ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this work we will consider the concepts of partial and complete observables for canonical general relativity. These concepts provide a method to calculate Dirac observables. The central result of this work is that one can compute Dirac observables for general relativity by dealing with just one constraint. For this we have to introduce spatial diffeomorphism invariant Hamiltonian constraints. It will turn out that these can be made to be Abelian. Furthermore the methods outlined here provide a connection between observables in the space--time picture, i.e. quantities invariant under space--time diffeomorphisms, and Dirac observables in the canonical picture.
We analyze a two-dimensional phase field model designed to describe the dynamics of crystalline grains. The phenomenological free energy is a functional of two order parameters. The first one reflects the orientational order while the second reflects the predominant local orientation of the crystal. We consider the gradient flow of this free energy. Solutions can be interpreted as ensembles of grains (in which the phase of the order parameter is approximately constant in space) separated by grain boundaries. We study the dynamics of the boundaries as well as the rotation of the grains. In the limit of the infinitely sharp interface, the normal velocity of the boundary is proportional to both its curvature and its energy. We obtain explicit formulas for the interfacial energy and mobility and study their behavior in the limit of a small misorientation. We calculate the rate of rotation of a grain in the sharp interface limit and find that it depends sensitively on the choice of the model.
We consider quantum cryptographic schemes where the carriers of information are 3-state particles. One protocol uses four mutually unbiased bases and appears to provide better security than obtainable with 2-state carriers. Another possible method allows quantum states to belong to more than one basis. The security is not better, but many curious features arise.
Within a minimal extension of the SM in 4+1 dimensions, we study how Kaluza Klein excitations of the SM gauge bosons affect the electroweak precision observables. Asymmetries in Z decays provide the dominant bound on the compactification scale M of the extra dimension. If the higgs is so light that will be discovered at LEP2, we find the following 95% CL bounds: M > 3.5 TeV (if the higgs lives in the extra dimension) and M > 4.3 TeV (if the higgs is confined to our 4 dimensions). In the second case Kaluza Klein modes give "universal"corrections and a good fit of precision data can be obtained with an heavier higgs (up to 500 GeV) and with a smaller M > 3.4 TeV.
The competition between the Ruderman-Kittel-Kasuya-Yosida effect and Kondo effect is a central subject of periodic Anderson model. By using the density matrix embedding theory, we study a three orbital periodic Anderson model, in which the effects of degenerate conduction orbitals via the local magnetic moments, number of electrons, and spin-spin correlation functions, are investigated. From the phase diagram at half filling, we find there exists two different anti-ferromagnetic phases and one paramagnetic phase. To explore the difference of the two anti-ferromagnetic phases, the topology of Fermi surface and the connection with standard periodic Anderson model are considered. The spin-spin correlation functions yield insight into the competition between Ruderman-Kittel-Kasuya-Yosida interaction and Kondo interaction. We further find there is a "scaling transformation" connects different ratio of the hybridization strength.
Active galactic nuclei (AGN) probably control the growth of their host galaxies via feedback in the form of wide-angle wind-driven outflows. These establish the observed correlations between supermassive black hole (SMBH) masses and host galaxy properties, e.g. the spheroid velocity dispersion $\sigma$. In this paper we consider the growth of the SMBH once it starts driving a large-scale outflow through the galaxy. To clear the gas and ultimately terminate further growth of both the SMBH and the host galaxy, the black hole must continue to grow its mass significantly, by up to a factor of a few, after reaching this point. The mass increment $\Delta M_{\rm BH}$ depends sensitively on both galaxy size and SMBH spin. The galaxy size dependence leads to $\Delta M_{\rm BH} \propto \sigma^5$ and a steepening of the $M-\sigma$ relation beyond the analytically calculated $M \propto \sigma^4$, in agreement with observation. Slowly--spinning black holes are much less efficient in producing feedback, so at any given $\sigma$ the slowest--spinning black holes should be the most massive. Current observational constraints are consistent with this picture, but insufficient to test it properly; however, this should change with upcoming surveys.
Various authors have suggested that the gamma-ray burst (GRB) central engine is a rapidly rotating, strongly magnetized, $(\sim 10^{15}-10^{16}$ G) compact object. The strong magnetic field can accelerate and collimate the relativistic flow and the rotation of the compact object can be the energy source of the GRB. The major problem in this scenario is the difficulty of finding an astrophysical mechanism for obtaining such intense fields. Whereas, in principle, a neutron star could maintain such strong fields, it is difficult to justify a scenario for their creation. If the compact object is a black hole, the problem is more difficult since, according to general relativity it has "no hair" (i.e., no magnetic field). Schuster, Blackett, Pauli, and others have suggested that a rotating neutral body can create a magnetic field by non-minimal gravitational-electromagnetic coupling (NMGEC). The Schuster-Blackett form of NMGEC was obtained from the Mikhail and Wanas's tetrad theory of gravitation (MW). We call the general theory NMGEC-MW.   We investigate here the possible origin of the intense magnetic fields $\sim 10^{15}-10^{16}$ G in GRBs by NMGEC-MW. Whereas these fields are difficult to explain astrophysically, we find that they are easily explained by NMGEC-MW. It not only explains the origin of the $\sim 10^{15}-10^{16}$G fields when the compact object is a neutron star, but also when it is a black hole.
It is well known that the density and anisotropy profile in the inner regions of a stellar system with positive phase-space distribution function are not fully independent. Here we study the interplay between density profile and orbital anisotropy at large radii in physically admissible (consistent) stellar systems. The analysis is carried out by using two-component (n-gamma,gamma_1) spherical self-consistent galaxy models, in which one density distribution follows a generalized gamma profile with external logarithmic slope n, and the other a standard gamma_1 profile (with external slope 4). The necessary and sufficient conditions for phase-space consistency are determined analytically, also in presence of a dominant massive central black hole, and the analytical phase-space distribution function of (n-gamma,1) models, and of n-gamma models with a central black hole, is derived for gamma=0,1,2. It is found that the density slope in the external regions of a stellar system can play an important role in determining the amount of admissible anisotropy: in particular, for fixed density slopes in the central regions, systems with a steeper external density profile can support more radial anisotropy than externally flatter models. This is quantified by an inequality formally identical to the ``cusp slope-central anisotropy'' theorem (An & Evans 2006), relating at all radii (and not just at the center) the density logarithmic slope and the anisotropy indicator in all Osipkov-Merritt systems [Abridged].
In this article we perform an extensive study of the spaces of automorphic forms for GL(2) of weight two and level N, for N an ideal in the ring of integers of the quartic CM field generated by the twelfth roots of unity. This study is conducted through the computation of the group cohomology of the congruence subgroup of upper triangular matrices modulo N, and the corresponding Hecke action which this space admits. Combining this Hecke data with the Faltings-Serre method for proving equivalence of Galois representations, we are able to provide the first known examples of modular elliptic curves over this field.
We consider the infall of a massive clump into a dark-matter halo as a simple and extreme model for the effect of baryonic physics (neglected in gravity-only simulations of large-scale structure formation) on the dark-matter. We find that such an infalling clump is extremely efficient in altering the structure of the halo and reducing its central density: a clump of 1% the mass of the halo can remove about twice its own mass from the inner halo and transform a cusp into a core or weaker cusp. If the clump is subsequently removed, mimicking a galactic wind, the central halo density is further reduced and the mass removed from the inner halo doubled. Lighter clumps are even more efficient: the ratio of removed mass to clump mass increases slightly towards smaller clump masses. This process is the more efficient the more radially anisotropic the initial dark-matter velocities. While such a clumpy infall may be somewhat unrealistic, it demonstrates that the baryons need to transfer only a small fraction of their initial energy to the dark matter via dynamical friction to explain the discrepancy between predicted dark-matter density profiles and those inferred from observations of dark-matter dominated galaxies.
This technical report describes the SViT approach for the Ego4D Point of No Return (PNR) Temporal Localization Challenge. We propose a learning framework StructureViT (SViT for short), which demonstrates how utilizing the structure of a small number of images only available during training can improve a video model. SViT relies on two key insights. First, as both images and videos contain structured information, we enrich a transformer model with a set of \emph{object tokens} that can be used across images and videos. Second, the scene representations of individual frames in video should "align" with those of still images. This is achieved via a "Frame-Clip Consistency" loss, which ensures the flow of structured information between images and videos. SViT obtains strong performance on the challenge test set with 0.656 absolute temporal localization error.
A spin-1/2, Ising trilayered ferrimagnetic system on square Bravais lattice is studied, employing Monte-Carlo simulation with the single spin-flip Metropolis algorithm. The bulk of such a system is formed by three layers, each of which is composed entirely either by A or B type of atoms, resulting in two distinct compositions: ABA and AAB and two different types of magnetic interactions: ferromagnetic between like atoms and antiferromagnetic between unlike atoms. For such systems, Inverse Absolute of Reduced Residual Magnetisation is the absolute value of the ratio of the extremum of the magnetisation in between compensation and critical points and the saturation magnetisation. Variation of relative interaction strengths in the Hamiltonian, for a range of values, leads to the shift of compensation point and critical point and changes in the magnitude of Inverse absolute of Reduced Residual magnetisation. Probable mathematical forms of dependences of the Inverse absolute of Reduced Residual magnetisation and temperature interval between the compensation and critical points on controlling parameters were proposed in the absence of applied magnetic field and have obtained phase diagrams for both types of configurations from these relations. This alternative description of the simulated systems may help technologists design magnetocaloric materials according to desired characteristics.
We revisit and analyze the thermodynamic efficiency of the Feynman-Smoluchowski (FS) ratchet, a classical thought experiment describing an autonomous heat-work converter. Starting from the full kinetics of the FS ratchet and deriving the exact forms of the hidden dissipations resulting from coarse-graining, we restate the historical controversy over its thermodynamic efficiency. The existence of hidden entropy productions implies that the standard framework of stochastic thermodynamics applied to the coarse-grained descriptions fails in capturing the dissipative feature of the system. In response to this problem, we explore an extended framework of stochastic thermodynamics to reconstruct the hidden entropy production from the coarse-grained dynamics. The approach serves as a key example of how we can systematically address the problem of thermodynamic efficiency in a multi-variable fluctuating non-equilibrium system.
We reinvestigate the interesting phenomenon of symmetry nonrestoration at high temperature in the multifield O(N_1) X O(N_2) model. We apply modified self-consistent resummation (MSCR) in order to obtain the scalar dressed masses and find in what circumstances a resummed multifield theory which has symmetry (non)restoration can be renormalized. It is shown that, aside from the consistency of the MSCR method, the basic ingredient that guarantees the renormalization of a multifield model within a resummation approach is the T^2 mass behavior of field theory at high temperature.
We have simulated numerically an automated version of Maxwell's demon inspired by Smoluchowski's ideas of 1912. Two gas chambers of equal volume are connected via an opening that is covered by a trapdoor. The trapdoor can open to the left but not to the right, and is intended to rectify naturally occurring fluctuations in density between the two chambers. Our results confirm that though the trapdoor behaves as a rectifier when large density differences are imposed by external means, it can not extract useful work from the thermal motion of the molecules when left on its own.
The small momentum fraction x behaviour of quarks in mesons is analysed in the 1+1-dimensional reduced model of large-N QCD by light-cone quantisation.
Remnant radio galaxies (RRGs), characterized by the cessation of AGN activity, represent a short-lived last phase of radio galaxy's life-cycle. Hitherto, searches for RRGs, mainly based on the morphological criteria, have identified large angular size sources resulting into a bias towards the remnants of powerful FR-II radio galaxies. In this study we make the first attempt to perform a systematic search for RRGs of small angular sizes ($<$30$^{\prime\prime}$) in the XMM-LSS field. By using spectral curvature criterion we discover 48 remnant candidates exhibiting strong spectral curvature ${\it i.e.}$; ${\alpha}_{\rm 150~MHz}^{\rm 325~MHz}$ - ${\alpha}_{\rm 325~MHz}^{\rm 1.4~GHz}$ $\geq$0.5. Spectral characteristics at higher frequency regime ($>$1.4 GHz) indicate that some of our remnant candidates can depict recurrent AGN activity with an active core. We place an upper limit on the remnant fraction ($f_{\rm rem}$) to be 3.9$\%$, which increases to 5.4$\%$ if flux cutoff limit of S$_{\rm 150~MHz}$ $\geq$10 mJy is considered. Our study unveils, hitherto unexplored, a new population of small-size ($<$200 kpc) remnant candidates that are often found to reside in less dense environments and at higher redshifts ($z$) $>$1.0. We speculate that a relatively shorter active phase and/or low jet power can be plausible reasons for the small size of remnant candidates.
The theory of magnetic symmetry in quasicrystals is used to characterize the nature of magnetic peaks, expected in elastic neutron diffraction experiments. It is established that there is no symmetry-based argument which forbids the existence of quasiperiodic long-range magnetic order. Suggestions are offered as to where one should look for the simplest kinds of antiferromagnetic quasicrystals.
We present integral equations for the area of minimal surfaces in AdS_3 ending on generic smooth boundary contours. The equations are derived from the continuum limit of the AMSV result for null polygonal boundary contours. Remarkably these continuum equations admit exact solutions in some special cases. In particular we describe a novel exact solution which interpolates between the circle and 4-cusp solutions.
Let A be a subset of $\F_p^n$, the $n$-dimensional linear space over the prime field $\F_p$ of size at least $\de N$ $(N=p^n)$, and let $S_v=P^{-1}(v)$ be the level set of a homogeneous polynomial map $P:\F_p^n\to\F_p^R$ of degree $d$, and $v\in\F_p^R$. We show, that under appropriate conditions, the set $A$ contains at least $c\, N|S|$ arithmetic progressions of length $l\leq d$ with common difference in $S_v$, where c is a positive constant depending on $\de$, $l$ and $P$. We also show that the conditions are generic for a class of sparse algebraic sets of density $\approx N^{-\eps}$.
Automatic and accurate segmentation for retinal and choroidal layers of Optical Coherence Tomography (OCT) is crucial for detection of various ocular diseases. However, because of the variations in different equipments, OCT data obtained from different manufacturers might encounter appearance discrepancy, which could lead to performance fluctuation to a deep neural network. In this paper, we propose an uncertainty-guided domain alignment method to aim at alleviating this problem to transfer discriminative knowledge across distinct domains. We disign a novel uncertainty-guided cross-entropy loss for boosting the performance over areas with high uncertainty. An uncertainty-guided curriculum transfer strategy is developed for the self-training (ST), which regards uncertainty as efficient and effective guidance to optimize the learning process in target domain. Adversarial learning with feature recalibration module (FRM) is applied to transfer informative knowledge from the domain feature spaces adaptively. The experiments on two OCT datasets show that the proposed methods can obtain significant segmentation improvements compared with the baseline models.
With the aid of an improved short-range approximation, the bound state energies and the scattering phase shifts for a Hulth\'en- type potential plus Yukawa potential are calculated within the framework of Nikiforov-Uvarov and standard methods, respectively. Our numerical calculations show that the presence of Yukawa potential has a significant influence on bound state energies and the wave number-dependent phase shifts for any arbitrary values of the screening parameter {\alpha} and angular momentum l.
In this paper, we introduce a model of Brownian polymer in a continuous random environment. The asymptotic behavior of the partition function associated to this polymer measure is studied, and we are able to separate a weak and strong disorder regime under some reasonable assumptions on the spatial covariance of the environment. Some further developments, concerning some concentration inequalities for the partition function, are given for the weak disorder regime.
We consider a dynamical brane world in a six dimensional spacetime containing a singularity. Using the Israel conditions we study the motion of a 4-brane embedded in this setup. We analize the brane behavior when its position is perturbed about a fixed point and solve the full non-linear dynamics in the several possible scenarios. We also investigate the possible gravitational shortcuts and calculate the delay between graviton and photon signals and the ratio of the corresponding subtended horizons.
Helical spin textures with the marked spin polarizations of topological surface states have been firstly unveiled by the state-of-the-art spin- and angle-resolved photoemission spectroscopy for two promising topological insulators Bi$_2$Te$_2$Se and Bi$_2$Se$_2$Te. The highly spin-polarized natures are found to be persistent across the Dirac point in both compounds. This novel finding paves a pathway to extending their utilization of topological surface state for future spintronic applications.
The Northern Sky Optical Cluster Survey is a project to create an objective catalog of galaxy clusters over the entire high-galactic-latitude Northern sky, with well understood selection criteria. We use the object catalogs generated from the Digitized Second Palomar Sky Survey (DPOSS, Djorgovski et al. 1999) as the basis for this survey. We apply a color criterion to select against field galaxies, and use a simple adaptive kernel technique to create galaxy density maps, combined with the bootstrap technique to make significance maps, from which density peaks are selected. This survey attempts to eliminate some of the subjective criteria and assumptions of past surveys, including detection by eye (Abell 1958, ACO 1989) and assumed luminosity functions and cluster profiles (PDCS, Postman et al. 1995). We also utilize more information (especially colors) than the most similar recent survey, the APM (Dalton et al. 1992). This paper presents the details of our cluster detection technique, as well as some initial results for two small areas totaling ~60 square degrees. We find a mean surface density of ~1.5 clusters per square degree, consistent with the detection of richness class 0 and higher clusters to z~0.3. In addition, we demonstrate an effective photometric redshift estimator for our clusters.
Aguirregabiria et al showed that Einstein, Landau and Lifshitz, Papapetrou, and Weinberg energy-momentum complexes coincide for all Kerr-Schild metric. Bringely used their general expression of the Kerr-Schild class and found energy and momentum densities for the Bonnor metric. We obtain these results without using Aguirregabiria et al results and verify that Bringley's results are correct. This also supports Aguirregabiria et al results as well as Cooperstock hypothesis. Further, we obtain the energy distribution of the space-time under consideration.
Electron spins and photons are complementary quantum-mechanical objects that can be used to carry, manipulate and transform quantum information. To combine these resources, it is desirable to achieve the coherent coupling of a single spin to photons stored in a superconducting resonator. Using a circuit design based on a nanoscale spin-valve, we coherently hybridize the individual spin and charge states of a double quantum dot while preserving spin coherence. This scheme allows us to achieve spin-photon coupling up to the MHz range at the single spin level. The cooperativity is found to reach 2.3, and the spin coherence time is about 60ns. We thereby demonstrate a mesoscopic device suitable for non-destructive spin read-out and distant spin coupling.
A family F is intersecting if any two members have a nonempty intersection. Erdos, Ko, and Rado showed that |F|\leq {n-1\choose k-1} holds for an intersecting family of k-subsets of [n]:={1,2,3,...,n}, n\geq 2k. For n> 2k the only extremal family consists of all k-subsets containing a fixed element. Here a new proof is presented. It is even shorter than the classical proof of Katona using cyclic permutations, or the one found by Daykin applying the Kruskal-Katona theorem.