ShantanuT01/DACTYL-Pretraining huggingface dataset:
Convolutional neural network training can suffer from diverse issues like exploding or vanishing gradients, scaling-based weight space symmetry and covariant-shift. In order to address these issues, researchers develop weight regularization methods and activation normalization methods. In this work we propose a weight soft-regularization method based on the Oblique manifold. The proposed method uses a loss function which pushes each weight vector to have a norm close to one, i.e. the weight matrix is smoothly steered toward the so-called Oblique manifold. We evaluate our method on the very popular CIFAR-10, CIFAR-100 and ImageNet 2012 datasets using two state-of-the-art architectures, namely the ResNet and wide-ResNet. Our method introduces negligible computational overhead and the results show that it is competitive to the state-of-the-art and in some cases superior to it. Additionally, the results are less sensitive to hyperparameter settings such as batch size and regularization factor.
We present fast and highly parallelized versions of Shor's algorithm. With a sizable quantum computer it would then be possible to factor numbers with millions of digits. The main algorithm presented here uses FFT-based fast integer multiplication. The quick reader can just read the introduction and the ``Results'' section.
Screened modified gravity predicts potentially large signatures in the peculiar velocity field that makes it an interesting probe to test gravity on cosmological scales. We investigate the signatures induced by the Symmetron and a Chameleon $f(R)$ model in the peculiar velocity field using $N$-body simulations. By studying fifth force and halo velocity profiles we identify three general categories of effects found in screened modified gravity models: a fully screened regime where we recover $\Lambda$CDM to high precision, an unscreened regime where the fifth force is in full operation, and, a partially screened regime where screening occurs in the inner part of a halo, but the fifth force is active at larger radii. These three regimes can be pointed out very clearly by analyzing the deviation in the maximum cluster velocity. Observationally, the partially screened regime is of particular interest since an uniform increase of the gravitational force - as present in the unscreened regime - is degenerate with the (dynamical) halo mass estimate, and, thus, hard to detect.
Numerical hydrodynamic simulation of inviscid and viscous flows have shown that significant outflows could be produced from the CENtrifugal pressure supported BOundary Layer or CENBOL of an advective disk. However, this barrier is weakened in presence of viscosity, more so, if there are explicit energy dissipations at the boundary layer itself. We study effects of viscosity and energy dissipation theoretically on the outflow rate and show that as the viscosity or energy dissipation (or both) rises, the prospect of formation of outflows is greatly reduced, thereby verifying results obtained through observations and numerical simulations. Indeed, we find that in a dissipative viscous flow, shocks in presence of outflows can be produced only if the Shakura-Sunyaev viscosity parameter {\alpha} is less than 0.2. This is a direct consequence of modification of the Rankine-Hugoniot relation across the shock in a viscous flow, when the energy dissipation and mass loss in the form of outflows from the post-shock region are included. If we ignore the effects of mass loss altogether, the standing dissipative shocks in viscous flows may occur only if {\alpha} < 0.27. These limits are tighter than the absolute limit of {\alpha} = 0.3 valid for a situation when the shock itself neither dissipates energy nor any outflow is formed. We compute typical viscosity parameters required to understand spectral and temporal properties of several black hole candidates such as GX399-4, MAXI J1659-152 and MAXI J1836-194 and find that required {\alpha} are indeed well within our prescribed limit.
We study the time evolution of single interval Renyi and entanglement entropies following local quantum quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width, \epsilon. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Renyi and entanglement entropies at order \epsilon^2 is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the \epsilon^2 correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential \mu. We calculate the time dependence of the order \epsilon^2 correction to the entanglement entropy for small \mu, and show that the contribution at order \mu^2 is universal. We verify our arguments against exact results for minimal models and the free fermion theory.
We have completed a Monte-Carlo simulation to estimate the effect of binary star orbits on the measured velocity dispersion in dwarf spheroidal galaxies. This paper analyses previous attempts at this calculation, and explains the simulations which were performed with mass, period and ellipticity distributions similar to that measured for the solar neighbourhood. The conclusion is that with functions such as these, the contribution of binary stars to the velocity dispersion is small. The distributions are consistent with the percentage of binaries detected by observations, although this is quite dependent on the measuring errors and on the number of years over which measurements have been taken. For binaries to be making a significant contribution to the dispersion measured in dSph galaxies, the distributions of the orbital parameters would need to be very different from those of stars in the solar neighbourhood. In particular more smaller period orbits with higher mass secondaries would be required. The shape of the velocity distribution may help to resolve this issue when more data becomes available. In general, the scenarios producing a larger apparent dispersion have a velocity distribution which deviates more clearly from Gaussian.
Ion conducting materials are critical components of batteries, fuel cells, and devices such as memristive switches. Analytical tools are therefore sought that allow the behavior of ions in solids to be monitored and analyzed with high spatial resolution and in real time. In principle, inelastic tunneling spectroscopy offers these capabilities. However, as its spectral resolution is limited by thermal softening of the Fermi-Dirac distribution, tunneling spectroscopy is usually constrained to cryogenic temperatures. This constraint would seem to render tunneling spectroscopy useless for studying ions in motion. We report here the first inelastic tunneling spectroscopy studies above room temperature. For these measurements, we have developed high-temperature-stable tunnel junctions that incorporate within the tunnel barrier ultrathin layers for efficient proton conduction. By analyzing the vibrational modes of O-H bonds in BaZrO3-based heterostructures, we demonstrate the detection of protons with a spectral resolution of 20 meV at 400 K (FWHM). Overturning the hitherto existing prediction for the spectral resolution limit of 186 meV (5.4 kBT at 400 K), this resolution enables high-temperature tunneling spectroscopy of ion conductors. With these advances, inelastic tunneling spectroscopy constitutes a novel, valuable analytical tool for solid-state ionics.
A tree containing exactly two non-pendant vertices is called a double-star. Let $k_1$ and $k_2$ be two positive integers. The double-star with degree sequence $(k_1+1, k_2+1, 1, \ldots, 1)$ is denoted by $S_{k_1, k_2}$. If $G$ is a cubic graph and has an $S$-decomposition, for a double-star $S$, then $S$ is isomorphic to $S_{1,1}$, $S_{1,2}$ or $S_{2,2}$. It is known that a cubic graph has an $S_{1,1}$-decomposition if and only if it contains a perfect matching. In this paper we study the $S_{1,2}$-decomposition of cubic graphs. First, we present some necessary conditions for the existence of an $S_{1,2}$-decomposition in cubic graphs. Then we prove that every $\{C_3, C_5, C_7\}$-free cubic graph of order $n$ with $\alpha(G)= \frac{3n}{8}$ has an $S_{1,2}$-decomposition, where $\alpha(G)$ denotes the independence number of $G$. Finally, we obtain some results on the $S_{1,r-1}$-decomposition of $r$-regular graphs.
Mott-Schottky analysis is adapted to determine the built-in bias (Vbi) and doping density (N) of lead sulfide-zinc oxide colloidal quantum dot heterojunction solar cells. We show that charge injection barriers at the solar cell's electrodes create a constant capacitance that distorts the junction's depletion capacitance and result in erroneous Vbi and N values when determined through Mott-Schottky analysis. The injection barrier capacitance is taken into account by incorporating a constant capacitance in parallel with the depletion capacitance.
Binding energy of the $1^-$ state (ortho-positronium) in QED is calculated using the one-photon exchange Bethe-Salpeter equation in the Feynman and Coulomb gauges for different coupling constants $\alpha$. Calculations show there is a remarkable difference in values of the binding energy for different coupling constants in these two gauges.
Light bridges are the most prominent manifestation of convection in sunspots. The brightest representatives are granular light bridges composed of features that appear to be similar to granules. An in-depth study of the convective motions, temperature stratification, and magnetic field vector in and around light bridge granules is presented with the aim of identifying similarities and differences to typical quiet-Sun granules. Spectropolarimetric data from the Hinode Solar Optical Telescope were analyzed using a spatially coupled inversion technique to retrieve the stratified atmospheric parameters of light bridge and quiet-Sun granules. Central hot upflows surrounded by cooler fast downflows reaching 10 km/s clearly establish the convective nature of the light bridge granules. The inner part of these granules in the near surface layers is field free and is covered by a cusp-like magnetic field configuration. We observe hints of field reversals at the location of the fast downflows. The quiet-Sun granules in the vicinity of the sunspot are covered by a low-lying canopy field extending radially outward from the spot. The similarities between quiet-Sun and light bridge granules point to the deep anchoring of granular light bridges in the underlying convection zone. The fast, supersonic downflows are most likely a result of a combination of invigorated convection in the light bridge granule due to radiative cooling into the neighboring umbra and the fact that we sample deeper layers, since the downflows are immediately adjacent to the slanted walls of the Wilson depression.
We establish the existence of an optimal control for a general class of singular control problems with state constraints. The proof uses weak convergence arguments and a time rescaling technique. The existence of optimal controls for Brownian control problems \citehar, associated with a broad family of stochastic networks, follows as a consequence.
The inhibition of the total HI $n\leftrightarrow 1$ transition rate by delayed resonant reabsorption of HI $(n+1)\to 1$ photons by HI $n\to 1$ line which is possible due to cosmological redshift is considered semi-analytically. The method taking into account this effect in the frame of simple three-level approximation model of recombination is suggested. It is confirmed that the resonant feedbacks affect ionization fraction at the level about 0.2% for the epoch of last scattering.   Similar consideration of HeI $2^1P\leftrightarrow 1^1S$ $\Rightarrow$ HeI $2^3P\leftrightarrow 1^1S$ feedback for helium is provided. It is confirmed that allowance of this feedback leads to increase of predicted free electron fraction by 0.12% at $z\simeq 2300$. It is shown that taking into account absorption and thermalization of HeI $2^1P\leftrightarrow 1^1S$ resonant superequilibrium photons (during their redshifting to the HeI $2^3P\leftrightarrow 1^1S$ frequency) by small amount of neutral hydrogen ($10^{\rm -7} - 10^{\rm -4}$ of total number of hydrogen atoms and ions) existing in helium recombination epoch is important for correct consideration of this helium feedback.
In this paper, we study the blow up of a sequence of (both extrinsic and intrinsic) biharmonic maps in dimension four with bounded energy and show that there is no neck in this process. Moreover, we apply the method to provide new proofs to the removable singularity theorem and energy identity theorem of biharmonic maps.
Recently, Valiviita et al. (2008) have reported a large-scale early-time instability in coupled dark energy and dark matter models. We take the same form of energy-momentum exchange and specialise to the case when the interaction rate is proportional to Hubble's parameter and the dark energy density only. Provided the coupling is made small enough for a given equation of state parameter, we show that the instability can be avoided. Expressions are derived for non-adiabatic modes on super-horizon scales in both the radiation and matter dominated regimes. We also examine the growth of dark matter perturbations in the sub-horizon limit. There we find that the coupling has almost no effect upon the growth of structure before dark energy begins to dominate. Once the universe begins to accelerate, the relative dark matter density fluctuations not only cease to grow as in uncoupled models, but actually decay as the universe continues to expand.
We prove the sharp bound of at most 64 lines on complex projective quartic surfaces (resp. affine quartics) that are not ruled by lines. We study configurations of lines on certain non-K3 surfaces of degree four and give various examples of singular quartics with many lines.
In this article we construct for any prime power $q$ and odd $n \ge 5$, a new $\mathbb{F}_{q^{2n}}$-maximal curve $\mathcal X_n$. Like the Garcia--G\" uneri--Stichtenoth maximal curves, our curves generalize the Giulietti--Korchm\'aros maximal curve, though in a different way. We compute the full automorphism group of $\mathcal X_n$, yielding that it has precisely $q(q^2-1)(q^n+1)$ automorphisms. Further, we show that unless $q=2$, the curve $\mathcal{X}_n$ is not a Galois subcover of the Hermitian curve. Finally, we find new values of the genus spectrum of $\mathbb{F}_{q^{2n}}$-maximal curves, by considering some Galois subcovers of $\mathcal X_n$.
General relativity predicts that the spin axes of the pulsars in the double-pulsar system (PSR J0737-3039A/B) will precess rapidly, in general leading to a change in the observed pulse profiles. We have observed this system over a one-year interval using the Parkes 64-m radio telescope at three frequencies: 680, 1390 and 3030 MHz. These data, combined with the short survey observation made two years earlier, show no evidence for significant changes in the pulse profile of PSR J0737-3039A, the 22-ms pulsar. The limit on variations of the profile 10% width is about 0.5 deg per year. These results imply an angle delta between the pulsar spin axis and the orbit normal of <~ 60 deg, consistent with recent evolutionary studies of the system. Although a wide range of system parameters remain consistent with the data, the model proposed by Jenet & Ransom (2004) can be ruled out. A non-zero ellipticity for the radiation beam gives slightly but not significantly improved fits to the data, so that a circular beam describes the data equally well within the uncertainties.
We compare mid-IR and ALMA far-IR images of 12 nearby Seyferts selected from GATOS. The mid-IR unresolved emission contributes more than 60% of the nuclear emission in most galaxies. By contrast, the ALMA 870micron continuum emission is mostly resolved and typically along the torus equatorial direction (Paper I, Garcia-Burillo et al. 2021). The Eddington ratios and nuclear hydrogen column densities NH of half the sample are favorable to launching polar and/or equatorial dusty winds, according to simulations. Six show mid-IR extended emission in the polar direction as traced by the NLR and perpendicular to the ALMA emission. In a few, the nuclear NH might be too high to uplift large quantities of dusty material along the polar direction. Five galaxies have low NH and/or Eddington ratios and thus polar dusty winds are not likely. We generate new CAT3D-WIND disk-wind model images. At low wind-to-disk cloud ratios the far-IR model images have disk- and ring-like morphologies. The X-shape associated with dusty winds is seen better in the far-IR at intermediate-high inclinations for the extended-wind configurations. In most models, the mid-IR emission comes from the inner part of the disk/cone. Extended bi-conical and one-sided polar mid-IR emission is seen in extended-wind configurations and high wind-to-disk cloud ratios. When convolved to our resolution, the model images reproduce qualitative aspects of the observed morphologies. Low-intermediate wind-to-disk ratios are required to account for the large fractions of unresolved mid-IR emission. This work and Paper I provide observational support for the torus+wind scenario. The wind component is more relevant at high Eddington ratios and/or AGN luminosities, and polar dust emission is predicted at NH of up to $10^{24}$cm$^{-2}$. The torus/disk component, on the other hand, prevails at low luminosities and/or Eddington ratios. (Abridged)
In the present paper Mori extremal rays of a smooth projective manifold X are divided into two classes: L-supported and L-negligible (where ``L'' stands for ``Lefschetz'' since the division comes from Hard Lefschetz Theorem). Roughly speaking: L-supported rays are strongly distinguishable in topology while L-negligible rays have very mild geometry.   Each L-supported ray R defines hyperplane in H^2(X,R) on which Lefschetz duality degenerates so it is a cohomology ring invariant. The hyperplane carries a multiplicity (cohomology ring invariant) which is related to the geometry of the ray R. The number of L-supported rays is bounded.   Although the number of L-negligible rays may be infinite and they are invisible in the cohomology ring, their geometry is easier than that of L-supported rays. They are classifieable in low dimensions. Each L-negligible ray contains lots of ``good'' rational curves whose deformation is of expected dimension. In effect, L-negligible rays are invariant under deformations of complex structure and can be used to compute Gromov-Witten invariants in symplectic geometry.
We have investigated the temperature evolution of magnetism and its interrelation with structural parameters in perovskite-based layered compound Sr$_2$IrO$_4$, which is believed to be a $J_{eff}$ = 1/2 Mott insulator. The structural distortion plays an important role in this material which induces a weak ferromagnetism in otherwise antiferromagnetically ordered magnetic state with transition temperature around 240 K. Interestingly, at low temperature below around 100 K, a change in magnetic moment has been observed. Temperature dependent x-ray diffraction measurements show sudden changes in structural parameters around 100 K are responsible for this. Resistivity measurements show insulating behavior throughout the temperature range across the magnetic phase transition. The electronic transport can be described with Mott's two-dimensional variable range hopping (VRH) mechanism, however, three different temperature ranges are found for VRH, which is a result of varying localization length with temperature. A negative magnetoresistance (MR) has been observed at all temperatures in contrast to positive behavior generally observed in strongly spin-orbit coupled materials. The quadratic field dependence of MR implies a relevance of a quantum interference effect.
In this paper we give the q-extension of Euler numbers which can be viewed as interpolating of the q-analogue of Euler zeta function ay negative integers, in the same way that Riemann zeta function interpolates Bernoulli numbers at negative integers. Finally we woll treat some identities of the q-extension of the euler numbers by using fermionic p-adic q-integration on Z_p.
We propose a new model suitable for a nonequilibrium molecular dynamics (MD) simulation of electrical conductors. The model consists of classical electrons and atoms. The atoms compose a lattice vibration system. The electrons are scattered by electron-electron and electron-atom interactions. Since the scattering cross section is physically more important than the functional form of a scattering potential, we propose to devise the electron-atom interaction potential in such a way that its scattering cross section agrees with that of quantum-mechanical one. To demonstrate advantages of the proposed model, we perform a nonequilibrium MD simulation assuming a doped semiconductor at room or higher temperature. In the linear response regime, we confirm Ohm's law, the dispersion relations and the fluctuation-dissipation relation. Furthermore, we obtain reasonable dependence of the electrical conductivity on temperature, despite the fact that our model is a classical model.
We calculate the conductance of a system of two spinless Luttinger liquid wires with different interaction strengths g_1, g_2, connected through a short junction, within the scattering state formalism. Following earlier work we formulate the problem in current algebra language, and calculate the scale dependent contribution to the conductance in perturbation theory keeping the leading universal contributions to all orders in the interaction strength. From that we derive a renormalization group (RG) equation for the conductance. The analytical solution of the RG-equation is discussed in dependence on g_1, g_2. The regions of stability of the two fixed points corresponding to conductance G=0 and G=1, respectively, are determined.
A nodal Enriques surface can have at most 8 nodes. We give an explicit description of Enriques surfaces with 8 nodes, showing that they are quotients of products of elliptic curves by a group isomorphic to $\Z_2^2$ or to $\Z_2^3$ acting freely in codimension 1. We use this result to show that if $S$ is a minimal surface of general type with $p_g=0$ such that the image of the bicanonical map is birational to an Enriques surface then $K^2_S=3$ and the bicanonical map is a morphism of degree 2.
We investigate the influence of light-matter interactions on correlated quantum matter by studying the paradigmatic Ising model subject to a quantum Rabi coupling. This type of coupling to a confined, spatially delocalized bosonic light mode, such as provided by an optical resonator, resembles a quantized transverse magnetic field of tunable strength. As a consequence, the symmetry-broken magnetic state breaks down for strong enough light-mater interactions to a paramagnetic state. The non-local character of the bosonic mode can change the quantum phase transition in a drastic manner, which we analyze quantitatively for the simplest case of a chain geometry (Dicke-Ising chain). The results show a direct transition between a magnetically ordered phase with zero photon density and a magnetically polarized phase with lasing behaviour of the light. Our predictions are equally valid for the dual quantized Ising chain in a conventional transverse magnetic field.
We study the problem of entropy increase of the Bernoulli-shift map without recourse to the concept of trajectory and we discuss whether, and under which conditions if it does, the distribution density entropy coincides with the Kolmogorov-Sinai entropy, namely, with the trajectory entropy.