ShantanuT01/DACTYL-Pretraining huggingface dataset:
Prior work has shown that the order in which different components of the face are learned using a sequential learner can play an important role in the performance of facial expression recognition systems. We propose FaceTopoNet, an end-to-end deep model for facial expression recognition, which is capable of learning an effective tree topology of the face. Our model then traverses the learned tree to generate a sequence, which is then used to form an embedding to feed a sequential learner. The devised model adopts one stream for learning structure and one stream for learning texture. The structure stream focuses on the positions of the facial landmarks, while the main focus of the texture stream is on the patches around the landmarks to learn textural information. We then fuse the outputs of the two streams by utilizing an effective attention-based fusion strategy. We perform extensive experiments on four large-scale in-the-wild facial expression datasets - namely AffectNet, FER2013, ExpW, and RAF-DB - and one lab-controlled dataset (CK+) to evaluate our approach. FaceTopoNet achieves state-of-the-art performance on three of the five datasets and obtains competitive results on the other two datasets. We also perform rigorous ablation and sensitivity experiments to evaluate the impact of different components and parameters in our model. Lastly, we perform robustness experiments and demonstrate that FaceTopoNet is more robust against occlusions in comparison to other leading methods in the area.
Using a sample of over 70, 000 red clump (RC) stars with $5$-$10$% distance accuracy selected from the LAMOST Spectroscopic Survey of the Galactic Anti-center (LSS-GAC), we study the radial and vertical gradients of the Galactic disk(s) mainly in the anti-center direction, covering a significant disk volume of projected Galactocentric radius $7 \leq R_{\rm GC} \leq 14$ kpc and height from the Galactic midplane $0 \leq |Z| \leq 3$ kpc. Our analysis shows that both the radial and vertical metallicity gradients are negative across much of the disk volume probed, and exhibit significant spatial variations. Near the solar circle ($7 \leq R_{\rm GC} \leq 11.5$ kpc), the radial gradient has a moderately steep, negative slope of $-0.08$ dex kpc$^{-1}$ near the midplane ($|Z| < 0.1$ kpc), and the slope flattens with increasing $|Z|$. In the outer disk ($11.5 < R_{\rm GC} \leq 14$ kpc), the radial gradients have an essentially constant, much less steep slope of $-0.01$ dex kpc $^{-1}$ at all heights above the plane, suggesting that the outer disk may have experienced an evolution path different from that of the inner disk. The vertical gradients are found to flatten largely with increasing $R_{\rm GC}$. However, the vertical gradient of the lower disk ($0 \leq |Z| \leq 1$ kpc) is found to flatten with $R_{\rm GC}$ quicker than that of the upper disk ($1 < |Z| \leq 3$ kpc). Our results should provide strong constraints on the theory of disk formation and evolution, as well as the underlying physical processes that shape the disk (e.g. gas flows, radial migration, internal and external perturbations).
The origin of nebular HeII emission, which is frequently observed in low-metallicity (O/H) star-forming galaxies, remains largely an unsolved question. Using the observed anticorrelation of the integrated X-ray luminosity per unit of star formation rate ($L_X/{\rm SFR}$) of an X-ray binary population with metallicity and other empirical data from the well-studied galaxy I Zw 18, we show that the observed HeII 4686 intensity and its trend with metallicity is naturally reproduced if the bulk of He$^+$ ionizing photons are emitted by the X-ray sources. We also show that a combination of X-ray binary population models with normal single and/or binary stellar models reproduces the observed $I(4686)/I(H\beta)$ intensities and its dependency on metallicity and age. We conclude that both empirical data and theoretical models suggest that high-mass X-ray binaries are the main source of nebular HeII emission in low-metallicity star-forming galaxies.
Eigenvalues and eigenfunctions of Mathieu's equation are found in the short wavelength limit using a uniform approximation (method of comparison with a `known' equation having the same classical turning point structure) applied in Fourier space. The uniform approximation used here relies upon the fact that by passing into Fourier space the Mathieu equation can be mapped onto the simpler problem of a double well potential. The resulting eigenfunctions (Bloch waves), which are uniformly valid for all angles, are then used to describe the semiclassical scattering of waves by potentials varying sinusoidally in one direction. In such situations, for instance in the diffraction of atoms by gratings made of light, it is common to make the Raman-Nath approximation which ignores the motion of the atoms inside the grating. When using the eigenfunctions no such approximation is made so that the dynamical diffraction regime (long interaction time) can be explored.
Emission lines formed in decretion disks of Be stars often undergo long-term cyclic variations, especially in the violet-to-red (V/R) ratio of their primary components. From observations of the bright Be-shell star zeta Tau, the possibly broadest and longest data set illustrating the prototype of this behaviour was compiled from our own and archival observations. It comprises optical and infrared spectra, broad-band polarimetry, and interferometric observations. From 3 V/R cycles between 1997 and 2008, a mean cycle length in H alpha of 1400-1430 days was derived. After each minimum in V/R, the shell absorption weakens and splits into two components, leading to 3 emission peaks. This phase makes the strongest contribution to the variability in cycle length. V/R curves of different lines are shifted in phase. Lines formed on average closer to the central star are ahead of the others. The shell absorption lines fall into 2 categories differing in line width, ionization/excitation potential, and variability of the equivalent width. The interferometry has resolved the continuum and the line emission in Br gamma and He I 2.06. The phasing of the Br gamma emission shows that the photocenter of the line-emitting region lies within the plane of the disk but is offset from the continuum source. The plane of the disk is constant throughout the observed V/R cycles. The self-consistent, one-armed, disk-oscillation model is developed in Paper II.
We study the initiation of thermonuclear detonations in tidally disrupted white dwarf stars by intermediate-mass ($10^3 M_\odot$) black holes. The length scales required to resolve the initiation mechanism are not easily reached in three-dimensions, so instead we have devised two-dimensional proxy models which, together with a logarithmic gridding strategy, can adequately capture detonation wave fronts as material undergoes simultaneous compression and stretching from tidal forces. We consider 0.15 and 0.6 solar mass white dwarf stars parameterized by tidal strengths in the range $\beta=4~\text{to}~23$. High spatial resolution elucidates the manner and conditions leading to thermonuclear detonation, linking the initiation sequence to stellar composition and tidal strength. All of our models suffer sustained detonations triggered by a combination of adiabatic compression, mild thermonuclear preconditioning, and collisional heating, in degrees depending primarily on tidal strength. We find many diagnostics, such as temperature, total released energy, and iron group products, are fairly well-converged (better than 10%) at resolutions below 10 km along the scale height of the orbital plane. The exceptions are intermediate mass transients like calcium, which remain uncertain up to factors of two even at 1 km resolution.
Human pose forecasting is a complex structured-data sequence-modelling task, which has received increasing attention, also due to numerous potential applications. Research has mainly addressed the temporal dimension as time series and the interaction of human body joints with a kinematic tree or by a graph. This has decoupled the two aspects and leveraged progress from the relevant fields, but it has also limited the understanding of the complex structural joint spatio-temporal dynamics of the human pose. Here we propose a novel Space-Time-Separable Graph Convolutional Network (STS-GCN) for pose forecasting. For the first time, STS-GCN models the human pose dynamics only with a graph convolutional network (GCN), including the temporal evolution and the spatial joint interaction within a single-graph framework, which allows the cross-talk of motion and spatial correlations. Concurrently, STS-GCN is the first space-time-separable GCN: the space-time graph connectivity is factored into space and time affinity matrices, which bottlenecks the space-time cross-talk, while enabling full joint-joint and time-time correlations. Both affinity matrices are learnt end-to-end, which results in connections substantially deviating from the standard kinematic tree and the linear-time time series. In experimental evaluation on three complex, recent and large-scale benchmarks, Human3.6M [Ionescu et al. TPAMI'14], AMASS [Mahmood et al. ICCV'19] and 3DPW [Von Marcard et al. ECCV'18], STS-GCN outperforms the state-of-the-art, surpassing the current best technique [Mao et al. ECCV'20] by over 32% in average at the most difficult long-term predictions, while only requiring 1.7% of its parameters. We explain the results qualitatively and illustrate the graph interactions by the factored joint-joint and time-time learnt graph connections.   Our source code is available at: https://github.com/FraLuca/STSGCN
One can get the impression from the Reissner-Nordstrom solution of Einstein's equations that the charge of a body reduces its gravitational field. This looks surprising since the energy of the electrostatic field surrounding a charged body, must contribute positively, as an additional, "electromagnetic mass", to the gravitational field produced by the body. We resolve this puzzle by showing that the mass M in the Reissner-Nordstrom solution is not the "bare mass" of the body, but its "renormalized mass". I. e. M, in addition to the bare mass, includes the total electromagnetic mass of the body. But at finite distances from the body only a part of the electromagnetic mass contributes to the gravitational field. That is why the gravity of a charged body is determined by the quantity smaller than M.
In this work we apply entropic sampling simulations to a three-state model which has exact solutions in the microcanonical and grand-canonical ensembles. We consider $N$ chains placed on an unidimensional lattice, such that each site may assume one of three-states: empty (state 1), with a single molecule energetically null (state 2), and with a single molecule with energy $\varepsilon$ (state 3). Each molecule, which we will treat here as dimers, consists of two monomers connected one to each other by a rod. The thermodynamic properties, such as internal energy, densities of dimers and specific heat were obtained as functions of temperature where the analytic results in the micro-canonical and grand-canonical ensembles were successfully confirmed by the entropic sampling simulations.
We investigate a mechanism for cooling a lead based on a process that replaces hot electrons by cold ones. The central idea is that a double quantum dot with an inhomogeneous Zeeman splitting acts as energy filter for the transported electrons. The setup is such that hot electrons with spin up are removed, while cold electrons with spin down are added. The required non-equilibrium condition is provided by the capacitive coupling of one quantum dot to the shot noise of a strongly biased quantum point contact in the tunnelling limit. Special attention is paid to the identification of an operating regime in which the net electrical current vanishes.
Shanks's infrastructure algorithm and Buchmann's algorithm for computing class groups and unit groups of rings of integers of algebraic number fields are most naturally viewed as computations inside Arakelov class groups. In this paper we discuss the basic properties of Arakelov class groups and of the set of reduced Arakelov divisors. As an application we describe Buchmann's algorithm in this context.
We propose a new design for a quantum information processor where qubits are encoded into Hyperfine states of ions held in a linear array of individually tailored microtraps and sitting in a spatially varying magnetic field. The magnetic field gradient introduces spatially dependent qubit transition frequencies and a type of spin-spin interaction between qubits. Single and multi-qubit manipulation is achieved via resonant microwave pulses as in liquid-NMR quantum computation while the qubit readout and reset is achieved through trapped-ion fluorescence shelving techniques. By adjusting the microtrap configurations we can tailor, in hardware, the qubit resonance frequencies and coupling strengths. We show the system possesses a side-band transition structure which does not scale with the size of the processor allowing scalable frequency discrimination between qubits. By using large magnetic field gradients, one can readout and reset the qubits in the ion chain via frequency selective optical pulses avoiding the need for many tightly focused laser beams for spatial qubit addressing.
In this paper, we consider a game played on a rectangular $m \times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along existing grid lines, until just $mn$ individual squares remain.   This paper enumerates the number of ways to break an $m \times n$ bar, which we call chocolate numbers, and introduces four new sequences related to these numbers. Using various techniques, we prove interesting divisibility results regarding these sequences.
Grain boundaries (GBs) play a fundamental role in the strengthening mechanism of crystalline structures by acting as an impediment to dislocation motion. However, the presence of an aggressive environment such as hydrogen increases the susceptibility to intergranular fracture. Further, there is a lack of systematic investigations exploring the role of hydrogen on the dislocation-grain-boundary (DGB) interactions. Thus, in this work, the effect of hydrogen on the interactions between a screw dislocation and <111> tilt GBs in {\alpha}-Fe were examined. Our simulations reveal that the outcome of the DGB interaction strongly depends on the underlying GB dislocation network. Further, there exists a strong correlation between the GB energy and the energy barrier for slip transmission. In other words, GBs with lower interfacial energy demonstrate a higher barrier for slip transmission. The introduction of hydrogen along the GB causes the energy barrier for slip transmission to increase consistently for all of the GBs examined. The energy balance for a crack initiation in the presence of hydrogen was examined with the help of our observations and previous findings. It was found that the presence of hydrogen increases the strain energy stored within the GB which could lead to a transgranular-to-intergranular fracture mode transition.
We describe a simple fully analytic model of the excursion set approach associated with two Gaussian random walks: the first walk represents the initial overdensity around a protohalo, and the second is a crude way of allowing for other factors which might influence halo formation. This model is richer than that based on a single walk, because it yields a distribution of heights at first crossing. We provide explicit expressions for the unconditional first crossing distribution which is usually used to model the halo mass function, the progenitor distributions, and the conditional distributions from which correlations with environment are usually estimated. These latter exhibit perhaps the simplest form of what is often called nonlocal bias, and which we prefer to call stochastic bias, since the new bias effects arise from `hidden-variables' other than density, but these may still be defined locally. We provide explicit expressions for these new bias factors. We also provide formulae for the distribution of heights at first crossing in the unconditional and conditional cases. In contrast to the first crossing distribution, these are exact, even for moving barriers, and for walks with correlated steps. The conditional distributions yield predictions for the distribution of halo concentrations at fixed mass and formation redshift. They also exhibit assembly bias like effects, even when the steps in the walks themselves are uncorrelated. Finally, we show how the predictions are modified if we add the requirement that halos form around peaks: these depend on whether the peaks constraint is applied to a combination of the overdensity and the other variable, or to the overdensity alone. Our results demonstrate the power of requiring models to reproduce not just halo counts but the distribution of overdensities at fixed protohalo mass as well.
The moduli space $M(c_2)$, of stable rank two vector bundles of degree one on a very general quintic surface $X\subset {\mathbb P}^3$, is irreducible for all $c_2\geq 4$ and empty otherwise.
In the high dimension (mean field) limit the susceptibility and the second moment correlation length of the Ising ferromagnet depend on temperature as chi(T)=tau^{-1} and xi(T)=T^{-1/2}tau^{-1/2} exactly over the entire temperature range above the critical temperature T_c, with the scaling variable tau=(T-T_c)/T. For finite dimension ferromagnets temperature dependent effective exponents can be defined over all T using the same expressions. For the canonical two dimensional square lattice Ising ferromagnet it is shown that compact "extended scaling" expressions analogous to the high dimensional limit forms give accurate approximations to the true temperature dependencies, again over the entire temperature range from T_c to infinity. Within this approach there is no cross-over temperature in finite dimensions above which mean-field-like behavior sets in.
We study the role of the scalar resonances f0(1370), f0(1500) and f0(1710) in the strong and radiative three-body decays of J/psi with J/psi to V + P P (gamma gamma) and J/psi to gamma + P P (V V), where P (V) denotes a pseudoscalar (vector) meson. We assume that the scalars result from a glueball-quarkonium mixing scheme while the dynamics of the transition process is described in an effective chiral Lagrangian approach. Present data on J/psi to V + P P are well reproduced, predictions for the radiative processes serve as further tests of this scenario.
It is known that any two-outcome quantum measurement can be decomposed into a continuous stochastic process using a feedback loop. In this article, we characterize which of these decompositions are possible when each iteration of the feedback loop consists of a weak measurement caused by an interaction with a probe system. We restrict ourselves to the case when the probe is a qubit and the interaction Hamiltonian between the probe and system is constant. We find that even given the ability to perform arbitrary unitary pulses throughout the continuous decomposition, only generalized measurements with two distinct singular values are achievable. However, this is sufficient to decompose a generalized qubit measurement using a qubit probe and a simple interaction Hamiltonian.
We present thermal and electrical transport measurements of low-density (10$^{14}$ m$^{-2}$), mesoscopic two-dimensional electron systems (2DESs) in GaAs/AlGaAs heterostructures at sub-Kelvin temperatures. We find that even in the supposedly strongly localised regime, where the electrical resistivity of the system is two orders of magnitude greater than the quantum of resistance $h/e^2$, the thermopower decreases linearly with temperature indicating metallicity. Remarkably, the magnitude of the thermopower exceeds the predicted value in non-interacting metallic 2DESs at similar carrier densities by over two orders of magnitude. Our results indicate a new quantum state and possibly a novel class of itinerant quasiparticles in dilute 2DESs at low temperatures where the Coulomb interaction plays a pivotal role.
I report on the communications and posters presented on exact solutions and their interpretation at the GRG18 Conference, Sydney.
The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. Motivated by the recent work [Faria, L., Figueiredo, C.M.H. de, Sykora, O., Vrt'o, I.: An improved upper bound on the crossing number of the hypercube. J. Graph Theory {\bf 59}, 145--161 (2008)] which solves the upper bound conjecture on the crossing number of $n$-dimensional hypercube proposed by Erd\H{o}s and Guy, we give upper and lower bounds of the crossing number of locally twisted cube, which is one of variants of hypercube.
Ferromagnetic contacts put in proximity with carbon nanotubes induce spin and orbital polarizations. These polarizations affect dramatically the Kondo correlations occurring in quantum dots formed in a carbon nanotube, inducing effective fields in both spin and orbital sectors. As a consequence, the carbon nanotube quantum dot spectral density shows a four-fold split SU(4) Kondo resonance. Furthermore, the presence of spin-orbit interactions leads to the occurrence of an additional polarization among time-reversal electronic states (polarization in the time-reversal symmetry or Kramers sector). Here, we estimate the magnitude for the Kramer polarization in realistic carbon nanotube samples and find that its contribution is comparable to the spin and orbital polarizations. The Kramers polarization generates a new type of effective field that affects only the time-reversal electronic states. We report new splittings of the Kondo resonance in the dot spectral density which can be understood only if Kramers polarization is taken into account. Importantly, we predict that the existence of Kramers polarization can be experimentally detected by performing nonlinear differential conductance measurements. We also find that, due to the high symmetry required to build SU(4) Kondo correlations, its restoration by applying an external field is not possible in contrast to the compensated SU(2) Kondo state observed in conventional quantum dots.
We study a class of extremal transitions between topological distinct Calabi--Yau manifolds which have an interpretation in terms of the special massless states of a type II string compactification. In those cases where a dual heterotic description exists the exceptional massless states are due to genuine strong (string-) coupling effects. A new feature is the appearance of enhanced non-abelian gauge symmetries in the exact nonperturbative theory.
The superspace formulation of the worldvolume action of twistor string models is considered. It is shown that for the Berkovits-Siegel closed twistor string such a formulation is provided by a N=4 twistor-like action of the tensionless superstring. A similar inverse twistor transform of the open twistor string model (Berkovits model) results in a dynamical system containing two copies of the D=4, N=4 superspace coordinate functions, one left-moving and one right-moving, that are glued by the boundary conditions.   We also discuss possible candidates for a tensionful superstring action leading to the twistor string in the tensionless limit as well as multidimensional counterparts of twistor strings in the framework of both `standard' superspace and superspace enlarged by tensorial coordinates (tensorial superspaces), which constitute a natural framework for massless higher spin theories.