ShantanuT01/DACTYL-Pretraining huggingface dataset:
I explore the properties of "dark gaps" - regions in quasar absorption spectra without significant transmission - with several simulations from the Cosmic Reionization On Computers (CROC) project. CROC simulations in largest available boxes (120 cMpc) come close to matching both the distribution of mean opacities and the frequency of dark gaps, but alas not in the same model: the run that matches the mean opacities fails to contain enough dark gaps and vice versa.:( Never-the-less, the run that matches the dark gap distributions serves as a counter-example to claims in the literature that the dark gap statistics requires a late end to reionization - in that run reionization ends at z=6.7 (likely too early).   While multiple factors contribute to the frequency of large dark gaps in the simulations, the primary factor that controls the overall shape of the dark gap distribution is the ionization level in voids - the lowest density regions produce the highest transmission spikes that terminate long gaps. As the result, the dark gap distribution correlates strongly with the fraction of the spectrum above the gap detection threshold, the observed distribution is matched by the simulation in which this fraction is 2%. Hence, the gap distribution by itself does not constrain the timing of reionization.
Contribution to a book entitled "Extraterrestrial seismology".
We review the prediction of fission properties of super-heavy elements (SHE) by self-consistent mean-field models thereby concentrating on the widely used Skyrme-Hartree-Fock (SHF) approach. We explain briefly the theoretical tools: the SHF model, the calibration of model parameters together with statistical analysis of uncertainties and correlations, and the involved computation of fission lifetimes. We present an overview of fission stability in comparison to other decay channels over the whole landscape of SHE reaching deep into the $r$-process domain. The main emphasis lies on a detailed discussion of the various ingredients determining eventually the fission properties. The main result is that fission is an involved process which explores many different influences with almost equal share, basic bulk properties (also known as liquid-drop model parameters), pairing strengths, and shell effects. %
The Bose-Einstein condensation (BEC) of photons has been realized in one- and two-dimensional systems. When considering the influence of finite-size effect, the condensation in the one-dimensional fibre is of special interest since such a condensation cannot occur in the thermodynamic limit due to the linear dispersion relation of photons. The finite-size effect must play a key role in this system and needs a detailed description. However, the previous theoretical analysis of finite-size effect is often not accurate enough and only gives the leading-order contribution due to a divergence difficulty. In this paper, by using an analytical continuation method to overcome the divergence difficulty, we give an analytical treatment for the finite-size effect in BEC. The analytical expressions of the critical temperature or critical particle number with higher order correction and the chemical potential below the transition point are presented. Our result shows that in a recent experiment, the deviation between experiment and theory is overestimated, most of which is caused by the inaccurate theoretical treatment of the finite-size effect. By taking into account the next-to-leading correction, we find that the actual deviation is much smaller.
Let $f$ be a primitive Hilbert modular form of parallel weight $2$ and level $N$ for the totally real field $F$, and let $p$ be a rational prime coprime to $2N$. If $f$ is ordinary at $p$ and $E$ is a CM extension of $F$ of relative discriminant $\Delta$ prime to $Np$, we give an explicit construction of the $p$-adic Rankin-Selberg $L$-function $L_{p}(f_E,\cdot)$. When the sign of its functional equation is $-1$, we show, under the assumption that all primes $\wp\vert p$ are principal ideals of ${\mathcal O}_{F}$ which split in ${\mathcal O}_{E}$, that its central derivative is given by the $p$-adic height of a Heegner point on the abelian variety $A$ associated with $f$.   This $p$-adic Gross--Zagier formula generalises the result obtained by Perrin-Riou when $F={\mathbf Q}$ and $(N,E)$ satisfies the so-called Heegner condition. We deduce applications to both the $p$-adic and the classical Birch and Swinnerton-Dyer conjectures for~$A$.
The present paper is a short review of different path integral representations of the partition function of quantum spin systems. To begin with, I consider coherent states for SU(2) algebra. Different parameterizations of the coherent states lead to different path integral representations. They all are unified within an U(1) gauge theory of quantum spin systems.
In a recent paper, Akbary and Wang gave a sufficient condition for x^u + x^r to permute GF(q), in terms of the period of a certain sequence involving sums of cosines. As an application they gave necessary and sufficient conditions in case u,r,q satisfy certain special properties. We show that the Akbary-Wang sufficient condition follows from a more general sufficient condition which does not involve sums of cosines. This leads to vastly simpler proofs of the Akbary-Wang results, as well as generalizations to polynomials of the form x^r*h(x^{(q-1)/d}).
In this note we look into detail at the box-counting dimension of subordinators. Given that $X$ is a non-decreasing Levy process, which is not a compound Poisson process, we show that in the limit, the minimum number of boxes of size $\delta$ that cover the range of $(X_s)_{s\leq t}$ is a.s. of order $t/U(\delta)$, where $U$ is the potential function of $X$. This is a more refined result than the lower and upper index of the box-counting dimension computed in the literature which deals with the asymptotic number of boxes at logarithmic scale.
The detection of vibrational excitations of individual molecules on surfaces by scanning tunneling spectroscopy does not obey strict selection rules but rather propensity rules. The experimental verification of these is challenging because it requires the independent variation of specific parameters, such as the electronic structure, while keeping the vibrational modes the same. Here, we make use of the versatile self-assembled structures of Fe-tetra-pyridyl-porphyrin molecules on a Au(111) surface. These exhibit different energy-level alignments of the frontier molecular orbitals, thus allowing the correlation of electronic structure and detection of vibrations. We identify up to seven vibrational modes in the tunneling spectra of the molecules in some of the arrangements, whereas we observe none in other structures. We find that the presence of vibrational excitations and their distribution along the molecule correlates with the observation of energetically low-lying molecular states. This correlation allows to explain the different numbers of vibrational signatures for molecules embedded within different structures as well as the bias asymmetry of the vibrational intensities within an individual molecule. Our observations are in agreement with a resonant enhancement of vibrations by the virtual excitation of electronic states.
We investigate star formation and dust heating in the compact FIR bright sources detected in the Herschel maps of M83. We use the source extraction code GETSOURCES to detect and extract sources in the FIR, as well as their photometry in the MIR and H{\alpha}. By performing infrared SED fitting and applying an H{\alpha} based star formation rate (SFR) calibration, we derive the dust masses and temperatures, SFRs, gas masses and star formation efficiencies (SFEs). The detected sources lie exclusively on the spiral arms and represent giant molecular associations (GMAs), with gas masses and sizes of 10^6-10^8 solar masses and 200-300 pc, respectively. The inferred parameters show little to no radial dependence and there is only a weak correlation between the SFRs and gas masses, which suggests that more massive clouds are less efficient at forming stars. Dust heating is mainly due to local star formation. However, although the sources are not optically thick, the total intrinsic young stellar population luminosity can almost completely account for the dust luminosity. This suggests that other radiation sources contribute to the dust heating as well and approximately compensate for the unabsorbed fraction of UV light.
In this work we introduce a completely general Chapman Enskog procedure in which we divide the local distribution into an isotropic distribution with anisotropic corrections. We obtain a recursion relation on all integrals of the distribution function required in the derivation of the moment equations. We obtain the hydrodynamic equations in terms only of the first few moments of the isotropic part of an arbitrary local distribution function.   The incompressible limit of the equations is completely independent of the form of the isotropic part of the distribution, whereas the energy equation in the compressible case contains an additional contribution to the heat flux. This additional term was also found by Boghosian and by Potiguar and Costa in the derivation of the Navier Stokes equations for Tsallis thermostatistics, and is the only additional term allowed by the Curie principle.
Classical scalar fields have been proposed as possible candidates for the dark matter component of the universe. Given the fact that super-massive black holes seem to exist at the center of most galaxies, in order to be a viable candidate for the dark matter halo a scalar field configuration should be stable in the presence of a central black hole, or at least be able to survive for cosmological time-scales. In the present work we consider a scalar field as a test field on a Schwarzschild background, and study under which conditions one can obtain long-lived configurations. We present a detailed study of the Klein-Gordon equation in the Schwarzschild spacetime, both from an analytical and numerical point of view, and show that indeed there exist quasi-stationary solutions that can remain surrounding a black hole for large time-scales.
The three concepts of exact, null and approximate controllabilities are analyzed from the exterior of the Moore--Gibson--Thompson equation associated with the fractional Laplace operator subject to the nonhomogeneous Dirichlet type exterior condition.
We study superstring theory in three dimensional Anti-de Sitter spacetime with NS-NS flux, focusing on the case where the radius of curvature is equal to the string length. This corresponds to the critical level k=1 in the Wess-Zumino-Witten description. Previously, it was argued that a transition takes place at this special radius, from a phase dominated by black holes at larger radius to one dominated by long strings at smaller radius. We argue that the infinite tower of modes that become massless at k=1 is a signal of this transition. We propose a simple two-dimensional conformal field theory as the holographic dual to superstring theory at k=1. As evidence for our conjecture, we demonstrate that at large N our putative dual exactly reproduces the full spectrum of the long strings of the weakly coupled string theory, including states unprotected by supersymmetry.
After introducing the notion of BPS preons as the basic constituents of M-theory, we discuss the recent negative results in the search for solutions of the D=10 and D=11 supergravity equations preserving 31/32 supersymmetries i.e., of preonic solutions. The absence of these supergravity preonic solutions may point out to a pure quantum nature of BPS preons, manifesting itself in the need of incorporating quantum (stringy/M-theoretic) corrections to the supergravity equations.
We show that in some cases the coherent state can have a larger violation of the Leggett-Garg inequality (LGI) than the cat state by numerical calculations. To achieve this result, we consider the LGI of the cavity mode weakly coupled to a zero-temperature environment as a practical instance of the physical system. We assume that the bosonic mode undergoes dissipation because of an interaction with the environment but is not affected by dephasing. Solving the master equation exactly, we derive an explicit form of the violation of the inequality for both systems prepared initially in the coherent state $|\alpha\rangle$ and the cat state $(|\alpha\rangle+|-\alpha\rangle)$. For the evaluation of the inequality, we choose the displaced parity operators characterized by a complex number $\beta$. We look for the optimum parameter $\beta$ that lets the upper bound of the inequality be maximum numerically. Contrary to our expectations, the coherent state occasionally exhibits quantum quality more strongly than the cat state for the upper bound of the violation of the LGI in a specific range of three equally spaced measurement times (spacing $\tau$). Moreover, as we let $\tau$ approach zero, the optimized parameter $\beta$ diverges and the LGI reveals intense singularity.
An $(n,s,q)$-graph is an $n$-vertex multigraph where every set of $s$ vertices spans at most $q$ edges. In this paper, we determine the maximum product of the edge multiplicities in $(n,s,q)$-graphs if the congruence class of $q$ modulo ${s\choose 2}$ is in a certain interval of length about $3s/2$. The smallest case that falls outside this range is $(s,q)=(4,15)$, and here the answer is $a^{n^2+o(n^2)}$ where $a$ is transcendental assuming Schanuel's conjecture. This could indicate the difficulty of solving the problem in full generality. Many of our results can be seen as extending work by Bondy-Tuza and F\"uredi-K\"undgen about sums of edge multiplicities to the product setting.   We also prove a variety of other extremal results for $(n,s,q)$-graphs, including product-stability theorems. These results are of additional interest because they can be used to enumerate and to prove logical 0-1 laws for $(n,s,q)$-graphs. Our work therefore extends many classical enumerative results in extremal graph theory beginning with the Erd\H{o}s-Kleitman-Rothschild theorem to multigraphs.
Semi-analytical models of galaxy formation can be used to predict the evolution of the number density of early-type galaxies as a function of the circular velocity at the virial radius, v_{c,vir}. Gravitational lensing probability and separation distribution on the other hand are sensitive to the velocity dispersion (or circular velocity) at about the effective radius. We adopt the singular isothermal ellipsoid (SIE) lens model to estimate the velocity dispersion at the effective radius. We use radio lenses from the Cosmic Lens All-Sky Survey and the PMN-NVSS Extragalactic Lens Survey to study how the velocity dispersions, \sigma_SIE, are related to v_{c,vir}. When we include both the lensing probability and separation distribution as our lensing constraints, we find \sigma_SIE /(200\kms) =   [(1.17_{-0.26}^{+0.40}) v_{c,vir}/ (200\kms)]^{0.22^{+0.05}_{-0.04}} for 200\kms \la \sigma_SIE \la 260\kms; at \sigma_SIE = 200\kms, the ratio \sqrt{2} \sigma_SIE / v_{c,vir} is about 1.65^{+0.57}_{-0.37} (68% CL) but decreases to 0.65_{-0.12}^{+0.15} (68% CL) for \sigma_SIE = 260\kms. These results are consistent with those of Seljak (2002) obtained from galaxy-galaxy weak lensing for galaxies of around L_*. However, our results clearly suggest that the ratio must vary significantly as \sigma_SIE is varied and are marginally discrepant with the Seljak results at \sigma_SIE = 260\kms. The scaling \sigma_SIE \propto v_{c,vir}^{0.22\pm 0.05} is broadly consistent with those from galaxy occupation statistics studies and the most recent galaxy-galaxy weak lensing study. (Abridged)
In the domain of visual tracking, most deep learning-based trackers highlight the accuracy but casting aside efficiency. Therefore, their real-world deployment on mobile platforms like the unmanned aerial vehicle (UAV) is impeded. In this work, a novel two-stage Siamese network-based method is proposed for aerial tracking, \textit{i.e.}, stage-1 for high-quality anchor proposal generation, stage-2 for refining the anchor proposal. Different from anchor-based methods with numerous pre-defined fixed-sized anchors, our no-prior method can 1) increase the robustness and generalization to different objects with various sizes, especially to small, occluded, and fast-moving objects, under complex scenarios in light of the adaptive anchor generation, 2) make calculation feasible due to the substantial decrease of anchor numbers. In addition, compared to anchor-free methods, our framework has better performance owing to refinement at stage-2. Comprehensive experiments on three benchmarks have proven the superior performance of our approach, with a speed of around 200 frames/s.
Estimating black hole masses of blazars is still a big challenge. Because of the contamination of jets, using the previously suggested size -- continuum luminosity relation can overestimate the broad line region (BLR) size and black hole mass for radio-loud AGNs, including blazars. We propose a new relation between the BLR size and $H_{\beta}$ emission line luminosity and present evidences for using it to get more accurate black hole masses of radio-loud AGNs. For extremely radio-loud AGNs such as blazars with weak/absent emission lines, we suggest to use the fundamental plane relation of their elliptical host galaxies to estimate the central velocity dispersions and black hole masses, if their velocity dispersions are not known but the host galaxies can be mapped. The black hole masses of some well-known blazars, such as OJ 287, AO 0235+164 and 3C 66B, are obtained using these two methods and the M - $\sigma$ relation. The implications of their black hole masses on other related studies are also discussed.
We investigate specializations of infinite families of regular Galois extensions over number fields. The problem to what extent the local behaviour of specializations of one single regular Galois extension can be prescribed has been investigated by D\`ebes and Ghazi in the unramified case, and by Legrand, Neftin and the author in general. Here, we generalize these results and give a partial solution to Grunwald problems using Galois extensions arising as specializations of a family of regular Galois extensions.
In a previous work [Dillon and Nakanishi, Eur.Phys.J B 87, 286 (2014)], we numerically calculated the transmission coefficient of the two-dimensional quantum percolation problem and mapped out in detail the three regimes of localization, i.e., exponentially localized, power-law localized, and delocalized which had been proposed earlier [Islam and Nakanishi, Phys.Rev. E 77, 061109 (2008)]. We now consider a variation on quantum percolation in which the hopping integral ($w$) associated with bonds that connect to at least one diluted site is not zero, but rather a fraction of the hopping integral (V=1) between non-diluted sites. We study the latter model by calculating quantities such as the transmission coefficient and the inverse participation ratio and find the original quantum percolation results to be stable for $w>0$ over a wide range of energy. In particular, except in the immediate neighborhood of the band center (where increasing $w$ to just $0.02*V$appears to eliminate localization effects), increasing $w$ only shifts the boundaries between the 3 regimes but does not eliminate them until $w$ reaches 10%-40% of $V$.
We consider univariate distributions with finite moments of all positive orders. The moment problem is to determine whether or not a given distribution is uniquely determined by the sequence of its moments. There is a huge literature on this classical topic. In this survey, we will focus only on the recent developments on the checkable moment-(in)determinacy criteria including Cramer's condition, Carleman's condition, Hardy's condition, Krein's condition and the growth rate of moments, which help us solve the problem more easily. Both Hamburger and Stieltjes cases are investigated. The former is concerned with distributions on the whole real line, while the latter deals only with distributions on the right half-line. Some new results or new simple (direct) proofs of previous criteria are provided. Finally, we review the most recent moment problem for products of independent random variables with different distributions, which occur naturally in stochastic modelling of complex random phenomena.
We present i and z photometry for 25 T dwarfs and one L dwarf. Combined with published photometry, the data show that the i - z, z - Y and z - J colors of T dwarfs are very red, and continue to increase through to the late-type T dwarfs, with a hint of a saturation for the latest types with T_eff ~ 600 K. We present new 0.7-1.0 um and 2.8-4.2 um spectra for the very late-type T dwarf UGPS J072227.51-054031.2, as well as improved astrometry for this dwarf. Examination of the spectral energy distribution using the new and published data, with Saumon & Marley models, shows that the dwarf has T_eff = 505 +/- 10 K, a mass of 3-11 M_Jupiter and an age between 60 Myr and 1 Gyr. This young age is consistent with the thin disk kinematics of the dwarf. The mass range overlaps with that usually considered to be planetary, despite this being an unbound object discovered in the field near the Sun. This apparently young rapid rotator is also undergoing vigorous atmospheric mixing, as determined by the IRAC and WISE-2 4.5 um photometry and the Saumon & Marley models. The optical spectrum for this 500 K object shows clearly detected lines of the neutral alkalis Cs and Rb, which are emitted from deep atmospheric layers with temperatures of 900-1200 K.
The B(E2:0_1^+ -> 2_1^+) values of the Ba isotopes (Z=56) exhibit a sharp increase in deformation as the neutron numbers approach the mid-shell value of N=66. This behavior is anomalous because the 2_1^+ level energies are very similar to those of the neighboring isotopes. By means of the axially-symmetric deformed Woods-Saxon (WS) hamiltonian plus the BCS method, we investigated the systematics of B(E2) of the Ba isotopes. We showed that 15% of the B(E2) values at N=66 was due to the level crossing, occurring at the deformation with beta being nearly 0.3, between the proton orbits originating from the orbits Omega=1/2^-(h11/2) and 9/2^+(g9/2) at zero deformation. The latter of these two was an intruder orbit originating from below the energy gap at Z=50, rising higher in energy with the deformation and intruding the Z=50-82 shell. These two orbits have the largest magnitude of the quadrupole moment with a different sign among the orbits near and below the Fermi surface. Occupancy and non-occupancy of these orbits by protons thus affect B(E2:0_1^+ -> 2_1^+) significantly.
Observations of the Milky Way by the SPI/INTEGRAL satellite have confirmed the presence of a strong 511 KeV gamma-ray line emission from the bulge, which require an intense source of positrons in the galactic center. These observations are hard to account for by conventional astrophysical scenarios, whereas other proposals, such as light DM, face stringent constraints from the diffuse gamma-ray background. Here we suggest that light superconducting strings could be the source of the observed 511 KeV emission. The associated particle physics, at the ~ 1 TeV scale, is within reach of planned accelerator experiments, while the distinguishing spatial distribution, proportional to the galactic magnetic field, could be mapped by SPI or by future, more sensitive, satellite missions.