ShantanuT01/DACTYL-Pretraining huggingface dataset:
Non-contact facial video-based heart rate estimation using remote photoplethysmography (rPPG) has shown great potential in many applications (e.g., remote health care) and achieved creditable results in constrained scenarios. However, practical applications require results to be accurate even under complex environment with head movement and unstable illumination. Therefore, improving the performance of rPPG in complex environment has become a key challenge. In this paper, we propose a novel video embedding method that embeds each facial video sequence into a feature map referred to as Multi-scale Adaptive Spatial and Temporal Map with Overlap (MAST_Mop), which contains not only vital information but also surrounding information as reference, which acts as the mirror to figure out the homogeneous perturbations imposed on foreground and background simultaneously, such as illumination instability. Correspondingly, we propose a two-stream Transformer model to map the MAST_Mop into heart rate (HR), where one stream follows the pulse signal in the facial area while the other figures out the perturbation signal from the surrounding region such that the difference of the two channels leads to adaptive noise cancellation. Our approach significantly outperforms all current state-of-the-art methods on two public datasets MAHNOB-HCI and VIPL-HR. As far as we know, it is the first work with Transformer as backbone to capture the temporal dependencies in rPPGs and apply the two stream scheme to figure out the interference from backgrounds as mirror of the corresponding perturbation on foreground signals for noise tolerating.
We show that the module of integral points on a Drinfeld module satisfies a an analogue of Dirichlet's unit theorem, despite its failure to be finitely generated. As a consequence, we obtain a construction of a canonical finitely generated sub-module of the module of integral points. We use the results to give a precise formulation of a conjectural analogue of the class number formula.
The presence of a zero texture in the neutrino mass matrix can indicate the presence of an underlying symmetry which can generate neutrino mass and mixing. In this paper, for the first time we study the four-zero textures of the low energy neutrino mass matrix in the presence of an extra light-sterile neutrino i.e., the 3+1 neutrino scheme. In our analysis we find that out of the 210 possible four-zero textures only 15 textures are allowed. We divide the allowed four-zero textures into two classes -- class $A$ in which the value of mass matrix element $M_{ee}$ is zero and class $B$ in which $M_{ee}$ is non-zero. In this way we obtain ten possible four-zero textures in class $A$ and five possible four-zero textures in class $B$. In our analysis we find that, for normal hierarchy the allowed number of textures in class $A$ ($B$) is nine (three). For the case of inverted hierarchy we find that, two textures in class $A$ are disallowed and these textures are different from the disallowed textures for normal hierarchy in class $A$. However, we find that all the five textures in class $B$ are allowed for the inverted hierarchy. Based on analytic expressions for the elements $M_{\alpha\beta}$, we discuss the reasons for certain textures being disallowed. We also discuss the correlations between the different parameters of the allowed textures. Finally, we present the implications of our study on experimental searches for neutrinoless double beta decay.
We describe a new geometrical solution to the Wheeler-DeWitt equation in two dimensional quantum gravity. The solution is the amplitude of a surface whose boundary consists of two tangent loops. We further discuss a new method for estimating singular geometries amplitudes, which uses explicit recursive counting of discrete surfaces.
We present results from timing and spectral analysis of the HMXB X-ray pulsar IGR J19294+1816 observed using \asr during its recent Type-I outburst in October, 2019. AstroSat observations sampled the outburst at the decline phase right after the outburst peak. We carried out timing analysis on the light curves obtained using the Large Area X-ray Proportional Counter (LAXPC) instrument on board AstroSat and measured a spin period of 12.485065$\pm$0.000015 s. The peak in the power density spectrum (PDS) corresponding to the spin period of 12.48 s also shows a broadened base. We also detected a Quasi Periodic Oscillation (QPO) feature at 0.032$\pm$0.002 Hz with an RMS fractional amplitude of $\sim$18% in the PDS. We further carried out a joint spectral analysis using both the Soft X-ray Telescope (SXT) and the LAXPC instruments and detected a Cyclotron Resonant Scattering Feature (CRSF) at 42.7$\pm$0.9 keV and an Fe emission line at 6.4$\pm$0.1 keV. IGR J19294+1816, being an intermediate spin pulsar, has exhibited a plethora of spectral and timing features during its most recent 2019 outburst, adding it to the list of transients that exhibit both a QPO as well as a CRSF.
We present maps of the sign of the Faraday Rotation measure [sign(RM)] obtained from multi-frequency radio observations on the Very Long Baseline Array (VLBA). Many of the Active Galactic Nuclei (AGN) considered have B-field structures with a central "spine" of B-field orthogonal to the jet and/or a longitudinal B-field near one or both edges of the jet. This structure can plausibly be interpreted as being caused by a helical/toroidal jet magnetic field. Faraday Rotation is a rotation of the plane of polarization that occurs when the polarized radiation passes through a magnetized plasma. The sign of the RM is determined by the direction of the line-of-sight B-Field in the region causing the Faraday Rotation, and an ordered toroidal or helical magnetic field associated with an AGN jet will thus produce a distinctive bilateral distribution of positive and negative RMs across the jet. We present and discuss sign(RM) maps and their possible interpretation regarding the magnetic field geometries for several sources.
We observe a method for finding weak Landau-Ginzburg models for Fano varieties and find them for smooth Fano threefolds of genera 9, 10, and 12.
We study the vanishing of $L(f,\chi,j)$ as $f$ runs through all classical forms in a $p$-adic Hida family (including forms with arbitrarily high nebentype at $p$), $\chi$ runs through all characters of $p$-power conductor, and $j$ is a critical value. We show that if infinitely many of these $L$-values vanish (apart from the ones forced to vanish by the sign of their functional equation) then this infinitude of vanishing must be exceptionally regular, so regular in fact that one can typically rule out this possibility in any given example. Indeed, we systematically verified that such regular vanishing does not occur in multiple Hida families twisted by a wide range of quadratic characters by computing the corresponding two-variable $p$-adic $L$-functions via overconvergent modular symbols.
We apply a computationally efficient technique to validate the global structure of the pulsar magnetosphere. In this first of a series of studies, a 3D, computationally intensive, implicit Crank-Nicolson finite-difference scheme is developed. The region of magnetic influence is evolved under the approximation of force-free electrodynamics. The main objective of this paper is to present our code and use it to demonstrate and verify the now widely - accepted global features of a pulsar magnetosphere. Our results qualitatively agree with previously developed time-dependent models for an oblique rotator. In line with earlier studies, we also demonstrate that our simulations can run for many stellar rotations. Once we extend our code, we believe that our implicit approach can be extremely useful to investigate magnetospheres filled with resistive plasma, develop better resolution current sheets and investigate small scale microphysics of pair creation using particle-in-cell techniques.
Baez-Duarte (1971) and Gilat (1972) gave examples of martingales that converge in probability (and hence in distribution) but not almost surely. Here such a martingale is constructed with uniformly bounded increments, and a construction is provided of two martingales with the same marginals, one of which converges almost surely, while the other does not converge in probability.
Passarino-Veltman (PV) reduction method has been proved to be very useful for the computation of general one-loop integrals. However, not much progress has been made when applying to higher loops. Recently, we have improved the PV-reduction method by introducing an auxiliary vector. In this paper, we apply our new method to the simplest two-loop integrals, i.e., the sunset topology. We show how to use differential operators to establish algebraic recursion relations for reduction coefficients. Our algorithm can be easily applied to the reduction of integrals with arbitrary high-rank tensor structures. We demonstrate the efficiency of our algorithm by computing the reduction with the total tensor rank up to four.
Rubinstein and Sarnak have shown, conditional on the Riemann hypothesis (RH) and the linear independence hypothesis (LI) on the non-real zeros of $\zeta(s)$, that the set of real numbers $x\ge2$ for which $\pi(x)>$ li$(x)$ has a logarithmic density, which they computed to be about $2.6\times10^{-7}$. A natural problem is to examine the actual primes in this race. We prove, assuming RH and LI, that the logarithmic density of the set of primes $p$ for which $\pi(p)>$ li$(p)$ relative to the prime numbers exists and is the same as the Rubinstein-Sarnak density. We also extend such results to a broad class of prime number races, including the "Mertens race" between $\prod_{p< x}(1-1/p)^{-1}$ and $e^{\gamma}\log x$ and the "Zhang race" between $\sum_{p\ge x}1/(p\log p)$ and $1/\log x$. These latter results resolve a question of the first and third author from a previous paper, leading to further progress on a 1988 conjecture of Erd\H{o}s on primitive sets.
We present new results from optical photometric and spectroscopic observations of the eruptive pre-main sequence star V2493 Cyg (HBC 722). The object has continued to undergo significant brightness variations over the past few months and is an ideal target for follow-up observations. We carried out CCD BVRI photometric observations in the field of V2493 Cyg ("Gulf of Mexico") from August 1994 to April 2012, i.e. at the pre-outburst states and during the phases of the outburst. We acquired high, medium, and low resolution spectroscopy of V2493 Cyg during the outburst. To study the pre-outburst variability of the target and construct its historical light curve, we searched for archival observations in photographic plate collections. Both CCD and photographic observations were analyzed using 15 comparison stars in the field of V2493 Cyg. The pre-outburst photographic and CCD photometric observations of V2493 Cyg show low-amplitude light variations typical of T Tauri stars. The recent photometric data show a slow light decrease from October 2010 to June 2011 followed by an increase in brightness that continued until early 2012. The spectral observations of V2493 Cyg are typical of FU Orionis stars absorption spectra with strong P Cyg profiles of H alpha and Na I D lines. On the basis of photometric monitoring performed over the past two years, the spectral properties at the maximal light, as well as the shape of long-term light curves, we confirm that the observed outburst of V2493 Cyg is of FU Orionis type.
We discus the role of QCD (Quantum Chromodynamics) to low energy phenomena involving the color-spin symmetry of the quark model. We then combine it with orbital and isospin symmetry to obtain wave functions with the proper permutation symmetry, focusing on multi quark systems.
Coalescing supermassive black hole binaries (BHBs) are expected to be the loudest sources of gravitational waves (GWs) in the Universe. Detection rates for ground or space-based detectors based on cosmological simulations and semi-analytic models are highly uncertain. A major difficulty stems from the necessity to model the BHB from the scale of the merger to that of inspiral. Of particular relevance to the GW merger timescale is the binary eccentricity. Here we present a self-consistent numerical study of the eccentricity of BHBs formed in massive gas-free mergers from the early stages of the merger to the hardening phase, followed by a semi-analytical model down to coalescence. We find that the early eccentricity of the unbound black hole pair is largely determined by the initial orbit. It systematically decreases during the dynamical friction phase. The eccentricity at binary formation is affected by stochasticity and noise owing to encounters with stars, but preserves a strong correlation with the initial orbital eccentricity. Binding of the black holes is a phase characterised by strong perturbations, and we present a quantitative definition of the time of binary formation. During hardening the eccentricity increases in minor mergers, unless the binary is approximately circular, but remains largely unchanged in major mergers, in agreement with predictions from semi-analytical models based on isotropic scattering experiments. Coalescence times due to hardening and GW emission in gas-poor non-rotating ellipticals are <~0.5 Gyr for the large initial eccentricities (0.5 < e < 0.9) typical of galaxy mergers in cosmological simulations.
Gordon introduced a class of matroids $M(n)$, for prime $n\ge 2$, such that $M(n)$ is algebraically representable, but only in characteristic $n$. Lindstr\"om proved that $M(n)$ for general $n\ge 2$ is not algebraically representable if $n>2$ is an even number, and he conjectured that if $n$ is a composite number it is not algebraically representable. We introduce a new kind of matroid called {\it harmonic matroids}, of which full algebraic matroids are an example. We prove the conjecture in this more general case.
We present new ${ }^{12}$CO(J=1-0) observations of Henize 2-10, a blue compact dwarf galaxy about 8.7 Mpc away, taken with the Atacama Large Millimeter Array. These are the highest spatial and spectral resolution observations, to date, of the molecular gas in this starburst galaxy. We measure a molecular mass of $1.2\times10^8 M_\odot$ in Henize 2-10, and most of the molecular gas is contained within a region having a size of about 310 pc. We use the CPROPS algorithm to identify 119 resolved giant molecular clouds distributed throughout the galaxy, and the molecular gas contained within these clouds make up between 45 to 70% of the total molecular mass. The molecular clouds in Henize 2-10 have similar median sizes (~26 pc), luminous masses (~$ 4\times 10^5$ $M_\odot$), and surface densities (~$180$ $M_\odot$ pc$^{-2}$) to Milky Way clouds. We provide evidence that Henize 2-10 clouds tend to be in virial equilibrium, with the virial and luminous masses scaling according to $M_{vir}\propto M_{lum}^{1.2\pm0.1}$, similar to clouds in the Milky Way. However, we measure a scaling relationship between luminous mass and size, $M_{vir}\propto R^{3.0\pm0.3}$, that is steeper than what is observed in Milky Way clouds. Assuming Henize 2-10 molecular clouds are virialized, we infer values of the CO-to-H$_2$ conversion factor ranging from 0.5 to 13 times the standard value in the Solar Neighborhood. Given star formation efficiencies as low as 5%, the most massive molecular clouds in Henize 2-10 currently have enough mass to form the next generation of super-star clusters in the galaxy.
A subset $S$ of the vertices $V$ of a connected graph $G$ resolves $G$ if no two vertices of $V$ share the same list of distances (shortest-path metric) with respect to the vertices of $S$ listed in a given order. The choice of such an $S$ in $V$ amounts to selecting a binary valued function $g$, said to be a resolving function, on $V$. The notion of a fractional resolving function is obtained by relaxing the codomain of $g$ to be the unit interval. Let $|g|=\sum_{v\in V}g(v)$. Given a finite collection $\mathcal{G}$ of connected graphs on a common vertex set $V$, the simultaneous metric dimension of $\mathcal{G}$ is the minimum cardinality of $|S|$ over all $S$ which resolve each member graph of $\mathcal{G}$. In this paper, we initiate the study of simultaneous fractional dimension ${\rm Sd}_f(\mathcal{G})$ of a graph family $\mathcal{G}$, defined to be the minimum $|g|$ over all functions $g$ each resolving all members of $\mathcal{G}$. We characterize the lower bound and examine the upper bound satisfied by ${\rm Sd}_f(\mathcal{G})$. We examine ${\rm Sd}_f(\mathcal{G})$ for families of vertex transitive graphs and for pairs $\{G,\overline{G}\}$ of complementary graphs, determining ${\rm Sd}_f(G,\overline{G})$ when $G$ is a tree or a unicyclic graph.
A generic approach for compiling any classical block compression algorithm into a quantum block compression algorithm is presented. Using this technique, compression asymptoticaly approaching the von Neumann entropy of a qubit source can be achieved. The automatically compiled algorithms are competitive (in time and space complexity) with hand constructed quantum block compression algorithms.
We use magnetoconductance measurements in dual-gated InSb nanowire devices together with a theoretical analysis of weak antilocalization to accurately extract spin-orbit strength. In particular, we show that magnetoconductance in our three-dimensional wires is very different compared to wires in two-dimensional electron gases. We obtain a large Rashba spin-orbit strength of $0.5 -1\,\text{eV\r{A}}$ corresponding to a spin-orbit energy of $0.25-1\,\text{meV}$. These values underline the potential of InSb nanowires in the study of Majorana fermions in hybrid semiconductor-superconductor devices.
We discuss a neutrino mass model based on the S4 discrete symmetry where the symmetry breaking is triggered by the boundary conditions of the bulk right-handed neutrino in the fifth spacial dimension. While the symmetry restricts bare mass parameters to flavor-diagonal forms, the viable mixing angles emerge from the wave functions of the Kaluza-Klein modes which carry symmetry breaking effect. The magnitudes of the lepton mixing angles, especially the reactor angle is related to the neutrino mass patterns and the model will be tested in future neutrino experiments, e.g., an early (late) discovery of the reactor angle favors the normal (inverted) hierarchy. The size of extra dimension has a connection to the possible mass spectrum; a small (large) volume corresponds to the normal (inverted) mass hierarchy.
In this paper we are concerned with contact process with random recovery rates on open clusters of bond percolation on $\mathbb{Z}^d$. Let $\xi$ be a positive random variable, then we assigned i. i. d. copies of $\xi$ on the vertices as the random recovery rates. Assuming that each edge is open with probability $p$ and $\log d$ vertices are occupied at $t=0$, we prove that the following phase transition occurs. When the infection rate $\lambda<\lambda_c=1/({p{\rm E}\frac{1}{\xi}})$, then the process dies out at time $O(\log d)$ with high probability as $d\rightarrow+\infty$, while when $\lambda>\lambda_c$, the process survives with high probability.
These are notes of my lectures given at the school on intersection theory and moduli at the ICTP, Trieste. We construct moduli spaces of K3 surfaces and higherdimensional hyperkaehler manifolds, including moduli spaces of (2,2)-conformal field theories associated to hyperkaehler manifolds, and describe their period domains. Recent results on these manifolds are discussed from the moduli space point of view. The second goal is to present a detailed account of mirror symmetry for K3 surfaces. Arguments due to Aspinwall and Morrison allow one to explain various versions of mirror symmetry (e.g. for lattice polarized or elliptic K3 surfaces) by the same general principle.
Star formation in massive galaxies is quenched at some point during hierarchical mass assembly. To understand where and when the quenching processes takes place, we study the evolution of the total star formation rate per unit total halo mass (\Sigma(SFR/M)) in three different mass scales: low mass halos (field galaxies), groups, and clusters, up to a redshift ~1.6. We use deep far-infrared PACS data at 100 and 160 um to accurately estimate the total star formation rate of the Luminous Infrared Galaxy population of 9 clusters with mass ~10^{15} M_{\odot}, and 9 groups/poor clusters with mass ~ 5 x 10^{13} M_{\odot}. Estimates of the field \Sigma(SFR/M) are derived from the literature, by dividing the star formation rate density by the mean comoving matter density of the universe. The field \Sigma(SFR/M) increases with redshift up to z~1 and it is constant thereafter. The evolution of the \Sigma(SFR/M)-z relation in galaxy systems is much faster than in the field. Up to redshift z~0.2, the field has a higher \Sigma(SFR/M) than galaxy groups and galaxy clusters. At higher redshifts, galaxy groups and the field have similar \Sigma(SFR/M), while massive clusters have significantly lower \Sigma(SFR/M) than both groups and the field. There is a hint of a reversal of the SFR activity vs. environment at z~1.6, where the group \Sigma(SFR/M) lies above the field \Sigma(SFR/M)-z relation. We discuss possible interpretations of our results in terms of the processes of downsizing, and star-formation quenching.
We give a criterion for a divisorial sheaf on a log terminal variety to be Cohen-Macaulay. The log canonical case and applications to moduli are also considered.
Navigation inside a closed area with no GPS-signal accessibility is a highly challenging task. In order to tackle this problem, recently the imaging-based methods have grabbed the attention of many researchers. These methods either extract the features (e.g. using SIFT, or SOSNet) and map the descriptive ones to the camera position and rotation information, or deploy an end-to-end system that directly estimates this information out of RGB images, similar to PoseNet. While the former methods suffer from heavy computational burden during the test process, the latter suffers from lack of accuracy and robustness against environmental changes and object movements. However, end-to-end systems are quite fast during the test and inference and are pretty qualified for real-world applications, even though their training phase could be longer than the former ones. In this paper, a novel multi-modal end-to-end system for large-scale indoor positioning has been proposed, namely APS (Alpha Positioning System), which integrates a Pix2Pix GAN network to reconstruct the point cloud pair of the input query image, with a deep CNN network in order to robustly estimate the position and rotation information of the camera. For this integration, the existing datasets have the shortcoming of paired RGB/point cloud images for indoor environments. Therefore, we created a new dataset to handle this situation. By implementing the proposed APS system, we could achieve a highly accurate camera positioning with a precision level of less than a centimeter.
Let F be a global function field of characteristic p>0, K/F an l-adic Lie extension unramified outside a finite set of places S and A/F an abelian variety without complex multiplication. We study Sel_A(K)_l^\vee (the Pontrjagin dual of the Selmer group) and (under some mild hypotheses) prove that it is a finitely generated Z_l[[\Gal(K/F)]]-module via generalizations of Mazur's Control Theorem. If Gal(K/F) has no elements of order l and contains a closed normal subgroup H such that Gal(K/F)/H\simeq Z_l, we are able to give sufficient conditions for Sel_A(K)_l^\vee to be finitely generated as Z_l[[H]]-module and, consequently, a torsion Z_l[[\Gal(K/F)]]-module. We deal with both cases l\neq p and l=p.
The compatibility between the general relativity and the mathematical property that the space-times are embedded manifolds are further examined. In particular we study the uniqueness of the signature of the embedding space for a given space-time. The interpretation of the twisting vector as a gauge potential is also implemented.