ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Khuri-Treiman formalism models the partial-wave expansion of a scattering amplitude as a sum of three individual truncated series, capturing the low-energy dynamics of the direct and cross channels. We cast this formalism into dispersive equations to study $\pi\pi$ scattering, and compare their expressions and numerical output to the Roy and GKPY equations. We prove that the Khuri-Treiman equations and Roy equations coincide when both are truncated to include only $S$- and $P$-waves. When higher partial waves are included, we find an excellent agreement between the Khuri-Treiman and the GKPY results. This lends credence to the notion that the Khuri-Treiman formalism is a reliable low-energy tool for studying hadronic reaction amplitudes.
Using the theory of minimal models of quasi-projective surfaces we give a new proof of the theorem of Lin-Zaidenberg which says that every topologically contractible algebraic curve in the complex affine plane has equation $X^n=Y^m$ in some algebraic coordinates on the plane. This gives also a proof of the theorem of Abhyankar-Moh-Suzuki concerning embeddings of the complex line into the plane. Independently, we show how to deduce the latter theorem from basic properties of $\mathbb{Q}$-acyclic surfaces.
In this work we discuss the measurement protocols for indirect determination of the isothermal entropy change associated with first order phase transitions in caloric materials. The magneto- structural phase transitions giving rise to giant magnetocaloric effects in Cu-doped MnAs and FeRh are used as case studies to exemplify how badly designed protocols may affect isothermal measure- ments and lead to incorrect entropy change estimations. Isothermal measurement protocols which allow correct assessment of the entropy change around first order phase transitions in both direct and inverse cases are presented.
We discuss properties of particles and fields in a multi-dimensional space-time, where the geometrization of gauge interactions can be performed. As far as spinors are concerned, we outline how the gauge coupling can be recognized by a proper dependence on extra-coordinates and by the dimensional reduction procedure. Finally applications to the Electro-Weak model are presented.
We theoretically propose a method to enhance dramatically a magneto-chiral(MC) effect by using the photonic crystals composed of a multiferroic material. The MC effect, the directional birefringence even for unpolarized light, is so small that it has been difficult to observe experimentally. Two kinds of periodic structures are investigated; (a) a multilayer and (b) a stripe composed of a magneto-chiral material and air. In both cases, the difference in reflectivity between different magnetization directions is enhanced by a factor of hundreds compared with a bulk material.
We report the first Far Ultraviolet Spectroscopic Explorer (FUSE) measurements of diffuse O VI (lambda,lambda 1032,1038) emission from the general diffuse interstellar medium outside of supernova remnants or superbubbles. We observed a 30arcsec x 30arcsec region of the sky centered at l = 315 and b = -41. From the observed intensities (2930+/-290(random)+/-410(systematic) and 1790+/-260(random)+/-250(systematic) photons/cm/cm/s/sr in the 1032 and 1038 Angstrom emission lines, respectively), derived equations, and assumptions about the source location, we calculate the intrinsic intensity, electron density, thermal pressure, and emitting depth. The intensities are too large for the emission to originate solely in the Local Bubble. Thus, we conclude that the Galactic thick disk and lower halo also contribute. High velocity clouds are ruled out because there are none near the pointing direction. The calculated emitting depth is small, indicating that the O VI-bearing gas fills a small volume. The observations can also be used to estimate the cooling rate of the hot interstellar medium and constrain models. The data also yield the first intensity measurement of the C II 3s2 S1/2 to 2p2 P3/2 emission line at 1037 Angstroms and place upper limits on the intensities of ultraviolet line emission from C I, C III, Si II, S III, S IV, S VI, and Fe III.
We focus on a class of BSDEs driven by a cadlag martingale and corresponding Markov type BSDE which arise when the randomness of the driver appears through a Markov process. To those BSDEs we associate a deterministic problem which, when the Markov process is a Brownian diffusion, is nothing else but a parabolic type PDE. The solution of the deterministic problem is intended as decoupled mild solution, and it is formulated with the help of a time-inhomogeneous semigroup.
Ultrathin Bi$_{2}$Te$_{3}$ single crystals laid on Scotch tape are investigated by Fourier transform infrared spectroscopy at $4$K and in a magnetic field up to $35$T. The magneto-transmittance spectra of the Bi$_{2}$% Te$_{3}$/tape composite are analyzed as a two-layer system and the optical conductivity of Bi$_{2}$Te$_{3}$ at different magnetic fields are extracted. We find that magnetic field modifies the optical conductivity in the following ways: (1) Field-induced transfer of the optical weight from the lower frequency regime ($<250$cm$^{-1}$) to the higher frequency regime ($% >250$cm$^{-1}$) due to the redistribution of charge carriers across the Fermi surface. (2) Evolving of a Fano-resonance-like spectral feature from an anti-resonance to a resonance with increasing magnetic field. Such behavior can be attributed to the electron-phonon interactions between the $% E_{u}^{1}$ optical phonon mode and the continuum of electronic transitions. (3) Cyclotron resonance resulting from the inter-valence band Landau level transitions, which can be described by the electrodynamics of massive Dirac holes.
The understanding of magnetic and electronic properties of rare-earth intermetallics is summarized. The properties of NdNi5 or ErNi5 are understood by considering a few electronic subsystems like the f electronic subsystem and the conduction-electron subsystem. The localized f electrons can give a substantial contribution to the low temperature specific heat with the entropy of R ln2 in case of Kramers ions. In this view the heavy-fermion behaviour is related with the removal of the Kramers degeneracy of the ground state of the f electronic subsystem.
We study a class of elliptic operators $A$ with unbounded coefficients defined in $I\times\CR^d$ for some unbounded interval $I\subset\CR$. We prove that, for any $s\in I$, the Cauchy problem $u(s,\cdot)=f\in C_b(\CR^d)$ for the parabolic equation $D_tu=Au$ admits a unique bounded classical solution $u$. This allows to associate an evolution family $\{G(t,s)\}$ with $A$, in a natural way. We study the main properties of this evolution family and prove gradient estimates for the function $G(t,s)f$. Under suitable assumptions, we show that there exists an evolution system of measures for $\{G(t,s)\}$ and we study the first properties of the extension of $G(t,s)$ to the $L^p$-spaces with respect to such measures.
The Hanbury Brown-Twiss experiment has proved to be an effective means of probing statistics of particles. Here, in a set-up involving edge-state quasiparticles in a fractional quantum Hall system, we show that a variant of the experiment composed of two sources and two sinks can be used to unearth fractional statistics. We find a clear cut signature of the statistics in the equal-time current-current correlation function for quasiparticle currents emerging from the two sources and collected at the sinks.
Quantum phase transitions between competing ground-state shapes of atomic nuclei with an odd number of protons or neutrons are investigated in a microscopic framework based on nuclear energy density functional theory and the particle-plus-boson-core coupling scheme. The boson-core Hamiltonian, as well as the single-particle energies and occupation probabilities of the unpaired nucleon, are completely determined by constrained self-consistent mean-field calculations for a specific choice of the energy density functional and paring interaction, and only the strength parameters of the particle-core coupling are adjusted to reproduce selected spectroscopic properties of the odd-mass system. We apply this method to odd-A Eu and Sm isotopes with neutron number $N \approx 90$, and explore the influence of the single unpaired fermion on the occurrence of a shape phase transition. Collective wave functions of low-energy states are used to compute quantities that can be related to quantum order parameters: deformations, excitation energies, E2 transition rates and separation energies, and their evolution with the control parameter (neutron number) is analysed.
Disparity estimation for binocular stereo images finds a wide range of applications. Traditional algorithms may fail on featureless regions, which could be handled by high-level clues such as semantic segments. In this paper, we suggest that appropriate incorporation of semantic cues can greatly rectify prediction in commonly-used disparity estimation frameworks. Our method conducts semantic feature embedding and regularizes semantic cues as the loss term to improve learning disparity. Our unified model SegStereo employs semantic features from segmentation and introduces semantic softmax loss, which helps improve the prediction accuracy of disparity maps. The semantic cues work well in both unsupervised and supervised manners. SegStereo achieves state-of-the-art results on KITTI Stereo benchmark and produces decent prediction on both CityScapes and FlyingThings3D datasets.
Let k be a field of characteristic 0. Let G be a reductive group over the ring of Laurent polynomials R=k[x_1^{\pm 1},...,x_n^{\pm 1}]. We prove that G has isotropic rank >=1 over R iff it has isotropic rank >=1 over the field of fractions k(x_1,...,x_n) of R, and if this is the case, then the natural map H^1_{et}(R,G)\to H^1_{\et}(k(x_1,...,x_n),G) has trivial kernel, and G is loop reductive, i.e. contains a maximal R-torus. In particular, we settle in positive the conjecture of V. Chernousov, P. Gille, and A. Pianzola that H^1_{Zar}(R,G)=* for such groups G. We also deduce that if G is a reductive group over R of isotropic rank >=2, then the natural map of non-stable K_1-functors K_1^G(R)\to K_1^G( k((x_1))...((x_n)) ) is injective, and an isomorphism if G is moreover semisimple.
Let $X$ be a compact real algebraic set of dimension $n$. We prove that every Euclidean continuous map from $X$ into the unit $n$-sphere can be approximated by regulous map. This strengthens and generalizes previously known results.
The origins of the diffuse flux of cosmogenic PeV neutrinos detected in the IceCube experiment during 2010 - 2017 remain unidentified. A population of extragalactic newly born fast spinning pulsars are investigated as possible candidates for generating the PeV energy scale neutrinos. A two-step mechanism of particle acceleration is adopted for transferring energy from star rotation to high energy electrons. Electrons might be boosted up to $\approx 0.01$ EeV energies and above, and produce ultra-high-energy (UHE) neutrinos and gamma rays when these electrons interact with low energy positrons and soft radiations in the acceleration zone. The theoretically derived extragalactic diffuse muon neutrino flux in the energy range [1-10] PeV is found consistent with the IceCube level if only a fraction ($\eta_{k} \approx 0.31\%$) of the total bolometric luminosity of pulsars are transferred to power the PeV neutrinos. Using the above value of the cosmic ray electron loading parameter $\eta_{k}$, the diffuse gamma ray flux from inverse Compton scattering off UHE electrons in the soft radiation field might be predicted from the model.
In this paper we describe an algorithm visiting all numerical semigroups up to a given genus using a well suited representation. The interest of this algorithm is that it fits particularly well the architecture of modern computers allowing very large optimizations: we obtain the number of numerical semigroups of genus g 67 and we confirm the Wilf conjecture for g 60.
The magnetic, thermal and transport properties as well as electronic band structure of MnPtSi are reported. MnPtSi is a metal that undergoes a ferromagnetic transition at $T_{\mathrm{C}}=340$(1) K and a spin-reorientation transition at $T_{\mathrm{N}}=326$(1) K to an antiferromagnetic phase. First-principles electronic structure calculations indicate a not-fully polarized spin state of Mn in a $d^5$ electron configuration with $J=S=3$/2, in agreement with the saturation magnetization of 3~$\mu_{\mathrm{B}}$ in the ordered state and the observed paramagnetic effective moment. A sizeable anomalous Hall effect in the antiferromagnetic phase alongside the computational study suggests that the antiferromagnetic structure is non-collinear. Based on thermodynamic and resistivity data we construct a magnetic phase diagram. Magnetization curves $M$($H$) at low temperatures reveal a metamagnetic transition of spin-flop type. The spin-flopped phase terminates at a critical point with $T_{\mathrm{cr}}\approx 300$ K and $H_{\mathrm{cr}}\approx 10$ kOe, near which a peak of the magnetocaloric entropy change is observed. Using Arrott plot analysis and magnetoresistivity data we argue that the metamagnetic transition is of a first-order type, whereas the strong field dependence of $T_{\mathrm{N}}$ and the linear relationship of the $T_{\mathrm{N}}$ with $M^2$ hint at its magnetoelastic nature.
Microscopic descriptions of exotic nuclei are the subject of much experimental and theoretical effort. Not only are such important in their own right but are also necessary for applications in nuclear astrophysics. Evaluations of model wave functions may be done with analyses of elastic and inelastic scattering from hydrogen. Those require a realistic model of nucleon-nucleus scattering as scattering from hydrogen translates to proton scattering in the inverse kinematics. The Melbourne g-folding model for intermediate energy is presented along with various examples. Implications for existing and future experimental and theoretical work are discussed.
Cosmic voids, the underdense regions in the universe, are particularly sensitive to diffuse density components such as cosmic neutrinos. This sensitivity is enhanced by the match between void sizes and the free-streaming scale of massive neutrinos. Using the massive neutrino simulations \texttt{MassiveNuS}, we investigate the effect of neutrino mass on dark matter halos as a function of environment. We find that the halo mass function depends strongly on neutrino mass and that this dependence is more pronounced in voids than in high-density environments. An observational program that measured the characteristic mass of the most massive halos in voids should be able to place novel constraints on the sum of the masses of neutrinos $\sum m_\nu$. The neutrino mass effect in the simulations is quite strong: In a 512$^3$ $h^{-3}$ Mpc$^3$ survey, the mean mass of the 1000 most massive halos in the void interiors is $(4.82 \pm 0.11) \times 10^{12} h^{-1}M_{\odot}$ for $\sum m_\nu = 0.6$ eV and $(8.21 \pm 0.13) \times 10^{12} h^{-1}M_{\odot}$ for $\sum m_\nu = 0.1$ eV. Subaru (SuMIRe), Euclid and WFIRST will have both spectroscopic and weak lensing surveys. Covering volumes at least 50 times larger than our simulations, they should be sensitive probes of neutrino mass through void substructure.
Results on stability of tautological sheaves on Hilbert schemes of points are extended to higher dimensions and transferred to abelian surfaces and to the restriction of tautological sheaves to generalised Kummer varieties. This provides a big class of new examples of stable sheaves on higher dimensional irreducible symplectic manifolds. Some aspects of deformations of tautological sheaves are studied.
We study Le Potier's strange duality conjecture on a rational surface. We focus on the case involving the moduli space of rank 2 sheaves with trivial first Chern class and second Chern class 2, and the moduli space of 1-dimensional sheaves with determinant $L$ and Euler characteristic 0. We show the conjecture for this case is true under some suitable conditions on $L$, which applies to $L$ ample on any Hirzebruch surface $\Sigma_e:=\mathbb{P}(\mathcal{O}_{\mathbb{P}^1}\oplus\mathcal{O}_{\mathbb{P}^1}(e))$ except for $e=1$. When $e=1$, our result applies to $L=aG+bF$ with $b\geq a+[a/2]$, where $F$ is the fiber class, $G$ is the section class with $G^2=-1$ and $[a/2]$ is the integral part of $a/2$.
Motivated by applications to geometric inequalities, Gozlan, Roberto, Samson, and Tetali introduced a transport problem for `weak' cost functionals. Basic results of optimal transport theory can be extended to this setup in remarkable generality. In this article we collect several problems from different areas that can be recast in the framework of weak transport theory, namely: the Schr\"odinger problem, the Brenier-Strassen theorem, optimal mechanism design, linear transfers and semimartingale transport. Our viewpoint yields a unified approach and often allows to strengthen the original results.
We give a congruence for L-functions coming from affine additive exponential sums over a finite field. Precisely, we give a congruence for certain operators coming from Dwork's theory. This congruence is very similar to the congruence of Manin for the characteristic polynomial of the action of Frobenius on the Jacobian of a curve defined over a finite field.
Text line segmentation is one of the key steps in historical document understanding. It is challenging due to the variety of fonts, contents, writing styles and the quality of documents that have degraded through the years.   In this paper, we address the limitations that currently prevent people from building line segmentation models with a high generalization capacity. We present a study conducted using three state-of-the-art systems Doc-UFCN, dhSegment and ARU-Net and show that it is possible to build generic models trained on a wide variety of historical document datasets that can correctly segment diverse unseen pages. This paper also highlights the importance of the annotations used during training: each existing dataset is annotated differently. We present a unification of the annotations and show its positive impact on the final text recognition results. In this end, we present a complete evaluation strategy using standard pixel-level metrics, object-level ones and introducing goal-oriented metrics.
The observed delay in the arrival times between high and low energy photons in gamma-ray bursts (GRBs) has been shown by Norris et al. to be correlated to the absolute luminosity of a GRB. Despite the apparent importance of this spectral lag, there has yet to be a full explanation of its origin. We put forth that the lag is directly due to the evolution of the GRB spectra. In particular, as the energy at which the GRB's $\nu F_{\nu}$ spectra is a maximum ($E_{pk}$) decays through the four BATSE channels, the photon flux peak in each individual channel will inevitably be offset producing what we measure as lag. We test this hypothesis by measuring the rate of $E_{pk}$ decay ($\Phi_{o}$) for a sample of clean single peaked bursts with measured lag. We find a direct correlation between the decay timescale and the spectral lag, demonstrating the relationship between time delay of the low energy photons and the decay of $E_{pk}$. This implies that the luminosity of a GRB is directly related to the burst's rate of spectral evolution, which we believe begins to reveal the underlying physics behind the lag-luminosity correlation. We discuss several possible mechanisms that could cause the observed evolution and its connection to the luminosity of the burst.
We present measurements of the electronic compressibility, $K$, of bilayer graphene in both zero and finite magnetic fields up to 14 T, and as a function of both the carrier density and electric field perpendicular to the graphene sheet. The low energy hyperbolic band structure of bilayer graphene is clearly revealed in the data, as well as a sizable asymmetry between the conduction and valence bands. A sharp increase in $K^{-1}$ near zero density is observed for increasing electric field strength, signaling the controlled opening of a gap between these bands. At high magnetic fields, broad Landau level (LL) oscillations are observed, directly revealing the doubled degeneracy of the lowest LL and allowing for a determination of the disorder broadening of the levels.
We present deep 3.6 cm radio continuum observations of the H II region NGC 2024 in Orion B obtained using the Very Large Array in its A-configuration, with $0\rlap.{''}2$ angular resolution. We detect a total of 25 compact radio sources in a region of $4' \times 4'$. We discuss the nature of these sources and its relation with the infrared and X-ray objects in the region. At least two of the radio sources are obscured proplyds whose morphology can be used to restrict the location of the main ionizing source of the region. This cluster of radio sources is compared with others that have been found in regions of recent star formation.
A model for two entangled systems in an EPR setting is shown to reproduce the quantum-mechanical outcomes and expectation values. Each system is represented by a small sphere containing a point-like particle embedded in a field. A quantum state appears as an equivalence class of several possible particle-field configurations. Contrarily to Bell-type hidden variables models, the fields account for the non-commutative aspects of the measurements and deny the simultaneous reality of incompatible physical quantities, thereby allowing to escape EPR's ``completeness or locality'' dilemma.
We study randomly growing trees governed by the affine preferential attachment rule. Starting with a seed tree $S$, vertices are attached one by one, each linked by an edge to a random vertex of the current tree, chosen with a probability proportional to an affine function of its degree. This yields a one-parameter family of preferential attachment trees $(T_n^S)_{n\geq|S|}$, of which the linear model is a particular case. Depending on the choice of the parameter, the power-laws governing the degrees in $T_n^S$ have different exponents.   We study the problem of the asymptotic influence of the seed $S$ on the law of $T_n^S$. We show that, for any two distinct seeds $S$ and $S'$, the laws of $T_n^S$ and $T_n^{S'}$ remain at uniformly positive total-variation distance as $n$ increases.   This is a continuation of Curien et al. (2015), which in turn was inspired by a conjecture of Bubeck et al. (2015). The technique developed here is more robust than previous ones and is likely to help in the study of more general attachment mechanisms.