ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the set $\mathscr C$ of mean square values of the moduli of the conjugates of cyclotomic integers $\beta$. For its $k$th derived set $\mathscr C^{(k)}$, we show that $\mathscr C^{(k)}=(k+1)\mathscr C\,\, (k\ge 0)$, so that also ${\mathscr C}^{(k)}+{\mathscr C}^{(\ell)}={\mathscr C}^{(k+\ell+1)}\,\,(k,\ell\ge 0)$. We also calculate the order type of $\mathscr C$, and show that it is the same as that of the set of PV numbers.   Furthermore, we describe precisely the restricted set $\mathscr C_p$ where the $\beta$ are confined to the ring $\mathbb Z[\omega_p]$, where $p$ is an odd prime and $\omega_p$ is a primitive $p$th root of unity. In order to do this, we prove that both of the quadratic polynomials $a^2+ab+b^2+c^2+a+b+c$ and $a^2+b^2+c^2+ab+bc+ca+a+b+c$ are universal.
Chiral symmetry is an important aspect of QCD. Modelling this via the Nambu-Jona-Lasinio model, we construct a complete relativistic transport theory for quarks and mesons. The collision integral is analysed in a systematic 1/N_c approximation, and via this, it is shown that one can naturally incorporate mesonic degrees of freedom plus the hadronization of quarks and antiquarks into mesons into the field theoretic description. Time permitting, some simulation results, on the level of the Vlasov equation and also including collisions in a relaxation time approach, will be discussed.
Recent works have shown how realistic talking face images can be obtained under the supervision of geometry guidance, e.g., facial landmark or boundary. To alleviate the demand for manual annotations, in this paper, we propose a novel self-supervised hybrid model (DAE-GAN) that learns how to reenact face naturally given large amounts of unlabeled videos. Our approach combines two deforming autoencoders with the latest advances in the conditional generation. On the one hand, we adopt the deforming autoencoder to disentangle identity and pose representations. A strong prior in talking face videos is that each frame can be encoded as two parts: one for video-specific identity and the other for various poses. Inspired by that, we utilize a multi-frame deforming autoencoder to learn a pose-invariant embedded face for each video. Meanwhile, a multi-scale deforming autoencoder is proposed to extract pose-related information for each frame. On the other hand, the conditional generator allows for enhancing fine details and overall reality. It leverages the disentangled features to generate photo-realistic and pose-alike face images. We evaluate our model on VoxCeleb1 and RaFD dataset. Experiment results demonstrate the superior quality of reenacted images and the flexibility of transferring facial movements between identities.
A generalized Kullback-Leibler relative entropy is introduced starting with the symmetric Jackson derivative of the generalized overlap between two probability distributions. The generalization retains much of the structure possessed by the original formulation. We present the fundamental properties including positivity, metricity, concavity, bounds and stability. In addition, a connection to shift information and behavior under Liouville dynamics are discussed.
Recent learning-based image fusion methods have marked numerous progress in pre-registered multi-modality data, but suffered serious ghosts dealing with misaligned multi-modality data, due to the spatial deformation and the difficulty narrowing cross-modality discrepancy. To overcome the obstacles, in this paper, we present a robust cross-modality generation-registration paradigm for unsupervised misaligned infrared and visible image fusion (IVIF). Specifically, we propose a Cross-modality Perceptual Style Transfer Network (CPSTN) to generate a pseudo infrared image taking a visible image as input. Benefiting from the favorable geometry preservation ability of the CPSTN, the generated pseudo infrared image embraces a sharp structure, which is more conducive to transforming cross-modality image alignment into mono-modality registration coupled with the structure-sensitive of the infrared image. In this case, we introduce a Multi-level Refinement Registration Network (MRRN) to predict the displacement vector field between distorted and pseudo infrared images and reconstruct registered infrared image under the mono-modality setting. Moreover, to better fuse the registered infrared images and visible images, we present a feature Interaction Fusion Module (IFM) to adaptively select more meaningful features for fusion in the Dual-path Interaction Fusion Network (DIFN). Extensive experimental results suggest that the proposed method performs superior capability on misaligned cross-modality image fusion.
Analyzing recent experimental results, we find similar behaviors and a deep analogy between three-junction superconducting qubits and suspended carbon nanotubes. When these different systems are ac-driven near their resonances, the resonance single-peak, observed at weak driving, splits into two sub-peaks (Fig. 1) when the driving increases. This unusual behavior can be explained by considering quantum tunneling in a double well potential for both systems. Inspired by these experiments, we propose a mechanical qubit based on buckling nanobars--a NEMS so small as to be quantum coherent.   To establish buckling nanobars as legitimate candidates for qubits, we calculate the effective buckling potential that produces the two-level system and identify the tunnel coupling between the two local states. We propose different designs of nanomechanical qubits and describe how they can be manipulated. Also, we outline possible decoherence channels and detection schemes. A comparison between nanobars and well studied superconducting qubits suggests several future experiments on quantum electromechanics.
In this paper, we study the shadow produced by rotating black holes with charge in the presence of an anisotropic matter field. We obtain the apparent shape and the corresponding observables characterizing the size, oblateness, and deviation of the center, for different values of the parameters of the model. We compare the new results with those corresponding to the Kerr-Newmann spacetime and we also discuss the observational prospects in this case.
The production of strange particles $\Xi_{c}^{+}, K^{-}$ is simulated in mid-rapidity $pp$ collisions at $\sqrt{s}=7$ TeV with $0.2 \leq pt \leq 6$~GeV/c using the {\footnotesize PACIAE} model. The results are consistent with LHCb experimental data on $\Xi_{c}^{+}$ and $K^{-}$ yield. Then, a dynamically constrained phase-space coalescence ({\footnotesize DCPC}) model plus {\footnotesize PACIAE} model was used to produce the $\Xi_{c}^{+}K^{-}$ bound states and study the narrow excited $\Omega_{c}^{0}$ states through $\Omega_{c}^{0} \to \Xi_{c}^{+}K^{-}$ in $pp$ collisions at $\sqrt{s}=7$ and 13 TeV. The yield, transverse momentum distribution, and rapidity distribution of the five new excited $\Omega_{c}^{0}$ states of $\Omega_{c}(3000)^{0}$, $\Omega_{c}(3050)^{0}$, $\Omega_{c}(3066)^{0}$,$\Omega_{c}(3090)^{0}$and $\Omega_{c}(3119)^{0}$ were predicted.
For two-dimensional last-passage time models of weakly increasing paths, interesting scaling limits have been proved for points close the axis (the hard edge). For strictly increasing paths of Bernoulli($p$) marked sites, the relevant boundary is the line $y=px$. We call this the soft edge to contrast it with the hard edge. We prove laws of large numbers for the maximal cardinality of a strictly increasing path in the rectangle $[\fl{p^{-1}n -xn^a}]\times[n]$ as the parameters $a$ and $x$ vary. The results change qualitatively as $a$ passes through the value 1/2.
Grothendieck-Chow motives of quadric hypersurfaces have provided many insights into the theory of quadratic forms. Subsequently, the landscape of motives of more general projective homogeneous varieties has begun to emerge. In particular, there have been many results which relate the motive of a one homogeneous variety to motives of other simpler or smaller ones. In this paper, we exhibit a relationship between motives of two homogeneous varieties by producing a natural rational map between them which becomes a projective bundle morphism after being resolved. This allows one to use formulas for projective bundles and blowing up to relate the motives of the two varieties. We believe that in the future this ideas could be used to discover more relationships between other types of homogeneous varieties.
In this paper, we investigate some chemokinematical properties of the Milky Way disk, by using a sample composed by 424 late-type dwarfs. We show that the velocity dispersion of a stellar group correlates with the age of this group, according to a law proportional to t^0.26, where t is the age of the stellar group. The temporal evolution of the vertex deviation is considered in detail. It is shown that the vertex deviation does not seem to depend strongly on the age of the stellar group. Previous studies in the literature seem to not have found it due to the use of statistical ages for stellar groups, rather than individual ages. The possibility to use the orbital parameters of a star to derive information about its birthplace is investigated, and we show that the mean galactocentric radius is likely to be the most reliable stellar birthplace indicator. However, this information cannot be presently used to derive radial evolutionary constraints, due to an intrinsic bias present in all samples constructed from nearby stars. An extensive discussion of the secular and stochastic heating mechanisms commonly invoked to explain the age-velocity dispersion relation is presented. We suggest that the age-velocity dispersion relation could reflect the gradual decrease in the turbulent velocity dispersion from which disk stars form, a suggestion originally made by Tinsley and Larson (1978) and supported by several more recent disk evolution calculations. A test to distinguish between the two types of models using high-redshift galaxies is proposed.
We propose a Transformer-based NeRF (TransNeRF) to learn a generic neural radiance field conditioned on observed-view images for the novel view synthesis task. By contrast, existing MLP-based NeRFs are not able to directly receive observed views with an arbitrary number and require an auxiliary pooling-based operation to fuse source-view information, resulting in the missing of complicated relationships between source views and the target rendering view. Furthermore, current approaches process each 3D point individually and ignore the local consistency of a radiance field scene representation. These limitations potentially can reduce their performance in challenging real-world applications where large differences between source views and a novel rendering view may exist. To address these challenges, our TransNeRF utilizes the attention mechanism to naturally decode deep associations of an arbitrary number of source views into a coordinate-based scene representation. Local consistency of shape and appearance are considered in the ray-cast space and the surrounding-view space within a unified Transformer network. Experiments demonstrate that our TransNeRF, trained on a wide variety of scenes, can achieve better performance in comparison to state-of-the-art image-based neural rendering methods in both scene-agnostic and per-scene finetuning scenarios especially when there is a considerable gap between source views and a rendering view.
In this work, we explore a link between an unbounded spin system given by a system of stochastic differential equations and a random walk. This allows us to study the decay of the (co)variance of functions with respect to time. We extend here the previous work of T. Bodineau and G. Graham to a more general class of graph and potential.
We examine the origin of possible failures of the quark-hadron local duality. In particular, we consider a correlator of two currents comprising heavy quark operators, and compare the evaluation by the Operator Product Expansion with the result obtained inserting an infinite set of hadronic states, in the N_c to infinity limit. Whereas the smeared spectral functions agree with each other, their local behaviour is different. The difference manifests itself in the form of a term O(Lambda/epsilon) (epsilon being the residual energy) that is not present in the expansion in powers of Lambda/epsilon predicted by the OPE.
We have fabricated longitudinal nanoconstrictions in the charge-density wave conductor (CDW) NbSe$_{3}$ using a focused ion beam and using a mechanically controlled break-junction technique. Conductance peaks are observed below the T$_{P1}$$=145 $K and T$_{P2}$$=59 $K CDW transitions, which correspond closely with previous values of the full CDW gaps $2\Delta_{1}$ and $2\Delta_{2}$ obtained from photo-emission. These results can be explained by assuming CDW-CDW tunneling in the presence of an energy gap corrugation $\epsilon_{2}$ comparable to $\Delta_{2}$, which eliminates expected peak at $\Delta_{1}+\Delta_{2}$. The nanometer length-scales our experiments imply indicate that an alternative explanation based on tunneling through back-to-back CDW-normal junctions is unlikely.
We show how to generate bilinear (quadratic) Hamiltonians in cavity quantum electrodynamics (QED) through the interaction of a single driven three-level atom with two (one) cavity modes. With this scheme it is possible to generate one-mode mesoscopic squeezed superpositions, two-mode entanglements, and two-mode squeezed vacuum states (such the original EPR state), without the need for Ramsey zones and external parametric amplification. The degree of squeezing achieved is up to 99% with currently feasible experimental parameters and the errors due to dissipative mechanisms become practically negligible.
We report physical properties of the conductive magnet PdCrO2 consisting of a layered structure with a triangular lattice of Cr3+ ions (S=3/2). We confirmed an antiferromagnetic transition at TN=37.5K by means of specific heat, electrical resistivity, magnetic susceptibility, and neutron scattering measurements. The critical behavior in the specific heat persists in an unusually wide temperature range above TN. This fact implies that spin correlations develop even at much higher temperature than TN. The observed sub-linear temperature dependence of the resistivity above TN is also attributed to the short-range correlations among the frustrated spins. While the critical exponent for the magnetization agrees reasonably with the prediction of the relevant model, that for the specific heat evaluated in the wide temperature range differs substantially from the prediction.
We prove a relative form of Verdier's specialization formula, and apply it to derive a Chern class identity predicted by string dualities.
We review the Lyan alpha emission in local star-forming galaxies. In most cases as already shown by the IUE, the emission is absent or much weaker than expected. This occurs because Lyman alpha photons can be resonantly scattered by the neutral gas and destroyed by even very low amounts of dust. However new Hubble Space Telescope observations (HST) indicate that other factors such as the velocity structure of the gas play a crucial role. Gas flows are likely to occur as powered by the kinetic energy released via stellar winds and supernova. We propose a scenario based on the hydrodynamics of superbubbles powered by massive bursts of star formation that naturally accounts for the variety of Lyman alpha line detections in star-forming galaxies. We caution with the attempts to derive the co-moving star formation rate at high redshift from Lyman alpha emission searches.
This work investigates the influence of the Lorentz symmetry breaking in the bending angle of massive particles and light for bumblebee black hole solutions. The solutions analyzed break the Lorentz symmetry due to a non-zero vacuum expectation value of the bumblebee field. We use the Ishihara method, which allows us to study the bending angle of light for finite distances, and it is applicable to non-asymptotically flat spacetimes when considering the receiver viewpoint. In order to analyze the deflection of massive particles, we systematize the Ishihara method for its application in the Jacobi metric. This systematization allows the study of the deflection angle of massive particles using the Gauss-Bonnet theorem. We consider two backgrounds: the first was found by Bertolami et al. and is asymptotically flat. The second was found recently by Maluf et al. and is not asymptotically flat due to an effective cosmological constant.
Processing the data of lunar laser ranging (LLR) points to the effect of anomalous increase in the lunar semimajor axis (with an excessive rate about 1.3 cm/yr), which cannot be attributed to the well-known tidal exchange of angular momentum between the Earth and Moon. The nature of this phenomenon is not quite clear yet, but one of the possible explanations is that it is a manifestation of the "residual" Hubble expansion, caused by some forms of an unclumped "dark matter" or "dark energy". If this is the case, a similar effect will reveal itself also in operation of space-based interferometers with sufficiently long arms (10^7 km or greater, e.g., LISA and ASTROD) and, therefore, should be taken into account in processing the data on gravitational-wave signals.
We present the derivation of the free-free emission on the Galactic plane between l=20 and 44 degrees and |b| < 4 degrees, using Radio Recombination Line (RRL) data from the HI Parkes All-Sky Survey (HIPASS). Following an upgrade on the RRL data reduction technique, which improves significantly the quality of the final RRL spectra, we have extended the analysis to three times the area covered in Alves et al. (2010). The final RRL map has an angular resolution of 14.8 arcmin and a velocity resolution of 20 km/s.   A map of the electron temperature (Te) of the ionised gas is derived for the area under study using the line and continuum data from the present survey. The mean Te on the Galactic plane is 6000 K. The first direct measure of the free-free emission is obtained based on the derived Te map. Subtraction of this thermal component from the total continuum leaves the first direct measure of the synchrotron emission at 1.4 GHz. A narrow component of width 2 degrees is identified in the latitude distribution of the synchrotron emission. We present a list of HII regions and SNRs extracted from the present free-free and synchrotron maps, where we confirm the synchrotron nature of three objects: G41.12-0.21, G41.15+0.39 and G35.59-0.44. We also identify a bright (42 Jy) new double radio galaxy, J1841-0152, previously unrecognised owing to the high optical extinction in the region.   The latitude distribution for the RRL-derived free-free emission shows that the WMAP Maximum Entropy Method (MEM) is too high by ~ 50 per cent, in agreement with other recent results. The extension of this study to the inner Galaxy region l=-50 to 50 degrees will allow a better overall comparison of the RRL result with WMAP.
The braneworlds models were inspired partly by Kaluza-Klein's theory, where both the gravitational and the gauge fields are obtained from the geometry of a higher dimensional space. The positive aspects of these models consist in perspectives of modifications it could bring in to particle physics, such as: unification in a TeV scale, quantum gravity in this scale and deviation of Newton's law for small distances. One of the principles of these models is to suppose that all space-times can be embedded in a bulk of higher dimension. The main result in these notes is a theorem showing a mathematical inconsistency of the Randall-Sundrum braneworld model, namely that the Schwarzschild space-time cannot be embedded locally and isometrically in a five dimensional bulk with constant curvature,(for example AdS-5). From the point of view of semi-Riemannian geometry this last result represents a serious restriction to the Randall-Sundrum's braneworld model.
Images from the Solar Dynamics Observatory (SDO) at 211A are used to identify the solar source of the type III radio bursts seen in WIND/WAVES dynamic spectra. We analyse a 2.5 hour period during which six strong bursts are seen. The radio bursts correlate very well with the EUV jets coming from the western side of a sunspot in AR11092. The EUV jet emission also correlates well with brightening at what looks like their footpoint at the edge of the umbra. For 10-15 min after strong EUV jets are ejected, the footpoint brightens at roughly 3 min intervals. In both the EUV images and the extracted light curves, it looks as though the brightening is related to the 3-min sunspot oscillations, although the correlation coefficient is rather low. The only open field near the jets is rooted in the sunspot. We conclude that active region EUV/X-ray jets and interplanetary electron streams originate on the edge of the sunspot umbra. They form along a current sheet between the sunspot open field and closed field connecting to underlying satellite flux. Sunspot running penumbral waves cause roughly 3-min jet footpoint brightening. The relationship between the waves and jets is less clear.
We consider the velocity dependence arising from scattering through dark multipole moments, and its effects on the consistency of the signals observed by DAMA and CoGeNT with the dark matter hypothesis. We focus on the effects of the experimental uncertainties on the fits, and show that the two experiments combined favor dark matter scattering with a velocity-dependent cross-section over standard velocity and spin-independent scattering. When appropriate uncertainties are taken into account, we show that agreement of the two signals with each other and with the results of null experiments can be obtained.
Basing upon dual analytic models, we present arguments in favor of the parametrization of generalized parton distributions (GPD) in the form (x/g_0)^{(1-x)\tilde\alpha(t)}, where \tilde\alpha(t)=\alpha(t)-\alpha(0) is the nonlinear part of the Regge trajectory and g_0 is a parameter, g_0>1. For linear trajectories it reduces to earlier proposals. We compare the calculated moments of these GPD with the experimental data on form factors and find that the effects from the nonlinearity of Regge trajectories are large. By Fourier-transforming the obtained GPD, we access the spatial distribution of protons in the transverse plane. The relation between dual amplitudes with Mandelstam analyticity and composite models in the infinite momentum frame is discussed, the integration variable in dual models being associated with the quark longitudinal momentum fraction x in the nucleon.
We developed an easy, upscalable process to prepare lateral spin-valve devices on epitaxially grown monolayer graphene on SiC(0001) and perform nonlocal spin transport measurements. We observe the longest spin relaxation times tau_S in monolayer graphene, while the spin diffusion coefficient D_S is strongly reduced compared to typical results on exfoliated graphene. The increase of tau_S is probably related to the changed substrate, while the cause for the small value of D_S remains an open question.