ShantanuT01/DACTYL-Pretraining huggingface dataset:
Following Anders and Archer, we say that an unordered rooted labeled forest avoids the pattern $\sigma\in\mathcal{S}_k$ if in each tree, each sequence of labels along the shortest path from the root to a vertex does not contain a subsequence with the same relative order as $\sigma$. For each permutation $\sigma\in\mathcal{S}_{k-2}$, we construct a bijection between $n$-vertex forests avoiding $(\sigma)(k-1)k:=\sigma(1)\cdots\sigma(k-2)(k-1)k$ and $n$-vertex forests avoiding $(\sigma)k(k-1):=\sigma(1)\cdots\sigma(k-2)k(k-1)$, giving a common generalization of results of West on permutations and Anders--Archer on forests. We further define a new object, the forest-Young diagram, which we use to extend the notion of shape-Wilf equivalence to forests. In particular, this allows us to generalize the above result to a bijection between forests avoiding $\{(\sigma_1)k(k-1), (\sigma_2)k(k-1), \dots, (\sigma_\ell)k(k-1)\}$ and forests avoiding $\{(\sigma_1)(k-1)k, (\sigma_2)(k-1)k, \dots, (\sigma_\ell)(k-1)k\}$ for $\sigma_1, \dots, \sigma_\ell \in \mathcal{S}_{k-2}$. Furthermore, we give recurrences enumerating the forests avoiding $\{123\cdots k\}$, $\{213\}$, and other sets of patterns. Finally, we extend the Goulden--Jackson cluster method to study consecutive pattern avoidance in rooted trees as defined by Anders and Archer. Using the generalized cluster method, we prove that if two length-$k$ patterns are strong-c-forest-Wilf equivalent, then up to complementation, the two patterns must start with the same number. We also prove the surprising result that the patterns $1324$ and $1423$ are strong-c-forest-Wilf equivalent, even though they are not c-Wilf equivalent with respect to permutations.
Solid-state electrolytes (SSE) with high ion conductivity are pivotal for the development and large-scale adoption of green-energy conversion and storage technologies such as fuel cells, electrocatalysts and solid-state batteries. Yet, SSE are extremely complex materials for which general rational design principles remain indeterminate. Here, we unite first-principles materials modelling, computational power and modern data analysis techniques to advance towards the solution of such a fundamental and technologically pressing problem. Our data-driven survey reveals that the correlations between ion diffusivity and other materials descriptors in general are monotonic, although not necessarily linear, and largest when the latter are of vibrational nature and explicitly incorporate anharmonic effects. Surprisingly, principal component and k-means clustering analysis show that elastic and vibrational descriptors, rather than the usual ones related to chemical composition and ion mobility, are best suited for reducing the high complexity of SSE and classifying them into universal classes. Our findings highlight the need of considering databases that incorporate temperature effects to improve our understanding of SSE and point towards a generalized approach to the design of energy materials.
Effects that are not captured by the generalized-gradient density-functional theory play a prominent effect on the structural binding, and on the electronic and optical properties of reduced-dimensional and weakly-bound materials. Here, we report the exfoliation energy of selenium and tellurium atomic chains with non-empirical van der Waals corrections, and their electronic and optical properties with the GW and Bethe-Salpeter formalisms. The exfoliation energy is found to be within 0.547 to 0.719 eV/u.c. for the selenium atomic chain, and 0.737 to 0.926 eV/u.c. for the tellurium atomic chain (u.c. stands for unit cell), depending on the approximation for the van der Waals interaction and the numerical tool chosen. The GW electronic bandgap turned out to be 5.22--5.47 (4.44--4.59) eV for the Se (Te) atomic chains, with the lowest bound obtained with the Godby-Needs (GB), and the upper bound to the Hybertsen-Louie (HL) plasmon-pole models (PPMs). The binding energy of the ground-state excitonic state ranges between 2.69 to 2.72 eV for selenium chains within the HL and GB PPM, respectively, and turned out to be 2.35 eV for tellurium chains with both approximations. The ground state excitonic wave function is localized within 50 \AA{} along the axis for both types of atomic chains, and its energy lies within the visible spectrum: blue [2.50(GN)--2.78(HL) eV] for selenium, and yellow--green [2.09(GN)--2.28(HL) eV] for tellurium, which could be useful for LED applications in the visible spectrum.
From the partial wave analysis, the phase shift D33 of pion nucleon scattering containing the D(1232) resonance, corresponding to isospin I=3/2 and angular momentum J=3/2, has been parameterized over the energy range 1100 < W < 1375 MeV, using p-Pi+ data. The result of our parameterization shows good agreement in comparison with the available experimental data.
We consider the vibrations and waves in the atmosphere under the gravitation on the flat earth. The stratified density distribution of the back ground equilibrium is supposed to touch the vacuum at the finite height of the stratosphere. We show that incompressible motions are possible to create vibrations or progressive waves with countably many time frequencies of the vibrations or speeds of the wave propagation which accumulate to 0, say, of countably infinitely many slow and slow modes.
We consider a sequence of i.i.d. random variables $\{\xi_k\}$under a sublinear expectation $\mathbb{E}=\sup_{P\in\Theta}E_P$. We first give a new proof to the fact that, under each $P\in\Theta$, any cluster point of the empirical averages $\bar{\xi}_n=(\xi_1+\cdots+\xi_n)/n$ lies in $[\underline{\mu}, \bar{\mu}]$ with $\underline{\mu}=-\mathbb{E}[-\xi_1], \bar{\mu}=\mathbb{E}[\xi_1]$. Then, we consider sublinear expectations on a Polish space $\Omega$, and show that for each constant $\mu\in [\underline{\mu},\bar{\mu}]$, there exists a probability $P_{\mu}\in\Theta$ such that \begin {eqnarray}\label {intro-a.s.} \lim_{n\rightarrow\infty}\bar{\xi}_n=\mu, \ P_{\mu}\textmd{-a.s.}, \end {eqnarray} supposing that $\Theta$ is weakly compact and $\{\xi_n\}\in L^1_{\mathbb{E}}(\Omega)$. Under the same conditions, we can get a generalization of (\ref {intro-a.s.}) in the product space $\Omega=\mathbb{R}^{\mathbb{N}}$ with $\mu\in [\underline{\mu},\bar{\mu}]$ replaced by $\Pi=\pi(\xi_1, \cdots,\xi_d)\in [\underline{\mu},\bar{\mu}]$, where $\pi$ is a Borel measurable function on $\mathbb{R}^d$, $d\in\mathbb{R}$. Finally, we characterize the triviality of the tail $\sigma$-algebra of i.i.d. random variables under a sublinear expectation.
We briefly overview our recent results on nonequilibrium interactions between neighboring electrically isolated nanostructures. One of the nanostructures is represented by an externally biased quantum point contact (drive-QPC), which is used to supply energy quanta to the second nanostructure (detector). Absorption of these nonequilibrium quanta of energy generates a dc-current in the detector, or changes its differential conductance. We present results for a double quantum dot, a single quantum dot or a second QPC placed in the detector circuit. In all three cases a detection of quanta with energies up to ~1 meV is possible for bias voltages across the drive-QPC in the mV range. The results are qualitatively consistent with an energy transfer mechanism based on nonequilibrium acoustic phonons.
Our aim of this paper is to propose a method of analytic continuation of Carlitz multiple (star) polylogarithms to the whole space by using Artin-Schreier equation and present a treatment of their branches by introducing the notion of monodromy modules. As applications of this method, we obtain (1) a method of continuation of the logarithms of higher tensor powers of Carlitz module, (2) the orthogonal property (Chang-Mishiba functional relations), (3) a branch independency of the Eulerian property.
We investigate the problem whether a function of several arguments can be reconstructed from its identification minors. We focus on functions with a unique identification minor, and we establish some positive and negative results on the reconstruction problem. In particular, we show that totally symmetric functions (of sufficiently large arity) are reconstructible and the class of functions weakly determined by the order of first occurrence (of sufficiently large arity) is weakly reconstructible.
The cosmological consequences of an interacting model in which vacuum decay law is deducted from the effect that vacuum decay has on the dark matter evolution are investigated. Here, the baryonic matter is also considered as a fluid gravitationally coupled with dark matter. It is made a careful analysis to constrain this model with the observational data of growth rate of cosmic structures. The theoretical growth rate is followed since the primordial recombination and the main physical processes on the baryonic component are considered. As a complementary constraint, this model is compared with the observed CMB-BAO ratio as well with the gas mass fraction of cluster of galaxies. We found the best fit values for dark matter $\Omega_{d0} = 0.269 ^{+0.023}_{-0.023}$ and for the decay parameter $\epsilon = 0.02 ^{+0.04}_{-0.05}$.
The conformal deformations are contained in two classes of mappings: quasiconformal and harmonic mappings. In this paper we consider the intersection of these classes. We show that, every $K$ quasiconformal harmonic mapping between $\,\mathscr C^{1,\mu}$ ($0<\alpha\le 1$) surfaces with $\,\mathscr C^{1,\mu}$ boundary is a Lipschitz mapping. This extends some recent results of several authors where the same problem has been considered for plane domains. As an application it is given an explicit Lipschitz constant of normalized isothermal coordinates of a disk-type minimal surface in terms of boundary curve only. It seems that this kind of estimates are new for conformal mappings of the unit disk onto a Jordan domain as well.
Commensurate-incommensurate transitions are ubiquitous in physics and are often accompanied by intriguing phenomena. In few-layer graphene (FLG) systems, commensurability between honeycomb lattices on adjacent layers is regulated by their relative orientation angle theta, which is in turn dependent on sample preparation procedures. Because incommensurability suppresses inter-layer hybridization, it is often claimed that graphene layers can be electrically isolated by a relative twist, even though they are vertically separated by a fraction of a nanometer. We present a theory of interlayer transport in FLG systems which reveals a richer picture in which the specific conductance depends sensitively on theta, single-layer Bloch state lifetime, in-plane magnetic field, and bias voltage. We find that linear and differential conductances are generally large and negative near commensurate values of theta, and small and positive otherwise.
Double slit interference is explained with the aid of what we call "21stcentury classical physics". We model a particle as an oscillator ("bouncer") in a thermal context, which is given by some assumed "zero-point" field of the vacuum. In this way, the quantum is understood as an emergent system, i.e., a steady-state system maintained by a constant throughput of (vacuum) energy. To account for the particle's thermal environment, we introduce a "path excitation field", which derives from the thermodynamics of the zero-point vacuum and which represents all possible paths a particle can take via thermal path fluctuations. The intensity distribution on a screen behind a double slit is calculated, as well as the corresponding trajectories and the probability density current. Further, particular features of the relative phase are shown to be responsible for nonlocal effects not only in ordinary quantum theory, but also in our classical approach.
Since their discovery more than 50 years ago, broadband radio studies of pulsars have generated a wealth of information about the underlying physics of radio emission. In order to gain some further insights into this elusive emission mechanism, we performed a multi-frequency study of two very well-known pulsars, PSR~B0919+06 and PSR~B1859+07. These pulsars show peculiar radio emission properties whereby the emission shifts to an earlier rotation phase before returning to the nominal emission phase in a few tens of pulsar rotations (also known as `swooshes'). We confirm the previous claim that the emission during the swoosh is not necessarily absent at low frequencies and the single pulses during a swoosh show varied behaviour at 220~MHz. We also confirm that in PSR~B0919+06, the pulses during the swoosh show a chromatic dependence of the maximum offset from the normal emission phase with the offset following a consistent relationship with observing frequency. We also observe that the flux density spectrum of the radio profile during the swoosh is inverted compared to the normal emission. For PSR~B1859+07, we have discovered a new mode of emission in the pulsar that is potentially quasi-periodic with a different periodicity than is seen in its swooshes. We invoke an emission model previously proposed in the literature and show that this simple model can explain the macroscopic observed characteristics in both pulsars. We also argue that pulsars that exhibit similar variability on short timescales may have the same underlying emission mechanism.
We show that the initial value problem associated to the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov equation$$ u\_t-D\_x^\alpha u\_{x} + u\_{xyy} = uu\_x,\quad (t,x,y)\in\R^3,\quad 1\le \alpha\le 2,$$is locally well-posed in the spaces $E^s$, $s\textgreater{}\frac 2\alpha-\frac 34$, endowed with the norm$\|f\|\_{E^s} = \|\langle |\xi|^\alpha+\mu^2\rangle^s\hat{f}\|\_{L^2(\R^2)}.$As a consequence, we get the global well-posedness in the energy space $E^{1/2}$ as soon as $\alpha\textgreater{}\frac 85$. The proof is based on the approach of the short time Bourgain spaces developed by Ionescu, Kenig and Tataru \cite{IKT} combined with new Strichartz estimates and a modified energy.
Multiple gaps in the tight-binding band of a pentagonal lattice are found. Unlike the Cairo pentagonal lattice this lattice is made of irregular pentagons with arms of different lengths. The tight-binding Hamiltonian is exactly solved to obtain analytic expressions of dispersion relations and eigenvectors. Four different band-gaps are identified along with two distinct indirect band-gaps at the Harrison point. Multiple band-gaps in this model may give rise to exotic electronic properties.
We present a new multi-component spectral energy distribution (SED) decomposition method and use it to analyze the ultraviolet to millimeter wavelength SEDs of a sample of dusty infrared-luminous galaxies. SEDs are constructed from spectroscopic and photometric data obtained with the Spitzer Space Telescope, in conjunction with photometry from the literature. Each SED is decomposed into emission from populations of stars, an AGN accretion disk, PAHs, atomic and molecular lines, and distributions of graphite and silicate grains. Decompositions of the SEDs of the template starburst galaxies NGC7714 and NGC2623 and the template AGNs PG0804+761 and Mrk463 provide baseline properties to aid in quantifying the strength of star-formation and accretion in the composite systems NGC6240 and Mrk1014. We find that obscured radiation from stars is capable of powering the total dust emission from NGC6240, although we cannot rule out a contribution from a deeply embedded AGN visible only in X-rays. The decomposition of Mrk1014 is consistent with ~65% of its power emerging from an AGN and ~35% from star-formation. We suggest that many of the variations in our template starburst SEDs may be explained in terms of the different mean optical depths through the clouds of dust surrounding the young stars within each galaxy. Prompted by the divergent far-IR properties of our template AGNs, we suggest that variations in the relative orientation of their AGN accretion disks with respect to the disks of the galaxies hosting them may result in different amounts of AGN-heated cold dust emission emerging from their host galaxies. We estimate that 30-50% of the far-IR and PAH emission from Mrk1014 may originate from such AGN-heated material in its host galaxy disk.
The role of nearby galactic sources, the supernova remnants, in formation of observed energy spectrum and anisotropy of high-energy cosmic rays is studied. The list of these sources is made up based on radio, X-ray and gamma-ray catalogues. The distant sources are treated statistically as ensemble of sources with random positions and ages. The source spectra are defined based on the modern theory of cosmic ray acceleration in supernova remnants while the propagation of cosmic rays in the interstellar medium is described in the frameworks of galactic diffusion model. Calculations of anisotropy are made to reproduce the experimental procedure of getting the two-dimensional anisotropy. The detailed comparison of calculations with cosmic ray data is made. We explained simultaneously the new cosmic ray data on a fine structure of all particle spectra around the knee and the amplitude and direction of the dipole component of anisotropy in the wide energy range 1 TeV - 1 EeV. Made assumptions do not look exotic, and they confirm the modern understanding of cosmic ray origin.
We consider heat transport in a Luttinger liquid (LL) with weak disorder and study the Lorenz number for this system. We start at a high-$T$ regime, and calculate both the electrical and thermal conductivities using a memory function approach. The resulting Lorenz number $L$ is independent of $T$ but depends explicitly on the LL exponents. Lowering $T$, however, allows for a renormalization of the LL exponents from their bare values by disorder, causing a violation of the Wiedemann-Franz law. Finally, we extend the discussion to quantum wire systems and study the wire size dependence of the Lorenz number.
We study a general method of the field intersection problem of generic polynomials over an arbitrary field $k$ via formal Tschirnhausen transformation. In the case of solvable quintic, we give an explicit answer to the problem by using multi-resolvent polynomials.
PKS B2152-699 has radio power characteristic of sources that dominate radio feedback. We present new deep ATCA, Chandra and optical observations, and test the feedback model. We report the first high-resolution observations of the radio jet. The inner jet extends ~8.5 kpc towards an optical emission-line High Ionization Cloud (HIC) before taking a zig-zag path to an offset position. Jet X-ray synchrotron radiation is seen. The HIC is associated with 0.3 keV X-ray gas of anomalously low metallicity. On larger scales the radio galaxy displays all three X-ray features that together confirm supersonic expansion of the lobes into the external medium: gas cavities, inverse-Compton emission showing excess internal lobe pressure, and high-contrast arms of temperature above the ~1 keV ambient medium. The well-formed S lobe on the counterjet side is expanding with a Mach number 2.2-3. We estimate a cavity power ~3x10^43 ergs/s, which falls well below previously reported correlations with radio power. The total inferred time-averaged jet power, ~4x10^44 ergs/s, is dominated by the kinetic and thermal energy of shocked gas, and if used instead would bring the source into better agreement with the correlations. The S hotspot is the more complex, with a spiral polarization structure. Its bright peak emits synchrotron X-rays. The fainter N hotspot is particularly interesting, with X-rays offset in the direction of the incoming jet by ~1 arcsec relative to the radio peak. Here modest (delta ~ 6) relativistic beaming and a steep radio spectrum cause the jet to be X-ray bright through inverse-Compton scattering before it decelerates. With such beaming, a modest proton content or small departure from minimum energy in the jet will align estimates of the instantaneous and time-averaged jet power. The hotspots suggest acceleration of electrons to a maximum energy ~10^13 eV in the jet termination shocks.
In this paper, we consider the well-known Fattorini's criterion for approximate controllability of infinite dimensional linear systems of type $y'=A y+Bu$. We precise the result proved by H. O. Fattorini in \cite{Fattorini1966} for bounded input $B$, in the case where $B$ can be unbounded or in the case of finite-dimensional controls. More precisely, we prove that if Fattorini's criterion is satisfied and if the set of geometric multiplicities of $A$ is bounded then approximate controllability can be achieved with finite dimensional controls. An important consequence of this result consists in using the Fattorini's criterion to obtain the feedback stabilizability of linear and nonlinear parabolic systems with feedback controls in a finite dimensional space. In particular, for systems described by partial differential equations, such a criterion reduces to a unique continuation theorem for a stationary system. We illustrate such a method by tackling some coupled Navier-Stokes type equations (MHD system and micropolar fluid system) and we sketch a systematic procedure relying on Fattorini's criterion for checking stabilizability of such nonlinear systems. In that case, the unique continuation theorems rely on local Carleman inequalities for stationary Stokes type systems.
We make use of Dirac LNH and results for a time varying fine structure constant in order to derive possible laws of variation for speed of light, the number of nucleons in the Universe, energy density and gravitational constant. By comparing with experimental bounds on G variation, we find that the deceleration paramenter of the present Universe is negative. This is coherent with recent Supernovae observations.
This paper deals with adjacency matrices of signed cycle graphs and chemical descriptors based on them. The eigenvalues and eigenvectors of the matrices are calculated and their efficacy in classifying different signed cycles is determined. The efficacy of some numerical indices is also examined.
The processes are investigated by which gas loses its angular momentum during the protogalactic collapse phase, leading to disk galaxies that are too compact with respect to the observations. High-resolution N-body/SPH simulations in a cosmological context are presented including cold gas and dark matter. A halo with quiet merging activity since z~3.8 and with a high spin parameter is analysed that should be an ideal candidate for the formation of an extended galactic disk. We show that the gas and the dark matter have similar specific angular momenta until a merger event occurs at z~2 with a mass ratio of 5:1. All the gas involved in the merger loses a substantial fraction of its specific angular momentum due to tidal torques and falls quickly into the center. Dynamical friction plays a minor role,in contrast to previous claims. In fact, after this event a new extended disk begins to form from gas that was not involved in the 5:1 merger event and that falls in subsequently. We argue that the angular momentum problem of disk galaxy formation is a merger problem: in cold dark matter cosmology substantial mergers with mass ratios of 1:1 to 6:1 are expected to occur in almost all galaxies. We suggest that energetic feedback processes could in principle solve this problem, however only if the heating occurs at the time or shortly before the last substantial merger event. Good candidates for such a coordinated feedback would be a merger-triggered star burst or central black hole heating. If a large fraction of the low angular momentum gas would be ejected as a result of these processes, late-type galaxies could form with a dominant extended disk component, resulting from late infall, a small bulge-to-disk ratio and a low baryon fraction, in agreement with observations.