ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper focuses on real-time all-frequency image-based rendering using an innovative solution for run-time computation of light transport. The approach is based on new results derived for non-linear phase shifting in the Haar wavelet domain. Although image-based methods for real-time rendering of dynamic glossy objects have been proposed, they do not truly scale to all possible frequencies and high sampling rates without trading storage, glossiness, or computational time, while varying both lighting and viewpoint. This is due to the fact that current approaches are limited to precomputed radiance transfer (PRT), which is prohibitively expensive in terms of memory requirements and real-time rendering when both varying light and viewpoint changes are required together with high sampling rates for high frequency lighting of glossy material. On the other hand, current methods cannot handle object rotation, which is one of the paramount issues for all PRT methods using wavelets. This latter problem arises because the precomputed data are defined in a global coordinate system and encoded in the wavelet domain, while the object is rotated in a local coordinate system. At the root of all the above problems is the lack of efficient run-time solution to the nontrivial problem of rotating wavelets (a non-linear phase-shift), which we solve in this paper.
Richard Stanely proposed, in a recent Amer. Math. Monthly Problem, to prove a nice explicit formula for the generating function for the number of n-letter words in {H,T} that have as many occurrences of HT as HH. In this article, we show how to prove this problem automatically, and ANY problem of that type, regardless of the size of the alphabet and the length of the two chosen strings
We present a practical and accurate density functional for the exchange-correlation energy of electrons in two dimensions. The exchange part is based on a recent two-dimensional generalized-gradient approximation derived by considering the limits of small and large density gradients. The fully local correlation part is constructed following the Colle-Salvetti scheme and a Gaussian approximation for the pair density. The combination of these expressions is shown to provide an efficient density functional to calculate the total energies of two-dimensional electron systems such as semiconductor quantum dots. Excellent performance of the functional with respect to numerically exact reference data for quantum dots is demonstrated.
Spin interference due to Rashba spin-orbit interaction (SOI) in a ballistic two-dimensional electron gas (2DEG) ring conductor submitted to a bias voltage is investigated theoretically. We calculate the scattering matrices and differential conductance with lead-ring junction coupling as an adjustable parameter. Due to the interference of electronic waves traversing the ring, the differential conductance modulated by both bias voltage and SOI exhibits a diamond-shaped pattern, thus termed as \ti{Rashba diamond}. This feature offers a supplementary degree of freedom to manipulate phase interference.
Spins transverse to the magnetization of a ferromagnet only survives over a short distance. We develop a drift-diffusion approach that captures the main features of transverse spin effects in systems with arbitrary spin textures (vortices, domain walls) and generalizes the Valet-Fert theory. In addition to the standard characteristic lengths (mean free path for majority and manority electrons, spin diffusion length), the theory introduces two lengths scales, the transverse spin coherence length and the (Larmor) spin precession length. We show how those lengths can be extracted from ab-initio calculations or measured with giant magneto-resistance experiments. In long (adiabatic) domain walls, we provide an analytic formula that expresses the so called "non-adiabatic" (or field like) torque in term of those lengths scales. However, this "non adiabatic" torque is no longer a simple material parameter and depends on the actual spin texture: in thin (< 10nm) domain walls, we observe very significant deviations from the adiabatic limit.
We consider diffusion-like paths that are explored by a particle moving via a conservative force while being in thermal equilibrium with its surroundings. To probe rare transitions, we use the Onsager-Machlup (OM) functional as a path probability distribution function for double-ended paths that are constrained to start and stop at predesignated points after a fixed time. We explore the continuous-time limit where the OM functional has been commonly regularized by using the Ito-Girsanov change of measure. When used as a path measure, the Ito-Girsanov expression generates an ensemble of double-ended paths that are unphysical. We expose the underlying reasons why this continuous-time limit does not, and cannot, generate a thermodynamic ensemble of paths. Furthermore, we show that the concept of the Most Probable Path and the Thermodynamic action are incompatible with such measures for discrete or continuous time diffusion processes.
In many real world networks, the number of links increases nonlinearly with the number of nodes. Models of such accelerated growth have been considered earlier with deterministic and stochastic number of links. Here we consider stochastic accelerated growth in a network where links are directed. With the number of out-going links following a power law distribution, the results are similar to the undirected case. As the accelerated growth is enhanced, the degree distribution becomes independent of the ``initial attractiveness'', a parameter which plays a key role in directed networks. As an example of a directed model with accelerated growth, the citation network is considered, in which the distribution of the number of outgoing link has an exponential tail. The role of accelerated growth is examined here with two different growth laws.
We use cosmological N-body simulations to investigate whether measurements of the moments of large-scale structure can yield constraints on primordial non-Gaussianity. We measure the variance, skewness, and kurtosis of the evolved density field from simulations with Gaussian and three different non-Gaussian initial conditions: a local model with f_NL=100, an equilateral model with f_NL=-400, and an orthogonal model with f_NL=-400. We show that the moments of the dark matter density field differ significantly between Gaussian and non-Gaussian models. We also make the measurements on mock galaxy catalogs that contain galaxies with clustering properties similar to those of luminous red galaxies (LRGs). We find that, in the case of skewness and kurtosis, galaxy bias reduces the detectability of non-Gaussianity, though we can still clearly discriminate between different models in our simulation volume. However, in the case of the variance, galaxy bias greatly amplifies the detectability of non-Gaussianity. In all cases we find that redshift distortions do not significantly affect the detectability. When we restrict our measurements to volumes equivalent to the Sloan Digital Sky Survey II (SDSS-II) or Baryon Oscillation Spectroscopic Survey (BOSS) samples, the probability of detecting a departure from the Gaussian model is high by using measurements of the variance, but very low by using only skewness and kurtosis measurements. We find that skewness and kurtosis measurements are never likely to yield useful constraints on primordial non-Gaussianity, but future surveys should be large enough to place meaningful constraints using measurements of the galaxy variance.(Abridged)
The Milky Way is filled with the tidally-disrupted remnants of globular clusters and dwarf galaxies. Determining the properties of these objects -- in particular, initial masses and density profiles -- is relevant to both astronomy and dark matter physics. However, most direct measures of mass cannot be applied to tidal debris, as the systems of interest are no longer in equilibrium. Since phase-space density is conserved during adiabatic phase mixing, Liouville's theorem provides a connection between stellar kinematics as measured by observatories such as Gaia and the original mass of the disrupted system. Accurately recovering the phase-space density is complicated by uncertainties resulting from measurement errors and orbital integration, which both effectively inject entropy into the system, preferentially decreasing the measured density. In this paper, we demonstrate that these two issues can be overcome. First, we measure the phase-space density of the globular cluster M4 in Gaia data, and use Liouville's theorem to derive its mass. We then show that, for tidally disrupted systems, the orbital parameters and thus phase-space density can be inferred by minimizing the phase-space entropy of cold stellar streams. This work is therefore a proof of principle that true phase-space density can be measured and the original properties of the star cluster reconstructed in systems of astrophysical interest.
In this paper we investigate Nash equilibrium payoffs for two-player nonzero-sum stochastic differential games whose cost functionals are defined by a system of coupled backward stochastic differential equations. We obtain an existence theorem and a characterization theorem for Nash equilibrium payoffs. For this end the problem is described equivalently by a stochastic differential game with jumps. But, however, unlike the work by Buckdahn, Hu and Li [9], here the important tool of a dynamic programming principle for stopping times has to be developed. Moreover, we prove that the lower and upper value functions are the viscosity solutions of the associated coupled systems of PDEs of Isaacs type, respectively. Our results generalize those by Buckdahn, Cardaliaguet and Rainer [7] and by Lin [16].
Numerical 1D-3V solutions of the Wong-Yang-Mills equations with anisotropic particle momentum distributions are presented. They confirm the existence of plasma instabilities for weak initial fields and their saturation at a level where the particle motion is affected, similar to Abelian plasmas. The isotropization of the particle momenta by strong random fields is shown explicitly, as well as their nearly exponential distribution up to a typical hard scale, which arises from scattering off field fluctuations. By variation of the lattice spacing we show that the effects described here are independent of the UV field modes near the end of the Brioullin zone.
A palindrome in base $g$ is an integer $N$ that remains the same when its digit expansion in base $g$ is reversed. Let $g$ and $h$ be given distinct integers $>1$. In this paper we discuss how many integers are palindromes in base $g$ and simultaneously palindromes in base $h$.
In body-centred-cubic (bcc) metals migrating 1/2<111> screw dislocations experience a periodic energy landscape with a triangular symmetry. Atomistic simulations, such as those performed using the nudged-elastic-band (NEB) method, generally predict a transition-pathway energy-barrier with a double-hump; contradicting Ab Initio findings. Examining the trajectories predicted by NEB for a particle in a Peierls energy landscape representative of that obtained for a screw dislocation, reveals an unphysical anomaly caused by the occurrence of monkey saddles in the landscape. The implications for motion of screws with and without stress are discussed.
A Woods-Saxon equivalent to a double folding potential in the surface region is obtained for the heavy-ion scattering potential. The Woods-Saxon potential has fixed geometry and was applied as a bare potential in the analysis of experimental data of several systems. A new analytical formula for the position and height of the Coulomb barrier is presented, which reproduces the results obtained using double folding potentials. This simple formula has been applied to estimate the fusion cross section above the Coulomb barrier. A comparison with experimental data is presented.
We have observed the ultracompact HII region G29.96-0.02 in the near infrared J, H, and K bands and in the Br-gamma line. By comparison with radio observations, we determine that the extinction to the nebula is AK = 2.14 with a 3 sigma uncertainty of 0.25. We identify the ionizing star and determine its intrinsic K magnitude. The star does not have an infrared excess and so appears to be no longer accreting. The K magnitude and the bolometric luminosity allow us to place limits on the location of the ionizing star in the HR diagram. The 3 sigma upper limit on the effective temperature of the ionizing star is 42500 K. We favor a luminosity appropriate for star with a mass in excess of about 60 solar masses. The limit on the temperature and luminosity exclude stars on the ZAMS and stars within 10^6 yr of the ZAMS. Since the age of the UC HII region is estimated to be only about 10^5 yr, we suggest that this is direct evidence that the stellar birth line for massive stars at twice solar metallicity must be significantly redder than the ZAMS.
This paper is concerned with the Laplace boundary-value problem with the directional derivative, corresponding to the specific nature of measurements of the longitudinal component of the photospheric magnetic field. Boundary conditions are specified by a distribution on the sphere of projection of the magnetic field vector unto a given direction. It is shown that the solution of this problem exists in the form of a spherical harmonic expansion, and uniqueness of this solution is proved. A conceptual sketch of numerical determination of the harmonic series coefficients is given. The field of application of the method is analyzed having regard to the peculiarities of actual data. Finally, we present differences in results derived from extrapolating the magnetic field from a synoptic map and a full-disk magnetogram.
Data diversity and volume are crucial to the success of training deep learning models, while in the medical imaging field, the difficulty and cost of data collection and annotation are especially huge. Specifically in robotic surgery, data scarcity and imbalance have heavily affected the model accuracy and limited the design and deployment of deep learning-based surgical applications such as surgical instrument segmentation. Considering this, we rethink the surgical instrument segmentation task and propose a one-to-many data generation solution that gets rid of the complicated and expensive process of data collection and annotation from robotic surgery. In our method, we only utilize a single surgical background tissue image and a few open-source instrument images as the seed images and apply multiple augmentations and blending techniques to synthesize amounts of image variations. In addition, we also introduce the chained augmentation mixing during training to further enhance the data diversities. The proposed approach is evaluated on the real datasets of the EndoVis-2018 and EndoVis-2017 surgical scene segmentation. Our empirical analysis suggests that without the high cost of data collection and annotation, we can achieve decent surgical instrument segmentation performance. Moreover, we also observe that our method can deal with novel instrument prediction in the deployment domain. We hope our inspiring results will encourage researchers to emphasize data-centric methods to overcome demanding deep learning limitations besides data shortage, such as class imbalance, domain adaptation, and incremental learning. Our code is available at https://github.com/lofrienger/Single_SurgicalScene_For_Segmentation.
The static and dynamic properties of a Cosserat-type lattice interface of finite thickness are studied, so that both displacements and rotational degrees of freedom are taken into account. The model allows considering interfaces with a beam-like microstructure and interfaces with finite size particles as particular cases. One-dimensional solutions describing shear and micro-rotations at the interface are obtained and discussed. Harmonic as well as localized solutions, and the properties of the interfaces as filters for elastic waves are investigated. It is shown that both systems with long- and short-wavelength localization may exist.
We consider the following combinatorial question. Let $$ S_0 \subset S_1 \subset S_2 \subset ...\subset S_m $$ be nested sets, where #$(S_i) = i$. A move consists of altering one of the sets $S_i$, $1 \le i \le m-1$, in a manner so that the nested condition still holds and #$(S_i)$ is still $i$. Our goal is to find a sequence of moves that exhausts through all subsets of $S_m$ (other than the initial sets $S_i$) with no repeats. We call this "Gray-coding through nested sets" because of the analogy with Frank Gray's theory of exhausting through integers while altering only one bit at a time. Our main result is an efficient algorithm that solves this problem. As a byproduct, we produce new families of cyclic Gray codes through binary $m$-bit integers.
We have obtained spectra for globular cluster candidates in M104 with LDSS-2 on the William Herschel Telescope, confirming 34 objects as M104 globular clusters. We find a cluster velocity dispersion of $\sim$ 260 km/sec, and the Projected Mass Estimator gives a mass of 5.0 (3.5,6.7) $\times 10^{11}$ M$_\odot$ for M104 within a projected radius of $\sim 330^{''}$ (14 kpc for D=8.55 Mpc). Our best estimate for the mass-to-light ratio is M/L$_{V_T}$= 16$^{+5.5}_{-5.0}$ within the same radius. Considering all of the possible sources of uncertainty, we find a lower limit of M/L_V= 5.3, which is larger than the M/L$_V$ found from rotation curve analyses inside 180$^{''}$. We thus conclude that the mass-to-light ratio increases with radius, or in other words that M104 possesses a dark matter halo. There is a marginal detection of rotation in the M104 cluster system at the 92.5% confidence level; larger samples will be needed to investigate this possibility. Interestingly, the M104 globular cluster and planetary nebulae (PNe) kinematics are roughly consistent inside $\sim 100^{''}$. Finally, we find a mean cluster metallicity of [Fe/H] = $-$0.70 $\pm$ 0.3, which is more typical of clusters in gE/cD galaxies than it is of clusters in other spirals.
On 2015 January 6-7, an interplanetary coronal mass ejection (ICME) was observed at L1. This event, which can be associated with a weak and slow coronal mass ejection, allows us to discuss on the differences between the boundaries of the magnetic cloud and the compositional boundaries. A fast stream from a solar coronal hole surrounding this ICME offers a unique opportunity to check the boundaries' process definition and to explain differences between them. Using Wind and ACE data, we perform a complementary analysis involving compositional, magnetic, and kinematic observations providing relevant information regarding the evolution of the ICME as travelling away from the Sun. We propose erosion, at least at the front boundary of the ICME, as the main reason for the difference between the boundaries, and compositional signatures as the most precise diagnostic tool for the boundaries of ICMEs.
We present a sample of 383 X-ray selected galaxy groups and clusters with spectroscopic redshift measurements (up to z ~ 0.79) from the 2XMMi/SDSS Galaxy Cluster Survey. The X-ray cluster candidates were selected as serendipitously detected sources from the 2XMMi-DR3 catalogue that were located in the footprint of the Sloan Digital Sky Survey (SDSS-DR7). The cluster galaxies with available spectroscopic redshifts were selected from the SDSS-DR10. We developed an algorithm for identifying the cluster candidates that are associated with spectroscopically targeted luminous red galaxies and for constraining the cluster spectroscopic redshift. A cross-correlation of the constructed cluster sample with published optically selected cluster catalogues yielded 264 systems with available redshifts. The present redshift measurements are consistent with the published values. The current cluster sample extends the optically confirmed cluster sample from our cluster survey by 67 objects. Moreover, it provides spectroscopic confirmation for 78 clusters among our published cluster sample, which previously had only photometric redshifts. Of the new cluster sample that comprises 67 systems, 55 objects are newly X-ray discovered clusters and 52 systems are sources newly discovered as galaxy clusters in optical and X-ray wavelengths. Based on the measured redshifts and the fluxes given in the 2XMMi-DR3 catalogue, we estimated the X-ray luminosities and masses of the cluster sample.
Using the strong coupling diagram technique, we study the one-band repulsive Hubbard model on a two-dimensional square lattice in a wide range of chemical potentials $\mu$. Infinite sequences of diagrams describing interactions of electrons with spin and charge fluctuations are taken into account. At low temperatures, regions of the negative electron compressibility are found for $\mu<0$ and $\mu>U$, where $U$ is the Hubbard repulsion. For even lower temperatures, in the neighborhood of these regions, states with the phase separation are revealed.
We study the law of a hypoelliptic Brownian motion on an infinite-dimensional Heisenberg group based on an abstract Wiener space. We show that the endpoint distribution, which can be seen as a heat kernel measure, is absolutely continuous with respect to a certain product of Gaussian and Lebesgue measures, that the heat kernel is quasi-invariant under translation by the Cameron-Martin subgroup, and that the Radon-Nikodym derivative is Malliavin smooth.
We reconsider fluctuations of Affleck-Dine (AD) field in a D-term inflation model. Contrary to the previous analysis, we find that the spectrum of the adiabatic fluctuations is almost scale invariant even if the AD field has a large initial value. Furthermore, we study the isocurvature fluctuations of the AD field and estimate the ratio of the isocurvature to adiabatic power spectrum. The dynamics of the inflaton and AD fields sets the upper bound for the value of the AD field, leading to a lower limit for isocurvature perturbation. It is shown that the recent Cosmic Microwave Background data give a constraint on the D-term inflation and the AD field.
The progenitor systems of Type-Ia supernovae (SNe Ia) are yet unknown. The collisional-triple SN Ia progenitor model posits that SNe Ia result from head-on collisions of binary white dwarfs (WDs), driven by dynamical perturbations by the tertiary stars in mild-hierarchical triple systems. To reproduce the Galactic SN Ia rate, at least ~30-55 per cent of all WDs would need to be in triple systems of a specific architecture. We test this scenario by searching the Gaia DR2 database for the postulated progenitor triples. Within a volume out to 120 pc, we search around Gaia-resolved double WDs with projected separations up to 300 au, for physical tertiary companions at projected separations out to 9000 au. At 120 pc, Gaia can detect faint low-mass tertiaries down to the bottom of the main sequence and to the coolest WDs. Around 27 double WDs, we identify zero tertiaries at such separations, setting a 95 per cent confidence upper limit of 11 per cent on the fraction of binary WDs that are part of mild hierarchical triples of the kind required by the model. As only a fraction (likely ~10 per cent) of all WDs are in <300 au WD binaries, the potential collisional-triple progenitor population appears to be at least an order of magnitude (and likely several) smaller than required by the model.
We analyze the Standard Model gauge group SU(3) x SU(2) x U(1) constructed in F-theory. The non-Abelian part SU(3) x SU(2) is described by singularities of Kodaira type. It is distinguished to naive product of SU(3) and SU(2), revealed by blow-up analysis, since the resolution procedures cannot be done separately to each group. The Abelian part U(1) is constructed by obtaining a desirable global two-form harboring it, using `factorization method' similar to the decomposition method of the spectral cover; It makes use of an extra section in the elliptic fiber of the Calabi-Yau manifold, on which F-theory is compactified. Conventional gauge coupling unification of SU(5) is achieved, without threshold correction from the flux along hypercharge direction.