ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper is devoted to studying constrained continuous-time Markov decision processes (MDPs) in the class of randomized policies depending on state histories. The transition rates may be unbounded, the reward and costs are admitted to be unbounded from above and from below, and the state and action spaces are Polish spaces. The optimality criterion to be maximized is the expected discounted rewards, and the constraints can be imposed on the expected discounted costs. First, we give conditions for the nonexplosion of underlying processes and the finiteness of the expected discounted rewards/costs. Second, using a technique of occupation measures, we prove that the constrained optimality of continuous-time MDPs can be transformed to an equivalent (optimality) problem over a class of probability measures. Based on the equivalent problem and a so-called $\bar{w}$-weak convergence of probability measures developed in this paper, we show the existence of a constrained optimal policy. Third, by providing a linear programming formulation of the equivalent problem, we show the solvability of constrained optimal policies. Finally, we use two computable examples to illustrate our main results.
We discuss mechanisms related to isospin transport in central collisions between neutron-rich systems at Fermi energies. A fully consistent study of the isospin distillation and expansion dynamics in two-component systems is presented in the framework of a stochastic transport theory. We analyze correlations between fragment observables, focusing on the study of the average N/Z of fragments, as a function of their kinetic energy. We identify an EOS-dependent relation between these observables, allowing to better characterize the fragmentation path and to access new information on the low density behavior of the symmetry energy.
We put to test the recently proposed non-linear flux ansatz for maximal supergravity in eleven dimensions, which gives the seven-dimensional flux in terms of the scalars and pseudoscalars of maximal N=8 supergravity, by considering a number of non-trivial solutions of gauged supergravity for which the higher dimensional solutions are known. These include the G$_2$ and SU(4)$^-$ invariant stationary points. The examples considered constitute a very non-trivial check of the ansatz, which it passes with remarkable success.
Helium diffusion in metals is the basic requirement of nucleation and growth of bubble, which gives rise to adverse degradation effects on mechanical properties of structural materials in reactors under irradiation. Multi-scale modeling scheme has been developed to study effects of helium on the long-term microstructural evolution. However, the implementation of Arrhenius law based on the quasi-equilibrium reaction process is not appropriate to predict the migration behavior of helium in metals due to low-energy barrier. A coarse-grained formula is required to incorporate the non-equilibrium nature, e.g., the dissipative friction coefficient $\gamma$. In this paper, we derive an analytical expression for $\gamma$ based on a coarse-grained model of Brownian motion upon a periodic potential, in terms of dissipative feature of the thermal excitations in the many-body dynamical system by constructing an adiabatic relaxation process, which is then confirmed by a numerical example of vacancy migration in BCC W. Then the many-body dynamics simulations are performed for helium migration in BCC W and Fe, where the classical mobility are obtained and in good agreement with the data from experiments and other calculations. Finally, we propose a coarse-grained formula for the helium migration in BCC W and Fe, i.e., Eq.(47) in the context, using the calculated parameters from the adiabatic relaxation simulations. This work would help to develop a new multi-scale modeling scheme for effects of helium in metals, as well as the atomistic reactions with low-energy pathways in materials science.
We consider synchrotron-like radiation in QCD by generalizing Schwinger's treatment of quantum synchrotron radiation in QED to the case of a constant chromomagnetic field. We suggest a novel mechanism for {\em jet quenching} in heavy ion collisions, whereby high-$p_t$ partons get depleted through strong (classical) color fields. The latters are encountered in the color glass condensate or in the form of expanding shells of exploding sphalerons. Unlike bremsstrahlung radiation through multiple soft rescattering, synchrotron radiation converts a jet into a wide shower of soft gluons. We estimate the energy loss through this mechanism and suggest that it contributes significantly to the unexpectedly strong jet quenching observed at RHIC.
3D scene understanding from point clouds plays a vital role for various robotic applications. Unfortunately, current state-of-the-art methods use separate neural networks for different tasks like object detection or room layout estimation. Such a scheme has two limitations: 1) Storing and running several networks for different tasks are expensive for typical robotic platforms. 2) The intrinsic structure of separate outputs are ignored and potentially violated. To this end, we propose the first transformer architecture that predicts 3D objects and layouts simultaneously, using point cloud inputs. Unlike existing methods that either estimate layout keypoints or edges, we directly parameterize room layout as a set of quads. As such, the proposed architecture is termed as P(oint)Q(uad)-Transformer. Along with the novel quad representation, we propose a tailored physical constraint loss function that discourages object-layout interference. The quantitative and qualitative evaluations on the public benchmark ScanNet show that the proposed PQ-Transformer succeeds to jointly parse 3D objects and layouts, running at a quasi-real-time (8.91 FPS) rate without efficiency-oriented optimization. Moreover, the new physical constraint loss can improve strong baselines, and the F1-score of the room layout is significantly promoted from 37.9% to 57.9%.
An approach is proposed for high resolution 3D reconstruction of an object using a Micro Air Vehicle (MAV). A system is described which autonomously captures images and performs a dense 3D reconstruction via structure from motion with no prior knowledge of the environment. Only the MAVs own sensors, the front facing camera and the Inertial Measurement Unit (IMU) are utilized. Precision agriculture is considered as an example application for the system.
We study the large-time behavior of (weak) solutions to a two-scale reaction-diffusion system coupled with a nonlinear ordinary differential equations modeling the partly dissipative corrosion of concrete (/cement)-based materials with sulfates. We prove that as $t\to\infty$ the solution to the original two-scale system converges to the corresponding two-scale stationary system. To obtain the main result we make use essentially of the theory of evolution equations governed by subdifferential operators of time-dependent convex functions developed combined with a series of two-scale energy-like time-independent estimates.
Mainstream lane marker detection methods are implemented by predicting the overall structure and deriving parametric curves through post-processing. Complex lane line shapes require high-dimensional output of CNNs to model global structures, which further increases the demand for model capacity and training data. In contrast, the locality of a lane marker has finite geometric variations and spatial coverage. We propose a novel lane marker detection solution, FOLOLane, that focuses on modeling local patterns and achieving prediction of global structures in a bottom-up manner. Specifically, the CNN models lowcomplexity local patterns with two separate heads, the first one predicts the existence of key points, and the second refines the location of key points in the local range and correlates key points of the same lane line. The locality of the task is consistent with the limited FOV of the feature in CNN, which in turn leads to more stable training and better generalization. In addition, an efficiency-oriented decoding algorithm was proposed as well as a greedy one, which achieving 36% runtime gains at the cost of negligible performance degradation. Both of the two decoders integrated local information into the global geometry of lane markers. In the absence of a complex network architecture design, the proposed method greatly outperforms all existing methods on public datasets while achieving the best state-of-the-art results and real-time processing simultaneously.
It is well know that systems with an interaction decaying as a power of the distance may have critical exponents that are different from those of short-range systems. The boundary between long-range and short-range is known, however the behavior in the crossover region is not well understood. In this paper we propose a general form for the crossover function and we compute it in a particular limit. We compare our predictions with the results of numerical simulations for two-dimensional long-range percolation.
The supersymmetric collective field theory with the potential $v'(x)=\omega x-{\eta\over x}$ is studied, motivated by the matrix model proposed by Jevicki and Yoneya to describe two dimensional string theory in a black hole background. Consistency with supersymmetry enforces a two band solution. A supersymmetric classical configuration is found, and interpreted in terms of the density of zeros of certain Laguerre polynomials. The spectrum of the model is then studied and is seen to correspond to a massless scalar and a majorana fermion. The $x$ space eigenfunctions are constructed and expressed in terms of Chebyshev polynomials. Higher order interactions are also discussed.
In 1895 Wiman introduced a Riemann surface $\mathcal{W}$ of genus $6$ over the complex field $\mathbb{C}$ defined by the homogeneous equation $\mathcal{W}:X^6+Y^6+Z^6+(X^2+Y^2+Z^2)(X^4+Y^4+Z^4)-12X^2 Y^2 Z^2=0$, and showed that its full automorphism group is isomorphic to the symmetric group $S_5$. The curve $\mathcal{W}$ was previously studied as a curve defined over a finite field $\mathbb{F}_{p^2}$ where $p$ is a prime, and necessary and sufficient conditions for its maximality over $\mathbb{F}_{p^2}$ were obtained. In this paper we first show that the result of Wiman concerning the automorphism group of $\mathcal{W}$ holds also over an algebraically closed field $\mathbb{K}$ of positive characteristic $p$, provided that $p \geq 7$. For $p=2,3$ the polynomial $X^6+Y^6+Z^6+(X^2+Y^2+Z^2)(X^4+Y^4+Z^4)-12X^2 Y^2 Z^2$ is not irreducible over $\mathbb{K}$, while for $p=5$ the curve $\mathcal{W}$ is rational and $Aut(\mathcal{W}) \cong PGL(2,\mathbb{K})$. We also show that the $\mathbb{F}_{19^2}$-maximal Wiman's sextic $\mathcal{W}$ is not Galois covered by the Hermitian curve $\mathcal{H}_{19}$ over $\mathbb{F}_{19^2}$.
The exclusive processes 2H(e,e'p)n, 3He(e,e'p)2H and 3He(e,e'p)(pn), have been analyzed using realistic few-body wave functions and treating the final state interaction (FSI) within a Generalized Eikonal Approximation (GEA), based upon the direct calculation of the Feynman diagrams describing the rescattering of the struck nucleon with the nucleons of the A-1 system. The approach represents an improvement of the conventional Glauber approach (GA), in that it allows one to take into account the effects of the nuclear excitation of the $A-1$ system on the rescattering of the struck nucleon. Using realistic three-body wave functions corresponding to the AV18 interaction, the results of our parameter free calculations are compared with available experimental data. It is found that in some kinematical conditions FSI effects represent small corrections, whereas in other kinematics conditions they are very large and absolutely necessary to provide a satisfactory agreement between theoretical calculations and experimental data. It is shown that in the kinematics of the experimental data which have been considered, covering the region of missing momentum and energy with p_m < 0.6 GeV/c and E_m < 100 MeV in the perpendicular kinematics, the GA and GEA predictions differ only by less than 3-4 %.
Quantum gravity is effective in domains where both quantum effects and gravity are essential, such as in the vicinity of space-time singularities. This paper will investigate the quantization of a black-hole gravity, particularly the region surrounding the singularity at the origin of the coordinate system. Describing the system with a Hamiltonian formalism, we apply the covariant integral quantization method to find the Wheeler-DeWitt equation of the model. We find that the quantized system has a discrete energy spectrum in the region inside the event horizon. Through the Kantowski-Sachs metric, it is possible to correlate the entropic time, which gives the dynamics for this model, to the cosmic time in a non-trivial way. Different configurations for the phase space of a Schwarzschild black hole are obtained in a semi-classical analysis. For lower-energy states, the quantum corrections result in singularity removal and wormhole formation.
The quantum critical point of the three-dimensional XY model in a symmetry-preserving field is investigated. The results of Monte Carlo simulations with the directed-loop algorithm show that the quantum critical behavior is characterized by the mean-field values of critical exponents. The system-size dependence of various quantities is compared to a simple field-theoretical argument that supports the mean-field scaling.
We determine the total dynamical matter density in the solar neighbourhood using the second Gaia data release (DR2). The dynamical matter density distribution is inferred in a framework of a Bayesian hierarchical model, which accounts for position and velocity of all individual stars, as well as the full error covariance matrix of astrometric observables, in a joint fit of the vertical velocity distribution and stellar number density distribution. This was done for eight separate data samples, with different cuts in observed absolute magnitude, each containing about 25,000 stars. The model for the total matter density does not rely on any underlying baryonic model, although we assumed that it is symmetrical, smooth, and monotonically decreasing with distance from the mid-plane. We infer a density distribution which is strongly peaked in the region close to the Galactic plane ($\lesssim 60$ pc), for all eight stellar samples. Assuming a baryonic model and a dark matter halo of constant density, this corresponds to a surplus surface density of approximately 5--9 M$_\odot$/pc$^2$. For the Sun's position and vertical velocity with respect to the Galactic plane, we infer $Z_\odot = 4.76\pm 2.27$ pc and $W_\odot = 7.24\pm 0.19$ km/s. These results suggest a surplus of matter close to the Galactic plane, possibly explained by an underestimated density of cold gas. We discuss possible systematic effects that could bias our result, for example unmodelled non-equilibrium effects, and how to account for such effects in future extensions of this work.
We calculated the 3D distribution of the area expansion factors in a potential magnetic field extrapolated from the high-resolution \textit{Hinode}/SOT magnetogram of a quiescent active region NOAA 11482. Retaining only closed loops within the computational box, we show that the distribution of area expansion factors show significant structure. Loop-like structures characterized by locally lower values of the expansion factor are embedded in a smooth background. These loop-like flux-tubes have squashed cross-sections and expand with height. The distribution of the expansion factors show overall increase with height, allowing an active region core characterized by low values of the expansion factor to be distinguished. The area expansion factors obtained from extrapolation of the SOT magnetogram are compared to those obtained from an approximation of the observed magnetogram by a series of 134 submerged charges. This approximation retains the general flux distribution in the observed magnetogram, but removes the small-scale structure in both the approximated magnetogram and the 3D distribution of the area expansion factors. We argue that the structuring of the expansion factor can be a significant ingredient in producing the observed structuring of the solar corona. However, due to the potential approximation used, these results may not be applicable to loops exhibiting twist neither to active regions producing significant flares.
We study a Dirac neutrino mass model of Davidson and Logan. In the model, the smallness of the neutrino mass is originated from the small vacuum expectation value of the second Higgs of two Higgs doublets. We study the one loop effective potential of the Higgs sector and examine how the small vacuum expectation is stable under the radiative correction. By deriving formulae of the radiative correction, we numerically study how large the one loop correction is and show how it depends on the quadratic mass terms and quartic couplings of the Higgs potential. The correction changes depending on the various scenarios for extra Higgs mass spectrum.
Using the tight-binding approach we study the electronic transport in a $\mathrm{MoS}_2$ zigzag ribbon with a spatially varying potential profile. Considering a ribbon with a smooth potential step in the Fermi energy regime where the transport is dominated by the edge modes, we find that the conductance exhibits sharp resonances due to the resonant transport through a n-p-n junction effectively created in the structure. We show that in a gated wire the current carried on the wire edges can be blocked despite the metallic band structure of the ribbon. For the Fermi energies corresponding to $\mathrm{MoS}_2$ bulk conduction band, we identify states of the semi-infinite wire that are polarized in the $K$, $K'$, $Q$ valleys and exhibit the valley Hall effect distinctly visible in a nonuniform ribbon. Finally, we show that well-defined momenta of the valley polarized modes allow nearly complete valley polarization of the current in a locally gated ribbon.
We show that a class of matrix theories can be understood as an extension of quantum field theory which has non-local interactions. This reformulation is based on the Wigner-Weyl transformation, and the interactions take the form of Moyal product on a doubled geometry. We recover local dynamics on the spacetime as a low-energy limit. This framework opens up the possibility for studying novel high-energy phenomena, including the unification of gauge and geometric symmetries in a gauge theory.
We present thermal Sunyaev-Zel'dovich effect (SZE) measurements for 42 galaxy clusters observed at 150 GHz with the APEX-SZ experiment. For each cluster, we model the pressure profile and calculate the integrated Comptonization $Y$ to estimate the total thermal energy of the intracluster medium (ICM). We compare the measured $Y$ values to X-ray observables of the ICM from the literature (cluster gas mass $M_{\rm{gas}}$, temperature $T_X$, and $Y_X =M_{\rm{gas}}T_X$) that relate to total cluster mass. We measure power law scaling relations, including an intrinsic scatter, between the SZE and X-ray observables for three subsamples within the set of 42 clusters that have uniform X-ray analysis in the literature. We observe that differences between these X-ray analyses introduce significant variability into the measured scaling relations, particularly affecting the normalization. For all three subsamples, we find results consistent with a self-similar model of cluster evolution dominated by gravitational effects. Comparing to predictions from numerical simulations, these scaling relations prefer models that include cooling and feedback in the ICM. Lastly, we measure an intrinsic scatter of $\sim28$ per cent in the $Y-Y_X\,$ scaling relation for all three subsamples.
This paper is devoted to investigate the exact solutions of Bianchi type $I$ spacetime in the context of $f(R,T)$ gravity [1], where $f(R,T)$ is an arbitrary function of Ricci scalar $R$ and trace of the energy momentum tensor $T$. For this purpose, we find two exact solutions using the assumption of constant deceleration parameter and variation law of Hubble parameter. The obtained solutions correspond to two different models of the universe. The physical behaviour of these models is also discussed.
We report on the methods and results of the first dedicated search for gravitational waves emitted during the inspiral of compact binaries with spinning component bodies. We analyze 788 hours of data collected during the third science run (S3) of the LIGO detectors. We searched for binary systems using a detection template family designed specially to capture the effects of the spin-induced precession of the orbital plane. We present details of the techniques developed to enable this search for spin-modulated gravitational waves, highlighting the differences between this and other recent searches for binaries with non-spinning components. The template bank we employed was found to yield high matches with our spin-modulated target waveform for binaries with masses in the asymmetric range 1.0 Msol < m1 < 3.0 Msol and 12.0 Msol < m2 < 20.0 Msol which is where we would expect the spin of the binary's components to have significant effect. We find that our search of S3 LIGO data had good sensitivity to binaries in the Milky Way and to a small fraction of binaries in M31 and M33 with masses in the range 1.0 Msol < m1, m2 < 20.0 Msol. No gravitational wave signals were identified during this search. Assuming a binary population with spinning components and Gaussian distribution of masses representing a prototypical neutron star - black hole system with m1 ~ 1.35 Msol and m2 ~ 5 Msol, we calculate the 90%-confidence upper limit on the rate of coalescence of these systems to be 15.9 yr^-1 L_10^-1, where L_10 is 10^10 times the blue light luminosity of the Sun.
We study the prospects of detecting magnetic helicity in galaxies by observing the dust polarization of the edge-on galaxy NGC 891. Our numerical results of mean-field dynamo calculations show that there should be a large-scale component of the rotationally invariant parity-odd B polarization that we predict to be negative in the first and third quadrants, and positive in the second and fourth quadrants. The large-scale parity-even E polarization is predicted to be negative near the axis and positive further away in the outskirts. These properties are shown to be mostly a consequence of the magnetic field being azimuthal and the polarized intensity being maximum at the center of the galaxy and are not a signature of magnetic helicity.
We summarize recent higher-order QCD results based, directly or indirectly, on the Mellin-space computation of the next-to-next-to-leading-order splitting functions governing the evolution of hadronic parton distributions. Specifically, we briefly present third-order results for the coefficient functions in inclusive deep-inelastic scattering (including the structure function F_3 not published so far), the on-shell quark and gluon form factors, and the total cross section for Higgs production at hadron colliders.
Strong winds from massive stars are a topic of interest to a wide range of astrophysical fields. In High-Mass X-ray Binaries the presence of an accreting compact object on the one side allows to infer wind parameters from studies of the varying properties of the emitted X-rays; but on the other side the accretor's gravity and ionizing radiation can strongly influence the wind flow. Based on a collaborative effort of astronomers both from the stellar wind and the X-ray community, this presentation attempts to review our current state of knowledge and indicate avenues for future progress.