ShantanuT01/DACTYL-Pretraining huggingface dataset:
We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering the classification of positive Einstein curvature tensors and the classical Cauchy-Choquet-Bruhat theorems in general relativity, we introduce concepts of types and rigidity. Then, abandoning the usual requirement of a Ricci-flat five dimensional space-time, we show that a unified geometrical frame can be set for gravitation and electromagnetism, giving, by projection on the classical 4-dimensional space-time, the known Einstein-Maxwell-Lorentz equations for charged fluids. Thus, although not introducing, at least at this stage, new physics, we get a very aesthetic presentation of classical physics in the spirit of general relativity. The usual physical concepts, such as mass, energy, charge, trajectory, Maxwell-Lorentz law, are shown to be only various aspects of the geometry, for example curvature, of space-time considered as a Lorentzian manifold; that is no physical objects are introduced in space-time, no laws are given, everything is only geometry. We will then extend this setting to more than 5 dimensions, giving a precise mathematical frame for possible additional physical effects, preserving gravitation and electromagnetism.
The ubiquitous ADE classification has induced many proposals of often mysterious correspondences both in mathematics and physics. The mathematics side includes quiver theory and the McKay Correspondence which relates finite group representation theory to Lie algebras as well as crepant resolutions of Gorenstein singularities. On the physics side, we have the graph-theoretic classification of the modular invariants of WZW models, as well as the relation between the string theory nonlinear $\sigma$-models and Landau-Ginzburg orbifolds. We here propose a unification scheme which naturally incorporates all these correspondences of the ADE type in two complex dimensions. An intricate web of inter-relations is constructed, providing a possible guideline to establish new directions of research or alternate pathways to the standing problems in higher dimensions.
The old issue of why there are more than one family of quarks and leptons is reinvestigated with an eye towards the use of anomaly as a tool for constraining the number of families. It is found that, by assuming the existence of right-handed neutrinos (which would imply that neutrinos will have a mass) and a new chiral SU(2) gauge theory, strong constraints on the number of families can be obtained. In addition, a model, based on that extra SU(2), is constructed where it is natural to have one "very heavy" fourth neutrino and three almost degenerate light neutrinos whose masses are all of the Dirac type.
In this paper we at first consider plane trees with the root vertex and a marked directed edge, outgoing from the root vertex. For such trees we introduce a new characteristic --- the \emph{parity}, using the bracket code. It turns out that the parity depends only on the root vertex (not on the marked edge). And in the case of an even number of vertices the parity does not depend on the root vertex also. Then we consider rotation groups of bipartite trees, study their properties and prove that in the case of even number of vertices rotation groups of even and odd trees are different.
This paper considers the question: how many times does a simple random walk revisit the most frequently visited site among the inner boundary points? It is known that in ${\mathbb{Z}}^2$, the number of visits to the most frequently visited site among all of the points of the random walk range up to time $n$ is asymptotic to $\pi^{-1}(\log n)^2$, while in ${\mathbb{Z}}^d$ $(d\ge3)$, it is of order $\log n$. We prove that the corresponding number for the inner boundary is asymptotic to $\beta_d\log n$ for any $d\ge2$, where $\beta_d$ is a certain constant having a simple probabilistic expression.
To better constrain the hypotheses proposed to explain why only a few quasars are radio loud (RL), we compare the characteristics of 1958 nearby $(z\le 0.3)$ SDSS quasars, covered by the FIRST and NVSS radio surveys. Only 22\% are RL with $\log(L_{1.4{\rm GHz}}) \ge 22.5$ W Hz$^{-1}$, the majority being compact (C), weak radio sources (WRS), with $\log(L_{1.4{\rm GHz}}) < 24.5$ W Hz$^{-1}$. 15\% of the RL quasars have extended radio morphologies: 3\% have a core and a jet (J), 2\% have a core with one lobe (L), and 10\% have a core with two lobes (T), the majority being powerful radio sources (PRS), with $\log(L_{1.4{\rm GHz}}) \ge 24.5$ W Hz$^{-1}$. In general, RL quasars have higher bolometric luminosities and ionisation powers than radio quiet (RQ) quasars. The WRS have comparable black hole (BH) masses as the RQ quasars, but higher accretion rates or radiative efficiencies. The PRS have higher BH masses than the WRS, but comparable accretion rates or radiative efficiencies. The WRS also have higher $FWHM_{\rm [OIII]}$ than the PRS, consistent with a coupling of the spectral characteristics of the quasars with their radio morphologies. Inspecting the SDSS images and applying a neighbour search algorithm reveal no difference between the RQ and RL quasars of their host galaxies, environments, and interaction. Our results prompt the conjecture that the phenomenon that sparks the radio-loud phase in quasars is transient, intrinsic to the AGN, and stochastic, due to the chaotic nature of the accretion process of matter onto the BHs.
We describe a systematic method of studying the action of the T-duality group O(d,d) on space-time fermions and R-R field strengths and potentials in type-II string theories, based on space-time supersymmetry. The formalism is then used to show that the couplings of non-Abelian D-brane charges to R-R potentials can be described by an appropriate Clifford multiplication.
The Fermi Gamma-ray Space Telescope, as an all-sky survey and monitoring mission, is producing daily/weekly sampled gamma-ray light curves for dozens of blazars and other high-energy sources. Highlights on MeV-GeV gamma-ray variability properties of these sources are reported together with a few remarks about some multi-waveband observing campaigns led by Fermi and targeted to known or newly discovered gamma-ray blazars.
We present a method we developed for the correction of the beam divergence in finite distance sources imaging through coded mask instruments. We discuss the defocusing artifacts induced by the finite distance showing two different approaches to remove such spurious effects. We applied our method to one-dimensional coded-mask systems, although it is also applicable to 2D systems as well. We provide a detailed mathematical description of the adopted method and of the systematics introduced in the reconstructed image (e. g. the fraction of source flux collected in the reconstructed peak counts). The accuracy of this method was tested by simulating point-like and extended sources at finite distance with the instrumental set-up of the SuperAGILE experiment, the one dimensional coded-mask X-ray imager on-board the AGILE mission. We obtained reconstructed images of good quality and high source location accuracy. Finally, we show the results obtained by applying this method to real data collected during the calibration campaign of SuperAGILE. Our method was demonstrated to be a powerful tool to investigate the imaging response of the experiment, particularly, the absorption due to the materials intercepting the line of sight of the instrument and the conversion between detector pixel and sky direction.
Energy density and energy flux was introduced along Takesue's method. Particle energies were localized at particle positions using Dirac delta function. The energy density was connected with the energy flux by continuity equation. New method was proposed to deal with multi--body interaction. Consequently, the energy current between particles could be calculated even if the multi--body interaction appeared. Moreover, An application to the molecular dynamics simulation of hydrogen adsorption on a graphene with modified Brenner reactive empirical bond order potential was demonstrated.
0.1-10 MeV observations of the black hole microquasar Cygnus X-1 have shown the presence of a spectral feature in the form of a power law in addition to the standard black body and Comptonization components observed by INTEGRAL. This so-called "high-energy tail" has recently been shown to be strong in its hard spectral state and interpreted as high-energy part of the emission from a compact jet. This result was, however, obtained from a data set dominated by hard state observations. In the soft state, only upper limits on the presence and hence the potential parameters of a high-energy tail could be derived. Using an extended data set we aim at obtaining better constraints on the properties of this spectral component in both states. We make use of data obtained from 15 years of observations with the INTEGRAL satellite. The data set is separated into the different states and we analyse stacked state-resolved spectra obtained from the X-ray monitors, the gamma-ray imager, and the gamma-ray spectrometer onboard. A high-energy component is detected in both states confirming its earlier detection in the hard state and its suspected presence in the soft state with INTEGRAL. We first characterize the high-energy tail components in the two states through a model-independent, phenomenological analysis. We then apply physical models based on hybrid Comptonization. The spectra are well modeled in all cases, with a similar goodness of the fits. While in the phenomenological approach the high-enery tail has similar indices in both states, the fits with the physical models seem to indicate different properties. We discuss the potential origins of the high-energy components in both states, and favor an interpretation where the part of the high-energy component is due to a compact jet in the hard state and hybrid Comptonization in either a magnetised or non-magnetised corona in the soft state.
We study semistable pairs on elliptic K3 surfaces with a section: we construct a family of moduli spaces of pairs, related by wall crossing phenomena, which can be studied to describe the birational correspondence between moduli spaces of sheaves of rank 2 and Hilbert schemes on the surface. In the 4-dimensional case, this can be used to get the isomorphism between the moduli space and the Hilbert scheme described by Friedman.
We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular we obtain solutions written in terms of Wright functions by exploiting operational rules involving the shift operator. We also consider fractional advection diffusion equations involving fractional powers of the negative Laplace operator and directional derivatives of fractional order and discuss the probabilistic interpretations of solutions.
Earlier studies have shown that, in a two component model of the universe with dark matter and the running vacuum energy which is phenomenologically a combination of $H^2$ and $\dot{H},$ produces either eternal deceleration or acceleration in the absence of a bare constant in the density of the running vacuum. In this paper we have shown that, in the interaction scenario, where the interaction between matter and vacuum is introduced through a phenomenological term, the two component model is capable of causing a transition from a prior decelerated to a later accelerated epoch without a bare constant in the running vacuum density. On contrasting the model with the cosmological data, we have found that the interaction coupling constant, is small enough, for a slow decay of the running vacuum. The model is subjected to dynamical system analysis which revealed that the end de Sitter phase of the model is a stable one. We did an analysis on the thermal behavior of the system, which shows that the entropy is bounded at the end stage so that the system is behaving like an ordinary macroscopic system. Apart from these we have also performed the state finder diagnostic analysis which implies the quintessence nature of running vacuum and confirms that the model will approach the standard $\Lambda$CDM in the future.
Since the rise of deep learning, many computer vision tasks have seen significant advancements. However, the downside of deep learning is that it is very data-hungry. Especially for segmentation problems, training a deep neural net requires dense supervision in the form of pixel-perfect image labels, which are very costly. In this paper, we present a new loss function to train a segmentation network with only a small subset of pixel-perfect labels, but take the advantage of weakly-annotated training samples in the form of cheap bounding-box labels. Unlike recent works which make use of box-to-mask proposal generators, our loss trains the network to learn a label uncertainty within the bounding-box, which can be leveraged to perform online bootstrapping (i.e. transforming the boxes to segmentation masks), while training the network. We evaluated our method on binary segmentation tasks, as well as a multi-class segmentation task (CityScapes vehicles and persons). We trained each task on a dataset comprised of only 18% pixel-perfect and 82% bounding-box labels, and compared the results to a baseline model trained on a completely pixel-perfect dataset. For the binary segmentation tasks, our method achieves an IoU score which is ~98.33% as good as our baseline model, while for the multi-class task, our method is 97.12% as good as our baseline model (77.5 vs. 79.8 mIoU).
We develop a novel bi-harmonic $\mathcal{N}=4$ superspace formulation of the $\mathcal{N}=4$ supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $\mathcal{N}=4$ SYM superfield constraints are solved in terms of on-shell $\mathcal {N}=2$ harmonic superfields. Such an approach provides a convenient tool of constructing the manifestly $\mathcal{N}=4$ supersymmetric invariants and further rewriting them in $\mathcal{N}= 2$ harmonic superspace. In particular, we present $\mathcal{N}=4$ superfield form of the leading term in the $\mathcal{N}=4$ SYM effective action which was known previously in $\mathcal{N}=2$ superspace formulation.
Magnetic fields have been detected in most if not all types of stars across the Hertzsprung-Russell diagram. Where present, these fields have the potential to significantly impact the evolution of their host stars. Furthermore, they themselves are affected by the various structural changes which occur in a star during its life. For example, the significant radius expansion during the post-main-sequence phase, due to flux conservation, may lead to a decrease in surface magnetic field strength, to a point where the magnetic field may no longer be detectable. As a result, it is a challenge to link the magnetic fields observed in main sequence (MS) stars with those observed in very late stage stars and even to those in post-MS stars. In this review, I present what we know, from observations, about magnetic stars at various stages of stellar evolution.
The papers shows an algorithm to search for approximations of reals to rationals of the form a/b^2 that runs on \sqrt(b) polynomial time steps.
Motivated by the recent experimental observation of the half-quantized thermal Hall conductivity for the candidate material of the Kitaev spin liquid, $\alpha$-RuCl$_3$[ Y. Kasahara et al., Nature 559, 227 (2018)], we investigate effects of non-Kitaev exchange interactions, which exist in the real material, on the gapped chiral spin liquid state realized in the case with an applied magnetic field. It is found that off-diagonal exchange interactions enhance significantly the mass gap of Majorana fermions. This result provides a possible explanation for robust quantization of the thermal Hall conductivity observed in the above-mentioned experiment. Furthermore, we demonstrate that if the Kitaev spin liquid state and the zigzag antiferromagnetic order coexist around the border of these two phases, off-diagonal exchange interactions can induce Fermi surfaces of Majorana fermions, leading to a state similar to the U(1) spin liquid.
We propose a simple yet effective approach to the problem of pedestrian detection which outperforms the current state-of-the-art. Our new features are built on the basis of low-level visual features and spatial pooling. Incorporating spatial pooling improves the translational invariance and thus the robustness of the detection process. We then directly optimise the partial area under the ROC curve (\pAUC) measure, which concentrates detection performance in the range of most practical importance. The combination of these factors leads to a pedestrian detector which outperforms all competitors on all of the standard benchmark datasets. We advance state-of-the-art results by lowering the average miss rate from $13\%$ to $11\%$ on the INRIA benchmark, $41\%$ to $37\%$ on the ETH benchmark, $51\%$ to $42\%$ on the TUD-Brussels benchmark and $36\%$ to $29\%$ on the Caltech-USA benchmark.
Existing video hash functions are built on three isolated stages: frame pooling, relaxed learning, and binarization, which have not adequately explored the temporal order of video frames in a joint binary optimization model, resulting in severe information loss. In this paper, we propose a novel unsupervised video hashing framework dubbed Self-Supervised Video Hashing (SSVH), that is able to capture the temporal nature of videos in an end-to-end learning-to-hash fashion. We specifically address two central problems: 1) how to design an encoder-decoder architecture to generate binary codes for videos; and 2) how to equip the binary codes with the ability of accurate video retrieval. We design a hierarchical binary autoencoder to model the temporal dependencies in videos with multiple granularities, and embed the videos into binary codes with less computations than the stacked architecture. Then, we encourage the binary codes to simultaneously reconstruct the visual content and neighborhood structure of the videos. Experiments on two real-world datasets (FCVID and YFCC) show that our SSVH method can significantly outperform the state-of-the-art methods and achieve the currently best performance on the task of unsupervised video retrieval.
We prove that the zero locus of an admissible normal function over an algebraic parameter space S is algebraic in the case where S is a curve.
We consider the gauge-boson sector of a locally SU(2) x U(1) invariant effective Lagrangian with ten dimension-six operators added to the Lagrangian of the Standard Model. These operators induce anomalous three- and four-gauge-boson couplings and an anomalous gamma gamma H coupling. In the framework of this effective Lagrangian we calculate the helicity amplitudes and differential and total cross sections for the process gamma gamma --> WW at a photon collider. We give relations between different parts of the amplitudes that show which linear combinations of anomalous couplings are measurable in this reaction. The transformation properties of the differential cross section under CP are discussed. We find that three linear combinations of CP conserving and of CP violating couplings can be measured independently of the photon polarisation in gamma gamma --> WW.
We study the impact of stellar winds and supernovae on the multi-phase interstellar medium using three-dimensional hydrodynamical simulations carried out with FLASH. The selected galactic disc region has a size of (500 pc)$^2$ x $\pm$ 5 kpc and a gas surface density of 10 M$_{\odot}$/pc$^2$. The simulations include an external stellar potential and gas self-gravity, radiative cooling and diffuse heating, sink particles representing star clusters, stellar winds from these clusters which combine the winds from indi- vidual massive stars by following their evolution tracks, and subsequent supernova explosions. Dust and gas (self-)shielding is followed to compute the chemical state of the gas with a chemical network. We find that stellar winds can regulate star (cluster) formation. Since the winds suppress the accretion of fresh gas soon after the cluster has formed, they lead to clusters which have lower average masses (10$^2$ - 10$^{4.3}$ M$_{\odot}$) and form on shorter timescales (10$^{-3}$ - 10 Myr). In particular we find an anti-correlation of cluster mass and accretion time scale. Without winds the star clusters easily grow to larger masses for ~5 Myr until the first supernova explodes. Overall the most massive stars provide the most wind energy input, while objects beginning their evolution as B-type stars contribute most of the supernova energy input. A significant outflow from the disk (mass loading $\gtrsim$ 1 at 1 kpc) can be launched by thermal gas pressure if more than 50% of the volume near the disc mid-plane can be heated to T > 3x10$^5$ K. Stellar winds alone cannot create a hot volume-filling phase. The models which are in best agreement with observed star formation rates drive either no outflows or weak outflows.
A National Research Council study on connecting quarks with the cosmos has recently posed a number of the more important open questions at the interface between particle physics and cosmology. These questions include the nature of dark matter and dark energy, how the Universe began, modifications to gravity, the effects of neutrinos on the Universe, how cosmic accelerators work, and whether there are new states of matter at high density and pressure. These questions are discussed in the context of the talks presented at this Summer Institute.
We consider Kerr-Newman-AdS-dS black holes near extremality and work out the near-horizon geometry of these near-extremal black holes. We identify the exact U(1)_L x U(1)_R isometries of the near-horizon geometry and provide boundary conditions enhancing them to a pair of commuting Virasoro algebras. The conserved charges of the corresponding asymptotic symmetries are found to be well defined and non-vanishing and to yield central charges c_L\neq0 and c_R=0. The Cardy formula subsequently reproduces the Bekenstein-Hawking entropy of the black hole. This suggests that the near-extremal Kerr-Newman-AdS-dS black hole is holographically dual to a non-chiral two-dimensional conformal field theory.
The nature of the progenitors of type Ia supernovae is still a mystery. While plausible candidates are known for both the single degenerate and double degenerate models, the observed numbers fall significantly short of what is required to reproduce the type Ia supernovae rate.   Some of the most promising single-degenerate type Ia progenitors are recurrent novae and super-soft sources (SSS). White dwarfs with higher mass transfer rates can also be type Ia supernova progenitors. For these rapidly accreting white dwarfs (RAWD), more material than is needed for steady burning accretes on the white dwarf, and extends the white dwarf's photosphere. Unlike super-soft sources, such objects will likely not be detectable at soft X-ray energies, but will be bright at longer wavelengths, such as the far ultraviolet (UV). Possible examples include LMC N66 and the V Sagittae stars.   We present a survey using multi-object spectrographs looking for RAWD in the central core of the SMC, from objects selected to be bright in the far UV and with blue far UV-V colors. While we find some unusual objects, and recover known planetary nebula and WR stars, we detect no candidate RAWD. The upper limits from this non-detection depending on our expectations of what a RAWD should look like, as well assumptions about the internal extinction of the SMC. Assuming they resemble LMC N66 or fainter versions of Wolf-Rayet stars we set an upper limit of 10-14 RAWD in the SMC. However, our survey is unlikely to detect objects like V Sge, and hence we cannot set meaningful upper limits if RAWD generally resemble these.