ShantanuT01/DACTYL-Pretraining huggingface dataset:
Weak gravitational lensing is one of the most promising tools to investigate the equation-of-state of dark energy. In order to obtain reliable parameter estimations for current and future experiments, a good theoretical understanding of dark matter clustering is essential. Of particular interest is the statistical precision to which weak lensing observables, such as cosmic shear correlation functions, can be determined. We construct a fitting formula for the non-Gaussian part of the covariance of the lensing power spectrum. The Gaussian contribution to the covariance, which is proportional to the lensing power spectrum squared, and optionally shape noise can be included easily by adding their contributions. Starting from a canonical estimator for the dimensionless lensing power spectrum, we model first the covariance in the halo model approach including all four halo terms for one fiducial cosmology and then fit two polynomials to the expression found. On large scales, we use a first-order polynomial in the wave-numbers and dimensionless power spectra that goes asymptotically towards $1.1 C_{pt}$ for $\ell \to 0$, i.e., the result for the non-Gaussian part of the covariance using tree-level perturbation theory. On the other hand, for small scales we employ a second-order polynomial in the dimensionless power spectra for the fit. We obtain a fitting formula for the non-Gaussian contribution of the convergence power spectrum covariance that is accurate to 10% for the off-diagonal elements, and to 5% for the diagonal elements, in the range $50 \lesssim \ell \lesssim 5000$ and can be used for single source redshifts $z_{s} \in [0.5,2.0]$ in WMAP5-like cosmologies.
When instantons are put into the Higgs phase, vortices are attached to instantons. We construct such composite solitons as 1/4 BPS states in five-dimensional supersymmetric U(Nc) gauge theory with Nf(>=Nc) fundamental hypermultiplets. We solve the hypermultiplet BPS equation and show that all 1/4 BPS solutions are generated by an Nc x Nf matrix which is holomorphic in two complex variables, assuming the vector multiplet BPS equation does not give additional moduli. We determine the total moduli space formed by topological sectors patched together and work out the multi-instanton solution inside a single vortex with complete moduli. Small instanton singularities are interpreted as small sigma-model lump singularities inside the vortex. The relation between monopoles and instantons in the Higgs phase is also clarified as limits of calorons in the Higgs phase. Another type of instantons stuck at an intersection of two vortices and dyonic instantons in the Higgs phase are also discussed.
Recent advances in deep neural networks have been developed via architecture search for stronger representational power. In this work, we focus on the effect of attention in general deep neural networks. We propose a simple and effective attention module, named Bottleneck Attention Module (BAM), that can be integrated with any feed-forward convolutional neural networks. Our module infers an attention map along two separate pathways, channel and spatial. We place our module at each bottleneck of models where the downsampling of feature maps occurs. Our module constructs a hierarchical attention at bottlenecks with a number of parameters and it is trainable in an end-to-end manner jointly with any feed-forward models. We validate our BAM through extensive experiments on CIFAR-100, ImageNet-1K, VOC 2007 and MS COCO benchmarks. Our experiments show consistent improvement in classification and detection performances with various models, demonstrating the wide applicability of BAM. The code and models will be publicly available.
In this paper, we prove an unconditionnal bound for the analytic rank (i.e the order of vanishing at the critical point of the $L$ function) of the new part $J^n_0(q)$, of the jacobian of the modular curve $X_0(q)$. Our main resultis the following upper bound: for $q$ prime, one has $$rank_a(J_0^n(q))\ll \dim J_0^n(q)$$ where the implied constant is absolute. All previously known non trivials bounds of $rank_a(J_0^n(q))$ assumed the generalized Riemann hypothesis; here, our proof is unconditionnal, and is based firstly on the construction by Perelli and Pomykala of a new test function in the context of Riemann-Weil explicit formulas, and secondly on a density theorem for the zeros of $L$ functions attached to new forms.
The analysis of phase shifts in executed and proposed interferometry experiments on photons and neutrons neglected forces exerted at the boundaries of spatial constrictions. When those forces are included it is seen that the observed phenomena are not in fact geometric in nature. A new proposal to be published by Allman et al. avoids that pitfall.
We establish a regularity criterion for the 3D full compressible magnetohydrodynamic equations with zero heat conductivity and vacuum in a bounded domain.
We investigate an initial-boundary value problem for a quasilinear nonhomogeneous, anisotropic Maxwell system subject to an absorbing boundary condition of Silver & M\"uller type in a smooth, bounded, strictly star-shaped domain of $\mathbb{R}^{3}$. Imposing usual smallness assumptions in addition to standard regularity and compatibility conditions, a nonlinear stabilizability inequality is obtained by showing nonlinear dissipativity and observability-like estimates enhanced by an intricate regularity analysis. With the stabilizability inequality at hand, the classic nonlinear barrier method is employed to prove that small initial data admit unique classical solutions that exist globally and decay to zero at an exponential rate. Our approach is based on a recently established local well-posedness theory in a class of $\mathcal{H}^{3}$-valued functions.
We propose a new method to numerically calculate transition points that belongs to 2D Ising universality class for quantum spin models. Generally, near the multicritical point, in conventional methods, a finite size correction becomes very large. To suppress the effect of the multicritical point, we use a z-axis twisted boundary condition and a y-axis twisted boundary condition. We apply our method to an S = 1/2 bond-alternating XXZ model. The multicritical point of this model has a BKT transition, where the correlation length diverges singularly. However, with our method, the convergence of calculation is highly improved, thus we can calculate the transition point even near the multicritical point.
We have quantized a flat cosmological model in the context of the metric f(R) models, using the causal Bohmian quantum theory. The equations are solved and then we have obtained how the quantum corrections influence the classical equations.
Nonlinear Compton scattering is calculated for the collision of an electron with a plane wave pulse. A mid infra-red (IR) peak arises in the photon spectrum due to long-range interference associated with the pulse envelope. The case of a flat-top pulse is studied as a toy model for pulse envelope effects and reduced to two final-state momentum integrations; the case of a sine-squared pulse is studied numerically. A perturbative expansion in charge-field coupling reveals that already at intermediate intensities, many orders are required to correctly capture the structure of the mid-IR peak. By regularising the classical result, it is shown that the mid-IR peak is due to plane-wave ponderomotive effects on the pulse envelope. Finally, it is shown that the mid-IR peak can be isolated using energy, angle and polarisation filters.
(Abridged) We use N-body simulations to study the effects that a divergent (i.e. "cuspy") dark matter (DM) profile introduces on the tidal evolution of dwarf spheroidal galaxies (dSphs). Our models assume cosmologically-motivated initial conditions where dSphs are DM-dominated systems on eccentric orbits about a host galaxy composed of a dark halo and a baryonic disc. We find that the resilience of dSphs to tidal stripping is extremely sensitive to the halo cuspiness; whereas dwarfs with a cored profile can be easily destroyed by the host disc, those with cusps always retain a bound remnant. For a given halo profile the evolution of the structural parameters as driven by tides is controlled solely by the total amount of mass lost. This information is used to construct a semi-analytic code that simulates the hierarchical build-up of spiral galaxies assuming different halo profiles and disc masses. We find that tidal encounters with discs tend to decrease the average mass of satellites at all galactocentric radii. Interestingly, satellites accreted before re-ionization (z>6), which may be singled out by anomalous metallicity patterns, survive only if haloes are cuspy. We show that the size-mass relation established from Milky Way (MW) dwarfs strongly supports the presence of cusps in the majority of these systems, as cored models systematically underestimate the masses of the known Ultra-Faint dSphs. Our models also indicate that a massive M31 disc may explain why many of its dSphs fall below the size-mass relationship derived from MW dSphs. We use our models to constrain the mass threshold below which star formation is suppressed in DM haloes, finding that luminous satellites must be accreted with masses above 10^8--10^9 M_sol in order to explain the size-mass relation observed in MW dwarfs.
We measure the projected number density profiles of galaxies and the splashback feature in clusters selected by the Sunyaev--Zeldovich (SZ) effect from the Advanced Atacama Cosmology Telescope (AdvACT) survey using galaxies observed by the Dark Energy Survey (DES). The splashback radius for the complete galaxy sample is consistent with theoretical measurements from CDM-only simulations, and is located at $2.4^{+0.3}_{-0.4}$ Mpc $h^{-1}$. We split the sample based on galaxy color and find significant differences in the profile shapes. Red galaxies and those in the green valley show a splashback-like minimum in their slope profile consistent with theoretical predictions, while the bluest galaxies show a weak feature that appears at a smaller radius. We develop a mapping of galaxies to subhalos in $N$-body simulations by splitting subhalos based on infall time onto the cluster halos. We find that the location of the steepest slope and differences in the shapes of the profiles can be mapped to differences in the average time of infall of galaxies of different colors. The minima of the slope in the galaxy profiles trace a discontinuity in the phase space of dark matter halos. By relating spatial profiles to infall time for galaxies of different colours, we can use splashback as a clock to understand galaxy quenching. We find that red galaxies have on average been in their clusters for over $3.2 ~\rm Gyrs$, green galaxies about $2.2 ~\rm Gyrs$, while blue galaxies have been accreted most recently and have not reached apocenter. Using the information from the complete radial profiles, we fit a simple quenching model and find that the onset of galaxy quenching in clusters occurs after a delay of about a gigayear, and that galaxies quench rapidly thereafter with an exponential timescale of $0.6$ Gyr.
Starting from an approximate microscopic model of a trapped Bose-condensed gas at finite temperatures, we derive an equation of motion for the condensate wavefunction and a quantum kinetic equation for the distribution function for the excited atoms. The kinetic equation includes collisions between the condensate and non-condensate atoms ($C_{12}$), in addition to collisions between the excited atoms as described by the Uehling-Uhlenbeck ($C_{22}$) collision integral. Assuming that the $C_{22}$ collision rate is sufficiently rapid to produce a local equilibrium Bose distribution, the kinetic equation can be used to derive hydrodynamic equations for the non-condensate. These equations include a description of the equilibration of the local chemical potentials of the condensate and non-condensate components which gives rise to a new relaxational mode associated with the exchange of atoms between the two components. We show how the Landau two-fluid equations emerge in the frequency domain $\omega \tau_\mu \ll 1$, where $\tau_\mu$ is a characteristic relaxation time of the equilibration process. This process provides an additional source of damping of the collective modes (first and second sound in the case of a uniform system). Our equations are consistent with the generalized Kohn theorem. Finally, a variational solution of the equations is developed which is used to determine some of the monopole, dipole and quadrupole normal modes of a trapped Bose gas in an isotropic trap.
We present a detailed study of the small frequency separations as diagnostics of the mass of the convective core and evolutionary stage of solar-type stars. We demonstrate how the small separations can be combined to provide sensitive tests for the presence of convective overshoot at the edge of the core. These studies are focused on low degree oscillation modes, the only modes expected to be detected in distant stars. Using simulated data with realistic errors, we find that the mass of the convective core can be estimated to within 5% if the total stellar mass is known. Systematic errors arising due to uncertainty in the mass could be up to 20%. The evolutionary stage of the star, determined in terms of the central hydrogen abundance using our proposed technique, however, is much less sensitive to the mass estimate.
We present results from an original observational campaign comprising five epoch optical photopolarimetrical observations of the BL Lac-type AGN OJ287 in the period 2012 November - 2013 April. The data are gathered with the Focal Reducer Rozhen 2 - FoReRo2 on the 2-m RCC telescope at NAO Rozhen, Bulgaria. We derive photometry and polarization in R-band, as well as position angle (P.A.). There are indications for correlation between polarization and brightness in R-band. Furthermore, observed variation in P.A. corresponds to a rotation of the plane of polarization of 5.80 deg per day.
Remote physiological measurements, e.g., remote photoplethysmography (rPPG) based heart rate (HR), heart rate variability (HRV) and respiration frequency (RF) measuring, are playing more and more important roles under the application scenarios where contact measurement is inconvenient or impossible. Since the amplitude of the physiological signals is very small, they can be easily affected by head movements, lighting conditions, and sensor diversities. To address these challenges, we propose a cross-verified feature disentangling strategy to disentangle the physiological features with non-physiological representations, and then use the distilled physiological features for robust multi-task physiological measurements. We first transform the input face videos into a multi-scale spatial-temporal map (MSTmap), which can suppress the irrelevant background and noise features while retaining most of the temporal characteristics of the periodic physiological signals. Then we take pairwise MSTmaps as inputs to an autoencoder architecture with two encoders (one for physiological signals and the other for non-physiological information) and use a cross-verified scheme to obtain physiological features disentangled with the non-physiological features. The disentangled features are finally used for the joint prediction of multiple physiological signals like average HR values and rPPG signals. Comprehensive experiments on different large-scale public datasets of multiple physiological measurement tasks as well as the cross-database testing demonstrate the robustness of our approach.
We study an evolving bipolar active region that exhibits flux cancellation at the internal polarity inversion line, the formation of a soft X-ray sigmoid along the inversion line and a coronal mass ejection. The evolution of the photospheric magnetic field is described and used to estimate how much flux is reconnected into the flux rope. About one third of the active region flux cancels at the internal polarity inversion line in the 2.5~days leading up to the eruption. In this period, the coronal structure evolves from a weakly to a highly sheared arcade and then to a sigmoid that crosses the inversion line in the inverse direction. These properties suggest that a flux rope has formed prior to the eruption. The amount of cancellation implies that up to 60% of the active region flux could be in the body of the flux rope. We point out that only part of the cancellation contributes to the flux in the rope if the arcade is only weakly sheared, as in the first part of the evolution. This reduces the estimated flux in the rope to $\sim\!30%$ or less of the active region flux. We suggest that the remaining discrepancy between our estimate and the limiting value of $\sim\!10%$ of the active region flux, obtained previously by the flux rope insertion method, results from the incomplete coherence of the flux rope, due to nonuniform cancellation along the polarity inversion line. A hot linear feature is observed in the active region which rises as part of the eruption and then likely traces out field lines close to the axis of the flux rope. The flux cancellation and changing magnetic connections at one end of this feature suggest that the flux rope reaches coherence by reconnection shortly before and early in the impulsive phase of the associated flare. The sigmoid is destroyed in the eruption but reforms within a few hours after a moderate amount of further cancellation has occurred.
We establish Strichartz estimates for the Schr\"odinger equation on Riemannian manifolds $(\Omega,\g)$ with boundary, for both the compact case and the case that $\Omega$ is the exterior of a smooth, non-trapping obstacle in Euclidean space. The estimates for exterior domains are scale invariant; the range of Lebesgue exponents $(p,q)$ for which we obtain these estimates is smaller than the range known for Euclidean space, but includes the key $L^4_tL^\infty_x$ estimate, which we use to give a simple proof of well-posedness results for the energy critical Schr\"odinger equation in 3 dimensions. Our estimates on compact manifolds involve a loss of derivatives with respect to the scale invariant index. We use these to establish well-posedness for finite energy data of certain semilinear Schr\"odinger equations on general compact manifolds with boundary.
To each permutation $\sigma$ in $S_{n}$ we associate a triangulation of a fixed $(n+2)$-gon. We then determine the fibers of this association and show that they coincide with the sylvester classes depicted By Novelli, Hivert and Thibon. A signed version of this construction allows us to reformulate the four color theorem in terms of the existence of a signable path between any two permutations in the Cayley graph of the symmetric group $S_{n}.
The presence of non-trivial magnetic topology can give rise to non-vanishing scalar spin chirality and consequently a topological Hall or Nernst effect. In turn, topological transport signals can serve as indicators for topological spin structures. This is particularly important in thin films or nanopatterned materials where the spin structure is not readily accessible. Conventionally, the topological response is determined by combining magnetotransport data with an independent magnetometry experiment. This approach is prone to introduce measurement artifacts. In this study, we report the observation of large topological Hall and Nernst effects in micropatterned thin films of Mn$_{1.8}$PtSn below the spin reorientation temperature $T_\mathrm{SR} \approx 190$K. The magnitude of the topological Hall effect $\rho_\mathrm{xy}^\mathrm{T} = 8$ n$\Omega$m is close to the value reported in bulk Mn$_2$PtSn, and the topological Nernst effect $S_\mathrm{xy}^\mathrm{T} = 115$ nV K$^{-1}$ measured in the same microstructure has a similar magnitude as reported for bulk MnGe ($S_\mathrm{xy}^\mathrm{T} \sim 150$ nV K$^{-1}$), the only other material where a topological Nernst was reported. We use our data as a model system to introduce a topological quantity, which allows to detect the presence of topological transport effects without the need for independent magnetometry data. Our approach thus enables the study of topological transport also in nano-patterned materials without detrimental magnetization related limitations.
We report a set of monogamy constraints on one-tangle, two-tangles, three-tangles and four-way correlations of a general four-qubit pure state. It is found that given a two-qubit marginal state $\rho$ of a four qubit pure state $\left\vert \Psi_{4}\right\rangle $, the non-Hermitian matrix $\rho\widetilde{\rho}$ where $\widetilde{\rho}$ $=\left( \sigma_{y} \otimes\sigma_{y}\right) \rho^{\ast}\left( \sigma_{y}\otimes\sigma_{y}\right) $, contains information not only about the entanglement properties of the two-qubits in state $\rho$ but also about three tangles involving the selected pair as well as four-way correlations of the pair of qubits in $\left\vert \Psi_{4}\right\rangle $. To extract information about tangles of a four-qubit state $\left\vert \Psi_{4}\right\rangle $, the coefficients in the characteristic polynomial of matrix $\rho\widetilde{\rho}$ are analytically expressed in terms of $2\times2$ matrices of state coefficients. Four-tangles distinguish between different types of entangled four-qubit pure states.
Hands are often severely occluded by objects, which makes 3D hand mesh estimation challenging. Previous works often have disregarded information at occluded regions. However, we argue that occluded regions have strong correlations with hands so that they can provide highly beneficial information for complete 3D hand mesh estimation. Thus, in this work, we propose a novel 3D hand mesh estimation network HandOccNet, that can fully exploits the information at occluded regions as a secondary means to enhance image features and make it much richer. To this end, we design two successive Transformer-based modules, called feature injecting transformer (FIT) and self- enhancing transformer (SET). FIT injects hand information into occluded region by considering their correlation. SET refines the output of FIT by using a self-attention mechanism. By injecting the hand information to the occluded region, our HandOccNet reaches the state-of-the-art performance on 3D hand mesh benchmarks that contain challenging hand-object occlusions. The codes are available in: https://github.com/namepllet/HandOccNet.
We present new $L^\infty$ a priori estimates for weak solutions of a wide class of subcritical $p$-laplacian equations in bounded domains. No hypotheses on the sign of the solutions, neither of the non-linearities are required. This method is based in elliptic regularity for the $p$-laplacian combined either with Gagliardo-Nirenberg or Caffarelli-Kohn-Nirenberg interpolation inequalities.   Let us consider a quasilinear boundary value problem $ -\Delta_p u= f(x,u),$ in $\Omega,$ with Dirichlet boundary conditions, where $\Omega \subset \mathbb{R}^N $, with $p<N,$ is a bounded smooth domain strictly convex, and $f$ is a subcritical Carath\'eodory non-linearity. We provide $L^\infty$ a priori estimates for weak solutions, in terms of their $L^{p^*}$-norm, where $p^*= \frac{Np}{N-p}\ $ is the critical Sobolev exponent.   By a subcritical non-linearity we mean, for instance, $|f(x,s)|\le |x|^{-\mu}\, \tilde{f}(s),$ where $\mu\in(0,p),$ and $\tilde{f}(s)/|s|^{p_{\mu}^*-1}\to 0$ as $|s|\to \infty$, here $p^*_{\mu}:=\frac{p(N-\mu)}{N-p}$ is the critical Sobolev-Hardy exponent. Our non-linearities includes non-power non-linearities.   In particular we prove that when $f(x,s)=|x|^{-\mu}\,\frac{|s|^{p^*_{\mu}-2}s}{\big[\log(e+|s|)\big]^\alpha}\,,$ with $\mu\in[1,p),$ then, for any $\varepsilon>0$ there exists a constant $C_\varepsilon>0$ such that for any solution $u\in H^1_0(\Omega)$, the following holds $$ \Big[\log\big(e+\|u\|_{\infty}\big)\Big]^\alpha\le C_\varepsilon \, \Big(1+\|u\|_{p^*}\Big)^{\, (p^*_{\mu}-p)(1+\varepsilon)}\, , $$ where $C_\varepsilon$ is independent of the solution $u$.