ShantanuT01/DACTYL-Pretraining huggingface dataset:
In the 1995 paper entitled "Noncommutative symmetric functions," Gelfand, et. al. defined two noncommutative symmetric function analogues for the power sum basis of the symmetric functions, along with analogues for the elementary and the homogeneous bases. They did not consider the noncommutative symmetric power sum duals in the quasisymmetric functions, which have since been explored only in passing by Derksen and Malvenuto-Reutenauer. These two distinct quasisymmetric power sum bases are the topic of this paper. In contrast to the simplicity of the symmetric power sums, or the other well known bases of the quasisymmetric functions, the quasisymmetric power sums have a more complex combinatorial description. As a result, although symmetric function proofs often translate directly to quasisymmetric analogues, this is not the case for quasisymmetric power sums. Neither is there a model for working with the quasisymmetric power sums in the work of Gelfand, et. al., which relies heavily on quasi-determinants (which can only be exploited by duality for our purposes) and is not particularly combinatorial in nature. This paper therefore offers a first glimpse at working with these two relatively unstudied quasisymmetric bases, avoiding duality where possible to encourage a previously unexplored combinatorial understanding.
In his work on modularity theorems, Wiles proved a numerical criterion for a map of rings $R\to T$ to be an isomorphism of complete intersections. He used this to show that certain deformation rings and Hecke algebras associated to a mod $p$ Galois representation at non-minimal level were isomorphic and complete intersections, provided the same was true at minimal level.   In this paper we study Hecke algebras acting on cohomology of Shimura curves arising from maximal orders in indefinite quaternion algebras over the rationals localized at a semistable irreducible mod $p$ Galois representation $\overline \rho$. If $\overline \rho$ is scalar at some primes dividing the discriminant of the quaternion algebra, then Hecke algebra is still isomorphic to the deformation ring, but is not a complete intersection, or even Gorenstein, so the Wiles numerical criterion cannot apply.   We consider a weight 2 newform $f$ which contributes to the cohomology of the Shimura curve and gives rise to an augmentation $\lambda_f$ of the Hecke algebra. We quantify the failure of the Wiles numerical criterion at $\lambda_f$ by computing the associated {\it Wiles defect} purely in terms of the local behavior at primes dividing the discriminant of the global Galois representation $\rho_f$ which $f$ gives rise to by the Eichler--Shimura construction. One of the main tools used in the proof is Taylor--Wiles--Kisin patching.
We present a method to create and erase spatially resolved doping profiles in graphene-hexagonal boron nitride (hBN) heterostructures. The technique is based on photo-induced doping by a focused laser and does neither require masks nor photo resists. This makes our technique interesting for rapid prototyping of unconventional electronic device schemes, where the spatial resolution of the rewritable, long-term stable doping profiles is only limited by the laser spot size (~600 nm) and the accuracy of sample positioning. Our optical doping method offers a way to implement and to test different, complex doping patterns in one and the very same graphene device, which is not achievable with conventional gating techniques.
The Lov\'asz Local Lemma is a seminal result in probabilistic combinatorics. It gives a sufficient condition on a probability space and a collection of events for the existence of an outcome that simultaneously avoids all of those events. Over the years, more general conditions have been discovered under which the conclusion of the lemma continues to hold. In this note we provide short proofs of two of those more general results: Shearer's lemma and the cluster expansion lemma, in their "lopsided" form. We conclude by using the cluster expansion lemma to prove that the symmetric form of the local lemma holds with probabilities bounded by $1/ed$, rather than the bound $1/e(d+1)$ required by the traditional proofs.
To estimate the parameters of the Galactic spiral structure - namely, the pitch angle i and the number of spiral arms,- data on Galactic masers with known trigonometric parallaxes were used. We applied the well-known method based on analysis of the "position angle - distance logarithm" diagram. Estimates of the pitch angle i obtained from four segments of different arms belonging to the global Galactic structure are self-consistent and close to i=-13+/-1 degrees. The segment which is most interesting is that of the Outer arm. It contains only three masers. Hence, in order to obtain correct estimates, we also used the data on 12 very young star clusters with distances determined by Camargo et al. from infrared photometry. The estimates obtained allow us to conclude in favor of the four-armed model of the Galactic spiral structure.
In this talk I report my recent study on the shear viscosity of neutron-rich nuclear matter from a relaxation time approach. An isospin- and momentum-dependent interaction is used in the study. Effects of density, temperature, and isospin asymmetry of nuclear matter on its shear viscosity have been discussed. Similar to the symmetry energy, the symmetry shear viscosity is defined and its density and temperature dependence are studied.
We investigate the Lagrangian perturbation theory of a homogeneous and isotropic universe in the non-relativistic limit, and derive the solutions up to the fourth order. These solutions are needed for example for the next-to-leading order correction of the (resummed) Lagrangian matter bispectrum, which we study in an accompanying paper. We focus on flat cosmologies with a vanishing cosmological constant, and provide an in-depth description of two complementary approaches used in the current literature. Both approaches are solved with two different sets of initial conditions---both appropriate for modelling the large-scale structure. Afterwards we consider only the fastest growing mode solution, which is not affected by either of these choices of initial conditions. Under the reasonable approximation that the linear density contrast is evaluated at the initial Lagrangian position of the fluid particle, we obtain the nth-order displacement field in the so-called initial position limit: the nth order displacement field consists of 3(n-1) integrals over n linear density contrasts, and obeys self-similarity. Then, we find exact relations between the series in Lagrangian and Eulerian perturbation theory, leading to identical predictions for the density contrast and the peculiar-velocity divergence up to the fourth order.
We develop a general condition on the cost function which is sufficient to imply Monge solution and uniqueness results in the multi-marginal optimal transport problem. This result unifies and generalizes several results in the rather fragmented literature on multi-marginal problems. We also provide a systematic way to generate new examples from old ones.
Electron transmission through semiconductor superlattices is studied with transfer matrix method and resonance theory. The formation of electron band-pass transmission is ascribed to the coupling of different modes in those semiconductor superlattices with the symmetric unit cell. Upon Fabry-P\'erot resonance condition, Bloch modes and two other resonant modes are identified to be related to the nature of the superlattice and its unit cell, respectively. The bands related to the unit cell and the superlattice overlap spontaneously in the tunneling region due to the shared wells, and the coupling of perfectly resonances results in the band-pass tunneling. Our findings provide a promising way to study electronic systems with more complicated superlattices or even optical systems with photonic crystals.
We present the luminosity function and color-redshift relation of a magnitude-limited sample of 145 mostly red field E/S0 galaxies at z < 1 from the DEEP Groth Strip Survey (GSS). Most of the E/S0s (86%) form a red envelope in the redshift-color diagram, consistent with predictions of spectral synthesis models in which the dominant stellar population is formed at redshifts z > 1.5. Constructing a luminosity function of the full sample of   145 E/S0s, we find that there is about 1.1--1.9 magnitude brightening in rest-frame B band luminosity back to z = 0.8 from z=0, consistent with other studies.   Together with the red colors, this brightening favors models in which the bulk of stars in red field E/S0s formed before z_{for} > 1.5 and have been evolving rather quiescently with few large starbursts since then.   Evolution in the number density of field E/S0 galaxies is harder to measure, and uncertainties in the raw counts and their ratio to local samples might amount to as much as a factor of two.   Within that uncertainty, the number density of red E/S0s to z = 0.8 seems relatively static, being comparable to or perhaps moderately less than that of local E/S0s depending on the assumed cosmology. A doubling of E/S0 number density since z = 1 can be ruled out with high confidence (97%) if \Omega_{m}=1.   Taken together, our results are consistent with the hypothesis that the majority of luminous field E/S0s were already in place by z = 1, that the bulk of their stars were already fairly old, and that their number density has not changed by large amounts since then.
The acceleration of energetic particle transport in high amplitude magnetosonic and Alfvenic turbulence is considered using the method of Monte Carlo particle simulations, involving integration of particle equations of motion. We derive the momentum diffusion coefficient in the presence of anisotropic turbulent wave in the high-magnetized plasma, for a flat and Kolmogorov-type turbulence spectrum. We confirm the quasilinear result (Shlickeiser & Miller (1997) of enhanced values of the momentum diffusion coefficient due to transit-time resonance interaction in the presence of isotropic fast-mode waves as compared to the case of slab Alfvenic waves of the same amplitude. The relation of the momentum diffusion coefficient to the turbulence amplitude and anisotropy is investigated.
We consider divisorial filtration on the rings of functions on hypersurface singularities associated with Newton diagrams and their analogues for plane curve singularities. We compute the multi-variable Poincar\'e series for the latter ones.
We present a novel approach to template matching that is efficient, can handle partial occlusions, and comes with provable performance guarantees. A key component of the method is a reduction that transforms the problem of searching a nearest neighbor among $N$ high-dimensional vectors, to searching neighbors among two sets of order $\sqrt{N}$ vectors, which can be found efficiently using range search techniques. This allows for a quadratic improvement in search complexity, and makes the method scalable in handling large search spaces. The second contribution is a hashing scheme based on consensus set maximization, which allows us to handle occlusions. The resulting scheme can be seen as a randomized hypothesize-and-test algorithm, which is equipped with guarantees regarding the number of iterations required for obtaining an optimal solution with high probability. The predicted matching rates are validated empirically and the algorithm shows a significant improvement over the state-of-the-art in both speed and robustness to occlusions.
In this paper we propose a real-time and robust solution to large-scale multiple rotation averaging. Until recently, Multiple rotation averaging problem had been solved using conventional iterative optimization algorithms. Such methods employed robust cost functions that were chosen based on assumptions made about the sensor noise and outlier distribution. In practice, these assumptions do not always fit real datasets very well. A recent work showed that the noise distribution could be learnt using a graph neural network. This solution required a second network for outlier detection and removal as the averaging network was sensitive to a poor initialization. In this paper we propose a single-stage graph neural network that can robustly perform rotation averaging in the presence of noise and outliers. Our method uses all observations, suppressing outliers effects through the use of weighted averaging and an attention mechanism within the network design. The result is a network that is faster, more robust and can be trained with less samples than the previous neural approach, ultimately outperforming conventional iterative algorithms in accuracy and in inference times.
In a telescoped double-walled nanotube (TDWNT), with the inner tube partially extracted from the outer tube, the total current is forced to flow between the layers. Considering the interlayer Hamiltonian as a perturbation, we can obtain an analytic formula for the interlayer conductance. The accuracy of the perturbation formula is systematically improved by including higher-order terms. The interlayer interaction effective in the perturbation formula is the product of the interlayer Hamiltonian and the wave function. It clarifies the effects of the spatial range of the interlayer Hamiltonian and the band energy shift.
Projection tends to skew the mass-observable relation of galaxy clusters by creating a small fraction of severely blended systems, those for which the measured observable property of a cluster is strongly boosted relative to the value of its primary host halo. We examine the bias in cosmological parameter estimates caused by incorrectly assuming a Gaussian (projection-free) mass-observable relation when the true relation is non-Gaussian due to projection. We introduce a mixture model for projection and explore Fisher forecasts for a survey of 5000 sq. deg. to z=1.1 and an equivalent mass threshold of 10^13.7 h^-1 solar masses. Using a blended fraction motivated by optical cluster finding applied to the Millennium Simulation and applying Planck and otherwise weak priors, we find that the biases in Omega_DE and w are significant, being factors of 2.8 and 2.4, respectively, times previous forecast uncertainties. Incorporating eight new degrees of freedom to describe cluster selection with projection increases the forecast uncertainty in Omega_DE and w by similar factors. Knowledge of these additional parameters at the 5% level limits degradation in dark energy constraints to <10% relative to projection-free forecasts. We discuss strategies for using simulations and complementary observations to characterize the fraction of blended clusters and their mass selection properties.
In this paper, we give an explicit bound for the height of integral points on $X_0(p)$ by using a very explicit version of the Chevalley-Weil principle. We improve the bound given by Sha in \cite{sha2014bounding1}.
By analogy with Carleson's observation on Cardy's formula describing crossing probabilities for the scaling limit of critical percolation, we exhibit ``privileged geometries'' for Stochastic Loewner Evolutions with various parameters, for which certain hitting distributions are uniformly distributed. Consequences for limiting probabilities of events concerning various critical plane discrete models are then examined.
In this paper we investigate supersymmetric effects to the threshold production cross section of top quark pairs in electron positron annihilation. In particular, we consider the complete one-loop corrections from the strong and weak sector of the Minimal Supersymmetric Standard Model.
We study time-inhomogeneous Markov chains with finite state spaces using Nash and logarithmic-Sobolev inequalities, and the notion of $c$-stability. We develop the basic theory of such functional inequalities in the time-inhomogeneous context and provide illustrating examples.
We present two initial profiles to the Camassa-Holm equation which yield solutions with accumulating breaking times.
We present a systematic survey of multiple velocity-resolved H$_2$O spectra using Herschel/HIFI towards nine nearby actively star forming galaxies. The ground-state and low-excitation lines (E$_{\rm up}\,\le 130\,{\rm K}$) show profiles with emission and absorption blended together, while absorption-free medium-excitation lines ($130\,{\rm K}\, \le\, E_{\rm up}\,\le\,350\,{\rm K}$) typically display line shapes similar to CO. We analyze the HIFI observation together with archival SPIRE/PACS H$_2$O data using a state-of-the-art 3D radiative transfer code which includes the interaction between continuum and line emission. The water excitation models are combined with information on the dust- and CO spectral line energy distribution to determine the physical structure of the interstellar medium (ISM). We identify two ISM components that are common to all galaxies: A warm ($T_{\rm dust}\,\sim\,40-70\,{\rm K}$), dense ($n({\rm H})\,\sim\,10^5-10^6\,{\rm cm^{-3}}$) phase which dominates the emission of medium-excitation H$_2$O lines. This gas phase also dominates the FIR emission and the CO intensities for $J_{\rm up} > 8$. In addition a cold ($T_{\rm dust}\,\sim\,20-30\,{\rm K}$), dense ($n({\rm H})\sim\,10^4- 10^5\,{\rm cm^{-3}}$) more extended phase is present. It outputs the emission in the low-excitation H$_2$O lines and typically also produces the prominent line absorption features. For the two ULIRGs in our sample (Arp 220 and Mrk 231) an even hotter and more compact (R$_s\,\le\,100$ pc) region is present which is possibly linked to AGN activity. We find that collisions dominate the water excitation in the cold gas and for lines with $E_{\rm up}\le300\,{\rm K}$ and $E_{\rm up}\le800\,{\rm K}$ in the warm and hot component, respectively. Higher energy levels are mainly excited by IR pumping.
The low temperature lattice structure and magnetic properties of Co$_{2.75}$Fe$_{0.25}$O$_4$ ferrite have been investigated using experimental results from synchrotron x-ray diffraction (SXRD), dc magnetization, ac susceptibility, neutron diffraction and neutron depolarization techniques. The samples have been prepared by chemical co-precipitation of the Fe and Co nitrates solution in high alkaline medium and subsequent thermal annealing of the precipitates in the temperature range of 200- 900 $^\circ$C. Rietveld refinement of the SXRD patterns at room temperature indicated two-phased cubic spinel structure for the samples annealed at temperatures 200-600 $^\circ$C. The samples annealed at temperatures 700 $^\circ$C and 900 $^\circ$C (CF90) have been best fitted with single phased lattice structure. Refinement of the neutron diffraction patterns in the temperature range of 5-300 K confirmed antiferromagnetic (AFM) Co$_3$O$_4$ and ferrimagnetic (FIM) Co$_{2.75}$Fe$_{0.25}$O$_4$ phases for the sample annealed at 600 $^\circ$C and single FIM phase of Co$_{2.75}$Fe$_{0.25}$O$_4$ for the CF90 sample. Magnetic measurements have shown a non-equilibrium magnetic structure, consisting of the high temperature FIM phase and low temperature AFM phase. The magnetic phases are sensitive to magnetic fields, where high temperature phase is suppressed at higher magnetic fields by enhancing the low temperature AFM phase, irrespective of annealing temperature of the samples.
Space asteroseismology reveals that stellar structure and evolution models of intermediate- and high-mass stars are in need of improvement in terms of angular momentum and chemical element transport. We aim to probe the interior structure of a hot massive star in the core-hydrogen burning phase of its evolution. We analyse CoRoT space photometry, Gaia DR2 space astrometry, and high-resolution high signal-to-noise HERMES and HARPS time-series spectroscopy of the slowly rotating B2V star HD 170580. From the time-series spectroscopy we derive $vsini=4\pm 2\,$km\,s$^{-1}$, where the uncertainty results from the complex pulsational line-profile variability. We detect 42 frequencies with amplitude above 5$\sigma$. Among these we identify 5 rotationally split triplets and 1 quintuplet. Asteroseismic modelling based on CoRoT, Gaia DR2 and spectroscopic data leads to a star of 8M$_\odot$ near core-hydrogen exhaustion and an extended overshoot zone. The detected low-order pressure-mode frequencies cannot be fit within the uncertainties of the CoRoT data by models without atomic diffusion.   Irrespective of this limitation, the low-order gravity modes reveal HD 170580 to be a slow rotator with an average rotation period between 73 and 98 d and a hint of small differential rotation. Future Gaia DR3 data taking into account the multiplicity of the star, along with long-term TESS photometry would allow to put better observational constraints on the asteroseismic models of this blue evolved massive star. Improved modelling with atomic diffusion, including radiative levitation, is needed to achieve compliance with the low helium surface abundance of the star. This poses immense computational challenges but is required to derive the interior rotation and mixing profiles of this star.
We study second order focal loci of nondegenerate plane congruences in P4(C) with degenerate focal conic. We show the projective generation of such congruences when the second order focal locus fills a component of the focal conic, improving a result of Corrado Segre
In this paper we analyze some properties of a scalar field configuration, where it is considered as a trapped Bose-Einstein condensate in a Schwarzschild-de Sitter background spacetime. In a natural way, the geometry of the curved spacetime provides an effective trapping potential for the scalar field configuration. This allows us to explore some thermodynamical properties of the system. Additionally, the curved geometry of the spacetime also induces a position dependent self-interaction parameter, which can be interpreted as a kind of gravitational Feshbach resonance, that could affect the stability of the cloud and could be used to obtain information about the interactions among the components of the system..
The relationship between the populations of optically and X-ray selected Active Galactic Nuclei (AGN) has been unclear due to divergent results from different studies. Arnold et al. (2009) claim that X-ray AGN are almost entirely disjoint from optical AGN, while the Swift-BAT 70-month hard X-ray survey reported that 553 of their 711 X-ray AGN are optical. In this work, we set out to understand this difference by cross-checking between these studies and examining their sampling and AGN-selection criteria. We also re-analyze the X-ray and optical AGN in 16 groups and clusters reported by Arnold et al. using our own optical spectrum fitting techniques. We find that 6 of the 8 X-ray AGN in the Arnold et al. sample are also optical AGN, contrary to Arnold et al.'s report that only 1 of the 8 X-ray AGN is also an optical AGN, thereby falsifies their conclusion that optical and X-ray AGN are nearly disjoint sets.
The conjecture is made that quantum mechanics is compatible with local hidden variables (or local realism). The conjecture seems to be ruled out by the theoretical argument of Bell, but it is supported by the empirical fact that nobody has been able to perform a loophole-free test of local realism in spite of renewed effort during almost 40 years.