ShantanuT01/DACTYL-Pretraining huggingface dataset:
Reliable and well-characterized quantum resources are indispensable ingredients in quantum information processing. Typically, in a realistic characterization of these resources, apparatuses come with intrinsic uncertainties that can manifest themselves in the form of systematic errors. While systematic errors are generally accounted for through careful calibration, the effect of remaining imperfections on the characterization of quantum resources has been largely overlooked in the literature. In this paper, we investigate the effect of systematic errors that arise from imperfect alignment of measurement bases --- an error that can conceivably take place due to the limited controlability of measurement devices. We show that characterization of quantum resources using quantum state tomography or entanglement witnesses can be undermined with an amount of such imprecision that is not uncommon in laboratories. Curiously, for quantum state tomography, we find that having entanglement can help to reduce the susceptibility to this kind of error. We also briefly discuss how a given entanglement witness can be modified to incorporate the effect of such errors.
RGBT tracking has attracted increasing attention since RGB and thermal infrared data have strong complementary advantages, which could make trackers all-day and all-weather work. However, how to effectively represent RGBT data for visual tracking remains unstudied well. Existing works usually focus on extracting modality-shared or modality-specific information, but the potentials of these two cues are not well explored and exploited in RGBT tracking. In this paper, we propose a novel multi-adapter network to jointly perform modality-shared, modality-specific and instance-aware target representation learning for RGBT tracking. To this end, we design three kinds of adapters within an end-to-end deep learning framework. In specific, we use the modified VGG-M as the generality adapter to extract the modality-shared target representations.To extract the modality-specific features while reducing the computational complexity, we design a modality adapter, which adds a small block to the generality adapter in each layer and each modality in a parallel manner. Such a design could learn multilevel modality-specific representations with a modest number of parameters as the vast majority of parameters are shared with the generality adapter. We also design instance adapter to capture the appearance properties and temporal variations of a certain target. Moreover, to enhance the shared and specific features, we employ the loss of multiple kernel maximum mean discrepancy to measure the distribution divergence of different modal features and integrate it into each layer for more robust representation learning. Extensive experiments on two RGBT tracking benchmark datasets demonstrate the outstanding performance of the proposed tracker against the state-of-the-art methods.
We establish an invariance principle for a one-dimensional random walk in a dynamical random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite box around the walker. The environment starts from equilibrium. After a suitable space-time rescaling, the random walk converges to a sum of two independent processes, a Brownian motion and a Gaussian process with stationary increments.
Revised spectroscopic parameters for the HF molecule and a new CN line list in the 2.3 mu region have been recently available, allowing a revision of the F content in AGB stars. AGB carbon stars are the only observationally confirmed sources of fluorine. Nowadays there is not a consensus on the relevance of AGB stars in its Galactic chemical evolution. The aim of this article is to better constrain the contribution of these stars with a more accurate estimate of their fluorine abundances. Using new spectroscopic tools and LTE spectral synthesis, we redetermine fluorine abundances from several HF lines in the K-band in a sample of Galactic and extragalactic AGB carbon stars of spectral types N, J and SC spanning a wide range of metallicities. On average, the new derived fluorine abundances are systematically lower by 0.33 dex with respect to previous determinations. This may derive from a combination of the lower excitation energies of the HF lines and the larger macroturbulence parameters used here as well as from the new adopted CN line list. Yet, theoretical nucleosynthesis models in AGB stars agree with the new fluorine determinations at solar metallicities. At low metallicities, an agreement between theory and observations can be found by handling in a different way the radiative/convective interface at the base of the convective envelope. New fluorine spectroscopic measurements agree with theoretical models at low and at solar metallicity. Despite this, complementary sources are needed to explain its observed abundance in the solar neighbourhood.
Consider the viscous Burgers equation on a bounded interval with inhomogeneous Dirichlet boundary conditions. Following the variational framework introduced by Bertini-De Sole-Gabrielli-Jona-Lasinio-Landim C, we analyze a Lyapunov functional for such equation which gives the large deviations asymptotics of a stochastic interacting particles model associated to the Burgers equation. We discuss the asymptotic behavior of this energy functional, whose minimizer is given by the unique stationary solution, as the length of the interval diverges. We focus on boundary data corresponding to a standing wave solution to the Burgers equation in the whole line. In this case, the limiting functional has in fact a one-parameter family of minimizers and we analyze the so-called development by Gamma-convergence; this amounts to compute the sharp asymptotic cost corresponding to a given shift of the stationary solution.
Intrinsic localized modes or discrete breathers are investigated by molecular dynamics simulations in free-standing graphene. Discrete breathers are generated either through thermal quenching of the graphene lattice or by proper initialization, with frequencies and lifetimes sensitively depending on the interatomic potential describing the carbon-carbon interaction. In the most realistic scenario, for which temperature-dependent molecular dynamics simulations in three dimension using a graphene-specific interatomic potential are performed, the breather lifetimes increase to hundreds of picoseconds even at relatively high temperatures. These lifetimes are much higher than those anticipated from earlier calculations, and may enable direct breather observation in Raman spectroscopy experiments.
Searches for the imprint of primordial gravitational waves in degree-scale CMB $B$-mode polarisation data must account for significant contamination from gravitational lensing. Fortunately, the lensing effects can be partially removed by combining high-resolution $E$-mode measurements with an estimate of the projected matter distribution. In the near future, experimental characteristics will be such that the latter can be reconstructed internally with high fidelity from the observed CMB, with the $EB$ quadratic estimator providing a large fraction of the signal-to-noise. It is a well-known phenomenon in this context that any overlap in modes between the $B$-field to be delensed and the $B$-field from which the reconstruction is derived leads to a suppression of delensed power going beyond that which can be attributed to a mitigation of the lensing effects. More importantly, the variance associated with this spectrum is also reduced, posing the question of whether the additional power suppression could help better constrain the tensor-to-scalar ratio, $r$. In this paper, we show this is not the case, as suggested but not quantified in previous work. We develop an analytic model for the biased delensed $B$-mode angular power spectrum, which suggests a simple renormalisation prescription to avoid bias on the inferred tensor-to-scalar ratio. With this approach, we learn that the bias necessarily leads to a degradation of the signal-to-noise on a primordial component compared to "unbiased delensing". Next, we assess the impact of removing from the lensing reconstruction any overlapping $B$-modes on our ability to constrain $r$, showing that it is in general advantageous to do this rather than modeling or renormalising the bias. Finally, we verify these results within a maximum-likelihood inference framework applied to simulations.
For some models of interacting fermions the known solution to the notorious sign-problem in Monte Carlo (MC) simulations is to work with macroscopic fermionic determinants; the price, however, is a macroscopic scaling of the numerical effort spent on elementary local updates. We find that the {\it ratio} of two macroscopic determinants can be found with any desired accuracy by considering truncated (local in space and time) matices. In this respect, MC for interacting fermionic systems becomes similar to that for the sign-problem-free bosonic systems with system-size independent update cost. We demonstrate the utility of the truncated-determinant method by simulating the attractive Hubbard model within the MC scheme based on partially summed Feynman diagrams. We conjecture that similar approach may be useful in other implementations of the sign-free determinant schemes.
In order to simulate the relativistic effects of the Dirac Brueckner Hartree Fock approach for finite nuclei the part of the Urbana 3 nucleon (3N) force is considered, which represents the enhancement of the small components of the Dirac spinors for the nucleons in the nuclear medium. This 3N force is included in a Brueckner Hartree Fock calculation with rearrangement terms using a realistic model for the NN interaction. The strength of the 3N force is adjusted to reproduce the empirical saturation point of nuclear matter and then used in corresponding studies of the closed shell nuclei $^{16}$O and $^{40}$Ca. Special attention is paid to a consistent treatment of the spectrum of particle states in the NN propagator of the Bethe-Goldstone equation.
A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums. Algorithms for the evaluation of nested and harmonic sums are used to reduce the expressions to get analytical or numerical results for the expansion coefficients. Methods to increase the precision of numerical results are discussed.
It is shown that each complex conjugate of a meromorphic modular form for $\mathrm{SL}_2(\mathbb{Z})$ of any complex weight $p$ occurs as the image of a harmonic modular form under the operator $2i y^p \, \partial_{\bar z}$. These harmonic lifts occur in holomorphic families with the weight as the parameter.
We revisit here a recent work on regular rotating black holes. We introduce a new mass function generalizing the commonly used Bardeen and Hayward mass functions and extend the recently proposed solutions in order to accommodate a cosmological constant $\Lambda$. We discuss some aspects of the causal structure (horizons) and the ergospheres of the new proposed solutions. We also show that, in contrast with the spherically symmetrical case, the black hole rotation will unavoidably lead to the violation of the weak energy condition for any physically reasonable choice of the mass function, reinforcing the idea the description of the interior region of a Kerr black hole is much more challenging than in the Schwarzschild case.
We investigate two-dimensional Ising systems with multisping interactions of three- (m=3) and four-body terms (m=4). The application of a new type of finite-size algorithm of de Oliveira allow us to clearly distinguish a first-order transition (in the m=4 case) from a continuous one (in the m=3 one). We also study the damage spreading in these systems. In this study, a dynamical phenomenon is observed to occur at a critical point separating a chaotic phase from a frozen one. However, the width of the interval where this transition happens does not yield a conclusive evidence about the order of the phase transition.
In this paper, we find an explicit formulas, or recurrences, in terms of generating functions for the cardinalities of the sets $S_n(T;\tau)$ of all permutations in $S_n$ that contain $\tau\in S_k$ exactly once and avoid a subset $T\subseteq S_3$, $|T|\geq2$. The main body of the paper is divided into three sections corresponding to the cases $|T|=2,3$ and $|T|\geq4$.
We present a method that allows us for the first time to estimate the signal-to-noise ratio (SNR) of the harmonic-space galaxy bispectrum induced by gravity, a complementary probe to already well established Fourier-space clustering analyses. We show how to do it considering only $\sim1000$ triangle configurations in multipole space, corresponding to a computational speedup of a factor $\mathcal{O}(10^2)-\mathcal{O}(10^3)$, depending on the redshift bin, when including mildly non-linear scales. Assuming observational specifications consistent with forthcoming spectroscopic and photometric galaxy surveys like the Euclid satellite and the Square Kilometre Array (phase 1), we show: that given a single redshift bin, spectroscopic surveys outperform photometric surveys; and that -- due to shot-noise and redshift bin width balance -- bins at redshifts $z\sim1$ bring higher cumulative SNR than bins at lower redshifts $z \sim 0.5$. Our results for the largest cumulative SNR $\sim 15$ suggest that the harmonic-space bispectrum is detectable within narrow ($\Delta z \sim 0.01$) spectroscopic redshift bins even when including only mildly non-linear scales. Tomographic reconstructions and inclusion of highly non-linear scales will further boost detectability with upcoming galaxy surveys. In addition, we discuss how, using the Karhunen-Lo\`eve transform, a detection analysis only requires a $1 \times 1$ covariance matrix for a single redshift bin.
We study the existence of positive bound states for the nonlinear elliptic system \[ \begin{cases} - \Delta u_i + \lambda_i u_i = \sum_{j=1}^d \beta_{ij} u_j^2 u_i & \text{in $\Omega$} \\ u_1 =\cdots = u_d=0 & \text{on $\partial \Omega$}, \end{cases} \] where $d \ge 2$, $\beta_{ij}= \beta_{ji}$, $\beta_{ii},\lambda_i >0$, and $\Omega$ is either a bounded domain of $\mathbb{R}^N$, or $\Omega=\mathbb{R}^N$, with $N \le 3$. In light of its applicability in several physical contexts, the problem has been intensively studied in recent years, and several results concerning existence, multiplicity and qualitative properties of the solutions are available if either $\beta_{ij}\le 0$ for every $i \neq j$, or $\beta_{ij}>0$ for every $i \neq j$ and some additional assumptions are satisfied. On the other hand, only very partial results are known in the case of \emph{simultaneous cooperation and competition}, that is, when there exist two pairs $(i_1,j_1)$ and $(i_2,j_2)$ such that $i_1 \neq j_1$, $i_2 \neq j_2$, $\beta_{i_1 j_1}>0$ and $\beta_{i_2,j_2}<0$. In this setting, we provide sufficient conditions on the coupling parameters $\beta_{ij}$ in order to have a positive solution. Our first main results establishes the existence of solutions with at least $m$ positive components for every $m \le d$. Any such solution is a minimizer of the energy functional $J$ restricted on a \emph{Nehari-type manifold} $\mathcal{N}$. By means of level estimates on the constrained second differential of $J$ on $\mathcal{N}$, we show that, under some additional assumptions, any such minimizer has all nontrivial components. In order to prove this second result, we analyse the phase separation phenomena which involve solutions of the system in a \emph{not completely competitive} framework.
Solid oxide fuel/electrolyzer cell (SOFC/SOEC) converts energy between chemical and electrical forms inversely. Yet electrolyte degradation takes place much more severe for SOEC than SOFC during long-term operations. By solving transport equations, we found very large oxygen potential gradients and sharp oxygen potential transitions at grain boundaries of polycrystalline SOFC/SOEC electrolyte. Surprisingly, an inversion of oxygen potential transitions was identified, suggesting a fundamentally different transport mechanism for minor electronic charge carriers. Such findings could be critical to understand and eliminate SOFC/SOEC degradations in practical applications.
Energy transport can reveal information about interacting many-body systems beyond other transport probes. In particular, in one dimension it has been shown that the energy current is directly proportional to the central charge, thus revealing information about the degrees of freedom of critical systems. In this work, we explicitly verify this result in two cases for translationally invariant systems based on explicit microscopic calculations. More importantly, we generalise the result to non-translation invariant setups and use this to study a composite system of two subsystems possessing different central charges. We find a bottleneck effect meaning the smaller central charge limits the energy transport.
We compute the simplest one-loop planar amplitudes in Higgsed ABJM theory at a generic point of the moduli space. We explicitly check that they can be expressed in terms of integrals which are invariant under dual conformal symmetry involving masses, in a similar fashion as in N=4 SYM.
In the present paper, we consider a class of two players infinite horizon differential games, with piecewise smooth costs exponentially discounted in time. Through the analysis of the value functions, we study in which cases it is possible to establish the existence Nash equilibrium solutions in feedback form. We also provide examples of piecewise linear costs whose corresponding games have either infinitely many Nash equilibria or no solutions at all.
Lattice translation symmetry gives rise to a large class of "weak" topological insulators (TIs), characterized by translation-protected gapless surface states and dislocation bound states. In this work we show that space group symmetries lead to constraints on the weak topological indices that define these phases. In particular we show that screw rotation symmetry enforces the Hall conductivity along the screw axis to be quantized in multiples of the screw rank, which generally applies to interacting systems. We further show that certain 3D weak indices associated with quantum spin Hall effects (class AII) are forbidden by the Bravais-lattice and by glide or even-fold screw symmetries. These results put a strong constraints on candidates of weak TIs in the experimental and numerical search for topological materials, based on the crystal structure alone.
Accretion models predict that fluorescence lines broadened by relativistic effects should arise from reflection of X-ray emission onto the inner region of the accretion disc surrounding the central black hole of active galactic nuclei (AGN). The theory behind the origin of relativistic lines is well established, and observational evidence from a moderate number of sources seems to support the existence of these lines. The aim of this work is to establish the fraction of AGN with relativistic Fe Kalpha lines, and study possible correlations with source physical properties. An XMM-Newton collection of 149 radio-quiet Type 1 AGN has been systematically and uniformly analyzed in order to search for significant evidence of a relativistically broadened Fe Kalpha line. To enable statistical studies, an almost complete, flux-limited subsample of 31 sources has been defined. The 2-10 keV spectra of the FERO sources have been compared with a complex model including most of the physical components observed in the X-ray spectra of Seyfert galaxies: a power law primary continuum modified by non-relativistic Compton reflection and warm absorption, plus a series of narrow Fe line reflection features. The observed fraction of sources in the flux-limited sample that show significant evidence of a relativistic Fe Kalpha line is 36%. The average line Equivalent Width (EW) is of the order of 100 eV, while the average disc inclination angle is 28+/-5 deg and the average power-law index of the radial disc emissivity law is 2.4+/-0.4. The spin value is well constrained only in 2 cases (MCG-6-30-15 and MRK509), and in the rest of the cases, whenever a constraint can be placed, it always implies the rejection of the static black hole solution. The Fe Kalpha line EW does not correlate with disc parameters or with system physical properties, such as black hole mass, accretion rate and hard X-ray luminosity.
For a converging sequence of exponential L\'evy models, we give conditions under which the associated sequence of option prices converges. We also study the behaviour of the prices when no such convergence holds. We then consider two special cases, first when the martingale measure is chosen by minimisation of entropy and then when it minimises Hellinger integrals.
We study the quantum corrections to the polarizability of isolated metallic mesoscopic systems using the loop-expansion in diffusive propagators. We show that the difference between connected (grand-canonical ensemble) and isolated (canonical ensemble) systems appears only in subleading terms of the expansion, and can be neglected if the frequency of the external field, $\omega$, is of the order of (or even slightly smaller than) the mean level spacing, $\Delta$. If $\omega \ll \Delta$, the two-loop correction becomes important. We calculate it by systematically evaluating the ballistic parts (the Hikami boxes) of the corresponding diagrams and exploiting electroneutrality. Our theory allows one to take into account a finite dephasing rate, $\gamma$, generated by electron interactions, and it is complementary to the non-perturbative results obtained from a combination of Random Matrix Theory (RMT) and the $\sigma$-model, valid at $\gamma \to 0$. Remarkably, we find that the two-loop result for isolated systems with moderately weak dephasing, $\gamma \sim \Delta$, is similar to the result of the RMT+$\sigma$-model even in the limit $\omega \to 0$. For smaller $\gamma$, we discuss the possibility to interpolate between the perturbative and the non-perturbative results. We compare our results for the temperature dependence of the polarizability of isolated rings to the experimental data of Deblock \emph{et al} [\prl \ {\bf 84}, 5379 (2000); \prb \ {\bf 65}, 075301 (2002)], and we argue that the elusive 0D regime of dephasing might have manifested itself in the observed magneto-oscillations. Besides, we thoroughly discuss possible future measurements of the polarizability, which could aim to reveal the existence of 0D dephasing and the role of the Pauli blocking at small temperatures.
The radiofrequency dielectric response of the lead-free Ba(Zr$_{0.5}$Ti$_{0.5}$)O$_3$ relaxor ferroelectric is simulated using a coarse-grained Hamiltonian. This concept, taken from Real-Space Renormalization Group theories, allows depicting the collective behavior of correlated local modes gathered in blocks. Free-energy barriers for their thermally activated collective hopping are deduced from this {\it ab-initio}-based approach, and used as input data of Kinetic Monte Carlo simulations. The resulting numerical scheme allows to simulate the dielectric response for external field frequencies ranging from the kHz up to a few tens of MHz for the first time, and to, e.g., demonstrate that local (electric or elastic) random fields lead to the dielectric relaxation in the radiofrequency range that has been observed in relaxors.