ShantanuT01/DACTYL-Pretraining huggingface dataset:
We associate to any complete spherical variety $X$ a certain nonnegative rational number $\wp(X)$, which we conjecture to satisfy the inequality $\wp(X) \le \operatorname{dim} X - \operatorname{rank} X$ with equality holding if and only if $X$ is isomorphic to a toric variety. We show that, for spherical varieties, our conjecture implies the generalized Mukai conjecture on the pseudo-index of smooth Fano varieties due to Bonavero, Casagrande, Debarre, and Druel. We also deduce from our conjecture a smoothness criterion for spherical varieties. It follows from the work of Pasquier that our conjecture holds for horospherical varieties. We are able to prove our conjecture for symmetric varieties.
The constraints imposed on the Minimal Supersymmetric Standard Model (MSSM) parameter space by the Large Hadron Collider (LHC) Higgs mass limit and gluino mass lower bound are revisited. We also analyze the thermal relic abundance of lightest neutralino, which is the Lightest Supersymmetric Particle (LSP). We show that the combined LHC and relic abundance constraints rule out most of the MSSM parameter space except a very narrow region with very large $\tan \beta~(\sim 50)$. Within this region, we emphasize that the spin-independent scattering cross section of the LSP with a proton is less than the latest Large Underground Xenon (LUX) limit by at least two order of magnitudes. Finally, we argue that non-thermal Dark Matter (DM) scenario may relax the constraints imposed on the MSSM parameter space. Namely, the following regions are obtained: $m_0\simeq {\cal O}(4)$ TeV and $m_{1/2}\simeq 600$ GeV for low $\tan\beta~(\sim 10)$; $m_0\sim m_{1/2} \simeq {\cal O}(1)$ TeV or $m_0 \simeq {\cal O}(4)$ TeV and $m_{1/2} \simeq 700$ GeV for large $\tan \beta~(\sim 50)$.
We perform two-dimensional resistive magnetohydrodynamic simulations of coronal jets driven by flux emergence along the lower boundary. The reconnection layers are susceptible the formation of blobs that are ejected in the jet. Our simulation with low plasma $\beta$ (Case I) shows that magnetic islands form easily and propagate upwards in the jet. These islands are multithermal and thus are predicted to show up in hot channels (335 \AA\, and 211 \AA) and the cool channel (304 \AA) in observations by the Atmospheric Imaging Assembly (AIA) on the \emph{Solar Dynamics Observatory}. The islands have maximum temperatures of 8 MK, lifetimes of 120 s, diameters of 6 Mm, and velocities of 200 km s$^{-1}$. These parameters are similar to the properties of blobs observed in EUV jets by AIA\@. The Kelvin-Helmholtz instability develops in our simulation with moderately high plasma $\beta$ (Case II), and leads to the formation of bright vortex-like blobs above the multiple high magneto-sonic Mach number regions that appear along the jet. These vortex-like blobs can also be identified in the AIA channels. However, they eventually move downward and disappear after the high magneto-sonic Mach number regions disappear. In the lower plasma $\beta$ case, the lifetime for the jet is shorter, the jet and magnetic islands are formed with higher velocities and temperatures, the current sheet fragments are more chaotic, and more magnetic islands are generated. Our results show that the plasmoid instability and Kelvin-Helmholtz instability along the jet are both possible causes of the formation of blobs observed at extreme ultraviolet (EUV) wavelengths.
We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations
Using tropical geometry we propose a mirror construction for monomial degenerations of Calabi-Yau varieties in toric Fano varieties. The construction reproduces the mirror constructions by Batyrev for Calabi-Yau hypersurfaces and by Batyrev and Borisov for Calabi-Yau complete intersections. We apply the construction to Pfaffian examples and recover the mirror given by Rodland for the degree 14 Calabi-Yau threefold in PP^6 defined by the Pfaffians of a general linear 7x7 skew-symmetric matrix.   We provide the necessary background knowledge entering into the tropical mirror construction such as toric geometry, Groebner bases, tropical geometry, Hilbert schemes and deformations. The tropical approach yields an algorithm which we illustrate in a series of explicit examples.
We establish that for any non-empty, compact set $K\subset\mathbb{R}_{\mathrm{sym}}^{3\times 3}$ the $1$- and $\infty$-symmetric div-quasiconvex hulls $K^{(1)}$ and $K^{(\infty)}$ coincide. This settles a conjecture in a recent work of Conti, M\"{u}ller and Ortiz (Symmetric Div-Quasiconvexity and the Relaxation of Static Problems. Arch. Ration. Mech. Anal. 235(2):841-880) in the affirmative. As a key novelty, we construct an $\mathrm{L}^{\infty}$-truncation that preserves both symmetry and solenoidality of matrix-valued maps in $\mathrm{L}^{1}$.
Strongly correlated Fermi systems are fundamental systems in physics that are best studied experimentally, which until very recently have lacked theoretical explanations. This review discusses the construction of a theory and the analysis of phenomena occurring in strongly correlated Fermi systems such as heavy-fermion (HF) metals and two-dimensional (2D) Fermi systems. It is shown that the basic properties and the scaling behavior of HF metals can be described within the framework of a fermion condensation quantum phase transition (FCQPT) and extended quasiparticle paradigm that allow us to explain the non-Fermi liquid behavior observed in strongly correlated Fermi systems. In contrast to the Landau paradigm stating that the quasiparticle effective mass is a constant, the effective mass of new quasiparticles strongly depends on temperature, magnetic field, pressure, and other parameters. Having analyzed collected facts on strongly correlated Fermi systems with quite different microscopic nature, we find these to exhibit the same non-Fermi liquid behavior at FCQPT. We show both analytically and using arguments based entirely on the experimental grounds that the data collected on very different strongly correlated Fermi systems have a universal scaling behavior, and materials with strongly correlated fermions can unexpectedly be uniform in their diversity. Our analysis of strongly correlated systems such as HF metals and 2D Fermi systems is in the context of salient experimental results. Our calculations of the non-Fermi liquid behavior, the scales and thermodynamic, relaxation and transport properties are in good agreement with experimental facts.
IGR J17480$-$2446 is an accreting X-ray pulsar in a low-mass X-ray binary harbored in the Galactic globular cluster Terzan 5. Compared with other accreting millisecond pulsars, IGR J17480$-$2446 is peculiar in its low spin frequency (11 Hz), which suggests that it might be a mildly recycled neutron star at the very early phase of mass transfer. However, this model seems to be in contrast with the low field strength deduced from the kiloHertz quasi-periodic oscillations observed in IGR J17480$-$2446. Here we suggest an alternative interpretation, assuming that the current binary system was formed during an exchange encounter either between a binary (which contains a recycled neutron star) and the current donor, or between a binary and an isolated, recycled neutron star. In the resulting binary, the spin axis of the neutron star could be parallel or anti-parallel with the orbital axis. In the later case, the abnormally low frequency of IGR J17480$-$2446 may result from the spin-down to spin-up evolution of the neutron star. We also briefly discuss the possible observational implications of the pulsar in this scenario.
(abridged) We present a comprehensive study of stellar stratification in young star clusters in the Large Magellanic Cloud (LMC). We apply our recently developed effective radius method for the assessment of stellar stratification on imaging data obtained with the Advanced Camera for Surveys of three young LMC clusters to characterize the phenomenon and develop a comparative scheme for its assessment in such clusters. The clusters of our sample, NGC 1983, NGC 2002 and NGC 2010, are selected on the basis of their youthfulness, and their variety in appearance, structure, stellar content, and surrounding stellar ambient. Our photometry is complete for magnitudes down to m_814 ~ 23 mag, allowing the calculation of the structural parameters of the clusters, the estimation of their ages and the determination of their stellar content. Our study shows that each cluster in our sample demonstrates stellar stratification in a quite different manner and at different degree from the others. Specifically, NGC 1983 shows to be partially segregated only for the faintest stars of the cluster, NGC 2002 shows evidence of strong stellar stratification for both bright and faint stars, and NGC 2010 is found not to be segregated. For the parametrization of the phenomenon of stellar stratification and its quantitative comparison among these clusters, we propose the slope derived from the change in the effective radius over the corresponding magnitude range as indicative parameter of the degree of stratification in the clusters. A positive value of this slope indicates mass segregation in the cluster, while a negative or zero value signifies the lack of the phenomenon.
The condition for the unitarity of a quantum field is investigated in semiclassical gravity from the Wheeler-DeWitt equation. It is found that the quantum field preserves unitarity asymptotically in the Lorentzian universe, but does not preserve unitarity completely in the Euclidean universe. In particular we obtain a very simple matter field equation in the basis of the generalized invariant of the matter field Hamiltonian whose asymptotic solution is found explicitly.
Classical physics is about real objects, like apples falling from trees, whose motion is governed by Newtonian laws. In standard Quantum Mechanics only the wave function or the results of measurements exist, and to answer the question of how the classical world can be part of the quantum world is a rather formidable task. However, this is not the case for Bohmian mechanics, which, like classical mechanics, is a theory about real objects. In Bohmian terms, the problem of the classical limit becomes very simple: when do the Bohmian trajectories look Newtonian?
In this paper, we study the relations between the numerical structure of the optimal solutions of a convex programming problem defined on the edge set of a simple graph and the stability number (i.e. the maximum size of a subset of pairwise non-adjacent vertices) of the graph. Our analysis shows that the stability number of every graph G can be decomposed in the sum of the stability number of a subgraph containing a perfect 2-matching (i.e. a system of vertex-disjoint odd-cycles and edges covering the vertex-set) plus a term computable in polynomial time. As a consequence, it is possible to bound from above and below the stability number in terms of the matching number of a subgraph having a perfect 2-matching and other quantities computable in polynomial time. Our results are closely related to those by Lorentzen, Balinsky, Spielberg, and Pulleyblank on the linear relaxation of the vertex-cover problem. Moreover, The convex programming problem involved has important applications in information theory and extremal set theory where, as a graph capacity formula, has been used to answer a longstanding open question about qualitatively independet sets in the sense of Renyi (L. Gargano, J. K{\"o}rner, and U. Vaccaro, "Sperner capacities", Graphs and combinatorics, 9:31-46, 1993).
We report observations during 2008 October of the first recorded superoutburst of a previously unknown SU UMa-type dwarf nova in Draco located at 19h 14m 43.52s +60d 52m 14.1s (J2000). Simbad lists a 21st magnitude star at this position with identifiers GSC2.3 N152008120 and USNO-B1.0 1508-0249096. The outburst reached magnitude 14.9, its amplitude was approximately 6 magnitudes and its duration at least 11 days. About 11 days after the end of the main outburst there was a short-lived rebrightening by more than 2 magnitudes. Superhumps were observed with a mean period of 0.07117(1) d and amplitude 0.12 mag. There was a distinct shortening in the superhump period around cycle 80 with Psh = 0.07137(2) d before and Psh = 0.07091(2) d after. We saw weak evidence of an increasing Psh before cycle 80 with dPsh/dt = 3.4(2.0) * 10-5.
We search for galaxies with a strong Balmer break (Balmer Break Galaxies; BBGs) at $z \sim 6$ over a 0.41 deg$^2$ effective area in the COSMOS field. Based on rich imaging data, including data obtained with the Atacama Large Millimeter/submillimeter Array (ALMA), three candidates are identified by their extremely red $K - [3.6]$ colors as well as by non-detection in X-ray, optical, far-infrared (FIR), and radio bands. The non-detection in the deep ALMA observations suggests that they are not dusty galaxies but BBGs at $z \sim 6$, although contamination from Active Galactic Nuclei (AGNs) at $z \sim 0$ cannot be completely ruled out for the moment. Our spectral energy distribution (SED) analyses reveal that the BBG candidates at $z \sim 6$ have stellar masses of $\approx 5 \times 10^{10} M_{\odot}$ dominated by old stellar populations with ages of $\gtrsim 700$ Myr. Assuming that all the three candidates are real BBGs at $z \sim 6$, we estimate the stellar mass density (SMD) to be $2.4^{+2.3}_{-1.3} \times 10^{4} M_{\odot}$ Mpc$^{-3}$. This is consistent with an extrapolation from the lower redshift measurements. The onset of star formation in the three BBG candidates is expected to be several hundred million years before the observed epoch of $z \sim 6$. We estimate the star-formation rate density (SFRD) contributed by progenitors of the BBGs to be 2.4 -- 12 $\times 10^{-5} M_{\odot}$ yr$^{-1} $Mpc$^{-3}$ at $z > 14$ (99.7\% confidence range). Our result suggests a smooth evolution of the SFRD beyond $z = 8$.
Multi-valued logic gates, which can handle quaternary numbers as inputs, are developed by exploiting the ballistic transport properties of quantum point contacts in series. The principle of a logic gate that finds the minimum of two quaternary number inputs is demonstrated. The device is scalable to allow multiple inputs, which makes it possible to find the minimum of multiple inputs in a single gate operation. Also, the principle of a half-adder for quaternary number inputs is demonstrated. First, an adder that adds up two quaternary numbers and outputs the sum of inputs is demonstrated. Second, a device to express the sum of the adder into two quaternary digits [Carry (first digit) and Sum (second digit)] is demonstrated. All the logic gates presented in this paper can in principle be extended to allow decimal number inputs with high quality QPCs.
This paper proposes the first real-world rolling shutter (RS) correction dataset, BS-RSC, and a corresponding model to correct the RS frames in a distorted video. Mobile devices in the consumer market with CMOS-based sensors for video capture often result in rolling shutter effects when relative movements occur during the video acquisition process, calling for RS effect removal techniques. However, current state-of-the-art RS correction methods often fail to remove RS effects in real scenarios since the motions are various and hard to model. To address this issue, we propose a real-world RS correction dataset BS-RSC. Real distorted videos with corresponding ground truth are recorded simultaneously via a well-designed beam-splitter-based acquisition system. BS-RSC contains various motions of both camera and objects in dynamic scenes. Further, an RS correction model with adaptive warping is proposed. Our model can warp the learned RS features into global shutter counterparts adaptively with predicted multiple displacement fields. These warped features are aggregated and then reconstructed into high-quality global shutter frames in a coarse-to-fine strategy. Experimental results demonstrate the effectiveness of the proposed method, and our dataset can improve the model's ability to remove the RS effects in the real world.
In this chapter, we will describe the storage and retrieval of quantum light (heralded single photons and entangled photons) in atomic ensembles in a solid state environment. We will consider ensembles of rare-earth ions embedded in dielectric crystals. We will describe the methods used to create quantum light spectrally compatible with the narrow atomic transitions, as well as possible protocols based on dipole rephasing that can be used to reversibly map the quantum light onto collective atomic excitations. We will review the experimental state of the art and describe in more detail quantum light storage experiments in neodymium and praseodymium doped crystals.
Smart meters enable remote and automatic electricity, water and gas consumption reading and are being widely deployed in developed countries. Nonetheless, there is still a huge number of non-smart meters in operation. Image-based Automatic Meter Reading (AMR) focuses on dealing with this type of meter readings. We estimate that the Energy Company of Paran\'a (Copel), in Brazil, performs more than 850,000 readings of dial meters per month. Those meters are the focus of this work. Our main contributions are: (i) a public real-world dial meter dataset (shared upon request) called UFPR-ADMR; (ii) a deep learning-based recognition baseline on the proposed dataset; and (iii) a detailed error analysis of the main issues present in AMR for dial meters. To the best of our knowledge, this is the first work to introduce deep learning approaches to multi-dial meter reading, and perform experiments on unconstrained images. We achieved a 100.0% F1-score on the dial detection stage with both Faster R-CNN and YOLO, while the recognition rates reached 93.6% for dials and 75.25% for meters using Faster R-CNN (ResNext-101).
It is proposed a formalism of quantification of the electric charges in the Kaluza Klein theory of five dimensions and a explanation of the cause of the variation of the electromagnetic fine-structure constant in cosmological times.There is a formalism that eliminates the problem that impeached the KK theory to complete the unification of the electromagnetic and the gravitational fields. The complete unification of these two fields is obtained. The radius of compactation is determined as 70,238 lengths of Planck.
Until now the known sources in the Galactic center with sufficiently smooth spectra and of sufficient brightness to be suitable for high resolution infrared absorption spectroscopy of interstellar gas occupied a narrow range of longitudes, from the central cluster of hot stars to approximately 30 pc east of the center. In order to more fully characterize the gas within the r ~ 180 pc central molecular zone it is necessary to find additional such sources that cover a much wider longitudinal range. We are in the process of identifying luminous dust-embedded objects suitable for spectroscopy within 1.2 deg in longitude and 0.1 deg in latitude of Sgr A* using the Spitzer GLIMPSE and the 2MASS catalogues. Here we present spectra of H3+ and CO towards two such objects, one located 140 pc west of Sgr A*, and the other located on a line of sight to the Sgr B molecular cloud complex 85 pc to the east of Sgr A*. The sightline to the west passes through two dense clouds of unusually high negative velocities and also appears to sample a portion of the expanding molecular ring. The spectra toward Sgr B reveal at least ten absorption components covering over 200 km/s and by far the largest equivalent width ever observed in an interstellar H3+line; they appear to provide the first near-infrared view into that hotbed of star formation.
Direct nanoimprinting provides a simple and high-throughput route for producing uniform nanopatterns at great precision and at low costs. However, applying this technique to crystalline metals has been considered as impossible due to intrinsic limitation from grain size effect. Here we demonstrate direct superplastic nanoimprinting (SPNI) of crystalline metals well below their melting temperatures (Tm), generating ordered nanowire arrays with aspect ratio up to ~2000. Our investigations of replicating metal hierarchical nanostructures show the capability of imprinting features as small as 8 nm, far smaller than the grain size of bulk metals. Most surprisingly, the prepared metal hierarchical nanostructures were found possessing perfect monocrystalline structures. These findings indicate that nanoimprinting of crystalline metals below Tm might be from lattice diffusion. SPNI as a one-step and highly controlled high-throughput fabrication method, could facilitate the applications of metal nanostructures in bio-sensing, diagnostic imaging, catalysis, food industry and environmental conservation.
By a poly-line drawing of a graph G on n vertices we understand a drawing of G in the plane such that each edge is represented by a polygonal arc joining its two respective vertices. We call a turning point of a polygonal arc the bend. We consider the class of graphs that admit a poly-line drawing, in which each edge has at most one bend (resp. two bends) and any two edges can cross only at a right angle. It is shown that the number of edges of such graphs is at most O(n) (resp. O(n \log^2 n)). This is a strengthening of a recent result of Didimo et al.
Gelfand-Tsetlin polytopes are classical objects in algebraic combinatorics arising in the representation theory of $\mathfrak{gl}_n(\mathbb{C})$. The integer point transform of the Gelfand-Tsetlin polytope $\mathrm{GT}(\lambda)$ projects to the Schur function $s_{\lambda}$. Schur functions form a distinguished basis of the ring of symmetric functions; they are also special cases of Schubert polynomials $\mathfrak{S}_{w}$ corresponding to Grassmannian permutations.   For any permutation $w \in S_n$ with column-convex Rothe diagram, we construct a polytope $\mathcal{P}_{w}$ whose integer point transform projects to the Schubert polynomial $\mathfrak{S}_{w}$. Such a construction has been sought after at least since the construction of twisted cubes by Grossberg and Karshon in 1994, whose integer point transforms project to Schubert polynomials $\mathfrak{S}_{w}$ for all $w \in S_n$. However, twisted cubes are not honest polytopes; rather one can think of them as signed polytopal complexes. Our polytope $\mathcal{P}_{w}$ is a convex polytope. We also show that $\mathcal{P}_{w}$ is a Minkowski sum of Gelfand-Tsetlin polytopes of varying sizes. When the permutation $w$ is Grassmannian, the Gelfand-Tsetlin polytope is recovered. We conclude by showing that the Gelfand-Tsetlin polytope is a flow polytope.
The impurity induced antiferromagnetic ordering of the doped spin-Peierls magnet Cu(1-x)Mg(x)GeO(3) was studied by ESR technique. Crystals with the Mg concentration x<4% demonstrate a coexistence of paramagnetic and antiferromagnetic ESR modes. This coexistence indicates the separation of a macroscopically uniform sample in the paramagnetic and antiferromagnetic phases. In the presence of the long-range spin-Peierls order (in a sample with x=1.71%) the volume of the antiferromagnetic phase immediately below the N\'{e}el point T_N is much smaller than the volume of the paramagnetic phase. In the presence of the short-range spin-Peierls order (in samples with x=2.88%, x= 3.2%) there are comparable volumes of paramagnetic and antiferromagnetic phases at T=T_N. The fraction of the antiferromagnetic phase increases with lowering temperature. In the absence of the spin-Peierls dimerization (at x=4.57%)the whole sample exhibits the transition into the antiferromagnetic state and there is no phase separation. The phase separation is explained by the consideration of clusters of staggered magnetization located near impurity atoms. In this model the areas occupied by coherently correlated spins expand with decreasing temperature and the percolation of the ordered area through a macroscopic distance occurs.