ShantanuT01/DACTYL-Pretraining huggingface dataset:
In Newtonian gravity, a stationary axisymmetric system admits a third, Carter-like constant of motion if its mass multipole moments are related to each other in exactly the same manner as for the Kerr black-hole spacetime. The Newtonian source with this property consists of two point masses at rest a fixed distance apart. The integrability of motion about this source was first studied in the 1760s by Euler. We show that the general relativistic analogue of the Euler problem, the Bach-Weyl solution, does not admit a Carter-like constant of motion, first, by showing that it does not possess a non-trivial Killing tensor, and secondly, by showing that the existence of a Carter-like constant for the two-center problem fails at the first post-Newtonian order.
Following \cite{Visintin}, we exploit the fractional perimeter of a set to give a definition of fractal dimension for its measure theoretic boundary. We calculate the fractal dimension of sets which can be defined in a recursive way and we give some examples of this kind of sets, explaining how to construct them starting from well known self-similar fractals. In particular, we show that in the case of the von Koch snowflake $S\subset\mathbb R^2$ this fractal dimension coincides with the Minkowski dimension, namely \begin{equation*} P_s(S)<\infty\qquad\Longleftrightarrow\qquad s\in\Big(0,2-\frac{\log4}{\log3}\Big). \end{equation*} We also study the asymptotics as $s\to1^-$ of the fractional perimeter of a set having finite (classical) perimeter.
Under a fourth order moment condition on the branching and a second order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous state and continuous time branching process with immigration on certain left non-Perron eigenvectors of the branching mean matrix is asymptotically mixed normal. With an appropriate random scaling, under some conditional probability measure, we prove asymptotic normality as well. In case of a non-trivial process, under a first order moment condition on the immigration mechanism, we also prove the convergence of the relative frequencies of distinct types of individuals on a suitable event; for instance, if the immigration mechanism does not vanish, then this convergence holds almost surely.
Intrinsic image decomposition (IID) is an under-constrained problem. Therefore, traditional approaches use hand crafted priors to constrain the problem. However, these constraints are limited when coping with complex scenes. Deep learning-based approaches learn these constraints implicitly through the data, but they often suffer from dataset biases (due to not being able to include all possible imaging conditions).   In this paper, a combination of the two is proposed. Component specific priors like semantics and invariant features are exploited to obtain semantically and physically plausible reflectance transitions. These transitions are used to steer a progressive CNN with implicit homogeneity constraints to decompose reflectance and shading maps.   An ablation study is conducted showing that the use of the proposed priors and progressive CNN increase the IID performance. State of the art performance on both our proposed dataset and the standard real-world IIW dataset shows the effectiveness of the proposed method. Code is made available at https://github.com/Morpheus3000/SIGNet
Conjectures of J. Igusa for p-adic local zeta functions and of J. Denef and F. Loeser for topological local zeta functions assert that (the real part of) the poles of these local zeta functions are roots of the Bernstein-Sato polynomials (i.e. the b-functions). We prove these conjectures for certain hyperplane arrangements, including the case of reduced hyperplane arrangements in three-dimensional affine space.
We address the problem of collective motion across a barrier like encountered in fission. A formula for the quantal decay rate is derived which bases on a recently developed variational approach for functional integrals. This formula can be applied to low temperatures that have not been accessible within the former PSPA type approach. To account for damping of collective motion one particle Green functions are dressed with appropriate self-energies.
This paper introduces the notion of a derived splinter. Roughly speaking, a scheme is a derived splinter if it splits off from the coherent cohomology of any proper cover. Over a field of characteristic 0, this condition characterises rational singularities by a result of Kov\'acs. Our main theorem asserts that over a field of characteristic p, derived splinters are the same as (underived) splinters, i.e., as schemes that split off from any finite cover. Using this result, we answer some questions of Karen Smith concerning extending Serre/Kodaira type vanishing results beyond the class of ample line bundles in positive characteristic; these are purely projective geometric statements independent of singularity considerations. In fact, we can prove "up to finite cover" analogues in characteristic p of many vanishing theorems one knows in characteristic 0. All these results fit naturally in the study of F-singularities, and are motivated by a desire to understand the direct summand conjecture
It has recently been shown that f(R) theories formulated in the Palatini variational formalism are able to avoid the big bang singularity yielding instead a bouncing solution. The mechanism responsible for this behavior is similar to that observed in the effective dynamics of loop quantum cosmology and an f(R) theory exactly reproducing that dynamics has been found. I will show here that considering more general actions, with quadratic contributions of the Ricci tensor, results in a much richer phenomenology that yields bouncing solutions even in anisotropic (Bianchi I) scenarios. Some implications of these results are discussed.
We classify all possible automorphism groups of smooth cubic surfaces over an algebraically closed field of arbitrary characteristic. As an intermediate step we also classify automorphism groups of quartic del Pezzo surfaces. We show that the moduli space of smooth cubic surfaces is rational in every characteristic, determine the dimensions of the strata admitting each possible isomorphism class of automorphism group, and find explicit normal forms in each case. Finally, we completely characterize when a smooth cubic surface in positive characteristic, together with a group action, can be lifted to characteristic zero.
The precise control of spins in semiconductor spintronic devices requires electrical means for generating spin packets with a well-defined initial phase. We demonstrate a pulsed electrical scheme that triggers the spin ensemble phase in a similar way as circularly-polarized optical pulses are generating phase coherent spin packets. Here, we use fast current pulses to initialize phase coherent spin packets, which are injected across an Fe/GaAs Schottky barrier into $n$-GaAs. By means of time-resolved Faraday rotation, we demonstrate phase coherence by the observation of multiple Larmor precession cycles for current pulse widths down to 500 ps at 17 K. We show that the current pulses are broadened by the charging and discharging time of the Schottky barrier. At high frequencies, the observable spin coherence is limited only by the finite band width of the current pulses, which is on the order of 2 GHz. These results therefore demonstrate that all-electrical injection and phase control of electron spin packets at microwave frequencies is possible in metallic-ferromagnet/semiconductor heterostructures.
We present a broadband polarization analysis of 36 discrete polarized radio sources over a very broad, densely-sampled frequency band. Our sample was selected on the basis of polarization behaviour apparent in narrowband archival data at 1.4 GHz: half the sample show complicated frequency-dependent polarization behaviour (i.e. Faraday complexity) at these frequencies, while half show comparatively simple behaviour (i.e. they appear Faraday simple). We re-observed the sample using the Australia Telescope Compact Array (ATCA) in full polarization, with 6 GHz of densely sampled frequency coverage spanning 1.3 to 10 GHz. We have devised a general polarization modelling technique that allows us to identify multiple polarized emission components in a source, and to characterize their properties. We detect Faraday complex behaviour in almost every source in our sample. Several sources exhibit particularly remarkable polarization behaviour. By comparing our new and archival data, we have identified temporal variability in the broadband integrated polarization spectra of some sources. In a number of cases, the characteristics of the polarized emission components, including the range of Faraday depths over which they emit, their temporal variability, spectral index, and the linear extent of the source, allow us to argue that the spectropolarimetric data encodes information about the magnetoionic environment of active galactic nuclei themselves. Furthermore, the data place direct constraints on the geometry and magnetoionic structure of this material. We discuss the consequences of restricted frequency bands on the detection and interpretation of polarization structures, and implications for upcoming spectropolarimetric surveys.
The average accuracy is one of major evaluation metrics for classification systems, while the accuracy deviation is another important performance metric used to evaluate various deep neural networks. In this paper, we present a new ensemble-like fast deep neural network, Harmony, that can reduce the accuracy deviation among categories without degrading overall average accuracy. Harmony consists of three sub-models, namely, Target model, Complementary model, and Conductor model. In Harmony, an object is classified by using either Target model or Complementary model. Target model is a conventional classification network for general categories, while Complementary model is a classification network especially for weak categories that are inaccurately classified by Target model. Conductor model is used to select one of two models. Experimental results demonstrate that Harmony accurately classifies categories, while it reduces the accuracy deviation among the categories.
Background: The astrophysical $r$-process occurs in an explosive astrophysical event under extremely neutron-rich conditions, leading to (n,$\gamma$)-($\gamma$,n) equilibrium along isotopic chains which peaks around neutron separation energies of a few MeV. Nuclei with larger $Z$ are usually produced by $\beta^-$-decay, but under certain conditions also $\alpha$-induced reactions may become relevant for the production of nuclei with $Z+2$.   Purpose: The uncertainties of the reaction rates of these $\alpha$-induced reactions are discussed within the statistical model. As an example, $\alpha$-induced ($\alpha$,n) and $(\alpha$,$x$n) reaction cross sections for the neutron-rich $^{86}$Se nucleus are studied in detail.   Method: In a first step, the relevance of ($\alpha$,n) and $(\alpha$,$x$n) reactions is analyzed. Next the uncertainties are determined from a variation of the $\alpha$-nucleus potential which is the all-dominant parameter for the astrophysical $Z \rightarrow Z+2$ reaction rate.   Results: It is found that the $r$-process flow towards nuclei with larger $Z$ is essentially influenced only by the $\alpha$-nucleus potential whereas the other ingredients of the statistical model play a very minor role. This finding is based on the fact that the flow towards larger $Z$ depends on the sum over all ($\alpha$,$x$n) cross sections which is practically identical to the total $\alpha$-induced reaction cross section.   Conclusions: $\alpha$-nucleus potentials play an important role under certain $r$-process conditions because the flow towards larger $Z$ depends sensitively on the total $\alpha$-induced reaction cross section. The uncertainty of the reaction rate is about a factor of two to three at higher temperatures and exceeds one order of magnitude at very low temperatures.
Optical control of the spin degree of freedom is often desired in application of the spin technology. Here we report spin-rotational excitations observed through inelastic light scattering of the hexagonal LuMnO3 in the antiferromagnetically (AFM) ordered state. We propose a model based on the spin-spin interaction Hamiltonian associated with the spin rotation of the Mn ions, and find that the spin rotations are angularly quantized by 60, 120, and 180 degrees. Angular quantization is considered to be a consequence of the symmetry of the triangular lattice of the Mn-ion plane in the hexagonal LuMnO3. These angularly-quantized spin excitations may be pictured as isolated flat bubbles in the sea of the ground state, which may lead to high-density information storage if applied to spin devices. Optically pumped and detected spin-excitation bubbles would bring about the advanced technology of optical control of the spin degree of freedom in multiferroic materials.
We predict that the collective excitations of an atomic array become entangled with the light of a high-finesse cavity mode when they are suitably coupled. This entanglement is of Einstein-Podolsky-Rosen type, it is robust against cavity losses and is a stationary property of the coupled system. It is generated when the atomic array is aligned along the cavity axis and driven transversally by a laser, when coherent scattering of photons into the cavity mode is suppressed because of phase-mismatching. We identify the parameter regimes under which entanglement is found and show that these are compatible with existing experimental setups.
In this paper we study the dynamic feedback stability for a simplified model of fluid-structure interaction on a tree. We prove that, under some conditions, the energy of the solutions of the system decay exponentially to zero when the time tends to infinity. Our technique is based on a frequency domain method and a special analysis for the resolvent.
PH3 is studied to understand the superconducting transition and responsible stoichiometry under high pressure by means of Raman, IR, and x-ray diffraction (XRD) measurements, and theoretical calculations. It is found PH3 is stable up to about 8 GPa and then starts to dehydrogenate through two dimerization processes at room temperature as pressure up to 25 GPa. Two resulting phosphorus hydrides, P2H4 and P4H6, are verified experimentally and can be recovered to ambient pressure. On further compression above 35 GPa, P4H6 directly decomposes into elemental phosphorus. The superconductivity transition temperatures of P4H6 at 100 and 200 GPa have been predicted to be 13 and 67 K in agreement with reported results, suggesting it might responsible for the superconductivity at higher pressures. Our results clearly show that P2H4 and P4H6 are only stable P-H compounds between PH3 and elemental phosphorus, shedding light on the superconducting mechanism.
A constituent quark model is developed for an arbitrary light- cone direction \omega. Form factors are obtained from free one-body electromagnetic current matrix elements. They are found to be \omega- independent for spin-0 mesons, the nucleon and \Lambda hyperon, while there is \omega-dependence for spin-1 systems like the deuteron.
To include the explicit valence gluon degrees of freedom into spectroscopy of the lowest states of heavy quarkonia, we consider, within an adiabatic model, the properties of the lowest hybrid $\bar{Q}Qg$-mesons and estimate the effects of their mixing with low-lying vector $\bar{c}c$-charmonia. The perspectives of compatibility of the resulting picture with data are discussed.
The J-Ks color distribution (CD) with a bin size of 0.05 magnitude for the entire Milky Way has been carried out by using the Two Micron All Sky Survey Point Source Catalog (2MASS PSC). The CDs are bimodal, which has a red peak at 0.8 < J-Ks < 0.85 and a blue peak at 0.3 < J-Ks < 0.4. The colors of the red peak are more or less the same for the whole sky, but that of the blue peak depend on Galactic latitude, (J-Ks ~ 0.35 at low Galactic latitudes and 0.35 < J-Ks < 0.4 for other sky areas). The blue peak dominates the bimodal CDs at low Galactic latitudes and becomes comparable with the red peak in other sky regions. In order to explain the bimodal distribution and the global trend shown by the all sky 2MASS CDs, we assemble an empirical HR diagram, which is composed by observational-based near infrared HR diagrams and color magnitude diagrams, and incorporate a Milky Way model. In the empirical HR diagram, the main sequence stars turnoff the thin disk is relatively bluer, (J-Ks)0 = 0.31, when we compare with the thick disk which is (J-Ks)0 = 0.39. The age of the thin/thick disk is roughly estimated to be around 4-5/8-9 Gyr according to the color-age relation of the main sequence turnoff. In general, the 2MASS CDs can be treated as a tool to census the age of stellar population of the Milky Way in a statistical manner and to our knowledge this is a first attempt to measure the age.
The scale invariant Poisson processes on (0,infty) play a central but mildly disguised role in number theory, combinatorics, and genetics. They give the continuous limits which underly and unify diverse discrete structures, including the prime factorization of a uniformly chosen integer, the factorization of polynomials over finite fields, the decomposition into cycles of random permutations, the decomposition into components of random mappings, and the Ewens sampling formula. They deserve attention as one of the fundamental and central objects of probability theory.
We discuss the production of multi-photons squeezed states induced by the time variation of the (Abelian) gauge coupling constant in a string cosmological context. Within a fully quantum mechanical approach we solve the time evolution of the mean number of produced photons in terms of the squeezing parameters and in terms of the gauge coupling. We compute the first (amplitude interference) and second order (intensity interference) correlation functions of the magnetic part of the photon background. The photons produced thanks to the variation of the dilaton coupling are strongly bunched for the realistic case where the growth of the dilaton coupling is required to explain the presence of large scale magnetic fields and, possibly of a Faraday rotation of the Cosmic Microwave Background.
Recently a new monoclinic phase in the PbZr(1-x)TixO3 ceramic system has been reported by Noheda et al. for the composition x= 0.48. In the present work, samples with Ti contents of x= 0.47 and 0.50, which are both tetragonal below their Curie points, have been investigated. In the sample with x= 0.50, the tetragonal phase was found to transform to a monoclinic phase at about 200 K as the temperature was lowered. The sample with x= 0.47 showed a complicated region of phase coexistence between 440-320 K, becoming rhombohedral at around 300 K. No further symmetry change was found down to 20 K. Dielectric measurements for these two samples are also reported. On the basis of these results, a preliminary phase diagram is presented. Optimum compositional homogeneity is needed to properly characterize the new monoclinic region.
The low-frequency and shot noises in spin-valve CoFeB/MgO/CoFeB magnetic tunneling junctions were studied at low temperature. The measured 1/f noise around the magnetic hysteresis loops of the free layer indicates that the main origin of the 1/f noise is the magnetic fluctuation, which is discussed in terms of a fluctuation-dissipation relation. Random telegraph noise (RTN) is observed to be symmetrically enhanced in the hysteresis loop with regard to the two magnetic configurations. We found that this enhancement is caused by the fluctuation between two magnetic states in the free layer. Although the 1/f noise is almost independent of the magnetic configuration, the RTN is enhanced in the antiparallel configuration. These findings indicate the presence of spin-dependent activation of RTN. Shot noise reveals the spin-dependent coherent tunneling process via a crystalline MgO barrier.
Cosmological birefringence is a rotation of the polarization plane of photons coming from sources of astrophysical and cosmological origin. The rotation can also depend on the energy of the photons and not only on the distance of the source and on the cosmological evolution of the underlying theoretical model. In this work, we constrain few selected models for cosmological birefringence, combining CMB and astrophysical data at radio, optical, X and gamma wavelengths, taking into account the specific energy and distance dependences.
We explore the relations between size, stellar mass and average stellar population age (indicated by D$_n4000$ indices) for a sample of $\sim11000$ intermediate-redshift galaxies from the SHELS spectroscopic survey (Geller et al. 2014) augmented by high-resolution Subaru Telescope Hyper Suprime-Cam imaging. In the redshift interval $0.1<z<0.6$, star forming galaxies are on average larger than their quiescent counterparts. The mass-complete sample of $\sim3500$ $M_*>10^{10}\, M_\odot$ quiescent galaxies shows that the average size of a $10^{11}\, M_\odot$ quiescent galaxy increases by $\lesssim25\%$ from $z\sim0.6$ to $z\sim0.1$. This growth rate is a function of stellar mass: the most massive ($M_*>10^{11}\, M_\odot$) galaxies grow significantly more slowly in size than an order of magnitude less massive quiescent systems that grow by 70\% in the $0.1\lesssim z\lesssim0.3$ redshift interval. For $M_*<10^{11}\, M_\odot$ galaxies age and size are anti-correlated at fixed mass; more massive quiescent systems show no significant trend in size with average stellar population age. The evolution in absolute and fractional abundances of quiescent systems at intermediate redshift are also a function of galaxy stellar mass. The suite of evolutionary trends suggests that galaxies more massive than $\sim10^{11}\, M_\odot$ have mostly assembled their mass by $z\sim0.6$. Quiescent galaxies with lower stellar masses show more complex evolution that is characterized by a combination of individual quiescent galaxy size growth (through mergers) and an increase in the size of newly quenched galaxies joining the population at later times (progenitor bias). The $M_*\sim10^{10}\, M_\odot$ population grows predominantly as a result of progenitor bias. For $M_*\sim5\times10^{10}\, M_\odot$ quiescent galaxies, mergers and progenitor bias make more comparable contributions to the size growth.[abridged]
With a goal toward deriving the physical conditions in external galaxies, we present a survey of the formaldehyde emission in a sample of starburst systems. By extending a technique used to derive the spatial density in star formation regions in our own Galaxy, we show how the relative intensity of the 1(10)-1(11) and 2(11)-2(12) K-doublet transitions of H2CO can provide an accurate densitometer for the active star formation environments found in starburst galaxies. Relying upon an assumed kinetic temperature and co-spatial emission and absorption from both H2CO transitions, our technique is applied to a sample of nineteen IR-bright galaxies which exhibit various forms of starburst activity. In the five galaxies of our sample where both H2CO transitions were detected we have derived spatial densities. We also use H2CO to estimate the dense gas mass in our starburst galaxy sample, finding similar mass estimates for the dense gas forming stars in these objects as derived using other dense gas tracers. A related trend can be seen when one compares L_IR to our derived n(H2) for the five galaxies within which we have derived spatial densities. Even though our number statistics are small, there appears to be a trend toward higher spatial density for galaxies with higher infrared luminosity. This is likely another representation of the L_IR-M_dense correlation.