ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we obtain two effective bounds for the $j$-invariant of integral points on certain modular curves which has positive genus and less than three cusps.
The stabilization of moduli is one of the main problems in string theory. In this talk I will discuss some stringy mechanisms based on non-geometrical compactifications to obtain four dimensional models with a reduced number of moduli.
Object detection in aerial images is an important task in environmental, economic, and infrastructure-related tasks. One of the most prominent applications is the detection of vehicles, for which deep learning approaches are increasingly used. A major challenge in such approaches is the limited amount of data that arises, for example, when more specialized and rarer vehicles such as agricultural machinery or construction vehicles are to be detected. This lack of data contrasts with the enormous data hunger of deep learning methods in general and object recognition in particular. In this article, we address this issue in the context of the detection of road vehicles in aerial images. To overcome the lack of annotated data, we propose a generative approach that generates top-down images by overlaying artificial vehicles created from 2D CAD drawings on artificial or real backgrounds. Our experiments with a modified RetinaNet object detection network show that adding these images to small real-world datasets significantly improves detection performance. In cases of very limited or even no real-world images, we observe an improvement in average precision of up to 0.70 points. We address the remaining performance gap to real-world datasets by analyzing the effect of the image composition of background and objects and give insights into the importance of background.
The Be phenomenon, i.e. the ejection of matter from Be stars into a circumstellar disk, has been a long lasting mystery. In the last few years, the CoRoT satellite brought clear evidence that Be outbursts are directly correlated to pulsations and rapid rotation. In particular the stochastic excitation of gravito-inertial modes, such as those detected by CoRoT in the hot Be star HD 51452, is enhanced thanks to rapid rotation. These waves increase the transport of angular momentum and help to bring the already rapid stellar rotation to its critical value at the surface, allowing the star to eject material. Below we summarize the recent observational and theoretical findings and describe the new picture of the Be phenomenon which arose from these results.
We show a possible way to construct a consistent formalism where the effective electric charge can change with space and time without destroying the invariance. In the previous work [1][2] we took the gauge coupling to be of the form $g(\phi)j_\mu (A^{\mu} +\partial^{\mu}B)$ where $B$ is an auxiliary field, $ \phi $ is a scalar field and the current $j_\mu$ is the Dirac current. This term produces a constraint $ (\partial_{\mu}\phi) j^{\mu}=0 $ which can be related to M.I.T bag model by boundary condition. In this paper we show that when we use the term $ g(\phi)j_{\mu}(A^{\mu} - \partial^{\mu}(\frac{1}{\square}\partial_{\rho}A^{\rho})) $, instead of the auxiliary field $ B $, there is a possibility to produce a theory with dynamical coupling constant, which does not produce any constraint or confinement. The coupling $ j_{\mu}^{A}(A^{\mu} - \partial^{\mu}(\frac{1}{\square}\partial_{\rho}A^{\rho})) $ where $ j_{\mu}^{A} $ is an anomalous current also discussed.
A field-theoretical description of the behavior of homogeneous, elastically isotropic, compressible systems characterized by two order parameters at the bicritical and tetracritical points is presented. For three-dimensional Ising-like systems, a similar description is performed in the two-loop approximation in three dimensions. The renormalization group equations are analyzed, and fixed points corresponding to different types of multicritical behavior are determined. It is shown that the effect of elastic strains causes a change from a bicritical behavior to a tetracritical one and leads to the appearance of a wide variety of multicritical points.
This note gives a simple proof that certain values of Artin's $L$-function, for a representation $\rho$ with character $\chi_\rho$, are stable under twisting by an even Dirichlet character $\chi$, up to an element generated over $\mathbb Q$ by the values of $\chi$ and $\chi_\rho$, and a product with a power of the Gauss sum $\tau(\chi)$ equal to the dimension of $\rho$. This extends a result due to J. Coates and S. Lichtenbaum.
Rosenhain's famous formula expresses the periods of first kind integrals of genus two hyperelliptic curves in terms of $\theta$-constants. In this paper we generalize the Rosenhain formula to higher genera hyperelliptic curves by means of the second Thomae formula for derivated non-singular $\theta$-constants.
We show that 1/f noise in a two-dimensional electron gas with hopping conduction can be explained by the modulation of conducting paths by fluctuating occupancy of non-conducting states. The noise is sensitive to the structure of the critical hopping network, which is varied by changing electron concentration, sample size and temperature. With increasing temperature, it clearly reveals the crossover between different hopping regimes.
The Chapman-Enskog method of kinetic theory is applied to two problems of synchronization of globally coupled phase oscillators. First, a modified Kuramoto model is obtained in the limit of small inertia from a more general model which includes ``inertial'' effects. Second, a modified Chapman-Enskog method is used to derive the amplitude equation for an O(2) Takens-Bogdanov bifurcation corresponding to the tricritical point of the Kuramoto model with a bimodal distribution of oscillator natural frequencies. This latter calculation shows that the Chapman-Enskog method is a convenient alternative to normal form calculations.
We report on a systematic computation of weight one cuspidal eigenforms for the group $\Gamma_1(N)$ in characteristic zero and in characteristic $p>2$. Perhaps the most surprising result was the existence of a mod 199 weight~1 cusp form of level 82 which does not lift to characteristic zero.
In this paper, we report the detection of ejecta in the middle-aged Galactic supernova remnant G296.1-0.5 with the X-ray Imaging Spectrometer onboard the Suzaku satellite. The spectra of three lobes, north, southeast and southwest and inter-lobe regions, consist of soft (0.3-2.0 keV) emission originated from non-equilibrium ionization plasma. In north, southeast and inter-lobe regions, the thermal emission can be represented by a one-component, in southwest region it can be represented by two- component non-equilibrium ionization (VNEI) model. The spectra of studied regions have lines of N, O, Ne, Mg and Si elements. Si emission from this remnant is shown for the first time in this work. Enhanced abundances of Ne, Mg and Si elements obtained show the ejecta contribution in all regions. Assuming that the remnant is in Sedov phase, we obtained ambient density n0 ~ 0.45 cm-3, age t ~ 2.8 x 104 yr, shock velocity Vs ~ 320 km s-1, shock temperature Ts ~ 1.2 x 106 K, and swept-up mass Msw ~ 340 M at an adopted distance of d=3 kpc.
Hartree-Fock-Bogoliubov calculations of hot fission in $^{240}\textrm{Pu}$ have been performed with a newly-implemented code that uses the D1S finite-range effective interaction. The hot-scission line is identified in the quadrupole-octupole-moment coordinate space. Fission-fragment shapes are extracted from the calculations. A benchmark calculation for $^{226}\textrm{Th}$ is obtained and compared to results in the literature. In addition, technical aspects of the use of HFB calculations for fission studies are examined in detail. In particular, the identification of scission configurations, the sensitivity of near-scission calculations to the choice of collective coordinates in the HFB iterations, and the formalism for the adjustment of collective-variable constraints are discussed. The power of the constraint-adjustment algorithm is illustrated with calculations near the critical scission configurations with up to seven simultaneous constraints.
Rare diseases have extremely low-data regimes, unlike common diseases with large amount of available labeled data. Hence, to train a neural network to classify rare diseases with a few per-class data samples is very challenging, and so far, catches very little attention. In this paper, we present a difficulty-aware meta-learning method to address rare disease classifications and demonstrate its capability to classify dermoscopy images. Our key approach is to first train and construct a meta-learning model from data of common diseases, then adapt the model to perform rare disease classification.To achieve this, we develop the difficulty-aware meta-learning method that dynamically monitors the importance of learning tasks during the meta-optimization stage. To evaluate our method, we use the recent ISIC 2018 skin lesion classification dataset, and show that with only five samples per class, our model can quickly adapt to classify unseen classes by a high AUC of 83.3%. Also, we evaluated several rare disease classification results in the public Dermofit Image Library to demonstrate the potential of our method for real clinical practice.
Two subanalytic subsets of $ \mathbb R^n$ are called $s$-equivalent at a common point $P$ if the Hausdorff distance between their intersections with the sphere centered at $P$ of radius $r$ vanishes to order $>s$ as $r$ tends to $0$. In this work we strengthen this notion in the case of real subanalytic subsets of $\mathbb R^n$ with isolated singular points, introducing the notion of tangential $s$-equivalence at a common singular point which considers also the distance between the tangent planes to the sets near the point. We prove that, if $V(f)$ is the zero-set of an analytic map $f$ and if we assume that $V(f)$ has an isolated singularity, say at the origin $O$, then for any $s\geq 1$ the truncation of the Taylor series of $f$ of sufficiently high order defines an algebraic set with isolated singularity at $O$ which is tangentially $s$-equivalent to $V(f)$.
The type-II Weyl/Dirac fermions are a generalization of conventional or type-I Weyl/Dirac fermions, whose conic spectrum is tilted such that the Fermi surface becomes lines in two dimensions, and surface in three dimensions rather than discrete points of the conventional Weyl/Dirac fermions. The mass-independent renormalization group calculations show that the tilting parameter decreases monotonically with respect to the length scale, which leads to a transition from two dimensional type-II Weyl/Dirac fermions to the type-I ones. Because of the non-trivial Fermi surface, a photon gains a finite mass partially via the chiral anomaly, leading to the strong screening effect of the Weyl/Dirac fermions. Consequently, anisotropic type-II Dirac semimetals become stable against the Coulomb interaction. This work provides deep insight into the interplay between the geometry of Fermi surface and the Coulomb interaction.
Insulator-metal transition is investigated self-consistently on the frustrated Shastry-Sutherland lattice in the framework of Slave-Boson mean-field theory. Due to the presence of quasi-flat band structure characteristic, the system displays a spin-density-wave (SDW) insulating phase at the weak doping levels, which is robust against frustration, and it will be transited into an SDW metallic phase at high doping levels. As further increasing the doping, the temperature or the frustration on the diagonal linking bonds, the magnetic order $m$ will be monotonically suppressed, resulting in the appearance of a paramagnetic metallic phase. Although the Fermi surface of the SDW metallic phase may be immersed by temperature, the number of mobile charges is robust against temperature at weak doping levels.
We discuss recent results from global electroweak fits and from the Tevatron and review the motivation for physics at the TeV energy scale.
We express the Hessian discriminant of a cubic surface in terms of fundamental invariants. This answers Question 15 from the \emph{27 questions on the cubic surface}. We also explain how to compute the fundamental invariants for smooth cubics of rank 6.
A proper choice of subsystems for a system of identical particles e.g., bosons, is provided by second-quantized modes i.e.,creation/annihilation operators. Here we investigate how the entanglement properties of bipartite gaussian states of bosons change when modes are changed by means of unitary, number conserving, Bogolioubov transformations. This set of "virtual" bi-partitions is then finite-dimensionally parametrized and one can quantitatively address relevant questions such as the determination of the minimal and maximal available entanglement. In particular, we show that in the class of bipartite gaussian states there are states which remain separable for every possible modes redefinition, while do not exist states which remain entangled for every possible modes redefinition
The copper ferrite thin films have been deposited by RF sputtering at a 50W rf power. The As-deposited films are annealed in air at $800^{\circ}$C and then slow cooled. The As-deposited (AD) as well as slow cooled (SC) films are studied using a SQUID Magnetometer. The M Vs H curves have been recorded at various temperatures between 5K to 300K. The coercivities obtained from the MH curves are then plotted against temperature (T). The magnetization in the films does not saturate, even at the highest field of 7T. The high field part of the M Vs H curves is fitted using the H1/2 term of Chikazumi expression M(H)= Q*(1- a /Hn), with n=1/2. The variation of coefficient 'a' of H1/2 term has been observed with temperature (T). An attempt has been made to correlate this with the coercivity (Hc) in the case of annealed films.
We use a combination of ab initio calculations and statistical mechanics to investigate the substitution of Li+ for Mg2+ in magnesium hydride (MgH2) accompanied by the formation of hydrogen vacancies with positive charge (with respect to the original ion at the site). We show here that the binding energy between dopants and vacancy defects leads to a significant fraction of trapped vacancies and therefore a dramatic reduction of the number of free vacancies available for diffusion. The concentration of free vacancies initially increases with dopant concentration, but reaches a maximum at around 1 mol% Li doping and slowly decreases with further doping. At the optimal level of doping, the corresponding concentration of free vacancies is much higher than the equilibrium concentrations of charged and neutral vacancies in pure MgH2 at typical hydrogen storage conditions. We also show that Li-doped MgH2 is thermodynamically metastable with respect to phase separation into pure magnesium and lithium hydrides at any significant Li concentration, even after considering the stabilization provided by dopant-vacancy interactions and configurational entropic effects. Our results suggest that lithium doping may enhance hydrogen diffusion hydride, but only to a limited extent determined by an optimal dopant concentration and conditioned to the stability of the doped phase.
Silicene and germanene are key materials for the field of valleytronics. However, interaction with the substrate, which is necessary to support the electronically active medium, becomes a major obstacle. In the present work, we propose a substrate (F-doped WS$_2$) that avoids detrimental effects and at the same time induces the required valley polarization, so that no further steps are needed for this purpose. The behavior is explained by proximity effects on silicene/germanene, as demonstrated by first-principles calculations. Broken inversion symmetry due to the presence of WS$_2$ opens a substantial band gap in silicene/germanene. F doping of WS$_2$ results in spin polarization, which, in conjunction with proximity-enhanced spin orbit coupling, creates sizable spin-valley polarization.
Let X be the blow-up of a smooth projective 4-fold Y along a smooth curve C and let E be the exceptional divisor. Assume that X is a Fano manifold and has an elementary extremal contraction $\phi: X \to Z$ of (3,1)-type such that E is $\phi$-ample (recall that a contraction map for a 4-fold is called (3,1)-type if the exceptional locus is a divisor and its image is a curve). We show that if the exceptional divisor of $\phi$ is smooth, then Y is isomorphic to $\mathbb{P}^{4}$ and C is an elliptic curve of degree 4.
We obtain convergence rates (in the Levi-Prokhorove metric) in the functional central limit theorem (CLT) for partial sums $S_n=\sum_{j=1}^{n}\xi_{j,n}$ of triangular arrays $\{\xi_{1,n},\xi_{2,n},...,\xi_{n,n}\}$ satisfying some mixing and moment conditions (which are not necessarily uniform in $n$). For certain classes of additive functionals of triangular arrays of contracting Markov chains (in the sense of Dobrushin) we obtain rates which are close to the best rates obtained for independent random variables. In addition, we obtain close to optimal rates in the usual CLT and a moderate deviations principle and some Rosenthal type inequalities. We will also discuss applications to some classes of local statistics (e.g. covariance estimators), as well as expanding non-stationary dynamical systems, which can be reduced to non-uniformly mixing triangular arrays by an approximation argument. The main novelty here is that our results are obtained without any assumptions about the growth rate of the variance of $S_n$. The result are obtained using a certain type of block decomposition, which, in a sense, reduces the problem to the case when the variance of $S_n$ is "not negligible" in comparison with the (new) number of summands.
Invited talk given at the conference QCD97, Montpellier, France. I report on rec ent work done in collaboration with Laurent Lellouch and Josep Taron concerning the derivation of rigorous lower bounds for the combination of light quark massese s m_s + m_u and m_d + m_u.
We present a likelihood profile stacking technique based on the {\it Fermi}-Large Area Telescope (LAT) data to explore the $\gamma$-ray characteristics of {\it Fermi}-LAT undetected astrophysical populations. The pipeline is applied to a sample of $\gamma$-ray unresolved extreme blazars, i.e., sources with the highest synchrotron peak frequencies ($\nu_{\rm Syn}^{\rm peak}\geqslant 10^{17}$ Hz), and we report a cumulative $\gamma$-ray detection with more than 32$\sigma$ confidence for 2 degrees of freedom. Comparing the generated stacked $\gamma$-ray spectrum with the sensitivity limits of the upcoming Cherenkov Telescope Array (CTA), we find that the {\it Fermi}-LAT undetected population of such extreme blazars, on average, may remain well below the CTA detection threshold due to their faintness and extragalactic background light (EBL) absorption. However, $\gamma$-ray detected blazars belonging to the same class are promising candidates for CTA observations. The EBL corrected stacked spectra of these sources do not show any softening up to 1 TeV. This finding suggests the inverse Compton peak of extreme blazars to lie above 1 TeV, thus indicating a hard intrinsic TeV spectrum. Our analysis also predicts that at 100 GeV, at least $\sim$10\% of the diffuse extragalactic $\gamma$-ray background originates from the $\gamma$-ray undetected extreme blazars. These results highlight the effectiveness of the developed stacking technique to explore the uncharted territory of $\gamma$-ray undetected astrophysical objects.
We show that the structure constants of $k$-Lie algebras, $k>3$, with a positive definite metric are the sum of the volume forms of orthogonal $k$-planes. This generalizes the result for $k=3$ in arXiv:0804.2662 and arXiv:0804.3078, and confirms a conjecture in math/0211170.
With the motive of unraveling the origin of native vacancy induced magnetization in ferroelectric perovskite oxide systems, here we explore the consequences of electronic structure modification in magnetic ordering of oxygen deficient epitaxial BaTiO$_{3-\delta}$ thin films. Our adapted methodology employs state-of-the-art experimental approaches viz. photo-emission, photo-absorption spectroscopies, magnetometric measurements duly combined with first principles based theoretical methods within the frame work of density functional theory (DFT and DFT+\textit{U}) calculations. Oxygen vacancy (O$ _{V} $) is observed leading partial population of Ti 3\textit{d} (t$_{2g}$), which induces defect state in electronic structure near the Fermi level and reduces the band gap. The oxygen deficient BaTiO$_{2.75} $ film reveals Mott-Hubbard insulator characteristic, in contrast to the band gap insulating nature of the stoichiometric BaTiO$ _{3}$. The observed magnetic ordering is attributed to the asymmetric distribution of spin polarized charge density in the vicinity of O$ _{V} $ site which originates unequal magnetic moment values at first and second nearest neighboring Ti sites, respectively. Hereby, we present an exclusive method for maneuvering the band gap and on-site electron correlation energy with consequences on magnetic properties of BaTiO$_{3-\delta}$ system, which can open a gateway for designing novel single phase multiferroic system.
We present the results of NuSTAR and XMM-Newton observations of the two ultraluminous X-ray sources (ULX) NGC 1313 X-1 and X-2. The combined spectral bandpass of the two satellites enables us to produce the first spectrum of X-1 between 0.3 and 30 keV, while X-2 is not significantly detected by NuSTAR above 10 keV. The NuSTAR data demonstrate that X-1 has a clear cutoff above 10 keV, whose presence was only marginally detectable with previous X-ray observations. This cutoff rules out the interpretation of X-1 as a black hole in a standard low/hard state, and it is deeper than predicted for the downturn of a broadened iron line in a reflection-dominated regime. The cutoff differs from the prediction of a single-temperature Comptonization model. Further, a cold disk-like black body component at ~0.3 keV is required by the data, confirming previous measurements by XMM-Newton only. We observe a spectral transition in X-2, from a state with high luminosity and strong variability to a lower-luminosity state with no detectable variability, and we link this behavior to a transition from a super-Eddington to a sub-Eddington regime.