ShantanuT01/DACTYL-Pretraining huggingface dataset:
This work brings techniques from the theory of recurrent integer sequences to the problem of balancedness of symmetric Boolean functions. In particular, the periodicity modulo $p$ ($p$ odd prime) of exponential sums of symmetric Boolean functions is considered. Periods modulo $p$, bounds for periods and relations between them are obtained for these exponential sums. The concept of avoiding primes is also introduced. This concept and the bounds presented in this work are used to show that some classes of symmetric Boolean functions are not balanced. In particular, every elementary symmetric Boolean function of degree not a power of 2 and less than 2048 is not balanced. For instance, the elementary symmetric Boolean function in $n$ variables of degree $1292$ is not balanced because the prime $p = 176129$ does not divide its exponential sum for any positive integer $n$. It is showed that for some symmetric Boolean functions, the set of primes avoided by the sequence of exponential sums contains a subset that has positive density within the set of primes. Finally, in the last section, a brief study for the set of primes that divide some term of the sequence of exponential sums is presented.
We cross-correlate galaxy weak lensing measurements from the Dark Energy Survey (DES) year-one (Y1) data with a cosmic microwave background (CMB) weak lensing map derived from South Pole Telescope (SPT) and Planck data, with an effective overlapping area of 1289 deg$^{2}$. With the combined measurements from four source galaxy redshift bins, we reject the hypothesis of no lensing with a significance of $10.8\sigma$. When employing angular scale cuts, this significance is reduced to $6.8\sigma$, which remains the highest signal-to-noise measurement of its kind to date. We fit the amplitude of the correlation functions while fixing the cosmological parameters to a fiducial $\Lambda$CDM model, finding $A = 0.99 \pm 0.17$. We additionally use the correlation function measurements to constrain shear calibration bias, obtaining constraints that are consistent with previous DES analyses. Finally, when performing a cosmological analysis under the $\Lambda$CDM model, we obtain the marginalized constraints of $\Omega_{\rm m}=0.261^{+0.070}_{-0.051}$ and $S_{8}\equiv \sigma_{8}\sqrt{\Omega_{\rm m}/0.3} = 0.660^{+0.085}_{-0.100}$. These measurements are used in a companion work that presents cosmological constraints from the joint analysis of two-point functions among galaxies, galaxy shears, and CMB lensing using DES, SPT and Planck data.
Consider (independent) first-passage percolation on the sites of the triangular lattice $\mathbb{T}$. Denote the passage time of the site $v$ in $\mathbb{T}$ by $t(v)$, and assume that $P(t(v)=0)=P(t(v)=1)=1/2$. Denote by $b_{0,n}$ the passage time from 0 to the halfplane $\{v\in\mathbb{T}:\mbox{Re}(v)\geq n\}$, and by $T(0,nu)$ the passage time from 0 to the nearest site to $nu$, where $|u|=1$. We prove that as $n\rightarrow\infty$, $b_{0,n}/\log n\rightarrow 1/(2\sqrt{3}\pi)$ a.s., $E[b_{0,n}]/\log n\rightarrow 1/(2\sqrt{3}\pi)$ and Var$[b_{0,n}]/\log n\rightarrow 2/(3\sqrt{3}\pi)-1/(2\pi^2)$; $T(0,nu)/\log n\rightarrow 1/(\sqrt{3}\pi)$ in probability but not a.s., $E[T(0,nu)]/\log n\rightarrow 1/(\sqrt{3}\pi)$ and Var$[T(0,nu)]/\log n\rightarrow 4/(3\sqrt{3}\pi)-1/\pi^2$. This answers a question of Kesten and Zhang (1997) and improves our previous work (2014). From this result, we derive an explicit form of the central limit theorem for $b_{0,n}$ and $T(0,nu)$. A key ingredient for the proof is the moment generating function of the conformal radii for conformal loop ensemble CLE$_6$, given by Schramm, Sheffield and Wilson (2009).
Spin-polarized transport through a marginal Fermi liquid (MFL) which is connected to two noncollinear ferromagnets via tunnel junctions is discussed in terms of the nonequilibrium Green function approach. It is found that the current-voltage characteristics deviate obviously from the ohmic behavior, and the tunnel current increases slightly with temperature, in contrast to those of the system with a Fermi liquid. The tunnel magnetoresistance (TMR) is observed to decay exponentially with increasing the bias voltage, and to decrease slowly with increasing temperature. With increasing the coupling constant of the MFL, the current is shown to increase linearly, while the TMR is found to decay slowly. The spin-valve effect is observed.
While in standard photoacoustic imaging the propagation of sound waves is modeled by the standard wave equation, our approach is based on a generalized wave equation with variable sound speed and material density, respectively. In this paper we present an approach for photoacoustic imaging, which in addition to recovering of the absorption density parameter, the imaging parameter of standard photoacoustics, also allows to reconstruct the spatially varying sound speed and density, respectively, of the medium. We provide analytical reconstruction formulas for all three parameters based in a linearized model based on single plane illumination microscopy (SPIM) techniques.
Recently, three new states of $\Xi_c^0$ were observed in the invariant mass spectrum of $\Lambda^+_cK^-$ by LHCb collaboration. In this work, we use a chiral quark model to investigate these three exited states with the help of Gaussian expansion method both in three-quark structure and in five-quark structure with all possible quantum numbers $IJ^P=\frac{1}{2}(\frac{1}{2})^-$, $\frac{1}{2}(\frac{3}{2})^-$, $\frac{1}{2}(\frac{5}{2})^-$, $\frac{3}{2}(\frac{1}{2})^-$, $\frac{3}{2}(\frac{3}{2})^-$ and $\frac{3}{2}(\frac{5}{2})^-$ . The calculations shows that the 2$S$ states of $\Xi_c'(2579)^0$ and $\Xi_c(2645)^0$ are comparable to experimental results; In addition, the resonance states of five-quark configuration are possible candidates of these new states with negative parity by using the real scaling method and their decay width are also given.
Using a combination of scanning tunneling spectroscopy and atomic lateral manipulation, we obtained a systematic variation of the Kondo temperature ($T_\mathrm K$) of Co atoms on Ag(111) as a function of the surface state contribution to the total density of states at the atom adsorption site ($\rho_s$). By sampling the $T_\mathrm K$ of a Co atom on positions where $\rho_s$ was spatially resolved beforehand, we obtain a nearly linear relationship between both magnitudes. We interpret the data on the basis of an Anderson model including orbital and spin degrees of freedom (SU(4)) in good agreement with the experimental findings. The fact that the onset of the surface band is near the Fermi level is crucial to lead to the observed linear behavior. In the light of this model, the quantitative analysis of the experimental data evidences that at least a quarter of the coupling of Co impurities with extended states takes place through the hybridization to surface states. This result is of fundamental relevance in the understanding of Kondo screening of magnetic impurities on noble metal surfaces, where bulk and surface electronic states coexist.
Recent formal classifications of crystalline topological insulators predict that the combination of time-reversal and rotational symmetry gives rise to topological invariants beyond the ones known for other lattice symmetries. Although the classification proves their existence, it does not indicate a way of calculating the values of those invariants. Here, we show that a specific set of concentric Wilson loops and line invariants yields the values of all topological invariants in two-dimensional systems with pure rotation symmetry in class AII. Examples of this analysis are given for specific models with two-fold and three-fold rotational symmetry. We find new invariants that relate to the presence of higher-order topology and corner charges.
The field of chemical evolution modeling of the Galaxy is experiencing in the last years a phase of high activity and important achievements. There are, however, several open questions which still need to be answered. In this review I summarize what have been the most important achievements and what are some of the most urgent questions to be answered.
The main step in numerical evaluation of classical Sl2 (Z) modular forms and elliptic functions is to compute the sum of the first N nonzero terms in the sparse q-series belonging to the Dedekind eta function or the Jacobi theta constants. We construct short addition sequences to perform this task using N + o(N) multiplications. Our constructions rely on the representability of specific quadratic progressions of integers as sums of smaller numbers of the same kind. For example, we show that every generalised pentagonal number c 5 can be written as c = 2a + b where a, b are smaller generalised pentagonal numbers. We also give a baby-step giant-step algorithm that uses O(N/ log r N) multiplications for any r > 0, beating the lower bound of N multiplications required when computing the terms explicitly. These results lead to speed-ups in practice.
The electronic and magnetic properties of Sr$_2$CoO$_4$ compound have been studied using $\emph{ab initio}$ electronic structure calculations. As opposed to GGA calculation, which gives ferromagnetic metallic solution, GGA+$U$ calculations provide two kind of ferromagnetic solutions: (i) half-metallic and (ii) metallic. The half-metallic solution is a ground state of the system and the metallic one is a metastable state. The strong hybridization between Co 3$d$ and O 2$p$ orbitals decides the electronic and magnetic properties of the compound. The total magnetic moment per formula unit is found to be $\sim$ 3 $\mu_B$ ($S$ = 3/2). Our calculations give the magnetocrystalline anisotropy energy of $\sim$ 2.7 meV, which provides a good description of experimentally observed large magnetocrystalline anisotropy. The Heisenberg exchange parameters up to fourth nearest neighbours are also calculated. The mean-field theory gives the $T_C$ = 887 K. The possible physical implications of the ferromagnetic half-metallic ground state are also discussed.
We study the algebraic geometrical background of the Penner--Kontsevich matrix model with the potential $N\alpha \tr {\bigl(- \fr 12 \L X\L X +\log (1-X)+X\bigr)}$. We show that this model describes intersection indices of linear bundles on the discretized moduli space right in the same fashion as the Kontsevich model is related to intersection indices (cohomological classes) on the Riemann surfaces of arbitrary genera. The special role of the logarithmic potential originated from the Penner matrix model is demonstrated. The boundary effects which was unessential in the case of the Kontsevich model are now relevant, and intersection indices on the discretized moduli space of genus $g$ are expressed through Kontsevich's indices of the genus $g$ and of the lower genera.
The computation of long range linear self-interaction forces in string and higher dimensional brane models requires the evaluation of the gradients of regularised values of divergent self-interaction potentials. It is shown that the appropriately regularised gradient in directions orthogonal to the brane surface will always be obtainable simply by multiplying the regularised potential components by just half the trace of the second fundamental tensor, except in the hypermembrane case for which the method fails. Whatever the dimension of the background this result is valid provided the codimension is two (the hyperstring case) or more, so it can be used for investigating brane-world scenarios with more than one extra space dimension.
Let $\Gamma$ be a simple connect graph on a finite vertex set $V$ and let $A$ be its adjacency matrix. Then $\Gamma$ is said to be \textit{singular} if and only if $0$ is an eigenvalue of $A.$ The \textit{nullity (singularity)} of $\Gamma,$ denoted by ${\rm null}(\Gamma),$ is the \textit{algebraic multiplicity} of the eigenvalue $0$ in the spectrum of $\Gamma.$ The general problem of characterising singular graphs is easy to state but it seems too difficult in this time. In this work, we investigate this problem for finite graphs on which the dihedral group $D_n$ acts vertex transitively as group of automorphisms. We determine the nullity of such graphs. We show that Cayley graphs over dihedral groups $D_{p^s} $ is non-singular if $|H \cap C_{p^s}|\neq |H \cap C_{p^s}b|$ and $|H|<p$ where $p$ is a prime number and $s \in \mathbb{N}.$
The comparison principle and the existence of the solution of the integro-differential equation with L{\'e}vy operators, in the framework of the viscosity solution, are shown in this paper. For the one dimensional case, a detailed estimate of the H{\"o}lder continuity of solutions is presented, by localizing the singularity of the L{\'e}vy measure.
We argue that given the experimental constraints on the Higgs mass the least fine tuned parameter space of minimal supersymmetric standard model is with negative stop masses squared at the grand unification scale. While stop mass squared is typically driven to positive values at the weak scale, the contribution to the Higgs mass squared parameter from the running can be arbitrarily small, which reduces fine tuning of electroweak symmetry breaking. At the same time the stop mixing is necessarily enhanced and the maximal mixing scenario for the Higgs mass can be generated radiatively even when starting with negligible mixing at the unification scale. This highly alleviates constraints on possible models for supersymmetry breaking in which fine tuning is absent.
We report on negative thermal expansion (NTE) in the high-field, half-magnetization plateau phase of the frustrated magnetic insulator CdCr2O4. Using dilatometry, we precisely map the phase diagram at fields of up to 30T, and identify a strong NTE associated with the collinear half-magnetization plateau for B > 27T. The resulting phase diagram is compared with a microscopic theory for spin-lattice coupling, and the origin of the NTE is identified as a large negative change in magnetization with temperature, coming from a nearly-localised band of spin excitations in the plateau phase. These results provide useful guidelines for the discovery of new NTE materials.
Using a new algorithm for estimating the actions of orbits a parametrised distribution function is automatically fitted to observational data for the solar neighbourhood. We adopt a gravitational potential that is generated by three discs (gas and both thin and thick stellar discs), a bulge and a dark halo, and fit the thin-disc component of the distribution function to the solar-neighbourhood velocity distribution from the Geneva-Copenhagen Survey. We find that the disc's vertical density profile is in good agreement with data at z<~500 pc. The thick-disc component of the distribution function is then used to extend the fit to data from Gilmore & Reid (1983) for z<~2.5 kpc. The resulting model predicts excellent fits to the profile of the vertical velocity dispersion \sigma_z(z) from the RAVE survey and to the distribution of v_\phi velocity components at |z|~1kpc from the SDSS survey. The ability of this model to predict successfully data that was not used in the fitting process suggests that the adopted gravitational potential (which is close to a maximum-disc potential) is close to the true one. We show that if another plausible potential is used, the predicted values of \sigma_z are too large. The models imply that in contrast to the thin disc, the thick disc has to be hotter vertically than radially, a prediction that it will be possible to test in the near future. When the model parameters are adjusted in an unconstrained manner, there is a tendency to produce models that predict unexpected radial variations in quantities such as scale height. This finding suggests that to constrain these models adequately one needs data that extends significantly beyond the solar cylinder. The models presented in this paper might prove useful to the interpretation of data for external galaxies that has been taken with an integral field unit.
Pierre Auger collaboration have recently put forward the hypothesis that the arrival directions of the highest energy cosmic rays correlate with the subset of local active galactic nuclei (AGN). We perform a blind test of AGN hypothesis using publicly available event sets collected by Yakutsk, AGASA and HiRes experiments. The consistency of the procedure requires the event energies to be normalized towards the common energy scale. The number of correlating events in resulting data-set is 3 of 21 which is consistent with expected random background.
Distance determinations of extremely-low-surface-brightness galaxies are expensive in terms of spectroscopic time. Because of this, their distances are often inferred by associating such galaxies with larger structures such as groups or clusters, leading to a systematic bias by selecting objects in high density environments. Here we report the discovery of a red ultra-diffuse galaxy (S82-DG-1: $r_{\mathrm{eff}}$ = 1.6 kpc; $<\mu _{g}>$ = 25.7 mag arcsec$^{-2}$; $g-i$ = 0.78 mag) located in a nearby cosmic void. We used multi-band luminosity functions of its globular clusters to obtain the distance to S82-DG-1, at 28.7$_{-3.6}^{+4.2}$ Mpc. Follow-up deep spectroscopy with the GTC telescope yields a redshift of 3353 $\pm$ 29 km s$^{-1}$, making its association with the NGC 1211 galaxy (one of the most isolated galaxies known) highly likely. Both galaxies have compatible distances and redshifts, share a high peculiar velocity ($\sim$1000 km s$^{-1}$) and lie within a void of radius 7 Mpc. The local surface density is $\Sigma_5 \sim 0.06$ Mpc$^{-2}$, an order of magnitude smaller than the field population and similar to the voids found in the GAMA survey. Our work shows: i) The high potential of using optical ground-based photometry of associated globular clusters to explore distances to ultra-diffuse galaxies and ii) the presence of red ultra-diffuse galaxies even in the most sparse environments, suggesting a wide range of formation mechanisms.
Several observed spectral properties of quasars are believed to be influenced by quasar orientation. In this investigation we examine the effect of orientation on the Mg II line located at 2798 {\AA} in a sample of 36 radio-loud quasars, with orientation angles having been obtained in a previous study using radio observations. We find no significant relationship between orientation angle and either Mg II line full-width at half-maximum or equivalent width. The lack of correlation with inclination angle contradicts previous studies which also use radio data as a proxy for inclination angle and suggests the Mg II emission region does not occupy a disk-like geometry. The lack of correlation with Mg II equivalent width, however, is reported in at least one previous study. Although the significance is not very strong (86 percent), there is a possible negative relationship between inclination angle and Fe II strength which, if true, could explain the Fe II anti-correlation with [O III ] strength associated with Eigenvector 1. Interestingly, there are objects having almost edge-on inclinations while still exhibiting broad lines. This could be explained by a torus which is either clumpy (allowing sight lines to the central engine) or mis-aligned with the accretion disk.
Few-shot object detection aims to detect instances of specific categories in a query image with only a handful of support samples. Although this takes less effort than obtaining enough annotated images for supervised object detection, it results in a far inferior performance compared to the conventional object detection methods. In this paper, we propose a meta-learning-based approach that considers the unique characteristics of each support sample. Rather than simply averaging the information of the support samples to generate a single prototype per category, our method can better utilize the information of each support sample by treating each support sample as an individual prototype. Specifically, we introduce two types of attention mechanisms for aggregating the query and support feature maps. The first is to refine the information of few-shot samples by extracting shared information between the support samples through attention. Second, each support sample is used as a class code to leverage the information by comparing similarities between each support feature and query features. Our proposed method is complementary to the previous methods, making it easy to plug and play for further improvement. We have evaluated our method on PASCAL VOC and COCO benchmarks, and the results verify the effectiveness of our method. In particular, the advantages of our method are maximized when there is more diversity among support data.
We report on unusually very hard spectral states in three confirmed neutron-star low-mass X-ray binaries (1RXS J180408.9-342058, EXO 1745-248, and IGR J18245-2452) at a luminosity between ~ 10^{36-37} erg s^{-1}. When fitting the Swift X-ray spectra (0.5 - 10 keV) in those states with an absorbed power-law model, we found photon indices of \Gamma ~ 1, significantly lower than the \Gamma = 1.5 - 2.0 typically seen when such systems are in their so called hard state. For individual sources very hard spectra were already previously identified but here we show for the first time that likely our sources were in a distinct spectral state (i.e., different from the hard state) when they exhibited such very hard spectra. It is unclear how such very hard spectra can be formed; if the emission mechanism is similar to that operating in their hard states (i.e., up-scattering of soft photons due to hot electrons) then the electrons should have higher temperatures or a higher optical depth in the very hard state compared to those observed in the hard state. By using our obtained \Gamma as a tracer for the spectral evolution with luminosity, we have compared our results with those obtained by Wijnands et al. (2015). We confirm their general results in that also our sample of sources follow the same track as the other neutron star systems, although we do not find that the accreting millisecond pulsars are systematically harder than the non-pulsating systems.
We investigate differential systems occurring in the study of particular non-isolated singularities, the so-called linear free divisors. We obtain a duality theorem for these D-modules taking into account filtrations, and deduce degeneration properties of certain Frobenius manifolds associated to linear sections of the Milnor fibres of the divisor.
We have used the unique low frequency sensitivity of the Large Phased Array radio telescope of Pushchino Radio Astronomy Observatory to collect dataset of the single pulse observations of second period pulsars of the Northern hemisphere. During observational sessions of 2011 - 2017 yrs. We have collected data on 71 pulsars at 111 MHz frequency using digital pulsar receiver. We have discovered Giant Radio Pulses (GRP) from pulsars B0301+09 and B1237+25, and confirmed early reported generation of anomalously strong (probable giant) pulses from B1133+16 on statistically significant dataset. Data for these pulsars and from B0950+08, B1112+50, early reported as pulsars generating GRPs were analyzed to evaluate their behavior on long time intervals. It was found that statistical criterion (power-law spectrum of GRPs distribution on energy and peak flux density) seems not to be strict for pulsars with the low magnetic field on light cylinder. Moreover, spectra of some of these pulsars demonstrate unstable behavior with the time and have complex multicomponent shape. In the dataset of B0950+08 we have detected strongest GRP from pulsars with the low magnetic field on light cylinder ever reported having the peak flux density as strong as 16.8 kJy.