ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present real space quantum Monte Carlo (QMC) calculations of the scandate LaScO$_3$ that proved to be challenging for traditional electronic structure approaches due to strong correlation effects resulting in inaccurate band gaps from DFT and $GW$ methods when compared with existing experimental data. Besides calculating an accurate QMC band gap corrected for supercell size biases and in agreement with numerous experiments, we also predict the cohesive energy of the crystal using the standard fixed-node QMC without any empirical or non-variational parameters. We show that promotion (optical) gap and fundamental gap agree with each other illustrating a clear absence of significant excitonic effects in the ideal crystal. We obtained these results in perfect consistency in two independent tracks that employ different basis sets (plane wave vs. localized gaussians), different codes for generating orbitals (\textsc{Quantum Espresso} vs. \textsc{Crystal}), different QMC codes (\textsc{Qmcpack} vs. \textsc{Qwalk}) and different high-accuracy pseudopotentials (ccECPs vs. Troullier-Martins) presenting the maturity and consistency of QMC methodology and tools for studies of strongly correlated problems.
Spin-polarized density functional calculations, magnetization, and neutron diffraction measurements are carried out to investigate the magnetic exchange interactions and strong correlation effects in Yb substituted inverse spinel nickel ferrite. In the pristine form, the compound is found to be a mixed insulator under the Zaanen-Sawtazsky-Allen classification scheme as it features both charge transfer and Mott insulator mechanism. Estimation of magnetic exchange couplings reveals that both octahedral-octahedral and octahedral-tetrahedral spin-spin interactions are antiferromagnetic which is typical of a spin-frustrated triangular lattice. However, the latter is dominant compared to the former leading to a forced parallel alignment of the spins at the octahedral site which is in agreement with the results of neutron diffraction measurements. The substituent Yb is found to be settled in +3 charge state, as confirmed from the XPS measurements, to behave like a spin-half impurity carried by the localized $f_{z(x^2-y^2)}$ orbital. The impurity $f$ spin significantly weakens the antiferromagnetic coupling with the spins at the tetrahedral site, which explains the experimental observation of fall in Curie temperature with Yb substitution.
A model of coupled antiferromagnetic spin-1/2 Heisenberg ladders is studied with numerical techniques. In the case of ferromagnetic interladder coupling we find that the dynamic and static structure factor has a peak at $(\pi,\pi/2)$ where the first (second) direction is along (transversal) to the ladders. Besides, we suggest that the intensity of this peak and the spin-spin correlation at the maximum distance along the ladder direction remain finite in the bulk limit for strong enough interladder coupling. We discuss the relevance of these results for magnetic compounds containing ladders coupled in a trellis lattice and for the stripe scenario in high-T$_c$ superconducting cuprates.
In this chapter, we review biomedical applications and breakthroughs via leveraging algorithm unrolling, an important technique that bridges between traditional iterative algorithms and modern deep learning techniques. To provide context, we start by tracing the origin of algorithm unrolling and providing a comprehensive tutorial on how to unroll iterative algorithms into deep networks. We then extensively cover algorithm unrolling in a wide variety of biomedical imaging modalities and delve into several representative recent works in detail. Indeed, there is a rich history of iterative algorithms for biomedical image synthesis, which makes the field ripe for unrolling techniques. In addition, we put algorithm unrolling into a broad perspective, in order to understand why it is particularly effective and discuss recent trends. Finally, we conclude the chapter by discussing open challenges, and suggesting future research directions.
We characterize the event of convergence of a local supermartingale. Conditions are given in terms of its predictable characteristics and quadratic variation. The notion of stationarily local integrability plays a key role.
We compile position and inclination angles for tilted ring fits to the warped dusty and gaseous disk spanning radius 1.8 to 6500 pc from recent observations. For radii exterior to a kpc, tilted ring orientations lie on an arc on a polar inclination versus position angle plot, suggesting that precession following a merger can account for the ring morphology. Three kinks in the ring orientations are seen on the polar plot, the one at radius of about 1.3 kpc we suspect corresponds to the location where self-gravity in the disk affects the ring precession rate. Another at a radius of about 600 pc may be associated with a gap in the gas distribution. A third kink is seen at a radius of 100 pc. A constant inclination tilted disk precessing about the jet axis may describe the disk between 100 and 20 pc but not interior to this. A model with disk orientation matching the molecular circumnuclear disk at 100 pc that decays at smaller radii to an inner flat disk perpendicular to the jet may account for disk orientations within 100 pc. Neither model would account for the cusps or changes in disk orientation at 100 or 600 pc.
Assuming a particular case of Borisov--Alexeev--Borisov conjecture, we prove that finite subgroups of the automorphism group of a finitely generated field over Q have bounded orders. Further, we investigate which algebraic varieties have groups of birational selfmaps satisfying the Jordan property.
We address the cosmological evolution of violent gravitational instability in high-redshift, massive, star-forming galactic discs. To this aim, we integrate in time the equations of mass and energy conservation under self-regulated instability of a two-component disc of gas and stars. The disc is assumed to be continuously fed by cold gas at the average cosmological rate. The gas forms stars and is partly driven away by stellar feedback. The gas and stars flow inward through the disc to a central bulge due to torques that drive angular momentum outwards. The gravitational energy released by the mass inflow down the gravitational potential gradient drives the disc turbulence that maintains the disc unstable with a Toomre instability parameter Q~1, compensating for the dissipative losses of the gas turbulence and raising the stellar velocity dispersion. We follow the velocity dispersion of stars and gas as they heat and cool respectively and search for disc `stabilization', to be marked by a low gas velocity dispersion comparable to the speed of sound ~10 km/s. We vary the model parameters that characterize the accreted gas fraction, turbulence dissipation rate, star-formation rate, and stellar feedback. We find that as long as the gas input roughly follows the average cosmological rate, the disc instability is a robust phenomenon at high redshift till z~1, driven by the high surface density and high gas fraction due to the intense cosmological accretion. For a broad range of model parameter values, the discs tend to `stabilize' at z~0-0.5 as they become dominated by hot stars. When the model parameters are pushed to extreme values, the discs may stabilize as early as z~2, with the gas loss by strong outflows serving as the dominant stabilizing factor.
The successful theoretical prediction and experimental demonstration of hybrid improper ferroelectricity (HIF) provides a new pathway to couple octahedral rotations, ferroelectricity, and magnetism in complex materials. To enable technological applications, a HIF with a small coercive field is desirable. We successfully grow Sr3Sn2O7 single crystals, and discover that they exhibit the smallest electric coercive field at room temperature among all known HIFs. Furthermore, we demonstate that a small external stress can repeatedly erase and re-generate ferroelastic domains. In addition, using in-plane piezo-response force microscopy, we characterize abundant charged and neutral domain walls. The observed small electrical and mechanical coercive field values are in accordance with the results of our first-principles calculations on Sr3Sn2O7, which show low energy barriers for both 90{\deg} and 180{\deg} polarization switching compared to those in other experimentally demonstrated HIFs. Our findings represent an advance towards the possible technological implemetation of functional HIFs.
We report a Karl G. Jansky Very Large Array search for redshifted CO(1-0) emission from three HI-absorption-selected galaxies at $z \approx 2$, identified earlier in their CO(3-2) or CO(4-3) emission. We detect CO(1-0) emission from DLA B1228-113 at $z\approx2.1933$ and DLA J0918+1636 at $z\approx2.5848$; these are the first detections of CO(1-0) emission in high-$z$ HI-selected galaxies. We obtain high molecular gas masses, $\rm M_{mol}\approx10^{11}\times(\alpha_{\rm CO}/4.36)\ M_\odot$, for the two objects with CO(1-0) detections, which are a factor of $\approx1.5-2$ lower than earlier estimates. We determine the excitation of the mid$-J$ CO rotational levels relative to the $J=1$ level, r$_{ J1}$, in HI-selected galaxies for the first time, obtaining r$_{\rm 31}=1.00\pm0.20$ and r$_{\rm 41}=1.03\pm0.23$ for DLA J0918+1636, and r$_{\rm 31}=0.86\pm0.21$ for DLA B1228-113. These values are consistent with thermal excitation of the $J=3,4$ levels. The excitation of the $J=3$ level in the HI-selected galaxies is similar to that seen in massive main-sequence and sub-mm galaxies at $z\gtrsim2$, but higher than that in main-sequence galaxies at $z\approx1.5$; the higher excitation of the galaxies at $z\gtrsim2$ is likely to be due to their higher star-formation rate (SFR) surface density. We use Hubble Space Telescope Wide Field Camera 3 imaging to detect the rest-frame near-ultraviolet emission of DLA B1228-113, obtaining an NUV SFR of $4.44\pm0.47$ M$_{\odot}$ yr$^{-1}$, significantly lower than that obtained from the total infrared luminosity, indicating significant dust extinction in the $z\approx2.1933$ galaxy.
Deep learning applied to the reconstruction of 3D shapes has seen growing interest. A popular approach to 3D reconstruction and generation in recent years has been the CNN encoder-decoder model usually applied in voxel space. However, this often scales very poorly with the resolution limiting the effectiveness of these models. Several sophisticated alternatives for decoding to 3D shapes have been proposed typically relying on complex deep learning architectures for the decoder model. In this work, we show that this additional complexity is not necessary, and that we can actually obtain high quality 3D reconstruction using a linear decoder, obtained from principal component analysis on the signed distance function (SDF) of the surface. This approach allows easily scaling to larger resolutions. We show in multiple experiments that our approach is competitive with state-of-the-art methods. It also allows the decoder to be fine-tuned on the target task using a loss designed specifically for SDF transforms, obtaining further gains.
Chemical processes on the surface of icy grains play an important role in the chemical evolution in molecular clouds. In particular, reactions involving non-energetic hydrogen atoms accreted from the gaseous phase have been extensively studied. These reactions are believed to effectively proceed only on the surface of the icy grains; thus, molecules embedded in the ice mantle are not considered to react with hydrogen atoms. Recently, Tsuge et al. (2020) suggested that non-energetic hydrogen atoms can react with CO molecules even in ice mantles via diffusive hydrogenation. This investigation was extended to benzene and naphthalene molecules embedded in amorphous solid water (ASW) in the present study, which revealed that a portion of these molecules could be fully hydrogenated in astrophysical environments. The penetration depths of non-energetic hydrogen atoms into porous and non-porous ASW were determined using benzene molecules to be >50 and ~10 monolayers, respectively (1 monolayer ~ 0.3 nm).
We describe electron spin resonance in a quantum spin liquid with significant spin-orbit coupling. We find that the resonance directly probes spinon continuum which makes it an efficient and informative probe of exotic excitations of the spin liquid. Specifically, we consider spinon resonance of three different spinon mean-field Hamiltonians, obtained with the help of projective symmetry group analysis, which model a putative quantum spin liquid state of the triangular rare-earth antiferromagnet YbMgGaO4. The band of absorption is found to be very broad and exhibit strong van Hove singularities of single spinon spectrum as well as pronounced polarization dependence.
We present here the natural extension of our Pila-Wilkie type estimates on the number of rational points of the trascendent part of a compact analytic subset of $\mathbb{F}_{q}((1/T))^{n}$ to analogous subsets of $K^{n}$, where $K$ is a general local field of any characteristic. That would integrate the analogous estimate provided by F. Loeser, G. Comte and R. Cluckers in characteristic 0.
New measurements with good statistics will make it possible to observe the time variation of cosmic antiprotons at 1 AU through the approaching peak of solar activity. We report a new computation of the interstellar antiproton spectrum expected from collisions between cosmic protons and the interstellar gas. This spectrum is then used as input to a steady-state drift model of solar modulation, in order to provide predictions for the antiproton spectrum as well as the antiproton/proton ratio at 1 AU. Our model predicts a surprisingly large, rapid increase in the antiproton/proton ratio through the next solar maximum, followed by a large excursion in the ratio during the following decade.
Zero forcing is a process that colors the vertices of a graph blue by starting with some vertices blue and applying a color change rule. Throttling minimizes the sum of the number of initial blue vertices and the time to color the graph. In this paper, we study throttling for skew zero forcing. We characterize the graphs of order $n$ with skew throttling numbers $1, 2, n-1$, and $n$. We find the exact skew throttling numbers of paths, cycles, and balanced spiders with short legs. In addition, we find a sharp lower bound on skew throttling numbers in terms of the diameter.
We consider some radiative corrections to the lowest order annihilation diagram for the orthopositronium decay rate. The insertion of the renormalized vertex correction in the annihilation graph gives $1.6283 (\alpha/\pi)^2 \Gamma_0$. We compute also the contribution of the square of the lowest order annihilation amplitude, which turns out to be $0.1702 (\alpha/\pi)^2 \Gamma_0$. Finally, we obtain a term $\alpha^2 \ln\alpha \Gamma_0$ arising from the correction to the light-light scattering block due to the exchange of one coulombic photon, in agreement with earlier computations.
A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation, we introduce a distance between observables to quantify an accuracy of measurement. We derive an inequality that relates the achievable accuracy with noncommutativity between two observables. As a byproduct a necessary condition for two positive operator valued measures to be simultaneously measurable is obtained.
We prove the existence and uniqueness of invariant measures for the fractional stochastic Burgers equation (FSBE) driven by fractional power of the Laplacian and space-time white noise. We show also that the transition measures of the solution converge to the invariant measure in the norm of total variation. To this end we show first two results which are of independent interest: that the semigroup corresponding to the solution of the FSBE is strong Feller and irreducible.
We present the results the photometric observations of the Type IIP supernova SN 2012aw obtained for the time interval from 7 till 371 days after the explosion. Using the previously published values of the photospheric velocities we've computed the hydrodynamic model which simultaneously reproduced the photometry observations and velocity measurements. The model was calculated with the multi-energy group radiation hydrodynamics code STELLA. We found the parameters of the pre-supernova: radius $R = 500 R_\odot$, nickel mass $M(^{56}$Ni$)$ $\sim 0.06 M_\odot$, pre-supernova mass $25 M_\odot$, mass of ejected envelope $23.6 M_\odot$, explosion energy $E \sim 2 \times 10^{51}$ erg. The model progenitor mass $M=25 M_\odot$ significantly exceeds the upper limit mass $M=17 M_\odot$, obtained from analysis the pre-SNe observations. This result confirms once more that the 'Red Supergiant Problem' must be resolved by stellar evolution and supernova explosion theories in interaction with observations.
The contact process with diffusion (PCPD) defined by the binary reactions 2 B -> 3 B, 2 B -> 0 and diffusive particle spreading exhibits an unusual active to absorbing phase transition whose universality class has long been disputed. Multiple studies have indicated that an explicit account of particle pair degrees of freedom may be required to properly capture this system's effective long-time, large-scale behavior. We introduce a two-species representation in which single particles B and pairs A are coupled according to the stochastic reactions B + B -> A, A -> A + B, A -> 0, and A -> B + B. Mean-field analysis reveals that the phase transition is driven by competition and balance between both species. We employ Monte Carlo simulations to demonstrate that this model captures the pertinent PCPD features. In the inactive phase, A particles rapidly go extinct, leaving the B species to undergo pure pair annihilation kinetics. At criticality, both A and B densities decay with the same exponents as the PCPD order parameters, and display mean-field scaling above the critical dimension 2. In one dimension, the critical exponents for the B species obtained from seed simulations agree well with previously reported exponent values. We demonstrate that the scaling properties of consecutive particle pairs in the PCPD are identical with that of the A species in the coupled model. This two-species picture resolves the conceptual difficulty for seed simulations in the original PCPD and naturally introduces multiple length and time scales, which cause strong corrections to scaling. The extracted moment ratios from our simulations indicate that our model displays the same temporal crossover behavior as the PCPD, which further corroborates its full dynamical equivalence with our coupled model.
We prove four identities for the squared central binomial coefficients. The first three of them reflect certain transformation properties of the complete elliptic integrals of the first and the second kind, while the last one is based on properties of the Lagrange polynomials.
We explore via linearized perturbation theory the Gregory-Laflamme instability of the NUT string (i.e the D=4 Lorentzian NUT solution uplifted to five dimensions). Our results indicate that the Gregory-Laflamme instability persists in the presence of a NUT charge $n$, the critical length of the extra-dimension increasing with $n$ for the same value of mass. The non-uniform branch of NUT strings is numerically extended into the full nonlinear regime.
We derive the Mode Coupling Theory (MCT) of the glass transition as a Landau theory, formulated as an expansion of the exact dynamical equations in the difference between the correlation function and its plateau value. This sheds light on the universality of MCT predictions. While our expansion generates higher order non-local corrections that modify the standard MCT equations, we find that the square root singularity of the order parameter, the scaling function in the \beta regime and the functional relation between the exponents defining the \alpha and \beta timescales are universal and left intact by these corrections.
Massive QCD at $\theta=\pi$ breaks CP spontaneously and admits domain walls whose dynamics and phases depend on the number of flavors and their masses. We discuss these issues within the Witten-Sakai-Sugimoto model of holographic QCD. Besides showing that this model reproduces all QCD expectations, we address two interesting claims in the literature. The first is about the possibility that the QCD domain-wall theory is fully captured by three-dimensional physics, only. The second regards the existence of quantum phases in certain Chern-Simons theories coupled to fundamental matter. Both claims are supported by the string theory construction.
We compute the distribution of likelihoods from the non-parametric iterative smoothing method over a set of mock Pantheon-like type Ia supernova datasets. We use this likelihood distribution to test whether typical dark energy models are consistent with the data and to perform parameter estimation. In this approach, the consistency of a model and the data is determined without the need for comparison with another alternative model. Simulating future WFIRST-like data, we study type II errors and show how confidently we can distinguish different dark energy models using this non-parametric approach.
Among log canonical surface singularities, the ones which have a rational homology disk smoothing are the cyclic quotient singularities $\frac{1}{n^2}(1,na-1)$ with gcd$(a,n)=1$, and three distinguished elliptic quotient singularities. We show the existence of smoothable KSBA normal surfaces with $\pi_1=1$, $p_g=0$, and $K^2=1,2$ for each of these three singularities. We also give a list of new (and old) normal surface singularities in smoothable KSBA surfaces for invariants $\pi_1=1$, $p_g=0$, and $K^2=1,2,3,4$.
Many problems and conjectures in extremal combinatorics concern polynomial inequalities between homomorphism densities of graphs where we allow edges to have real weights. Using the theory of graph limits, we can equivalently evaluate polynomial expressions in homomorphism densities on kernels $W$, i.e., symmetric, bounded, and measurable functions $W$ from $[0,1]^2 \to \mathbb{R}$. In 2011, Hatami and Norin proved a fundamental result that it is undecidable to determine the validity of polynomial inequalities in homomorphism densities for graphons (i.e., the case where the range of $W$ is $[0,1]$, which corresponds to unweighted graphs, or equivalently, to graphs with edge weights between $0$ and $1$). The corresponding problem for more general sets of kernels, e.g., for all kernels or for kernels with range $[-1,1]$, remains open. For any $a > 0$, we show undecidability of polynomial inequalities for any set of kernels which contains all kernels with range $\{0,a\}$. This result also answers a question raised by Lov\'asz about finding computationally effective certificates for the validity of homomorphism density inequalities in kernels.