ShantanuT01/DACTYL-Pretraining huggingface dataset:
We develop local cohomology techniques to study the finite slope part of the coherent cohomology of Shimura varieties. The local cohomology groups we consider are a generalization of overconvergent modular forms, and they are defined by using a stratification on the Shimura variety obtained from the Bruhat stratification on a flag variety via the Hodge-Tate period map. We construct a spectral sequence from the local cohomologies to the classical cohomology and use it to obtain classicality and vanishing results. We also develop a theory of p-adic families and construct eigenvarieties. As an application, we prove some new properties of Galois representations arising from certain non-regular algebraic cuspidal automorphic representations.
We describe the special relativistic extension of the CRONOS code, which has been used for studies of gamma-ray binaries in recent years. The code was designed to be easily adaptable, allowing the user to easily change existing functionalities or introduce new modules tailored to the problem at hand. Numerically, the equations are treated using a finite-volume Godunov scheme on rectangular grids, which currently support Cartesian, spherical, and cylindrical coordinates. The employed reconstruction technique, the approximate Riemann solver and the equation of state can be chosen dynamically by the user. Further, the code was designed with stability and robustness in mind, detecting and mitigating possible failures early on. We demonstrate the code's capabilities on an extensive set of validation problems.
We consider a one-dimensional nonlocal nonlinear equation of the form: $\partial_t u = (\Lambda^{-\alpha} u)\partial_x u - \nu \Lambda^{\beta}u$ where $\Lambda =(-\partial_{xx})^{\frac 12}$ is the fractional Laplacian and $\nu\ge 0$ is the viscosity coefficient. We consider primarily the regime $0<\alpha<1$ and $0\le \beta \le 2$ for which the model has nonlocal drift, fractional dissipation, and captures essential features of the 2D $\alpha$-patch models. In the critical and subcritical range $1-\alpha\le \beta \le 2$, we prove global wellposedness for arbitrarily large initial data in Sobolev spaces. In the full supercritical range $0 \le \beta<1-\alpha$, we prove formation of singularities in finite time for a class of smooth initial data. Our proof is based on a novel nonlocal weighted inequality which can be of independent interest.
We demonstrate the appearance of zero-energy bound states satisfying the $\mathbb{Z}_4$ parafermionic algebra in interacting quantum wires with Rashba spin-orbit coupling and proximity-induced superconductivity.   The fourfold degeneracy of these states is protected by time-reversal symmetry and fermion-parity conservation, and leads to an $8 \pi$ periodicity of the Josephson current due to the tunneling of fractionalized excitations with charge $e/2$. Even in the presence of perturbations, we propose that this periodicity will remain visible in driven, current-biased Shapiro step measurements on current state-of-the-art Rashba wires.
In this work, we exploit the task of joint classification and weakly supervised localization of thoracic diseases from chest radiographs, with only image-level disease labels coupled with disease severity-level (DSL) information of a subset. A convolutional neural network (CNN) based attention-guided curriculum learning (AGCL) framework is presented, which leverages the severity-level attributes mined from radiology reports. Images in order of difficulty (grouped by different severity-levels) are fed to CNN to boost the learning gradually. In addition, highly confident samples (measured by classification probabilities) and their corresponding class-conditional heatmaps (generated by the CNN) are extracted and further fed into the AGCL framework to guide the learning of more distinctive convolutional features in the next iteration. A two-path network architecture is designed to regress the heatmaps from selected seed samples in addition to the original classification task. The joint learning scheme can improve the classification and localization performance along with more seed samples for the next iteration. We demonstrate the effectiveness of this iterative refinement framework via extensive experimental evaluations on the publicly available ChestXray14 dataset. AGCL achieves over 5.7\% (averaged over 14 diseases) increase in classification AUC and 7%/11% increases in Recall/Precision for the localization task compared to the state of the art.
We show how minimal elements of a stopping time $\sigma$-algebra can be expressed in terms of the minimal elements of the $\sigma$-algebra of the underlying filtration. This facilitates an intuitive interpretation of stopping time $\sigma$-algebras. An example is provided.
We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all Burniat surfaces.   The semiorthogonal complement $\mathcal A$ of $\Upsilon$ is an "almost phantom" category: it has trivial Hochschild homology, and $K_0(\mathcal A)=\bZ_2^6$.
An asymptotic formula is proved for the k-fold divisor function averaged over homogeneous polynomials of degree k in k-1 variables coming from incomplete norm forms.
Models for the characteristically soft X-ray spectrum of the compact X-ray source V1498 Aql (=4U 1957+11) have ranged from optically thick Comptonization to multicolor accretion disk models. We critically examine the X-ray spectrum of V1408 Aql via archival Advanced Satellite for Cosmology and Astrophysics (ASCA) data, archival Roentgensatellit (ROSAT) data, and recent Rossi X-Ray Timing Explorer (RXTE) data. Although we are able to fit a variety of X-ray spectral models to these data, we favor an interpretation of the X-ray spectrum as being due to an accretion disk viewed at large inclination angles. Evidence for this hypothesis includes long term (117 day, 235 day, 352 day) periodicities seen by the RXTE All Sky Monitor (ASM), which we interpret as being due to a warped precessing disk, and a 1 keV feature in the ASCA data, which we interpret as being the blend of L fluorescence features from a disk atmosphere or wind. We also present timing analysis of the RXTE data and find upper limits of 4% for the root mean square (rms) variability between f=0.001-16 Hz. The situation of whether the compact object is a black hole or neutron star is still ambiguous; however, it now seems more likely that an X-ray emitting, warped accretion disk is an important component of this system.
The prediction of the antenna radiation pattern can be extremely complex for antenna system composed of several reflector surfaces. Typically, at mm-wavelengths, telescopes are composed of mirrors and shields, and an accurate prediction of the whole system response is therefore complicated. This is the case for the optical system of the ESA Planck mission. Planck represents the third generation of mm-wave instruments designed for space observations of CMB anisotropies over the whole sky, and has unprecedented sensitivity and angular resolution. The Low Frequency Instrument (LFI) is one of the two instruments onboard the satellite. LFI consists of an array of 46 cooled HEMT-based receivers coupled to the 1.5 meter off-axis dual reflector telescope by an array of 23 dual profiled corrugated feed horns working at four frequencies between 30 and 100 GHz. Owing to the small level of CMB anisotropies, the control of the systematic effects is mandatory, and this is assured by means of a dedicated instrument design and by an accurate knowledge of instrument characteristics. The telescope is a source of systematic errors both in the main beam region (aberrations) and in the sidelobes region (straylight contamination) and efficient and accurate radiation pattern simulations of the telescope-feed system are needed. We report on the simulations of the full pattern applied to the Planck/LFI-Telescope system. These simulations, based on advanced GTD methods, are used to evaluate the straylight rejection of the entire optical system, by applying a new approach for evaluating the sidelobes in a rigorous way, even at very low levels.
We have developed a method for selecting the most luminous galaxies detected by IRAS based on their extreme values of R, the ratio of 60 micron and B-band luminosity. These objects have optical counterparts that are close to or below the limits of Schmidt surveys. We have tested our method on a 1079 deg^2 region of sky, where we have selected a sample of IRAS sources with 60 micron flux densities greater than 0.2 Jy, corresponding to a redshift limit z~1 for objects with far-IR luminosities of 10^{13} L_sun. Optical identifications for these were obtained from the UK Schmidt Telescope plates, using the likelihood ratio method. Optical spectroscopy has been carried out to reliably identify and measure the redshifts of six objects with very faint optical counterparts, which are the only objects with R>100 in the sample. One object is a hyperluminous infrared galaxy (HyLIG) at z=0.834. Of the remaining, fainter objects, five are ultraluminous infrared galaxies (ULIGs) with a mean redshift of 0.45, higher than the highest known redshift of any non-hyperluminous ULIG prior to this study. High excitation lines reveal the presence of an active nucleus in the HyLIG, just as in the other known infrared-selected HyLIGs. In contrast, no high excitation lines are found in the non-hyperluminous ULIGs. We discuss the implications of our results for the number density of HyLIGs at z<1 and for the evolution of the infrared galaxy population out to this redshift, and show that substantial evolution is indicated. Our selection method is robust against the presence of gravitational lensing if the optical and infrared magnification factors are similar, and we suggest a way of using it to select candidate gravitationally lensed infrared galaxies.
We apply parquet-diagram summation methods for the calculation of the superfluid gap in $S$-wave pairing in neutron matter for realistic nucleon-nucleon interactions such as the Argonne $v_6$ and the Reid $v_6$ potentials. It is shown that diagrammatic contributions that are outside the parquet class play an important role. These are, in variational theories, identified as so-called "commutator contributions". Moreover, using a particle-hole propagator appropriate for a superfluid system results in the suppression of the spin-channel contribution to the induced interaction. Applying these corrections to the pairing interaction, our results agree quite well with Quantum Monte Carlo data.
For every integer $k \geq 3$ we construct a $k$-gonal curve $C$ along with a very ample divisor of degree $2g + k - 1$ (where $g$ is the genus of $C$) to which the vanishing statement from the Green-Lazarsfeld gonality conjecture does not apply.
We reexamine the problem of a hole moving in an antiferromagnetic spin background and find that the injected hole will always pick up a sequence of nontrivial phases from the spin degrees of freedom. Previously unnoticed, such a string-like phase originates from the hidden Marshall signs which are scrambled by the hopping of the hole. We can rigorously show that this phase string is non-repairable at low energy and give a general proof that the spectral weight Z must vanish at the ground-state energy due to the phase string effect. Thus, the quasiparticle description fails here and the quantum interference effect of the phase string dramatically affects the long-distance behavior of the injected hole. We introduce a so-called phase-string formulation of the t-J model for a general number of holes in which the phase string effect can be explicitly tracked. As an example, by applying this new mathematical formulation in one dimension, we reproduce the well-known Luttinger-liquid behaviors of the asymptotic single-electron Green's function and the spin-spin correlation function. We can also use the present phase string theory to justify previously developed spin-charge separation theory in two dimensions, which offers a systematic explanation for the transport and magnetic anomalies in the high-T_c cuprates.
Fix a positive integer $g$ and a squarefree integer $m$. We prove the existence of a genus $g$ curve $C/\mathbb{Q}$ such that the mod $m$ representation of its Jacobian is tame. The method is to analyse the period matrices of hyperelliptic Mumford curves, which could be of independent interest. As an application, we study the tame version of the inverse Galois problem for symplectic matrix groups over finite fields.
The time evolution in a supersymmetric extension of the Kodomtsev-Petviashvilli hierarchy, a classical integrable system, is shown to be Hamiltonian. The canonical bracket associated to the Hamiltonian evolution is the classical analog of the antibracket encountered in the quantization of gauge theories. This provides a new understanding of supersymmetric Hamiltonian systems.
We present the hydrodynamic BL Herculis-type models which display a long-term modulation of pulsation amplitudes and phases. The modulation is either strictly periodic or it is quasi-periodic, with the modulation period and modulation pattern varying from one cycle to the other. Such behaviour has not been observed in any BL Her variable so far, however, it is a common property of their lower luminosity siblings - RR Lyrae variables showing the Blazhko effect. These models provide a support for the recent mechanism proposed by Buchler & Kollath to explain this still mysterious phenomenon. In their model, a half-integer resonance that causes the period doubling effect, discovered recently in the Blazhko RR Lyrae stars, is responsible for the modulation of the pulsation as well. Although our models are more luminous than is appropriate for RR Lyrae stars, they clearly demonstrate, through direct hydrodynamic computation, that the mechanism can indeed be operational.   Of great importance are models which show quasi-periodic modulation - a phenomenon observed in Blazhko RR Lyrae stars. Our models coupled with the analysis of the amplitude equations show that such behaviour may be caused by the dynamical evolution occurring in the close proximity of the unstable single periodic saddle point.
Studies of large-scale structures in the Universe, such as superstructures or cosmic voids, have been widely used to characterize the properties of the cosmic web through statistical analyses. On the other hand, the 2-point correlation function of large-scale tracers such as galaxies or halos provides a reliable statistical measure. However, this function applies to the spatial distribution of point-like objects, and therefore it is not appropriate for extended large structures which strongly depart from spherical symmetry. Here we present an analysis based on the standard correlation function formalism that can be applied to extended objects exhibiting arbitrary shapes. Following this approach, we compute the probability excess $\Xi$ of having spheres sharing parts of cosmic structures with respect to a realization corresponding to a distribution of the same structures in random positions. For this aim, we identify superstructures defined as Future Virialized Structures (FVSs) in semi-anaytic galaxies on the MPDL2 MultiDark simulation. We have also identified cosmic voids to provide a joint study of their relative distribution with respect to the superstructures. Our analysis suggests that $\Xi$ provides useful characterizations of the large scale distribution, as suggested from an analysis of sub-sets of the simulation. Even when superstructure properties may exhibit negligible variations across the sub-sets, $\Xi$ has the sensitivity to statistically distinguish sub-boxes that departs from the mean at larger scales. Thus, our methods can be applied in analysis of future surveys to provide characterizations of large-scale structure suitable to distinguish different theoretical scenarios.
Robustness of convolutional neural networks (CNNs) has gained in importance on account of adversarial examples, i.e., inputs added as well-designed perturbations that are imperceptible to humans but can cause the model to predict incorrectly. Recent research suggests that the noises in adversarial examples break the textural structure, which eventually leads to wrong predictions. To mitigate the threat of such adversarial attacks, we propose defective convolutional networks that make predictions relying less on textural information but more on shape information by properly integrating defective convolutional layers into standard CNNs. The defective convolutional layers contain defective neurons whose activations are set to be a constant function. As defective neurons contain no information and are far different from standard neurons in its spatial neighborhood, the textural features cannot be accurately extracted, and so the model has to seek other features for classification, such as the shape. We show extensive evidence to justify our proposal and demonstrate that defective CNNs can defense against black-box attacks better than standard CNNs. In particular, they achieve state-of-the-art performance against transfer-based attacks without any adversarial training being applied.
We consider the fractional unforced Burgers equation in the one-dimensional space-periodic setting: $$\partial u/\partial t+(f(u))_x +\nu \Lambda^{\alpha} u= 0, t \geq 0,\ \mathbb{x} \in \mathbb{T}^d=(\mathbb{R}/\mathbb{Z})^d.$$ Here $f$ is strongly convex and satisfies an additional growth condition, $\Lambda=\sqrt{-\Delta}$, $\nu$ is small and positive, while $\alpha \in (1,\ 2)$ is a constant in the subcritical range.   For solutions $u$ of this equation, we generalise the results obtained for the case $\alpha=2$ (i.e. when $-\Lambda^{\alpha}$ is the Laplacian) in [10]. We obtain sharp estimates for the time-averaged Sobolev norms of $u$ as a function of $\nu$. These results yield sharp estimates for natural analogues of quantities characterising the hydrodynamical turbulence, namely the averages of the increments and of the energy spectrum. In the inertial range, these quantities behave as a power of the norm of the relevant parameter, which is respectively the separation $\ell$ in the physical space and the wavenumber $\mathbf{k}$ in the Fourier space.   The form of all estimates is the same as in the case $\alpha=2$; the only thing that changes (except implicit constants) is that $\nu$ is replaced by $\nu^{1/(\alpha-1)}$.
Spin Hall effect converts charge current to spin current, which can exert spin-torque to switch the magnetization of a nanomagnet. Recently, it is shown that the ratio of spin current to charge current using spin Hall effect can be made more than unity by using the areal geometry judiciously, unlike the case of conventional spin-transfer-torque switching of nanomagnets. This can enable energy-efficient means to write a bit of information in nanomagnets. Here, we study the energy dissipation in such spin Hall devices. By solving stochastic Landau-Lifshitz-Gilbert equation of magnetization dynamics in the presence of room temperature thermal fluctuations, we show a methodology to simultaneously reduce switching delay, its variance and energy dissipation, while lateral dimensions of the spin Hall devices are scaled down.
The main essence of this paper is to investigate the performance of RetinaNet based object detectors on pedestrian detection. Pedestrian detection is an important research topic as it provides a baseline for general object detection and has a great number of practical applications like autonomous car, robotics and Security camera. Though extensive research has made huge progress in pedestrian detection, there are still many issues and open for more research and improvement. Recent deep learning based methods have shown state-of-the-art performance in computer vision tasks such as image classification, object detection, and segmentation. Wider pedestrian detection challenge aims at finding improve solutions for pedestrian detection problem. In this paper, We propose a pedestrian detection system based on RetinaNet. Our solution has scored 0.4061 mAP. The code is available at https://github.com/miltonbd/ECCV_2018_pedestrian_detection_challenege.
Extremely high velocity (EHV) wings, with full widths of 72 to 140 km/s, are seen on the CO J=3-2 lines toward W3 IRS 5, GL 490, NGC 2071, W28 A2, GL 2591, S140, and Cepheus A.   The results of our survey suggest that EHV wings are common around infrared sources of moderate to high luminosity (500 to 4x10^5 Lsun) in dense regions. Line ratios imply that the EHV gas is usually optically thin and warm. Characteristic velocities range from 20 to 40 km/s, yielding timescales of 1600-4200 yr. Since most sources in this study are producing some ionizing photons, these short timescales suggest that neutral winds coexist with ionizing photons.   We examined two possible sources for the EHV CO emission: a neutral stellar wind; and swept-up or entrained molecular gas. Neither can be ruled out. If the high-velocity (HV) gas is swept up by a momentum-conserving stellar wind traced by the extremely high velocity CO emission, most of the C in the winds from luminous objects cannot be in CO. If the EHV and HV forces are equal, the fraction of C in a form other than CO increases with source luminosity and with the production rate of ionizing photons.
Spatial modulations, such as multilayers, to realize topological materials have recently been studied in theoretical and experimental works. In this paper, we investigate properties of the multilayers of the nodal-line semimetal (NLS) and the normal insulator. We consider two types of multilayers, with the stacking direction being perpendicular or parallel to the plane where the nodal line lies. In particular, we show that when the stacking direction is parallel to the plane, the nodal lines remain but they change their shapes because of the folding of the Brillouin zone. We also study the multilayers with magnetization. One can expect that the quantum anomalous Hall (QAH) phase emerges in some cases, depending on the direction of the magnetization. If the magnetization is along the $C_2$-invariant axis, the multilayer becomes the Weyl semimetal phase if the $C_2$-invariant axis intersects the nodal lines, and otherwise it becomes the QAH phases.
A scanning force microscope with a base temperature below 300 mK is used for measuring the local electron density of a two-dimensional electron gas embedded in an Ga[Al]As heterostructure. At different separations between AFM tip and sample, a dc-voltage is applied between the tip and the electron gas while simultaneously recording the frequency shift of the oscillating tip. Using a plate capacitor model the local electron density can be extracted from the data. The result coincides within 10% with the data obtained from transport measurements.
We put forward the idea that the quark-gluon plasma might exist way below the usual confinement temperature $T_c$. Our argument rests on the possibility that the plasma produced in heavy-ion collisions could reach a transient quasi-equilibrium with `over-occupied' gluon density, as advocated by Blaizot et al. Taking further into account that gluons acquire an effective mass by interaction effects, they can have a positive chemical potential and therefore behave similarly to non-relativistic bosons. Relevant properties of this dense state of interacting gluons, which we dub serried glue, can then be inferred on rather general grounds from Maxwell's relation.