ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, mean-field theory is presented, for both statics and dynamics, and its validity tested self-consistently. As is well known, the mean-field approximation breaks down below four spatial dimensions, where it can be replaced by a scaling phenomenology. The Ginzburg-Landau formalism can then be used to justify the phenomenological theory using the renormalization group, which elucidates the physical and mathematical mechanism for universality. In the second part of the paper it is shown how near pattern forming linear instabilities of dynamical systems, a formally similar Ginzburg-Landau theory can be derived for nonequilibrium macroscopic phenomena. The real and complex Ginzburg-Landau equations thus obtained yield nontrivial solutions of the original dynamical system, valid near the linear instability. Examples of such solutions are plane waves, defects such as dislocations or spirals, and states of temporal or spatiotemporal (extensive) chaos.
Consider the positive, radial solutions of the nonlinear biharmonic equation $\Delta^2 u = u^p$. There is a critical power $p_c$ such that solutions are linearly stable if and only if $p\geq p_c$. We obtain their asymptotic expansion at infinity in the case that $p\geq p_c$.
Commonly used boundary conditions in reconstructing $f(T)$ gravity from holographic Ricci dark energy model (RDE) are found to cause some problem, we therefore propose new boundary conditions in this paper. By reconstructing $f(T)$ gravity from the RDE with these new boundary conditions, we show that the new ones are better than the present commonly used ones since they can give the physically expected information, which is lost when the commonly used ones are taken in the reconstruction, of the resulting $f(T)$ theory. Thus, the new boundary conditions proposed here are more suitable for the reconstruction of $f(T)$ gravity.
By combining the formalism of \cite{RHE} with a discrete approach close to the considerations of \cite{Davie}, we interpret and solve the rough partial differential equation $dy_t=A y_t \, dt+\sum_{i=1}^m f_i(y_t) \, dx^i_t$ ($t\in [0,T]$) on a compact domain $\mathcal{O}$ of $\R^n$, where $A$ is a rather general elliptic operator of $L^p(\mathcal{O})$ ($p>1$), $f_i(\vp)(\xi):=f_i(\vp(\xi))$ and $x$ is the generator of a $2$-rough path. The (global) existence, uniqueness and continuity of a solution is established under classical regularity assumptions for $f_i$. Some identification procedures are also provided in order to justify our interpretation of the problem.
The Ramsey number r(K_3,Q_n) is the smallest integer N such that every red-blue colouring of the edges of the complete graph K_N contains either a red n-dimensional hypercube, or a blue triangle. Almost thirty years ago, Burr and Erd\H{o}s conjectured that r(K_3,Q_n) = 2^{n+1} - 1 for every n \in \N, but the first non-trivial upper bound was obtained only recently, by Conlon, Fox, Lee and Sudakov, who proved that r(K_3,Q_n) \le 7000 \cdot 2^n. Here we show that r(K_3,Q_n) = (1 + o(1)) 2^{n+1} as n \to \infty.
We study the image of the $\ell$-adic Galois representations associated to the four vector valued Siegel modular forms appearing in the work of Chenevier and Lannes. These representations are symplectic of dimension $4$. Following a method of Dieulefait, we determine the primes $\ell$ for which these representations are absolutely irreducible. In addition, we show that their image is "full" for all primes $\ell$ such that the associated residual representation is absolutely irreducible, except in two cases.
We study the nonrelativistic limit of solitary waves from Nonlinear Maxwell-Klein-Gordon equations (NMKG) to Nonlinear Schrodinger-Poisson equations (NSP). It is known that the existence or multiplicity of positive solutions depends on the choices of parameters the equations contain. In this paper, we prove that for a given positive solitary wave of NSP, which is found in Ruiz's work \cite{R}, there corresponds a family of positive solitary waves of NMKG under the nonrelativistic limit. Notably, our results contain a new result of existence of positive solutions to (NMKG) with lower order nonlinearity.
A large labeled dataset is a key to the success of supervised deep learning, but for medical image segmentation, it is highly challenging to obtain sufficient annotated images for model training. In many scenarios, unannotated images are abundant and easy to acquire. Self-supervised learning (SSL) has shown great potentials in exploiting raw data information and representation learning. In this paper, we propose Hierarchical Self-Supervised Learning (HSSL), a new self-supervised framework that boosts medical image segmentation by making good use of unannotated data. Unlike the current literature on task-specific self-supervised pretraining followed by supervised fine-tuning, we utilize SSL to learn task-agnostic knowledge from heterogeneous data for various medical image segmentation tasks. Specifically, we first aggregate a dataset from several medical challenges, then pre-train the network in a self-supervised manner, and finally fine-tune on labeled data. We develop a new loss function by combining contrastive loss and classification loss and pretrain an encoder-decoder architecture for segmentation tasks. Our extensive experiments show that multi-domain joint pre-training benefits downstream segmentation tasks and outperforms single-domain pre-training significantly. Compared to learning from scratch, our new method yields better performance on various tasks (e.g., +0.69% to +18.60% in Dice scores with 5% of annotated data). With limited amounts of training data, our method can substantially bridge the performance gap w.r.t. denser annotations (e.g., 10% vs.~100% of annotated data).
We find the classical supersymmetric vacuum states of a class of N = 1* field theories obtained by mass deforming superconformal models with simple gauge groups and N = 4 or N =2 supersymmetry. In particular, new classical vacuum states for mass-deformed N = 4 models with Sp(2N) and SO(N) gauge symmetry are found. We also derive the classical vacua for various mass-deformed N=2 models with Sp(2N) and SU(N) gauge groups and antisymmetric (and symmetric) hypermultiplets. We suggest interpretations of the mass-deformed vacua in terms of three-branes expanded into five-brane configurations.
We introduce a new map between a q-deformed gauge theory on a general GL_{q}(N)-covariant quantum hyperplane and an ordinary gauge theory in a full analogy with Seiberg-Witten map. Perturbative analysis of the q-deformed QED at the classical level is presented and gauge fixing a la BRST is discussed
Arrays of interacting magnetic nanostructures were introduced recently as a powerful approach to investigate experimentally the exotic many-body physics of frustrated spin models. Following a similar strategy based on lithographically-patterned magnetic lattices, we provide a first attempt to fabricate a lab-on-chip platform to explore the physics of vertex models. The central idea of this work is to replace the spin degree of freedom of artificial frustrated spin systems by a local micromagnetic knob, which can be finely tuned by a proper design of the vertex geometry. This concept is demonstrated both numerically and experimentally on the celebrated six vertex model, and we show how all variants of this model can be apprehended through the engineering of magnetic square lattices. Our results open new avenues to design arrays of magnetic nanostructures not only to study a wide range of frustrated spin models, but to explore vertex models as well.
We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss the use of weak coupling methods. We study the phase structure as a function of the number of flavors and their masses. We also introduce effective theories that describe low energy excitations at high baryon density. Finally, we study the possibility of kaon condensation at very large baryon density.
The large electronic polarization in III-V nitrides allow for novel physics not possible in other semiconductor families. In this work, interband Zener tunneling in wide-bandgap GaN heterojunctions is demonstrated by using polarization-induced electric fields. The resulting tunnel diodes are more conductive under reverse bias, which has applications for zero-bias rectification and mm-wave imaging. Since interband tunneling is traditionally prohibitive in wide-bandgap semiconductors, these polarization-induced structures and their variants can enable a number of devices such as multijunction solar cells that can operate under elevated temperatures and high fields.
Within the framework of potential scattering theory we derive an analytical two-potential formula for the on-shell partial wave scattering amplitude. This formula embodies a large number of possible applications, including long range Coulomb forces as well as short distance singular potentials. As an example illustrating the use of the formula we analyze the determination of the strong proton-proton scattering s-wave phase shift from the experimentally determined Coulomb phase when the one pion exchange and two pion exchange chiral potentials are taken into account and analyze the relevant scales of the problem.
We derive a simple formula for the action of any supersymmetric solution to minimal gauged supergravity in the AdS$_4$/CFT$_3$ correspondence. Such solutions are equipped with a supersymmetric Killing vector, and we show that the holographically renormalized action may be expressed entirely in terms of the weights of this vector field at its fixed points, together with certain topological data. In this sense, the classical gravitational partition function localizes in the bulk. We illustrate our general formula with a number of explicit examples, in which exact dual field theory computations are also available, which include supersymmetric Taub-NUT and Taub-bolt type spacetimes, as well as black hole solutions. Our simple topological formula also allows us to write down the action of any solution, provided it exists.
We present a general discussion of the mean field dynamics of finite nuclei prepared under extreme conditions of temperature and pressure. We compare the prediction of semi-classical approximation with complete quantum simulations. Many features of the dynamics are carefully studied such as the collective expansion, the evaporation process, the different time-scale... This study points out many quantitative differences between quantum and semi-classical approaches. Part of the differences are related to numerical features inherent in semi-classical simulations but most of them are a direct consequence of the non treatment of nuclei as quantal objects. In particular, we show that because of a too strong damping in semi-classical approaches the expansion of hot nuclei is quenched and the speed of the collective motion reduced.
We explore the implications of models of the Hyades moving group in which it has a resonant origin, for regions of the Galaxy beyond the Solar neighbourhood. We show that while models associated with different resonances can produce nearly identical substructure in the local velocity distribution, the velocity distribution away from the Solar neighbourhood has different properties for different models. In particular there is a variation between different models of where in Galactocentric radius the observed Hyades signal in velocity space is strongest, at a given Galactic azimuth. We note, however, that the uncertainties in currently available data, primarily due to uncertain distances to stars, hide these signatures rather effectively, meaning we are not yet able to determine which resonance is the cause of the Hyades.
We propose an analogue of Dubrovin's conjecture for the case where Fano manifolds have quantum connections of exponential type. It includes the case where the quantum cohomology rings are not necessarily semisimple. The conjecture is described as an isomorphism of two linear algebraic structures, which we call "mutation systems". Given such a Fano manifold $X$, one of the structures is given by the Stokes structure of the quantum connection of $X$, and the other is given by a semiorthogonal decomposition of the derived category of coherent sheaves on $X$. We also prove the conjecture for a class of smooth Fano complete intersections in a projective space.
The search for signs of extraterrestrial technology, or technosignatures, includes the search for objects which collect starlight for some technological use, such as those composing a Dyson sphere. These searches typically account for a star's light and some blackbody temperature for the surrounding structure. However, such a structure inevitably returns some light back to the surface of its star, either from direct reflection or thermal re-emission. In this work, we explore how this feedback may affect the structure and evolution of stars, and when such feedback may affect observations. We find that in general this returned light can cause stars to expand and cool. Our MESA models show that this energy is only transported toward a star's core effectively by convection, so low mass stars are strongly affected, while higher mass stars with radiative exteriors are not. Ultimately, the effect only has significant observational consequences for spheres with very high temperatures (much higher than the often assumed ~300 K) and/or high specular reflectivity. Lastly, we produce color-magnitude diagrams of combined star-Dyson sphere systems for a wide array of possible configurations.
We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular polynomials attached to Drinfeld modules.
This review recaps significant results as they apply to non-dwarf galaxies, including the Milky Way, spiral disks and bulges, and elliptical and lenticular galaxies. Conclusions that span the galaxy types treated here are as follows. All galaxies, on average, have heavy element abundances (metallicities) that systematically decrease outward from their galactic centers while their global metallicities increase with galaxy mass. Abundance gradients are steepest in normal spirals and are seen to be progressively flatter going in order from barred spirals, lenticulars, and ellipticals. For spiral galaxies, local metallicity appears to be correlated with total (disk plus bulge) surface density. Observed abundance patterns indicate that N production is dominated by primary processes at low metallicity and secondary processes at high metallicity; C production increases with increasing metallicity; and O, Ne, S, and Ar are produced in lockstep independent of metallicity. In elliptical galaxies, nuclear abundances are in the range [Z/H] = 0.0 to 0.4, but the element mixture is not scaled-solar. In large elliptical galaxies [Mg/Fe] is in the range 0.3 to 0.5, decreasing to ~0 in smaller elliptical galaxies. Other light elements track the Mg enhancement, but the heavier Ca tracks Fe. Velocity dispersion appears to be a key parameter in the modulation of [Mg/Fe], but the cause of the connection is unclear.
Magnetars are the strongest magnets in the present universe and the combination of extreme magnetic field, gravity and density makes them unique laboratories to probe current physical theories (from quantum electrodynamics to general relativity) in the strong field limit. Magnetars are observed as peculiar, burst--active X-ray pulsars, the Anomalous X-ray Pulsars (AXPs) and the Soft Gamma Repeaters (SGRs); the latter emitted also three "giant flares," extremely powerful events during which luminosities can reach up to 10^47 erg/s for about one second. The last five years have witnessed an explosion in magnetar research which has led, among other things, to the discovery of transient, or "outbursting," and "low-field" magnetars. Substantial progress has been made also on the theoretical side. Quite detailed models for explaining the magnetars' persistent X-ray emission, the properties of the bursts, the flux evolution in transient sources have been developed and confronted with observations. New insight on neutron star asteroseismology has been gained through improved models of magnetar oscillations. The long-debated issue of magnetic field decay in neutron stars has been addressed, and its importance recognized in relation to the evolution of magnetars and to the links among magnetars and other families of isolated neutron stars. The aim of this paper is to present a comprehensive overview in which the observational results are discussed in the light of the most up-to-date theoretical models and their implications. This addresses not only the particular case of magnetar sources, but the more fundamental issue of how physics in strong magnetic fields can be constrained by the observations of these unique sources.
In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincar\'{e} inequalities, general Beckner inequalities...). We also discuss the quantitative behaviour of relative entropy along a symmetric diffusion semi-group. In particular, we exhibit an example where Poincar\'{e} inequality can not be used for deriving entropic convergence whence weak logarithmic Sobolev inequality ensures the result.
We use the Fundamental Plane of Elliptical Galaxies to constrain the so-called Hybrid Gravity, a modified theory of gravity where General Relativity is improved by further degrees of freedom of metric-affine Palatini formalism of $f(\cal R)$ gravity. Because the Fundamental Plane is connected to the global properties of elliptical galaxies, it is possible to obtain observational constraints on the parameters of Hybrid Gravity in the weak field limit. We analyze also the velocity distribution of elliptical galaxies comparing our theoretical results in the case of Hybrid Gravity with astronomical data for elliptical galaxies. In this way, we are able to constrain the Hybrid Gravity parameters $m_\phi$ and $\phi_0$. We show that the Fundamental Plane, i.e. $v_c/\sigma$ relations, can be used as a standard tool to probe different theories of gravity in the weak field limit. We conclude that Hybrid Gravity is able to explain elliptical galaxies with different stellar kinematics without the dark matter hypothesis.
We study random families of subsets of $\mathbb{N}$ that are similar to exchangeable random partitions, but do not require constituent sets to be disjoint: Each element of ${\mathbb{N}}$ may be contained in multiple subsets. One class of such objects, known as Indian buffet processes, has become a popular tool in machine learning. Based on an equivalence between Indian buffet and scale-invariant Poisson processes, we identify a random scaling variable whose role is similar to that played in exchangeable partition models by the total mass of a random measure. Analogous to the construction of exchangeable partitions from normalized subordinators, random families of sets can be constructed from randomly scaled subordinators. Coupling to a heavy-tailed scaling variable induces a power law on the number of sets containing the first $n$ elements. Several examples, with properties desirable in applications, are derived explicitly. A relationship to exchangeable partitions is made precise as a correspondence between scaled subordinators and Poisson-Kingman measures, generalizing a result of Arratia, Barbour and Tavare on scale-invariant processes.
We consider the geometric global quantum discord (GGQD) of two-qubit systems. By analyzing the symmetry of geometric global quantum discord we give an approach for deriving analytical formulae of the extremum problem which lies at the core of computing the GGQD for arbitrary two-qubit states. Furthermore, formulae of GGQD of arbitrary two-qubit states and some concrete examples are presented.
A new family of integer-valued Cauchy-type distributions is introduced, the {\it Cauchy-Cacoullos family}. The characteristic function is evaluated, showing some interesting distributional properties, similar to the ordinary (continuous) Cauchy scale family. The results are extendable to discrete Student-type distributions with odd degrees of freedom.   Keywords: Fourier series; discrete Student distribution; Cauchy-Cacoullos family.
We obtained SOAR telescope B and V photometry of 14 star clusters and 2 associations in the Bridge tidal structure connecting the LMC and SMC. These objects are used to study the formation and evolution of star clusters and associations under tidal stresses from the Clouds. Typical star clusters in the Bridge are not richly populated and have in general relatively large diameters (~30-35 pc), being larger than Galactic counterparts of similar age. Ages and other fundamental parameters are determined with field-star decontaminated photometry. A self-consistent approach is used to derive parameters for the most-populated sample cluster NGC 796 and two young CMD templates built with the remaining Bridge clusters. We find that the clusters are not coeval in the Bridge. They range from approximately a few Myr (still related to optical HII regions and WISE and Spitzer dust emission measurements) to about 100-200 Myr. The derived distance moduli for the Bridge objects suggests that the Bridge is a structure connecting the LMC far-side in the East to the foreground of the SMC to the West. Most of the present clusters are part of the tidal dwarf candidate D 1, which is associated with an H I overdensity. We find further evidence that the studied part of the Bridge is evolving into a tidal dwarf galaxy, decoupling from the Bridge.
We study the quantum corrections to the moduli space of the quiver gauge theory corresponding to regular and fractional D3-branes at the dP_1 singularity. We find that besides the known runaway behavior at the lowest step of the duality cascade, there is a runaway direction along a mesonic branch at every higher step of the cascade. Moreover, the algebra of the chiral operators which obtain the large expectation values is such that we reproduce Altmann's first order deformation of the dP_1 cone.
In this contribution, we test our previously published one-dimensional PDR model for deriving total hydrogen volume densities from HI column density measurements in extragalactic regions by applying it to the Taurus molecular cloud, where its predictions can be compared to available data. Also, we make the first direct detailed comparison of our model to CO(1-0) and far-infrared emission. Using an incident UV flux G0 of 4.25 ({\chi} = 5) throughout the main body of the cloud, we derive total hydrogen volume densities of \approx 430 cm-3, consistent with the extensive literature available on Taurus. The distribution of the volume densities shows a log-normal shape with a hint of a power-law shape on the high density end. We convert our volume densities to H2 column densities assuming a cloud depth of 5 parsec and compare these column densities to observed CO emission. We find a slope equivalent to a CO conversion factor relation that is on the low end of reported values for this factor in the literature (0.9 x 1020 cm-2 (K km s-1)-1), although this value is directly proportional to our assumed value of G0 as well as the cloud depth. We seem to under-predict the total hydrogen gas as compared to 100 {\mu}m dust emission, which we speculate may be caused by a higher actual G0 incident on the Taurus cloud than is generally assumed.