ShantanuT01/DACTYL-Pretraining huggingface dataset:
In a recent work [8], we have described a formulation of a model quantum field theory in terms of a multi-time wave function and proposed a suitable system of multi-time Schroedinger equations governing the evolution of that wave function. Here, we provide further evidence that multi-time wave functions provide a viable formulation of relevant quantum field theories by describing a multi-time formulation, analogous to the one in [8], of another model quantum field theory. This model involves three species of particles, say x-particles, anti-x-particles, and y-particles, and postulates that a y-particle can decay into a pair consisting of an x and an anti-x particle, and that an x-anti-x pair, when they meet, annihilate each other creating a y-particle. (Alternatively, the model can also be interpreted as representing beta decay.) The wave function is a multi-time version of a time-dependent state vector in Fock space (or rather, the appropriate product of Fock spaces) in the particle-position representation. We write down multi-time Schroedinger equations and verify that they are consistent, provided that an even number of the three particle species involved are fermionic.
For a fixed integer h>=1, let G be a tripartite graph with N vertices in each vertex class, N divisible by 6h, such that every vertex is adjacent to at least 2N/3+h-1 vertices in each of the other classes. We show that if N is sufficiently large, then G can be tiled perfectly by copies of K_{h,h,h}. This extends the work in [19] and also gives a sufficient condition for tiling by any (fixed) 3-colorable graph. Furthermore, we show that this minimum-degree condition is best possible and provide very tight bounds when N is divisible by h but not by 6h.
The time-independent Schroedinger and Klein-Gordon equations - as well as any other Helmholtz-like equation - were recently shown to be associated with exact sets of ray-trajectories (coupled by a "Wave Potential" function encoded in their structure itself) describing any kind of wave-like features, such as diffraction and interference. This property suggests to view Wave Mechanics as a direct, causal and realistic, extension of Classical Mechanics, based on exact trajectories and motion laws of point-like particles "piloted" by de Broglie's matter waves and avoiding the probabilistic content and the wave-packets both of the standard Copenhagen interpretation and of Bohm's theory.
Weakly supervised object detection (WSOD) focuses on training object detector with only image-level annotations, and is challenging due to the gap between the supervision and the objective. Most of existing approaches model WSOD as a multiple instance learning (MIL) problem. However, we observe that the result of MIL based detector is unstable, i.e., the most confident bounding boxes change significantly when using different initializations. We quantitatively demonstrate the instability by introducing a metric to measure it, and empirically analyze the reason of instability. Although the instability seems harmful for detection task, we argue that it can be utilized to improve the performance by fusing the results of differently initialized detectors. To implement this idea, we propose an end-to-end framework with multiple detection branches, and introduce a simple fusion strategy. We further propose an orthogonal initialization method to increase the difference between detection branches. By utilizing the instability, we achieve 52.6% and 48.0% mAP on the challenging PASCAL VOC 2007 and 2012 datasets, which are both the new state-of-the-arts.
Improving earlier estimates of several authors we show that the number E(X) of Goldbach exceptional even integers (that is, even integers which cannot be written as the sum of two primesw) below X satisfies tho bound E(X) < X^0.72 for sufficiently large X. In the proof crucial role is played by the explicit formula for the contribution of the major arcs proved in Part I of this series (arXiv:1804.05561). In this new version some misprints are corrected and an explanatory sentence is added to the common proof of theorems C and D.
For a multipartite quantum system of the dimension $d_1\otimes d_2\otimes... d_n$, $d_1\ge d_2\ge...\ge d_n$, is there an entangled state {\em maximum} in the sense that all other states in the system can be obtained from the state through local quantum operations and classical communications (LOCC)? When $d_1\ge\Pi_{i=2}^n d_i$, such state exists. We show that this condition is also necessary. Our proof, somewhat surprisingly, uses results from algebraic complexity theory.
We present results from a 35 ks {\em Chandra}/ACIS-I observation of the hot ICM around the FR II radio galaxy 3C 388. 3C 388 resides in a cluster environment with an ICM temperature of $\sim$3.5 keV. We detect cavities in the ICM coincident with the radio lobes. The enthalpy of these cavities is $\sim1.2\times10^{60}$ ergs. The work done on the gas by the inflation of the lobes is $\sim3\times10^{59}$ ergs, or $\sim$0.87 keV per particle out to the radius of the lobes. The radiative timescale for gas at the center of the cluster at the current temperature is a few Gyrs. The gas in the core was probably cooler and denser before the outburst, so the cooling time was considerably shorter. We are therefore likely to be witnessing the quenching of a cluster cooling flow by a radio galaxy outburst. The mechanical power of the lobes is at least 20 times larger than the radiative losses out to the cooling radius. Outbursts of similar power with a $\sim$5% duty cycle would be more than sufficient to continually reheat the cluster core over the Hubble time and prevent the cooling of any significant amount of gas. The mechanical power of the outburst is also roughly two orders of magnitude larger than either the X-ray luminosity of the active nucleus or the radio luminosity of the lobes. The equipartition pressure of the radio lobes is more than an order of magnitude lower than that of the ambient medium, indicating that the pressure of the lobe is dominated by something other than the relativistic electrons radiating at GHz frequencies.
We examine the generation of a magnetic field in a solar-like star and its effects on the internal distribution of the angular velocity. We suggest that the evolution of a rotating star with magnetic fields leads to an equilibrium value of the differential rotation. This equilibrium is determined by the magnetic coupling, which favours a constant rotation profile, and meridional circulation which tends to build differential rotation. The global equilibrium stage is close to solid body rotation between about 0.7 and 0.2 R_sun, in good agreement with helioseismic measurements.
We prove Orlicz-space versions of Hardy and Landau-Kolmogorov inequalities for Gaussian measures on the n-dimensional Euclidean space.
The theory for time-resolved photoemission spectroscopy as applied to pump-probe experiments is developed and solved for the generic case of a strongly correlated material. The formal development incorporates all of the nonequilibrium effects of the pump pulse and the finite time width of the probe pulse. While our formal development is completely general, in our numerical illustration for the Hubbard model, we assume the pump pulse drives the electrons into a nonequilibrium configuration, which rapidly thermalizes to create a hot (quasi-equilibrium) electronic system, and we then study the effects of windowing that arise from the finite width of the probe pulse. We find sharp features in the spectra are broadened, particularly the quasiparticle peak of strongly correlated metals at low temperature.
Let f_n^r(k) be the number of 132-avoiding permutations on n letters that contain exactly r occurrences of 12... k, and let F_r(x;k) and F(x,y;k) be the generating functions defined by $F_r(x;k)=\sum_{n\gs0} f_n^r(k)x^n$ and $F(x,y;k)=\sum_{r\gs0}F_r(x;k)y^r$. We find an explcit expression for F(x,y;k) in the form of a continued fraction. This allows us to express F_r(x;k) for $1\ls r\ls k$ via Chebyshev polynomials of the second kind.
The research of infall motion is a common means to study molecular cloud dynamics and the early process of star formation. Many works had been done in-depth research on infall. We searched the literature related to infall study of molecular cloud since 1994, summarized the infall sources identified by the authors. A total of 456 infall sources are catalogued. We classify them into high-mass and low-mass sources, in which the high-mass sources are divided into three evolutionary stages: prestellar, protostellar and HII region. We divide the sources into clumps and cores according to their sizes. The H$_2$ column density values range from 1.21$\times$ 10$^{21}$ to 9.75 $\times$ 10$^{24}$ cm$^{-2}$, with a median value of 4.17$\times$ 10$^{22}$ cm$^{-2}$. The H$_2$ column densities of high-mass and low-mass sources are significantly separated. The median value of infall velocity for high-mass clumps is 1.12 km s$^{-1}$, and the infall velocities of low-mass cores are virtually all less than 0.5 km s$^{-1}$. There is no obvious difference between different stages of evolution. The mass infall rates of low-mass cores are between 10$^{-7}$ and 10$^{-4}$ M$_{\odot} \text{yr}^{-1}$, and those of high-mass clumps are between 10$^{-4}$ and 10$^{-1}$ M$_{\odot} \text{yr}^{-1}$ with only one exception. We do not find that the mass infall rates vary with evolutionary stages.
The ground-state phase diagram of a frustrated S=1 Heisenberg spin chain with uniaxial single-ion-type anisotropy is studied using the infinite-system density-matrix renormalization-group method. Particular attention is paid to "chiral" phases, in which the long-range order parameter is a vector chirality. It is found that, in addition to the Haldane, large-D (LD), and double-Haldane phases, the phase diagram includes three different chiral phases, i.e., the gapless chiral, chiral-Haldane, and chiral-LD phases. These chiral phases are distinguished from each other by the energy gap and the string long-range order.
We discuss the implementation of leading-order photon production in nonequilibrium partonic transport simulations. In this framework photons are produced by microscopic scatterings, where we include the exact matrix elements of Compton scattering, quark-antiquark annihilation, and bremsstrahlung processes. We show how the hard-thermal loop inspired screening of propagators has to be modified such that the microscopic production rate agrees well with the analytically known resummed leading-order rate. We model the complete quark-gluon plasma phase of heavy-ion collisions by using the partonic transport approach called the Boltzmann approach to multiparton scatterings (BAMPS), which solves the ultrarelativistic Boltzmann equation with Monte Carlo methods. We show photon spectra and elliptic flow of photons from BAMPS and discuss nonequilibrium effects. Due to the slow quark chemical equilibration in BAMPS, the yield is lower than the results from other groups; in turn we see a strong effect from scatterings of energetic jet-like partons with the medium. This nonequilibrium photon production can dominate the thermal emission, such that the spectra are harder and the photonic elliptic flow of the quark-gluon plasma becomes negative.
We study {\em sign-restricted matrices} (SRMs), a class of rectangular $(0, \pm 1)$-matrices generalizing the alternating sign matrices (ASMs). In an SRM each partial column sum, starting from row 1, equals 0 or 1, and each partial row sum, starting from column 1, is nonnegative. We determine the maximum number of nonzeros in SRMs and characterize the possible row and column sum vectors. Moreover, a number of results on interchange operations are shown, both for SRMs and, more generally, for $(0, \pm 1)$-matrices. The Bruhat order on ASMs can be extended to SRMs with the result a distributive lattice. Also, we study polytopes associated with SRMs and some relates decompositions.
Semiconductor spin qubits based on spin-orbit states are responsive to electric field excitation allowing for practical, fast and potentially scalable qubit control. Spin-electric susceptibility, however, renders these qubits generally vulnerable to electrical noise, which limits their coherence time. Here we report on a spin-orbit qubit consisting of a single hole electrostatically confined in a natural silicon metal-oxide-semiconductor device. By varying the magnetic field orientation, we reveal the existence of operation sweet spots where the impact of charge noise is minimized while preserving an efficient electric-dipole spin control. We correspondingly observe an extension of the Hahn-echo coherence time up to 88 $\mu$s, exceeding by an order of magnitude the best reported values for hole-spin qubits, and approaching the state-of-the-art for electron spin qubits with synthetic spin-orbit coupling in isotopically-purified silicon. This finding largely enhances the prospects of silicon-based hole spin qubits for scalable quantum information processing.
We propose a nonlocal entanglement concentration protocol (ECP) for $N$-photon systems in a partially entangled W state, resorting to some ancillary single photons and the parity-check measurement based on cross-Kerr nonlinearity. One party in quantum communication first performs a parity-check measurement on her photon in an $N$-photon system and an ancillary photon, and then she picks up the even-parity instance for obtaining the standard W state. When she obtains an odd-parity instance, the system is in a less-entanglement state and it is the resource in the next round of entanglement concentration. By iterating the entanglement concentration process several times, the present ECP has the total success probability approaching to the limit in theory. The present ECP has the advantage of a high success probability. Moreover, the present ECP requires only the $N$-photon system itself and some ancillary single photons, not two copies of the systems, which decreases the difficulty of its implementation largely in experiment. It maybe have good applications in quantum communication in future.
Two port s-matrix for a complex PT-symmetric potential may have uni-modular eigenvalues. If this happens for all energies, there occurs a perfect emission of waves at both ends. We call this phenomenon transparency which is distinctly different from coherent perfect absorption with or without lasing. Using the versatile PT-symmetric complex Scarf II (scattering) potential, we demonstrate analytically that the transparency can occur regardless of whether PT-symmetry is unbroken or broken or if there are only scattering states. In these three cases, for a given value of the strength of the real part; the strength of the imaginary part $|V_2|$ of the potential lies in $(0, V_{\alpha}), (V_{\alpha}, V_{\beta})$ and $(0,V_{\beta})$ respectively. Several other numerically solved potentials also support our findings.
Building on the work of Goto, Nishida and Watanabe on symbolic Rees algebras of monomial primes, we prove that the moduli space of stable rational curves with n punctures is not a Mori Dream Space for n>133. This answers the question of Hu and Keel.
It is shown here that the diameter of the $d$-dimensional cyclohedron is not greater than $\lceil 5d/2\rceil-2$. It is also shown that the $5/2$ coefficient in this upper bound is asymptotically sharp. More precisely, the $d$-dimensional cyclohedron has diameter at least $5d/2-4\sqrt{d}-4$.
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant entities in these equations. Ambiguities in the definitions of the electromagnetic fields are pointed out, and in fact are shown to be essential in such a system of coordinates. The Lorentz force is found to have an extra term in this frame, which has its origins in relativistic mass. A related term in the energy equation, which allows inertia to be gained even during strict corotation, suggests ways existing pulsar magnetosphere models may be modified to match observed `braking indices' more closely.
We search for the gamma-ray counterparts of stellar-mass black holes using long-term Fermi archive to investigate the electrostatic acceleration of electrons and positrons in the vicinity of the event horizon, by applying the pulsar outer-gap model to their magnetosphere. When a black hole transient (BHT) is in a low-hard or quiescent state, the radiatively inefficient accretion flow cannot emit enough MeV photons that are required to sustain the force-free magnetosphere in the polar funnel via two-photon collisions. In this charge-starved gap region, an electric field arises along the magnetic field lines to accelerate electrons and positrons into ultra-relativistic energies. These relativistic leptons emit copious gamma-rays via the curvature and inverse-Compton (IC) processes. It is found that these gamma-ray emissions exhibit a flaring activity when the plasma accretion rate stays typically between 0.01 and 0.005 percent of the Eddington value for rapidly rotating, stellar-mass black holes. By analyzing the detection limit determined from archival Fermi/LAT data, we find that the 7-year averaged duty cycle of such flaring activities should be less than 5% and 10% for XTE J1118+480 and 1A 0620-00, respectively, and that the detection limit is comparable to the theoretical prediction for V404 Cyg. It is predicted that the gap emission can be discriminated from the jet emission, if we investigate the high-energy spectral behaviour or observe nearby BHTs during deep quiescence simultaneously in infrared wavelength and very-high energies.
Recent reports claiming tentative association of the massive star binary system gamma^2 Velorum (WR 11) with a high-energy gamma-ray source observed by Fermi-LAT contrast the so-far exclusive role of Eta Carinae as the hitherto only detected gamma-ray emitter in the source class of particle-accelerating colliding-wind binary systems. We aim to shed light on this claim of association by providing dedicated model predictions for the nonthermal photon emission spectrum of WR 11. We use three-dimensional magneto-hydrodynamic modeling to trace the structure and conditions of the wind-collision region of WR 11 throughout its 78.5 day orbit, including the important effect of radiative braking in the stellar winds. A transport equation is then solved in the wind-collision region to determine the population of relativistic electrons and protons which are subsequently used to compute nonthermal photon emission components. We find that - if WR 11 be indeed confirmed as the responsible object for the observed gamma-ray emission - its radiation will unavoidably be of hadronic origin owing to the strong radiation fields in the binary system which inhibit the acceleration of electrons to energies suffciently high for observable inverse Compton radiation. Different conditions in wind-collision region near the apastron and periastron configuration lead to significant variability on orbital time scales. The bulk of the hadronic gamma-ray emission originates at a 400 solar radii wide region at the apex.
A numerical method close to the Strutinsky procedure (but better) is proposed to calculate the deformation energy of nuclei. Quadrupole (triaxial) deformations are considered. Theoretical as well as practical aspects of the method are reviewed in this paper. A complete fortran program illustrates the feasibility of the method.
Let $\mathcal{X}$ be a tame proper Deligne-Mumford stack of the form $[M/G]$ where $M$ is a scheme and $G$ is an algebraic group. We prove that the stack $\mathcal{K}_{g,n}(\mathcal{X},d)$ of twisted stable maps is a quotient stack and can be embedded into a smooth Deligne-Mumford stack. When $G$ is finite, we give a more precise construction of $\mathcal{K}_{g,n}(\mathcal{X},d)$ using Hilbert schemes and admissible $G$-covers.
Even though the term `organic electronics' evokes rather organic devices, a significant part of its scope deals with physical properties of `active elements' such as organic films and interfaces. Examination of the film growth and the evolution of the interface formation are particularly needful for the understanding a mechanism controlling their final properties. Performing such experiments in an ultra-high vacuum allows both to `stretch' the time scale for pseudo real-time observations and to control properties of the probed systems on the atomic level. Photoemission technique probes directly electronic and chemical structure and it has thereby established among major tools employed in the field. This review primarily focuses to electronic properties of oligomeric molecular films and their interfaces examined by photoemission. Yet, it does not aspire after a complete overview on the topic; it rather aims to otherwise standard issues encountered at the photoemission characterization and analysis of the organic materials, though requiring to consider particularities of molecular films in terms of the growth, electronic properties, and their characterization and analysis. In particular, the fundamental electronic parameters of molecular films such as the work function, the ionization energy, and the interfacial energy level alignment, and their interplay, will be pursued with considering often neglected influence of the molecular orientation. Further, the implication on the band bending in molecular films based on photoemission characterization, and a model on the driving mechanism for the interfacial energy level alignment will be addressed.
By constructing a new family of successful couplings, the Driver-type integration by parts formula is established for the operator associated with stochastic differential equation driven by fractional Brownian motion. As applications, shift Harnack type inequalities are presented and then the absolute continuity of the solution is proved.
Unipolar induction (UI) is a fundamental physical process, which occurs when a conducting body transverses a magnetic field. It has been suggested that UI is operating in RX J0806+15 and RX J1914+24, which are believed to be ultra-compact binaries with orbital periods of 5.4 min and 9.6 min respectively. The UI model predicts that those two sources may be electron cyclotron maser sources at radio wavelengths. Other systems in which UI has been predicted to occur are short period extra-solar terrestrial planets with conducting cores. If UI is present, circularly polarised radio emission is predicted to be emitted. We have searched for this predicted radio emission from short period binaries using the VLA and ATCA. In one epoch we find evidence for a radio source, coincident in position with the optical position of RX J0806+15. Although we cannot completely exclude that this is a chance alignment between the position of RX J0806+15 and an artifact in the data reduction process, the fact that it was detected at a significance level of 5.8 sigma and found to be transient, suggests that it is more likely that RX J0806+15 is a transient radio source. We find an upper limit on the degree of circular polarisation to be ~50%. The inferred brightness temperature exceeds 10^18 K, which is too high for any known incoherent process, but is consistent with maser emission and UI being the driving mechanism. We did not detect radio emission from ES Cet, RX J1914+24 or Gliese 876.