ShantanuT01/DACTYL-Pretraining huggingface dataset:
The mixing properties (or sensitivity to initial conditions) of two-dimensional Henon map have been explored numerically at the edge of chaos. Three independent methods, which have been developed and used so far for the one-dimensional maps, have been used to accomplish this task. These methods are (i)measure of the divergence of initially nearby orbits, (ii)analysis of the multifractal spectrum and (iii)computation of nonextensive entropy increase rates. The obtained results strongly agree with those of the one-dimensional cases and constitute the first verification of this scenario in two-dimensional maps. This obviously makes the idea of weak chaos even more robust.
It is shown here that electrons on the surface of a nanotube in a perpendicular magnetic field undergo spin-chirality separation along the circumference. Stripes of spin-polarization propagate along the tube, with a spatial pattern that can be modulated by the electron filling.
Although deep learning has yielded impressive performance for face recognition, many studies have shown that different networks learn different feature maps: while some networks are more receptive to pose and illumination others appear to capture more local information. Thus, in this work, we propose a deep heterogeneous feature fusion network to exploit the complementary information present in features generated by different deep convolutional neural networks (DCNNs) for template-based face recognition, where a template refers to a set of still face images or video frames from different sources which introduces more blur, pose, illumination and other variations than traditional face datasets. The proposed approach efficiently fuses the discriminative information of different deep features by 1) jointly learning the non-linear high-dimensional projection of the deep features and 2) generating a more discriminative template representation which preserves the inherent geometry of the deep features in the feature space. Experimental results on the IARPA Janus Challenge Set 3 (Janus CS3) dataset demonstrate that the proposed method can effectively improve the recognition performance. In addition, we also present a series of covariate experiments on the face verification task for in-depth qualitative evaluations for the proposed approach.
We study the contribution of galaxies with different properties to the global densities of star formation rate (SFR), atomic (HI) and molecular hydrogen (H2) as a function of redshift. We use the GALFORM model of galaxy formation, which is set in the LCDM framework. This model includes a self-consistent calculation of the SFR, which depends on the H2 content of galaxies. The predicted SFR density and how much of this is contributed by galaxies with different stellar masses and infrared luminosities are in agreement with observations. The model predicts a modest evolution of the HI density at z<3, which is also in agreement with the observations. The HI density is predicted to be always dominated by galaxies with SFR<1Msun/yr. This contrasts with the H2 density, which is predicted to be dominated by galaxies with SFR>10Msun/yr. Current high-redshift galaxy surveys are limited to detect carbon monoxide in galaxies with SFR>30Msun/yr, which in our model make up, at most, 20% of the H2 in the universe. In terms of stellar mass, the predicted H2 density is dominated by massive galaxies, Mstellar>10^10Msun, while the HI density is dominated by low mass galaxies, Mstellar<10^9Msun. In the context of upcoming neutral gas surveys, we suggest that the faint nature of the galaxies dominating the HI content of the Universe will hamper the identification of optical counterparts, while for H2, we expect follow up observations of molecular emission lines of already existing galaxy catalogues to be able to uncover the H2 density of the Universe.
This paper is devoted to self-consistent modeling of the magnetically supported accretion disk with optically thick warm corona based on first principles. In our model, we consider the gas heating by magneto-rotational instability (MRI) dynamo. Our goal is to show that the proper calculation of the gas heating by magnetic dynamo can build up the warm, optically thick corona above the accretion disk around black hole of stellar mass. Using vertical model of the disk supported and heated by the magnetic field together with radiative transfer in hydrostatic and radiative equilibrium we developed relaxation numerical scheme which allows us to compute the transition form the disk to corona in a self consistent way. We demonstrate here that the warm (up to 5 keV), optically thick (up to 10 Thompson optical depths), Compton cooled corona can form due to the magnetic heating. Such warm corona is stronger for higher accretion rate and larger magnetic field strength. The radial extent of the warm corona is limited by the occurrence of the local thermal instability, which purely depends on radiative processes. The obtained coronal parameters are in agreement with those constrained from X-ray observations. The warm magnetically supported corona is tends to appear in the inner disk regions. It may be responsible for Soft X-ray excess seen in accreting sources. For lower accretion rates and weaker magnetic field parameters, thermal instability prevents warm corona to exist, giving rise to eventual clumpiness or ionized outflow.
We give a signed fundamental domain for the action on $\mathbb{R}^{r_1}_+\times{\mathbb{C}^*}^{r_2}$ of the totally positive units $E_+$ of a number field $k$ of degree $n=r_1+2r_2$ which we assume is not totally complex. Here $r_1$ and $r_2$ denote the number of real and complex places of $k$ and $\mathbb{R}_+$ denotes the positive real numbers. The signed fundamental domain consists of $n$-dimensional $k$-rational cones $C_\alpha$, each equipped with a sign $\mu_\alpha=\pm1$, with the property that the net number of intersections of the cones with any $E_+$-orbit is 1.   The cones $C_\alpha$ and the signs $\mu_\alpha$ are explicitly constructed from any set of fundamental totally positive units and a set of $3^{r_2}$ "twisters", i.e. elements of $k$ whose arguments at the $r_2$ complex places of $k$ are sufficiently varied. Introducing twisters gives us the right number of generators for the cones $C_\alpha $ and allows us to make the $C_\alpha$ turn in a controlled way around the origin at each complex embedding.
We propose a variational quantum attack algorithm (VQAA) for classical AES-like symmetric cryptography, as exemplified the simplified-data encryption standard (S-DES). In the VQAA, the known ciphertext is encoded as the ground state of a Hamiltonian that is constructed through a regular graph, and the ground state can be found using a variational approach. We designed the ansatz and cost function for the S-DES's variational quantum attack. It is surprising that sometimes the VQAA is even faster than Grove's algorithm as demonstrated by our simulation results. The relationships of the entanglement entropy, concurrence and the cost function are investigated, which indicate that entanglement plays a crucial role in the speedup.
The first principles calculations (GGA) have been applied to study the crystallographic defects in $\alpha$-PbO in order to understand an origin of $n$- and $p$-type conductivity in otherwise undoped $\alpha$-PbO. It was found that deposition in the oxygen-deficient environment to be defined in our simulations by the Pb-rich/O-poor limit stimulates a formation of the O vacancies and the Pb interstitials both to be characterized by quite low formation energies $\sim$ 1.0 eV. The O vacancy being occupied by two electrons shifts a balance of electrons and holes between these two defects to excess of electrons (four electrons against two holes) that causes the $n$-type doping. For the Pb-poor/O-rich limit, an excess of oxygen triggers a formation of the O interstitials characterized by such a low formation energy that spontaneous appearance of this defect is predicted. It is shown that the concentration of the O interstitials is able to reach the extreme magnitude equal to number of the possible defect sites ($\sim 10^{22}$cm$^{-3}$). The localized state formed by the O interstitial is occupied by two holes and because there are no other defects in reasonable concentration to balance the hole redundancy, $p$-type doping is induced.
The model proposed originally by Mannheim and Kazanas for fitting the shapes of galactic rotation curves has recently been considered by Grumiller to describe gravity of a central object at large distances. Herein we employ the same geometry within the context of nonlinear electrodynamics (NED). Pure electrical NED model is shown to generate the novel Rindler acceleration term in the metric which explains anomalous behaviors of test particles / satellites. Remarkably a pure magnetic model of NED yields flat rotation curves that may account for the missing dark matter. Weak and Strong Energy conditions are satisfied in such models of NED.
Analytical wormhole solutions in Brans-Dicke theory in the presence of matter are presented. It is shown that the wormhole throat must not be necessarily threaded with exotic matter.
The paper concerns spontaneous asymptotic phase-locking and synchronization in two-qubit systems undergoing continuous Markovian evolution described by Lindbladian dynamics with normal Lindblad operators. Using analytic methods, all phase-locking-enforcing mechanisms within the given framework are obtained and classified. Detailed structures of their respective attractor spaces are provided and used to explore their properties from various perspectives. Amid phase-locking processes those additionally enforcing identical stationary parts of both qubits are identified, including as a special case the strictest form of synchronization conceivable. A prominent basis is presented which reveals that from a physical point of view two main types of phase-locking mechanisms exist. The ability to preserve information about the initial state is explored and an upper bound on the amplitude of oscillations of the resulting phase-locked dynamics is established. Permutation symmetry of both asymptotic states and phase-locking mechanisms is discussed. Lastly, the possibility of entanglement production playing the role of a phase-locking witness is rebutted by three analytically treatable examples.
We will discuss the key concepts in density functional theory (DFT), how it can be used to model experimental data, and consider how the synergy between DFT and experiment can give significant insights. The discussion will centre on the scanning tunnelling microscope (STM) and surface problems, tracking the author's personal interest, though the general principles are widely applicable.
We give a short overview on our work on ancestral lineages in spatial population models with local regulation. We explain how an ancestral lineage can be interpreted as a random walk in a dynamic random environment. Defining regeneration times allows to prove central limit theorems for such walks. We also consider several ancestral lineages in the same population and show for one prototypical example that in one dimension the corresponding system of coalescing walks converges to the Brownian web.
We give a corrected statement of the theorem of Gurjar and Miyanishi, which classifies smooth affine surfaces of Kodaira dimension zero, whose coordinate ring is factorial and has trivial units. Denote the class of such surfaces by $\mathcal{S}_{0}$. An infinite series of surfaces in $\mathcal{S}_{0}$, not listed by Gurjar and Miyanishi, was recently obtained by Freudenburg, Kojima and Nagamine as affine modifications of the plane. We complete their list to a series containing arbitrarily high-dimensional families of pairwise non-isomorphic surfaces in $\mathcal{S}_{0}$. Moreover, we classify them up to a diffeomorphism, showing that each occurs as an interior of a 4-manifold whose boundary is an exceptional surgery on a 2-bridge knot. In particular, we show that $\mathcal{S}_{0}$ contains countably many pairwise non-homeomorphic surfaces.
Ab initio modeling of molecular electronics is nowadays routinely performed by combining the Density Functional Theory (DFT) and Nonequilibrium Green function (NEGF) techniques. This method has its roots in the current formula given by Meir and Wingreen, and we discuss some applications and accompanying pitfalls and restrictions of this approach. Quite recently papers have begun to appear where inelastic effects are considered, and we illustrate these new developments by describing our own work on transport in atomic gold wires.
In this article we perform dynamical analysis of a broad class of barotropic fluids in the spatially curved Friedmann-Robertson-Walker (FRW) spacetime background without considering the cosmological constant. The first part of our study concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS) having as the only assumption the non-negativity of the fluid's energy density. After defining a new set of dimensionless variables and a new evolution parameter, we introduce the function $\Gamma$ that encodes the EoS. In this general setup several features of the system are identified: critical points, invariant subsets and the characteristics of the function $\Gamma$, along with their cosmological interpretations. The second part of our work provides two examples with specific $\Gamma$ functions. In the first example we provide a $\Gamma$ function and then we exhibit how it can be trimmed down to a specific class of EoS through physical arguments, while in the second example we discuss the quadratic EoS studied in Phys.Rev. D {\bf 74}, 023523 (2006) by comparing our approach with their analysis.
The energies and transition rates to $J=1^{+} T=1$ and $J=2^{+} T=0,1$ states in ^{12}C with matrix elements fitted to realistic $G$ matrix elements obtained in non-relativistic approaches are studied. Then the effects of varying the strengths of the two-body tensor and spin-orbit interactions are also considered. The calculations are done in both a small space (0p) and a large space (0p + $2\hbar\omega$). In the small space the B(M1) from ground to the $J=1^{+} T=1$ is enhanced and gets closer to experiment if the strength of the spin-orbit interaction is increased and/or if that of the tensor interaction is made weaker. In a large space the spin B(M1) gets reduced by almost a factor of two. A `self-weakening' mechanism for the tensor interaction which succeeded in explaining anomalies in other nuclei does not seem to work for this case.
The conventional order parameters in quantum matters are often characterized by 'spontaneous' broken symmetries. However, sometimes the broken symmetries may blend with the invariant symmetries to lead to mysterious emergent phases. The heavy fermion metal URu2Si2 is one such example, where the order parameter responsible for a second-order phase transition at Th = 17.5 K has remained a long-standing mystery. Here we propose via ab-initio calculation and effective model that a novel spin-orbit density wave in the f-states is responsible for the hidden-order phase in URu2Si2. The staggered spin-orbit order 'spontaneous' breaks rotational, and translational symmetries while time-reversal symmetry remains intact. Thus it is immune to pressure, but can be destroyed by magnetic field even at T = 0 K, that means at a quantum critical point. We compute topological index of the order parameter to show that the hidden order is topologically invariant. Finally, some verifiable predictions are presented.
We present a comprehensive description of the theory and practice of opacity calculations from the infrared to the ultraviolet needed to generate models of the atmospheres of brown dwarfs and extrasolar giant planets. Methods for using existing line lists and spectroscopic databases in disparate formats are presented and plots of the resulting absorptive opacities versus wavelength for the most important molecules and atoms at representative temperature/pressure points are provided. Electronic, ro-vibrational, bound-free, bound-bound, free-free, and collision-induced transitions and monochromatic opacities are derived, discussed, and analyzed. The species addressed include the alkali metals, iron, heavy metal oxides, metal hydrides, $H_2$, $H_2O$, $CH_4$, $CO$, $NH_3$, $H_2S$, $PH_3$, and representative grains. [Abridged]
Radial abundance gradients are a common feature of spiral galaxies, and in the case of the Galaxy both the magnitude of the gradients and their variations are among the most important constraints of chemical evolution models. Planetary nebulae (PN) are particularly interesting objects to study the gradients and their variations. Owing to their bright emission spectra, they can be observed even at large galactocentric distances, and the derived abundances are relatively accurate, with uncertainties of about 0.1 to 0.2 dex, particularly for the elements that are not synthesized in their progenitor stars. On the other hand, as the offspring of intermediate mass stars, with main sequence masses in the interval of 1 to 8 solar masses, they are representative of objects with a reasonable age span. In this paper, we present an estimate of the time variation of the O/H radial gradient in a sample containing over 200 nebulae with accurate abundances. Our results are consistent with a flattening of the O/H gradient roughly from -0.11 dex/kpc to -0.06 dex/kpc during the last 9 Gyr, or from -0.08 dex/kpc to -0.06 dex/kpc during the last 5 Gyr.
Secure multi-party computing, also called "secure function evaluation", has been extensively studied in classical cryptography. We consider the extension of this task to computation with quantum inputs and circuits. Our protocols are information-theoretically secure, i.e. no assumptions are made on the computational power of the adversary. For the weaker task of verifiable quantum secret sharing, we give a protocol which tolerates any t < n/4 cheating parties (out of n). This is shown to be optimal. We use this new tool to show how to perform any multi-party quantum computation as long as the number of dishonest players is less than n/6.
We condition a Brownian motion with arbitrary starting point $y \in \mathbb{R}$ on spending at most $1$ time unit below $0$ and provide an explicit description of the resulting process. In particular, we provide explicit formulas for the distributions of its last zero $g=g^y$ and of its occupation time $\Gamma=\Gamma^y$ below $0$ as functions of $y$. This generalizes a result of Benjamini and Berestycki from 2011, which covers the special case $y=0$. Additionally, we study the behavior of the distributions of $g^y$ and $\Gamma^y$, respectively, for $y \to \pm\infty$.
We develop a new theory of $L$-series based on replacing Dirichlet characters mod $N$ by symmetric functions mod $N$ in order to calculate explicitly the sums of infinite series more closely related to $\zeta(2n+1)$, specifically $\zeta(3)$, $\zeta(5)$. This generalizes the corresponding theory of sums of $L$-series associated to Dirichlet characters.
GRB 970815 was a well-localized gamma-ray burst (GRB) detected by the All-Sky Monitor (ASM) on the Rossi X-Ray Timing Explorer (RXTE) for which no afterglow was identified despite follow-up ASCA and ROSAT pointings and optical imaging to limiting magnitude R>23. While an X-ray source, AX/RX J1606.8+8130, was detected just outside the ASM error box, it was never associated with the GRB because it was not clearly fading and because no optical afterglow was ever found. We recently obtained an upper limit for this source with Chandra that is at least factor of 100 fainter than the ASCA detection. We also made deep optical observations of the AX/RX J1606.8+8130 position, which is blank to limits V>25.2 and I>24.0. In view of these extreme limits we conclude that AX/RX J1606.8+8130 was indeed the afterglow of GRB 970815, which corresponds to an optically "dark" GRB. AX/RX J1606.8+8130 can therefore be ruled out as the counterpart of the persistent EGRET source 3EG J1621+8203. The early light curves from BATSE and the RXTE ASM show spectral softening between multiple peaks of prompt emission. We propose that GRB 970815 might be a case in which the properties of an X-ray flash (XRF) and a "normal" GRB coincide in a single event.
We consider the $0$-order perturbed Lam\'e operator $-\Delta^\ast + V(x)$. It is well known that if one considers the free case, namely $V=0,$ the spectrum of $-\Delta^\ast$ is purely continuous and coincides with the non-negative semi-axis. The first purpose of the paper is to show that, at least in part, this spectral property is preserved in the perturbed setting. Precisely, developing a suitable multipliers technique, we will prove the absence of point spectrum for Lam\'e operator with potentials which satisfy a variational inequality with suitable small constant. We stress that our result also covers complex-valued perturbation terms. Moreover the techniques used to prove the absence of eigenvalues enable us to provide uniform resolvent estimates for the perturbed operator under the same assumptions about $V$.
We prove that if $X$ and $Y$ are two Gaussian fields with equivalent spectral densities, they have the same sample paths properties in any separable Banach space continuously embedded in $\mathcal{C}^0(K)$ where $K$ is a compact set of $\mathbb{R}^d$.
Test-time adaptation (TTA) has increasingly been an important topic to efficiently tackle the cross-domain distribution shift at test time for medical images from different institutions. Previous TTA methods have a common limitation of using a fixed learning rate for all the test samples. Such a practice would be sub-optimal for TTA, because test data may arrive sequentially therefore the scale of distribution shift would change frequently. To address this problem, we propose a novel dynamic learning rate adjustment method for test-time adaptation, called DLTTA, which dynamically modulates the amount of weights update for each test image to account for the differences in their distribution shift. Specifically, our DLTTA is equipped with a memory bank based estimation scheme to effectively measure the discrepancy of a given test sample. Based on this estimated discrepancy, a dynamic learning rate adjustment strategy is then developed to achieve a suitable degree of adaptation for each test sample. The effectiveness and general applicability of our DLTTA is extensively demonstrated on three tasks including retinal optical coherence tomography (OCT) segmentation, histopathological image classification, and prostate 3D MRI segmentation. Our method achieves effective and fast test-time adaptation with consistent performance improvement over current state-of-the-art test-time adaptation methods. Code is available at: https://github.com/med-air/DLTTA.
A non-equilibrium Green's function method is applied to model high-field quantum transport and electron-phonon resonances in semiconductor superlattices. The field-dependent density of states for elastic (impurity) scattering is found non-perturbatively in an approach which can be applied to both high and low electric fields. I-V curves, and specifically electron-phonon resonances, are calculated by treating the inelastic (LO phonon) scattering perturbatively. Calculations show how strong impurity scattering suppresses the electron-phonon resonance peaks in I-V curves, and their detailed sensitivity to the size, strength and concentration of impurities.
Let $G$ be a graph with $n$ vertices, and let $L(G)$ and $Q(G)$ be the Laplacian matrix and signless Laplacian matrix of $G$, respectively. The polynomial $\pi(L(G);x)={\rm per}(xI-L(G))$ (resp. $\pi(Q(G);x)={\rm per}(xI-Q(G))$) is called {\em Laplacian permanental polynomial} (resp. {\em signless Laplacian permanental polynomial}) of $G$. In this paper, we show that two classes of bicyclic graphs are determined by their (signless) Laplacian permanental polynomials.
Robert Denomme and Gordan Savin made a primality test for Fermat numbers 2^(2^k)+1 using elliptic curves. We propose another primality test using elliptic curves for Fermat numbers and also give primality tests for integers of the form 2^(2k+1)\pm2^(k+1)+1.