ShantanuT01/DACTYL-Pretraining huggingface dataset:
A multiple instance learning (MIL) method, extended Function of Multiple Instances ($e$FUMI), is applied to ballistocardiogram (BCG) signals produced by a hydraulic bed sensor. The goal of this approach is to learn a personalized heartbeat "concept" for an individual. This heartbeat concept is a prototype (or "signature") that characterizes the heartbeat pattern for an individual in ballistocardiogram data. The $e$FUMI method models the problem of learning a heartbeat concept from a BCG signal as a MIL problem. This approach elegantly addresses the uncertainty inherent in a BCG signal e. g., misalignment between training data and ground truth, mis-collection of heartbeat by some transducers, etc. Given a BCG training signal coupled with a ground truth signal (e.g., a pulse finger sensor), training "bags" labeled with only binary labels denoting if a training bag contains a heartbeat signal or not can be generated. Then, using these bags, $e$FUMI learns a personalized concept of heartbeat for a subject as well as several non-heartbeat background concepts. After learning the heartbeat concept, heartbeat detection and heart rate estimation can be applied to test data. Experimental results show that the estimated heartbeat concept found by $e$FUMI is more representative and a more discriminative prototype of the heartbeat signals than those found by comparison MIL methods in the literature.
Given a subset $S=\{s_0, s_1\}$ of the complex plane with two points and an infinite subset ${\mathscr S}$ of $S\times {\mathbb N}$, where ${\mathbb N}=\{0,1,2,\dots\}$ is the set of nonnegative integers, we ask for a lower bound for the order of growth of a transcendental entire function $f$ such that $f^{(n)}(s)\in{\mathbb Z}$ for all $(s,n)\in{\mathscr S}$.   We first take ${\mathscr S}=\{s_0,s_1\}\times 2{\mathbb N}$, where $2{\mathbb N}=\{0,2,4,\dots\}$ is the set of nonnegative even integers. We prove that an entire function $f$ of sufficiently small exponential type such that $f^{(2n)}(s_0)\in{\mathbb Z}$ and $f^{(2n)}( s_1)\in{\mathbb Z}$ for all sufficiently large $n$ must be a polynomial. The estimate we reach is optimal, as we show by constructing a noncountable set of examples. The main tool, both for the proof of the estimate and for the construction of examples, is Lidstone polynomials.   Our second example is $(\{s_0\}\times (2{\mathbb N}+1))\cup( \{ s_1\}\times 2{\mathbb N})$ (odd derivatives at $s_0$ and even derivatives at $ s_1$). We use analogs of Lidstone polynomials which have been introduced by J.M.~Whittaker and studied by I.J.~Schoenberg.   Finally, using results of W.~Gontcharoff, A. J.~Macintyre and J.M.~Whittaker, we prove lower bounds for the exponential type of a transcendental entire function $f$ such that, for each sufficiently large $n$, one at least of the two numbers $f^{(n)}(s_0)$, $f^{(n)}(s_1)$ is in ${\mathbb Z}$.
We introduce the notion of confinement of decompositions for forms or vector of forms. The confinement, when it holds, lowers the number of parameters that one needs to consider, in order to find all the possible decompositions of a given set of data. With the technique of confinement, we obtain here two results. First, we give a new, shorter proof of a result by London (\cite{London90}) that $3$ general plane cubics have $2$ simultaneous Waring decompositions of rank $6$. Then we compute, with the software Bertini, that $4$ general plane quartics have $18$ different decompositions of rank $10$ (a result which was not known before).
This appendix provides a short proof for sample path continuity of the Brownian motion induced by an arbitrary centered Gaussian measure on a separable Banach space, and also some perturbation results for the spectrum of compact self-adjoint operators on a Hilbert space.
We consider an \eps-approximation by n-term partial sums of the Karhunen-Lo\`eve expansion to d-parametric random fields of tensor product-type in the average case setting. We investigate the behavior, as d tends to infinity, of the information complexity n(\eps,d) of approximation with error not exceeding a given level \eps. It was recently shown by M.A. Lifshits and E.V. Tulyakova that for this problem one observes the curse of dimensionality (intractability) phenomenon. The aim of this paper is to give the exact asymptotic expression for the information complexity n(\eps,d).
By making use of Duan-Ge's decomposition theory of gauge potential and the Duan's topological current theory proposed by Prof. Duan Yi-Shi, we study a two component superfluid Bose condensed system, which is supposed being realized in the interior of neutron stars in the form of a coexistent neutron superfluid and protonic superconductor. We propose that this system possesses vortex lines. The topological charge of the vortex lines are characterized by the Hopf indices and the Brower degrees of $\phi$-mapping.
If a system is driven at finite-rate through a phase transition by varying an intensive parameter, the order parameter shatters into finite domains. The Kibble-Zurek mechanism predicts the typical size of these domains, which are governed only by the rate of driving and the spatial and dynamical critical exponents. We show that also the irreversible entropy production fulfills a universal behavior, which however is determined by an additional critical exponent corresponding to the intensive control parameter. Our universal prediction is numerically tested in two systems exhibiting noise-induced phase transitions.
The notion of an atom-light quantum interface has been developed in the past decade, to a large extent due to demands within the new field of quantum information processing and communication. A promising type of such interface using large atomic ensembles has emerged in the past several years. In this article we review this area of research with a special emphasis on deterministic high fidelity quantum information protocols. Two recent experiments, entanglement of distant atomic objects and quantum memory for light are described in detail.
In this paper we study the Sobolev Trace Theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. Then we give local conditions on the exponents and on the domain (in the spirit of Adimurthy and Yadava) in order to satisfy such conditions, and therefore to ensure the existence of extremals.
We give an asymptotic expression for the number of nonsingular integer n-by-n-matrices with primitive row vectors, determinant k, and Euclidean matrix norm less than T, for large T.   We also investigate the density of matrices with primitive rows in the space of matrices with determinant k, and determine its asymptotics for large k.
The thermodynamic and magnetocaloric properties of a generalized spin-$(1/2,s)$ Fisher's super-exchange antiferromagnet are exactly investigated by using the decoration-iteration mapping transformation. Besides the critical temperature, sublattice magnetization, total magnetization, entropy and specific heat, the isothermal entropy change and adiabatic temperature change are rigorously calculated in order to examine cooling efficiency of the model in a vicinity of the first- and second-order phase transitions. It is shown that an enhanced inverse magnetocaloric effect occurs around the temperature interval $T_c(B\neq 0) \lesssim T < T_c(B = 0)$ for any magnetic-field change $\Delta B: 0 \to B$. The most pronounced inverse magnetocaloric effect can be found nearby the critical field, which corresponds to the zero-temperature phase transition from the long-range ordered ground state to the paramagnetic one. The observed phenomenon increases with the increasing value of decorating spins. Furthermore, sufficiently high values of decorating spins have also linked to a possibility of observing reentrant phase transitions at finite temperatures.
We have developed a theory of a Josephson junction formed by two tunnel-coupled Bose-Einstein condensates in a double-well potential in the regime of strong atom-atom interaction for an arbitrary total number $N$ of bosons in the condensates. The tunnel resonances in the junction are shown to be periodically spaced by the interaction energy, forming a single-atom staircase sensitive to the parity of $N$ even for large $N$. One of the manifestations of the staircase structure is the periodic modulation with the bias energy of the visibility of the interference pattern in lattices of junctions.
We demonstrate that for a cosmic variance limited experiment, CMB E polarization alone places stronger constraints on cosmological parameters than CMB temperature. For example, we show that EE can constrain parameters better than TT by up to a factor 2.8 when a multipole range of l=30-2500 is considered. We expose the physical effects at play behind this remarkable result and study how it depends on the multipole range included in the analysis. In most relevant cases, TE or EE surpass the TT based cosmological constraints. This result is important as the small scale astrophysical foregrounds are expected to have a much reduced impact on polarization, thus opening the possibility of building cleaner and more stringent constraints of the LCDM model. This is relevant specially for proposed future CMB satellite missions, such as CORE or PRISM, that are designed to be cosmic variance limited in polarization till very large multipoles. We perform the same analysis for a Planck-like experiment, and conclude that even in this case TE alone should determine the constraint on $\Omega_ch^2$ better than TT by 15%, while determining $\Omega_bh^2$, $n_s$ and $\theta$ with comparable accuracy. Finally, we explore a few classical extensions of the LCDM model and show again that CMB polarization alone provides more stringent constraints than CMB temperature in case of a cosmic variance limited experiment.
We present results from the "Weather on Other Worlds" Spitzer Exploration Science program to investigate photometric variability in L and T dwarfs, usually attributed to patchy clouds. We surveyed 44 L3-T8 dwarfs, spanning a range of $J-K_s$ colors and surface gravities. We find that 14/23 (61%; 95% confidence interval: 41%-78%) of our single L3-L9.5 dwarfs are variable with peak-to-peak amplitudes between 0.2% and 1.5%, and 5/16 (31%; 95% confidence interval: 14%-56%) of our single T0-T8 dwarfs are variable with amplitudes between 0.8% and 4.6%. After correcting for sensitivity, we find that 80% (95% confidence interval: 53%-100%) of L dwarfs vary by >0.2%, and 36% (95% confidence interval: 19%-52%) of T dwarfs vary by >0.4%. Given viewing geometry considerations, we conclude that photospheric heterogeneities causing >0.2% 3-5-micron flux variations are present on virtually all L dwarfs, and probably on most T dwarfs. A third of L dwarf variables show irregular light curves, indicating that L dwarfs may have multiple spots that evolve over a single rotation. Also, approximately a third of the periodicities are on time scales >10 h, suggesting that slowly-rotating brown dwarfs may be common. We observe an increase in the maximum amplitudes over the entire spectral type range, revealing a potential for greater temperature contrasts in T dwarfs than in L dwarfs. We find a tentative association (92% confidence) between low surface gravity and high-amplitude variability among L3-L5.5 dwarfs. Although we can not confirm whether lower gravity is also correlated with a higher incidence of variables, the result is promising for the characterization of directly imaged young extrasolar planets through variability.
Comparing K+ spectra at low transverse momenta for different symmetric collision systems at beam energies around 1 AGeV allows for a direct determination of both the strength of the K+ nucleus potential as well as of the K+N rescattering cross section in a hadronic environment. Other little known or unknown quantities which enter the K+ dynamics, like the production cross sections of K+ mesons or the hadronic equation of state, do not spoil this signal as they cancel by using ratios of spectra. This procedure is based on transport model calculations using the Isospin Quantum Molecular Dynamics (IQMD) model which describes the available data quantitatively.
We present population-orbit superposition models for external galaxies based on Schwarzschild's orbit-superposition method, by tagging the orbits with age and metallicity. The models fit the density distributions, as well as kinematic, age and metallicity maps from Integral Field Unit (IFU) spectroscopy observations. We validate the method and demonstrate its power by applying it to mock data, similar to those obtained by the Multi-Unit Spectroscopic Explorer (MUSE) IFU on the Very Large Telescope (VLT). These mock data are created from Auriga galaxy simulations, viewed at three different inclination angles ($\vartheta=40^o, 60^o, 80^o$). Constrained by MUSE-like mock data, our model can recover the galaxy's stellar orbit distribution projected in orbital circularity $\lambda_z$ vs. radius $r$, the intrinsic stellar population distribution in age $t$ vs. metallicity $Z$, and the correlation between orbits' circularity $\lambda_z$ and stellar age $t$. A physically motivated age-metallicity relation improves recovering the intrinsic stellar population distributions. We decompose galaxies into cold, warm and hot + counter-rotating components based on their orbit circularity distribution, and find that the surface density, mean velocity, velocity dispersion, age and metallicity maps of each component from our models well reproduce those from simulation, especially for projections close to edge-on. These galaxies exhibit strong global age vs. $\sigma_z$ relation, which is well recovered by our model. The method has the power to reveal the detailed build-up of stellar structures in galaxies, and offers a complement to local resolved, and high-redshift studies of galaxy evolution.
An $L(h_1, h_2, \ldots, h_l)$-labelling of a graph $G$ is a mapping $\phi: V(G) \rightarrow \{0, 1, 2, \ldots\}$ such that for $1\le i\le l$ and each pair of vertices $u, v$ of $G$ at distance $i$, we have $|\phi(u) - \phi(v)| \geq h_i$. The span of $\phi$ is the difference between the largest and smallest labels assigned to the vertices of $G$ by $\phi$, and $\lambda_{h_1, h_2, \ldots, h_l}(G)$ is defined as the minimum span over all $L(h_1, h_2, \ldots, h_l)$-labellings of $G$.   In this paper we study $\lambda_{h, 1, \ldots, 1}$ for Cartesian products of graphs, where $(h, 1, \ldots, 1)$ is an $l$-tuple with $l \ge 3$. We prove that, under certain natural conditions, the value of this and three related invariants on a graph $H$ which is the Cartesian product of $l$ graphs attain a common lower bound. In particular, the chromatic number of the $l$-th power of $H$ equals this lower bound plus one. We further obtain a sandwhich theorem which extends the result to a family of subgraphs of $H$ which contain a certain subgraph of $H$. All these results apply in particular to the class of Hamming graphs: if $q_1\ge \cdots \ge q_d\ge 2$ and $3\le l\le d$ then the Hamming graph $H=H_{q_1,q_2,\ldots ,q_d}$ satisfies $\lambda_{q_l,1,\ldots,1}(H) = q_1q_2\ldots q_l-1$ whenever $q_1q_2\ldots q_{l-1}>3(q_{l-1}+1)q_l\ldots q_d$. In particular, this settles a case of the open problem on the chromatic number of powers of the hypercubes.
The presence of subphases in spin-density wave (SDW) phase of (TMTSF)2PF6 below T* ~ 4K has been suggested by several experiments but the nature of the new phase is still controversial. We have investigated the temperature dependence of the angular dependence of the magnetoresistance in the SDW phase which shows different features for temperatures above and below T*. For T > 4K the magnetoresistance can be understood in terms of the Landau quantization of the quasiparticle spectrum in a magnetic field, where the imperfect nesting plays the crucial role. We propose that below T* ~ 4K the new unconventional SDW (USDW) appears modifying dramatically the quasiparticle spectrum. Unlike conventional SDW the order parameter of USDW depends on the quasiparticle momentum. The present model describes many features of the angular dependence of magnetoresistance reasonably well. Therefore, we may conclude that the subphase in (TMTSF)2PF6 below T* ~ 4K is described as SDW plus USDW.
We constrain Galactic foreground contamination of the Python V cosmic microwave background anisotropy data by cross correlating it with foreground contaminant emission templates. To model foreground emission we use 100 and 12 $\mu$m dust emission templates and two point source templates based on the PMN survey. The analysis takes account of inter-modulation correlations in 8 modulations of the data that are sensitive to a large range of angular scales and also densely sample a large area of sky. As a consequence the analysis here is highly constraining. We find little evidence for foreground contamination in an analysis of the whole data set. However, there is indication that foregrounds are present in the data from the larger-angular-scale modulations of those Python V fields that overlap the region scanned earlier by the UCSB South Pole 1994 experiment. This is an independent consistency cross-check of findings from the South Pole 1994 data.
We continue our study of the thermodynamic geometry of the spin one model from paper I by probing the state space geometry of the Blume Emery Griffiths (BEG) model, and its limiting case of the Blume Capel model, in their mean field approximation. By accounting for the stochastic variables involved we construct from the thermodynamic state space two complimentary two-dimensional geometries with curvatures $R_m$ and $R_q$ which are shown to encode correlations in the model's two order parameters, namely, the magnetization $m$ and the quadrupole moment $q$. The geometry is investigated in the zero as well as the non zero magnetic field region. We find that the relevant scalar curvatures diverge to negative infinity along the critical lines with the correct scaling and amplitude. We then probe the geometry of phase coexistence and find that the relevant curvatures predict the coexistence curve remarkably well via their respective $R$-crossing diagrams. We also briefly comment on the effectiveness of the geometric correlation length compared to the commonly used Ornstein-Zernicke type correlation length vis-a-vis their scaling properties.
Previous studies have shown that the orientation relationships which develop in hetero-epitaxy are strongly influenced by the alignment of steps in the deposit with the pre-existing steps of the substrate. In this paper we use a combination of experiments with computer simulations to identify the important influence of substrate step structure on the eventual orientation relationships that develop in the deposit. We have made use of Ag deposited on Ni as it has been used extensively as a model system for the study of hetero-epitaxy. This system displays a large lattice mismatch of 16%. It is shown that on any surface vicinal to Ni(111), which has two possible kinds of <110> steps (A-steps with {100} ledges and B-steps with {111} ledges), a Ag deposit adopts a single orientation relationship because only A-steps remain stable in the presence of Ag.
We present a phase-coherent timing solution for RX J0420.0-5022, the coolest (kT=45 eV) and fastest-spinning (P=3.45 s) of the seven so-called isolated neutron stars (INSs). Using 14 observations with the XMM-Newton spacecraft in 2010-2011, we were able to measure a spin-down rate nudot=(-2.3+/-0.2)e-15 Hz/s (Pdot=(2.8+/-0.3)e-14 s/s), from which we infer a dipolar magnetic field of 1.0e13 G. With reasonable confidence we were able to extend the timing solution back to archival XMM-Newton from 2002 and 2003, giving the same solution but with considerably more precision. This gives RX J0420 the lowest dipole magnetic field of the INSs. Our spectroscopy does not confirm the broad absorption feature at 0.3 keV hinted at in earlier observations, although difficulties in background subtraction near that energy make conclusions difficult. With this, all 6 of the INSs that have confirmed periodicities now have constrained spin-downs from coherent solutions. The evidence that the INSs are qualitatively different from rotation-powered pulsars now appears robust, with the likely conclusion that their characteristic ages are systematically older than their true ages, because their fields have decayed. The field decay probably also causes them to be systematically hotter than pulsars of the same (true) age.
This work is concerned with the broad question of propagation of regularity for smooth solutions to non-linear Vlasov equations. For a class of equations (that includes Vlasov-Poisson and relativistic Vlasov-Maxwell), we prove that higher regularity in space is propagated, locally in time, into higher regularity for the moments in velocity of the solution. This in turn can be translated into some anisotropic Sobolev higher regularity for the solution itself, which can be interpreted as a kind of weak propagation of space regularity. To this end, we adapt the methods introduced in the context of the quasineutral limit of the Vlasov-Poisson system in [D. Han-Kwan and F. Rousset, Ann. Sci. \'Ecole Norm. Sup., 2016].
This paper studies the distribution of chain and maximal chain lengths in a causal set. We first provide a new derivation for these distributions for a causal set uniformly embedded in Minkowski space, for various dimensionalities, which includes a correction to previously available expressions. Results of numerical simulations show a better agreement with the improved theoretical distributions. As examples of applications of those distributions, we then expand on previous work of ours regarding their use in establishing whether a causal set is manifoldlike and, if it is, finding its dimensionality. We then compare this measure of the dimension with other methods in the literature.
We report on single-pulse observations of the Galactic Center magnetar PSR J1745$-$2900 that were made using the Parkes 64-m radio telescope with a central frequency of 3.1 GHz at five observing epochs between 2013 July and August. The shape of the integrated pulse profiles was relatively stable across the five observations, indicating that the pulsar was in a stable state between MJDs 56475 and 56514. This extends the known stable state of this pulsar to 6.8 months. Short term pulse shape variations were also detected. It is shown that this pulsar switches between two emission modes frequently and that the typical duration of each mode is about ten minutes. No giant pulses or subpulse drifting were observed. Apparent nulls in the pulse emission were detected on MJD 56500. Although there are many differences between the radio emission of magnetars and normal radio pulsars, they also share some properties. The detection of mode changing and pulse nulling in PSR J1745$-$2900 suggests that the basic radio emission process for magnetars and normal pulsars is the same.
We offer an example of an network model with a power law degree distribution, P(k) ~ k^{-alpha}, for nodes but which nevertheless has a well-defined geography and a nonzero threshold percolation probability for alpha>2, the range of real-world contact networks. This is different from the p_c=0 for alpha<3 results for well-mixed scale-free networks. In our lattice-based scale-free network, individuals link to nearby neighbors on a lattice. Even considerable additional small-world links do not change our conclusion of nonzero thresholds. When applied to disease propagation, these results suggest that random immunization may be more successful in controlling human epidemics than previously suggested if there is geographical clustering.