. Finally, we find evidence that HD 55776 may be orbited by a white dwarf companion.
We show that the analysis presented in a recent comment by Coll and Ferrando \cite{comment} (qr-qc/0312058) is based on the erroneous assumption that the chemical potential and fractional concentration of a {\it mixture} of perfect fluids are unknown variables.
The time evolution of a wavepacket in strained graphene is studied within the tight-binding model and continuum model. The effect of an external magnetic field, as well as a strain-induced pseudo-magnetic field, on the wave packet trajectories and zitterbewegung are analyzed. Combining the effects of strain with those of an external magnetic field produces an effective magnetic field which is large in one of the Dirac cones, but can be practically zero in the other. We construct an efficient valley filter, where for a propagating incoming wave packet consisting of momenta around the K and K' Dirac points, the outgoing wave packet exhibits momenta in only one of these Dirac points, while the components of the packet that belong to the other Dirac point are reflected due to the Lorentz force. We also found that the zitterbewegung is permanent in time in the presence of either external or strain-induced magnetic fields, but when both the external and strain-induced magnetic fields are present, the zitterbewegung is transient in one of the Dirac cones, whereas in the other cone the wave packet exhibits permanent spatial oscillations.
This paper introduces a device, algorithm and graphical user interface to obtain anthropometric measurements of foot. Presented device facilitates obtaining scale of image and image processing by taking one image from side foot and underfoot simultaneously. Introduced image processing algorithm minimizes a noise criterion, which is suitable for object detection in single object images and outperforms famous image thresholding methods when lighting condition is poor. Performance of image-based method is compared to manual method. Image-based measurements of underfoot in average was 4mm less than actual measures. Mean absolute error of underfoot length was 1.6mm, however length obtained from side foot had 4.4mm mean absolute error. Furthermore, based on t-test and f-test results, no significant difference between manual and image-based anthropometry observed. In order to maintain anthropometry process performance in different situations user interface designed for handling changes in light conditions and altering speed of the algorithm.
The present understanding of the structure of the Hoyle state in 12C is reviewed. Most of the theoretical approaches to the Hoyle state are shortly summarized. The corresponding results are analyzed with respect to whether they give evidence to the alpha particle condensation structure of the Hoyle state (and other Hoyle-like states in heavier self-conjugate nuclei) or not.
This thesis is dedicated to study the thermodynamic properties of a magnetized neutral vector boson gas at any temperature, with the aim to provide equations of state that allow more general and precise descriptions of astrophysical phenomena. The all temperature analytical expressions for the thermodynamic magnitudes, as well as their non relativistic limits, are obtained starting from the energy spectrum given by Proca's theory. With these expressions, and considering the system under astrophysical conditions (particle densities, temperatures and magnetic fields in the order of the estimated for Neutron Stars), we investigate the Bose Einstein condensation, the magnetic properties and the equations of state of the gas, making a special emphasis on the influence of antiparticles and magnetic field. In all cases, the results are compared with their analogues in the low temperature and the non relativistic limits. This allows us to establish the ranges of validity of these approximations and to achieve a better understanding of their effects on the studied system.
The phenomenology of exchange bias effects observed in structurally single-phase alloys and compounds but composed of a variety of coexisting magnetic phases such as ferromagnetic, antiferromagnetic, ferrimagnetic, spin-glass, cluster-glass and disordered magnetic states are reviewed. The investigations on exchange bias effects are discussed in diverse types of alloys and compounds where qualitative and quantitative aspects of magnetism are focused based on macroscopic experimental tools such as magnetization and magnetoresistance measurements. Here, we focus on improvement of fundamental issues of the exchange bias effects rather than on their technological importance.
The centroid energy of the Fe K$\alpha$ line has been used to identify the progenitors of supernova remnants (SNRs). These investigations generally considered the energy of the centroid derived from the spectrum of the entire remnant. Here we use {\it XMM-Newton} data to investigate the Fe K$\alpha$ centroid in 6 SNRs: 3C~397, N132D, W49B, DEM L71, 1E 0102.2-7219, and Kes 73. In Kes 73 and 1E 0102.2-7219, we fail to detect any Fe K$\alpha$ emission. We report a tentative first detection of Fe K$\alpha$ emission in SNR DEM L71, with a centroid energy consistent with its Type Ia designation. In the remaining remnants, the spatial and spectral sensitivity is sufficient to investigate spatial variations of the Fe K$\alpha$ centroid. We find in N132D and W49B that the centroids in different regions are consistent with that derived from the overall spectrum, although not necessarily with the remnant type identified via other means. However, in SNR 3C~397, we find statistically significant variation in the centroid of up to 100 eV, aligning with the variation in the density structure around the remnant. These variations span the intermediate space between centroid energies signifying core-collapse and Type Ia remnants. Shifting the dividing line downwards by 50 eV can place all the centroids in the CC region, but contradicts the remnant type obtained via other means. Our results show that caution must be used when employing the Fe K$\alpha$ centroid of the entire remnant as the sole diagnostic for typing a remnant.
We investigate the performance of quantum parameter estimation based on a qubit probe in a dissipative bosonic environment beyond the traditional paradigm of weak-coupling and rotating-wave approximations. By making use of an exactly numerical hierarchical equations of motion method, we analyze the influences of the non-Markovian memory effect induced by the environment and the form of probe-environment interaction on the estimation precision. It is found that (i) the non-Markovianity can effectively boost the estimation performance and (ii) the estimation precision can be improved by introducing a perpendicular probe-environment interaction. Our results indicate the scheme of parameter estimation in a noisy environment can be optimized via engineering the decoherence mechanism.
This paper studies the local exact controllability and the local stabilization of the semilinear Schr\"odinger equation posed on a product of $n$ intervals ($n\ge 1$). Both internal and boundary controls are considered, and the results are given with periodic (resp. Dirichlet or Neumann) boundary conditions. In the case of internal control, we obtain local controllability results which are sharp as far as the localization of the control region and the smoothness of the state space are concerned. It is also proved that for the linear Schr\"odinger equation with Dirichlet control, the exact controllability holds in $H^{-1}(\Omega)$ whenever the control region contains a neighborhood of a vertex.
Quantum confinement increases the spacing between energy levels as the nanocrystallite size is decreased. Its qualitative features hold both for states localized near the center of a nanocrystallite and those near the surface, such as states due primarily to dangling bonds. However, different quantitative features are expected because of the different size constraints on each of these states. Since the majority of atoms in a typical nanocrystallite are on the surface, contrasting confinement effects between these two types may prove useful in predicting how surface state dependent properties, such as optical absorption, change with the size of the nanocrystallite. By applying first principles pseudopotential methods to indium doped, uncapped CdSe nanocrystallites containing 17 and 34 atoms, we identify center and surface localized states. Using the lowest occupied energy state as a reference, the energy of a state localized near the center is found to increase 24 mRy from the 34 to 17 atom nanocrystallite. An equivalent surface state within the two cases studied is not found, but the energy level spacing is speculated to increase on the order of 100 mRy between the 34 and 17 atom cases based on states that are highly local to the surface, but not equivalent. Furthermore, we find it's necessary for the impurity to sit at the center of the nanocrystallite in order for the impurity states to be electrically active.
We propose and prove several regularity criteria for the 2D and 3D Kuramoto-Sivashinsky equation, in both its scalar and vector forms. In particular, we examine integrability criteria for the regularity of solutions in terms of the scalar solution $\phi$, the vector solution $u\triangleq\nabla\phi$, as well as the divergence $\text{div}(u)=\Delta\phi$, and each component of $u$ and $\nabla u$. We also investigate these criteria computationally in the 2D case, and we include snapshots of solutions for several quantities of interest that arise in energy estimates.
We use measurements of weak gravitational shear around a sample of massive galaxy clusters at z = 0.3 to constrain their average radial density profile. Our results are consistent with the density profiles of CDM halos in numerical simulations and inconsistent with simple models of self-interacting dark matter. Unlike some other recent studies, we are not probing the scales where the baryonic mass component becomes dynamically important, and so our results should be directly comparable to CDM N-body simulations.
We present the discovery of five millisecond pulsars (MSPs) from the PALFA Galactic plane survey using Arecibo. Four of these (PSRs J0557+1551, J1850+0244, J1902+0300, and J1943+2210) are binary pulsars whose companions are likely white dwarfs, and one (PSR J1905+0453) is isolated. Phase-coherent timing solutions, ranging from $\sim$1 to $\sim$3 years in length, and based on observations from the Jodrell Bank and Arecibo telescopes, provide precise determinations of spin, orbital, and astrometric parameters. All five pulsars have large dispersion measures ($>100$ pc cm$^{-3}$, within the top 20% of all known Galactic field MSPs) and are faint (1.4 GHz flux density < 0.1 mJy, within the faintest 5% of all known Galactic field MSPs), illustrating PALFA's ability to find increasingly faint, distant MSPs in the Galactic plane. In particular, PSR J1850+0244 has a dispersion measure of 540 pc cm$^{-3}$, the highest of all known MSPs. Such distant, faint MSPs are important input for accurately modeling the total Galactic MSP population.
Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical experiments. However, the intrinsic multimode spectral-temporal structure of pulsed PDC often poses a severe hindrance for the direct implementation of the heralding of pure single-photon states or, for example, continuous-variable entanglement distillation experiments. To get rid of multimode effects narrowband frequency filtering is frequently applied to achieve a single-mode behavior.   A rigorous theoretical description to accurately describe the effects of filtering on PDC, however, is still missing. To date, the theoretical models of filtered PDC are rooted in the discrete-variable domain and only account for filtering in the low gain regime, where only a few photon pairs are emitted at any single point in time. In this paper we extend these theoretical descriptions and put forward a simple model, which is able to accurately describe the effects of filtering on PDC in the continuous-variable domain.   This developed straightforward theoretical framework enables us to accurately quantify the trade-off between suppression of higher-order modes, reduced purity and lowered Einstein-Podolsky-Rosen (EPR) entanglement, when narrowband filters are applied to multimode type-II PDC.
We describe a finite-difference method for locating apparent horizons and illustrate its capabilities on boosted Kerr and Schwarzschild black holes. Our model spacetime is given by the Kerr-Schild metric. We apply a Lorentz boost to this spacetime metric and then carry out a 3+1 decomposition. The result is a slicing of Kerr/Schwarzschild in which the black hole is propagated and Lorentz contracted. We show that our method can locate distorted apparent horizons efficiently and accurately.
The canonical transformation diagonalizing the one-particle tight binding Hamiltonian for an alternating chain with two non-equivalent sites per unit cell has been used to introduce the Hubbard-like interactions (on-site, inter-site, bond-site and intra-bond) in the corresponding two-band model. The considerations have been restricted to the particular case, suggested by the undistorted 3/4-filled $CuO_{3}$ chain, where the alternating structure comes only from non-equal on-site atomic energies and the gap between the two bands is sufficiently large. The renormalization group method has been then applied to the upper band of this model and the corresponding phase diagram has been analyzed in terms of some renormalized (density dependent) Hubbard-type couplings for arbitrary filling of the upper band. The particular case of $CuO_{3}$ chain is also discussed and the corresponding phase diagram has been drawn in terms of the original (and realistic) coupling constants.
With the prevalence of digital cameras, the number of digital images increases quickly, which raises the demand for non-manual image quality assessment. While there are many methods considered useful for detecting blurriness, in this paper we propose and evaluate a new method that uses a deep convolutional neural network, which can determine whether an image is blurry or not. Experimental results demonstrate the effectiveness of the proposed scheme and are compared to deterministic methods using the confusion matrix.
The discrete membrane model is a Gaussian random interface whose inverse covariance is given by the discrete biharmonic operator on a graph. In literature almost all works have considered the field as indexed over $\mathbb{Z}^d$, and this enabled one to study the model using methods from partial differential equations. In this article we would like to investigate the dependence of the membrane model on a different geometry, namely trees. The covariance is expressed via a random walk representation which was first determined by Vanderbei (1984). We exploit this representation on $m$-regular trees and show that the infinite volume limit on the infinite tree exists when $m\ge 3$. Further we determine the behavior of the maximum under the infinite and finite volume measures.
Recently, numerical calculations of the magnetic field evolution in neutron stars demonstrated the possible existence of a Hall attractor, a stage at which the evolution of the field driven by the Hall cascade ends. The existence of such a stage in neutron star magnetic evolution is very important, and can be potentially probed by observations. Here we discuss three types of objects which could have reached this stage. First, we briefly describe the evolution of normal radio pulsars with ages about a few hundred thousand years. Then we analyse in more detail observations of RX J1856.5-3754, one of the Magnificent Seven, focusing on the surface temperature distribution and comparing model predictions with the temperature map inferred from X-ray observations. Finally, we discuss the necessity of the Hall attractor stage to explain the hypothetical existence of accreting magnetars. We conclude that at the moment there is no direct confirmation of the Hall attractor stage in known sources. However, more detailed observations in the near future can demonstrate existence (or absence) of this stage of the crustal magnetic field evolution.
We present results of an HI study of a complete sample of nearby radio galaxies. Our goal is to investigate whether merger or interaction events could be at the origin of the radio-AGN activity. Around five of our radio galaxies, hosted mainly by early-type galaxies, we detect extended HI in emission. In most cases this HI is distributed in large (up to 190 kpc) and massive (up to M(HI) ~ 10^10 M(sun)) disk- or ring-like structures, that show fairly regular rotation around the host galaxy. This suggests that in these systems a major merger did occur, but at least several Gyr ago. For the HI-rich radio galaxy B2 0648+27 we confirm such a merger origin through the detection of a post-starburst stellar population that dominates the visible light throughout this system. The timescale of the current episode of radio-AGN activity in our HI-rich radio galaxies is many orders of magnitude smaller than the merger timescales. Therefore the radio-AGN activity either started late in the lifetime of the merger event, or is not directly related to the merger event at all. Another intriguing result is that the HI-rich (> 10^9 M(sun)) radio galaxies in our sample all have compact radio sources, while none of the extended radio sources contain these amounts of extended HI. This strongly suggests that there is a relation between the size of the radio jet and the presence of large amounts of neutral gas associated with the host galaxy.
We give estimates for the probability that a chordal, radial or two-sided radial SLE$_\kappa$ curve retreats far from its terminal point after coming close to it, for $\kappa \leq 4$. The estimates are uniform over all initial segments of the curve, and are sharp up to a universal constant.