ShantanuT01/DACTYL-Pretraining huggingface dataset:
The focus of this chapter lies on the possible experimental tests of leptogenesis scenarios. We consider both leptogenesis generated from oscillations, as well as leptogenesis from out-of-equilibrium decays. As the Akhmedov-Rubakov-Smirnov (ARS) mechanism allows for heavy neutrinos in the GeV range, this opens up a plethora of possible experimental tests, e.g. at neutrino oscillation experiments, neutrinoless double beta decay, and direct searches for neutral heavy leptons at future facilities. In contrast, testing leptogenesis from out-of-equilibrium decays is a quite difficult task. We comment on the necessary conditions for having successful leptogenesis at the TeV-scale. We further discuss possible realizations and their model specific testability in extended seesaw models, models with extended gauge sectors, and supersymmetric leptogenesis. Not being able to test high-scale leptogenesis directly, we present a way to falsify such scenarios by focusing on their washout processes. This is discussed specifically for the left-right symmetric model and the observation of a heavy $W_R$, as well as model independently when measuring $\Delta L = 2$ washout processes at the LHC or neutrinoless double beta decay.
We present a magnetization measurement probing the transition from a quantum Hall to insulating (QH-I) state for a two-dimensional electron gas in a disordered GaAs/AlGaAs heterostructure. Using a highly sensitive DC torque magnetometer, we discover an abrupt change in the orbital magnetization precisely at the critical point for the QH-I transition. Since this transition is predicted to be a second order quantum phase transition, a thermodynamic signature in magnetization is totally unexpected. The observed feature is reminiscent of the well-known de Haas-van Alphen oscillations arising from discontinuous jumps of the chemical potential as Landau Levels are successively populated.
The long time behavior of solutions to the defocusing modified Korteweg-de vries (MKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach is based on the nonlinear steepest descent method of Deift and Zhou and its reformulation by Dieng and McLaughlin through $\overline{\partial}$-derivatives. To extend the asymptotics to solutions with initial data in lower regularity spaces, we apply a global approximation via PDE techniques.
We study the uniform time reversal invariant $U(1)$ quantum spin liquid (QSL) with low energy fermionic quasi-particles for rare earth pyrochlore magnets and explore its magnetic instability employing an augmented fermionic parton mean field theory approach. Self consistent calculations stabilise an uniform $U(1)$ QSL with both gapped and gapless parton excitations as well as fractionalised magnetically ordered phases in an experimentally relevant part of the phase diagram near the classical phase boundaries of the magnetically ordered phases. The gapped QSL has a band-structure with a non-zero $Z_2$ topological invariant. The fractionalised magnetic ordered phases bears signature of both QSL through fermionic excitations as well as magnetic order. Thus this provides a possible way to understand the unconventional diffuse neutron scattering in rare-earth pyrochlores such as Yb$_2$Ti$_2$O$_7$, Er$_2$Sn$_2$O$_7$ and Er$_2$Pt$_2$O$_7$ at low/zero external magnetic fields. We calculate the dynamic spin structure factor to understand the nature of the diffuse two-particle continuum.
The ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model with spatially anisotropic couplings on a square lattice are investigated by a spin-rotation-invariant Green's-function approach and by Lanczos diagonalizations on lattices up to 36 sites supplemented by finite-size scaling. We focus on the anisotropy-driven transition from the N\'eel state to a paramagnetic state with antiferromagnetic short-range order and on the spatial dependence of spin correlation functions. Our principal result is that a rather sharp crossover in the magnetic behavior occurs at the coupling ratio $R_0\simeq 0.2$ ($R=J_y/J_x$).
We consider the linear stochastic wave equation driven by a Gaussian noise. We show that the solution satisfies a certain form of strong local nondeterminism and we use this property to derive the exact uniform modulus of continuity for the solution.
In this review, we describe our current understanding of cluster formation: from the general picture of collapse from initial density fluctuations in an expanding Universe to detailed simulations of cluster formation including the effects of galaxy formation. We outline both the areas in which highly accurate predictions of theoretical models can be obtained and areas where predictions are uncertain due to uncertain physics of galaxy formation and feedback. The former includes the description of the structural properties of the dark matter halos hosting cluster, their mass function and clustering properties. Their study provides a foundation for cosmological applications of clusters and for testing the fundamental assumptions of the standard model of structure formation. The latter includes the description of the total gas and stellar fractions, the thermodynamical and non-thermal processes in the intracluster plasma. Their study serves as a testing ground for galaxy formation models and plasma physics. In this context, we identify a suitable radial range where the observed thermal properties of the intra-cluster plasma exhibit the most regular behavior and thus can be used to define robust observational proxies for the total cluster mass. We put particular emphasis on examining assumptions and limitations of the widely used self-similar model of clusters. Finally, we discuss the formation of clusters in non-standard cosmological models, such as non-Gaussian models for the initial density field and models with modified gravity, along with prospects for testing these alternative scenarios with large cluster surveys in the near future.
We explore the accretion states of tidal disruption events (TDEs) using a sample of 7 X- ray bright sources. To this end, we estimate the relative contribution of the disk and corona to the observed X-ray emission through spectral modeling, and assess the X-ray brightness (through ${\alpha}$_ox, L$_{2 keV}$ and f$_{Edd,X}$) as a function of the Eddington ratio. We report strong positive correlations between ${\alpha}$_ox and f$_{Edd,bol}$; f$_{Edd,X}$ and f$_{Edd,UV}$ ; and an anti-correlation for L$_{2 keV}$ and f$_{Edd,UV}$. TDEs at high f$_{Edd,bol}$ have thermal dominated X-ray spectra and high (soft) ${\alpha}$_ox, whereas those at low f$_{Edd,bol}$ show a significant power-law contribution and low (hard) ${\alpha}$_ox. Similar to X-ray binaries and active galactic nuclei, the transition between X-ray spectral states occurs around f$_{Edd,bol}$ ${\approx}$ 0.03, although the uncertainty is large due to the small sample size. Our results suggest that X-ray surveys are more likely to discover TDEs at low f$_{Edd,bol}$, whereas optical surveys are more sensitive to TDEs at high Eddington ratios. The X-ray and optical selected TDEs have different UV and X-ray properties, which should be taken into account when deriving rates, luminosity and black hole mass functions. TDEs around the most massive supermassive black holes are observed in the hard state; this could indicate that TDE evolution is faster around more massive BHs.
Taking advantage of human pose data for understanding human activities has attracted much attention these days. However, state-of-the-art pose estimators struggle in obtaining high-quality 2D or 3D pose data due to occlusion, truncation and low-resolution in real-world un-annotated videos. Hence, in this work, we propose 1) a Selective Spatio-Temporal Aggregation mechanism, named SST-A, that refines and smooths the keypoint locations extracted by multiple expert pose estimators, 2) an effective weakly-supervised self-training framework which leverages the aggregated poses as pseudo ground-truth instead of handcrafted annotations for real-world pose estimation. Extensive experiments are conducted for evaluating not only the upstream pose refinement but also the downstream action recognition performance on four datasets, Toyota Smarthome, NTU-RGB+D, Charades, and Kinetics-50. We demonstrate that the skeleton data refined by our Pose-Refinement system (SSTA-PRS) is effective at boosting various existing action recognition models, which achieves competitive or state-of-the-art performance.
We consider static axially symmetric Einstein-Yang-Mills black holes in the isolated horizon formalism. The mass of these hairy black holes is related to the mass of the corresponding particle-like solutions by the horizon mass. The hairy black holes violate the ``quasi-local uniqueness conjecture'', based on the horizon charges.
A well-known observation of Serre and Tate is that the Hecke algebra acts locally nilpotently on modular forms mod 2 on $\mathrm{SL}_2(\mathbb{Z})$. We give an algorithm for calculating the degree of Hecke nilpotency for cusp forms, and we obtain a formula for the total number of cusp forms mod 2 of any given degree of nilpotency. Using these results, we find that the degrees of Hecke nilpotency in spaces $M_k$ have no limiting distribution as $k \rightarrow \infty$. As an application, we study the parity of the partition function using Hecke nilpotency.
Motivated from time-inconsistent stochastic control problems, we introduce a new type of coupled forward-backward stochastic systems, namely, flows of forward-backward stochastic differential equations. They are systems consisting of a single forward SDE and a continuum of BSDEs, which are defined on different time-intervals and connected via an equilibrium condition. We formulate a notion of equilibrium solutions in a general framework and prove small-time well-posedness of the equations. We also consider discretized flows and show that their equilibrium solutions approximate the original one, together with an estimate of the convergence rate.
This work is a contribution to the understanding of the electrical resistivity in strontium ferromolybdate (SFMO) ceramics. It demonstrates that an appropriate thermal treatment leads to the formation of dielectric SrMoO4 shells at the surface of SFMO nanograins. In samples without SrMoO4 shells, the sign of the temperature coefficient of resistance changes with increasing temperature from negative at very low temperature to positive at higher temperatures. Samples exhibiting a negative temperature coefficient contain SrMoO4 shells and demonstrate a behavior of the resistivity that can be described in terms of the fluctuation-induced tunneling model, and near room temperature the conductivity mechanism converts to a variable-range hopping one. The results of this work serve as a starting point for the understanding of the low-field magnetoresistance which is very promising for spintronic device application.
Hardy's proof is considered the simplest proof of nonlocality. Here we introduce an equally simple proof that (i) has Hardy's as a particular case, (ii) shows that the probability of nonlocal events grows with the dimension of the local systems, and (iii) is always equivalent to the violation of a tight Bell inequality.
In this article we initiate the mathematical study of the dynamics of a system of nonlinear Partial Differential Equations modelling the motion of incompressible, isothermal and conducting modified bipolar fluids in presence of magnetic field. We mainly prove the existence of weak solutions to the model. We also prove the existence of a trajectory attractor to the translation semigroup acting on the trajectories of the set of weak solutions and that of external forces. Some results concerning the structure of this trajectory attractor are also given. The results from this paper may be useful in the investigation of some system of PDEs arising from the coupling of incompressible fluids of $p$-structure and the Maxwell equations.
We propose a contraction of the de Sitter quantum group leading to the quantum Poincare group in any dimensions. The method relies on the coaction of the de Sitter quantum group on a non--commutative space, and the deformation parameter $q$ is sent to one. The bicrossproduct structure of the quantum Poincar\'e group is exhibited and shown to be dual to the one of the $\kappa$--Poincar\'e Hopf algebra, at least in two dimensions.
On account of its polarizability and magnetic field sensitivity, as well as the role of neutral helium in partially ionized solar environments, the neutral helium triplet (orthohelium) system provides important, yet under-utilized, diagnostics of solar coronal rain. This work describes off-limb observations of coronal rain in NOAA Active Region 12468 obtained in the He I 10830 $\AA$ triplet using the Massively MultipleXed Imaging Spectrograph experiment at the Dunn Solar Telescope along with co-temporal observations from NASA's Solar Dynamics Observatory and the Interface Region Imaging Spectrograph. We detect rain simultaneously in the IRIS 1400 $\AA$ and 2796 $\AA$ channels and in He I 10830 $\AA$. The large degree of spatial coherence present between all channels agrees with previous observations of the multi-thermal nature of coronal rain. A statistical analysis of He I spectral profiles for rain identified via automated detection indicate He I line radiances are, on average, $10^{4}$ ergs cm$^{-2}$ s$^{-1}$ sr$^{-1}$; the average translational velocity is 70 km s$^{-1}$ and Doppler widths are distributed around 10 km s$^{-1}$. Based on these results, forward models of expected He I polarized signals allow us to estimate, using synthetic observables and an inversion algorithm including fits for the scattering angle constraining the material's location along-the-line of sight, the magnetic sensitivity of the upcoming National Science Foundation's Daniel K. Inouye Solar Telescope. We predict joint observations of the He I 10830 $\AA$ and 5876 $\AA$ multiplets, using first-light instrumentation, will provide inverted magnetic field errors of $\pm3.5$ G ($2\sigma$) for spatial scales of $0.5''$ ($\sim360$ km) assuming dynamically-limited integration times of 5.5 seconds.
In this paper we consider the curves $C_k^{(p,a)} : y^p-y=x^{p^k+1}+ax$ defined over $\mathbb F_p$ and give a positive answer to a conjecture about a divisibility condition on $L$-polynomials of the curves $C_k^{(p,a)}$. Our proof involves finding an exact formula for the number of $\mathbb F_{p^n}$-rational points on $C_k^{(p,a)}$ for all $n$, and uses a result we proved elsewhere about the number of rational points on supersingular curves.
Crowd behavior understanding is crucial yet challenging across a wide range of applications, since crowd behavior is inherently determined by a sequential decision-making process based on various factors, such as the pedestrians' own destinations, interaction with nearby pedestrians and anticipation of upcoming events. In this paper, we propose a novel framework of Social-Aware Generative Adversarial Imitation Learning (SA-GAIL) to mimic the underlying decision-making process of pedestrians in crowds. Specifically, we infer the latent factors of human decision-making process in an unsupervised manner by extending the Generative Adversarial Imitation Learning framework to anticipate future paths of pedestrians. Different factors of human decision making are disentangled with mutual information maximization, with the process modeled by collision avoidance regularization and Social-Aware LSTMs. Experimental results demonstrate the potential of our framework in disentangling the latent decision-making factors of pedestrians and stronger abilities in predicting future trajectories.
Magnetoconductance of a gated two-dimensional electron gas (2DEG) in the inversion layer on p-type HgCdTe crystal is investigated. At strong magnetic fields, characteristic features such as quantum Hall effect of a 2DEG with single subband occupation are observed. At weak magnetic fields, weak antilocalization effect in ballistic regime is observed. Phase coherence time and zero-field spin-splitting are extracted according to Golub's model. The temperature dependence of dephasing rate is consistent with Nyquist mechanism including both singlet and triplet channel interactions.
We investigate the Brown-York stress tensor for curvature-squared theories. This requires a generalized Gibbons-Hawking term in order to establish a well-posed variational principle, which is achieved in a universal way by reducing the number of derivatives through the introduction of an auxiliary tensor field. We examine the boundary stress tensor thus defined for the special case of `massive gravity' in three dimensions, which augments the Einstein-Hilbert term by a particular curvature-squared term. It is shown that one obtains finite results for physical parameters on AdS upon adding a `boundary cosmological constant' as a counterterm, which vanishes at the so-called chiral point. We derive known and new results, like the value of the central charges or the mass of black hole solutions, thereby confirming our prescription for the computation of the stress tensor. Finally, we inspect recently constructed Lifshitz vacua and a new black hole solution that is asymptotically Lifshitz, and we propose a novel and covariant counterterm for this case.
In his fresh "Comment" (arXiv:0711.0137v1), A. Mostafazadeh reacts on my very recent letter (arXiv:0710.5653v1) where I tried to clarify certain misunderstandings which occurred in A. M., Phys. Lett. B \textbf{650}, 208 (2007) [arXiv:0706.1872v2, "Paper"]. As long as the "Comment" offers a new support of the original assertions made in the "Paper", I feel obliged to re-clarify the matter by extending my argumentation. I insist that it is possible to escape the main conclusion of the "Paper", indeed. In particular, I point out a gap in the new calculations in "Comment", add a few remarks on the notation and reconfirm that the unitarity of the time-evolution DOES NOT require the time-independence of the metric operator.
Low-temperature, electronic transport in Landau levels N>1 of a two-dimensional electron system is strongly anisotropic. At half-filling of either spin level of each such Landau level the magnetoresistance either collapses to form a deep minimum or is peaked in a sharp maximum, depending on the in-plane current direction. Such anisotropies are absent in the N=0 and N=1 Landau level, which are dominated by the states of the fractional quantum Hall effect. The transport anisotropies may be indicative of a new many particle state, which forms exclusively in higher Landau levels.
We consider a threshold epidemic model on a clustered random graph with overlapping communities. In other words, our epidemic model is such that an individual becomes infected as soon as the proportion of her infected neighbors exceeds the threshold q of the epidemic. In our random graph model, each individual can belong to several communities. The distributions for the community sizes and the number of communities an individual belongs to are arbitrary.   We consider the case where the epidemic starts from a single individual, and we prove a phase transition (when the parameter q of the model varies) for the appearance of a cascade, i.e. when the epidemic can be propagated to an infinite part of the population. More precisely, we show that our epidemic is entirely described by a multi-type (and alternating) branching process, and then we apply Sevastyanov's theorem about the phase transition of multi-type Galton-Watson branching processes. In addition, we compute the entries of the matrix whose largest eigenvalue gives the phase transition.
In this article, we consider random walk on the infinite cluster of bond percolation on $\Z^d (d \geq 2)$. We show that the Laplace transformation of the number of visited points $N\_n$, has a behaviour as the random walk was on $\Z^d$. More precisely, for all $0<\alpha<1$, we proved that there exist constants $C\_i$ and $C\_s$ such that for all infinite cluster that contains the origin, we have: $$ e^{-C\_i n^{\frac{d}{d+2}}} \leq \E\_0^{\omega} (\alpha^{N\_n}) \leq e^{-C\_sn^{\frac{d}{d+2}}}.$$ Our approach is based on finding an isoperimetric inequalities on the infinite cluster, lifted on a wreath product which give good behaviour. The problem of the isoperimetry on wreath product was already raised by A.Ershler.
(Abridged) Based on the rapidly increasing all-sky data of Faraday rotation measures and polarised synchrotron radiation, the Milky Way's magnetic field is now modelled with an unprecedented level of detail and complexity. We aim to complement this heuristic approach with a physically motivated, quantitative Galactic dynamo model -- a model that moreover allows for the evolution of the system as a whole, instead of just solving the induction equation for a fixed static disc. Building on the framework of mean-field magnetohydrodynamics and extending it to the realm of a hybrid evolution, we perform three-dimensional global simulations of the Galactic disc. Closure coefficients embodying the mean-field dynamo are calibrated against resolved box simulations of supernova-driven interstellar turbulence. The emerging dynamo solutions comprise a mixture of the dominant axisymmetric S0 mode, with even parity, and a subdominant A0 mode, with odd parity. Notably, such a superposition of modes creates a strong localised vertical field on one side of the Galactic disc. We moreover find significant radial pitch angles, which decay with radius -- explained by flaring of the disc. In accordance with previous work, magnetic instabilities appear to be restricted to the less-stirred outer Galactic disc. Their main effect is to create strong fields at large radii such that the radial scale length of the magnetic field increases from 4 kpc (for the case of a mean-field dynamo alone) to about 10 kpc in the hybrid models. There remain aspects (e.g., spiral arms, X-shaped halo fields, fluctuating fields) that are not captured by the current model and that will require further development towards a fully dynamical evolution. Nevertheless, the work presented demonstrates that a hybrid modelling of the Galactic dynamo is feasible and can serve as a foundation for future efforts.
We study the absorption of plane waves by Kerr black holes. We calculate the absorption cross section: the area of the black hole shadow at a finite wavelength. We present a unified picture of the absorption of all massless bosonic fields, focussing on the on-axis incidence case. We investigate the spin-helicity effect, arising from a coupling between dragging of frames and the helicity of a polarized wave. We introduce and calibrate an extended sinc approximation which provides new quantitative data on the spin-helicity effect in strong-field gravity.
The ortho-to-para ratio (OPR) of H$_2$O is thought to be sensitive to the temperature of water formation. The OPR of H$_2$O is thus useful to study the formation mechanism of water. We investigate the OPR of water in the Orion PDR (Photon-dominated region), at the Orion Bar and Orion S positions, using data from {\it Herschel}/HIFI. We detect the ground-state lines of ortho- and para-H$_2$$^{18}$O in the Orion Bar and Orion S and we estimate the column densities using LTE and non-LTE methods. Based on our calculations, the ortho-to-para ratio (OPR) in the Orion Bar is 0.1 $-$ 0.5, which is unexpectedly low given the gas temperature of $\sim$ 85 K, and also lower than the values measured for other interstellar clouds and protoplanetary disks. Toward Orion S, our OPR estimate is below 2. This low OPR at 2 positions in the Orion PDR is inconsistent with gas phase formation and with thermal evaporation from dust grains, but it may be explained by photodesorption.