ShantanuT01/DACTYL-Pretraining huggingface dataset:
We determine the structure of a finite subset $A$ of an abelian group given that $|2A|<3(1-\epsilon)|A|$, $\epsilon>0$; namely, we show that $A$ is contained either in a "small" one-dimensional coset progression, or in a union of fewer than $\epsilon^{-1}$ cosets of a finite subgroup.   The bounds $3(1-\epsilon)|A|$ and $\epsilon^{-1}$ are best possible in the sense that none of them can be relaxed without tightened another one, and the estimate obtained for the size of the coset progression containing $A$ is sharp.   In the case where the underlying group is infinite cyclic, our result reduces to the well-known Freiman's $(3n-3)$-theorem; the former thus can be considered as an extension of the latter onto arbitrary abelian groups, provided that there is "not too much torsion involved".
We report broadband spin-wave spectroscopy on kagome artificial spin ice (ASI) made of large arrays of interconnected Ni$_{80}$Fe$_{20}$ nanobars. Spectra taken in saturated and disordered states exhibit a series of resonances with characteristic magnetic field dependencies. Making use of micromagnetic simulations, we identify resonances that reflect the spin-solid-state and monopole-antimonopole pairs on Dirac strings. The latter resonances allow for the generation of highly-charged vertices in ASIs via microwave assisted switching. Our findings open further perspectives for fundamental studies on ASIs and their usage in reprogrammable magnonics.
We present a comparative study of absolute distances to a sample of very nearby, bright Type Ia supernovae (SNe) derived from high cadence, high signal-to-noise, multi-band photometric data. Our sample consists of four SNe: 2012cg, 2012ht, 2013dy and 2014J. We present new homogeneous, high-cadence photometric data in Johnson-Cousins BVRI and Sloan g'r'i'z' bands taken from two sites (Piszkesteto and Baja, Hungary), and the light curves are analyzed with publicly available light curve fitters (MLCS2k2, SNooPy2 and SALT2.4). When comparing the best-fit parameters provided by the different codes, it is found that the distance moduli of moderately-reddened SNe Ia agree within ~0.2 mag, and the agreement is even better (< 0.1 mag) for the highest signal-to-noise BVRI data. For the highly-reddened SN~2014J the dispersion of the inferred distance moduli is slightly higher. These SN-based distances are in good agreement with the Cepheid distances to their host galaxies. We conclude that the current state-of-the-art light curve fitters for Type Ia SNe can provide consistent absolute distance moduli having less than ~0.1 -- 0.2 mag uncertainty for nearby SNe. Still, there is room for future improvements to reach the desired ~0.05 mag accuracy in the absolute distance modulus.
The tensor square conjecture states that for $n \geq 10$, there is an irreducible representation $V$ of the symmetric group $S_n$ such that $V \otimes V$ contains every irreducible representation of $S_n$. Our main result is that for large enough $n$, there exists an irreducible representation $V$ such that $V^{\otimes 4}$ contains every irreducible representation. We also show that tensor squares of certain irreducible representations contain $(1-o(1))$-fraction of irreducible representations with respect to two natural probability distributions. Our main tool is the semigroup property, which allows us to break partitions down into smaller ones.
The iron abundance relative to alpha-elements in the circumnuclear region of quasars is regarded as a clock of the star formation history and, more specifically, of the enrichment by SNIa. We investigate the iron abundance in a sample of 22 quasars in the redshift range 3.0<z<6.4 by measuring their rest frame UV FeII bump, which is shifted into the near-IR, and by comparing it with the MgII 2798 flux. The observations were performed with a device that can obtain near-IR spectra in the range 0.8-2.4 um in one shot, thereby enabling an optimal removal of the continuum underlying the FeII bump. We detect iron in all quasars including the highest redshift (z=6.4) quasar currently known. The uniform observational technique and the wide redshift range allows a reliable study of the trend of the FeII/MgII ratio with redshift. We find the FeII/MgII ratio is nearly constant at all redshifts, although there is marginal evidence for a higher FeII/MgII ratio in the quasars at z~6. If the FeII/MgII ratio reflects the Fe/alpha abundance, this result suggests that the z~6 quasars have already undergone a major episode of iron enrichment. We discuss the possible implications of this finding for the star formation history at z>6. We also detect a population of weak iron emitters at z~4.5, which are possibly hosted in systems that evolved more slowly. Alternatively, the trend of the FeII/MgII ratio at high redshift may reflect significantly different physical conditions of the circumnuclear gas in such high redshift quasars.
Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this space, the set of potentials associated to a known solution are transformed into a new set, either by continuous transformations or by discrete transformations. In view of this method, and upon consideration of continuous transformations, we arrive at some exact, stationary axisymmetric solutions to the Einstein field equations in vacuum, that may be of geometrical or/and physical interest.
We introduce the operation of forming the tensor product in the theory of analytic Frobenius manifolds. Building on the results for formal Frobenius manifolds which we extend to the additional structures of Euler fields and flat identities, we prove that the tensor product of pointed germs of Frobenius manifolds exists. Furthermore, we define the notion of a tensor product diagram of Frobenius manifolds with factorizable flat identity and prove the existence such a diagram and hence a tensor product Frobenius manifold. These diagrams and manifolds are unique up to equivalence. Finally, we derive the special initial conditions for a tensor product of semi--simple Frobenius manifolds in terms of the special initial conditions of the factors.
Synchrotron X-rays can be a useful tool to investigate electron acceleration at young supernova remnants (SNRs). At present, since the magnetic field configuration around the shocks of SNRs is uncertain, it is not clear whether electron acceleration is limited by SNR age, synchrotron cooling, or even escape from the acceleration region. We study whether the acceleration mechanism can be constrained by the cutoff shape of the electron spectrum around the maximum energy. We derive analytical formulae of the cutoff shape in each case where the maximum electron energy is determined by SNR age, synchrotron cooling and escape from the shock. They are related to the energy dependence of the electron diffusion coefficient. Next, we discuss whether information on the cutoff shape can be provided by observations in the near future which will simply give the photon indices and the flux ratios in the soft and hard X-ray bands. We find that if the power-law index of the electron spectrum is independently determined by other observations, then we can constrain the cutoff shape by comparing theoretical predictions of the photon indices and/or the flux ratios with observed data which will be measured by NuSTAR and/or ASTRO-H. Such study is helpful in understanding the acceleration mechanism. In particular, it will supply another independent constraint on the magnetic field strength around the shocks of SNRs.
We use an empirical tight-binding approach to calculate electron and hole states in [111]-grown PbSe nanowires. We show that the valley-orbit and spin-orbit splittings are very sensitive to the atomic arrangement within the nanowire elementary cell and differ for [111]-nanowires with microscopic $D_{3d}$, $C_{2h}$ and $D_{3}$ symmetries. For the nanowire diameter below 4 nm the valley-orbit splittings become comparable with the confinement energies and the $\boldsymbol{k}\cdot\boldsymbol{p}$ method is inapplicable. Nanowires with the $D_{3}$ point symmetry having no inversion center exhibit giant spin splitting $E = \alpha k_z$, linear in one-dimensional wave vector $k_z$, with the constant $\alpha$ up to 1 eV$\cdot$\AA.
In the present paper we study twisted foldings of root systems which generalize usual involutive foldings corresponding to automorphisms of Dynkin diagrams. Our motivating example is the Lusztig projection of the root system of type $E_8$ onto the subring of icosians of the quaternion algebra which gives the root system of type $H_4$.   Using moment graph techniques for any such folding we construct a map at the equivariant cohomology level. We show that this map commutes with characteristic classes and Borel maps. We also introduce and study its restrictions to the usual cohomology of projective homogeneous varieties, to group cohomology and to their virtual analogues for finite reflection groups.
We report on low temperature susceptibility and magnetization measurements made on single crystals of the recently discovered heavy-fermion superconductor UTe$_2$ and compare the results with the two ambient pressure ferromagnetic superconductors URhGe and UCoGe. Hysteresis curves in the superconducting phase show a familiar diamond shape superimposed on a large paramagnetic background. The Meissner state was measured by zero field cooling in small fields of a few Oe as well as ac susceptibility measurements in small fields and resulted in 100\% shielding, with a sharp transition. However the field cooling Meissner-Ochsenfeld effect (expulsion of flux) was negligible in fields greater than just a few Oe, but becomes nearly 30\% of the perfect diamagnetic signal when the field was reduced to 0.01~Oe. The critical current due to flux pinning was studied by ac susceptibility techniques. Over the range in fields and temperature of this study, no signature of a ferromagnetic transition could be discerned. The lower critical field $H_{\rm c1}$ has been measured along the three crystalographic axes, and surprisingly, the anisotropy of $H_{\rm c1}$ contradicts that of the upper critical field. We discuss this discrepancy and show that it may provide additional support for a magnetic field-dependent pairing mediated by ferromagnetic fluctuations in UTe$_2$.
Observations of black hole binaries (BHBs) have established a rich phenomenology of X-ray states. The soft states range from the low variability, accretion disc dominated thermal state (TD) to the higher variability, non-thermal steep power law state (SPL). The disc component in all states is typically modeled with standard thin disc accretion theory. However, this theory is inconsistent with optical/UV spectral, variability, and gravitational microlensing observations of active galactic nuclei (AGNs), the supermassive analogs of BHBs. An inhomogeneous disc (ID) model with large (~0.4 dex) temperature fluctuations in each radial annulus can qualitatively explain all of these AGN observations. The inhomogeneity may be a consequence of instabilities in radiation dominated discs, and therefore may be present in BHBs as well. We show that ID models can explain many features of the TD and SPL states of BHBs. The observed relationships between spectral hardness, disc fraction, and rms variability amplitude in BHBs are reproduced with temperature fluctuations similar to those inferred in AGNs, suggesting a unified picture of luminous accretion discs across orders of magnitude in black hole mass. This picture can be tested with spectral fitting of ID models, X-ray polarization observations, and radiation MHD simulations. If BHB accretion discs are indeed inhomogeneous, only the most disc dominated states (disc fraction > 0.95) can be used to robustly infer black hole spin using current continuum fitting methods.
We present a quantum key distribution protocol based on four-level particles entanglement. Furthermore, a controlled quantum key distribution protocol is proposed by utilizing three four-level particles. We show that the two protocols are secure.
We present ab initio density functional calculations that show P (Al) dopant atoms in small hydrogen-terminated Si crystals to be negatively (positively) charged. These signs of the dopant charges are reversed relative to the same dopants in bulk Si. We predict this novel reversal of the dopant charge (and electronic character of the doping) to occur at crystal sizes of order 100 Si atoms. We explain it as a result of competition between fundamental principles governing charge transfer in bulk semiconductors and molecules and predict it to occur in nanocrystals of most semiconductors.
Ideal hydroynamics provides an excellent description of all aspects of the single-particle spectra of all hadrons with transverse momenta below about 1.5-2 GeV/c at RHIC. This is shown to require rapid local thermalization at a time scale below 1 fm/c and at energy densities which exceed the critical value for color deconfinement by an order of magnitude. The only known thermalized state at such energy densities is the quark-gluon plasma (QGP). The rapid thermalization indicates that the QGP is a strongly interacting liquid rather than the weakly interacting gas of quarks and gluons that was previously expected.
We report on polarimetric observations of 100 pulsars centered on 774 MHz, made using the Green Bank Telescope, presenting their polarization profiles and polarized flux densities and comparing them with previous observations when possible. For 67 pulsars, these are the first such measurements made. Polarization profiles of 8 millisecond pulsars in our sample show wide profiles and flat position-angle curves. Strong linear polarization, sometimes approaching 100% of the total intensity, has been detected in all or a part of the average pulse profiles of some pulsars. In general, circular polarization is very weak, although it is observed to be extremely strong in the leading component of PSR J1920+2650. Sense reversal of circular polarization as a function of pulse phase has been detected from both core and other components of more than 20 pulsars. Any relationship between the spin-down luminosity and the percentage of linear polarization is not evident in our data at this frequency.
Previous results from the authors concerning the arising a tiny photon anomalous paramagnetic moment are also interpreted as a red-shift in analogy to the gravitational known effect. It is due to the photon interaction with the magnetized virtual electron-positron background which withdraw transverse momentum from photons and is polarization-dependent. If the photon frequency red-shift implies a change in time, a clock would go faster for increasing magnetic field intensity.
Based on the assumption that some apparent properties of the observable universe are accurate at a reasonable level of approximation, a tentative is made to independently derive the values of the baryon density parameter, the Hubble constant, the cosmic microwave background temperature and the helium mass fraction. The obtained values are in excellent agreement with those given by the most recent observational data.
Early magnetographic observations indicated that magnetic field in the solar photosphere has unresolved small-scale structure. Near-infrared and optical data with extremely high spatial resolution show that these structures have scales of few tens of kilometres, which are not resolved in the majority of solar observations. The goal of this study is to establish the effect of unresolved photospheric magnetic field structure on Stokes profiles observed with relatively low spatial resolution. Ultimately, we aim to develop methods for fast estimation of the photospheric magnetic filling factor and line-of-sight gradient of the photospheric magnetic field, which can be applied to large observational data sets. We exploit 3D MHD models of magneto-convection developed using MURAM code. Corresponding profiles of Fe I 6301.5 and 6302.5 $\mathrm{\AA}$ spectral lines are calculated using NICOLE radiative transfer code. The resulting I and V Stokes [x,y,$\lambda$] cubes with reduced spatial resolution of 150 km are used to calculate magnetic field values as they would be obtained in observations with Hinode/SOT or SDO/HMI. Three different methods of the magnetic filling factor estimation are considered: the magnetic line ratio method, Stokes V width method and a simple statistical method. We find that the statistical method and the Stokes V width method are sufficiently reliable for fast filling factor estimations. Furthermore, we find that Stokes $I\pm V$ bisector splitting gradient can be used for fast estimation of line-of-sight gradient of the photospheric magnetic field.
In section 1 we consider a 3-tuple $S=(|S|,\preccurlyeq,E)$ where $|S|$ is a finite set, $\preccurlyeq$ a partial ordering on $|S|,$ and $E$ a set of unordered pairs of distinct members of $|S|,$ and study, as a function of $n\geq 0,$ the number of maps $\varphi:|S|\to\{1,\dots,n\}$ which are both isotone with respect to the ordering $\preccurlyeq,$ and have the property that $\varphi(x)\neq \varphi(y)$ whenever $\{x,y\}\in E.$ We prove a number-theoretic result about this function, and use it in section 7 to recover a ring-theoretic identity of G. P. Hochschild.   In section 2 we generalize a result of R. Stanley on the sign-imbalance of posets in which the lengths of all maximal chains have the same parity.   In sections 3-6 we study the linearization-count and sign-imbalance of a lexicographic sum of $n$ finite posets $P_i$ $(1\leq i\leq n)$ over an $n$-element poset $P_0.$ We note how to compute these values from the corresponding counts for the given posets $P_i,$ and for a lexicographic sum over $P_0$ of chains of lengths $\mathrm{card}(P_i).$ This makes the behavior of lexicographic sums of chains over a finite poset $P_0$ of interest, and we obtain some general results on the linearization-count and sign-imbalance of these objects.
Emergent electromagnetic induction based on electrodynamics of noncollinear spin states may enable dramatic miniaturization of inductor elements widely used in electric circuits, yet many issues are to be solved toward application. One such problem is how to increase working temperature. We report the large emergent electromagnetic induction achieved around and above room temperature based on short-period ($\leq$ 3 nm) spin-spiral states of a metallic helimagnet ${\rm YMn}_{6}{\rm Sn}_{6}$. The observed inductance value $L$ and its sign are observed to vary to a large extent, depending not only on the spin helix structure controlled by temperature and magnetic field but also on the current density. The present finding on room-temperature operation and possible sign control of $L$ may provide a new step toward realizing microscale quantum inductors.
Magnetic tunnel junctions with crystalline MgO tunnel barrier and amorphous CoFeB electrodes received much attention due to their high tunnel magneto resistance ratio at room temperature. One important parameter for achieving high tunnel magneto resistance ratios is to control the boron diffusion from the electrodes especially during post growth annealing. By high resolution transmission electron microscopy and electron energy loss spectroscopy techniques we show that the cap layer material adjacent to the electrodes and the MgO deposition method are crucial to control boron redistribution. It is pointed out, that Ta cap layers acts as sinks for boron during annealing in contrast to Ru layers. Furthermore, radio frequency sputtered MgO tunneling barriers contain a rather high concentraion of boron in trigonal [BO$_3$]$^{3-}$ - environment after annealing in contrast to electron beam evaporated MgO which is virtually free from any boron. Our data further indicate that neither boron nor oxygen-vacancy-related gap states in the bulk of MgO barriers affect spin polarized transport for tunnel magneto resistance ratios at the level of 200%.
We investigated the optical light curve of T Pyx during its 2011 outburst through compiling a database of SMEI and AAVSO observations. The SMEI light curve, providing unprecedented detail with high cadence data during t=1.5-49 days post-discovery, was divided into four phases based on the idealised nova optical light curve; the initial rise, the pre-maximum halt (or the 'plateau'), the final rise, and the early decline. Variation in the SMEI light curve reveals a strongly detected period of 1.44\pm0.04 days before the visual maximum. The spectra from the LT and SMARTS telescopes were investigated during t=0.8-80.7 and 155.1-249.9 days. The nova was observed very early in its rise and a distinct high velocity ejection phase was evident. A marked drop and then gradual increase in derived ejection velocities were present. Here we propose two different stages of mass loss, a short-lived phase occurring immediately after outburst followed by a more steadily evolving and higher mass loss phase. The overall spectral development follows that typical of a Classical Nova and comparison to the photometric behaviour reveals consistencies with the simple evolving pseudo-photosphere model of the nova outburst. The optical spectra are also compared to X-ray and radio light curves. Weak [Fe X] 6375A emission was marginally detected before the rise in X-ray emission. The middle of the plateau in the X-ray light curve is coincident with the appearance of high ionization species detected in optical spectra and the peak of the high frequency radio flux.
We consider the stochastic continuity equation perturbed by a fractional Brownian motion and the drift is allowed to be discontinuous. We show that for almost all paths of the fractional Brownian motion there exists a solution to the equation.
The ESO Public Kilo-Degree Survey (KiDS) is an optical wide-field imaging survey carried out with the VLT Survey Telescope and the OmegaCAM camera. KiDS will scan 1500 square degrees in four optical filters (u, g, r, i). Designed to be a weak lensing survey, it is ideal for galaxy evolution studies, thanks to the high spatial resolution of VST, the good seeing and the photometric depth. The surface photometry have provided with structural parameters (e.g. size and S\'ersic index), aperture and total magnitudes have been used to derive photometric redshifts from Machine learning methods and stellar masses/luminositites from stellar population synthesis. Our project aimed at investigating the evolution of the colour and structural properties of galaxies with mass and environment up to redshift $z \sim 0.5$ and more, to put constraints on galaxy evolution processes, as galaxy mergers.
A quantitative investigation of spin-pumping-induced spin-transport in n-GaAs was conducted at room temperature (RT). GaAs has a non-negligible spin orbit interaction, so that electromotive force due to the inverse spin Hall effect (ISHE) of GaAs contributed to the electromotive force detected with a platinum (Pt) spin detector. The electromotive force detected by the Pt spin detector had opposite polarity to that measured with a Ni80Fe20/GaAs bilayer due to the opposite direction of spin current flow, which demonstrates successful spin transport in the n-GaAs channel. A two-dimensional spin-diffusion model that considers the ISHE in the n-GaAs channel reveals an accurate spin diffusion length of t_s = 1.09 um in n-GaAs (NSi = 4x10^16 cm-3) at RT, which is approximately half that estimated by the conventional model.
We review a new iterative procedure to solve the low-lying states of the Schroedinger equation, done in collaboration with Richard Friedberg. For the groundstate energy, the $n^{th}$ order iterative energy is bounded by a finite limit, independent of $n$; thereby it avoids some of the inherent difficulties faced by the usual perturbative series expansions. For a fairly large class of problems, this new procedure can be proved to give convergent iterative solutions. These convergent solutions include the long standing difficult problem of a quartic potential with either symmetric or asymmetric minima.