ShantanuT01/DACTYL-Pretraining huggingface dataset:
A system of an array of side-coupled quantum-dots attached to a quantum wire is studied theoretically. Transport through the quantum wire is investigated by means of a noninteracting Anderson tunneling Hamiltonian. Analytical expressions of the transmission probability and phase are given. The transmission probability shows an energy spectrum with forbidden and allowed bands that depends on the up-down asymmetry of the system. In up-down symmetry only the gap survives, and in up-down asymmetry an allowed band is formed. We show that the allowed band arises by the indirect coupling between the up and down quantum dots. In addition, the band edges can be controlled by the degree of asymmetry of the quantum dots. We discuss the analogy between this phenomenon with the Dicke effect in optics.
We prove vanishing results for unramified stable cohomology of finite groups of Lie type.
The Fermi Large Area Telescope (LAT) is the most sensitive instrument ever deployed in space for observing gamma-ray emission >100 MeV. This sensitivity has enabled the LAT to detect gamma-ray emission from the Sun during quiescent periods from pions produced by cosmic-ray protons interacting in the solar atmosphere and from cosmic-ray electrons interacting with solar optical photons. The LAT has detected high-energy gamma-ray emission associated with GOES M-class and X-class X-ray flares accompanied by coronal mass ejections and solar energetic particle events. In a number of cases, LAT has detected gamma rays with energies up to several hundreds of MeV during the impulsive phase and gamma rays up to GeV energies sustained for several hours after the impulsive phase. This presentation focuses on observations in the impulsive emission phase in solar flares, including the modest GOES M2-class flare at SOL2010-06-12T0057 and more recent detections, such as the bright X-class flares of March 2012.
In this paper we consider a class of gradient systems of type $$ -c_i \Delta u_i + V_i(x)u_i=P_{u_i}(u),\quad u_1,..., u_k>0 \text{in}\Omega, \qquad u_1=...=u_k=0 \text{on} \partial \Omega, $$ in a bounded domain $\Omega\subseteq \R^N$. Under suitable assumptions on $V_i$ and $P$, we prove the existence of ground-state solutions for this problem. Moreover, for $k=2$, assuming that the domain $\Omega$ and the potentials $V_i$ are radially symmetric, we prove that the ground state solutions are foliated Schwarz symmetric with respect to antipodal points. We provide several examples for our abstract framework.
We give two variational formulas (qVar1) and (qVar2) for the quenched free energy of a random walk in random potential (RWRP) when (i) the underlying walk is directed or undirected, (ii) the environment is stationary and ergodic, and (iii) the potential is allowed to depend on the next step of the walk which covers random walk in random environment (RWRE). In the directed i.i.d. case, we also give two variational formulas (aVar1) and (aVar2) for the annealed free energy of RWRP. These four formulas are the same except that they involve infima over different sets, and the first two are modified versions of a previously known variational formula (qVar0) for which we provide a short alternative proof. Then, we show that (qVar0) always has a minimizer, (aVar2) never has any minimizers unless the RWRP is an RWRE, and (aVar1) has a minimizer if and only if the RWRP is in the weak disorder regime. In the latter case, the minimizer of (aVar1) is unique and it is also the unique minimizer of (qVar1), but (qVar2) has no minimizers except for RWRE. In the case of strong disorder, we give a sufficient condition for the nonexistence of minimizers of (qVar1) and (qVar2) which is satisfied for the log-gamma directed polymer with a sufficiently small parameter. We end with a conjecture which implies that (qVar1) and (qVar2) have no minimizers under very strong disorder.
The question how the extremal values of a stochastic process achieved on different time intervals are correlated to each other has been discussed within the last few years on examples of the running maximum of a Brownian motion, of a Brownian Bridge and of a Slepian process. Here, we focus on the two-time correlations of the running range of Brownian motion - the maximal extent of a Brownian trajectory on a finite time interval. We calculate exactly the covariance function of the running range and analyse its asymptotic behaviour. Our analysis reveals non-trivial correlations between the value of the largest descent (rise) of a BM from the top to a bottom on some time interval, and the value of this property on a larger time interval.
Rapid variability of the TeV emission in several blazars implies a central black hole mass $M_{BH}<10^8M_\odot$, appreciably smaller than the values estimated from the $M_{BH}-L_{bulg}$ relation, and Doppler factors for the $\gamma$-ray emitting fluid much larger than those associated with radio patterns. We discuss the conditions in the central engine required to account for the short timescales and large luminosities observed, and propose some explanations for the inferred kinematics of the source on various scales.
The existence of quantized vibrations is utilized to explain narrow nucleon resonances below the pion threshold. A Goldstone boson with a mass of 35 MeV is derived from the experimental dibaryon masses. The quantum of 35 MeV is recognized as part of the Nambu empirical mass series. We present a few explanations to suggest why this light boson is difficult to locate in experiments. The KARMEN timing anomaly is discussed. The vibration-rotational model of elementary particles is reviewed in regards to the Diakonov-Petrov argument against mixing of these modes. The existence of a theta(1640)D03 partner to the theta(1540)+ is predicted.
We construct vertex operators for massless higher spin fields in RNS superstring theory and compute some of their three-point correlators, describing gauge-invariant cubic interactions of the massless higher spins. The Fierz-Pauli on-shell conditions for the higher spins (including tracelessness and vanishing divergence) follow from the BRST-invariance conditions for the vertex operators constructed in this paper. The gauge symmetries of the massless higher spins emerge as a result of the BRST nontriviality conditions for these operators, being equivalent to transformations with the traceless gauge parameter in the Fronsdal's approach. The gauge invariance of the interaction terms of the higher spins is therefore ensured automatically by that of the vertex operators in string theory. We develop general algorithm to compute the cubic interactions of the massless higher spins and use it to explicitly describe the gauge-invariant interaction of two $s=3$ and one $s=4$ massless particles.
We develop a new analysis method that allows us to compare multi-dimensional observables to a theoretical model. The method is based on unsupervised clustering algorithms which assign the observational and simulated data to clusters in high dimensionality. From the clustering result, a goodness of fit (the p-value) is determined with the Fisher-Freeman-Halton test. We first show that this approach is robust for 2D Gaussian distributions. We then apply the method to the observed MW satellites and simulated satellites from the fiducial model of our semi-analytic code A-SLOTH. We use the following 5 observables of the galaxies in the analysis: stellar mass, virial mass, heliocentric distance, mean stellar metallicity [Fe/H], and stellar metallicity dispersion {\sigma}[Fe/H]. A low p-value returned from the analysis tells us that our A-SLOTH fiducial model does not reproduce the mean stellar metallicity of the observed MW satellites well. We implement an ad-hoc improvement to the physical model and show that the number of dark matter merger trees which have p-values > 0.01 increases from 3 to 6. This method can be extended to data with higher dimensionality easily. We plan to further improve the physical model in A-SLOTH using this method to study elemental abundances of stars in the observed MW satellites.
We analyze a sample of 30,000 nearby obscured AGNs with optical spectra from SDSS and mid-IR photometry from WISE. Our aim is to investigate the AGN host galaxy properties with mid-IR luminosities as AGN activity indicator, and to compare with previous studies based on [OIII] emission lines. First we find that the [3.4] - [4.6] colour has weak dependence on host stellar age, but strong dependence on AGN activity. We then use a "pair-matching" technique to subtract the host 4.6 micron contribution. By combining Seyferts with a sample of SDSS quasars at z < 0.7, we show that the [OIII] and the intrinsic AGN 4.6 micron luminosities correlate roughly linearly over 4 orders of magnitude, but with substantial scatter. We also compare the partition functions of the total integrated 4.6 micron and [OIII] line luminosities from Seyferts and a sub-population of LINERs with significant nuclear 4.6 micron emission, as function of a variety of host galaxy properties, finding that they are identical. We conclude, therefore, that [OIII] as an AGN indicator shows no particular biases as compared to the 4.6 micron luminosity. Our results also demonstrate that some LINERs do fit in with the expectations of the simple Unified Model.
It is very useful and increasingly popular to extract accurate road centerlines from very-high-resolution (VHR) re- mote sensing imagery for various applications, such as road map generation and updating etc. There are three shortcomings of current methods: (a) Due to the noise and occlusions (owing to vehicles and trees), most road extraction methods bring in heterogeneous classification results; (b) Morphological thinning algorithm is widely used to extract road centerlines, while it pro- duces small spurs around the centerlines; (c) Many methods are ineffective to extract centerlines around the road intersections. To address the above three issues, we propose a novel method to ex- tract smooth and complete road centerlines via three techniques: the multiscale joint collaborative representation (MJCR) & graph cuts (GC), tensor voting (TV) & non-maximum suppression (NMS) and fitting based connection algorithm. Specifically, a MJCR-GC based road area segmentation method is proposed by incorporating mutiscale features and spatial information. In this way, a homogenous road segmentation result is achieved. Then, to obtain a smooth and correct road centerline network, a TV-NMS based centerline extraction method is introduced. This method not only extracts smooth road centerlines, but also connects the discontinuous road centerlines. Finally, to overcome the ineffectiveness of current methods in the road intersection, a fitting based road centerline connection algorithm is proposed. As a result, we can get a complete road centerline network. Extensive experiments on two datasets demonstrate that our method achieves higher quantitative results, as well as more satisfactory visual performances by comparing with state-of-the- art methods.
We study the evolution of gene frequencies in a population living in $\mathbb{R}^d$, modelled by the spatial Lambda Fleming-Viot process with natural selection (Barton, Etheridge and Veber, 2010 and Etheridge, Veber and Yu, 2014). We suppose that the population is divided into two genetic types, $a$ and $A$, and consider the proportion of the population which is of type $a$ at each spatial location. If we let both the selection intensity and the fraction of individuals replaced during reproduction events tend to zero, the process can be rescaled so as to converge to the solution to a reaction-diffusion equation (typically the Fisher-KPP equation, as in Etheridge, Veber and Yu, 2014). We show that the rescaled fluctuations converge in distribution to the solution to a linear stochastic partial differential equation. Depending on whether offspring dispersal is only local or if large scale extinction-recolonization events are allowed to take place, the limiting equation is either the stochastic heat equation with a linear drift term driven by space-time white noise or the corresponding fractional heat equation driven by a coloured noise which is white in time. If individuals are diploid (i.e. either $AA$, $Aa$ or $aa$) and if natural selection favours heterozygous ($Aa$) individuals, a stable intermediate gene frequency is maintained in the population. We give estimates for the asymptotic effect of random fluctuations around the equilibrium frequency on the local average fitness in the population. In particular, we find that the size of this effect - known as the drift load - depends crucially on the dimension $d$ of the space in which the population evolves, and is reduced relative to the case without spatial structure.
The physics of radio emission from cosmic-ray induced air showers is shortly summarized. It will be shown that the radio signal at different distances from the shower axis provides complementary information on the longitudinal shower evolution, in particular the early part, and on the distribution of the electrons in the shower core. This complements the information obtained from surface, fluorescence, and muon detectors and is very useful in getting a comprehensive picture of an air shower.
A brief review of the attempts to define ``elements of reality'' in the framework of quantum theory is presented. It is noted that most definitions of elements of reality have in common the feature to be a definite outcome of some measurement. Elements of reality are extended to pre- and post-selected systems and to measurements which fulfill certain criteria of weakness of the coupling. Some features of the newly introduced concepts are discussed.
We report the results of comprehensive study of the critical dynamics of the prototype perovskite antiferroelectric PbZrO$_3$. The combination of inelastic X-ray and diffuse X-ray scattering techniques and Brillouin light scattering was used. It is found that the dispersion of the TA phonons is strongly anisotropic. The dispersion curve of the in-plane polarized TA phonons propagating in [1 1 0] direction demonstrates pronounced softening. Slowing down of the excitations at R-point is found, it is manifested in growing of the central peak. This slowing down is too weak to be considered as a primary origin of the corresponding order parameter. Obtained results are treated in terms of TA--TO flexoelectric mode coupling. It is demonstrated that the structural phase transformation in PbZrO$_3$ can be considered as the result of the only intrinsic instability associated with the ferroelectric soft mode.
We prove global existence and scattering for the defocusing, cubic nonlinear Schr\"odinger equation in $H^s(\rr^3)$ for $s > {4/5}$. The main new estimate in the argument is a Morawetz-type inequality for the solution $\phi$. This estimate bounds $\|\phi(x,t)\|_{L^4_{x,t}(\rr^3 \times \rr)}$, whereas the well-known Morawetz-type estimate of Lin-Strauss controls $\int_0^{\infty}\int_{\rr^3}\frac{(\phi(x,t))^4}{|x|} dx dt
We use A_{infinity}-formalism to study variation of cohomology spaces under formal deformations of coherent sheaves on projective varieties. As an application we describe formal neighborhoods of twisted Brill-Noether loci at some points. Another application is a computation of the Fourier-Mukai transform of some natural line bundles on symmetric powers of a curve.
The theory of regularity structures enables the definition of the following parabolic Anderson model in a very rough environment: $\partial_{t} u_{t}(x) = \frac12 \Delta u_{t}(x) + u_{t}(x) \, \dot W_{t}(x)$, for $t\in\mathbb{R}_{+}$ and $x\in \mathbb{R}^{d}$, where $\dot W_{t}(x)$ is a Gaussian noise whose space time covariance function is singular. In this rough context, we shall give some information about the moments of $u_{t}(x)$ when the stochastic heat equation is interpreted in the Skorohod as well as the Stratonovich sense. Of special interest is the critical case, for which one observes a blowup of moments for large times.
The plasma contributing to emission from the Sun between the cool chromosphere ($\le 10^4$K) and hot corona ($\ge 10^6$K) has been subjected to many different interpretations. Here we look at the magnetic structure of this transition region (TR) plasma, based upon the implications of CLASP2 data of an active region recently published by Ishikawa et al., and earlier IRIS and SDO data of quiet regions. Ishikawa et al. found that large areas of sunspot plages are magnetically unipolar as measured in the cores of \ion{Mg}{2} resonance lines, formed in the lower transition region under low plasma-$\beta$ conditions. Here we show that IRIS images in the line cores have fibrils which well aligned with the overlying coronal loop segments seen in the 171 \AA{} channel of SDO. When the TR emission in active regions arise from plasma magnetically and thermally connected to the corona, then the line cores can provide the first credible magnetic boundary conditions for force-free calculations extended to the corona. We also re-examine IRIS images of dynamic TR cool loops previously reported as a major contributor to transition region emission from the quiet Sun. Dynamic cool loops contribute only a small fraction of the total TR emission from the quiet Sun.
We establish a congruence satisfied by the integer group determinants for the non-abelian Heisenberg group of order $p^3$. We characterize all determinant values coprime to $p$, give sharp divisibility conditions for multiples of $p$, and determine all values when $p=3$. We also provide new sharp conditions on the power of $p$ dividing the group determinants for $\mathbb Z_p^2$.   For a finite group, the integer group determinants can be understood as corresponding to Lind's generalization of the Mahler measure. We speculate on the Lind-Mahler measure for the discrete Heisenberg group and for two other infinite non-abelian groups arising from symmetries of the plane and 3-space.
The distribution of the muon content of highly inclined Monte Carlo cosmic ray showers is affected by the influence of Earth's geomagnetic field. It is found that the shapes of the positive and negative muon distributions get affected/modified by the influence of the Earth's geomagnetic field. Such a correlation between the earth's geomagnetic activity and the cosmic ray (CR) air shower muons is found sensitive to the primary cosmic ray mass composition.
We examine length measurement in curved spacetime, based on the 1+3-splitting of a local observer frame. This situates extended objects within spacetime, in terms of a given coordinate which serves as an external reference. The radar metric is shown to coincide with the spatial projector, but these only give meaningful results on the observer's 3-space, where they reduce to the metric. Examples from Schwarzschild spacetime are given.
We present a general self-consistent lepto/hadronic jet model for the non-thermal electromagnetic emission of microquasars. The model is applied to the low-mass microquasar (LMMQ) GX 339-4 and predicts its high-energy features. We assume that both leptons and hadrons are accelerated up to relativistic energies by diffusive shock acceleration, and calculate their contribution to the electromagnetic spectrum through all main radiative processes. The radiative contribution of secondary particles (pions, muons and electron-positron pairs) is included. We use a set of simultaneous observations in radio and X-rays to constrain the model parameters and find the best fit to the data. We obtain different spectral energy distributions that can explain the observations, and make predictions for the high-energy emission. Observations with gamma-ray instruments like Fermi can be used to test the model and determine the proton content of the jets. Finally, we estimate the positron injection in the surrounding medium. Our findings support the suggested association between LMMQs and the observed distribution of the 511 keV line flux observed by INTEGRAL.
A new analysis of the radiatively generated, LO quark (u,d,s,c,b) and gluon densities in the real, unpolarized photon, improved in respect to our paper [1], is presented. We perform four new global fits to the experimental data for F2^gamma, two using a standard FFNS approach and two based on ACOT(chi) scheme [2], leading to the FFNS(CJK) and CJK models. We also present the analysis of the uncertainties of the new CJK 2 parton distributions due to the experimental errors, the very first such analysis performed for the photon. This analysis is based on the Hessian method, for a comparison for chosen cross-sections we use also the Lagrange method.
Context: With the launch of space missions devoted to asteroseismology (like COROT), the scientific community will soon have accurate measurements of pulsation frequencies in many rapidly rotating stars.   Aims: The present work focuses on the effects of rotation on pulsations of rapidly rotating stars when both the Coriolis and centrifugal accelerations require a non-perturbative treatment.   Method: We develop a 2-dimensional spectral numerical approach which allows us to compute acoustic modes in centrifugally distorted polytropes including the full influence of the Coriolis force. This method is validated through comparisons with previous studies, and the results are shown to be highly accurate.   Results: In the frequency range considered and with COROT's accuracy, we establish a domain of validity for perturbative methods, thus showing the need for complete calculations beyond v.sin i = 50 km/s for a R = 2.3 R_\odot, M = 1.9 M_\odot polytropic star. Furthermore, it is shown that the main differences between complete and perturbative calculations come essentially from the centrifugal distortion.
Identifying different objects (man and cup) is an important problem on its own, but identifying the relationship between them (holding) is critical for many real world use cases. This paper describes an approach to reduce a visual relationship detection problem to object detection problems. The method was applied to Google AI Open Images V4 Visual Relationship Track Challenge, which was held in conjunction with 2018 European Conference on Computer Vision (ECCV 2018) and it finished as a prize winner. The challenge was to build an algorithm that detects pairs of objects in particular relations: things like "woman playing guitar," "beer on table," or "dog inside car.".
For an $r$-uniform hypergraph $H$ and a family of $r$-uniform hypergraphs $\mathcal{F}$, the relative Tur\'{a}n number $\mathrm{ex}(H,\mathcal{F})$ is the maximum number of edges in an $\mathcal{F}$-free subgraph of $H$. In this paper we give lower bounds on $\mathrm{ex}(H,\mathcal{F})$ for certain families of hypergraph cycles $\mathcal{F}$ such as Berge cycles and loose cycles. In particular, if $\mathcal{C}_\ell^3$ denotes the set of all $3$-uniform Berge $\ell$-cycles and $H$ is a 3-uniform hypergraph with maximum degree $\Delta$, we prove \[\mathrm{ex}(H,\mathcal{C}_4^{3})\ge \Delta^{-3/4-o(1)}e(H),\] \[\mathrm{ex}(H,\mathcal{C}_5^{3})\ge \Delta^{-3/4-o(1)}e(H),\] and these bounds are tight up to the $o(1)$ term.
After recalling several constructions of the moduli space of curves of genus zero by different people we give our alternative construction of the moduli space. This gives a simple description of the intersection ring of this space. We give a basis for the Chow groups and an explicit duality between the Chow groups in complementary degrees. There is a recursive description of this algebra by S. Keel. Our presentation is simpler in the sense that there are fewer generators and fewer relations and our description is explicit.