ShantanuT01/DACTYL-Pretraining huggingface dataset:
Finding an Andrews--Gordon type generating function identity for a linked partition ideal is difficult in most cases. In this paper, we will handle this problem in the setting of graph theory. With the generating function of directed graphs with an ``empty'' vertex, we then turn our attention to a $q$-difference system. This $q$-difference system eventually yields a factorization problem of a special type of column functional vectors involving $q$-multi-summations. Finally, using a recurrence relation satisfied by certain $q$-multi-summations, we are able to provide non-computer-assisted proofs of some Andrews--Gordon type generating function identities. These proofs also have an interesting connection with binary trees.
We re-examine the assembly history of field spheroidals as a potentially powerful discriminant of galaxy formation models. Whereas monolithic collapse and hierarchical, merger-driven, models suggest radically different histories for these galaxies, neither the theoretical predictions nor the observational data for field galaxies have been sufficiently reliable for precise conclusions to be drawn. A major difficulty in interpreting the observations, reviewed here, concerns the taxonomic definition of spheroidals in merger-based models. Using quantitative measures of recent star formation activity drawn from the internal properties of a sample of distant field galaxies in the Hubble Deep Fields, we undertake a new analysis to assess the continuous formation of spheroidal galaxies. Whereas abundances and redshift distributions of modelled spheroidals are fairly insensitive to their formation path, we demonstrate that the distribution and amount of blue light arising from recent mergers provides a more sensitive approach. With the limited resolved data currently available, the rate of mass assembly implied by the observed colour inhomogeneities is compared to that expected in popular Lambda-dominated cold dark matter models of structure formation. These models produce as many highly inhomogeneous spheroidals as observed, but underpredict the proportion of homogeneous, passive objects. We conclude that colour inhomogeneities, particularly when combined with spectroscopic diagnostics for large, representative samples of field spheroidals, will be a more valuable test of their physical assembly history than basic source counts and redshift distributions. Securing such data should be a high priority for the Advanced Camera for Surveys on Hubble Space Telescope.
We report the detection of the first extrasolar planet, ET-1 (HD 102195b), using the Exoplanet Tracker (ET), a new generation Doppler instrument. The planet orbits HD 102195, a young star with solar metallicity that may be part of the local association. The planet imparts radial velocity variability to the star with a semiamplitude of $63.4\pm2.0$ m s$^{-1}$ and a period of 4.11 days. The planetary minimum mass ($m \sin i$) is $0.488\pm0.015$ $M_J$.
The partition function of a family of four dimensional N=2 gauge theories has been recently related to correlation functions of two dimensional conformal Toda field theories. For SU(2) gauge theories, the associated two dimensional theory is A_1 conformal Toda field theory, i.e. Liouville theory. For this case the relation has been extended showing that the expectation value of gauge theory loop operators can be reproduced in Liouville theory inserting in the correlators the monodromy of chiral degenerate fields. In this paper we study Wilson loops in SU(N) gauge theories in the fundamental and anti-fundamental representation of the gauge group and show that they are associated to monodromies of a certain chiral degenerate operator of A_{N-1} Toda field theory. The orientation of the curve along which the monodromy is evaluated selects between fundamental and anti-fundamental representation. The analysis is performed using properties of the monodromy group of the generalized hypergeometric equation, the differential equation satisfied by a class of four point functions relevant for our computation.
In this paper we present a finite field analogue for one of the Appell series. We shall derive its transformations, reduction formulas as well as generating functions.
During its nine-year lifetime, the Energetic Gamma Ray Experiment Telescope (EGRET) on the Compton Gamma Ray Observatory (CGRO) detected 1506 cosmic photons with measured energy E>10 GeV. Of this number, 187 are found within 1 degree of sources that are listed in the Third EGRET Catalog and were included in determining the detection likelihood, flux, and spectra of those sources. In particular, five detected EGRET pulsars are found to have events above 10 GeV, and together they account for 37 events. A pulsar not included in the Third EGRET Catalog has 2 events, both with the same phase and in one peak of the lower-energy gamma-ray light-curve. Most of the remaining 1319 events appear to be diffuse Galactic and extragalactic radiation based on the similarity of the their spatial and energy distributions with the diffuse model and in the E>100, MeV emission. No significant time clustering which would suggest a burst was detected.
We study the Poisson equation in a perforated domain with homogeneous Dirichlet boundary conditions. The size of the perforations is denoted by $\epsilon$ > 0, and is proportional to the distance between neighbouring perforations. In the periodic case, the homogenized problem (obtained in the limit $\epsilon$ $\rightarrow$ 0) is well understood (see [21]). We extend these results to a non-periodic case which is defined as a localized deformation of the periodic setting. We propose geometric assumptions that make precise this setting, and we prove results which extend those of the periodic case: existence of a corrector, convergence to the homogenized problem, and two-scale expansion.
We study the effective ways for generating the linear see-saw neutrino mass relations and large neutrino mixing angles in two classes of grand unified SO(10) models where the texture of Dirac neutrino mass matrix is related to either the charged lepton mass matrix (case A) or the up-quark mass matrix (case B). We also briefly analyse their stability criteria and they are found to be stable under under radiative corrections at low energies.
(Abridged) Exploiting the sensitivity and broad band width of NOEMA, we have studied the molecular gas and dust in the galaxy HerBS-89a, at z=2.95. High angular resolution images reveal a partial 1.0" diameter Einstein ring in the dust continuum emission and the molecular emission lines of 12CO(9-8) and H2O(2_02-1_11). We report the detection of the three fundamental transitions of the molecular ion OH+, seen in absorption; the molecular ion CH+(1-0) seen in absorption (and tentatively in emission); two transitions of amidogen (NH2), seen in emission; and HCN(11-10) and/or NH(1_2-0_1) seen in absorption. The NOEMA data are complemented with VLA data tracing the 12CO(1-0) emission line, which provides a measurement of the total mass of molecular gas and an anchor for a CO excitation analysis. In addition, we present HST imaging that reveals the foreground lensing galaxy in the near-infrared. Together with data from the GTC, we derive a photometric redshift of z(phot)~0.9 for the foreground lensing galaxy. Modelling the lensing of HerBS-89a, we reconstruct the dust continuum and molecular emission lines (magnified by a factor ~4-5) in the source plane. The 12CO(9-8) and H2O emission lines have comparable spatial and kinematic distributions; the source-plane reconstructions do not clearly distinguish between a one-component and a two-component scenario, but the latter accounts for the observed broad line widths. HerBS-89a is a powerful star forming galaxy with a dust-to-gas ratio delta(GDR)~80, a SFR = 614 +/- 59 Msun/yr and a depletion timescale tau(depl) = (3.4 +/- 1.0) 1e8 years. The OH+ and CH+ absorption lines, all have their main velocity component red-shifted by \Delta(V)~100 km/s relative to the global CO reservoir. We argue that these absorption lines trace a rare example of gas inflow towards the center of the galaxy.
Given a collection $\C$ of subsets of a finite set $X$, let $\bigcup \C = \cup_{S \in \C}S$. Philip Hall's celebrated theorem \cite{hall} concerning `systems of distinct representatives' tells us that for any collection $\C$ of subsets of $X$ there exists an injective (i.e. one-to-one) function $f: \C \to X$ with $f(S) \in S$ for all $S \in \C$ if and and only if $\C$ satisfies the property that for all non-empty subsets $\C'$ of $\C$ we have $|\bigcup \C'| \geq |\C'|$. Here we show that if the condition   $|\bigcup \C'| \geq |\C'|$ is replaced by the stronger condition $|\bigcup \C'| \geq |\C'|+2$, then we obtain a characterization of this condition for a collection of 3-element subsets of $X$ in terms of the existence of an injective function from $\C$ to the vertices of a tree whose vertex set includes $X$ and that satisfies a certain median condition. We then describe an extension of this result to collections of arbitrary-cardinality subsets of $X$.
Asteroseismology allows us to probe the physical conditions inside the core of red giant stars. This relies on the properties of the global oscillations with a mixed character that are highly sensitive to the physical properties of the core. However, overlapping rotational splittings and mixed-mode spacings result in complex structures in the mixed-mode pattern, which severely complicates its identification and the measurement of the asymptotic period spacing. This work aims at disentangling the rotational splittings from the mixed-mode spacings, in order to open the way to a fully automated analysis of large data sets. An analytical development of the mixed-mode asymptotic expansion is used to derive the period spacing between two consecutive mixed modes. The \'echelle diagrams constructed with the appropriately stretched periods are used to exhibit the structure of the gravity modes and of the rotational splittings. We propose a new view on the mixed-mode oscillation pattern based on corrected periods, called stretched periods, that mimic the evenly spaced gravity-mode pattern. This provides a direct understanding of all oscillation components, even in the case of rapid rotation. The measurement of the asymptotic period spacing and the signature of the structural glitches on mixed modes are then made easy. This work opens the possibility to derive all seismic global parameters in an automated way, including the identification of the different rotational multiplets and the measurement of the rotational splitting, even when this splitting is significantly larger than the period spacing. Revealing buoyancy glitches provides a detailed view on the radiative core.
We present the results of energy-dependent and single-energy partial-wave analyses of pi-N elastic scattering data with laboratory kinetic energies below 2.1 GeV. We have considered the effect of adding dispersion-relation constraints required for a more reliable extraction of the pi-N sigma term. The results of these new fits are compared with those generated previously, using a reduced set of constraints, and with a fit which has only utilized forward constraints associated with the S-wave scattering lengths. We compare the results in terms of their resonance spectra and preferred values for the pi-N-N coupling and pi-N sigma term.
In this work, we prove a generalization of Osgood's test for the explosion of the solutions of initial-value problems. We also establish a comparison criterion for the solution of integral equations with noise, and provide estimations of the time of explosion of problems arising in the investigation of crack failures where the noise is the absolute value of the Brownian motion
An effective Hamiltonian and equations of motion for treating both the resonant dipole-dipole interaction between two-level atoms and the resonant atom-field interaction are derived, which can suitably be used for studying the influence of arbitrary dispersing and absorbing material surroundings on these interactions. It is shown that the dipole-dipole interaction and the atom-field interaction, respectively, are closely related to the real part and the imaginary part of the (classical) Green tensor. The theory is applied to the study of the transient behavior of two atoms that initially share a single excitation, with special emphasis on the role of the two competing processes of virtual and real photon exchange in the energy transfer between the atoms. To illustrate the powerfulness of the theory, specific results for the case of the atoms being near a dispersing and absorbing microsphere are presented. In particular, the regimes of weak and strong atom-field coupling are addressed.
We study the dynamical response of frustrated, quasi-one-dimensional spin-1/2 Heisenberg antiferromagnets at finite temperatures. We allow for the presence of a Dzyaloshinskii-Moriya interaction. We concentrate on a model of weakly coupled planes of anisotropic triangular lattices. Combining exact results for the dynamical response of one dimensional Heisenberg chains with a Random Phase Approximation (RPA) in the frustrated interchain couplings, we calculate the dynamical susceptibility in the disordered phase. We investigate the instability of the disordered phase to the formation of collective modes. We find a very weak instability to the formation of incommensurate magnetic order and determine the ordering temperature and wave vector. We also determine the effects of uniform magnetic fields on the ordering transition.
Intracellular transport in living cells is often spatially inhomogeneous with an accelerated effective diffusion close to the cell membrane and a ballistic motion away from the centrosome due to active transport along actin filaments and microtubules, respectively. Recently it was reported that the mean first passage time (MFPT) for transport to a specific area on the cell membrane is minimal for an optimal actin cortex width. In this paper we ask whether this optimization in a two-compartment domain can also be achieved by passive Brownian particles. We consider a Brownian motion with different diffusion constants in the two shells and a potential barrier between the two and investigate the narrow escape problem by calculating the MFPT for Brownian particles to reach a small window on the external boundary. In two and three dimensions, we derive asymptotic expressions for the MFPT in the thin cortex and small escape region limits confirmed by numerical calculations of the MFPT using the finite element method and stochastic simulations. From this analytical and numeric analysis we finally extract the dependence of the MFPT on the ratio of diffusion constants, the potential barrier height and the width of the outer shell. The first two are monotonous whereas the last one may have a minimum for a sufficiently attractive cortex, for which we propose an analytical expression of the potential barrier height matching very well the numerical predictions.
This paper proposes a new approach for face verification, where a pair of images needs to be classified as belonging to the same person or not. This problem is relatively new and not well-explored in the literature. Current methods mostly adopt techniques borrowed from face recognition, and process each of the images in the pair independently, which is counter intuitive. In contrast, we propose to extract cross-image features, i.e. features across the pair of images, which, as we demonstrate, is more discriminative to the similarity and the dissimilarity of faces. Our features are derived from the popular Haar-like features, however, extended to handle the face verification problem instead of face detection. We collect a large bank of cross-image features using filters of different sizes, locations, and orientations. Consequently, we use AdaBoost to select and weight the most discriminative features. We carried out extensive experiments on the proposed ideas using three standard face verification datasets, and obtained promising results outperforming state-of-the-art.
A microscopic theory of control of spatial-temporal congested traffic pattern at freeway bottlenecks is presented. Based on empirical spatial-temporal features of congested patterns at freeway bottlenecks which have recently been found, different control strategies for prevention or reducing of the patterns are simulated and compared. The studied control strategies include the on-ramp metering with feedback and automatic cruise control (ACC) vehicles. A recent microscopic traffic flow model within the author's three-phase traffic theory is used for validation of spatial-temporal congested pattern control.
This paper is concerned with the following Lotka-Volterra competition system with advection in a periodic habitat \begin{equation*} \begin{cases} \frac{\partial u_1}{\partial t} =d_1(x)\frac{\partial^2 u_1}{\partial x^2}-a_1(x)\frac{\partial u_1}{\partial x}+u_1\left(b_1(x)-a_{11}(x)u_1-a_{12}(x)u_2\right),\\ \frac{\partial u_2}{\partial t} =d_2(x)\frac{\partial^2 u_2}{\partial x^2}-a_2(x)\frac{\partial u_2}{\partial x}+u_2\left(b_2(x)-a_{21}(x)u_1-a_{22}(x)u_2\right), \end{cases} t>0,~x\in\Bbb R, \end{equation*} where $d_i(\cdot)$, $a_i(\cdot)$, $b_i(\cdot)$, $a_{ij}(\cdot)$ $(i,j=1,2)$ are $L$-periodic functions in $C^\nu(\Bbb{R})$ with some $\nu\in(0,1)$. Under certain assumptions, the system admits two periodic locally stable steady states $(u_1^*(x),0)$ and $(0,u_2^*(x))$. In this work, we first establish the existence of the pulsating front $U(x,x+ct)=(U_1(x,x+ct),U_2(x,x+ct))$ connecting two periodic solutions $(0,u_2^*(x))$ and $(u_1^*(x),0)$ at infinities. By using a dynamical method, we confirm further that the pulsating front is asymptotically stable for front-like initial values. As a consequence of the global asymptotically stability, we finally show that the pulsating front is unique up to translation.
Irradiating ${\rm Cu}_2{\rm Mo}({\rm CN})_8\cdot 8{\rm H}_2{\rm O}$ with blue light induces a global magnetization, whereas succeeding irradiations with red or longer-wavelength light demagnetize this material. We solve the time-dependent Schr\"odinger equation for an extended Hubbard model to reproduce the photoreversible magnetism. Monitoring the photoinduced optical-conductivity and angle-resolved-photoemission spectra, we reveal that the magnetic round trip by way of ferromagnetism is far from a return in terms of electronics. While visible-light-induced magnetization has never been observed in the tungsten analog ${\rm Cu}_2{\rm W}({\rm CN})_8\cdot 5{\rm H}_2{\rm O}$, infrared-light irradiation may magnetize this material as well.
We present a method for training a regression network from image pixels to 3D morphable model coordinates using only unlabeled photographs. The training loss is based on features from a facial recognition network, computed on-the-fly by rendering the predicted faces with a differentiable renderer. To make training from features feasible and avoid network fooling effects, we introduce three objectives: a batch distribution loss that encourages the output distribution to match the distribution of the morphable model, a loopback loss that ensures the network can correctly reinterpret its own output, and a multi-view identity loss that compares the features of the predicted 3D face and the input photograph from multiple viewing angles. We train a regression network using these objectives, a set of unlabeled photographs, and the morphable model itself, and demonstrate state-of-the-art results.
We report on Cyg X-1 observations performed by the SPI telescope onboard the INTEGRAL mission and distributed over more than 6 years. We investigate the variability of the intensity and spectral shape of this peculiar source in the hard X-rays domain, and more particularly up to the MeV region. We first study the total averaged spectrum which presents the best signal to noise ratio (4 Ms of data). Then, we refine our results by building mean spectra by periods and gathering those of similar hardness.   Several spectral shapes are observed with important changes in the curvature between 20 and 200 keV, even at the same luminosity level. In all cases, the emission decreases sharply above 700 keV, with flux values above 1 MeV (or upper limits) well below the recently reported polarised flux (Laurent et al. 2011), while compatible with the MeV emission detected some years ago by CGRO/COMPTEL (McConnell et al., 2002).   Finally, we take advantage of the spectroscopic capability of the instrument to seek for spectral features in the 500 keV region with negative results for any significant annihilation emission on 2 ks and days timescales, as well as in the total dataset.
Fast radio bursts, or FRBs, are transient sources of unknown origin. Recent radio and optical observations have provided strong evidence for an extragalactic origin of the phenomenon and the precise localization of the repeating FRB 121102. Observations using the Karl G. Jansky Very Large Array (VLA) and very-long-baseline interferometry (VLBI) have revealed the existence of a continuum non-thermal radio source consistent with the location of the bursts in a dwarf galaxy. All these new data rule out several models that were previously proposed, and impose stringent constraints to new models. We aim to model FRB 121102 in light of the new observational results in the active galactic nucleus (AGN) scenario. We propose a model for repeating FRBs in which a non-steady relativistic $e^\pm$-beam, accelerated by an impulsive magnetohydrodynamic (MHD)-driven mechanism, interacts with a cloud at the centre of a star-forming dwarf galaxy. The interaction generates regions of high electrostatic field called cavitons in the plasma cloud. Turbulence is also produced in the beam. These processes, plus particle isotropization, the interaction scale, and light retardation effects, provide the necessary ingredients for short-lived, bright coherent radiation bursts. The mechanism studied in this work explains the general properties of FRB 121102, and may also be applied to other repetitive FRBs. Coherent emission from electrons and positrons accelerated in cavitons provides a plausible explanation of FRBs.
CO isotopes are able to probe the different components in protostellar clouds. These components, core, envelope and outflow have distinct physical conditions and sometimes more than one component contributes to the observed line profile. In this study we determine how CO isotope abundances are altered by the physical conditions in the different components. We use a 3D molecular line transport code to simulate the emission of four CO isotopomers, 12CO J=2-1, 13CO J=2-1, C18O J=2-1 and C17O J=2-1 from the Class 0/1 object L483, which contains a cold quiescent core, an infalling envelope and a clear outflow. Our models replicate JCMT (James Clerk Maxwell Telescope) line observations with the inclusion of freeze-out, a density profile and infall. Our model profiles of 12CO and 13CO have a large linewidth due to a high velocity jet. These profiles replicate the process of more abundant material being susceptible to a jet. C18O and C17O do not display such a large linewidth as they trace denser quiescent material deep in the cloud.