ShantanuT01/DACTYL-Pretraining huggingface dataset:
In the context of Calabi-Yau string models we explore the origin of characteristic pattern of quark-lepton masses and the CKM matrix. The discrete $R$-symmetry $Z_K \times Z_2$ is introduced and the $Z_2$ is assigned to the $R$-parity. The gauge symmetry at the string scale, $SU(6) \times SU(2)_R$, is broken into the standard model gauge group at a very large intermediate energy scale. At energies below the intermediate scale down-type quarks and also leptons are mixed with unobserved heavy states, respectively. On the other hand, there are no such mixings for up-type quarks. Due to the large mixings between light states and heavy ones we can derive phenomenologically viable fermion mass hierarchies and the CKM matrix. Mass spectra for intermediate-scale matter beyond the MSSM are also determined. Within this framework proton lifetime is long enough to be consistent with experimental data. As for the string scale unification of gauge couplings, however, consistent solutions are not yet found.
I investigate the suggestion that the Hyades moving group in the Solar neighbourhood is the result of a recent inner Lindblad resonance. I use dynamical "torus" models of the Galaxy to understand the expected distribution of solar neighbourhood stars in angle coordinates for phase-mixed models and models which include a resonant component. I show that attempts to find the signatures of resonances in angle coordinates are strongly influenced by selection effects, including rather subtle effects associated with the relationship between action and angle for stars at a given point. These effects mean that one can not use simple tests to determine whether substructures seen in the Solar neighbourhood are associated with any given resonance.
Face age progression, which aims to predict the future looks, is important for various applications and has been received considerable attentions. Existing methods and datasets are limited in exploring the effects of occupations which may influence the personal appearances. In this paper, we firstly introduce an occupational face aging dataset for studying the influences of occupations on the appearances. It includes five occupations, which enables the development of new algorithms for age progression and facilitate future researches. Second, we propose a new occupational-aware adversarial face aging network, which learns human aging process under different occupations. Two factors are taken into consideration in our aging process: personality-preserving and visually plausible texture change for different occupations. We propose personalized network with personalized loss in deep autoencoder network for keeping personalized facial characteristics, and occupational-aware adversarial network with occupational-aware adversarial loss for obtaining more realistic texture changes. Experimental results well demonstrate the advantages of the proposed method by comparing with other state-of-the-arts age progression methods.
In this article, a sublinear expectation induced by $G$-expectation is introduced, which is called $G$-evaluation for convenience. As an application, we prove that any $\xi\in L^\beta_G(\Omega_T)$ with some $\beta>1$ the decomposition theorem holds and any $\beta>1$ integrable symmetric $G$-martingale can be represented as an It$\hat{o}'s$ integral w.r.t $G$-Brownian motion. As a byproduct, we prove a regular property for $G$-martingale: Any $G$-martingale $\{M_t\}$ has a quasi-continuous version
Mott physics is characterized by an interaction-driven metal-to-insulator transition in a partially filled band. In the resulting insulating state, antiferromagnetic orders of the local moments typically develop, but in rare situations no long-range magnetic order appears, even at zero temperature, rendering the system a quantum spin liquid. A fundamental and technologically critical question is whether one can tune the underlying energetic landscape to control both metal-to-insulator and N\'eel transitions, and even stabilize latent metastable phases, ideally on a platform suitable for applications. Here we demonstrate how to achieve this in ultrathin films of NdNiO3 with various degrees of lattice mismatch, and report on the quantum critical behaviours not reported in the bulk by transport measurements and resonant X-ray spectroscopy/scattering. In particular, on the decay of the antiferromagnetic Mott insulating state into a non-Fermi liquid, we find evidence of a quantum metal-to-insulator transition that spans a non-magnetic insulating phase.
We investigate the question under which conditions the algebraic difference between two independent random Cantor sets $C_1$ and $C_2$ almost surely contains an interval, and when not. The natural condition is whether the sum $d_1+d_2$ of the Hausdorff dimensions of the sets is smaller (no interval) or larger (an interval) than 1. Palis conjectured that \emph{generically} it should be true that $d_1+d_2>1$ should imply that $C_1-C_2$ contains an interval. We prove that for 2-adic random Cantor sets generated by a vector of probabilities $(p_0,p_1)$ the interior of the region where the Palis conjecture does not hold is given by those $p_0,p_1$ which satisfy $p_0+p_1>\sqrt{2}$ and $p_0p_1(1+p_0^2+p_1^2)<1$. We furthermore prove a general result which characterizes the interval/no interval property in terms of the lower spectral radius of a set of $2\times 2$ matrices.
We performed 2D, axisymmetric, MHD simulations with Cosmos++ in order to examine the growth of the magnetorotational instability (MRI) in core--collapse supernovae. We have initialized a non--rotating 15 solar mass progenitor, infused with differential rotation and poloidal magnetic fields. The collapse of the iron core is simulated with the Shen EOS, and the parametric Ye and entropy evolution. The wavelength of the unstable mode in the post--collapse environment is expected to be only ~ 200 m. In order to achieve the fine spatial resolution requirement, we employed remapping technique after the iron core has collapsed and bounced.   The MRI unstable region appears near the equator and angular momentum and entropy are transported outward. Higher resolution remap run display more vigorous overturns and stronger transport of angular momentum and entropy. Our results are in agreement with the earlier work by Akiyama et al. (2003) and Obergaulinger et al. (2009).
For dimensions $N \geq 4$, we consider the Br\'ezis-Nirenberg variational problem of finding \[ S(\epsilon V) := \inf_{0\not\equiv u\in H^1_0(\Omega)} \frac{\int_\Omega |\nabla u|^2 \, dx +\epsilon \int_\Omega V\, |u|^2 \, dx}{\left(\int_\Omega |u|^q \, dx \right)^{2/q}}, \] where $q=\frac{2N}{N-2}$ is the critical Sobolev exponent and $\Omega \subset \mathbb{R}^N$ is a bounded open set. We compute the asymptotics of $S(0) - S(\epsilon V)$ to leading order as $\epsilon \to 0+$. We give a precise description of the blow-up profile of (almost) minimizing sequences and, in particular, we characterize the concentration points as being extrema of a quotient involving the Robin function. This complements the results from our recent paper in the case $N = 3$.
We have conducted a study of extra-planar diffuse ionized gas using the first year data from the MaNGA IFU survey. We have stacked spectra from 49 edge-on, late-type galaxies as a function of distance from the midplane of the galaxy. With this technique we can detect the bright emission lines Halpha, Hbeta, [OII]3726, 3729, [OIII]5007, [NII]6549, 6584, and [SII]6717, 6731 out to about 4 kpc above the midplane. With 16 galaxies we can extend this analysis out to about 9 kpc, i.e. a distance of ~2R_e, vertically from the midplane. In the halo, the surface brightnesses of the [OII] and Halpha emission lines are comparable, unlike in the disk where Halpha dominates. When we split the sample by specific star formation rate, concentration index, and stellar mass, each subsample's emission line surface brightness profiles and ratios differ, indicating that extra-planar gas properties can vary. The emission line surface brightnesses of the gas around high specific star formation rate galaxies are higher at all distances, and the line ratios are closer to ratios characteristic of HII regions compared with low specific star formation rate galaxies. The less concentrated and lower stellar mass samples exhibit line ratios that are more like HII regions at larger distances than their more concentrated and higher stellar mass counterparts. The largest difference between different subsamples occurs when the galaxies are split by stellar mass. We additionally infer that gas far from the midplane in more massive galaxies has the highest temperatures and steepest radial temperature gradients based on their [NII]/Halpha and [OII]/Halpha ratios between the disk and the halo.
Some established views of the solar magnetic cycle are discussed critically, with focus on two aspects at the core of most models: the role of convective turbulence, and the role of the `tachocline' at the base of the convection zone. The standard view which treats the solar cycle as a manifestation of the interaction between convection and magnetic fields is shown to be misplaced. The main ingredient of the solar cycle, apart from differential rotation, is instead buoyant instability of the magnetic field itself. This view of the physics of the solar cycle was already established in the 1950s, but has been eclipsed mathematically by mean field turbulence formalisms which make poor contact with observations and have serious theoretical problems. The history of this development in the literature is discussed critically. The source of the magnetic field of the solar cycle is currently assumed to be located in the `tachocline': the shear zone at the base of the convection zone. While the azimuthal field of the cycle is indeed most likely located at the base of the convection zone, it cannot be powered by the radial shear of the tachocline as assumed in these models, since the radiative interior does not support significant shear stresses. Instead, it must be the powered by the latitudinal gradient in rotation rate in the convection zone, as in early models of the solar cycle. Possible future directions for research are briefly discussed.
We study the spin dynamics of an electron-hole pair in a random hyperfine magnetic field and an external field, B0, under a resonant drive with frequency omega0 = gamma B0. The fact that the pair decays by recombination exclusively from a singlet configuration, S, in which the spins of the pair-partners are entangled, makes this dynamics highly nontivial. Namely, as the amplitude, B1, of the driving field grows, mixing all of the triplet components, the long-living modes do not disappear, but evolve from T+, T- into (T+ +/- sqrt(2) T0 + T-)/2. Upon further increase of B1, the lifetime of the S-mode is cut in half, while the T0-mode transforms into an antisymmetric combination (T- - T-)/sqrt(2) and acquires a long lifetime, in full analogy to the superradiant and subradiant modes in the Dicke effect. Peculiar spin dynamics translates into a peculiar dependence on B1. In particular, at small B1, the radiation-induced correction to the current is linear in B1.
A finite-strain formulation is developed, implemented and tested for a constitutive model capable of describing the transition from granular to fully dense state during cold forming of ceramic powder. This constitutive model (as well as many others employed for geomaterials) embodies a number of features, such as pressure-sensitive yielding, complex hardening rules and elastoplastic coupling, posing considerable problems in a finite-strain formulation and numerical implementation. A number of strategies are proposed to overcome the related problems, in particular, a neo-Hookean type of modification to the elastic potential and the adoption of the second Piola-Kirchhoff stress referred to the intermediate configuration to describe yielding. An incremental scheme compatible with the formulation for elastoplastic coupling at finite strain is also developed, and the corresponding constitutive update problem is solved by applying a return mapping algorithm.
We derive a formula for the spacetime volume of a small causal cone. We use this formula within the context of causal set theory to construct causal set expressions for certain geometric quantities relating to a spacetime with a spacelike hypersurface. We also consider a scalar field on the causal set, and obtain causal set expressions relating to its normal derivatives with respect to the hypersurface.
As primitives for entanglement generation, controlled phase gates take a central role in quantum computing. Especially in ideas realizing instances of quantum computation in linear optical gate arrays a closer look can be rewarding. In such architectures, all effective non-linearities are induced by measurements: Hence the probability of success is a crucial parameter of such quantum gates. In this note, we discuss this question for controlled phase gates that implement an arbitrary phase with one and two control qubits. Within the class of post-selected gates in dual-rail encoding with vacuum ancillas we identify the optimal success probabilities. We construct networks that allow for an implementation by means of todays experimental capabilities in detail. The methods employed here appear specifically useful with the advent of integrated linear optical circuits, providing stable interferometers on monolithic structures.
The four-site DCA method of including intersite correlations in the dynamical mean field theory is used to investigate the metal-insulator transition in the Hubbard model. At half filling a gap-opening transition is found to occur as the interaction strength is increased beyond a critical value. The gapped behavior found in the 4-site DCA approximation is shown to be associated with the onset of strong antiferromagnetic and singlet correlations and the transition is found to be potential energy driven. It is thus more accurately described as a Slater phenomenon (induced by strong short ranged order) than as a Mott phenomenon. Doping the gapped phase leads to a non-Fermi-liquid state with a Fermi surface only in the nodal regions and a pseudogap in the antinodal regions at lower dopings $x \lesssim 0.15$ and to a Fermi liquid phase at higher dopings.
We study the ergodic behaviour of a discrete-time process $X$ which is a Markov chain in a stationary random environment. The laws of $X_t$ are shown to converge to a limiting law in (weighted) total variation distance as $t\to\infty$. Convergence speed is estimated and an ergodic theorem is established for functionals of $X$.   Our hypotheses on $X$ combine the standard "small set" and "drift" conditions for geometrically ergodic Markov chains with conditions on the growth rate of a certain "maximal process" of the random environment. We are able to cover a wide range of models that have heretofore been untractable. In particular, our results are pertinent to difference equations modulated by a stationary Gaussian process. Such equations arise in applications, for example, in discretized stochastic volatility models of mathematical finance.
We prepared Ga0.95Mn0.05As films on top of periodic arrays of InAs quantum dots. X-ray diffraction reveals periodically strained films, commensurate to substrate's patterning. The dots produce a tensile strain in GaMnAs while between the dots strain is compressive. Our experiments confirm that the average tensile strain in the film increases with decreasing dots separation. This trend in strain is accompanied by an increase of the out-of-plane magnetization component familiar from the established relation between strain and magnetic anisotropy in GaMnAs films. Our work provides a new route for controlling magneto-crystalline anisotropies in GaMnAs on a nanometer scale.
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent random variables $(Y_n)_{n\in \mathbb{N}}$ distributed according to $\nu$, which is often the only available knowledge of $\nu$. Furthermore, the algorithm is easy to implement, because it evolves like a Brownian motion between the random times when it jumps in direction of one of the $Y_n$, $n\in\mathbb{N}$. Its principle is based on simulated annealing and homogenization, so that temperature and approximations schemes must be tuned up (plus a regularizing scheme if $\nu$ does not admit a H\"{o}lderian density). The analysis of the convergence is restricted to the case where the state space is a circle. In its principle, the proof relies on the investigation of the evolution of a time-inhomogeneous $\mathbb{L}^2$ functional and on the corresponding spectral gap estimates due to Holley, Kusuoka and Stroock. But it requires new estimates on the discrepancies between the unknown instantaneous invariant measures and some convenient Gibbs measures.
We review some recent experimental and theoretical work on the correlation among hadrons produced at intermediate $p_T$ at RHIC. The topics include: forward and backward asymmetry with and without trigger at mid-rapidity, associated-particle distribution on the near side, the $\Omega$ puzzle and its solution, associated particles on the away side, and two-jet recombination at LHC.
Resolving the conductance of the topological surface states (TSSs) from the bulk contribution has been a great challenge for studying the transport property of topological insulators. By developing a non-purturbative diffusion equation that describes fully the spin-charge dynamics in the strong spin-orbit coupling regime, we present a proposal to read the charge transport information of TSSs from its spin dynamics which can be isolated from the bulk contribution by time-resolved second harmonic generation pump-probe measurement. We demonstrate the qualitatively different Dyaknov-Perel spin relaxation behavior between the TSSs and the two-dimensional spin-orbit coupling electron gas. The decay time of both in-plane and out-of-plane spin polarization is naturally proved to be identical to the charge transport time. The out-of-plane spin dynamics is shown to be in the experimentally reachable regime of the femtosecond pump probe spectroscopy and thereby we suggest experiments to detect the charge transport property of the TSSs from their unique spin dynamics.
The theory of Mellin transform is an incredibly useful tool in evaluating some of the well known results for the zeta function. Ramanujan in his quarterly reports \cite{1} gave a theorem for Mellin transform which is now known as Ramanujan's master theorem \cite{2}. In this paper, we have derived some extended versions of Ramanujan's master theorem based on our previous results \cite{3} and applied them to some special functions such as known as the Riesz function $R(z)$ and generalized binomial function. Some asymptotic expansions using extended Ramanujan's master theorem are also derived.
In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials.   We present explicit and self-contained proof for all of them, using a uniform terminology and technique.
We utilize H1 and ZEUS data for exclusive electroproduction of photons, $\rho^0$- and $\phi$-mesons to access generalized parton distributions at small momentum fraction. To do so, we employ state-of-the art techniques, based on next-to-leading order perturbation theory, flexible model parametrization, and Bayesian inference. We provide a partonic interpretation of our analysis, where emphasize is given to the transverse distribution of sea quarks and gluons.
The temperature corrections to the current algebra Gell-Mann, Oakes, and Renner (GMOR) relation in $SU(2)\otimes SU(2)$ are investigated in the framework of QCD sum rules. There are no corrections at leading order in the quark masses. At the next to leading order we find corrections of the form $m_{q}^2\; T^{2}$, which are small except near the critical temperature. As a by-product we obtain the temperature behaviour of the pion mass, which is essentially constant, except near the critical temperature where it increases with $T$.
Using localization methods on the moduli space of stable quasimaps to Grassmannian, we give explicit formulas of $J$-function and double $J$-function of stable quasimaps for complete intersection in Grassmannian.
We collect some results in combinatorial geometry that follow from an inequality of Langer in algebraic geometry. Langer's inequality gives a lower bound on the number of incidences between a point set and its spanned lines, and was recently used by Han to improve the constant in the weak Dirac conjecture. Here we observe that this inequality also leads to improved constants in Beck's theorem, which states that a finite point set in the real or complex plane has many points on a line or spans many lines. Most of the proofs that we use are not original, and the goal of this note is mainly to carefully record the quantitative results in one place. We also include some discussion of possible further improvements to these statements.
Since 2005, the blazar 3C 454.3 has shown remarkable flaring activity at all frequencies, and during the last four years it has exhibited more than one gamma-ray flare per year, becoming the most active gamma-ray blazar in the sky. We present for the first time the multi-wavelength AGILE, SWIFT, INTEGRAL, and GASP-WEBT data collected in order to explain the extraordinary gamma-ray flare of 3C 454.3 which occurred in November 2010. On 2010 November 20 (MJD 55520), 3C 454.3 reached a peak flux (E>100 MeV) of F_gamma(p) = (6.8+-1.0)E-5 ph/cm2/s on a time scale of about 12 hours, more than a factor of 6 higher than the flux of the brightest steady gamma-ray source, the Vela pulsar, and more than a factor of 3 brighter than its previous super-flare on 2009 December 2-3. The multi-wavelength data make a thorough study of the present event possible: the comparison with the previous outbursts indicates a close similarity to the one that occurred in 2009. By comparing the broadband emission before, during, and after the gamma-ray flare, we find that the radio, optical and X-ray emission varies within a factor 2-3, whereas the gamma-ray flux by a factor of 10. This remarkable behavior is modeled by an external Compton component driven by a substantial local enhancement of soft seed photons.
Basing on the kwon experimental measurements of differential cross sections on n3He elastic scattering in the angular energy range 200 - 1600 the standard phase shifts analysis was performed at the energies from 1 MeV up to 5 MeV.
Studying the series expansion of the thermodynamic potential for the hard-core N3 lattice-gas model, we provide evidence for a first-order phase-transition with a finite jump in density and entropy, in agreement with numerical transfer matrix calculations. The solid branch terminates at the transition, while the fluid branch continues beyond the critical activity, describing a meta-stable super-cooled fluid. It terminates with density 0.85 (relative to the closest packing density) and finite entropy per site. This termination density is close to the random-closest-packing density of the glassy state obtained for infinitely-fast cooling. The model thus exhibits a thermodynamic meta-stable glassy phase with finite Edwards' compactivity.
We analyse the internal dynamics of star-forming HII regions and their efficiency in interacting with the ISM. We use GHaFaS (Fabry-Perot) data of the nearby spiral galaxy M83 to perform multiple-Gaussian fitting to the integrated Halpha emission line for 136 HII regions, advanced instrumental response subtraction and to study the Luminosity-velocity dispersion relation. We find that the best way of dealing with instrumental response effects is convolving its actual shape with the Gaussian before fitting and that in our data almost none of the regions need a secondary Gaussian.