ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we prove under mild hypotheses the Iwasawa main conjectures of Lei--Loeffler--Zerbes for modular forms of weight $2$ at non-ordinary primes. Our proof is based on the study of the two-variable analogues of these conjectures formulated by B\"uy\"ukboduk--Lei for imaginary quadratic fields in which $p$ splits, and on anticyclotomic Iwasawa theory. As application of our results, we deduce the $p$-part of the Birch and Swinnerton-Dyer formula in analytic ranks $0$ or $1$ for abelian varieties over $\mathbb{Q}$ of ${\rm GL}_2$-type for non-ordinary primes $p>2$.
It is shown that kinetic freeze-out in relativistic heavy-ion collisions invariably entails a non-trivial dependence of the freeze-out temperature on the collision centrality. The centrality independence of the chemical freeze-out temperature observed in Au+Au collisions at RHIC is therefore inconsistent with the hypothesis that hadron abundances decouple kinetically from inelastic hadron-hadron interactions. On the other hand, it is consistent with the hypothesis that chemical decoupling is driven by the quark-hadron phase transition, and that the observed universal chemical freeze-out reflects its critical temperature, independent of the dynamical state of the collision fireball as it passes through the phase transition.
It is well known that Yukawa potentials permit bound states in the Schrodinger equation only if the ratio of the exchanged mass to bound mass is below a critical multiple of the coupling constant. However, arguments suggested by the Darwin term imply a more complex situation. By numerically studying the Dirac equation with a Yukawa potential we investigate this amplification effect.
(abridged) We study the low energy events observed by Kamiokande-II. We focus on the event 6 of 6.3 MeV and also on the other events that at 1 sigma fall below the energy threshold: events 3,4,10,12. The volume distribution is not a uniform distribution at 3 sigma, that suggests the presence of background events close or at the border of the volume used for the analysis, including the events 3,4,10. We checked the expected energy distribution assuming that the signal is due to nubar(e)p-->e+n and that the average antineutrino energy is 14 MeV. The agreement with the observations is not perfect but it is acceptable at the 11 % confidence level if we include the peak of low energy background events; otherwise, we face a 2.9 sigma problem. The expected energy distribution implies that the evidence for supernova neutrinos is at 10 sigma and that 1-3 background events are plausible. This conclusion does not change strongly when we model the time distribution of the signal taking into account the presence of an initial luminous phase of neutrino emission. This suggests however that some of the early events are due to supernova neutrinos and not to background. In summary, we formulate the hypothesis that some of the observed low energy events are due to background and that some among them belong to a peculiar phase of emission, that could be further characterized by low energy neutrinos. Such an interpretation diminishes to a minimum the postulated number of background events and thus improves the agreement between the a priori and the a posteriori expectations on the number of background events. We argue on these grounds that there is no significant disagreement between the average energy of the supernova neutrinos seen in Kamiokande-II and the conventional expectations.
We study the spectra of mixed graphs about its Hermitian adjacency matrix of the second kind (i.e. N-matrix) introduced by Mohar [1]. We extend some results and define one new Hermitian adjacency matrix, and the entry corresponding to an arc from $u$ to $v$ is equal to the $k$-th( or the third) root of unity, i.e. ${\omega} = cos(2{\pi}/k) + \textbf{i} \ sin(2{\pi}/k), k {\geq} 3$; the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. In this paper, we characterize the cospectrality conditions for a mixed graph and its underlying graph. In section 4, we determine a sharp upper bound on the spectral radius of mixed graphs, and provide the corresponding extremal graphs.
Variational quantum algorithms constitute one of the most widespread methods for using current noisy quantum computers. However, it is unknown if these heuristic algorithms provide any quantum-computational speedup, although we cannot simulate them classically for intermediate sizes. Since entanglement lies at the core of quantum computing power, we investigate its role in these heuristic methods for solving optimization problems. In particular, we use matrix product states to simulate the quantum approximate optimization algorithm with reduced bond dimensions $D$, a parameter bounding the system entanglement. Moreover, we restrict the simulation further by deterministically sampling solutions. We conclude that entanglement plays a minor role in the MaxCut and Exact Cover 3 problems studied here since the simulated algorithm analysis, with up to $60$ qubits and $p=100$ algorithm layers, shows that it provides solutions for bond dimension $D \approx 10$ and depth $p \approx 30$. Additionally, we study the classical optimization loop in the approximated algorithm simulation with $12$ qubits and depth up to $p=4$ and show that the approximated optimal parameters with low entanglement approach the exact ones.
We explore the possibility of extrapolating state of the art lattice QCD calculations of nucleon form factors to the physical regime. We find that the lattice results can be reproduced using the Light Front Cloudy Bag Model by letting its parameters be analytic functions of the quark mass. We then use the model to extend the lattice calculations to large values of Q^{2} of interest to current and planned experiments. These functions are also used to define extrapolations to the physical value of the pion mass, thereby allowing us to study how the predicted zero in G_{E}(Q^{2})/G_{M}(Q^{2}) varies as a function of quark mass.
Charge and spin order is intimately related to superconductivity in copper oxide superconductors. To elucidate the competing orders in various nickel oxide compounds are crucial given the fact that superconductivity has been discovered in Nd$_{0.8}$Sr$_{0.2}$NiO$_2$ films. Herein, we report structural, electronic transport, magnetic, and thermodynamic characterizations on single crystals of La$_3$Ni$_2$O$_7$ and La$_3$Ni$_2$O$_6$. La$_3$Ni$_2$O$_7$ is metallic with mixed Ni$^{2+}$ and Ni$^{3+}$ valent states. Resistivity measurements yield two transition-like kinks at $\sim$110 and 153 K, respectively. The kink at 153 K is further revealed from magnetization and specific heat measurements, indicative of the formation of charge and spin order. La$_3$Ni$_2$O$_6$ single crystals obtained from topochemical reduction of La$_3$Ni$_2$O$_7$ are insulating and show an anomaly at $\sim$176 K on magnetic susceptibility. The transition-like behaviors of La$_3$Ni$_2$O$_7$ and La$_3$Ni$_2$O$_6$ are analogous to the charge and spin order observed in La$_4$Ni$_3$O$_{10}$ and La$_4$Ni$_3$O$_8$, suggesting charge and spin order is a common feature in the ternary La-Ni-O system with mixed-valent states of nickel.
We introduce subspace rank as a tool for studying ranks of tensors and X-rank more generally. We derive a new upper bound for the rank of a tensor and determine the ranks of partially symmetric tensors in C^2 \otimes C^b \otimes C^b. We review the literature from a geometric perspective.
We explore the accuracy of the clustering-based redshift inference within the MICE2 simulation. This method uses the spatial clustering of galaxies between a spectroscopic reference sample and an unknown sample. The goal of this study is to give a preview of the redshift accuracy one can reach with this method. To do so, we first highlight the requirements of this technique in term of number of objects in both the reference and unknown samples. We also confirm that this method does not require a representative spectroscopic sample for calibration.   We estimate that a density of spectroscopic objects of $10^{-5}$ arcmin$^{-2}$ per redshift bin of width $\delta z = 0.01$ over $9000 \ \text{deg}^{2}$ allows to reach 0.1 \% accuracy in the mean redshift for a galaxy density compatible with next generation of cosmological surveys. This number is compatible with the density of the Quasi Stellar Objects in BOSS. Second we demonstrate our ability to measure individual redshifts for galaxies independently from the photometric redshifts procedure. The resulting individual clustering redshifts have a bias=$-0.001$, an outlier fraction of $\eta=3.57\%$ and a scatter of $\sigma=0.027$ to $i<25$. The advantage of this procedure is threefold: i) it allows the use of clustering redshifts for any field in astronomy, ii) it allows the possibility to combine photometric and clustering based redshifts to get an improved redshift estimation, iii) it allows the use of cluster-$z$ to define tomographic bins for weak lensing. Finally we explore this last option and build 5 clustering redshift selected tomographic bins from redshift 0.2 to 1. We found a bias on the mean redshift estimate of $0.002$ per bin.
We present new observations of HCN and HCO+in the circumnuclear disk (CND) of the Galaxy, obtained with the APEX telescope. We have mapped emission in rotational lines of HCN J = 3-2, 4-3, and 8-7, as well as HCO+ J = 3-2, 4-3, and 9-8. We also present spectra of H13CN and H13CO+ toward four positions in the CND. Using the intensities of all of these lines, we present an excitation analysis for each molecule using the non-LTE radiative transfer code RADEX. The HCN line intensities toward the northern emission peak of the CND yield log densities (cm^-3) of 5.6 +0.6/-0.6, consistent with those measured with HCO+, as well as with densities recently reported for this region from an excitation analysis of highly-excited lines of CO. These densities are too low for the gas to be tidally stable. The HCN line intensities toward the CND's southern emission peak yield log densities of 6.5 +0.5/-0.7, higher than densities determined for this part of the CND with CO (although the densities measured with HCO+, log [n] = 5.6 +0.2/-0.2, are more consistent with the CO-derived densities). We investigate whether the higher densities we infer from HCN are affected by mid-infrared radiative excitation of this molecule through its 14 micron rovibrational transitions. We find that radiative excitation is important for at least one clump in the CND, where we additionally detect the J = 4-3, v2=1 vibrationally-excited transition of HCN, which is excited by dust temperatures of > 125-150 K. If this hot dust is present elsewhere in the CND, it could lower our inferred densities, potentially bringing the HCN-derived densities for the Southern part of the CND into agreement with those measured using HCO+ and CO. Additional sensitive, high-resolution submillimeter observations, as well as mid-infrared observations, would be useful to assess the importance of the radiative excitation of HCN in this environment.
We consider strongly stratified forced turbulence in a plane-parallel layer with helicity and corresponding large-scale dynamo action in the lower part and non-helical turbulence in the upper. The magnetic field is found to develop strongly concentrated bipolar structures near the surface. They form elongated bands with a sharp interface between opposite polarities. Unlike earlier experiments with imposed magnetic field, the inclusion of rotation does not strongly suppress the formation of these structures. We perform a systematic numerical study of this phenomenon by varying magnetic Reynolds number, scale separation ratio, and Coriolis number. We focus on the formation of a current sheet between bipolar regions where reconnection of oppositely oriented field lines occurs. We determine the reconnection rate by measuring either the inflow velocity in the vicinity of the current sheet or by measuring the electric field in the reconnection region. We demonstrate that for large Lundquist numbers, S>10^3, the reconnection rate is nearly independent of S in agreement with results of recent numerical simulations performed by other groups in simpler settings.
Multi-modal data fusion has recently been shown promise in classification tasks in remote sensing. Optical data and radar data, two important yet intrinsically different data sources, are attracting more and more attention for potential data fusion. It is already widely known that, a machine learning based methodology often yields excellent performance. However, the methodology relies on a large training set, which is very expensive to achieve in remote sensing. The semi-supervised manifold alignment (SSMA), a multi-modal data fusion algorithm, has been designed to amplify the impact of an existing training set by linking labeled data to unlabeled data via unsupervised techniques. In this paper, we explore the potential of SSMA in fusing optical data and polarimetric SAR data, which are multi-sensory data sources. Furthermore, we propose a MAPPER-induced manifold alignment (MIMA) for semi-supervised fusion of multi-sensory data sources. Our proposed method unites SSMA with MAPPER, which is developed from the emerging topological data analysis (TDA) field. To our best knowledge, this is the first time that SSMA has been applied on fusing optical data and SAR data, and also the first time that TDA has been applied in remote sensing. The conventional SSMA derives a topological structure using k-nearest-neighbor (kNN), while MIMA employs MAPPER, which considers the field knowledge and derives a novel topological structure through the spectral clustering in a data-driven fashion. Experiment results on data fusion with respect to land cover land use classification and local climate zone classification suggest superior performance of MIMA.
In this paper we study flat deformations of real subschemes of $\mathbb{P}^n$, hyperbolic with respect to a fixed linear subspace, i.e. admitting a finite surjective and real fibered linear projection. We show that the subset of the corresponding Hilbert scheme consisting of such subschemes is closed and connected in the classical topology. Every smooth variety in this set lies in the interior of this set. Furthermore, we provide sufficient conditions for a hyperbolic subscheme to admit a flat deformation to a smooth hyperbolic subscheme. This leads to new examples of smooth hyperbolic varieties.
We investigate Riemann's xi function $\xi(s):=\frac{1}{2}s(s-1)\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)$ (here $\zeta(s)$ is the Riemann zeta function). The Riemann Hypothesis (RH) asserts that if $\xi(s)=0$, then $\mathrm{Re}(s)=\frac{1}{2}$. P\'olya proved that RH is equivalent to the hyperbolicity of the Jensen polynomials $J^{d,n}(X)$ constructed from certain Taylor coefficients of $\xi(s)$. For each $d\geq 1$, recent work proves that $J^{d,n}(X)$ is hyperbolic for sufficiently large $n$. Here we make this result effective. Moreover, we show how the low-lying zeros of the derivatives $\xi^{(n)}(s)$ influence the hyperbolicity of $J^{d,n}(X)$.
The very first stars in the Universe can be very massive, up to $10^6M_\odot$. They would leave behind massive black holes that could act as seeds for growing super massive black holes of active galactic nuclei. Given the anticipated fast rotation such stars would end their live as super massive collapsars and drive powerful magnetically-dominated jets. In this paper we investigate the possibility of observing the bursts of high-energy emission similar to the Long Gamma Ray Bursts associated with normal collapsars. We show that during the collapse of supercollapsars, the Blandford-Znajek mechanism can produce jets as powerful as few$\times10^{51}$erg/s and release up to $10^{56}$erg of the black hole rotational energy. Due to the higher intrinsic time scale and higher redshift the initial bright phase of the burst can last for about $10^5$ seconds whereas the central engine would remain active for about 10 days. Due to the high redshift the burst spectrum is expected to be soft, with the spectral energy distribution peaking at around 60keV. The peak total flux density is relatively low, few$\times 10^{-7}erg\, cm^{-2} s^{-1}$, but not prohibitive. The such events should be rear 0.03 year$^{-1}$, the observations needs long term program and could be done in future.
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of speed. Other types of computation using radically different architectures, including neuromorphic and quantum, promise breakthroughs in both speed and efficiency. Quantum computing exploits the coherence and superposition properties of quantum systems to explore many possible computational paths in parallel. This provides a fundamentally more efficient route to solving some types of computational problems, including several of relevance to biological simulations. In particular, optimisation problems, both convex and non-convex, feature in many biological models, including protein folding and molecular dynamics. Early quantum computers will be small, reminiscent of the early days of digital silicon computing. Understanding how to exploit the first generation of quantum hardware is crucial for making progress in both biological simulation and the development of the next generations of quantum computers. This review outlines the current state-of-the-art and future prospects for quantum computing, and provides some indications of how and where to apply it to speed up bottlenecks in biological simulation.
In models of large extra dimensions, the string and Planck scales become accessible at future colliders. When the energy scale is above the string scale or Planck scale a number of interesting phenomena occur, namely, production of stringy states, $p$-branes, string balls, black hole, etc. In this Proceedings, we summarize a recent work \cite{me0} on the production of black holes, string balls, and $p$-branes at hadronic supercolliders, and discuss their signatures.
We present the first three-dimensional radiation-magnetohydrodynamic simulations of the photoionisation of a dense, magnetised molecular globule by an external source of ultraviolet radiation. We find that, for the case of a strong ionising field, significant deviations from the non-magnetic evolution are seen when the initial magnetic field threading the globule has an associated magnetic pressure that is greater than one hundred times the gas pressure. In such a strong-field case, the photoevaporating globule will adopt a flattened or "curled up" shape, depending on the initial field orientation, and magnetic confinement of the ionised photoevaporation flow can lead to recombination and subsequent fragmentation during advanced stages of the globule evolution. We find suggestive evidence that such magnetic effects may be important in the formation of bright, bar-like emission features in H II regions. We include simple but realistic fits to heating and cooling rates in the neutral and molecular gas in the vicinity of a high-mass star cluster and show that the frequently used isothermal approximation can lead to an overestimate of the importance of gravitational instability in the radiatively imploded globule. For globules within 2 parsecs of a high-mass star cluster, we find that heating by stellar x rays prevents the molecular gas from cooling below 50 K.
Some of the more promising ideas about the origin of the high frequency variability (kHz QPOs) in the observed X-ray emissions of low-mass X-ray binaries are contrasted with less promising ones.
Multi-face tracking in unconstrained videos is a challenging problem as faces of one person often appear drastically different in multiple shots due to significant variations in scale, pose, expression, illumination, and make-up. Existing multi-target tracking methods often use low-level features which are not sufficiently discriminative for identifying faces with such large appearance variations. In this paper, we tackle this problem by learning discriminative, video-specific face representations using convolutional neural networks (CNNs). Unlike existing CNN-based approaches which are only trained on large-scale face image datasets offline, we use the contextual constraints to generate a large number of training samples for a given video, and further adapt the pre-trained face CNN to specific videos using discovered training samples. Using these training samples, we optimize the embedding space so that the Euclidean distances correspond to a measure of semantic face similarity via minimizing a triplet loss function. With the learned discriminative features, we apply the hierarchical clustering algorithm to link tracklets across multiple shots to generate trajectories. We extensively evaluate the proposed algorithm on two sets of TV sitcoms and YouTube music videos, analyze the contribution of each component, and demonstrate significant performance improvement over existing techniques.
We infer the absolute time dependence of kinematic gas temperature along a proposed orbit of molecular clouds in the Central Molecular Zone (CMZ) of the Galactic Center (GC). Ammonia gas temperature maps are one of the results of the "Survey of Water and Ammonia in the Galactic Center" (SWAG, PI: J. Ott); the dynamical model of molecular clouds in the CMZ was taken from Kruijssen et al. (2015). We find that gas temperatures increase as a function of time in both regimes before and after the cloud passes pericenter on its orbit in the GC potential. This is consistent with the recent proposal that pericenter passage triggers gravitational collapse. Other investigated quantities (line width, column density, opacity) show no strong sign of time dependence but are likely dominated by cloud-to-cloud variations.
We present an all-fibre source of high-purity heralded single photons with an integrated conditional optical gate that reduces uncorrelated noise by almost an order of magnitude. Generating photon pairs by four-wave mixing in photonic crystal fibre, we observe with the noise gate active a factor of 7 reduction in the rate of single counts in the heralded channel with no measurable drop in coincidence count rate. In contrast to electronic post-selection of coincidence events, the real reduction in the flux of unwanted photons is beneficial for example to avoid bleaching light-sensitive samples or in generating entangled states.
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical algorithm. It is possible to use Grover algorithm, taking profit of its ability to find a specific value in a unordered database, to find, for example, the zero of a logical function; the minimal or maximal value in a database or to recognize if an odd number is prime or not. Here we show quantum algorithms to solve those cited mathematical problems. The solution requires the use of a quantum bit string comparator being used as oracle. This quantum circuit compares two quantum states and identifies if they are equal or, otherwise, which of them is the largest. Moreover, we also show the quantum bit string comparator allow us to implement conditional statements in quantum computation, a fundamental structure for designing of algorithms.