ShantanuT01/DACTYL-Pretraining huggingface dataset:
The self-consistent equations for MI phase transition are formulated. We assume two order parameters which describe the phase transition. The first one is the density distribution at MI boundary $\rho (\vec r)$. The second one is a two component complex vector in spin space $\Psi (\vec r)$. It determines electron density in metallic or semimetallic phase in the presence of external magnetic field. Two different components of the vector describe possible spin states of electrons inserted in the external magnetic field.   The first order type MI phase transition determined by the variation of the density distribution is considered by means of the gradient expansion of Cahn and Hillard type \cite{CahnHillard}. The second order type transition of electron density beside MI boundary is described by Ginzburg -- Landau expansion \cite{LandLif2}. The interaction between these two parameters is assumed to be linear as a function of electron density with a coefficient which depends on metallic density (cf. \cite{JinwuYe_Lubensky}). The obtained nonlinear equations are exactly solved in the case of MI boundary in the presence of the parallel to the boundary or perpendicular to it uniform magnetic field. The surface tension $\Sigma _{mi}$ at the MI boundary is calculated. It is shown that $\Sigma _{mi}$ is singular. In particular, $\Sigma _{mi}\sim n^{3/2}$ as $ n\Rightarrow 0$ and $\Sigma _{mi}\sim (T-T_c (\vec h))^{3/2} .$ $T_c (\vec h)$ is the transition temperature in the presence of external magnetic field at MI phase transition. \par The singular behavior of $\Sigma _{mi}$ leads to an emphasized hysteresis at MI transition.
I describe the scenario of molecular cloud (MC) evolution that has emerged over the past decade or so. MCs can start out as cold atomic clouds formed by compressive motions in the warm neutral medium (WNM) of galaxies. Such motions can be driven by large-scale instabilities, or by local turbulence. The compressions induce a phase transition to the cold neutral medium (CNM) to form growing cold atomic clouds, which in their early stages may constitute thin CNM sheets. Several dynamical instabilities soon destabilize a cloud, rendering it turbulent. For solar neighborhood conditions, a cloud is coincidentally expected to become molecular, magnetically supercritical, and gravitationally dominated at roughly the same column density, $N \sim 1.5 \times 10^21 \psc \approx 10 \Msun$ pc$^{-2}$. At this point, the cloud begins to contract gravitationally. However, before its global collapse is completed ($\sim 10^7$ yr later), the nonlinear density fluctuations within the cloud, which have shorter local free-fall times, collapse first and begin forming stars, a few Myr after the global contraction started. Large-scale fluctuations of lower mean densities collapse later, so the formation of massive star-forming regions is expected to occur late in the evolution of a large cloud complex, while scattered low-mass regions are expected to form earlier. Eventually, the local star formation episodes are terminated by stellar feedback, which disperses the local dense gas, although more work is necessary to clarify the details and characteristic scales of this process.
The Escalator Boxcar Train method (EBT) is a numerical method for structured population models of McKendrick-von Foerster type. Those models consist of a certain class of hyperbolic partial differential equations and describe time evolution of the distribution density of the structure variable describing a feature of individuals in the population. The method was introduced in late eighties and widely used in theoretical biology, but its convergence was proven only in recent years using the framework of measure-valued solutions. Till now the EBT method was developed only for scalar equation models. In this paper we derive a full numerical EBT scheme for age-structured, two-sex population model (Fredrickson-Hoppensteadt model), which consists of three coupled hyperbolic partial differential equations with nonlocal boundary conditions. It is the first step towards extending the EBT method to systems of structured population equations.
We consider a model of a Brownian motor composed of two coupled overdamped degrees of freedom moving in periodic potentials and driven by two heat reservoirs. This model exhibits a spontaneous breaking of symmetry and gives rise to directed transport in the case of a non- vanishing interparticle interaction strength. For strong coupling between the particles we derive an expression for the propagation velocity valid for arbitrary periodic potentials. In the limit of strong coupling the model is equivalent to the B\"uttiker-Landauer model [1-3] for a single particle diffusing in an environment with position dependent temperature. By using numerical calculations of the Fokker-Planck equation and simulations of the Langevin equations we study the model for arbitrary coupling, retrieving many features of the strong coupling limit. In particular, directed transport emerges even for symmetric potentials. For distinct heat reservoirs the heat currents are well-defined quantities allowing a study of the motor efficiency. We show that the optimal working regime occurs for moderate coupling. Finally, we introduce a model with discrete phase space which captures the essential features of the continuous model, can be solved in the limit of weak coupling, and exhibits a larger efficiency than the continuous counterpart.
In this note, we prove that every fibre space structures of a projective irreducible symplectic manifold is a lagrangian fibration.
Motivated by experimental progress in the growth of heavy transition metal oxides, we theoretically study a class of lattice models of interacting fermions with strong spin-orbit coupling. Focusing on interactions of intermediate strength, we derive a low-energy effective field theory for a fully gapped, topologically ordered, fractionalized state with an eight-fold ground-state degeneracy. This state is a fermionic symmetry-enriched topological phase with particle-number conservation and time-reversal symmetry. The topological terms in the effective field theory describe a quantized magnetoelectric response and nontrivial mutual braiding statistics of dynamical extended vortex loops with emergent fermions in the bulk. We explicitly compute the expected mutual statistics in a specific model on the pyrochlore lattice within a slave-particle mean-field theory. We argue that our model also provides a possible condensed-matter realization of oblique confinement.
Type IIB string theory expanded around D3 brane backgrounds describes the dynamics of D3 branes as solitonic objects. On the other hand, there is a fundamental description of them via Polchinski's open strings with Dirichlet boundary conditions. Since these two descriptions describe the dynamics of the same objects, D3 branes, it is natural to believe that they are dual. Therefore at this level, we have a string-string duality as opposed to a string-field theory duality. Once we take the same limits in both descriptions, Maldacena Conjecture in its weaker form follows. We try to make this viewpoint precise and study the implication of it for the stronger form of Maldacena Conjecture.
This paper presents a method of zero-shot learning (ZSL) which poses ZSL as the missing data problem, rather than the missing label problem. Specifically, most existing ZSL methods focus on learning mapping functions from the image feature space to the label embedding space. Whereas, the proposed method explores a simple yet effective transductive framework in the reverse way \--- our method estimates data distribution of unseen classes in the image feature space by transferring knowledge from the label embedding space. In experiments, our method outperforms the state-of-the-art on two popular datasets.
We perform a sub-threshold follow-up search for continuous nearly-monochromatic gravitational waves from the central compact objects associated with the supernova remnants Vela Jr., Cassiopeia A, and SNR G347.3$-$0.5. Across the three targets, we investigate the most promising ~ 10,000 combinations of gravitational wave frequency and frequency derivative values, based on the results from an Einstein@Home search of the LIGO O1 observing run data, dedicated to these objects. The selection threshold is set so that a signal could be confirmed using the newly released O2 run LIGO data. In order to achieve best sensitivity we perform two separate follow-up searches, on two distinct stretches of the O2 data. Only one candidate survives the first O2 follow-up investigation, associated with the central compact object in SNR G347.3-0.5, but it is not conclusively confirmed. In order to assess a possible astrophysical origin we use archival X-ray observations and search for amplitude modulations of a pulsed signal at the putative rotation frequency of the neutron star and its harmonics. This is the first extensive electromagnetic follow-up of a continuous gravitational wave candidate performed to date. No significant associated signal is identified. New X-ray observations contemporaneous with the LIGO O3 run will enable a more sensitive search for an electromagnetic counterpart. A focused gravitational wave search in O3 data based on the parameters provided here should be easily able to shed light on the nature of this outlier. Noise investigations on the LIGO instruments could also reveal the presence of a coherent contamination.
We study the coexistence of phases in a two--species model whose free energy is given by the scaling limit of a system with long range interactions (Kac potentials) which are attractive between particles of the same species and repulsive between different species.
We observed the narrow-line quasar SDSS J094857.3+002225, which has the highest known radio loudness for a narrow-line Seyfert~1 galaxy (NLS1), at 1.7--15.4 GHz with the Very Long Baseline Array (VLBA). This is the first very-long-baseline interferometry (VLBI) investigation for a radio-loud NLS1. We independently found very high brightness temperatures from (1) its compactness in a VLBA image and (2) flux variation among the VLBA observation, our other observations with the VLBA, and the Very Large Array (VLA). A Doppler factor larger than 2.7--5.5 was required to meet an intrinsic limit of brightness temperature in the rest frame. This is evidence for highly relativistic nonthermal jets in an NLS1. We suggest that the Doppler factor is one of the most crucial parameters determining the radio loudness of NLS1s. The accretion disk of SDSS J094857.3+002225 is probably in the very high state, rather than the high/soft state, by analogy with X-ray binaries with strong radio outbursts and superluminal jets such as GRS 1915+105.
We develop a semiclassical kinetic theory for electron spin relaxation in semiconductors. Our approach accounts for elastic as well as inelastic scattering and treats Elliott-Yafet and motional-narrowing processes, such as D'yakonov-Perel' and variable g-factor processes, on an equal footing. Focusing on small spin polarizations and small momentum transfer scattering, we derive, starting from the full quantum kinetic equations, a Fokker-Planck equation for the electron spin polarization. We then construct, using a rigorous multiple time scale approach, a Bloch equation for the macroscopic ($\vec{k}$-averaged) spin polarization on the long time scale, where the spin polarization decays. Spin-conserving energy relaxation and diffusion, which occur on a fast time scale, after the initial spin polarization has been injected, are incorporated and shown to give rise to a weight function which defines the energy averages required for the calculation of the spin relaxation tensor in the Bloch equation. Our approach provides an intuitive way to conceptualize the dynamics of the spin polarization in terms of a ``test'' spin polarization which scatters off ``field'' particles (electrons, impurities, phonons). To illustrate our approach, we calculate for a quantum well the spin lifetime at temperatures and densities where electron-electron and electron-impurity scattering dominate. The spin lifetimes are non-monotonic functions of temperature and density. Our results show that at electron densities and temperatures, where the cross-over from the non-degenerate to the degenerate regime occurs, spin lifetimes are particularly long.
Previous studies by our group have shown that three-dimensional high-frequency quantitative ultrasound methods have the potential to differentiate metastatic lymph nodes from cancer-free lymph nodes dissected from human cancer patients. To successfully perform these methods inside the lymph node parenchyma, an automatic segmentation method is highly desired to exclude the surrounding thin layer of fat from quantitative ultrasound processing and accurately correct for ultrasound attenuation. In high-frequency ultrasound images of lymph nodes, the intensity distribution of lymph node parenchyma and fat varies spatially because of acoustic attenuation and focusing effects. Thus, the intensity contrast between two object regions (e.g., lymph node parenchyma and fat) is also spatially varying. In our previous work, nested graph cut demonstrated its ability to simultaneously segment lymph node parenchyma, fat, and the outer phosphate-buffered saline bath even when some boundaries are lost because of acoustic attenuation and focusing effects. This paper describes a novel approach called graph cut with locally adaptive energy to further deal with spatially varying distributions of lymph node parenchyma and fat caused by inhomogeneous acoustic attenuation. The proposed method achieved Dice similarity coefficients of 0.937+-0.035 when compared to expert manual segmentation on a representative dataset consisting of 115 three-dimensional lymph node images obtained from colorectal cancer patients.
We construct some $n$-dimensional eigenvarieties for finite slope overconvergent eigenforms over some unitary Shimura varieties with signature $(1,n-1)\times(0,n)\times\cdots\times(0,n)$ by adapting Andreatta-Iovita-Pilloni's method. We also show that there are some Galois pseudo-characters over our eigenvarieties by studying analytic continuation of finite slope eigenforms over these Shimura varieties.
We study a geometric analogue of the Iwasawa Main Conjecture for constant ordinary abelian varieties over $\ZZ_p^d$-extensions of function fields ramifying at a finite set of places.
We prove scattering for a massless wave equation which is critical in two space dimensions. Our method combines conformal inversion with decay estimates from Struwe's previous work on global existence of a similar equation.
A general type of ray class fields of global function fields is investigated. The systematic computation of their genera leads to new examples of curves over finite fields with comparatively many rational points.
We propose an end-to-end deep learning method that learns to estimate emphysema extent from proportions of the diseased tissue. These proportions were visually estimated by experts using a standard grading system, in which grades correspond to intervals (label example: 1-5% of diseased tissue). The proposed architecture encodes the knowledge that the labels represent a volumetric proportion. A custom loss is designed to learn with intervals. Thus, during training, our network learns to segment the diseased tissue such that its proportions fit the ground truth intervals. Our architecture and loss combined improve the performance substantially (8% ICC) compared to a more conventional regression network. We outperform traditional lung densitometry and two recently published methods for emphysema quantification by a large margin (at least 7% AUC and 15% ICC), and achieve near-human-level performance. Moreover, our method generates emphysema segmentations that predict the spatial distribution of emphysema at human level.
The reggeized gluon states, which are also called Reggeons, appear in the scattering amplitude of hadrons in Regge limit. The wave-function of Reggeons satisfy the BKP equation, which in multi-colour limit of Quantum Chromodynamics is equivalent to the Schrodinger equation of the XXX Heisenberg SL(2,C) spin chain model. In this work we solve the BKP equation, show the spectrum of the energy and other integrals of motion for a number of Reggeons N=2,...,8. Moreover, we consider deep inelastic scattering where due to the reggeized gluons states we are able to calculate anomalous dimensions and corresponding to their twists.
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is therefore critical to develop novel approaches that can bridge the gap between exact solutions that are costly, and fast heuristics that offer no quality assurances. In this paper, we propose a hybrid quantum-classical algorithm for robust fitting. Our core contribution is a novel robust fitting formulation that solves a sequence of integer programs and terminates with a global solution or an error bound. The combinatorial subproblems are amenable to a quantum annealer, which helps to tighten the bound efficiently. While our usage of quantum computing does not surmount the fundamental intractability of robust fitting, by providing error bounds our algorithm is a practical improvement over randomised heuristics. Moreover, our work represents a concrete application of quantum computing in computer vision. We present results obtained using an actual quantum computer (D-Wave Advantage) and via simulation. Source code: https://github.com/dadung/HQC-robust-fitting
We construct an analogue of the ring of algebraic numbers, living in a quotient of the product of all finite fields of prime order. We use this ring to deduce some results about linear recurrent sequences.
In this paper we study automatic recognition of cars of four types: Bus, Truck, Van and Small car. For this problem we consider two data driven frameworks: a deep neural network and a support vector machine using SIFT features. The accuracy of the methods is validated with a database of over 6500 images, and the resulting prediction accuracy is over 97 %. This clearly exceeds the accuracies of earlier studies that use manually engineered feature extraction pipelines.
First-principles calculations for pristine neutral ferroelectric domain walls in BiFeO$_3$ reveal that excess electrons are selectively trapped by the domain walls, while holes are only weakly attracted. Such trapped excess electrons may be responsible for the thermally activated electrical conductivity at domain walls observed in experiments. In the case of a periodic array of domain walls, the trapped excess electrons create a zigzag potential, whose amplitude depends on the electron concentration in the material and the domain-wall distance. The potential is asymmetric for 71{\deg} and 109{\deg} domain walls. This could modify the open-circuit voltage in a solar cell and hence influence the photoelectric effect in BiFeO$_3$.
Novel superhard materials, especially those with superior thermal and chemical stability, are needed to replace diamond. Carbon nitrides (C-N), which are likely to possess these charac- teristics and have even been expected to be harder than diamond, are excellent candidates. Here we report three new superhard and thermodynamically stable carbon nitride phases. Based on a systematic evolutionary structure searches, we report a complete phase diagram of the C-N system at 0-300 GPa and analyze the hardest metastable structures. Surprising- ly, we find that at zero pressure, the earlier proposed graphitic-C3N4 structure (P-6m2) is dynamically unstable and the lowest energy form of structures based on s-triazine unit and s-heptazine unit have similar topology and belong to the same space group.
Two-dimensional (2D) layered semiconductors, with their ultimate atomic thickness, have shown promise to scale down transistors for modern integrated circuitry. However, the electrical contacts that connect these materials with external bulky metals are usually unsatisfactory, which limits the transistor performance. Recently, contacting 2D semiconductors using coplanar 2D conductors has shown promise in reducing the problematic high resistance contacts. However, many of these methods are not ideal for scaled production. Here, we report on the large-scale, spatially controlled chemical assembly of the integrated 2H-MoTe2 field-effect transistors (FETs) with coplanar metallic 1T' MoTe2 contacts via phase engineered approaches. We demonstrate that the heterophase FETs exhibit ohmic contact behavior with low contact resistance, resulting from the coplanar seamless contact between 2H and 1T' MoTe2 confirmed by transmission electron microscopy characterizations. The average mobility of the heterophase FETs was measured to be as high as 23 cm2 V-1 s-1 (comparable with those of exfoliated single crystals), due to the large 2H MoTe2 single-crystalline domain (486{\mu}m). By developing a patterned growth method, we realize the 1T' MoTe2 gated heterophase FET array whose components of channel, gate, and contacts are all 2D materials. Finally, we transfer the heterophase device array onto a flexible substrate and demonstrate the near-infrared photoresponse with high photoresponsivity (~1.02 A/W). Our study provides a basis for the large-scale application of phase-engineered coplanar MoTe2 semiconductors-meter structure in advanced electronics and optoelectronics.
We present evolutionary models for young low mass stars and brown dwarfs taking into account episodic phases of accretion at early stages of the evolution, a scenario supported by recent large surveys of embedded protostars. An evolution including short episodes of vigorous accretion ($\mdot \ge 10^{-4} \msolyr$) followed by longer quiescent phases ($\mdot < 10^{-6} \msolyr$) can explain the observed luminosity spread in HR diagrams of star forming regions at ages of a few Myr, for objects ranging from a few Jupiter masses to a few tenths of a solar mass. The gravitational contraction of these accreting objects strongly departs from the standard Hayashi track at constant $\te$. The best agreement with the observed luminosity scatter is obtained if most of the accretion shock energy is radiated away. The obtained luminosity spread at 1 Myr in the HR diagram is equivalent to what can be misinterpreted as a $\sim$ 10 Myr age spread for non-accreting objects. We also predict a significant spread in radius at a given $\te$, as suggested by recent observations. These calculations bear important consequences on our understanding of star formation and early stages of evolution and on the determination of the IMF for young ($\le$ a few Myr) clusters. Our results also show that the concept of a stellar birthline for low-mass objects has no valid support.
In five dimensions, we consider a model described by the Einstein gravity with a source given by a scalar field and various Abelian gauge fields with dilatonic-like couplings. For this model, we are able to construct two dyonic black holes whose three-dimensional horizons are modeled by two nontrivial homogeneous Thurston's geometries. The dyonic solutions are of Lifshitz type with an arbitrary value of the dynamical exponent. In fact, the first gauge field ensures the anisotropy asymptotic while the remaining Abelian fields sustain the electric and magnetic charges. Using the Hamiltonian formalism, the mass, the electric and magnetic charges are explicitly computed. Interestingly enough, the dyonic solutions behave like Chern-Simons vortices in the sense that their electric and magnetic charges turn to be proportional. The extension with an hyperscaling violating factor is also scrutinized where we notice that for specific values of the violating factor, purely magnetic solutions are possible.