ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Horton-Strahler (HS) index $r=\max{(i,j)}+\delta_{i,j}$ has been shown to be relevant to a number of physical (such at diffusion limited aggregation) geological (river networks), biological (pulmonary arteries, blood vessels, various species of trees) and computational (use of registers) applications. Here we revisit the enumeration problem of the HS index on the rooted, unlabeled, plane binary set of trees, and enumerate the same index on the ambilateral set of rooted, plane binary set of trees of $n$ leaves. The ambilateral set is a set of trees whose elements cannot be obtained from each other via an arbitrary number of reflections with respect to vertical axes passing through any of the nodes on the tree. For the unlabeled set we give an alternate derivation to the existing exact solution. Extending this technique for the ambilateral set, which is described by an infinite series of non-linear functional equations, we are able to give a double-exponentially converging approximant to the generating functions in a neighborhood of their convergence circle, and derive an explicit asymptotic form for the number of such trees.
Absorption along quasar sightlines remains among the most sensitive direct measures of HeII reionization in much of the intergalactic medium (IGM). Until recently, fewer than a half-dozen unobscured quasar sightlines suitable for the HeII Gunn-Peterson test were known; although these handful demonstrated great promise, the small sample size limited confidence in cosmological inferences. We have recently added nine more such clean HeII quasars, exploiting SDSS quasar samples, broadband UV imaging from GALEX, and high-yield UV spectroscopic confirmations from HST. Here we markedly expand this approach by cross-correlating SDSS DR7 and GALEX GR4+5 to catalog 428 SDSS and 165 other quasars with z>2.78 having likely (~70%) GALEX detections, suggesting they are bright into the far-UV. Reconnaissance HST Cycle 16 Supplemental prism data for 29 of these new quasar-GALEX matches spectroscopically confirm 17 as indeed far-UV bright. At least 10 of these confirmations have clean sightlines all the way down to HeII Lyman-alpha, substantially expanding the number of known clean HeII quasars, and reaffirming the order of magnitude enhanced efficiency of our selection technique. Combined confirmations from this and our past programs yield more than twenty HeII quasars, quintupling the sample. These provide substantial progress toward a sample of HeII quasar sightlines large enough, and spanning a sufficient redshift range, to enable statistical IGM studies that may avoid individual object peculiarity and sightline variance. Our expanded catalog of hundreds of high-likelihood far-UV-bright QSOs additionally will be useful for understanding the extreme-UV properties of the quasars themselves.
Predominantly preliminary single and double inclusive momentum spectra of 158 AGeV Pb+Pb collisions, recently measured by the NA44 and NA49 Collaborations, are reproduced using the relativistic hydrodynamical model HYLANDER-C. Two different equations of state, which both contain a phase transition to a quark-gluon plasma, can be used to reproduce the (preliminary) data. The space-time geometries in the two calculations differ strongly. However, the Bose-Einstein correlation functions of identical pion pairs do not show such a strong, but still a significant sensitivity to the effects of the equations of state.
The spectral function of protons in the asymmetric nuclear matter is calculated in the self-consistent T-matrix approach. The spectral function per proton increases with increasing asymmetry. This effect and the density dependence of the spectral function partially explain the observed increase of the spectral function with the mass number of the target nuclei in electron scattering experiments.
With the aim of considering models with persistent memory we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macrovolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates.   Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
We use combinatorial and generating function techniques to enumerate various sets of involutions which avoid 231 or contain 231 exactly once. Interestingly, many of these enumerations can be given in terms of $k$-generalized Fibonacci numbers.
Quasi-periodic fluctuations in the light curves of blazars can provide insight into the underlying emission process. This type of flux modulation hints at periodic physical processes that result in emission. CTA 102, a flat spectrum radio quasar at $z=1.032$, has displayed significant activity since 2016. The multi-waveband light curve of CTA 102 shows signs of quasi-periodic oscillations during the 2016-2017 flare. Our goal is to quantify the presence of any periodicity in the emitted flux during the mentioned period and to explore the causes that can give rise to it. Techniques such as the Lomb-Scargle periodogram and weighted wavelet z-transform were employed to observe the power emitted at different frequencies. To quantify the significance of the dominant period, Monte-Carlo techniques were employed considering an underlying smooth bending power-law model for the power spectrum. In addition, the light curve was modeled using an autoregressive process to analytically obtain the significance of the dominant period. Lastly, the light curve was modeled using a generalized autoregressive integrated moving average process to check whether introducing a periodic component results in a statistically preferable model. Significant, simultaneous quasi-periodic oscillations (QPOs) were observed in the $\gamma$-ray and optical fluxes of blazar CTA 102 during its 2016-2017 flare. The periodic flux modulation had a dominant period of $\sim$ 7.6 days and lasted for $\sim$ 8 cycles (MJD 57710-57770). All of the methods used point toward significant ($>4\sigma$) quasi-periodic modulation in both $\gamma$-ray and optical fluxes. Several possible models were explored while probing the origin of the periodicity, and by extension, the 2016--2017 optical flare. The best explanation for the detected QPO appears to be a region of enhanced emission, moving helically inside the jet.
By means of scanning tunneling spectroscopy (STS) we study the electronic structure of the III-V semiconductor surface InAs(111)A in the field emission regime (above the vacuum level). At high sample bias voltages (approaching +10 V), a series of well defined resonances are identified as the typical Stark shifted image states that are commonly found on metallic surfaces in the form of field emission resonances (FER). At lower bias voltages, a more complex situation arises. Up to three double peaks are identified as the first three FERs that are split due to their interaction with the periodic surface potential. The high corrugation of this potential is also quantified by means of density functional theory (DFT) calculations. Another sharp resonance not belonging to the FER series is associated with an unoccupied surface state.
We discuss the spectral asymptotics of some open subsets of the real line with random fractal boundary and of a random fractal, the continuum random tree. In the case of open subsets with random fractal boundary we establish the existence of the second order term in the asymptotics almost surely and then determine when there will be a central limit theorem which captures the fluctuations around this limit. We will show examples from a class of random fractals generated from Dirichlet distributions as this is a relatively simple setting in which there are sets where there will and will not be a central limit theorem. The Brownian continuum random tree can also be viewed as a random fractal generated by a Dirichlet distribution. The first order term in the spectral asymptotics is known almost surely and here we show that there is a central limit theorem describing the fluctuations about this, though the positivity of the variance arising in the central limit theorem is left open. In both cases these fractals can be described through a general Crump-Mode-Jagers branching process and we exploit this connection to establish our central limit theorems for the higher order terms in the spectral asymptotics. Our main tool is a central limit theorem for such general branching processes which we prove under conditions which are weaker than those previously known.
We consider the problem of extending partial edge colorings of hypercubes. In particular, we obtain an analogue of the positive solution to the famous Evans' conjecture on completing partial Latin squares by proving that every proper partial edge coloring of at most $d-1$ edges of the $d$-dimensional hypercube $Q_d$ can be extended to a proper $d$-edge coloring of $Q_d$. Additionally, we characterize which partial edge colorings of $Q_d$ with precisely $d$ precolored edges are extendable to proper $d$-edge colorings of $Q_d$, and consider some related edge precoloring extension problems of hypercubes.
Using data from the HST Medium Deep Survey, a long-term Key Project, together with generically similar archived data, we have discovered evidence for weak gravitational `shear' of background field galaxies (I = 22 -- 26) in the vicinity of isolated, foreground galaxies ( I = 15 -- 22), especially those of early type. The statistical lensing is demonstrated by the slight preferential orientation of the major axes of the background galaxies in directions at right angles to the lines joining them to the foreground ones. The detected shear is at the level of $\delta\phi = 2.5^{o}\pm 1.2^{o}$ averaged over the background galaxies at about ~10 half-light radii from 400 foreground ellipticals, corresponding to a polarization of about 0.04. A positive but less significant result is also reported for foreground spirals. This result excludes the de Vaucouleurs model for the mass distribution of ellipticals, but is consistent with elliptical galaxies having total M/L ~ 100 and extensive dark halos.
We have used specific heat and neutron diffraction measurements on single crystals of URu$_{2-x}$Fe$_x$Si$_2$ for Fe concentrations $x$ $\leq$ 0.7 to establish that chemical substitution of Ru with Fe acts as "chemical pressure" $P_{ch}$ as previously proposed by Kanchanavatee et al. [Phys. Rev. B {\bf 84}, 245122 (2011)] based on bulk measurements on polycrystalline samples. Notably, neutron diffraction reveals a sharp increase of the uranium magnetic moment at $x=0.1$, reminiscent of the behavior at the "hidden order" (HO) to large moment antiferromagnetic (LMAFM) phase transition observed at a pressure $P_x\approx$ 0.5-0.7~GPa in URu$_2$Si$_2$. Using the unit cell volume determined from our measurements and an isothermal compressibility $\kappa_{T} = 5.2 \times 10^{-3}$ GPa$^{-1}$ for URu$_2$Si$_2$, we determine the chemical pressure $P_{ch}$ in URu$_{2-x}$Fe$_x$Si$_2$ as a function of $x$. The resulting temperature $T$-chemical pressure $P_{ch}$ phase diagram for URu$_{2-x}$Fe$_x$Si$_2$ is in agreement with the established temperature $T$-external pressure $P$ phase diagram of URu$_2$Si$_2$.
In this short note we define a Poissonian model of directed random graphs which generalises the undirected Poissonian random graph process introduced in [Norros, I.; Reittu, H. "On a conditionally Poissonian graph process." Adv. in Appl. Probab. 38 (2006), no. 1, 59--75]. We discuss the relation of our model to the Norros-Reittu model, characterise the limiting distribution of the degree of a typical vertex and discuss the component structure of the model in some special cases which are relevant to the theory of infection processes.
We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic-oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas.
We will present a novel elementary and self-contained proof of the local Kronecker-Weber theorem. Apart from discrete valuation theory, it does not make use of any tools beyond those introduced in a second undergraduate course on algebra. In particular, we will not make use of results from local class field theory or Galois cohomology.
As first discovered by Choptuik, the black hole threshold in the space of initial data for general relativity shows both surprising structure and surprising simplicity. Universality, power-law scaling of the black hole mass, and scale echoing have given rise to the term "critical phenomena". They are explained by the existence of exact solutions which are attractors within the black hole threshold, that is, attractors of codimension one in phase space, and which are typically self-similar. This review gives an introduction to the phenomena, tries to summarize the essential features of what is happening, and then presents extensions and applications of this basic scenario. Critical phenomena are of interest particularly for creating surprising structure from simple equations, and for the light they throw on cosmic censorship. They may have applications in quantum black holes and astrophysics.
Locality Sensitive Hashing (LSH) based algorithms have already shown their promise in finding approximate nearest neighbors in high dimen- sional data space. However, there are certain scenarios, as in sequential data, where the proximity of a pair of points cannot be captured without considering their surroundings or context. In videos, as for example, a particular frame is meaningful only when it is seen in the context of its preceding and following frames. LSH has no mechanism to handle the con- texts of the data points. In this article, a novel scheme of Context based Locality Sensitive Hashing (conLSH) has been introduced, in which points are hashed together not only based on their closeness, but also because of similar context. The contribution made in this article is three fold. First, conLSH is integrated with a recently proposed fast optimal sequence alignment algorithm (FOGSAA) using a layered approach. The resultant method is applied to video retrieval for extracting similar sequences. The pro- posed algorithm yields more than 80% accuracy on an average in different datasets. It has been found to save 36.3% of the total time, consumed by the exhaustive search. conLSH reduces the search space to approximately 42% of the entire dataset, when compared with an exhaustive search by the aforementioned FOGSAA, Bag of Words method and the standard LSH implementations. Secondly, the effectiveness of conLSH is demon- strated in action recognition of the video clips, which yields an average gain of 12.83% in terms of classification accuracy over the state of the art methods using STIP descriptors. The last but of great significance is that this article provides a way of automatically annotating long and composite real life videos. The source code of conLSH is made available at http://www.isical.ac.in/~bioinfo_miu/conLSH/conLSH.html
A subposet $Q'$ of a poset $Q$ is a copy of a poset $P$ if there is a bijection $f$ between elements of $P$ and $Q'$ such that $x\leq y$ in $P$ iff $f(x)\leq f(y)$ in $Q'$. For posets $P, P'$, let the poset Ramsey number $R(P,P')$ be the smallest $N$ such that no matter how the elements of the Boolean lattice $Q_N$ are colored red and blue, there is a copy of $P$ with all red elements or a copy of $P'$ with all blue elements. We provide some general bounds on $R(P,P')$ and focus on the situation when $P$ and $P'$ are both Boolean lattices. In addition, we give asymptotically tight bounds for the number of copies of $Q_n$ in $Q_N$ and for a multicolor version of a poset Ramsey number.
The projection-operator formalism of Feshbach is applied to resonance scattering in a single-channel case. The method is based on the division of the full function space into two segments, internal (localized) and external (infinitely extended). The spectroscopic information on the resonances is obtained from the non-Hermitian effective Hamilton operator $H_{\rm eff}$ appearing in the internal part due to the coupling to the external part. As well known, additional so-called cut-off poles of the $S$-matrix appear, generally, due to the truncation of the potential. We study the question of spurious $S$ matrix poles in the framework of the Feshbach formalism. The numerical analysis is performed for exactly solvable potentials with a finite number of resonance states. These potentials represent a generalization of Bargmann-type potentials to accept resonance states. Our calculations demonstrate that the poles of the $S$ matrix obtained by using the Feshbach projection-operator formalism coincide with both the complex energies of the physical resonances and the cut-off poles of the $S$-matrix.
We consider a strongly correlated quantum dot, tunnel coupled to two superconducting leads and capacitively coupled to a single mode microwave cavity. When the superconducting gap is the largest energy scale, multiple Shiba states are formed inside the gap. The competition of these states for the ground state signals a quantum phase transition. We demonstrate that photonic measurements can be used to probe such localized Shiba states. Moreover, the quantum phase transition can be pinpointed exactly from the sudden change in the transmission signal. Calculations were performed using the numerical renormalization group approach.
We report distance measurements for the Norma cluster based on the near-infrared $J$- and $K_s$-band Fundamental Plane (FP) relations. Our simultaneous $J$ and $K_s$-band photometry analyses were performed using 31 early-type galaxies in the nearby Norma cluster obtained using the 1.4 m InfraRed Survey Facility (IRSF) at the South African Astronomical Observatory. Our final $K_s$-band FP sample consists of 41 early-type galaxies from the Norma cluster observed using the IRSF and the New Technology Telescope (NTT) at the European Southern Observatory. This is the largest cluster sample used for peculiar velocity studies in the Great Attractor region to date. From the $K_s$-band FP, we find a distance to the Norma cluster of $4915 \pm 121$ km s$^{-1}$. The implied peculiar velocity for Norma is $44 \pm 151$ km s$^{-1}$ which further supports a small peculiar velocity for the Norma cluster.
We construct relativistic models of charged dust thick disks for a particular conformastatic spacetime through a Miyamoto-Nagai transformation used in Newtonian gravity to model disk like galaxies. Two simple families of thick disk models and a family of thick annular disks based on the field of an extreme Reissner-Nordstr\"om black hole and a Morgan-Morgan-like metric are considered. The electrogeodesic motion of test particles around the structures are analyzed. Also the stability of the particles against radial perturbation is studied using an extension of the Rayleigh criteria of stability of a fluid in rest in a gravitational field. The models built satisfy all the energy conditions.
The development of space-borne missions has significantly improved the quality of the measured spectra of solar-like oscillators. Their $p$-mode line profiles can now be resolved, and the asymmetries inferred for a variety of stars other than the Sun. However, it has been known for a long time that the asymmetries of solar $p$-modes are reversed between the velocity and the intensity spectra. Understanding the origin of this reversal is necessary in order to use asymmetries as a tool for seismic diagnosis. For stars other than the Sun, only the intensity power spectrum is sufficiently resolved to allow for an estimation of mode asymmetries. We recently developed an approach designed to model and predict these asymmetries in the velocity power spectrum of the Sun and to successfully compare them to their observationally derived counterparts. In this paper we expand our model and predict the asymmetries featured in the intensity power spectrum. We find that the shape of the mode line profiles in intensity is largely dependent on how the oscillation-induced variations of the radiative flux are treated, and that modelling it realistically is crucial to understanding asymmetry reversal. Perturbing a solar-calibrated grey atmosphere model, and adopting the quasi-adiabatic framework as a first step, we reproduce the asymmetries observed in the solar intensity spectrum for low-frequency modes. We conclude that, unlike previously thought, it is not necessary to invoke an additional mechanism (e.g. non-adiabatic effects, coherent non-resonant background signal) to explain asymmetry reversal. This additional mechanism is necessary, however, to explain asymmetry reversal for higher-order modes.
Molecular-dynamics simulation can give atomistic information on the processes occurring in nanoindentation experiments. In particular, the nucleation of dislocation loops, their growth, interaction and motion can be studied. We investigate how realistic the interatomic potentials underlying the simulations have to be in order to describe these complex processes. Specifically we investigate nanoindentation into a Cu single crystal. We compare simulations based on a realistic many-body interaction potential of the embedded-atom-method type with two simple pair potentials, a Lennard-Jones and a Morse potential. We find that qualitatively many aspects of nanoindentation are fairly well reproduced by the simple pair potentials: elastic regime, critical stress and indentation depth for yielding, dependence on the crystal orientation, and even the level of the hardness. The quantitative deficits of the pair potential predictions can be traced back (i) to the fact that the pair potentials are unable in principle to model the elastic anisotropy of cubic crystals; (ii) as the major drawback of pair potentials we identify the gross underestimation of the stable stacking fault energy. As a consequence these potentials predict the formation of too large dislocation loops, the too rapid expansion of partials, too little cross slip and in consequence a severe overestimation of work hardening.