ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a new approach to fluctuation identities for reflected L\'{e}vy processes with one-sided jumps. This approach is based on a number of easy to understand observations and does not involve excursion theory or It\^{o} calculus. It also leads to more general results.
Seshadri constants express the so called local positivity of a line bundle on a projective variety. They were introduced by Demailly. The original idea of using them towards a proof of the Fujita conjecture failed but they quickly became a subject of intensive study quite in their own right. Lazarsfeld's book "Positivity in Algebraic Geometry" contains a whole chapter devoted to local positivity and serves as a very enjoyable introduction to Seshadri constants. Since this book has appeared, the subject witnessed quite a bit of development. It is the aim of these notes to give an account of recent progress as well as to discuss many open questions and provide some examples.
Mammogram inspection in search of breast tumors is a tough assignment that radiologists must carry out frequently. Therefore, image analysis methods are needed for the detection and delineation of breast masses, which portray crucial morphological information that will support reliable diagnosis. In this paper, we proposed a conditional Generative Adversarial Network (cGAN) devised to segment a breast mass within a region of interest (ROI) in a mammogram. The generative network learns to recognize the breast mass area and to create the binary mask that outlines the breast mass. In turn, the adversarial network learns to distinguish between real (ground truth) and synthetic segmentations, thus enforcing the generative network to create binary masks as realistic as possible. The cGAN works well even when the number of training samples are limited. Therefore, the proposed method outperforms several state-of-the-art approaches. This hypothesis is corroborated by diverse experiments performed on two datasets, the public INbreast and a private in-house dataset. The proposed segmentation model provides a high Dice coefficient and Intersection over Union (IoU) of 94% and 87%, respectively. In addition, a shape descriptor based on a Convolutional Neural Network (CNN) is proposed to classify the generated masks into four mass shapes: irregular, lobular, oval and round. The proposed shape descriptor was trained on Digital Database for Screening Mammography (DDSM) yielding an overall accuracy of 80%, which outperforms the current state-of-the-art.
Upcoming surveys with new radio observatories such as the Square Kilometer Array will generate a wealth of imaging data containing large numbers of radio galaxies. Different classes of radio galaxies can be used as tracers of the cosmic environment, including the dark matter density field, to address key cosmological questions. Classifying these galaxies based on morphology is thus an important step toward achieving the science goals of next generation radio surveys. Radio galaxies have been traditionally been classified as Fanaroff-Riley (FR) I and II, although some exhibit more complex 'bent' morphologies arising from environmental factors or intrinsic properties. In this work we present the FIRST Classifier, an on-line system for automated classification of Compact and Extended radio sources. We developed the FIRST Classifier based on a trained Deep Convolutional Neural Network Model to automate the morphological classification of compact and extended radio sources observed in the FIRST radio survey. Our model achieved an overall accuracy of 97% and a recall of 98%, 100%, 98% and 93% for Compact, BENT, FRI and FRII galaxies respectively. The current version of the FIRST classifier is able to predict the morphological class for a single source or for a list of sources as Compact or Extended (FRI, FRII and BENT).
This paper describes a technique of real time head gesture recognition system. The method includes Gaussian mixture model (GMM) accompanied by optical flow algorithm which provided us the required information regarding head movement. The proposed model can be implemented in various control system. We are also presenting the result and implementation of both mentioned method.
3D and 4D printing are cutting-edge technologies for precise and expedited manufacturing of objects ranging from plastic to metal. Recent advances in 3D and 4D printing technologies in dentistry and maxillofacial surgery enable dentists to custom design and print surgical drill guides, temporary and permanent crowns and bridges, orthodontic appliances and orthotics, implants, mouthguards for drug delivery. In the present review, different 3D printing technologies available for use in dentistry are highlighted together with a critique on the materials available for printing. Recent reports of the application of these printed platformed are highlighted to enable readers appreciate the progress in 3D/4D printing in dentistry.
We present a solvable ladder model which displays magnetization plateaus at fractional values of the total magnetization. Plateau signatures are also shown to exist along special lines. The model has isotropic Heisenberg interactions with additional many-body terms. The phase diagram can be calculated exactly for all values of the rung coupling and the magnetic field. We also derive the anomalous behaviour of the susceptibility near the plateau boundaries. There is good agreement with the phase diagram obtained recently for the pure Heisenberg ladders by numerical and perturbative techniques.
In this paper, we study damped oscillating form of dark energy for explaining dynamics of universe. First of all, we consider universe is filled with an ideal fluid which has damped oscillating dark energy in terms of this case we calculate several physical quantities such as Hubble parameter, acceleration parameter, energy density, pressure and others for dark energy, dark energy-matter coupling and non-coupling cases. Secondly, we consider as universe is filled with scalar field instead of an ideal fluid we obtain these physical quantities in terms of scalar potential and kinetic term for the same cases in scalar-tensor formalism. Finally, we show that ideal fluid description and scalar-tensor description of dark energy give mathematically equivalent results for this EoS parameter, even if they haven't same physical meaning.
In this work, we investigate warm inflationary models in the context of a general scalar-tensor theory of gravity which is coupled to radiation through a dissipation term. We first derive the potential of exponential and hyperbolic tangent forms. We consider a dissipation parameter of the form $\Gamma = C_{1}T$ with $C_1$ being a coupling parameter and focus only on the strong regime of which the interaction between inflaton and radiation fluid has been taken into account. We compute inflationary observables and constrain the parameters of our model using current Planck 2018 data. From our analysis, we discover that the weak coupling limit $\xi\ll 1$ is needed in order to have the derived $n_s$ and $r$ consistent with the Planck 2018 observational constraints. Particularly, we constrain the potential scale $V_{0}$ of the models.
How to effectively approximate real-valued parameters with binary codes plays a central role in neural network binarization. In this work, we reveal an important fact that binarizing different layers has a widely-varied effect on the compression ratio of network and the loss of performance. Based on this fact, we propose a novel and flexible neural network binarization method by introducing the concept of layer-wise priority which binarizes parameters in inverse order of their layer depth. In each training step, our method selects a specific network layer, minimizes the discrepancy between the original real-valued weights and its binary approximations, and fine-tunes the whole network accordingly. During the iteration of the above process, it is significant that we can flexibly decide whether to binarize the remaining floating layers or not and explore a trade-off between the loss of performance and the compression ratio of model. The resulting binary network is applied for efficient pedestrian detection. Extensive experimental results on several benchmarks show that under the same compression ratio, our method achieves much lower miss rate and faster detection speed than the state-of-the-art neural network binarization method.
Motivated by recent experiments and computational results on pyrochlore iridates, we compare single-particle properties of Y2Ir2O7 obtained from single-site dynamical mean-field calculations with results within the TRILEX approximation, where the latter takes non-local correlations into account. Our calculations are all based on ab-initio calculations within density-functional theory, and take spin-orbit coupling into account. In order to make the treatment within TRILEX feasible, we first define a single-band jeff = 1/2 model, by comparing its spectral features within DMFT to a three-band model that includes both jeff = 1/2 and jeff = 3/2 orbitals. Our calculations show consistently a paramagnetic metallic phase at small interaction values, and an insulating antiferromagnetic phase at larger interaction values. The critical interactions, however, differ between single-site and TRILEX calculations. The antiferromagnetic phase shows the already predicted all-in/all-out magnetic ordering. Different to the single-site results, the TRILEX calculation gives also evidence for the Weyl-semimetal regime in the vicinity of the metal-insulator transition.
In this paper, we address the problem of denoising images degraded by Poisson noise. We propose a new patch-based approach based on best linear prediction to estimate the underlying clean image. A simplified prediction formula is derived for Poisson observations, which requires the covariance matrix of the underlying clean patch. We use the assumption that similar patches in a neighborhood share the same covariance matrix, and we use off-the-shelf Poisson denoising methods in order to obtain an initial estimate of the covariance matrices. Our method can be seen as a post-processing step for Poisson denoising methods and the results show that it improves upon several Poisson denoising methods by relevant margins.
We consider a general family of quantum key distribution (QKD) protocols utilizing displaced thermal states with discretized modulations. Separating the effects of the Gaussian channel and the non-Gaussian distribution, we have studied the dependence of the secret key generation rate on the magnitude of modulations (the strength of the modulated signal). We show that in the limit of strong signal, QKD is impossible: from the perspective of an efficient eavesdropper, the ensemble of transmitted states is effectively classical. This constitutes a quantum correction to performance of finite-length QKD protocols. We demonstrate that two regimes must be distinguished: weak and strong thermal noise. In the case of strong noise, the security boundary is mostly determined by the weak-signal limit. When the noise is weak, however, QKD may become possible only when the signal strength exceeds some critical value.
Eternal inflation requires upward fluctuations of the energy in a Hubble volume, which appear to violate the energy conditions. In particular, a scalar field in an inflating spacetime should obey the averaged null energy condition, which seems to rule out eternal inflation. Here we show how eternal inflation is possible when energy conditions (even the null energy condition) are obeyed. The critical point is that energy conditions restrict the evolution of any single quantum state, while the process of eternal inflation involves repeatedly selecting a subsector of the previous state, so there is no single state where the conditions are violated.
Sparsity-regularized synthetic aperture radar (SAR) imaging framework has shown its remarkable performance to generate a feature enhanced high resolution image, in which a sparsity-inducing regularizer is involved by exploiting the sparsity priors of some visual features in the underlying image. However, since the simple prior of low level features are insufficient to describe different semantic contents in the image, this type of regularizer will be incapable of distinguishing between the target of interest and unconcerned background clutters. As a consequence, the features belonging to the target and clutters are simultaneously affected in the generated image without concerning their underlying semantic labels. To address this problem, we propose a novel semantic information guided framework for target oriented SAR image formation, which aims at enhancing the interested target scatters while suppressing the background clutters. Firstly, we develop a new semantics-specific regularizer for image formation by exploiting the statistical properties of different semantic categories in a target scene SAR image. In order to infer the semantic label for each pixel in an unsupervised way, we moreover induce a novel high-level prior-driven regularizer and some semantic causal rules from the prior knowledge. Finally, our regularized framework for image formation is further derived as a simple iteratively reweighted $\ell_1$ minimization problem which can be conveniently solved by many off-the-shelf solvers. Experimental results demonstrate the effectiveness and superiority of our framework for SAR image formation in terms of target enhancement and clutters suppression, compared with the state of the arts. Additionally, the proposed framework opens a new direction of devoting some machine learning strategies to image formation, which can benefit the subsequent decision making tasks.
We introduce a Grothendieck ring of higher Artin stacks generalizing the Grothendieck ring of algebraic varieties. We show that this ring is not trivial by noticing that it factors the invariant "number of rational points over a finite field". We also introduce the notion of "special Artin stacks", which by definition have affine homotopy groups \pi_{i}, and furthermore unipotent for i>1. Our principal theorem states that the natural inclusion morphism from the Grothendieck ring of varieties to the Grothendieck ring of special Artin stacks is an isomorphism after inverting the class of the affine line L and the classes of L^{i}-1 for all i>0. We deduce from this that several numerical invariants defined for varieties (e.g. Hodge numbers, l-adic Euler characteristic ...) extend uniquely to invariants defined for special Artin stacks. In particular we obtain a trace formula for special Artin stacks of finite type over a finite field, identifying the number of rational points as the trace of the Frobenius acting on the l-adic Euler characteristic.
We revisit the F-term hybrid inflation model in supergravity. In particular, we point out that a constant term in the superpotential has significant effects on the inflaton dynamics. It is shown that the hybrid inflation model suffers from several potential problems: tuning of the initial condition, gravitino overproduction and formation of cosmic strings, for both minimal and non-minimal Kahler potentials. These problems can only be avoided in gauge-mediated SUSY breaking models where the gravitino is relatively light and the constant term in the superpotential is not important. Implications on the non-thermal leptogenesis scenario are also described.
It is concluded in the literature that Ellis wormhole is unstable under small perturbations and would decay either to the Schwarzschild black hole or expand away to infinity. While this deterministic conclusion of instability is correct, we show that the Ellis wormhole reduces to Schwarzschild black hole \textit{only} when the Ellis solution parameter $\gamma $ assumes a complex value $-i$. We shall then reexamine stability of Ellis and phantom wormholes from the viewpoint of local and asymptotic observers by using a completely different approach, viz., we adapt Tangherlini's nondeterministic, prequantal statistical simulation about photon motion in the real optical medium to an effective medium reformulation of motions obtained via Hamilton's optical-mechanical analogy in a gravity field. A crucial component of Tangherlini's idea is the observed increase of momentum of the photons entering a real medium. We show that this fact has a heuristic parallel in the effective medium\ version of the Pound-Rebka experiment in gravity. Our conclusion is that there is a non-zero probability that Ellis and phantom wormholes could appear stable or unstable depending on the location of observers and on the values of $\gamma$, leading to the possibility of \textit{ghost wormholes} (like ghost stars). The Schwarzschild horizon, however, would always appear certainly stable ($R=1$, $T=0$) to observers regardless of their location. Phantom wormholes of bounded mass in the extreme limit $a\rightarrow -1$ are also shown to be stable just as the Schwarzschild black hole is. We shall propose a thought experiment showing that our non-deterministic results could be numerically translated into observable deterministic signatures of ghost wormholes.
In this paper we prove that the inductively defined graph dimension has a simple additive property under the join operation. The dimension of the join of two simple graphs is one plus the sum of the dimensions of the component graphs: $\mathrm{dim}\, (G_1+ G_2) = 1 +\mathrm{dim}\, G_1+ \mathrm{dim}\, G_2$. We use this formula to derive an expression for the inductive dimension of an arbitrary finite simple graph from its minimum edge clique cover. A corollary of the formula is that any arbitrary finite simple graph whose maximal cliques are all of order $N$ has dimension $N-1$. We finish by finding lower and upper bounds on the inductive dimension of a simple graph in terms of its clique number.
We perform a set of numerical experiments studying the interaction of Type I X-ray bursts with thin, Shakura-Sunyaev type accretion discs. Careful observations of X-ray spectra during such bursts have hinted at changes occurring in the inner regions of the disc. We now clearly demonstrate a number of key effects that take place simultaneously, including: evidence for weak, radiation-driven outflows along the surface of the disc; significant levels of Poynting-Robertson (PR) drag, leading to enhanced accretion; and prominent heating in the disc, which increases the height, while lowering the density and optical depth. The PR drag causes the inner edge of the disc to retreat from the neutron star surface toward larger radii and then recover on the timescale of the burst. We conclude that the rich interaction of an X-ray burst with the surrounding disc provides a novel way to study the physics of accretion onto compact objects.
We investigated the analytical solution of fractional order K(m,n) type equation with variable coefficient which is an extended type of KdV equations into a genuinely nonlinear dispersion regime. By using the Lie symmetry analysis, we obtain the Lie point symmetries for this type of time-fractional partial differential equations (PDE). Also we present the corresponding reduced fractional differential equations (FDEs) corresponding to the time-fractional K(m,n) type equation.
Observables of cosmic structures are usually not the underlying matter field but biased tracers of matter, such as galaxies or halos. We show how the bias found in Newtonian N-body simulations can be interpreted in terms of the weak-field limit of General Relativity (GR). For this we employ standard Newtonian simulations of cold dark matter and incorporate GR/radiation via a weak-field dictionary that we have recently developed. We find that even when a simple local biasing scheme is employed in the Newtonian simulation, the relativistic bias becomes inherently scale-dependent due to the presence of radiation and GR corrections. This scale-dependence could be in principle observed on large scales in upcoming surveys. As a working example, we apply our methodology to Newtonian simulations for the spherical collapse and recover permille-level agreement between the approaches for extracting the relativistic bias on all considered scales.
We develop a fairly explicit Kuznetsov formula on GL(3) and discuss the analytic behaviour of the test functions on both sides. Applications to Weyl's law, exceptional eigenvalues, a large sieve and L-functions are given.
We investigated a wealth of X-ray and gamma-ray spectral energy distribution (SED) and multi-band light curve (LC) data of the gamma-ray binary HESS J0632+057 using a phenomenological intrabinary shock (IBS) model. Our baseline model assumes that the IBS is formed by colliding winds from a putative pulsar and its Be companion, and particles accelerated in the IBS emit broadband radiation via synchrotron (SY) and inverse-Compton upscattering (ICS) processes. Adopting the latest orbital solution and system geometry (Tokayer et al. 2021), we reproduced the global X-ray and TeV LC features, two broad bumps at $\phi \sim 0.3$ and $\sim0.7$, with the SY and ICS model components. We found these TeV LC peaks originate from ICS emission caused by the enhanced seed photon density near periastron and superior conjunction or Doppler-beamed emission of bulk-accelerated particles in the IBS at inferior conjunction. While our IBS model successfully explained most of the observed SED and LC data, we found that phase-resolved SED data in the TeV band require an additional component associated with ICS emission from pre-shock particles (produced by the pulsar wind). This finding indicates a possibility of delineating the IBS emission components and determining the bulk Lorentz factors of the pulsar wind at certain orbital phases.
Formation of a canted spiral magnetic order is studied in the framework of a mean-field approximation of the Hubbard model. It is revealed that this magnetic state can be stabilized under certain conditions in layered systems with a relatively small interplane electron hopping. Example of an experimentally observed magnetic structure of La$_{2-x}$Sr$_x$CuO$_4$ is considered. It is shown that the canting magnetic order can be described in terms of a simple non-relativistic band magnetism.
This paper deals with the spherically symmetric flow of compressible viscous and polytropic ideal fluid in unbounded domain exterior to a ball in $\mathbb{R}^n$ with $n\ge2$. We show that the global solutions are convergent as time goes to infinity. The critical step is obtaining the point-wise bound of the specific volume $v(x,t)$ and the absolute temperature $\theta(x,t)$ from up and below both for $x$ and $t$. Note that the initial data can be arbitrarily large and, compared with \cite{nn}, our method applies to the spatial dimension $n=2.$ The proof is based on the elementary energy methods.