ShantanuT01/DACTYL-Pretraining huggingface dataset:
The behaviour of carbon-oxygen white dwarfs (WDs) subject to direct helium accretion is extensively studied. We aim to analyze the thermal response of the accreting WD to mass deposition at different time scales. The analysis has been performed for initial WDs masses and accretion rates in the range (0.60 - 1.02) Msun and 1.e-9 - 1.e-5 Msun/yr, respectively. Thermal regimes in the parameters space M_{WD} - dot{M}_{He}, leading to formation of red-giant-like structure, steady burning of He, mild, strong and dynamical flashes have been identified and the transition between those regimes has been studied in detail. In particular, the physical properties of WDs experiencing the He-flash accretion regime have been investigated in order to determine the mass retention efficiency as a function of the accretor total mass and accretion rate. We also discuss to what extent the building-up of a He-rich layer via H-burning could be described according to the behaviour of models accreting He-rich matter directly. Polynomial fits to the obtained results are provided for use in binary population synthesis computations. Several applications for close binary systems with He-rich donors and CO WD accretors are considered and the relevance of the results for the interpretation of He-novae is discussed.
Monte Carlo simulations using entropic sampling to estimate the number of configurations of a given energy are a valuable alternative to traditional methods. We introduce {\it tomographic} entropic sampling, a scheme which uses multiple studies, starting from different regions of configuration space, to yield precise estimates of the number of configurations over the {\it full range} of energies, {\it without} dividing the latter into subsets or windows. Applied to the Ising model on the square lattice, the method yields the critical temperature to an accuracy of about 0.01%, and critical exponents to 1% or better. Predictions for systems sizes L=10 - 160, for the temperature of the specific heat maximum, and of the specific heat at the critical temperature, are in very close agreement with exact results. For the Ising model on the simple cubic lattice the critical temperature is given to within 0.003% of the best available estimate; the exponent ratios $\beta/\nu$ and $\gamma/\nu$ are given to within about 0.4% and 1%, respectively, of the literature values. In both two and three dimensions, results for the {\it antiferromagnetic} critical point are fully consistent with those of the ferromagnetic transition. Application to the lattice gas with nearest-neighbor exclusion on the square lattice again yields the critical chemical potential and exponent ratios $\beta/\nu$ and $\gamma/\nu$ to good precision.
Taking into account a neutral massive scalar field minimally coupled to gravity, in a Robertson-Walker metric, it is shown that when the final state is connected with the initial one by means of a Bogoliubov transformation, which does not include the single-mode rotation operator, the mean value of created particles is conserved. When the rotation operator is considered, it is still possible to use the approach of single-mode squeezed operators and get the entropy as the logarithm of the created particles.
In this paper, we considered the isentropic Navier-Stokes equations for compressible fluids with density-dependent viscosities in $\mathbb{R}^3$. These systems come from the Boltzmann equations through the Chapman-Enskog expansion to the second order, cf.\cite{tlt}, and are degenerate when vacuum appears. We firstly establish the existence of the unique local regular solution (see Definition \ref{d1} or \cite{sz3}) when the initial data are arbitrarily large with vacuum at least appearing in the far field. Moreover it is interesting to show that we could't obtain any global regular solution that the $L^\infty$ norm of $u$ decays to zero as time $t$ goes to infinity.
On the basis of the pseudopotential plane-wave(PP-PW) method in combination with the local-density-functional theory(LDFT), complete stress-strain curves for the uniaxial loading and uniaxial deformation along the [001] and [111] directions, and the biaxial proportional extension along [010] and [001] of aluminium are obtained. During the uniaxial loading, certain general behaviors of energy versus stretch and the load versus the stretch are confirmed; in each acse, there exist three special unstressed structures: f.c.c., b.c.c. and f.c.t. for [001]; f.c.c., s.c. and b.c.c. for [111]. Using stability criteria, we find that all of these state are unstable, and always occur together with shear instability, except the natural f.c.c. structure. A Bain transformation from the stable f.c.c. structure to the stable b.c.c. configuration cannot be obtained by uniaxial compression along any equivalent [001] and [111] direction. The tensile strength are similar for the two directions. For the higher energy barrier of [111] direction, the compressive strength is greater than that for the [001] direction. With increase in the ratio of the biaxial proportional extension, the stress and tensile strength increase; however, the critical strain does not change significantly. Our results add to the existing ab initio database for use in fitting and testing interatomic potentials.
We pose the question of what is the best generalization of the factorial and the binomial coefficient. We give several examples, derive their combinatorial properties, and demonstrate their interrelationships.   On cherche ici \`a d\'eterminer est la meilleure g\'en\'eralisation possible des factorielles et des coefficients du bin\^oome. On s'interesse \`a plusieurs exemples, \`a leurs propri\'et\'es combinatoires, et aux differentes relations qu'ils mettent en jeu.
We present results from Chandra and XMM-Newton observations of the bright group of galaxies HCG 62. There are two cavities at about 30'' northeast and 20'' southwest of the central galaxy in the Chandra image. The energy spectrum shows no significant change in the cavity compared with that in the surrounding region. The radial X-ray profile is described by a sum of 3-beta components with core radii about 2, 10, and 160 kpc, respectively. We studied radial distributions of temperature and metal abundance with joint spectral fit for the Chandra and XMM-Newton data, and two temperatures were required in the inner r< 2' (35 kpc) region. The sharp drop of temperature at r about 5' implies the gravitational mass density even lower than the gas density, suggesting the gas may not be in hydrostatic equilibrium. Fe and Si abundances are 1-2 solar at the center and drop to about 0.1 solar at r about 10'. O abundance is less than 0.5 solar and shows a flatter profile. Observed metal distribution supports the view that iron and silicon are produced by type Ia supernova in the central galaxy, while galactic winds by type II supernova have caused wide distribution of oxygen. The supporting mechanism of the cavity is discussed. Pressure for the sum of electrons and magnetic field is too low to displace the hot group gas, and the required pressure due to high energy protons are nearly 700 times higher than the electron pressure. This leaves the origin of the cavities a puzzle, and we discuss other possible origins of the cavities.
We begin with a discussion on two apparently disconnected topics - one related to nonperturbative superpotential generated from wrapping an M2-brane around a supersymmetric three cycle embedded in a G_2-manifold evaluated by the path-integral inside a path-integral approach of [1], and the other centered around the compact Calabi-Yau CY_3(3,243) expressed as a blow-up of a degree-24 Fermat hypersurface in WCP^4[1,1,2,8,12]. For the former, we compare the results with the ones of Witten on heterotic world-sheet instantons [2]. The subtopics covered in the latter include an N=1 triality between Heterotic, M- and F-theories, evaluation of RP^2-instanton superpotential, Picard-Fuchs equation for the mirror Landau-Ginsburg model corresponding to CY_3(3,243), D=11 supergravity corresponding to M-theory compactified on a `barely' G_2 manifold involving CY_3(3,243) and a conjecture related to the action of antiholomorphic involution on period integrals. We then show an indirect connection between the two topics by showing a connection between each one of the two and Witten's MQCD [3]. As an aside, we show that in the limit of vanishing "\zeta", a complex constant that appears in the Riemann surfaces relevant to definining the boundary conditions for the domain wall in MQCD, the infinite series of [4] used to represent a suitable embedding of a supersymmetric 3-cycle in a G_2-mannifold, can be summed.
We study the almost sure convergence of the normalized columns in an infinite product of nonnegative matrices, and the almost sure rank one property of its limit points. Given a probability on the set of $2\times2$ nonnegative matrices, with finite support $\mathcal A=\{A(0),\dots,A(s-1)\}$, and assuming that at least one of the $A(k)$ is not diagonal, the normalized columns of the product matrix $P_n=A(\omega_1)\dots A(\omega_n)$ converge almost surely (for the product probability) with an exponential rate of convergence if and only if the Lyapunov exponents are almost surely distinct. If this condition is satisfied, given a nonnegative column vector $V$ the column vector $\frac{P_nV}{\Vert P_nV\Vert}$ also converges almost surely with an exponential rate of convergence. On the other hand if we assume only that at least one of the $A(k)$ do not have the form $\begin{pmatrix}a&0\\0&d\end{pmatrix}$, $ad\ne0$, nor the form $\begin{pmatrix}0&b\\d&0\end{pmatrix}$, $bc\ne0$, the limit-points of the normalized product matrix $\frac{P_n}{\Vert P_n\Vert}$ have almost surely rank 1 -although the limits of the normalized columns can be distinct- and $\frac{P_nV}{\Vert P_nV\Vert}$ converges almost surely with a rate of convergence that can be exponential or not exponential.
It is well known that particles can get trapped by randomly placed obstacles when they are pushed too much. We present a model where the current in a disordered medium dies at a large external field, but is reborn when the activity is increased. By activity we mean the time-variation of the external driving at a constant time-averaged field. A different interpretation of the resurgence of the current is that the particles are capable of taking an infinite sequence of potential barriers via a mechanism similar to stochastic resonance. We add a discussion regarding the role of "shaking" in processes of relaxation.
Conformal symmetry of QCD is restored at the Wilson-Fisher critical point in noninteger $4-2\epsilon$ space-time dimensions. Correlation functions of multiplicatively renormalizable operators with different anomalous dimensions at the critical point vanish identically. We show that this property allows one to calculate off-diagonal parts of the anomalous dimension matrices for leading-twist operators from a set of two-point correlation functions of gauge-invariant operators which can be evaluated using standard computer algebra techniques. As an illustration, we present the results for the NNLO anomalous dimension matrix for flavor-singlet QCD operators for spin $N\le 8$.
A graph K is multiplicative if a homomorphism from any product G x H to K implies a homomorphism from G or from H. Hedetniemi's conjecture states that all cliques are multiplicative. In an attempt to explore the boundaries of current methods, we investigate strongly multiplicative graphs, which we define as K such that for any connected graphs G,H with odd cycles C,C', a homomorphism from $(G \times C') \cup (C \times H) \subseteq G \times H$ to K implies a homomorphism from G or H.   Strong multiplicativity of K also implies the following property, which may be of independent interest: if G is non-bipartite, H is a connected graph with a vertex h, and there is a homomorphism $\phi \colon G \times H \to K$ such that $\phi(-,h)$ is constant, then H admits a homomorphism to K.   All graphs currently known to be multiplicative are strongly multiplicative. We revisit the proofs in a different view based on covering graphs and replace fragments with more combinatorial arguments. This allows us to find new (strongly) multiplicative graphs: all graphs in which every edge is in at most square, and the third power of any graph of girth >12. Though more graphs are amenable to our methods, they still make no progress for the case of cliques. Instead we hope to understand their limits, perhaps hinting at ways to further extend them.
Primordial Black Holes (PBHs) are black holes that may have been created in the early Universe and could be as large as supermassive black holes or as small as the Planck scale. It is believed that a black hole has a temperature inversely proportional to its mass and will thermally emit all species of fundamental particles. PBHs with initial masses of 5.0 x 10^14 g should be expiring today with bursts of high-energy gamma radiation in the GeV/TeV energy range. The High Altitude Water Cherenkov (HAWC) observatory is sensitive to the high end of the PBH gamma-ray burst spectrum. Due to its large field of view, duty cycle above 90% and sensitivity up to 100 TeV, the HAWC observatory is well suited to perform a search for PBH bursts. We report that if the PBH explodes within 0.25 light years from Earth and within 26 degrees of zenith, HAWC will have a 95% probability of detecting the PBH burst at the 5 sigma level. Conversely, a null detection from a 2 year or longer HAWC search will set PBH upper limits which are significantly better than the upper limits set by any previous PBH search.
We define monoidal components attached to perverse sheaves on abelian varieties and discuss their properties.
A hyperbolic model for diffusion, nonlinear transport (or advection) and production of a scalar quantity, is considered. The model is based on a constitutive law of Cattaneo-Maxwell type expressing non-Fickian diffusion by means of a relaxation time relation. The production or source term is assumed to be of logistic type. This paper studies the existence and spectral stability properties of spatially periodic traveling wave solutions to this system. It is shown that a family of subcharacteristic periodic waves emerges from a local Hopf bifurcation around a critical value of the wave speed. These waves have bounded fundamental period and small-amplitude. In addition, it is shown that these waves are spectrally unstable as solutions to the hyperbolic system. For that purpose, it is proved that the Floquet spectrum of the linearized operator around a wave can be approximated by a linear operator whose point spectrum intersects the unstable half plane of complex numbers with positive real part.
One of the methods for stratifying different molecular classes of breast cancer is the Nottingham Prognostic Index Plus (NPI+) which uses breast cancer relevant biomarkers to stain tumour tissues prepared on tissue microarray (TMA). To determine the molecular class of the tumour, pathologists will have to manually mark the nuclei activity biomarkers through a microscope and use a semi-quantitative assessment method to assign a histochemical score (H-Score) to each TMA core. Manually marking positively stained nuclei is a time consuming, imprecise and subjective process which will lead to inter-observer and intra-observer discrepancies. In this paper, we present an end-to-end deep learning system which directly predicts the H-Score automatically. Our system imitates the pathologists' decision process and uses one fully convolutional network (FCN) to extract all nuclei region (tumour and non-tumour), a second FCN to extract tumour nuclei region, and a multi-column convolutional neural network which takes the outputs of the first two FCNs and the stain intensity description image as input and acts as the high-level decision making mechanism to directly output the H-Score of the input TMA image. To the best of our knowledge, this is the first end-to-end system that takes a TMA image as input and directly outputs a clinical score. We will present experimental results which demonstrate that the H-Scores predicted by our model have very high and statistically significant correlation with experienced pathologists' scores and that the H-Score discrepancy between our algorithm and the pathologists is on par with the inter-subject discrepancy between the pathologists.
We calculate the dynamical structure factors of the magnetization-plateau state in the $S=1/2$ bond-alternating spin chain with a next-nearest-neighbor interaction. The results show characteristic behaviors depending on the next-nearest-neighbor interaction $\alpha$ and the bond-alternation $\delta$. We discuss the lower excited states in comparison with the exact excitation spectrums of an effective Hamiltonian. From the finite size effects, characteristics of the lowest excited states are investigated. The dispersionless mode of the lowest excitation appears in adequate sets of $\alpha$ and $\delta$, indicating that the lowest excitation is localized spatially and forms an isolated mode below the excitation continuum. We further calculate the static structure factors. The largest intensity is located at $q=\pi$ for small $\delta$ in fixed $\alpha$. With increasing $\delta$, the wavenumber of the largest intensity shifts towards $q=\pi/2$, taking the incommensurate value.
We show how parametric resonance mechanism follows quench mechanism in the classical linear sigma model. The parametric resonance amplifies long wavelength modes of the pion for more than $10 fm/c$. The shifting from the quench mechanism to the parametric resonance mechanism is described by a time dependent quantity. After the quench mechanism is over, that quantity has an oscillating part, which causes the parametric resonance. Since its frequency is $2 m_\pi ~(m_\pi$ : pion mass), very long wavelength modes such as k = 40 MeV of the pion are amplified by the parametric resonance.
Many planet candidates have been detected by radial velocity variations of the primary star; they are planet candidates, because of the unknown orbit inclination. Detection of the wobble in the two other dimensions, to be measured by astrometry, would yield the inclination and, hence, true mass of the companions. We aim to show that planets can be confirmed or discovered in a close visual stellar binary system by measuring the astrometric wobble of the exoplanet host star as periodic variation of the separation, even from the ground. We test the feasibility with HD 19994, a visual binary with one radial velocity planet candidate. We use the adaptive optics camera NACO at the VLT with its smallest pixel scale (13 mas) for high precision astrometric measurements. The separations measured in single 120 images taken within one night are shown to follow white noise, so that the standard deviation can be devided by the square root of the number of images to obtain the precision. In this paper we present the first results and investigate the achievable precision in relative astrometry with adaptive optics. With a careful data reduction it is possible to achieve a relative astrometric precision as low as 50 micro arc sec for a 0.6 arc sec, binary with VLT/NACO observations in one hour, the best relative astrometric precision ever achieved with a single telescope from the ground. The relative astrometric precision demonstrated here with AO at an 8-m mirror is sufficient to detect the astrometric signal of the planet HD 19994 Ab as periodic variation of the separation between HD 19994 A and B.
The Wilson loop in the non-commutative dipole field theory is re-examined within the framework of dual gravity description. In contrast to the previous investigations, we let the dual string be moving along the deformed $S^5$ and find the exact expression of the interquark potential. The potential shows a Coulomb behavior at all distance and does not have a minimum distance between quarks, which exhibits in the static configuration. After comparing the potential of the static and moving configurations we find that while the dual string is static at long distance it will transit to a moving configuration at short distance. We also analyze an electric dipole system and find that it shows a similar transition property. Finally, we mention the unsuitable approximation made in the previous paper [hep-th/0701069] and find that the interquark potential in a gauge theory with a non-constant non-commutativity has a Coulomb behavior at all distance.
The magnetic ground state of two isostructural coordination polymers (i) the quasi two-dimensional S = 1/2 square-lattice antiferromagnet [Cu(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$; and (ii) a new compound [Co(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$, were examined with neutron powder diffraction measurements. We find the ordered moments of the Heisenberg S = 1/2 Cu(II) ions in [Cu(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$ are 0.6(1)$\mu_{B}$, whilst the ordered moments for the Co(II) ions in [Co(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$ are 3.02(6)$\mu_{B}$. For Cu(II), this reduced moment indicates the presence of quantum fluctuations below the ordering temperature. We show from heat capacity and electron spin resonance measurements, that due to the crystal electric field splitting of the S = 3/2 Co(II) ions in [Co(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$, this isostructual polymer also behaves as an effective spin-half magnet at low temperatures. The Co moments in [Co(HF$_{2}$)(pyrazine)$_{2}$]SbF$_{6}$ show strong easy-axis anisotropy, neutron diffraction data which do not support the presence of quantum fluctuations in the ground state and heat capacity data which are consistent with 2D or close to 3D spatial exchange anisotropy.
Cross-scene model adaption is crucial for camera relocalization in real scenarios. It is often preferable that a pre-learned model can be fast adapted to a novel scene with as few training samples as possible. The existing state-of-the-art approaches, however, can hardly support such few-shot scene adaption due to the entangling of image feature extraction and scene coordinate regression. To address this issue, we approach camera relocalization with a decoupled solution where feature extraction, coordinate regression, and pose estimation are performed separately. Our key insight is that feature encoder used for coordinate regression should be learned by removing the distracting factor of coordinate systems, such that feature encoder is learned from multiple scenes for general feature representation and more important, view-insensitive capability. With this feature prior, and combined with a coordinate regressor, few-shot observations in a new scene are much easier to connect with the 3D world than the one with existing integrated solution. Experiments have shown the superiority of our approach compared to the state-of-the-art methods, producing higher accuracy on several scenes with diverse visual appearance and viewpoint distribution.