ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigated the temperature-dependent optical conductivity of NaV2O5 in the energy range 4 meV-4 eV. The intensities and the polarization dependence of the detected electronic excitations give a direct indication for a broken-parity electronic ground-state and for a non-centrosymmetric crystal structure of the system in the high-temperature phase. A direct two-magnon optical absorption process, proposed in this Letter, is in quantitative agreement with the optical data. By analyzing the optically allowed phonons at various temperatures above and below the phase transition, we conclude that a second-order change to a larger unit cell takes place below 34 K.
In this paper, we study central values of the family of quadratic twists of modular $L$-functions of moduli $8p$, with $p$ ranging over odd primes. Assuming the truth of the generalized Riemann hypothesis, we establish a positive proportion non-vanishing result for the corresponding $L$-values.
In this paper, we prove that a fuzzy set--valued Brownian motion $B_t$, as defined in [1], can be handle by an $R^d$--valued Wiener process $b_t$, in the sense that $B_t =\indicator{b_t}$; i.e. it is actually the indicator function of a Wiener process.
We continue the investigation of two-loop string corrections to the energy of a folded string with a spin S in AdS_5 and an angular momentum J in S^5, in the scaling limit of large J and S with ell=pi J/(lambda^(1/2) ln S)=fixed. We compute the generalized scaling function at two-loop order f_2(ell) both for small and large values of ell matching the predictions based on the asymptotic Bethe ansatz. In particular, in the small ell expansion, we derive an exact integral form for the ell-dependent coefficient of the Catalan's constant term in f_2(ell). Also, by resumming a certain subclass of multi-loop Feynman diagrams we obtain an exact expression for the leading (ln ell) part of f(lambda^(1/2), ell) which is valid to any order in the alpha'~1/lambda^(1/2) expansion. At large ell the string energy has a BMN-like expansion and the first few leading coefficients are expected to be the same at weak and at strong coupling. We provide a new example of this non-renormalization for the term which is generated at two loops in string theory and at one-loop in gauge theory (sub-sub-leading in 1/J). We also derive a simple algebraic formula for the term of maximal transcendentality in f_2(ell) expanded at large ell. In the second part of the paper we initiate the study of 2-loop finite size corrections to the string energy by formally compactifying the spatial world-sheet direction in the string action expanded near long fast-spinning string. We observe that the leading finite-size corrections are of "Casimir" type coming from terms containing at least one massless propagator. We consider in detail the one-loop order (reproducing the leading Landau-Lifshitz model prediction) and then focus on the two-loop contributions to the (1/ln S) term (for J=0). We find that in a certain regularization scheme used to discard power divergences the two-loop coefficient of the (1/ln S) term appears to vanish.
Tests of the integrality properties of a scalar operator in topological strings on a resolved conifold background or orientifold of conifold backgrounds have been performed for arborescent knots and some non-arborescent knots. The recent results on polynomials for those knots colored by SU(N) and SO(N) adjoint representations are useful to verify Marino's integrality conjecture up to two boxes in the Young diagram. In this paper, we review the salient aspects of the integrality properties and tabulate explicitly for an arborescent knot and a link. In our knotebook website, we have put these results for over 100 prime knots available in Rolfsen table and some links. The first application of the obtained results, an observation of the Gaussian distribution of the LMOV invariants is also reported.
Double-diffusive convection, often referred to as semi-convection in astrophysics, occurs in thermally and compositionally stratified systems which are stable according to the Ledoux-criterion but unstable according to the Schwarzchild criterion. This process has been given relatively little attention so far, and its properties remain poorly constrained. In this paper, we present and analyze a set of three-dimensional simulations of this phenomenon in a Cartesian domain under the Boussinesq approximation. We find that in some cases the double-diffusive convection saturates into a state of homogeneous turbulence, but with turbulent fluxes several orders of magnitude smaller than those expected from direct overturning convection. In other cases the system rapidly and spontaneously develops closely-packed thermo-compositional layers, which later successively merge until a single layer is left. We compare the output of our simulations with an existing theory of layer formation in the oceanographic context, and find very good agreement between the model and our results. The thermal and compositional mixing rates increase significantly during layer formation, and increase even further with each merger. We find that the heat flux through the staircase is a simple function of the layer height. We conclude by proposing a new approach to studying transport by double-diffusive convection in astrophysics.
The Square Kilometre Array (SKA) will conduct the biggest spectroscopic galaxy survey ever, by detecting the 21cm emission line of neutral hydrogen (HI) from around a billion galaxies over 3/4 of the sky, out to a redshift of z~2. This will allow the redshift-space matter power spectrum, and corresponding dark energy observables, to be measured with unprecedented precision. In this paper, we present an improved model of the HI galaxy number counts and bias from semi-analytic simulations, and use it to calculate the expected yield of HI galaxies from surveys with a variety of Phase 1 and 2 SKA configurations. We illustrate the relative performance of the different surveys by forecasting errors on the radial and transverse scales of the baryon acoustic oscillation (BAO) feature, finding that the full "billion galaxy survey" with SKA2 will deliver the largest dark energy figure of merit of any current or future large-scale structure survey.
The exponential generating function for the sequence A143405 in the OEIS is exp(exp(x)*(exp(x) - 1)). This paper analyzes the more general generating function exp(m*exp(b*x) + r*exp(d*x) + s) and provides asymptotics for the sequences A143405, A355291, A002872, A002874 and others in the OEIS.
We consider the fractional Ornstein-Uhlenbeck process with an unknown drift parameter and known Hurst parameter $H$. We propose a new method to test the hypothesis of the sign of the parameter and prove the consistency of the test. Contrary to the previous works, our approach is applicable for all $H\in(0,1)$. We also study the estimators for drift parameter for continuous and discrete observations and prove their strong consistency for all $H\in(0,1)$.
We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or log-periodicity) is found in a time series. We investigate general situations with non-Gaussian correlated noises and present synthetic tests on the detectability and statistical significance of periodic components. Increasing heavy-tailness (respectively correlations describing persistence) tends to decrease (respectively increase) the false-alarm probability of finding a large spurious Lomb peak. Increasing anti-persistence tends to decrease the false-alarm probability. We also study the interplay between heavy-tailness and long-range correlations. In order to fully determine if a Lomb peak signals a genuine rather than a spurious periodicity, one should in principle characterize the Lomb peak height, its width and its relations to other peaks in the complete spectrum. As a step towards this full characterization, we construct the joint-distribution of the frequency position (relative to other peaks) and of the height of the highest peak of the power spectrum. We also provide the distributions of the ratio of the second highest Lomb peak to the maximum peak. Using the insight obtained by the present statistical study, we re-examine previously reported claims of ``log-periodicity'' and find that the credibility for log-periodicity in 2D-freely decaying turbulence is weakened while it is strengthened for fracture, for the ion-signature prior to the Kobe earthquake and for financial markets.
We present LOFAR observations at 150 MHz of the borderline FRI/FRII giant radio galaxy NGC 6251. This paper presents the most sensitive and highest-resolution images of NGC 6251 at these frequencies to date, revealing for the first time a low-surface-brightness extension to the northern lobe, and a possible backflow associated with the southern lobe. The integrated spectra of components of NGC 6251 are consistent with previous measurements at higher frequencies, similar to results from other LOFAR studies of nearby radio galaxies. We find the outer structures of NGC 6251 to be either at equipartition or slightly electron dominated, similar to those of FRII sources rather than FRIs; but this conclusion remains tentative because of uncertainties associated with the geometry and the extrapolation of X-ray measurements to determine the external pressure distribution on the scale of the outer lobes. We place lower limits on the ages of the extension of the northern lobe and the backflow of the southern lobe of $t \gtrsim 250$ Myr and $t \gtrsim 210$ Myr respectively. We present the first detection of polarisation at 150 MHz in NGC 6251. Taking advantage of the high Faraday resolution of LOFAR, we place an upper limit on the magnetic field in the group of $B < 0.2 (\Lambda_B / 10 {\rm kpc})^{-0.5} \mu$G for a coherence scale of $\Lambda_B < 60 {\rm kpc}$ and $B < 13 \mu$G for $\Lambda_B = 240$ kpc.
We discuss the angular distribution of the lepton pair in the Drell-Yan process, hadron+hadron -> \gamma^* X -> l^+ l^- X. This process gives information on the spin-density matrix \rho^{(q,\bar{q})} of the annihilating quark-antiquark pair in q+\bar{q} -> l^+ l^-. There is strong experimental evidence that even for unpolarised initial hadrons \rho^{(q,\bar{q})} is nontrivial, and therefore the quark-antiquark system is polarised. We discuss the possibilities of a general \rho^{(q,\bar{q})} -which could be entangled- and a factorising \rho^{(q,\bar{q})}. We argue that instantons may lead to a nontrivial \rho^{(q,\bar{q})} of the type indicated by experiments.
Association schemes are combinatorial objects that allow us solve problems in several branches of mathematics. They have been used in the study of permutation groups and graphs and also in the design of experiments, coding theory, partition designs etc. In this paper we show some techniques for computing properties of association schemes. The main framework arises from the fact that we can characterize completely the Bose-Mesner algebra in terms of a zero-dimensional ideal. A Gr\"obner basis of this ideal can be easily derived without the use of Buchberger algorithm in an efficient way. From this statement, some nice relations arise between the treatment of zero-dimensional ideals by reordering techniques (FGLM techniques) and some properties of the schemes such as P-polynomiality, and minimal generators of the algebra.
Majorana zero modes are leading candidates for topological quantum computation due to non-local qubit encoding and non-abelian exchange statistics. Spatially separated Majorana modes are expected to allow phase-coherent single-electron transport through a topological superconducting island via a mechanism referred to as teleportation. Here we experimentally investigate such a system by patterning an elongated epitaxial InAs-Al island embedded in an Aharonov-Bohm interferometer. With increasing parallel magnetic field, a discrete sub-gap state in the island is lowered to zero energy yielding persistent 1e-periodic Coulomb blockade conductance peaks (e is the elementary charge). In this condition, conductance through the interferometer is observed to oscillate in a perpendicular magnetic field with a flux period of h/e (h is Planck's constant), indicating coherent transport of single electrons through the islands, a signature of electron teleportation via Majorana modes, could also be observed, suggesting additional non-Majorana mechanisms for 1e transport through these moderately short wires.
The magnetic phase diagram of the quasi one-dimensional spinchain system CsNiF$_3$ below the N\'eel temperature is determined. For magnetic fields perpendicular to the spin chains incommensurate phases are predicted. From linear spin-wave theory we obtain the instability line of the paramagnetic phase as a function of the strength and the direction of the field. The system undergoes a transition to a commensurate or an incommensurate phase depending on the direction of the magnetic field. In the commensurate phase the characterizing wave vector is locked to values describing a two-sublattice structure, whereas in the incommensurate phase the wave vector changes continuously between the corresponding two-sublattice wave vectors.
Mean-field frozen percolation is a random graph-valued process, which adjusts the dynamics of the classical Erdos-Renyi process with an additional mechanism to 'freeze' potential giant components before they can form. It is known to exhibit self-organised criticality from a wide class of initial graphs. We show that a family of inhomogeneous random graphs with finitely-many types form a stable class under these dynamics. We study how the survival of a vertex depends on its initial type, and establish a hydrodynamic limit for the process recording surviving vertices of each type, in terms of multitype branching processes which approximate the graphs. The parameters of these branching processes are eventually critical, and their evolution in time is described by solutions to an unusual class of differential equations driven by Perron-Frobenius eigenvectors.
The amount and nature of the evolution of the X-ray properties of clusters of galaxies provides information on the formation of structure in the universe and on the properties of the universe itself. The cluster luminosity - temperature relation does not evolve strongly, suggesting that the hot X-ray gas had a more complicated thermodynamic history than simply collapsing into the cluster potential well. Cluster X-ray luminosities do evolve. The dependence of this evolution on redshift and luminosity is characterized using two large high redshift samples. Cluster X-ray temperatures also evolve. This evolution constrains the dark matter and dark energy content of the universe as well as other parameters of cosmological interest.
3D point cloud completion, the task of inferring the complete geometric shape from a partial point cloud, has been attracting attention in the community. For acquiring high-fidelity dense point clouds and avoiding uneven distribution, blurred details, or structural loss of existing methods' results, we propose a novel approach to complete the partial point cloud in two stages. Specifically, in the first stage, the approach predicts a complete but coarse-grained point cloud with a collection of parametric surface elements. Then, in the second stage, it merges the coarse-grained prediction with the input point cloud by a novel sampling algorithm. Our method utilizes a joint loss function to guide the distribution of the points. Extensive experiments verify the effectiveness of our method and demonstrate that it outperforms the existing methods in both the Earth Mover's Distance (EMD) and the Chamfer Distance (CD).
Let $r\geq2$ and $r$ be even. An $r$-hypergraph $G$ on $n$ vertices is called odd-colorable if there exists a map $\varphi:[n]\rightarrow\lbrack r]$ such that for any edge $\{j_{1},j_{2},\cdots,j_{r}\}$ of $G$, we have $\varphi(j_{1})+\varphi(j_{2})+\cdot\cdot\cdot+\varphi(j_{r})\equiv r/2(\operatorname{mod}r).$ In this paper, we first determine that, if $r=2^{q}(2t+1)$ and $n\ge 2^{q}(2^{q}-1)r$, then the maximum chromatic number in the class of the odd-colorable $r$-hypergraphs on $n$ vertices is $2^q$, which answers a question raised by V. Nikiforov recently in [V. Nikiforov, Hypergraphs and hypermatrices with symmetric spectrum. Prinprint available in arXiv:1605.00709v2, 10 May, 2016]. We also study some applications of the symmetric spectral property of the odd-colorable $r$-graphs given in that same paper by V. Nikiforov. We show that the Laplacian spectrum and the signless Laplacian spectrum of an $r$-hypergraph $G$ are equal if and only if $G$ is odd-colorable, and then study some further applications of these spectral properties.
We show electrical coherent manipulation of quadrupole-split nuclear spin states in a GaAs/AlGaAs heterostructure on the basis of the breakdown of quantum Hall effect. The electric quadrupole splitting in nuclear spin energy levels is intentionally enhanced by applying an external stress to the heterostructure. Nuclear magnetic resonance spectra with clearly separated triple peaks are obtained, and Rabi oscillations are observed between the nuclear spin energy levels. The decay of the spin-echo signal is compared between the cases before and after the enhancement of quadrupole splitting.
A significant fraction ($\sim 30$ %) of the gamma-ray sources listed in the second $\textit{Fermi}$ LAT (2FGL) catalog is still of unknown origin, being not yet associated with counterparts at lower energies. Using the available information at lower energies and optical spectroscopy on the selected counterparts of these gamma-ray objects we can pinpoint their exact nature. Here we present a pilot project pointing to assess the effectiveness of the several classification methods developed to select gamma-ray blazar candidates. To this end, we report optical spectroscopic observations of a sample of 5 gamma-ray blazar candidates selected on the basis of their infrared WISE colors or of their low-frequency radio properties. Blazars come in two main classes: BL Lacs and FSRQs, showing similar optical spectra except for the stronger emission lines of the latter. For three of our sources the almost featureless optical spectra obtained confirm their BL Lac nature, while for the source WISEJ022051.24+250927.6 we observe emission lines with equivalent width $EW\sim 31$ $\AA$, identifying it as a FSRQ with $z = 0.48$. The source WISEJ064459.38+603131.7, although not featuring a clear radio counterpart, shows a blazar-like spectrum with weak emission lines with $EW \sim 7$ $\AA$, yielding a redshift estimate of $z=0.36$. In addition we report optical spectroscopic observations of 4 WISE sources associated with known gamma-ray blazars without a firm classification or redshift estimate. For all of these latter sources we confirm a BL Lac classification, with a tentative redshift estimate for the source WISEJ100800.81+062121.2 of $z = 0.65$.
We report local roughness exponents, $\alpha_{\text{loc}}$, for three interface growth models in one dimension which are believed to belong the non-linear molecular-beam-epitaxy (nMBE) universality class represented by the Villain-Lais-Das Sarma (VLDS) stochastic equation. We applied an optimum detrended fluctuation analysis (ODFA) [Luis et al., Phys. Rev. E 95, 042801 (2017)] and compared the outcomes with standard detrending methods. We observe in all investigated models that ODFA outperforms the standard methods providing exponents in the narrow interval $\alpha_{\text{loc}}\in[0.96,0.98]$ consistent with renormalization group predictions for the VLDS equation. In particular, these exponent values are calculated for the Clarke-Vvdensky and Das Sarma-Tamborenea models characterized by very strong corrections to the scaling, for which large deviations of these values had been reported. Our results strongly support the absence of anomalous scaling in the nMBE universality class and the existence of corrections in the form $\alpha_{\text{loc}}=1-\epsilon$ of the one-loop renormalization group analysis of the VLDS equation.
We propose a simple statistical model for the density of states for quarks and gluons in a QGP droplet, making the Thomas-Fermi model of the atom and the Bethe-model for the nucleons as templates for constructing the density of states for the quarks and gluons with due modifications for the `hot' relativistic QGP state as against the `cold' non-relativistic atom and nucleons, which were the subject of the earlier `forebears' of the present proposal.We introduce `flow-parameters' $\gamma_{q,g}$ for the quarks and the gluons to take care of the hydrodynamical (plasma) flows in the QGP system as was done earlier by Peshier in his thermal potential for the QGP. By varying $\gamma_{g}$ about the `Peshier-Value' of $\gamma_{q} = 1/6$, we find that the model allows a window in the parametric space in the range $8\gamma_{q} \leq \gamma_{g} \leq 12\gamma_{q}$, with $\gamma_{q} =1/6$ (Peshier-Value), when stable QGP droplets of radii $\sim$ $6 fm$ appear at transition temperatures $100 MeV \leq T \leq 250 MeV$. The smooth cut at the phase boundary of the Free energy vs. droplet radius suggests a First - Order phase transition .On the whole the model offers a robust tool for studying QGP phenomenology as and when data from various ongoing experiments are available .
In this paper, three Computational Topology methods (namely effective homology, persistent homology and discrete vector fields) are mixed together to produce algorithms for homological digital image processing. The algorithms have been implemented as extensions of the Kenzo system and have shown a good performance when applied on some actual images extracted from a public dataset.
We theoretically investigate the influence of gravity on laser light in a hemispherical optical cavity, operating on Earth. The propagation of light in such a cavity is modeled by a Gaussian beam, affected by the Earth's gravitational field. On laboratory scale, this field is described by the spacetime of homogeneous gravity, known as Rindler spacetime. In that spacetime, the beam is bent downwards and acquires a height dependent phase shift. As a consequence the phase fronts of the laser light differ from those of a usual Gaussian beam. Assuming that the initial beam enters the cavity along its symmetry axis, these gravitational effects cause variations of the beam phase with every cavity round trip. Detailed calculations are performed to investigate how these phase variations depend on the beam parameters and the cavity setup. Moreover, we discuss the implications of our findings for cavity calibration techniques and cavity-based laser stabilization procedures.
Galaxy clusters are known to host a variety of extended radio sources: tailed radio galaxies whose shape is modelled by the interaction with the intra-cluster medium (ICM); radio bubbles filling cavities in the ICM distribution and rising buoyantly through the thermal gas; diffuse giant radio sources ("halos" and "relics") revealing the presence of relativistic electrons and magnetic fields in the intra-cluster volume. It is currently the subject of an active debate how the non-thermal components that we observe at radio wavelengths affect the physical properties of the ICM and depend on the dynamical state of galaxy clusters. In this work we start our SKA1 feasibility study of the "radio cluster zoo" through simulations of a typical radio-loud cluster, hosting several bright tailed radio galaxies and a diffuse radio halo. Realistic simulations of SKA1 observations are obtained through the MeqTrees software. A new deconvolution algorithm, based on sparse representations and optimised for the detection of faint diffuse astronomical sources, is tested and compared to the classical CLEAN method.
Associated with every graph $G$ of chromatic number $\chi$ is another graph $G'$. The vertex set of $G'$ consists of all $\chi$-colorings of $G$, and two $\chi$-colorings are adjacent when they differ on exactly one vertex. According to a conjecture of Bj\"{o}rner and Lov\'asz, this graph $G'$ must be disconnected. In this note we give a counterexample to this conjecture.