ShantanuT01/DACTYL-Pretraining huggingface dataset:
We report observations of well developed half integer quantum Hall effect (QHE) on mono layer graphene films of 7 mm \times 7 mm in size. The graphene films are grown by chemical vapor deposition (CVD) on copper, then transferred to SiO_{2} /Si substrates, with typical carrier mobilities \approx 4000 cm^{2} /Vs. The large size graphene with excellent quality and electronic homogeneity demonstrated in this work is promising for graphene-based quantum Hall resistance standards, and can also facilitate a wide range of experiments on quantum Hall physics of graphene and practical applications exploiting the exceptional properties of graphene.
$ $The aim of this thesis is to lower the bound on square-free primitive roots modulo primes. Let $g^{\Box}(p)$ be the least square-free primitive root modulo $p$. We have proven the following two theorems.   Theorem 0.1. $$g^{\Box}(p) < p^{0.88}\quad\text{for all primes }p.$$ Theorem 0.2. $$g^{\Box}(p) < p^{0.63093}\quad\text{for all primes } p < 2.5\times10^{15} \text{ and }p > 9.63\times10^{65}.$$   Theorem 0.1 shows an improvement in the best known bound while Theorem 0.2 shows for which primes we can prove the theoretical lower bound.   After some introductory information in Chapter 1, we will start to prove the above theorems in Chapter 2. We will introduce an indicator function for primitive roots of primes in {\S}2.1 and together with results from {\S}1.2.1, {\S}1.2.3 and {\S}1.2.4 we will outline the first step in proving a general theorem of the above form. The next two stages in the proof will be outlined in Chapter 3. These two stages require the introduction of the prime sieve. Before defining the sieve in {\S}3.2 we will introduce the $e-$free integers which will play an important role in defining the sieve.   In {\S}3.2 we will obtain results that do not require computation, including Theorem 0.2. An algorithm is then introduced in {\S}3.3 which is the last stage of the proof. There we will complete the proof of Theorem 0.1.
We use empirical techniques to interpret the near-infrared colours of a sample of 5800 galaxies drawn from Sloan Digital Sky Survey (SDSS) main spectroscopic sample with YJHK photometry from the UK Infrared Deep Sky Survey (UKIDSS) data release one. We study correlations between near-IR colours measured within SDSS fibre and physical parameters derived from the spectra. These parameters include specific star formation rate, stellar age, metallicity and dust attenuation. All correlations are analyzed for samples of galaxies that are closely matched in redshift, in stellar mass and in concentration index. Whereas more strongly star-forming galaxies have bluer optical colours, the opposite is true at near-IR wavelengths -- galaxies with higher specific star formation rate have redder near-IR colours. This result agrees qualitatively with the predictions of models in which Thermally Pulsing Asymptotic Giant Branch (TP-AGB) stars dominate the H and K-band light of a galaxy following a burst of star formation. We also find a surprisingly strong correlation between the near-IR colours of star-forming galaxies and their dust attenuation as measured from the Balmer decrement. Unlike optical colours, however, near-IR colours exhibit very little dependence on galaxy inclination. This suggests that the correlation of near-IR colours with dust attenuation arises because TP-AGB stars are the main source of dust in the galaxy. Finally, we compare the near-IR colours of the galaxies in our sample to the predictions of three different stellar population models: the Bruzual & Charlot 2003 model, a preliminary version of a new model under development by Charlot & Bruzual, which includes a new prescription for AGB star evolution, and the Maraston 2005 model.
We investigate the effect of interactions in the Topological Insulator in 3+1 dimensions. We show that for a particular type of interactions, the Electrodynamics response is equivalent to the response of non-interacting Topological Insulator in 4+1 dimensions.
For these two decades, the Arakawa-Kaneko zeta function has been studied actively. Recently Kaneko and Tsumura constructed its variants from the viewpoint of poly-Bernoulli numbers. In this paper, we generalize their zeta functions of Arakawa-Kaneko type to those with indices in which positive and negative integers are mixed. We show that values of these functions at positive integers can be expressed in terms of the multiple Hurwitz zeta star values.
Bayesian statistical methods of Gregory-Loredo and the Bretthorst generalization of the Lomb-Scargle periodogram have been applied for studying activity cycles of the early K-type subgiant star CF Oct. We have used a ~45 year long dataset derived from archival photographic observations, published photoelectric photometry, Hipparcos data series and All Sky Automated Survey archive. We have confirmed the already known rotational period for the star of 20.16 d and have shown evidences that it has exhibited changes from 19.90 d to 20.45 d. This is an indication for stellar surface differential rotation.The Bayesian magnitude and time--residual analysis reveals clearly at least one long-term cycle. The cycle lenght's posterior distributions appear to be multimodal with a pronounced peak at a period of 7.1 y with FWHM of 54 d for time-residuals and at a period of 9.8 y with FWHM of 184 d for magitude data. These results are consistent with the previously postulated cycle of 9+/-3 years.
The energy spectrum of cosmic rays between 10**16 eV and 10**18 eV, derived from measurements of the shower size (total number of charged particles) and the total muon number of extensive air showers by the KASCADE-Grande experiment, is described. The resulting all-particle energy spectrum exhibits strong hints for a hardening of the spectrum at approximately 2x10**16 eV and a significant steepening at c. 8x10**16 eV. These observations challenge the view that the spectrum is a single power law between knee and ankle. Possible scenarios generating such features are discussed in terms of astrophysical processes that may explain the transition region from galactic to extragalactic origin of cosmic rays.
Let X be a projective manifold of dimension n. Beltrametti and Sommese conjectured that if A is an ample divisor such that $K_X+(n-1)A$ is nef, then $K_X+(n-1)A$ has non-zero global sections. We prove a weak version of this conjecture in arbitrary dimension. In dimension three, we prove the stronger non-vanishing conjecture of Ambro, Ionescu and Kawamata and give an application to Seshadri constants.
Modern galaxy formation theory suggests that the misalignment between stellar and gaseous components usually results from an external gas accretion and/or interaction with other galaxies. The extreme case of the kinematic misalignment is demonstrated by so-called galaxies with counterrotation that possess two distinct components rotating in opposite directions with respect to each other. We provide an in-deep analysis of galaxies with counterrotation from IllustrisTNG100 cosmological simulations. We have found $25$ galaxies with substantial stellar counterrotation in the stellar mass range of $2\times10^{9}-3\times10^{10}$~\Msun. In our sample the stellar counterrotation is a result of an external gas infall happened $\approx 2-8$~Gyr ago. The infall leads to the initial removal of pre-existing gas, which is captured and mixed together with the infalling component. The gas mixture ends up in the counterrotating gaseous disc. We show that $\approx 90\%$ of the stellar counterrotation formed in-situ, in the counterrotating gas. During the early phases of the infall, gas can be found in inclined extended and rather thin disc-like structures, and in some galaxies they are similar to (nearly-)~polar disc or ring-like structures. We discuss a possible link between the gas infall, AGN activity and the formation of misaligned components. In particular, we suggest that the AGN activity does not cause the counterrotation, although it is efficiently triggered by the retrograde gas infall, and it correlates well with the misaligned component appearance. We also find evidence of the stellar disc heating visible as an increase of the vertical-to-radial velocity dispersion ratio above unity in both co- and counterrotating components, which implies the importance of the kinematical misalignment in shaping the velocity ellipsoids in disc galaxies.
Multifunctional lattice materials are of great interest to modern engineering including aerospace, robotics, wave control, and sensing. In this work, we proposed and developed a new class of functional lattice materials called liquid metal lattice materials, which are composed of liquid metals and elastomer coatings organized in a co-axial way. This hybrid design enables the liquid metal lattice materials with a thermal-activated shape memory effect and hence a variety of intriguing functionalities including recoverable energy absorption, tunable shape and rigidity, deployable and reconfigurable behaviors. The fabrication of liquid metal lattice materials is realised by a hybrid manufacturing approach combining 3D printing, vacuum casting, and coating. The mechanical properties and functionalities of these liquid metal lattice materials are studied via experimental testing. We expect that this new class of lattice materials will greatly expand the current realm of lattice materials and lead to novel multifunctional applications.
We prove a quantitative version of a Silverstein's Theorem on a condition for convergence in probability of the norm of random matrix. More precisely, we show that for a random matrix whose entries are i.i.d. random variables, $w_{i,j}$, satisfying certain natural conditions, is not small with large probability.
The average particle multiplicity density dN/deta is the dynamical quantity which reflects some regularities of particle production in low-pT range. The quantity is an important ingredient of z-scaling. Experimental results on charged particle density are available for pp, pA and AA collisions while experimental properties of the jet density are still an open question. The goal of this work is to find the variable which will reflect the main features of the jet production in low transverse energy range and play the role of the scale factor for the scaling function psi(z) and variable z in data z-presentation. The appropriate candidate is the variable we called "scaled jet energy density". Scaled jet energy density is the probability to have a jet with defined ET in defined xT and pseudorapidity regions. The PYTHIA6.2 Monte Carlo generator is used for calculation of scaled jet energy density in proton-proton collisions over a high energy range (sqrt s = 200-14000 GeV) and at eta = 0. The properties of the new variable are discussed and sensitivity to "physical scenarios" applied in the standard Monte Carlo generator is noted. The results of scaled jet energy density at LHC energies are presented and compared with predictions based on z-scaling.
In this paper, we consider the question of correcting mock modular forms in order to obtain $p$-adic modular forms. In certain cases we show that a mock modular form $M^+$ is a $p$-adic modular form. Furthermore, we prove that otherwise the unique correction of $M^+$ is intimately related to the shadow of $M^+$.
We study the magnetic field evolution of an isolated spiral galaxy, using isolated Milky Way-mass galaxy formation simulations and a novel prescription for magnetohydrodynamic (MHD) supernova feedback. Our main result is that a galactic dynamo can be seeded and driven by supernova explosions, resulting in magnetic fields whose strength and morphology is consistent with observations. In our model, supernovae supply thermal energy, and a low level magnetic field along with their ejecta. The thermal expansion drives turbulence, which serves a dual role by efficiently mixing the magnetic field into the interstellar medium, and amplifying it by means of turbulent dynamo. The computational prescription for MHD supernova feedback has been implemented within the publicly available ENZO code, and is fully described in this paper. This improves upon ENZO's existing modules for hydrodynamic feedback from stars and active galaxies. We find that the field attains $\mu G$-levels over Gyr-time scales throughout the disk. The field also develops large-scale structure, which appears to be correlated with the disk's spiral arm density structure. We find that seeding of the galactic dynamo by supernova ejecta predicts a persistent correlation between gas metallicity and magnetic field strength. We also generate all-sky maps of the Faraday rotation measure from the simulation-predicted magnetic field, and present a direct comparison with observations.
Long-tail distribution is widely spread in real-world applications. Due to the extremely small ratio of instances, tail categories often show inferior accuracy. In this paper, we find such performance bottleneck is mainly caused by the imbalanced gradients, which can be categorized into two parts: (1) positive part, deriving from the samples of the same category, and (2) negative part, contributed by other categories. Based on comprehensive experiments, it is also observed that the gradient ratio of accumulated positives to negatives is a good indicator to measure how balanced a category is trained. Inspired by this, we come up with a gradient-driven training mechanism to tackle the long-tail problem: re-balancing the positive/negative gradients dynamically according to current accumulative gradients, with a unified goal of achieving balance gradient ratios. Taking advantage of the simple and flexible gradient mechanism, we introduce a new family of gradient-driven loss functions, namely equalization losses. We conduct extensive experiments on a wide spectrum of visual tasks, including two-stage/single-stage long-tailed object detection (LVIS), long-tailed image classification (ImageNet-LT, Places-LT, iNaturalist), and long-tailed semantic segmentation (ADE20K). Our method consistently outperforms the baseline models, demonstrating the effectiveness and generalization ability of the proposed equalization losses. Codes will be released at https://github.com/ModelTC/United-Perception.
We report the results of the monitoring campaign of the transient X-ray pulsar SMC X-2 performed with the Swift/XRT telescope over the period of 2015 September - 2016 January during the Type II outburst. During this event, the bolometric luminosity of the source ranged from $\simeq10^{39}$ down to several$\times10^{34}$ erg/s. Moreover, we discovered its dramatic drop by a factor of more than 100 below the limiting value of $L_{\rm lim}\simeq4\times10^{36}$ erg/s, which can be interpreted as a transition to the propeller regime. These measurements make SMC X-2 the sixth pulsating X-ray source where such a transition is observed and allow us to estimate the magnetic field of the neutron star in the system $B\simeq3\times10^{12}$ G, which is in agreement with independent results of the spectral analysis.
Let $P^k_\ell$ denote the loose $k$-path of length $\ell$ and let define $f^k_\ell(n,m)$ as the minimum value of $\Delta(H)$ over all $P^k_\ell$-free $k$-graphs $H$ with $n$ vertices and $m$ edges. In the paper we study the behavior of $f^4_2(n,m)$ and $f^3_3(n,m)$ and characterize the structure of extremal hypergraphs. In particular, it is shown that when $m\sim n^2/8$ the value of each of these functions drops down from $\Theta(n^2)$ to $\Theta(n)$.
In double quantum wells electrons experience a Lorentz force oriented perpendicular to the structure plane when an electric current is driven perpendicular to the direction of an in-plane magnetic field. Consequently, the excess charge is accumulated in one of the wells. The polarization of a bilayer electron system and the corresponding Hall voltage are shown to contribute substantially to the in-plane conductivity.
We study the the moduli space of KSBA stable pairs $(X,sS+\sum a_i F_i)$, consisting of a Weierstrass fibration $X$, its section $S$, and some fibers $F_i$. We find a compactification which is a DM stack, and we describe the objects on the boundary. We show that the fibration in the definition of Weierstrass fibration extends to the boundary, and it is equidimensional when $s \ll 1$. We prove that there are wall-crossing morphisms when the weights $s$ and $a_i$ change. When $s=1$, this recovers the work of La Nave (arXiv:math/0205035); and a special case of the work of Ascher-Bejleri (arXiv:1702.06107).
We study energy spectrum for hydrogen atom with deformed Heisenberg algebra leading to minimal length. We develop correct perturbation theory free of divergences. It gives a possibility to calculate analytically in the 3D case the corrections to $s$-levels of hydrogen atom caused by the minimal length. Comparing our result with experimental data from precision hydrogen spectroscopy an upper bound for the minimal length is obtained.
A classical theorem in continued fractions due to Serret shows that for any two irrational numbers x and y related by a transformation $\gamma$ in PGL(2,Z) there exist s and t for which the complete quotients x_s and y_t coincide. In this paper we give an upper bound in terms of $\gamma$ for the smallest indices s and t.
Blue straggler stars (BSS) are peculiar objects which normally appear as a single broad sequence along the extension of the main sequence. Only four globular clusters (GCs) have been observed to have two distinct and parallel BSS sequences. For the first time for any open cluster (OC), we report double BSS sequences in Berkeley 17. Using the machine-learning based membership algorithm ML-MOC on Gaia EDR3 data, we identify 627 cluster members, including 21 BSS candidates out to 15 arcmin from the cluster center. Both the BSS sequences are almost equally populated and parallel to one another in Gaia as well as in Pan-STARRS colour-magnitude diagram (CMD). We statistically confirm their presence and report that both BSS sequences are highly segregated compared to the reference population out to $\sim$5.5 arcmin and not segregated thereafter. The lower densities of OCs make BSS formation impossible via the collisional channel. Therefore, mass transfer seems to be the only viable channel for forming candidates of both sequences. The gap between the red and blue BSS sequences, on the other hand, is significant and presents a great opportunity to understand the connection between BSS formation and internal as well as external dynamics of the parent clusters.
I discuss a scaling limit, where open strings in the WZW-model behave as dipoles with charges confined to a spherical brane and projected to the lowest Landau level. Then I show how the joining and splitting interactions of these dipoles are naturally described using the fuzzy sphere algebra.
Vision transformers (ViTs) have become the popular structures and outperformed convolutional neural networks (CNNs) on various vision tasks. However, such powerful transformers bring a huge computation burden, because of the exhausting token-to-token comparison. The previous works focus on dropping insignificant tokens to reduce the computational cost of ViTs. But when the dropping ratio increases, this hard manner will inevitably discard the vital tokens, which limits its efficiency. To solve the issue, we propose a generic self-slimmed learning approach for vanilla ViTs, namely SiT. Specifically, we first design a novel Token Slimming Module (TSM), which can boost the inference efficiency of ViTs by dynamic token aggregation. As a general method of token hard dropping, our TSM softly integrates redundant tokens into fewer informative ones. It can dynamically zoom visual attention without cutting off discriminative token relations in the images, even with a high slimming ratio. Furthermore, we introduce a concise Feature Recalibration Distillation (FRD) framework, wherein we design a reverse version of TSM (RTSM) to recalibrate the unstructured token in a flexible auto-encoder manner. Due to the similar structure between teacher and student, our FRD can effectively leverage structure knowledge for better convergence. Finally, we conduct extensive experiments to evaluate our SiT. It demonstrates that our method can speed up ViTs by 1.7x with negligible accuracy drop, and even speed up ViTs by 3.6x while maintaining 97% of their performance. Surprisingly, by simply arming LV-ViT with our SiT, we achieve new state-of-the-art performance on ImageNet. Code is available at https://github.com/Sense-X/SiT.
This paper presents no new results; its goals are purely pedagogical. A special case of the Cartan Decomposition has found much utility in the field of quantum computing, especially in its sub-field of quantum compiling. This special case allows one to factor a general 2-qubit operation (i.e., an element of U(4)) into local operations applied before and after a three parameter, non-local operation. In this paper, we give a complete and rigorous proof of this special case of Cartan's Decomposition. From the point of view of QC programmers who might not be familiar with the subtleties of Lie Group Theory, the proof given here has the virtues, that it is constructive in nature, and that it uses only Linear Algebra. The constructive proof presented in this paper is implemented in some Octave/Matlab m-files that are included with the paper. Thus, this paper serves as documentation for the attached m-files.
We propose a method for Saimaa ringed seal (Pusa hispida saimensis) re-identification. Access to large image volumes through camera trapping and crowdsourcing provides novel possibilities for animal monitoring and conservation and calls for automatic methods for analysis, in particular, when re-identifying individual animals from the images. The proposed method NOvel Ringed seal re-identification by Pelage Pattern Aggregation (NORPPA) utilizes the permanent and unique pelage pattern of Saimaa ringed seals and content-based image retrieval techniques. First, the query image is preprocessed, and each seal instance is segmented. Next, the seal's pelage pattern is extracted using a U-net encoder-decoder based method. Then, CNN-based affine invariant features are embedded and aggregated into Fisher Vectors. Finally, the cosine distance between the Fisher Vectors is used to find the best match from a database of known individuals. We perform extensive experiments of various modifications of the method on a new challenging Saimaa ringed seals re-identification dataset. The proposed method is shown to produce the best re-identification accuracy on our dataset in comparisons with alternative approaches.
A correlation is established between the neutron multiplicity and the neutrons number in the fission state of Curium and Californium isotopes within a microscopic study using relativistic mean field formalism. The study includes the isotopes of Cm and Cf nuclei near the valley of stability, and hence is likely to play an important role in the artificial synthesis of superheavy nuclei. The static fission path, the neutron$-$proton asymmetry, the evolution of the neck and their composition in terms of nucleon numbers are also estimated. We find a maximum ratio for average neutron to proton density, which is about $1.6$ in the breakdown of the liquid$-$drop picture for $^{248}$Cm and $^{252}$Cf. A strong dependence of the neutron$-$proton asymmetry on the neutron multiplicity in an isotopic chain is also observed.
One possible solution to the strong CP problem is that CP is an exact symmetry, spontaneously broken at some scale. Some years ago, Nelson and Barr suggested a mechanism for obtaining $\theta=0$ at tree level in this framework, and showed that radiative corrections were small in some non-supersymmetric models. Further investigations suggested that the same could be true in supersymmetric theories. In this note, we show that these analyses assumed an extraordinarily high degree of degeneracy among squark masses and among other supersymmetry breaking parameters. We argue, using naturalness as well as expectations from string theory, that this is not very plausible.