ShantanuT01/DACTYL-Pretraining huggingface dataset:
We prove existence, uniqueness and optimal regularity of solutions to the stationary obstacle problem defined by the fractional Laplacian operator with drift, in the subcritical regime. We localize our problem by considering a suitable extension operator introduced by L. Caffarelli and L. Silvestre. The structure of the extension equation is different from the one considered by L. Caffarelli, S. Salsa and L. Silvestre in their study of the obstacle problem for the fractional Laplacian without drift, in that the obstacle function has less regularity, and exhibits some singularities. To take into account the new features of the problem, we prove a new Almgren-type monotonicity formula, which we then use to establish the optimal regularity of solutions.
Let k be a global field, p an odd prime number different from char(k) and S, T disjoint, finite sets of primes of k. Let G_S^T(k)(p)=Gal(k_S^T(p)|k) be the Galois group of the maximal p-extension of k which is unramified outside S and completely split at T. We prove the existence of a finite set of primes S_0, which can be chosen disjoint from any given set M of Dirichlet density zero, such that the cohomology of G_{S\cup S_0}^T(k)(p) coincides with the etale cohomology of the associated marked arithmetic curve. In particular, cd G_{S\cup S_0}^T(k)(p)=2. Furthermore, we can choose S_0 in such a way that k_{S\cup S_0}^T(p) realizes the maximal p-extension k_\p(p) of the local field k_\p for all \p\in S\cup S_0, the cup-product H^1(G_{S\cup S_0}^T(k)(p),\F_p) \otimes H^1(G_{S\cup S_0}^T(k)(p),\F_p) --> H^2(G_{S\cup S_0}^T(k)(p),\F_p) is surjective and the decomposition groups of the primes in S establish a free product inside G_{S\cup S_0}^T(k)(p). This generalizes previous work of the author where similar results were shown in the case T=\emptyset under the restrictive assumption p\nmid Cl(k) and \zeta_p\notin k.
This work is concerned with the gradient flow of absolutely $p$-homogeneous convex functionals on a Hilbert space, which we show to exhibit finite ($p<2$) or infinite extinction time ($p \geq 2$). We give upper bounds for the finite extinction time and establish convergence rates of the flow. Moreover, we study next order asymptotics and prove that asymptotic profiles of the solution are eigenfunctions of the subdifferential operator of the functional. To this end, we compare with solutions of an ordinary differential equation which describes the evolution of eigenfunction under the flow. Our work applies, for instance, to local and nonlocal versions of PDEs like $p$-Laplacian evolution equations, the porous medium equation, and fast diffusion equations, herewith generalizing many results from the literature to an abstract setting.   We also demonstrate how our theory extends to general homogeneous evolution equations which are not necessarily a gradient flow. Here we discover an interesting integrability condition which characterizes whether or not asymptotic profiles are eigenfunctions.
We investigate the impact of optically induced F\"orster coupling in van der Waals heterostructures consisting of graphene and a monolayer transition metal dichalcogenide (TMD). In particular, we predict the corresponding dephasing rates and a fast energy transfer between the TMD layer and graphene being in the picosecond range. Exemplary we find a transition rate of thermalized excitons of about 4 ps$^{-1}$ in a MoSe$_2$-graphene stack at room temperature. This timescale is in good agreement with the recently measured exciton lifetime in this heterostructure.
Visual attention, derived from cognitive neuroscience, facilitates human perception on the most pertinent subset of the sensory data. Recently, significant efforts have been made to exploit attention schemes to advance computer vision systems. For visual tracking, it is often challenging to track target objects undergoing large appearance changes. Attention maps facilitate visual tracking by selectively paying attention to temporal robust features. Existing tracking-by-detection approaches mainly use additional attention modules to generate feature weights as the classifiers are not equipped with such mechanisms. In this paper, we propose a reciprocative learning algorithm to exploit visual attention for training deep classifiers. The proposed algorithm consists of feed-forward and backward operations to generate attention maps, which serve as regularization terms coupled with the original classification loss function for training. The deep classifier learns to attend to the regions of target objects robust to appearance changes. Extensive experiments on large-scale benchmark datasets show that the proposed attentive tracking method performs favorably against the state-of-the-art approaches.
We have fabricated electric double-layer field-effect devices to electrostatically dope our active materials, either $x$=0.015 Ga$_{1-x}$Mn$_x$As or $x$=3.2$\times10^{-4}$ Ga$_{1-x}$Be$_x$As. The devices are tailored for interrogation of electric field induced changes to the frequency dependent conductivity in the accumulation or depletions layers of the active material via infrared (IR) spectroscopy. The spectra of the (Ga,Be)As-based device reveal electric field induced changes to the IR conductivity consistent with an enhancement or reduction of the Drude response in the accumulation and depletion polarities, respectively. The spectroscopic features of this device are all indicative of metallic conduction within the GaAs host valence band (VB). For the (Ga,Mn)As-based device, the spectra show enhancement of the far-IR itinerant carrier response and broad mid-IR resonance upon hole accumulation, with a decrease of these features in the depletion polarity. These later spectral features demonstrate that conduction in ferromagnetic (FM) Ga$_{1-x}$Mn$_x$As is distinct from genuine metallic behavior due to extended states in the host VB. Furthermore, these data support the notion that a Mn-induced impurity band plays a vital role in the electron dynamics of FM Ga$_{1-x}$Mn$_x$As. We add, a sum-rule analysis of the spectra of our devices suggests that the Mn or Be doping does not lead to a substantial renormalization of the GaAs host VB.
We present a method which uses cuts in colour-colour and reduced proper motion-colour space to select white dwarfs without the recourse to spectroscopy while allowing an adjustable compromise between completeness and efficiency. Rather than just producing a list of white dwarf candidates, our method calculates a probability of being a white dwarf (Pwd) for any object with available multi band photometry and proper motion. We applied this method to all objects in the SDSS DR10 photometric footprint and to a few selected sources in DR7 which did not have reliable photometry in DR9 or DR10. This application results in a sample of 61969 DR10 and 3799 DR7 photometric sources with calculated Pwd from which it is possible to select a sample of ~23000 high-fidelity white dwarf candidates with Teff >~ 7000 K and <= 19. This sample contains over 14000 high confidence white dwarfs candidates which have not yet received spectroscopic follow-up. These numbers show that, to date, the spectroscopic coverage of white dwarfs in the SDSS photometric footprint is, on average, only ~40% complete. While we describe here in detail the application of our selection to the SDSS catalogue, the same method could easily be applied to other multi colour, large area surveys. We also publish a list of 8701 bright (<= 19) WDs with SDSS spectroscopy, of which 1781 are new identifications in DR9/10.
We classify the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation. This classification also includes, as a proper subset, the classification of toric surface patches from geometric modeling which have linear precision. Besides the well-known tensor product patches and B\'ezier triangles, we identify a family of toric patches with trapezoidal shape, each of which has linear precision. B\'ezier triangles and tensor product patches are special cases of trapezoidal patches.
(abridged) The far-UV wavelength range (912-2000A) provides access to atomic and molecular transitions of many species the interstellar medium (ISM), circumgalactic medium (CGM), and intergalactic medium, within phases spanning a wide range of ionization, density, temperature, and molecular gas fraction. Far-UV space telescopes have enabled detailed studies of the ISM in the Milky Way thanks to absorption features appearing in the UV spectra of hot stars and yielding fundamental insights into the composition and physical characteristics of all phases of the ISM along with the processes that influence them. However, we have yet to design a spectrometer able to observe the full UV domain at resolving power R>10^5 with a signal-to-noise ratio SNR>500. Such a resolution is necessary to resolve lines from both the cold molecular hydrogen and the warm metal ions with a turbulent velocity of about 1 km s-1, and to differentiate distinct velocity components. Future UV spectroscopic studies of the Milky Way ISM must revolutionize our understanding of the ISM as a dynamical, unstable, and magnetized medium, and rise to the challenge brought forward by current theories. Another interesting prospect is to transpose the same level of details that has been reached for the Milky Way to the ISM in external galaxies, in particular in metal-poor galaxies, where the ISM chemical composition, physical conditions, and topology change dramatically, with significant consequences on the star-formation properties. Finally, we need to be able to perform statistical analyses of background quasar lines of sight intersecting the CGM of galaxies at various redshifts and to comprehend the role of gas exchanges and flows for galaxy evolution.
Neutron diffraction measurements were carried out on single crystals and powders of Yb2Pt2Pb, where Yb moments form planes of orthogonal dimers in the frustrated Shastry-Sutherland Lattice (SSL). Yb2Pt2Pb orders antiferromagnetically at TN=2.07 K, and the magnetic structure determined from these measurements features the interleaving of two orthogonal sublattices into a 5*5*1 magnetic supercell that is based on stripes with moments perpendicular to the dimer bonds, which are along (110) and (-110). Magnetic fields applied along (110) or (-110) suppress the antiferromagnetic peaks from an individual sublattice, but leave the orthogonal sublattice unaffected, evidence for the Ising character of the Yb moments in Yb2Pt2Pb. Specific heat, magnetic susceptibility, and electrical resistivity measurements concur with neutron elastic scattering results that the longitudinal critical fluctuations are gapped with E about 0.07 meV.
Consider the unsteady neutron transport equation with diffusive boundary condition in 2D convex domains. We establish the diffusive limit with both initial layer and boundary layer corrections. The major difficulty is the lack of regularity in the boundary layer with geometric correction. Our contribution relies on a detailed analysis of asymptotic expansions inspired by the compatibility condition and an intricate $L^{2m}-L^{\infty}$ framework which yields stronger remainder estimates.
We study the Torelli morphism from the moduli space of stable curves to the moduli space of principally polarized stable semi-abelic pairs. We give two characterizations of its fibers, describe its injectivity locus, and give a sharp upper bound on the cardinality of the finite fibers. We also bound the dimension of the infinite fibers. In particular, we obtain that the compactified Torelli map is injective away from curve with separating nodes if and only if the genus is at most 4.
The deflection of light in the strong field limit is an important test for alternative theories of gravity. However, solutions for the metric that allow for analytic computations are not always available. We implement a hybrid analytic-numerical approximation to determine the deflection angle in static, spherically symmetrics pacetimes. We apply this to a set of numerical black hole solutions within the class of theories known as Degenerate Higher Order Scalar-tensor Theories. Comparing our results to a more time consuming full numerical integration, we find that we can accurately describe the deflection angle for light rays passing at arbitrary distances from the photon sphere with a combination of two analytic-numerical approximations. Furthermore, we find a range of parameters where our DHOST black holes predict strong lensing effects whose size is comparable with the uncertainty in the properties of the supermassive black hole in M87 reported by the Event Horizon Telescope, showing that strong lensing is a viable alternative to put constraints on these models.
In this paper, we study the linear systems $|-mK_X|$ on Fano varieties $X$ with klt singularities. In a given dimension $d$, we prove $|-mK_X|$ is non-empty and contains an element with "good singularities" for some natural number $m$ depending only on $d$; if in addition $X$ is $\epsilon$-lc for some $\epsilon>0$, then we show that we can choose $m$ depending only on $d$ and $\epsilon$ so that $|-mK_X|$ defines a birational map. Further, we prove Shokurov's conjecture on boundedness of complements, and show that certain classes of Fano varieties form bounded families.
The bulk of cosmic matter resides in a dilute reservoir that fills the space between galaxies, the intergalactic medium (IGM). The history of this reservoir is intimately tied to the cosmic histories of structure formation, star formation, and supermassive black hole accretion. Our models for the IGM at intermediate redshifts (2<z<5) are a tremendous success, quantitatively explaining the statistics of Lyman-alpha absorption of intergalactic hydrogen. However, at both lower and higher redshifts (and around galaxies) much is still unknown about the IGM. We review the theoretical models and measurements that form the basis for the modern understanding of the IGM, and we discuss unsolved puzzles (ranging from the largely unconstrained process of reionization at high-z to the missing baryon problem at low-z), highlighting the efforts that have the potential to solve them.
The density dependent hadron field (DDRH) theory, previously applied to isospin nuclei and hypernuclei is used to describe $\beta$-stable matter and neutron stars under consideration of the complete baryon octet. The meson-hyperon vertices are derived from Dirac-Brueckner calculations of nuclear matter and extended to hyperons. We examine properties of density dependent interactions derived from the Bonn A and from the Groningen NN potential as well as phenomenological interactions. The consistent treatment of the density dependence introduces rearrangement terms in the expression for the baryon chemical potential. This leads to a more complex condition for the $\beta$-equilibrium compared to standard relativistic mean field (RMF) approaches. We find a strong dependence of the equation of state and the particle distribution on the choice of the vertex density dependence. Results for neutron star masses and radii are presented. We find a good agreement with other models for the maximum mass. Radii are smaller compared to RMF models and indicate a closer agreement with results of non-relativistic Brueckner calculations.
We show an interesting connexion between the coarse-grained distribution function arising in the theory of violent relaxation for collisionless stellar systems (Lynden-Bell 1967) and the notion of superstatistics introduced recently by Beck & Cohen (2003). We also discuss the analogies and differences between the statistical equilibrium state of a multi-components self-gravitating system and the metaequilibrium state of a collisionless stellar system. Finally, we stress the important distinction between mixing entropies, generalized entropies, H-functions, generalized mixing entropies and relative entropies.
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum random trees; second-order limits of distances in random graphs; isometry classes of metric spaces with probability measures; limits of dense random graphs; and more sophisticated uses in finitary combinatorics.
I review the literature on observational aspects of waves in the solar chromosphere in the first part of this contribution. High-frequency waves are invoked to build elaborate cool-star chromosphere heating theories but have not been detected decisively so far, neither as magnetic modes in network elements nor as acoustic modes in below-the-canopy internetwork regions. Three-minute upward-propagating acoustic shocks are thoroughly established through numerical simulation as the cause of intermittent bright internetwork grains, but their pistoning and their role in the low-chromosphere energy budget remain in debate. Three-minute wave interaction with magnetic canopies is a newer interest, presently progressing through numerical simulation. Three-minute umbral flashes and running penumbral waves seem a similar acoustic-shock phenomenon awaiting numerical simulation. The low-frequency network Doppler modulation remains enigmatic. In the second part, I address low-frequency ultraviolet brightness variations of the internetwork chromosphere in more detail. They contribute about half of the internetwork brightness modulation and presumably figure in cool-star basal flux. They appear to be a mixture of inverse-contrast granular overshoot at small scales and gravity-wave interference at mesogranular scales. I present TRACE evidence for the latter interpretation, and speculate that the low-frequency brightness minima map canopy heights.
A local analogue of the Grothendieck Conjecture is an equivalence of the category of complete discrete valuation fields $K$ with finite residue fields of characteristic $p\ne 0$ and the category of absolute Galois groups of fields $K$ together with their ramification filtrations. The case of characteristic 0 fields $K$ was considered by Mochizuki several years ago. Then the author proved it by different method if $p>2$ (but $\operatorname{char}K=0$ or $p$). This paper represents a modified approach: it covers the case $p=2$, contains considerable technical simplifications and replaces the Galois group of $K$ by its maximal pro-$p$-quotient. Special attention is paid to the procedure of recovering field isomorphisms coming from isomorphisms of Galois groups, which are compatible with the corresponding ramification filtrations.
In this work we give a geometric proof of Hrushovski's generalization of the Lang-Weil estimates on the number of points in the intersection of a correspondence with the graph of Frobenius.
This paper compares three different types of ``onset of chaos'' in the logistic and generalized logistic map: the Feigenbaum attractor at the end of the period doubling bifurcations; the tangent bifurcation at the border of the period three window; the transition to chaos in the generalized logistic with inflection 1/2 ($x_{n+1} = \mu x_{n}^{1/2}$), in which the main bifurcation cascade, as well as the bifurcations generated by the periodic windows in the chaotic region, collapse in a single point. The occupation number and the Tsallis entropy are studied. The different regimes of convergence to the attractor, starting from two kinds of far-from-equilibrium initial conditions, are distinguished by the presence or absence of log-log oscillations, by different power-law scalings and by a gap in the saturation levels. We show that the escort distribution implicit in the Tsallis entropy may tune the log-log oscillations or the crossover times.
We discuss two-dimensional mapping of the near-infrared emission-line intensity distributions and kinematics of the narrow-line region (NLR) of NGC 4151, obtained with the Gemini Near-Infrared Integral Field Spectrograph, with a projected spatial resolution of ~8pc. The ionized gas intensity distribution follows the projected bi-cone morphology observed in previous optical narrow-band images, and its kinematics reveal outflows along the bi-cone. We propose a kinematic model in which the gas in the NLR moves at a velocity of ~600 km s^-1 up to ~100 pc from the nucleus. A completely distinct morphology and kinematic structure is observed for the molecular gas, which avoids the region of the bi-cone and has velocities close to systemic, and is consistent with an origin in the galaxy plane. The molecular gas thus traces the AGN feeding, while the ionized gas traces its feedback.
In this study, the quantum state depression (QSD) in semiconductor quantum well (QW) is investigated. The QSD emerge from the ridged geometry of the QW boundary. Ridges impose additional boundary conditions on the electron wave function and some quantum states become forbidden. State density reduces in all energy bands, including conduction band (CB). Hence, electrons, rejected from the filled bands, must occupy quantum states in the empty bands due to Pauli Exclusion principle. Both the electron concentration in CB and Fermi energy increases as in the case of donor doping. Since quantum state density is reduced, the ridged quantum well (RQW) exhibits quantum properties at widths approaching 200 nm. Wide RQW can be used to improve photon confinement in QW-based optoelectronics devices. Reduction in the state density increases the carrier mobility and makes the ballistic transport regime more pronounced in the semiconductor QW devices. Furthermore, the QSD doping does not introduce scattering centers and can be used for power electronics.
We analyze a double-slit experiment when the interfering particle is "mesoscopic" and one endeavors to obtain Welcher Weg information by shining light on it. We derive a compact expression for the visibility of the interference pattern: coherence depends on both the spatial and temporal features of the wave function during its travel to the screen. We set a bound on the temperature of the mesoscopic particle in order that its quantum mechanical coherence be maintained.
The chromatic threshold $\delta_\chi(H,p)$ of a graph $H$ with respect to the random graph $G(n,p)$ is the infimum over $d > 0$ such that the following holds with high probability: the family of $H$-free graphs $G \subset G(n,p)$ with minimum degree $\delta(G) \ge dpn$ has bounded chromatic number. The study of the parameter $\delta_\chi(H) := \delta_\chi(H,1)$ was initiated in 1973 by Erd\H{o}s and Simonovits, and was recently determined for all graphs $H$. In this paper we show that $\delta_\chi(H,p) = \delta_\chi(H)$ for all fixed $p \in (0,1)$, but that typically $\delta_\chi(H,p) \ne \delta_\chi(H)$ if $p = o(1)$. We also make significant progress towards determining $\delta_\chi(H,p)$ for all graphs $H$ in the range $p = n^{-o(1)}$. In sparser random graphs the problem is somewhat more complicated, and is studied in a separate paper.
A visibility representation of a graph $G$ is an assignment of the vertices of $G$ to geometric objects such that vertices are adjacent if and only if their corresponding objects are "visible" each other, that is, there is an uninterrupted channel, usually axis-aligned, between them. Depending on the objects and definition of visibility used, not all graphs are visibility graphs. In such situations, one may be able to obtain a visibility representation of a graph $G$ by allowing vertices to be assigned to more than one object. The {\it visibility number} of a graph $G$ is the minimum $t$ such that $G$ has a representation in which each vertex is assigned to at most $t$ objects.   In this paper, we explore visibility numbers of trees when the vertices are assigned to unit hypercubes in $\mathbb{R}^n$. We use two different models of visibility: when lines of sight can be parallel to any standard basis vector of $\mathbb{R}^n$, and when lines of sight are only parallel to the $n$th standard basis vector in $\mathbb{R}^n$. We establish relationships between these visibility models and their connection to trees with certain cubicity values.