ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we study the deformation of the n-dimensional strictly convex hypersurface in $\mathbb R^{n+1}$ whose speed at a point on the hypersurface is proportional to $\alpha$-power of positive part of Gauss Curvature. For $\frac{1}{n}<\alpha \leq 1$, we prove that there exist the strictly convex smooth solutions if the initial surface is strictly convex and smooth and the solution hypersurfaces converge to a point. We also show the asymptotic behavior of the rescaled hypersurfaces, in other words, the rescaled manifold converges to a strictly convex smooth manifold. Moreover, there exists a subsequence whose the limit satisfies a certain equation.
We prove that some discretization schemes for the 2D Navier-Stokes equations subject to a random perturbation converge in $L^2(\Omega)$. This refines previous results which only established the convergence in probability of these numerical approximations. Using exponential moment estimates of the solution of the stochastic NS equations and convergence of a localized scheme, we can prove strong convergence of fully implicit and semi-implicit time Euler discretizations, and of a splitting scheme. The speed of the $L^2(\Omega)$-convergence depends on the diffusion coefficient and on the viscosity parameter.
At low redshift, the majority of supermassive black hole (SMBH) mass estimates are obtained from modeling stellar kinematics or ionized gas dynamics in the vicinity of the galaxy nucleus. For large early type galaxies, stellar kinematics models predict higher masses than gas-dynamical models. In the case of M87, this discrepancy is larger than 2 $\sigma$. Critical to gas-dynamical modeling is the assumed underlying dynamical state of the gas: that it lies on circular Keplerian orbits, potentially with some additional turbulent pressure support. This is inconsistent with models of the gas flow about low-accretion-rate SMBHs and at odds with observations of the Galactic Center. We present a simple model for non-Keplerian gas disks and explore their implications for SMBH mass measurements. We show that a larger central black hole with gas experiencing small amounts of sub-Keplerian motion can produce velocity curves similar to models that just contain circular Keplerian motions and a lower black hole mass. However, these non-Keplerian models are distinguishable from low-mass Keplerian models primarily through measurements of the velocity dispersion, wherein non-Keplerian models produce higher and narrower peak dispersions. Away from the galaxy center, but still within the circumnuclear gas disk, non-Keplerian models also become distinguishable from Keplerian models via a shift in the velocity curve. The velocity model presented in this paper is capable of resolving the discrepancy between the ionized gas dynamics and stellar kinematics mass estimates, and is applicable to gas-dynamical mass estimates of SMBHs in general.
We present a multi-wavelength analysis of gamma-ray burst GRB 090727, for which optical emission was detected during the prompt gamma-ray emission by the 2-m autonomous robotic Liverpool Telescope and subsequently monitored for a further two days with the Liverpool and Faulkes telescopes. Within the context of the standard fireball model, we rule out a reverse shock origin for the early time optical emission in GRB 090727 and instead conclude that the early time optical flash likely corresponds to emission from an internal dissipation processes. Putting GRB 090727 into a broader observational and theoretical context, we build a sample of 36 gamma-ray bursts (GRBs) with contemporaneous early time optical and gamma-ray detections. From these GRBs, we extract a sub-sample of 18 GRBs, which show optical peaks during prompt gamma-ray emission, and perform detailed temporal and spectral analysis in gamma-ray, X-ray, and optical bands. We find that in most cases early time optical emission shows sharp and steep behaviour, and notice a rich diversity of spectral properties. Using a simple internal shock dissipation model, we show that the emission during prompt GRB phase can occur at very different frequencies via synchrotron radiation. Based on the results obtained from observations and simulation, we conclude that the standard external shock interpretation for early time optical emission is disfavoured in most cases due to sharp peaks ($\Delta t/t < 1$) and steep rise/decay indices, and that internal dissipation can explain the properties of GRBs with optical peaks during gamma-ray emission.
It is common to measure a single sample using multiple different microscopy methods that have variable scales, rotation and translation. Registering hyperspectral images of two dimensional materials is particularly difficult due to the lack of keypoints on unprepared substrates. Identifying variations in the strain of these samples can assist in the registration of these samples by creating keypoints to correlate images. Registration of these images allow for multimodal analysis from these various instruments by aligning multiple images into a single coordinate space. This is done by Hough transformations and arbitrary resolution definitions to generate a new coordinate frame where spatial information may be preserved and correlated on a pixel by pixel basis. Such multimodal image alignment may be used to correlate data from various instruments. Strain information is extracted from the Raman spectra and the resulting hyperspectral image is used to register the Raman information with the other modes of microscopy.
In this paper, we propose a new single shot method for multi-person 3D human pose estimation in complex images. The model jointly learns to locate the human joints in the image, to estimate their 3D coordinates and to group these predictions into full human skeletons. The proposed method deals with a variable number of people and does not need bounding boxes to estimate the 3D poses. It leverages and extends the Stacked Hourglass Network and its multi-scale feature learning to manage multi-person situations. Thus, we exploit a robust 3D human pose formulation to fully describe several 3D human poses even in case of strong occlusions or crops. Then, joint grouping and human pose estimation for an arbitrary number of people are performed using the associative embedding method. Our approach significantly outperforms the state of the art on the challenging CMU Panoptic and a previous single shot method on the MuPoTS-3D dataset. Furthermore, it leads to good results on the complex and synthetic images from the newly proposed JTA Dataset.
We present reduction theorems for the problem of optimal unambiguous state discrimination (USD) of two general density matrices. We show that this problem can be reduced to that of two density matrices that have the same rank $n$ and are described in a Hilbert space of dimensions $2n$. We also show how to use the reduction theorems to discriminate unambiguously between N mixed states (N \ge 2).
We show that maximal atmospheric and large solar neutrino mixing can be implemented in SU(5) gauge theories, by making use of the $U(1)_F$ symmetry associated with a suitably defined family number $F$, together with a $\mathbbm{Z}_2$ symmetry which does not commute with $F$. $U(1)_F$ is softly broken by the mass terms of the right-handed neutrino singlets, which are responsible for the seesaw mechanism; in addition, $U(1)_F$ is also spontaneously broken at the electroweak scale. In our scenario, lepton mixing stems exclusively from the right-handed-neutrino Majorana mass matrix, whereas the CKM matrix originates solely in the up-type-quark sector. We show that, despite the non-supersymmetric character of our model, unification of the gauge couplings can be achieved at a scale $10^{16} \mathrm{GeV} < m_U < 10^{19} \mathrm{GeV}$; indeed, we have found a particular solution to this problem which yields results almost identical to the ones of the Minimal Supersymmetric Standard Model.
In the present article, the authors intend to propose a new theory which potentially allows the propagation of the formation and the evolution of quarkonium in a thermal BIon. When quarks are close to each other, quarkonium behaves like a scalar and by their getting away, it transits to a fermionic system. In order to analyze this particular behaviour, a new outlook approach needs to be adopted as the concurrent view is found deficient to analyse the aforesaid behaviour. Therefore, the authors' post deliberation accept the fermions and fermionic being cognate. We need to accept a theory that the origin of fermions and bosons be the same. However, in $M$-theory, these particles are independent and for this reason, \textbf{we use a new broader theory based on Lie-$N$-Algebra and we call it BLNA (Broad Lie-$N$-Algebra)} theory. Thus, the BLNA in a way the $M$-theory with $11$ dimensions. In this model, two types of energies with opposite signs emerge from nothing such as the sum over them becomes zero. They produce two types of branes with opposite quantum numbers and bosonic fields, which interact with each other and get compact. By compacting branes, the quarks and anti-quarks are produced on branes and exchange the graviton and the gravitino. These particles produce two types of wormholes which act opposite to each other. They preclude from closing or getting away of branes from each other and also occurrence of confinement. This confined potential which emerges from these wormholes depends on the separation distance between quarks and anti-quarks and also on temperature of system and is reduced to predicted potential in experiments and QCD. Also, total entropy of this system grows with increasing temperature and produces a repulsive force which leads to the separation of quarks and anti-quarks and also to the emergence of deconfinement.
We consider a ``one current'' state, which is obtained by the application of a color current on the ``adjoint'' vacuum. This is done in $QCD_2$, with the underlying quarks in the fundamental representation. The quarks are taken to be massless, in which case the theory on the light-front can be ``currentized'', namely, formulated in terms of currents only. The adjoint vacuum is shown to be the application of a current derivative, at zero momentum, on the singlet vacuum. We apply the operator $M^2=2P^+P^-$ on these states and find that in general they are not eigenstates of $M^2$ apart from the large $N_f$ limit. Problems with infra-red regularizations are pointed out. We discuss the fermionic structure of these states.
We consider theoretically the formation and stability of quasi-one dimensional many-body excitons in GaAs quantum wire structures under external photoexcitation conditions by solving the dynamically screened Bethe-Salpeter equation for realistic Coulomb interaction. In agreement with several recent experimental findings the calculated excitonic peak shows very weak carrier density dependence upto (and even above) the Mott transition density, $n_c\sim3\times10^5$ cm$^{-1}$. Above $n_c$ we find considerable optical gain demonstrating compellingly the possibility of one-dimensional quantum wire laser operation.
We consider the general case of an accelerating, expanding and shearing model of a radiating relativistic star using Lie symmetries. We obtain the Lie symmetry generators that leave the equation for the junction condition invariant, and find the Lie algebra corresponding to the optimal system of the symmetries. The symmetries in the optimal system allow us to transform the boundary condition to ordinary differential equations. The various cases for which the resulting systems of equations can be solved are identified. For each of these cases the boundary condition is integrated and the gravitational potentials are found explicitly. A particular group invariant solution produces a class of models which contains Euclidean stars as a special case. Our generalized model satisfies a linear equation of state in general. We thus establish a group theoretic basis for our generalized model with an equation of state. By considering a particular example we show that the weak, dominant and strong energy conditions are satisfied.
Let us consider a Lie (super)algebra $G$ spanned by $T_{\alpha}$ where $T_{\alpha}$ are quantum observables in BV-formalism. It is proved that for every tensor $c^{\alpha_1...\alpha_k}$ that determines a homology class of the Lie algebra $G$ the expression $c^{\alpha_1...\alpha_k}T_{\alpha _1}...T_{\alpha_k}$ is again a quantum observables. This theorem is used to construct quantum observables in BV sigma-model. We apply this construction to explain Kontsevich's results about the relation between homology of the Lie algebra of Hamiltonian vector fields and topological invariants of manifolds.
Combining theorems of Voisin and Marian, Shen, Yin and Zhao, we compute the dimensions of the orbits under rational equivalence in the Mukai system of rank two and genus two. We produce several examples of algebraically coisotropic and constant cycle subvarieties.
Using Monte Carlo simulations, we determine the phase diagram of a diffusive two-temperature XY model. When the two temperatures are equal the system becomes the equilibrium XY model with the continuous Kosterlitz-Thouless (KT) vortex-antivortex unbinding phase transition. When the two temperatures are unequal the system is driven by an energy flow through the system from the higher temperature heat-bath to the lower temperature one and reaches a far-from-equilibrium steady state. We show that the nonequilibrium phase diagram contains three phases: A homogenous disordered phase and two phases with long range, spin-wave order. Two critical lines, representing continuous phase transitions from a homogenous disordered phase to two phases of long range order, meet at the equilibrium the KT point. The shape of the nonequilibrium critical lines as they approach the KT point is described by a crossover exponent of phi = 2.52 \pm 0.05. Finally, we suggest that the transition between the two phases with long-range order is first-order, making the KT-point where all three phases meet a bicritical point.
Shot noise measurements are widely used for the characterization of nonequilibrium configurations in electronic conductors. The recently introduced quantum tomography approach was implemented for the studies of electronic wavefunctions of few-electron excitations created by periodic voltage pulses in phase-coherent ballistic conductors based on the high-quality GaAs two-dimensional electron gas. Still relying on the manifestation of Fermi correlations in noise, we focus on the simpler and more general approach beneficial for the local measurements of energy distribution (ED) in electronic systems with arbitrary excitations with well-defined energies and random phases. Using biased diffusive metallic wire as a testbed, we demonstrate the power of this approach and extract the well-known double-step ED from the shot noise of a weakly coupled tunnel junction. Our experiment paves the way for the local measurements of generic nonequilibrium configurations applicable to virtually any conductor.
In 1899, Hutchinson presented a way to obtain a three-parameter family of Hessians of cubic surfaces as blowups of Kummer surfaces. We show that this family consists of those Hessians containing an extra class of conic curves. Based on this, we find the invariant of a cubic surface C in pentahedral form that vanishes if its Hessian is in Hutchinson's family, and we give an explicit map between cubic surfaces in pentahedral form and blowups of Kummer surfaces.
We provide general arguments regarding the connection between low-energy theories (gravity and quantum field theory) and a hypothetical fundamental theory of quantum gravity, under the assumptions of (i) validity of the holographic bound and (ii) preservation of unitary evolution at the level of the fundamental theory. In particular, the appeal to the holographic bound imposed on generic physical systems by the Bekenstein-Hawking entropy implies that both classical geometry and quantum fields propagating on it should be regarded as phenomena emergent from the dynamics of the fundamental theory. The reshuffling of the fundamental degrees of freedom during the unitary evolution then leads to an entanglement between geometry and quantum fields. The consequences of such scenario are considered in the context of black hole evaporation and the related information-loss issue: we provide a simplistic toy model in which an average loss of information is obtained as a consequence of the geometry-field entanglement.
We propose a new method for evaluating incomplete and complete fusion cross sections separately using the Continuum-Discretized Coupled-Channels method. This method is applied to analysis of the deuteron induced reaction on a 7Li target up to 50 MeV of the deuteron incident energy. Effects of deuteron breakup on this reaction are explicitly taken into account. Results of the method are compared with those of the Glauber model, and the difference between the two is discussed. It is found that the energy dependence of the incomplete fusion cross sections obtained by the present calculation is almost the same as that obtained by the Glauber model, while for the complete fusion cross section, the two models give markedly different energy dependence. We show also that a prescription for evaluating incomplete fusion cross sections proposed in a previous study gives much smaller result than an experimental value.
We present the algorithm and main results of our semi-numerical simulation, islandFAST, which is developed from the 21cmFAST and designed for the late stage of reionization. The islandFAST predicts the evolution and size distribution of the large scale under-dense neutral regions (neutral islands), and we find that the late Epoch of Reionization (EoR) proceeds very fast, showing a characteristic scale of the neutral islands at each redshift. Using islandFAST, we compare the impact of two types of absorption systems, i.e. the large scale under-dense neutral islands versus small scale over-dense absorbers, in regulating the reionization process. The neutral islands dominate the morphology of the ionization field, while the small scale absorbers dominate the mean free path of ionizing photons, and also delay and prolong the reionization process. With our semi-numerical simulation, the evolution of the ionizing background can be derived self-consistently given a model for the small absorbers. The hydrogen ionization rate of the ionizing background is reduced by an order of magnitude in the presence of dense absorbers.
We have realized ambipolar ionic liquid gated field-effect transistors based on WS2 mono- and bilayers, and investigated their opto-electronic response. A thorough characterization of the transport properties demonstrates the high quality of these devices for both electron and hole accumulation, which enables the quantitative determination of the band gap ({\Delta}1L = 2.14 eV for monolayers and {\Delta}2L = 1.82 eV for bilayers). It also enables the operation of the transistors in the ambipolar injection regime with electrons and holes injected simultaneously at the two opposite contacts of the devices in which we observe light emission from the FET channel. A quantitative analysis of the spectral properties of the emitted light, together with a comparison with the band gap values obtained from transport, show the internal consistency of our results and allow a quantitative estimate of the excitonic binding energies to be made. Our results demonstrate the power of ionic liquid gating in combination with nanoelectronic systems, as well as the compatibility of this technique with optical measurements on semiconducting transition metal dichalcogenides. These findings further open the way to the investigation of the optical properties of these systems in a carrier density range much broader than that explored until now.
We describe a simple family of analytical coordinate systems for the Schwarzschild spacetime. The coordinates penetrate the horizon smoothly and are spatially isotropic. Spatial slices of constant coordinate time $t$ feature a trumpet geometry with an asymptotically cylindrical end inside the horizon at a prescribed areal radius $R_0$ (with $0<R_{0}\leq M$) that serves as the free parameter for the family. The slices also have an asymptotically flat end at spatial infinity. In the limit $R_{0}=0$ the spatial slices lose their trumpet geometry and become flat -- in this limit, our coordinates reduce to Painlev\'e-Gullstrand coordinates.
The field of quantum information has been growing fast over the past decade. Optical quantum computation, based on the concepts of KLM and cluster states, has witnessed experimental realizations of larger and more complex systems in terms of photon number. Quantum optical systems, which offer long coherence times and easy manipulation of single qubits, allow us to probe quantum properties of the light itself and of the physical systems around it. Recently, a linear scheme for quantum computing, relying on the bosonic nature of particles, has been proposed and realized experimentally with photons. The ability to efficiently measure superpositions of quantum states consisting of several photons is essential to the characterization of such systems. In fact, the entire field of quantum information completely relies on the ability to recover quantum states from measurements. However, the characterization of quantum states requires many measurements, and often necessitates complicated measurements schemes; for example, characterizing qubits requires measurements. Here, we utilize structure, inherent to physically interesting quantum states of light, in order to reduce the complexity in the recovery of a quantum state. In particular, we devise a method enabling the recovery of three-photon quantum states from only two-fold correlation measurements in a single setting. The ability to take two-fold coincidences instead of three-fold offers the recovery of the quantum states in far less measurements and in a considerably higher SNR, because detection of two-photon events is much more likely than that of three-photon ones. The concept suggested here paves the way to further ideas on structure-based super resolution in quantum state tomography, such as recovering a quantum state in an unknown basis in a single setup and recovering the state of several photons without number resolving detectors.
We present a demonstration of delensing the observed cosmic microwave background (CMB) B-mode polarization anisotropy. This process of reducing the gravitational-lensing generated B-mode component will become increasingly important for improving searches for the B modes produced by primordial gravitational waves. In this work, we delens B-mode maps constructed from multi-frequency SPTpol observations of a 90 deg$^2$ patch of sky by subtracting a B-mode template constructed from two inputs: SPTpol E-mode maps and a lensing potential map estimated from the $\textit{Herschel}$ $500\,\mu m$ map of the CIB. We find that our delensing procedure reduces the measured B-mode power spectrum by 28% in the multipole range $300 < \ell < 2300$; this is shown to be consistent with expectations from theory and simulations and to be robust against systematics. The null hypothesis of no delensing is rejected at $6.9 \sigma$. Furthermore, we build and use a suite of realistic simulations to study the general properties of the delensing process and find that the delensing efficiency achieved in this work is limited primarily by the noise in the lensing potential map. We demonstrate the importance of including realistic experimental non-idealities in the delensing forecasts used to inform instrument and survey-strategy planning of upcoming lower-noise experiments, such as CMB-S4.