ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we derive eight basic identities of symmetry in three variables related to generalized Euler polynomials and alternating generalized power sums. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the $p$-adic fermionic integral expression of the generating function for the generalized Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating generalized power sums.
Temperature dependence of the X-ray absorption near-edge structure (XANES) spectra at the Pr $L_{3}$- and Tb $L_{3}$-edges was measured for the (Pr$_{1-y}$Tb$_{y})_{0.7}$Ca$_{0.3}$CoO$_{3}$ system, in which a metal-insulator (MI) and spin-state (SS) transition took place simultaneously at a critical temperature $T_{\rm MI}$. A small increase in the valence of the terbium ion was found below $T_{\rm MI}$, besides the enhancement of the praseodymium valence; the trivalent states, which are stable at room temperature, change to a 3+/4+ ionic mixture at low temperatures. In particular for the $y$=0.2 sample, the average valence determined at 8 K amounts to 3.03+ and 3.25+ for the Tb and Pr ion, respectively. In analogous (Pr$_{1-y}$RE$_{y})_{0.7}$Ca$_{0.3}$CoO$_{3}$ samples (RE=Sm and Eu), in which the MI-SS transition also took place, no valence shift of the RE ion was detected in the XANES spectra at the RE ion $L_{3}$-edge. The role of the substituted RE ion for the Pr-site on the MI-SS transition is discussed.
We compute the on-shell action of static, BPS black holes in AdS$_4$ from ${\cal N}=2$ gauged supergravity coupled to vector multiplets and show that it is equal to minus the entropy of the black hole. Holographic renormalization is used to demonstrate that with appropriate boundary conditions on the scalar fields, the divergent and finite contributions from the asymptotic boundary vanish. The entropy arises from the extrinsic curvature on $\Sigma_g\times S^1$ evaluated at the horizon, where $\Sigma_g$ may have any genus $g\geq 0$. This provides a clarification of the equivalence between the partition function of the twisted ABJM theory on $\Sigma_g\times S^1$ and the entropy of the dual black hole solutions. It also demonstrates that the complete entropy resides on the AdS$_2\times \Sigma_g$ horizon geometry, implying the absence of hair for these gravity solutions.
We present an analytical and numerical study of the fluorescence spectra of a bistable driven system by means of Keldysh diagram technique in pseudo--particle representation. The spectra exhibit smooth transition between ultra-quantum and the quasiclassical limits and indicate the threshold value of the external field when changing of the most probable stable state occurs. The analysis of the fluorescence spectra also allows to determine the most probable stable state of the system. It was also shown that at integer and half-integer detuning-nonlinearity ratio multiphoton resonance leads to abrupt changes in fluorescence spectra. It was also revealed that the fluorescence spectra are symmetric in the limit of zero environment temperature. The predicted features of the spectra could be observed in experiments with ultra-high quality resonators in either microwave or optical domain.
We introduce the problem of GIT stability for syzygy points of canonical curves with a view toward a GIT construction of the canonical model of the moduli space of stable curves. As the first step in this direction, we prove semi-stability of the first syzygy point for a general canonical curve of odd genus.
We analyse the algebras generated by free component quantum fields together with the susy generators $Q,\bar Q$. Restricting to hermitian fields we first construct the scalar field algebra from which various scalar superfields can be obtained by exponentiation. Then we study the vector algebra and use it to construct the vector superfield. Surprisingly enough, the result is totally different from the vector multiplet in the literature. It contains two hermitian four-vector components instead of one and a spin-3/2 field similar to the gravitino in supergravity.
Learning spatial-temporal relation among multiple actors is crucial for group activity recognition. Different group activities often show the diversified interactions between actors in the video. Hence, it is often difficult to model complex group activities from a single view of spatial-temporal actor evolution. To tackle this problem, we propose a distinct Dual-path Actor Interaction (DualAI) framework, which flexibly arranges spatial and temporal transformers in two complementary orders, enhancing actor relations by integrating merits from different spatiotemporal paths. Moreover, we introduce a novel Multi-scale Actor Contrastive Loss (MAC-Loss) between two interactive paths of Dual-AI. Via self-supervised actor consistency in both frame and video levels, MAC-Loss can effectively distinguish individual actor representations to reduce action confusion among different actors. Consequently, our Dual-AI can boost group activity recognition by fusing such discriminative features of different actors. To evaluate the proposed approach, we conduct extensive experiments on the widely used benchmarks, including Volleyball, Collective Activity, and NBA datasets. The proposed Dual-AI achieves state-of-the-art performance on all these datasets. It is worth noting the proposed Dual-AI with 50% training data outperforms a number of recent approaches with 100% training data. This confirms the generalization power of Dual-AI for group activity recognition, even under the challenging scenarios of limited supervision.
Let $X$ be a subvariety of dimension n of the projective space over $\overline{\mathbb{Q}}$, and $H_{norm}(X;D)$ the normalized arithmetic Hilbert function of $X$ introduced by Philippon and Sombra. We show that this function admits the following asymptotic expansion $H_{norm}(X;D) = \frac{\widehat{h}(X)}{(n + 1)!}D^{n+1} + o(D^{n+1})$ where $\widehat{h}(X)$ is the normalized height of $X$. This gives a positive answer to a question raised by Philippon and Sombra.
The magnetic structure and the multiferroic relaxation dynamics of NaFeGe$_2$O$_6$ were studied by neutron scattering on single crystals partially utilizing polarization analysis. In addition to the previously reported transitions, the incommensurate spiral ordering of Fe$^{3+}$ moments in the $ac$ plane develops an additional component along the crystallographic $b$ direction below $T\approx 5\text{ K}$, which coincides with a lock-in of the incommensurate modulation. The quasistatic control of the spin-spiral handedness, respectively of the vector chirality, by external electric fields proves the invertibility of multiferroic domains down to the lowest temperature. Time-resolved measurements of the multiferroic domain inversion in NaFeGe$_2$O$_6$ reveal a simple temperature and electric-field dependence of the multiferroic relaxation that is well described by a combined Arrhenius-Merz relation, as it has been observed for TbMnO$_3$. The maximum speed of domain wall motion is comparable to the spin wave velocity.
Numerous activities in our daily life, including transactions, access to services and transportation, require us to verify who we are by showing our ID documents containing face images, e.g. passports and driver licenses. An automatic system for matching ID document photos to live face images in real time with high accuracy would speedup the verification process and remove the burden on human operators. In this paper, by employing the transfer learning technique, we propose a new method, DocFace, to train a domain-specific network for ID document photo matching without a large dataset. Compared with the baseline of applying existing methods for general face recognition to this problem, our method achieves considerable improvement. A cross validation on an ID-Selfie dataset shows that DocFace improves the TAR from 61.14% to 92.77% at FAR=0.1%. Experimental results also indicate that given more training data, a viable system for automatic ID document photo matching can be developed and deployed.
This is a preliminary version of the paper for the Lecture Notes Series.
Visual dialog is a task of answering a series of inter-dependent questions given an input image, and often requires to resolve visual references among the questions. This problem is different from visual question answering (VQA), which relies on spatial attention (a.k.a. visual grounding) estimated from an image and question pair. We propose a novel attention mechanism that exploits visual attentions in the past to resolve the current reference in the visual dialog scenario. The proposed model is equipped with an associative attention memory storing a sequence of previous (attention, key) pairs. From this memory, the model retrieves the previous attention, taking into account recency, which is most relevant for the current question, in order to resolve potentially ambiguous references. The model then merges the retrieved attention with a tentative one to obtain the final attention for the current question; specifically, we use dynamic parameter prediction to combine the two attentions conditioned on the question. Through extensive experiments on a new synthetic visual dialog dataset, we show that our model significantly outperforms the state-of-the-art (by ~16 % points) in situations, where visual reference resolution plays an important role. Moreover, the proposed model achieves superior performance (~ 2 % points improvement) in the Visual Dialog dataset, despite having significantly fewer parameters than the baselines.
We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection $X$ of $N$ one-dimensional manifolds and the corresponding set of boundary conditions (self-adjoint extensions) of the Dirac operator $D$. The set of boundary conditions encodes the topology and is parameterized by unitary matrices $g_N$. A particular geometry is described by a spectral triple $x(g_N)=(A_X,{\cal H}_X, D(g_N))$. We define a partition function for the sum over all $g_N$. In this model topology fluctuates but the dimension is kept fixed. We use the spectral principle to obtain an action for the set of boundary conditions. Together with invariance principles the procedure fixes the partition function for fluctuating topologies. In the simplest case the model has one free-parameter $\beta $ and it is equivalent to a one plaquette gauge theory. We argue that topology becomes localized at $\beta=\infty$ for any value of $N$. Moreover, the system undergoes a third-order phase transition at $\beta=1$ for large $N$. We give a topological interpretation of the phase transition by looking how it affects the topology.
In recent years post-Newtonian approximations for isolated slowly-moving systems in general relativity have been studied by means of matched asymptotic expansions. A paper by Poujade & Blanchet in 2002 made great progress by effectively reducing the use of such expansions to an algorithmic form. It gave systematic procedures for the development of both near-zone and far-zone asymptotic expansions, avoiding the divergent integrals which often bedevilled such methods, and showed that these two expansions could be made to match exactly, a result described there as somewhat remarkable.   This paper revisits that work and shows that there is unfortunately an error in it which invalidates the results of the matching process as given therein. The present paper identifies that error and shows how it may be corrected to give valid matching results. The correction is presented in a redevelopment somewhat different from that of their paper. This shows that far from being somewhat remarkable, it is in fact inevitable that the match is exact. It is indeed remarkable that they could carry both expansions to the point at which matching becomes possible, but if it can be done at all, then the match is necessarily exact.   A companion paper will apply this asymptotic matching to a model problem in which the correct near-zone expansion was obtained by approximation from an exact solution. It will be shown that there is a discrepancy between this expansion and results from the original development of Poujade & Blanchet but that the corrected development presented here reproduces the result of the model problem exactly.
Three red giants (HD 49566 (G5III), HD 169370 (K0III) and HD 169751 (K2III)) have been observed in the CoRoT seismo field and additional ground-based spectra have been acquired. We present preliminary results of a detailed study of these stars using the observational constraints from the spectra and CoRoT data, and models from the YREC stellar evolution code.
For a finite mean supercriticial Bellman-Harris process, there exist numbers $\chi_t$ (the Seneta constants) such that $\chi_t$ times the size of the population at time $t$ converges almost surely to a non-degenerate limit. We obtain a characterisation of the slowly varying part of the Seneta constants under the assumption that the life-time distribution of particles is strongly non-lattice.
We demonstrate the existence of long-lived prethermalized states in the Mott insulating Hubbard model driven by periodic electric fields. These states, which also exist in the resonantly driven case with a large density of photo-induced doublons and holons, are characterized by a nonzero current and an effective temperature of the doublons and holons which depends sensitively on the driving condition. Focusing on the specific case of resonantly driven models whose effective time-independent Hamiltonian in the high-frequency driving limit corresponds to noninteracting fermions, we show that the time evolution of the double occupation can be reproduced by the effective Hamiltonian, and that the prethermalization plateaus at finite driving frequency are controlled by the next-to-leading order correction in the high-frequency expansion of the effective Hamiltonian. We propose a numerical procedure to determine an effective Hubbard interaction that mimics the correlation effects induced by these higher order terms.
We calculate the one-electron spectral function of the attractive-U Hubbard model in two dimensions. We work in the intermediate coupling and low density regime and evaluate analytically the self-energy. The results are obtained in a framework based on the self-consistent T-matrix approximation. We also calculate the chemical potential of the bound pairs as a function of temperature. On the basis of this calculation we analyze the low-temperature resistivity and specific heat in the normal state of this system. We compare our results with recent beautiful tunneling experiments in the underdoped regime of HTSC-materials.
The results of photometric decomposition of surface brightness distributions in 85 early-type unbarred galaxies are presented. The SDSS r-images are analysed. Double-tiered exponential disks are found in all galaxies which are studied; the statistics of the disk parameters is derived.
By applying particle-number projection to the static-path approximation (SPA), the heat capacity and the breakdown of pairing correlations are investigated in the thermally excited, superfluid systems 172Yb, 94Mo, and 56Fe. For the heavy nucleus 172Yb, the heat capacities in both the SPA and the number-projected SPA (NPSPA) exhibit an S shape; the difference between the SPA and NPSPA heat-capacity curves is not very large and the particle-number projection thereby enhances the S shape already seen in the SPA. The temperature at which the S-shape of heat capacity curve occurs parallels the temperature of the breakdown of pairing correlations as indicated by the effective pairing gap. However, for the comparatively lighter nuclei 94Mo and 56Fe, the SPA does not produce an S-shaped heat capacity on its own; only after particle-number projection the S shape appears in the heat-capacity curve. For 94Mo, we compare the NPSPA result with thermal odd-even mass differences, which are regarded as a direct measure of the pairing gap.
We present a study of the temporal evolution of coronal loops in active regions and its implications for the dynamics in coronal loops. We analyzed images of the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO) at multiple temperatures to detect apparent motions in the coronal loops. Quasi-periodic brightness fluctuations propagate upwards from the loop footpoint in hot emission at 1MK, while sporadic downflows are seen in cool emission below 1MK. The upward motion in hot emission increases just after the cool downflows. The apparent propagating pattern suggests a hot upflow from the loop footpoints, and is considered to supply hot plasma into the coronal loop, but a wavelike phenomenon cannot be ruled out. Coronal condensation occasionally happens in the coronal loop, and the cool material flows down to the footpoint. Emission from cool plasma could have a significant contribution to hot AIA channels in the event of coronal condensation.
We consider a small metallic particle (quantum dot) where ferromagnetism arises as a consequence of Stoner instability. When the particle is connected to electrodes, exchange of electrons between the particle and the electrodes leads to a temperature- and bias-driven Brownian motion of the direction of the particle magnetization. Under certain conditions this Brownian motion is described by the stochastic Landau-Lifshitz-Gilbert equation. As an example of its application, we calculate the frequency-dependent magnetic susceptibility of the particle in a constant external magnetic field, which is relevant for ferromagnetic resonance measurements.
We present a proposal for protecting states against decoherence, based on the engineering of pointer states. We apply this procedure to the vibrational motion of a trapped ion, and show how to protect qubits, squeezed states, approximate phase eigenstates and superpositions of coherent states.
For an integer $k\geq 2$, let $(L_{n}^{(k)})_{n}$ be the $k-$generalized Lucas sequence which starts with $0,\ldots,0,2,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all the integers that appear in different generalized Lucas sequences; i.e., we study the Diophantine equation $L_n^{(k)}=L_m^{(\ell)}$ in nonnegative integers $n,k,m,\ell$ with $k, \ell\geq 2$. The proof of our main theorem uses lower bounds for linear forms in logarithms of algebraic numbers and a version of the Baker-Davenport reduction method. This paper is a continuation of the earlier work [4].
This paper addresses the controversy between Mayers, Lo and Chau on one side, and Yuen on the opposite side, on whether there exist or not unconditionally secure protocols. For such purpose, a complete classification of all possible bit commitment protocols is given, including all possible cheating attacks. For the simplest class of protocols (non-aborting and with complete and perfect verification), it is shown how naturally a game-theoretical situation arises. For these protocols, bounds for the cheating probabilities are derived, which turn out to be different from those given in the impossibility proof. The whole classification and analysis has been carried out using a "finite open system" approach. The discrepancy with the impossibility proof is explained on the basis of the implicit adoption of a "closed system approach"--equivalent to modeling the commitment as performed by two fixed machines interacting unitarily in a overall "closed system". However, it is shown that the closed system approach for the classification of commitment protocols unavoidably leads to infinite dimensions, which then invalidate the continuity argument at the basis of the impossibility proof.
In this work the authors consider an inverse source problem in the following stochastic fractional diffusion equation $$\partial_t^\alpha u(x,t)+\mathcal{A} u(x,t)=f(x)h(t)+g(x) \dot{\mathbb{W}}(t).$$ The interested inverse problem is to reconstruct $f(x)$ and $g(x)$ by the statistics of the final time data $u(x,T).$ Some direct problem results are proved at first, such as the existence, uniqueness, representation and regularity of the solution. Then the reconstruction scheme for $f$ and $g$ is given. To tackle the ill-posedness, the Tikhonov regularization is adopted. Finally we give a regularized reconstruction algorithm and some numerical results are displayed.
It is more important to estimate the rate of convergence to a stationary distribution rather than only to prove the existence one in many applied problems of reliability and queuing theory. This can be done via standard methods, but only under assumptions about an exponential distribution of service time, independent intervals between recovery times, etc. Results for such simplest cases are well-known. Rejection of these assumptions results to rather complex stochastic processes that cannot be studied using standard algorithms. A more sophisticated approach is needed for such processes. That requires generalizations and proofs of some classical results for a more general case. One of them is the generalized Lorden's inequality proved in this paper. We propose the generalized version of this inequality for the case of dependent and arbitrarily distributed intervals between recovery times. This generalization allows to find upper bounds for the rate of convergence for a wide class of complicated processes arising in the theory of reliability. The rate of convergence for a two-component process has been obtained via the generalized Lorden's inequality in this paper.
In recent years, two-dimensional (2D) layered semiconductors have received much attention for their potential in next-generation electronics and optoelectronics. Wide-bandgap 2D semiconductors are especially important in blue and ultraviolet wavelength region, while there are very few 2D materials in this region. Here, monolayer \b{eta}-type zirconium nitride chloride (\b{eta}-ZrNCl) is isolated for the first time, which is an air-stable layered material with a bandgap of ~3.0 eV in bulk. Systematical investigation of layer-dependent Raman scattering of ZrNCl from monolayer, bilayer, to bulk reveals a blue shift of its out-of-plane A1g peak at ~189 cm-1. Importantly, this A1g peak is absent in monolayer, suggesting that it is a fingerprint to quickly identify monolayer and for the thickness determination of 2D ZrNCl. The back-gate field-effect transistor based on few-layer ZrNCl shows a high on/off ratio of 108. These results suggest the potential of 2D \b{eta}-ZrNCl for electronic applications.
In this paper we introduce a particular class of Heffter arrays, called globally simple Heffter arrays, whose existence gives at once orthogonal cyclic cycle decompositions of the complete graph and of the cocktail party graph. In particular we provide explicit constructions of such decompositions for cycles of length $k\leq 10$. Furthermore, starting from our Heffter arrays we also obtain biembeddings of two $k$-cycle decompositions on orientable surfaces.