ShantanuT01/DACTYL-Pretraining huggingface dataset:
We introduce a notion of fractional Laplacian for functions which grow more than linearly at infinity. In such case, the operator is not defined in the classical sense: nevertheless, we can give an ad-hoc definition which can be useful for applications in various fields, such as blowup and free boundary problems.   In this setting, when the solution has a polynomial growth at infinity, the right hand side of the equation is not just a function, but an equivalence class of functions modulo polynomials of a fixed order.   We also give a sharp version of the Schauder estimates in this framework, in which the full smooth H\"older norm of the solution is controlled in terms of the seminorm of the nonlinearity.   Though the method presented is very general and potentially works for general nonlocal operators, for clarity and concreteness we focus here on the case of the fractional Laplacian.
Random deflated risk models have been considered in recent literatures. In this paper, we investigate second-order tail behavior of the deflated risk X=RS under the assumptions of second-order regular variation on the survival functions of the risk R and the deflator S. Our findings are applied to approximation of Value at Risk, estimation of small tail probability under random deflation and tail asymptotics of aggregated deflated risk
The short review of theoretical aspects of ultra high energy (UHE) neutrinos. The accelerator sources, such as Supernovae remnants, Gamma Ray Bursts, AGN etc are discussed. The top-down sources include Topological Defects (TDs), Superheavy Dark Matter (SHDM) and Mirror Matter. The diffuse fluxes are considered accordingly as that of cosmogenic and top-down neutrinos. Much attention is given to the cascade upper limit to the diffuse neutrino fluxes in the light of Fermi-LAT data on diffuse high energy gamma radiation. This is most general and rigorous upper limit, valid for both cosmogenic and top-down models. At present upper limits from many detectors are close to the cascade upper limit, and 5 yr IceCube upper limit will be well below it.
We study the transient heat current out of a confined electron system into a weakly coupled electrode in response to a voltage switch. We show that the decay of the Coulomb interaction energy for this repulsive system exhibits signatures of electron-electron attraction, and is governed by an interaction-independent rate. This can only be understood from a general duality that relates the non-unitary evolution of a quantum system to that of a dual model with inverted energies. Deriving from the fermion-parity superselection postulate, this duality applies to a large class of open systems.
The branching of (k-1)-Schur functions into k-Schur functions was given by Lapointe, Lam, Morse and Shimozono as chains in a poset on k-shapes. The k-Schur functions are the parameterless case of a more general family of symmetric functions over Q(t), conjectured to satisfy a k-branching formula given by weights on the k-shape poset. A concept of a (co)charge on a k-tableau was defined by Lapointe and Pinto. Although it is not manifestly positive, they prove it is compatible with the k-shape poset for standard k-tableau and the positivity follows. Morse introduced a manifestly positive notion of affine (co)charge on k-tableaux and conjectured that it matches the statistic of Lapointe-Pinto. Here we prove her conjecture and the positivity of k-(co)charge for semi-standard tableaux follows.
Let $k$ be a perfect field of characteristic $p>0$, $\mathcal{V}$ a complete discrete valuation ring with residue field $k$ and field of fractions $K$ of characteristic 0, and $S$ a separated $k$-scheme of finite type. When $S$ is smooth over $k$, we partially prove here a conjecture of Berthelot about the overconvergence of the higher direct images of the structure sheaf under a proper smooth morphism $f:X\to S$; when $k$ is perfect and $\mathcal{V}$ is tamely ramified such direct images are always convergent, not only for the structure sheaf but also for (almost) every convergent $F$-isocrystals. More generally, we prove this overconvergence when $f$ is liftable over $\mathcal{V}$, or when $X$ is a relative complete intersection in some projective spaces over $S$, and taking as coefficients any overconvergent isocrystals. We then apply these results to $L$-functions with coefficients such direct images with Frobenius structure: we derive rationality or meromorphy for these $L$-functions (Dwork's conjecture), and we study their $p$-adic unit zeroes and poles (Katz's conjecture) ; and explicit case concerns the ordinary abelian schemes. A more precise presentation of results by chapters is given in the introduction.
Topological measures and deficient topological measures are defined on open and closed subsets of a topological space, generalize regular Borel measures, and correspond to (non-linear in general) functionals that are linear on singly generated subalgebras or singly generated cones of functions. They lack subadditivity, and many standard techniques of measure theory and functional analysis do not apply to them. Nevertheless, we show that many classical results of probability theory hold for topological and deficient topological measures. In particular, we prove a version of Aleksandrov's Theorem for equivalent definitions of weak convergence of deficient topological measures. We also prove a version of Prokhorov's Theorem which relates the existence of a weakly convergent subsequence in any sequence in a family of topological measures to the characteristics of being a uniformly bounded in variation and uniformly tight family. We define Prokhorov and Kantorovich-Rubenstein metrics and show that convergence in either of them implies weak convergence of (deficient) topological measures on metric spaces. We also generalize many known results about various dense and nowhere dense subsets of deficient topological measures. The present paper constitutes a first step to further research in probability theory and its applications in the context of topological measures and corresponding non-linear functionals.
We measure the sizes of 82 massive (M>10^11 M_sun) galaxies at 1.7<z<3 utilizing deep HST NICMOS data taken in the GOODS North and South fields. Our sample is almost an order of magnitude larger than previous studies at these redshifts, providing the first statistical study of massive galaxy sizes at z>2, confirming the extreme compactness of these galaxies. We split our sample into disk-like (n<2) and spheroid-like (n>2) galaxies based on their Sersic indices, and find that at a given stellar mass disk-like galaxies at z~2.3 are a factor of 2.6+/-0.3 smaller than present day equal mass systems, and spheroid-like galaxies at the same redshifts are 4.3+/-0.7 smaller than comparatively massive elliptical galaxies today. At z>2 our results are compatible with both a leveling off, or a mild evolution in size. Furthermore, the high density (~2x10^10 M_sun kpc^-3) of massive galaxies at these redshifts, which are similar to present day globular clusters, possibly makes any further evolution in sizes beyond z=3 unlikely.
Various lines of evidence suggest that the cores of a large portion of early-type galaxies (ETGs) are virtually evacuated of warm ionised gas. This implies that the Lyman-continuum (LyC) radiation produced by an assumed active galactic nucleus (AGN) can escape from the nuclei of these systems without being locally reprocessed into nebular emission, which would prevent their reliable spectroscopic classification as Seyfert galaxies with standard diagnostic emission-line ratios. The spectral energy distribution (SED) of these ETGs would then lack nebular emission and be essentially composed of an old stellar component and the featureless power-law (PL) continuum from the AGN. A question that arises in this context is whether the AGN component can be detected with current spectral population synthesis in the optical, specifically, whether these techniques effectively place an AGN detection threshold in LyC-leaking galaxies. To quantitatively address this question, we took a combined approach that involves spectral fitting with STARLIGHT of synthetic SEDs composed of stellar emission that characterises a 10 Gyr old ETG and an AGN power-law component that contributes a fraction $0\leq x_{\mathrm{AGN}} < 1$ of the monochromatic luminosity at $\lambda_0=$ 4020 \AA. In addition to a set of fits for PL distributions $F_{\nu} \propto \nu^{-\alpha}$ with the canonical $\alpha=1.5$, we used a base of multiple PLs with $0.5 \leq \alpha \leq 2$ for a grid of synthetic SEDs with a signal-to-noise ratio of 5-$10^3$. Our analysis indicates an effective AGN detection threshold at $x_{\mathrm{AGN}}\simeq 0.26$, which suggests that a considerable fraction of ETGs hosting significant accretion-powered nuclear activity may be missing in the AGN demographics.
We provide a generalization of an algebraic linear combination for the trace of certain elliptic modular forms, and through specializing the expression at a suitable pair consisting of an elliptic curve over algebraic number fields and its a certain cyclic subgroup with finite order, show a formula between distinct algebraic number fields, the one related to modular forms and the other related to elliptic curves.
We construct explicit examples of non-relativistic supersymmetric field theories on curved Newton-Cartan three-manifolds. These results are obtained by performing a null reduction of four-dimensional supersymmetric field theories on Lorentzian manifolds and the Killing spinor equations that their supersymmetry parameters obey. This gives rise to a set of algebraic and differential Killing spinor equations that are obeyed by the supersymmetry parameters of the resulting three-dimensional non-relativistic field theories. We derive necessary and sufficient conditions that determine whether a Newton-Cartan background admits non-trivial solutions of these Killing spinor equations. Two classes of examples of Newton-Cartan backgrounds that obey these conditions are discussed. The first class is characterised by an integrable foliation, corresponding to so-called twistless torsional geometries, and includes manifolds whose spatial slices are isomorphic to the Poincar\'e disc. The second class of examples has a non-integrable foliation structure and corresponds to contact manifolds.
In this note we demonstrate that the algebra associated with coordinate transformations might contain the origins of a scalar field that can behave as an inflaton and/or a source for dark energy. We will call this particular scalar field the diffeomorphism scalar field. In one dimension, the algebra of coordinate transformations is the Virasoro algebra while the algebra of gauge transformations is the Kac-Moody algebra. An interesting representation of these algebras corresponds to certain field theories that have meaning in any dimension. In particular the so called Kac-Moody sector corresponds to Yang-Mills theories and the Virasoro sector corresponds to the diffeomorphism field theory that contains the scalar field and a rank-two symmetric, traceless tensor. We will focus on the contributions of the diffeomorphism scalar field to cosmology. We show that this scalar field can, qualitatively, act as a phantom dark energy, an inflaton, a dark matter source, and the cosmological constant Lambda.
The perovskite-like transition-metal oxide Gd$_{1-x}$Sr$_x$TiO$_3$ is investigated by measurements of resistivity, specific-heat, and electron paramagnetic resonance (EPR). Approaching the metal-to-insulator transition from the metallic regime ($x \geq 0.2$), the Sommerfeld coefficient $\gamma$ of the specific heat becomes strongly enhanced and the resistivity increases quadratically at low temperatures, which both are fingerprints of strong electronic correlations. The temperature dependence of the dynamic susceptibility, as determined from the Gd$^{3+}$-EPR linewidth, signals the importance of strong spin fluctuations, as observed in heavy-fermion compounds.
We present light curve solutions of the W UMa-type eclipsing binary OGLE-GD-ECL-04451, observed by both the \emph{Optical Gravitational Lensing Ex-periment} (\emph{OGLE}) program in 2006 and the \emph{Antarctica Survey Telescope} (\emph{AST3-1}) in 2012 at Dome A. We analyzed this binary system with the Wilson-Devinney(W-D) method 2013 version and derived the mass ratio $q=2.91 \pm 0.07$, the inclination $i=76.86^\circ \pm 0.23^\circ$, and the light variattion amplitud was $0^m.51$ based on the \emph{OGLE} data. From the \emph{AST3-1}'s data, we find that the amplitude dropped to $0^m.44$(2012) and the difference of magnitudes of the two light maxima is $0^m.03$. A hot spot was then added on the surface of the secondary to demonstrate the amplitude change and O'Conell effect of the binary system.
We present a CARMA 1.3 mm continuum survey toward 9 Class 0 protostars in the Perseus molecular cloud at $\sim$0.3$^{\prime\prime}$ (70 AU) resolution. This study approximately doubles the number of Class 0 protostars observed with spatial resolutions $<$ 100 AU at millimeter wavelengths, enabling the presence of protostellar disks and proto-binary systems to be probed. We detect flattened structures with radii $>$ 100 AU around 2 sources (L1448 IRS2 and Per-emb-14) and these sources may be strong disk candidates. Marginally-resolved structures with position angles within 30$^{\circ}$ of perpendicular to the outflow are found toward 3 protostars (L1448 IRS3C, IRAS 03282+3035, and L1448C) and are considered disk candidates. Two others (L1448 IRS3B and IRAS 03292+3039) have resolved structure, possibly indicative of massive inner envelopes or disks; L1448 IRS3B also has a companion separated by 0.9$^{\prime\prime}$ ($\sim$210 AU). IC348-MMS does not have well-resolved structure and the candidate first hydrostatic core L1451-MMS is marginally resolved on 1$^{\prime\prime}$ scales. The strong disk candidate sources were followed-up with C$^{18}$O ($J=2\rightarrow1$) observations, detecting velocity gradients consistent with rotation, but it is unclear if the rotation is Keplerian. We compare the observed visibility amplitudes to radiative transfer models, finding that visibility amplitude ratios suggest a compact component (possibly a disk) is necessary for 5 of 9 Class 0 sources; envelopes alone may explain the other 4 systems. We conclude that there is evidence for the formation of large disks in the Class 0 phase with a range of radii and masses dependent upon their initial formation conditions.
Predictions for the two-photon exchange (TPE) correction to unpolarized $ep$ elastic cross section, obtained within two different approaches, are confronted and discussed in detail. In the first one the TPE correction is extracted from experimental data by applying the Bayesian neural network (BNN) statistical framework. In the other the TPE is given by box diagrams, with the nucleon and the $P_{33}$ resonance as the hadronic intermediate states. Two different form factor parametrizations for both the proton and the $P_{33}$ resonance are taken into consideration. Proton form factors are obtained from the global fit of the full model (with the TPE correction) to the unpolarized cross section data. Predictions of both methods agree well in the intermediate $Q^2$ range, $(1,3)$ GeV$^2$. Above $Q^2=3$ GeV$^2$ the agreement is on $2\sigma$ level. Below $Q^2=1$ GeV$^2$ the consistency between both approaches is broken. The values of the proton radius extracted within both models are given. In both cases predictions for VEPP-3 experiment have been obtained and confronted with the preliminary experimental results.
Hydrogen atmosphere white dwarfs with metals, so-called DAZs, require external accretion of material to explain the presence of weak metal line absorption in their photospheres. The source of this material is currently uknown, but could come from the interstellar medium, unseen companions, or relic planetesimals from asteroid belt or Kuiper belt analogues. Mid-infrared photometry of these white dwarfs provide additional information to solve the mystery of this accretion and to look for evidence of planetary systems that have survived post main sequence evolution. We present {\em Spitzer} IRAC photometry of five DAZs and search for excesses due to unseen companions or circumstellar dust disks. Three of our targets show unexpected {\em deficits} in flux, which we tentatively attribute to absorption due to SiO and CO.
While thousands of experimental physicists and chemists are currently trying to build scalable quantum computers, it appears that simulation of quantum computation will be at least as critical as circuit simulation in classical VLSI design. However, since the work of Richard Feynman in the early 1980s little progress was made in practical quantum simulation. Most researchers focused on polynomial-time simulation of restricted types of quantum circuits that fall short of the full power of quantum computation. Simulating quantum computing devices and useful quantum algorithms on classical hardware now requires excessive computational resources, making many important simulation tasks infeasible. In this work we propose a new technique for gate-level simulation of quantum circuits which greatly reduces the difficulty and cost of such simulations. The proposed technique is implemented in a simulation tool called the Quantum Information Decision Diagram (QuIDD) and evaluated by simulating Grover's quantum search algorithm. The back-end of our package, QuIDD Pro, is based on Binary Decision Diagrams, well-known for their ability to efficiently represent many seemingly intractable combinatorial structures. This reliance on a well-established area of research allows us to take advantage of existing software for BDD manipulation and achieve unparalleled empirical results for quantum simulation.
We consider properties of narrow baryon states observed recently in reaction $pp\to p\pi^+X$. Two lowest of them (with mass 1004 and 1044 MeV, respectively) are stable against strog decay. Moreover we conclude that they cannot decay to $\gamma N$ and thus this states are a kind of metastable levels in quark system. The simplest decay channel is assumed to be $2\gamma N$ and possible quark configuration with such properties is discussed. New experiment for verification of status of this states in $\gamma N$ collision is proposed.
In this paper we prove a conjecture due to Goncharov and Manin which states that the periods of the moduli spaces $\mathfrak{M}_{0,n}$ of Riemann spheres with $n$ marked points are multiple zeta values. In order to do this, we introduce a differential algebra of multiple polylogarithms on $\mathfrak{M}_{0,n}$, and prove that it is closed under the operation of taking primitives. The main idea is to apply a version of Stokes' formula iteratively, and to exploit the geometry of the moduli spaces to reduce each period integral to multiple zeta values.   We also give a geometric interpretation of the double shuffle relations, by showing that they are two extremal cases of general product formulae for periods which arise by considering natural maps between moduli spaces.
The processes driving gas accretion on to supermassive black holes (SMBHs) are still poorly understood. Angular momentum conservation prevents gas within $\sim10\,$pc of the black hole from reaching radii $\sim10^{-3}\,$pc where viscous accretion becomes efficient. Here we present simulations of the collapse of a clumpy shell of swept-up isothermal gas, which is assumed to have formed as a result of feedback from a previous episode of AGN activity. The gas falls towards the SMBH forming clumps and streams, which intersect, collide, and often form a disc. These collisions promote partial cancellations of angular momenta, resulting in further infall and more collisions. This continued collisional cascade generates a tail of gas with sufficiently small angular momenta and provides a viable route for gas inflow to sub-parsec scales. The efficiency of this process hardly depends on details, such as gas temperature, initial virial ratio and power spectrum of the gas distribution, as long as it is not strongly rotating.   Adding star formation to this picture might explain the near-simultaneous formation of the S-stars (from tidally disrupted binaries formed in plunging gas streams) and the sub-parsec young stellar disc around Sgr A$^{\!\star}$.
We present experimental results on thermoelectric power ({\em S}) and electrical resistivity ($\rho $) of pseudobinary alloys Ho(Al$_x$Co$_{1-x}$)$_2$ ($0 \leq x \leq 0.1 $), in the temperature range 4.2 K to 300 K. The work focuses on the effects of static (induced by alloying) and dynamic (induced by temperature) disorder on the magnetic state and electronic transport in a metallic system with itinerant metamagnetic instability. Spatial fluctuations of the local magnetic susceptibility in the alloys lead to a development of a partially ordered magnetic ground state of the itinerant 3d electron system. This results in a strong increase of the residual resistivity and a suppression of the temperature-dependent resistivity. Thermopower exhibits a complex temperature variation in both the magnetically ordered and in the paramagnetic state. This complex temperature variation is referred to the electronic density of states features in vicinity of Fermi energy and to the interplay of magnetic and impurity scattering. Our results indicate that the magnetic enhancement of the Co 3d-band in RCo$_{\rm 2}$--based alloys upon a substitution of Co by non-magnetic elements is mainly related to a progressive localization of the Co -- 3d electrons caused by disorder. We show that the magnitude of the resistivity jump at the Curie temperature for RCo$_{\rm 2}$ compounds exhibiting a first order phase transition is a non-monotonic function of the Curie temperature due to a saturation of the 3d--band spin fluctuation magnitude at high temperatures.
We analyze the biquadratic bilinear Heisenberg magnet on a honeycomb lattice via Schwinger boson formalism. Due to their vulnerability to quantum fluctuations, non conventional lattices (kagome, triangular and honeycomb for example) have been cited as candidates to support spin liquid states. Such states without long range order at zero temperature are known in one-dimensional spin models but their existence in higher dimensional systems is still under debate. Biquadratic interaction is responsible for various possibilities and phases as it is well-founded for one-dimensional systems. Here we have used a bosonic representation to study the properties at zero and finite low temperatures of the biquadratic term in the two-dimensional hexagonal honeycomb lattice. The results show a ordered state at zero temperature but much more fragile than that of a square lattice; the behavior at finite low temperatures is in accordance with expectations.
In metallic ferromagnets, an electric current is accompanied by a flux of angula r momentum, also called spin current. In multilayers, spatial variations of the spin current correspond to drive torques exerted on a magnetic layer. These torq ues result in spin precession above a certain current threshold. The usual kind of spin current is associated with translation of the spin-up and spin-down Ferm i surfaces in momentum space. We discuss a different kind of spin current, assoc iated with expansion and contraction of the Fermi surfaces. It is more nonlocal in nature, and may exist even in locations where the electrical current density is zero. It is larger than the usual spin current, in a ratio of 10 or 100, and is dominant in most cases. The new spin current is proportional to the differenc e Delta-mu = 0.001 eV between spin-up and spin-down Fermi levels, averaged over the entire Fermi surface. Conduction processes, spin relaxation, and spin-wave emission in the multilayer can be described by an equivalent electrical circuit resembling an unbalanced dc Wheatstone bridge. And Delta-mu corresponds to the output voltage of the bridge.