ShantanuT01/DACTYL-Pretraining huggingface dataset:
The homogeneous form $\Phi_n(X,Y)$ of degree $\varphi(n)$ which is associated with the cyclotomic polynomial $\phi_n(X)$ is dubbed a {\it cyclotomic binary form}. A positive integer $m\ge 1$ is said to be {\it representable by a cyclotomic binary form} if there exist integers $n,x,y$ with $n\ge 3$ and $\max\{|x|, |y|\}\ge 2$ such that $\Phi_n(x,y)=m$. We prove that the number $a_m$ of such representations of $m$ by a cyclotomic binary form is finite. More precisely, we have $\,\varphi(n) \le ({2}/ {\log 3})\log m\, $ and $\, \max\{|x|,|y|\} \le ({2}/{\sqrt{3}})\, m^{1/\varphi(n)}.\,$ We give a description of the asymptotic cardinality of the set of values taken by the forms for $n\geq 3$. This will imply that the set of integers $m$ such that $a_m\neq 0$ has natural density 0. We will deduce that the average value of the integers $a_m$ among the nonzero values of $a_m$ grows like $\sqrt{\log \, m}$.
A shape change of the self-consistent mean-field induced by a configuration change is discussed within the conventional constrained Hartree-Fock (CHF) theory. It is stressed that a single-particle level crossing dynamics should be treated carefully, because the shape of the mean-field in such a finite many-body system as the nucleus strongly changes depending on its configuration. This situation is clearly shown by applying an adiabatic assumption, where the most energetically favorable single-particle states are assumed to be occupied. The excited HF states and the continuously-connected potential energy curves are given by applying the configuration dictated CHF method. The effect of pairing correlation is discussed in the level crossing region. Triaxial deformed results in our Hartree-Fock-Bogoliubov (HFB) calculation with Gogny force nicely reproduce the available experimental data of Ge isotopes. From our numerical calculation, it is concluded that the CHFB state is more fragile than the CHF state in the level crossing region.
We present a fully nonlinear calculation of the waveform of the gravitational radiation emitted in the fission of a vacuum white hole. At early times, the waveforms agree with close-approximation perturbative calculations but they reveal dramatic time and angular dependence in the nonlinear regime. The results pave the way for a subsequent computation of the radiation emitted after a binary black hole merger.
Spectroscopic detection of narrow emission lines traces the presence of circumstellar mass distributions around massive stars exploding as core-collapse supernovae. Transient emission lines disappearing shortly after the supernova explosion suggest that the spatial extent of such material is compact, and hence imply an increased mass loss shortly prior to explosion. Here, we present a systematic survey for such transient emission lines (Flash Spectroscopy) among Type II supernovae detected in the first year of the Zwicky Transient Facility (ZTF) survey. We find that at least six out of ten events for which a spectrum was obtained within two days of estimated explosion time show evidence for such transient flash lines. Our measured flash event fraction ($>30\%$ at $95\%$ confidence level) indicates that elevated mass loss is a common process occurring in massive stars that are about to explode as supernovae.
An extensive spectroscopic study was carried out for the beryllium abundances of 200 red giants (mostly of late G and early K type), which were determined from the near-UV Be II 3131.066 line based on high-dispersion spectra obtained by Subaru/HDS, with an aim of investigating the nature of surface Be contents in these evolved giants; e.g., dependence upon stellar parameters, degree of peculiarity along with its origin and build-up timing. We found that Be is considerably deficient (to widely different degree from star to star) in the photosphere of these evolved giants by ~1-3 dex (or more) compared to the initial abundance. While the resulting Be abundances (A(Be)) appear to weakly depend upon T_eff, log g, [Fe/H], M, age, and v_sin i, this may be attributed to the metallicity dependence of A(Be) coupled with the mutual correlation between these stellar parameters, since such tendencies almost disappear in the metallicity-scaled Be abundance ([Be/Fe]). By comparing the Be abundances (as well as their correlations with Li and C) to the recent theoretical predictions based on sophisticated stellar evolution calculations, we concluded that such a considerable extent/diversity of Be deficit is difficult to explain only by the standard theory of first dredge-up in the envelope of red giants, and that some extra mixing process (such as rotational or thermohaline mixing) must be responsible, which presumably starts to operate already in the main-sequence phase. This view is supported by the fact that appreciable Be depletion is seen in less evolved intermediate-mass B-A type stars near to the main sequence.
Analyses of multiple pulse sequences of B2303+30 reveal that this pulsar has two distinct emission modes. One mode (B) follows a steady even-odd pattern and is more intense. The second mode (Q) is characteristically weak, but has intermittent driftbands with a periodicity of approximately 3 P/cycles, and nulls much more frequently than the B mode. Both modes occur with roughly equal frequency and their profiles have a similar single-humped form with a slight asymmetry. Our observations and analyses strongly suggest that the subpulse driftrates in both modes are linked in a series of cycles, which can be modelled as relaxing oscillations in the underlying circulation rate.
QCD justification of SU(m/n) supergroups are shown to provide a basis for the existence of an approximate hadronic supersymmetry. Effective Hamiltonian of the relativistic quark model is derived, leading to hadronic mass formulae in remarkable agreement with experiments. Bilocal approximation to hadronic structure and incorporation of color through octonion algebra (based on quark-antidiquark symmetry) is also shown to predict exotic diquark-antidiquark ($D-\bar{D}$) meson states. A minimal supersymmetric sceme based on $SU(3)^c \times SU(6/1)$ that excludes exotics is constructed. Symmetries of three quark systems and possible relativistic formulation of the quark model through the spin realization of Wess-Zumino algebra is presented.
The normalized state $\ket{\psi(t)}=c_1(t)\ket{1}+c_2(t)\ket{2}$ of a single two-level system performs oscillations under the influence of a resonant driving field. It is assumed that only one realization of this process is available. We show that it is possible to approximately visualize in real time the evolution of the system as far as it is given by $|c_2(t)|^2$. For this purpose we use a sequence of particular unsharp measurements separated in time. They are specified within the theory of generalized measurements in which observables are represented by positive operator valued measures (POVM). A realization of the unsharp measurements may be obtained by coupling the two-level system to a meter and performing the usual projection measurements on the meter only.
Na-ion conduction, and correlations between Na-ion conduction pathways and crystal structure have been investigated as a function of temperature in the layered battery material Na2Ni2TeO6 by impedance spectroscopy and neutron diffraction, respectively. The impedance data reveal an ionic conductivity 2x10-4 S/m at 323 K which strongly enhances with increasing temperature and attains a high value of ~ 0.03 S/m at 423 K. The temperature dependent conductivity data show an Arrhenius type behavior with average activation energy (Ea) of ~ 0.58(3) eV for T > 383 K. By employing soft-bond valence sum analysis of the neutron diffraction patterns we experimentally demonstrate the site-specific Na-ion conductions, through visualization of microscopic sodium-ion conduction pathways, and verify the recent theoretical results of Molecular dynamic simulation. Our results reveal two-dimensional Na-ion conduction pathways that are confined within the ab planes of Na layers. Crystal structural study indicates that the layered structure involving Na ion layers is responsible for high ionic conductivity, and the local crystallographic environment of Na ion sites is responsible for site-specific conductivity. Our study further reveals that up to 500 K, the ionic conduction is governed by the Na ions located at the Na1 and Na2 sites, whereas, all the Na ions located at the three Na-sites contribute to the conduction process above 500 K. Our neutron diffraction study also establishes that the crystal structure of Na2Ni2TeO6 is stable at least up to 725 K (the highest measured temperature), however, with an anisotropic thermal expansion (c/a ~ 3).
The unique nature of histopathology images opens the door to domain-specific formulations of image translation models. We propose a difficulty translation model that modifies colorectal histopathology images to be more challenging to classify. Our model comprises a scorer, which provides an output confidence to measure the difficulty of images, and an image translator, which learns to translate images from easy-to-classify to hard-to-classify using a training set defined by the scorer. We present three findings. First, generated images were indeed harder to classify for both human pathologists and machine learning classifiers than their corresponding source images. Second, image classifiers trained with generated images as augmented data performed better on both easy and hard images from an independent test set. Finally, human annotator agreement and our model's measure of difficulty correlated strongly, implying that for future work requiring human annotator agreement, the confidence score of a machine learning classifier could be used as a proxy.
The Mori's memory function approach to spin dynamics in doped antiferromagnetic insulator combined with the assumption of temperature independent static spin correlations and constant collective mode damping leads to w/T scaling in a broad range. The theory involving a nonuniversal scaling parameter is used to analyze recent inelastic neutron scattering results for underdoped cuprates. Adopting modified damping function also the emerging central peak in low-doped cuprates at low temperatures can be explained within the same framework.
We present the high-energy emission properties of GRB 160509A, from its prompt mission to late afterglow phase. GRB 160509A contains two emission episodes: 0-40s and 280-420s after the burst onset (t0). The relatively high fluence of GRB 160509A allows us to establish an evolving spectrum above 100 MeV. During the first emission episode, the >100 MeV spectrum is soft with \Gamma=>3.0, which can be smoothly connected to keV energies with a Band function with a high-energy cutoff. The >100 MeV spectrum rapidly changes to a hard spectrum with \Gamma<=1.5 after t0+40s. The existence of very energetic photons, e.g., a 52 GeV that arrives t0+77 seconds, and a 29 GeV that arrives t0+70 ks, is hard to reconcile by the synchrotron emission from forward-shock electrons, but likely due to inverse Compton mechanism (e.g., synchrotron self-Compton emission). A soft spectrum (\Gamma~2) between 300s and 1000s after the burst onset is also found at a significance of about 2 standard deviations, which suggests a different emission mechanism at work for this short period of time. GRB 160509A represents the latest example where inverse Compton emission has to be taken into account in explaining the afterglow GeV emission, which had been suggested long before the launch of Fermi LAT.
The pyramid-to-dome transition in Ge$_{x}$Si$_{1-x}$ on Si(100) initiated by step bunching on pyramidal quantum dots is atomistically simulated using a novel multi-state lattice model incorporating effective surface reconstructions. Results are explained by a simple theory based on a shallow island approximation. Under given deposition conditions in $d$ dimensions, the shape transition is shown to occur at island size $n_c$ following $n_c^{1/d} \propto x^{-\zeta}$ independent of temperature and deposition rate, where $\zeta\alt 2$ and $x$ is the actual Ge concentration in the island. The transition has an energy barrier dominated by the facet interface energy. Fast deposition however can out-run and delay the transition to larger island sizes.
The Navier-Stokes-Voigt equations are a regularization of the Navier-Stokes equations that share some of its asymptotic and statistical properties and have been used in direct numerical simulations of the latter. In this article we characterize the decay rate of solutions to the Navier-Stokes-Voigt equations in terms of the decay character of the initial datum and study the long time behaviour of its solutions by comparing them to solutions to the linear part.
We know that any prime number of form $4s+1$ can be written as a sum of two perfect square numbers. As a consequence of Goldbach's weak conjecture, any number great than $10$ can be represented as a sum of four primes. We are motivated to consider an equation with some constraints about digital sum for the four primes. And we conclude that the square root of the digital sum of the four primes will greater than $4$ and will not be a multiple of $3$ if the equation has solutions. In the proof, we give the method of determining whether a number is a perfect square.
We solve the mean-field $\phi^4$ model in an external magnetic field in the microcanonical ensemble using two different methods. The first one is based on Rugh's microcanonical formalism and leads to express macroscopic observables, such as temperature, specific heat, magnetization and susceptibility, as time averages of convenient functions of the phase-space. The approach is applicable for any finite number of particles $N$. The second method uses large deviation techniques and allows us to derive explicit expressions for microcanonical entropy and for macroscopic observables in the $N \to\infty$ limit. Assuming ergodicity, we evaluate time averages in molecular dynamics simulations and, using Rugh's approach, we determine the value of macroscopic observables at finite $N$. These averages are affected by a slow time evolution, often observed in systems with long-range interactions. We then show how the finite $N$ time averages of macroscopic observables converge to their corresponding $N\to\infty$ values as $N$ is increased. As expected, finite size effects scale as $N^{-1}$.
We measure the surface of CH$_3$NH$_3$PbI$_3$ single crystals by making use of two photon photoemission spectroscopy. Our method monitors the electronic distribution of photoexcited electrons, explicitly discriminating the initial thermalization from slower dynamical processes. The reported results disclose the fast dissipation channels of hot carriers (0.25 ps), set a upper bound to the surface induced recombination velocity ($<4000$ cm/s) and reveal the dramatic effect of shallow traps on the electrons dynamics. The picosecond localization of excited electrons in degraded CH$_3$NH$_3$PbI$_3$ samples is consistent with the progressive reduction of photoconversion efficiency in operating devices. Minimizing the density of shallow traps and solving the aging problem may boost the macroscopic efficiency of solar cells to the theoretical limit.
We prove that the moduli spaces of K3 surfaces with non-symplectic involution are rational for four deformation types. With the previous results, this establishes the rationality of those moduli spaces except two classical cases.
We associate to a regular system of weights a weighted projective line over an algebraically closed field of characteristic zero in two different ways. One is defined as a quotient stack via a hypersurface singularity for a regular system of weights and the other is defined via the signature of the same regular system of weights.   The main result in this paper is that if a regular system of weights is of dual type then these two weighted projective lines have equivalent abelian categories of coherent sheaves. As a corollary, we can show that the triangulated categories of the graded singularity associated to a regular system of weights has a full exceptional collection, which is expected from homological mirror symmetries.   Main theorem of this paper will be generalized to more general one, to the case when a regular system of weights is of genus zero, which will be given in the joint paper with Kajiura and Saito. Since we need more detailed study of regular systems of weights and some knowledge of algebraic geometry of Deligne--Mumford stacks there, the author write a part of the result in this paper to which another simple proof based on the idea by Geigle--Lenzing can be applied.
With the rapid development of asteroseismology thanks to space-based photometry missions such as CoRoT, Kepler, TESS, and in the future, PLATO, and the use of inversion techniques, quasi-model-independent constraints on the stellar properties can be extracted from a given stellar oscillation spectrum. In this context, inversions based on frequency separation ratios, that are less sensitive to surface effects, appear as a promising technique to constrain the properties of stellar convective cores. We developed an inversion based on frequency separation ratios with the goal of damping the surface effects of the oscillation frequencies. Using this new inversion, we defined a new indicator to constrain the boundary mixing properties of convective cores in solar-like oscillators. We verified our inversion technique by conducting tests in a controlled environment, where the stellar mass and radius are known exactly, and conducted an extensive hare and hounds exercise. The inversion is not affected by surface effects. With the construction of an extensive set of models, favoured and forbidden regions can be highlighted in the parameter space. If the ratios are well fitted, the inversion is unsurprisingly not providing additional information. The indicator coupled with the inversion based on frequency separation ratios seems promising at probing the properties of convective cores, especially for F-type stars exhibiting solar-like oscillations.
Using a chirally symmetric Lagrangian, which contains quarks as elementary degrees of freedom and mesons as bound states, we investigate the expansion and hadronization of a fireball, which initially contains only quarks and produces mesons by collisions. For this model, we study the time scales of expansion and thermal and chemical equilibration. We find that the expansion progresses relatively fast, leaving not necessarily enough time to establish thermal and chemical equilibrium. Mesons are produced in the bulk of the fireball rather than at a surface, at a temperature below the Mott temperature. Initial density fluctuations become amplified during the expansion. These observations challenge the applicability of hydrodynamical approaches to the expansion of a quark-gluon plasma.
We discuss the role of fixed scalars($\nu,\lambda$) in scattering off a five-dimensional balck hole. The issue is to explain the disagreement of the greybody factor for $\lambda$ between the semiclassical and effective string calculations. In the effective string approach, this is related to the operators with dimension (3,1) and (1,3). On the semiclassical calculation, this originates from a complicated mixing between $\lambda$ and other fields. Hence it may depend on the decoupling procedure. It is shown that $\lambda$ depends on the gauge choices such as the harmonic, dilaton gauges, and the Krasnitz-Klebanov setting for $h_{\mu\nu}$. It turns out that $\nu$ plays a role of test field well, while the role of $\lambda$ is obscure.
This paper extends previous results of the authors, concerning the behaviour of the equimultiple locus of algebroid surfaces under blowing--up, to arbitrary characteristic.
We study the dynamics of condensation in a misanthrope process with nonlinear jump rates and factorized stationary states. For large enough density, it is known that such models have a phase separated state, with a non-zero fraction of the total mass concentrating in a single lattice site. It has been established in [B Waclaw and M R Evans, Phys. Rev. Lett., 108(7):070601, 2012] for asymmetric dynamics that such processes exhibit explosive condensation, where the time to reach the stationary state vanishes with increasing system size. This constitutes a spatially extended version of instantaneous gelation which has previously been studied only in mean-field coagulation models. We show that this phenomenon also occurs for symmetric dynamics in one dimension if the non-linearity is strong enough, and we find a coarsening regime where the time to stationarity diverges with the system size for weak non-linearity. In higher space dimensions explosive condensation is expected to be generic for all parameter values. Our results are based on heuristic mean field arguments which are confirmed by simulation data.
In this article we prove that solutions of singular fully nonlinear partial differential equations are $C^{1,\beta}$. We also prove the simplicity of the principal eigenvalues for the Dirichlet Problem associated to these operators using that regularity, a strict comparison principle and Sard's theorem.
To see the feasibility of a large-scale quantum computing, it is required to accurately analyze the performance and the quantum resource. However, most of the analysis reported so far have focused on the statistical examination, i.e., simply calculating the performance and resource based on individual data, and even worse usually only a few components have been considered. In this work, to achieve more exact analysis, we propose an integrated analysis method for a practical quantum computing model with three components (\textit{algorithm}, \textit{error correction} and \textit{device}) under a realistic quantum computer system architecture. To implement the above method, we develop a quantum computing framework composed of three functional layers: compile, system and building block. This framework can support, for the first time, the mapping of quantum algorithm from physical qubit level to system architecture level with a given fault-tolerant scheme. Therefore, the proposed method can measure the effect of dynamic situation when the quantum computer practically runs. By using our method, we found that Shor algorithm to factorize 512-bit integer requires $8.78\times 10^ 5$ hours. We also show how the proposed method can be used for analyzing optimal concatenation level and code distance of fault-tolerant quantum computing.
The HiRes and AGASA Collaborations have published contradictory energy spectra for energies above the GZK cut-off. In this article, we investigate the acceptance of fluorescence telescopes to different primary particles at the highest energies. Using CORSIKA shower simulations without and with the new pre-showering scheme, which allows photons to interact in the Earth magnetic field, we estimate the aperture of the HiRes I telescope for gammas and protons primaries. We calculate the dependence of the telescope sensitivity to primary particle identity. We also investigate the possibility that systematic differences in shower development for hadrons and gammas could mask or distort vital features of the cosmic ray energy spectrum at energies above the photo-pion production threshold. The impact of these effects on the true acceptance of a fluorescence detector is analyzed in the context of top-down production models.
We study the effects, to all orders in the Planck length from a generalized uncertainty principle (GUP), on the statistical entropy of massive scalar bulk fields in the Randall-Sundrum black brane world. We show that the Bekenstein-Hawking area law is not preserved, and contains small corrections terms proportional to the black hole inverse area.