ShantanuT01/DACTYL-Pretraining huggingface dataset:
The pairing Hamiltonian constitutes an important approximation in many- body systems, it is exactly soluble and quantum integrable. On the other hand, the continuum single particle level density (CSPLD) contains information about the continuum energy spectrum. The question whether one can use the Hamiltonian with constant pairing strength for correlations in the continuum is still unanswered. In this paper we generalize the Richardson exact solution for the pairing Hamiltonian including correlations in the continuum. The resonant and non-resonant continuum are included through the CSPLD. The resonant correlations are made explicit by using the Cauchy theorem. Low lying states with seniority zero and two are calculated for the even Carbon isotopes. We conclude that energy levels can indeed be calculated with constant pairing in the continuum using the CSPLD. It is found that the nucleus $^{24}$C is unbound. The real and complex energy representation of the continuum is developed and their differences are shown. The trajectory of the pair energies in the continuum for the nucleus $^{28}$C is shown.
Irrational conformal field theory (ICFT) includes rational conformal field theory as a small subspace, and the affine-Virasoro Ward identities describe the biconformal correlators of ICFT. We reformulate the Ward identities as an equivalent linear partial differential system with flat connections and new non-local conserved quantities. As examples of the formulation, we solve the system of flat connections for the coset correlators, the correlators of the affine-Sugawara nests and the high-level $n$-point correlators of ICFT.
Since the discovery of a neutrino flux in excess of the atmospheric background by the IceCube Collaboration, searches for the astrophysical sources have been ongoing. Due to the steeply falling background towards higher energies, the PeV events detected in three years of IceCube data are the most likely ones to be of extraterrestrial origin. Even excluding the PeV events detected so far, the neutrino flux is well above the atmospheric background, so it is likely that a number of sub-PeV events originate from the same astrophysical sources that produce the PeV events. We study the high-energy properties of AGN that are positionally coincident with the neutrino events from three years of IceCube data and show the results for event number 4. IC 4 is a event with a low angular error (7.1$^\circ$) and a large deposited energy of 165 TeV. We use multiwavelength data, including Fermi/LAT and X-ray data, to construct broadband spectra and present parametrizations of the broadband spectral energy distributions with logarithmic parabolas. Assuming the X-ray to {\gamma}-ray emission in blazars originates in the photoproduction of pions by accelerated protons, their predicted neutrino luminosity can be estimated. The measurements of the diffuse extragalactic background by Fermi/LAT gives us an estimate of the flux contributions from faint unresolved blazars. Their contribution increases the number of expected events by a factor of $\sim$2. We conclude that the detection of the IceCube neutrinos IC4, IC14, and IC20 can be explained by the integral emission of blazars, even though no individual source yields a sufficient energy output.
Let $A$ be a finite multiset of integers. If $B$ be a multiset such that $A$ and $B$ are $t$-complementing multisets of integers, then $B$ is periodic. We obtain the Biro-type upper bound for the smallest such period of $B$: Let $\epsilon>0$. We assume that $\textrm{diam}(A)\ge n_0(\epsilon)$ and that $\sum_{a\in A}w_A(a)\leq (\textrm{diam}(A)+1)^{c}$, where $c$ is any constant such that $c< 100\log2-2$. Then $B$ is periodic with period \[\log k\leq (\textrm{diam}(A)+1)^{1/3+\epsilon}. \]
We consider D1-string in a constant R-R 3-form flux background and analyze its low energy limit. The leading order low energy theory has reparametrization symmetry and is a generalization of an earlier work by Takhtajan. We show that the dynamical evolution of the theory takes a generalized Hamiltonian form in terms of a Nambu bracket. This description is formulated in terms of reparametrization invariant quantities and requires no fixing of the reparametrization symmetry. We also show that a Nambu- Poisson (p + 2)-bracket arises naturally in the reparametrization invariant description of the low energy theory of a p-brane in a constant (p + 2)-form flux background. For example, our results apply for a fundamental string in a constant NS-NS 3-form flux H3 and an M2-brane in a constant 4-form flux F4.
Ever since the discovery of Cosmic Rays (CRs), significant advancements have been made in modeling their propagation in the Galaxy and in the Heliosphere. However, propagation models suffer from degeneracy of many parameters. To complicate the picture the precision of recent data have started challenging existing models.   To tackle these issues we use available multifrequency observations of the interstellar emission from radio to gamma rays, together with direct CR measurements, to study local interstellar spectra (LIS) and propagation models.   As a result, the electron LIS is characterized without any assumption on solar modulation, and favorite propagation models are put forward. More precisely, our analysis leads to the following main conclusions: (1) the electron injection spectrum needs at least a break below a few GeV; (2) even though consistent with direct CR measurements, propagation models producing a LIS with large all-electron density from a few hundreds of MeV to a few GeV are disfavored by both radio and gamma-ray observations; (3) the usual assumption that direct CR measurements, after accounting for solar modulation, are representative of the proton LIS in our ~1 kpc region is challenged by the observed local gamma-ray HI emissivity.   We provide the resulting proton LIS, all-electron LIS, and propagation parameters, based on synchrotron, gamma-ray, and direct CR data. A plain diffusion model and a tentative diffusive-reacceleration model are put forward. The various models are investigated in the inner-Galaxy region in X-rays and gamma rays. Predictions of the interstellar emission for future gamma-ray instruments (e-ASTROGAM and AMEGO) are derived.
We consider kinetic models for a multi component gas mixture without chemical reactions. In the literature, one can find two types of BGK models in order to describe gas mixtures. One type has a sum of BGK type interaction terms in the relaxation operator, for example the model described by Klingenberg, Pirner and Puppo, 2017 which contains well-known models of physicists and engineers for example Hamel, 1965, and Gross and Krook, 1956, as special cases. The other type contains only one collision term on the right-hand side, for example the well-known model of Andries, Aoki and Perthame, 2002. For each of these two models we prove existence, uniqueness and positivity of solutions in the first part of the paper. In the second part, we use the first model in order to determine an unknown function in the energy exchange of the macroscopic equations for gas mixtures described by Dellacherie.
The integer $d$ is called an exponential divisor of $n=\prod_{i=1}^r p_i^{a_i}>1$ if $d=\prod_{i=1}^r p_i^{c_i}$, where $c_i \mid a_i$ for every $1\le i \le r$. The integers $n=\prod_{i=1}^r p_i^{a_i}, m=\prod_{i=1}^r p_i^{b_i}>1$ having the same prime factors are called exponentially coprime if $(a_i,b_i)=1$ for every $1\le i\le r$.   In the paper we investigate asymptotic properties of certain arithmetic functions involving exponential divisors and exponentially coprime integers.
Jets often have a helical structure containing ejected plasma that is both hot and also cooler and denser than the corona. Various mechanisms have been proposed to explain how jets are primarily attributed to a magnetic reconnection between the emergence of magnetic flux and environment or that of twisted photospheric motions that bring the system into a state of instability. Multi-wavelength observations of a twisted jet observed with AIA and IRIS were used to understand how the twist was injected into the jet. We followed the magnetic history of the active region based on the analysis of HMI vector magnetic field computed with the UNNOFIT code. This region is the result of the collapse of two emerging magnetic fluxes (EMFs) overlaid by arch filament systems that have been well-observed with AIA, IRIS, and NVST in H-alpha. In the magnetic field maps, we found evidence of the pattern of a long sigmoidal flux rope (FR) along the polarity inversion line between the two EMFs, which is the site of the reconnection. Before the jet, an extension of the FR was present and a part of it was detached and formed a small bipole with a bald patch (BP) region, which dynamically became an X-current sheet over the dome of one EMF where the reconnection took place. At the time of the reconnection, the Mg II spectra exhibited a strong extension of the blue wing that is decreasing over a distance of 10 Mm (from -300 km/s to a few km/s). This is the signature of the transfer of the twist to the jet. A comparison with numerical magnetohydrodynamics (MHD) simulations confirms the existence of the long FR. We conjecture that there is a transfer of twist to the jet during the extension of the FR to the reconnection site without FR eruption. There connection would start in the low atmosphere in the BP reconnection region and extend at an X-point along the current sheet formed above.
In this paper, we investigate the dark matter halo density profile of M33. We find that the HI rotation curve of M33 is best described by a NFW dark matter halo density profile model, with a halo concentration of cvir = 4.0\pm1.0 and a virial mass of Mvir = (2.2\pm0.1)\times10^11 Msun. We go on to use the NFW concentration (cvir)of M33, along with the values derived for other galaxies (as found in the literature), to show that cvir correlates with both spiral arm pitch angle and supermassive black hole mass.
We study sequences of nonlocal quadratic forms and function spaces that are related to Markov jump processes in bounded domains with a Lipschitz boundary. Our aim is to show the convergence of these forms to local quadratic forms of gradient type. Under suitable conditions we establish the convergence in the sense of Mosco. Our framework allows bounded and unbounded nonlocal operators to be studied at the same time. Moreover, we prove that smooth functions with compact support are dense in the nonlocal function spaces under consideration.
Let M be a compact manifold of dimension n, P = P(h) a semiclassical pseudodifferential operator on M, and u = u(h) an L^2 normalised family of functions such that Pu is O(h) in L^2(M) as h goes to 0. Let H be a compact submanifold of M. In a previous article, the second-named author proved estimates on the L^p norms, p > 2, of u restricted to H, under the assumption that the u are semiclassically localised and under some natural structural assumptions about the principal symbol of P. These estimates are of the form Ch^d(n;k;p) where k=dimH (except for a logarithmic divergence in the case k = n-2; p = 2). When H is a hypersurface, i.e. k = n-1, we have d(n;n-1;2)=1/4, which is sharp when M is the round n-sphere and H is an equator. In this article, we assume that H is a hypersurface, and make the additional geometric assumption that H is curved with respect to the bicharacteristic flow of P. Under this assumption we improve the estimate from d=1/4 to 1/6, generalising work of Burq-Gerard-Tzvetkov and Hu for Laplace eigenfunctions. To do this we apply the Melrose-Taylor theorem, as adapted by Pan and Sogge, for Fourier integral operators with folding canonical relations.
LUCIAE is a Monte Carlo program that, connected to FRITIOF, implements both the Firecracker Model (FCM), a possible mechanism for collective multi-gluon emission from the colour fields of interacting strings, and the reinteraction of the final state hadrons in relativistic heavy ion collisions. This paper includes a brief presentation of the dynamics of LUCIAE with an emphasis on the new features in this version, as well as a description of the program.
The problem of gravitational wave parameter estimation and source localization is crucial in gravitational wave astronomy. Gravitational waves emitted by compact binary coalescences in the sensitivity band of second-generation ground-based detectors could have non-negligible eccentricities. Thus it is an interesting topic to study how the eccentricity of a binary source affects and improves the accuracy of its localization (and the signal-to-noise ratio). In this work we continue to investigate this effect with the enhanced postcircular waveform model. Using the Fisher information matrix method, we determine the accuracy of source localization with three ground-based detector networks. As expected, the accuracy of source localization is improved considerably with more detectors in a network. We find that the accuracy also increases significantly by increasing the eccentricity for the large total mass ($M\ge 40M_\odot$) binaries with all three networks. For the small total mass ($M<40 M_\odot$) binaries, this effect is negligible. For the smaller total mass ($M<5 M_\odot$) binaries, the accuracy could be even worse at some orientations with increasing eccentricity. This phenomenon comes mainly from how well the frequency of the higher harmonic modes induced by increasing eccentricity coincides with the sensitive bandwidth of the detectors. For the case of the $100 M_\odot$ black hole binary, the improvement factor is about $2$ in general when the eccentricity grows from $0.0$ to $0.4$. For the cases of the $22 M_\odot$ black hole binary and the $2.74 M_\odot$ neutron star binary, the improvement factor is less than $1.1$, and it may be less than 1 at some orientations.
In this work we study the relation between the set of symmetric operators and the set of mutually unbiased operators from finite plane geometry point of view. Here symmetric operators are generalization of symmetric informationally complete probability-operator measurements (SIC POMs), while mutually unbiased operators are the operator generalization of mutually unbiased bases (MUB). We also discuss the implication of this relation to the particular cases of rank-1 SIC POMs and MUB.
Face detection is a fundamental problem in computer vision. It is still a challenging task in unconstrained conditions due to significant variations in scale, pose, expressions, and occlusion. In this paper, we propose a multi-branch fully convolutional network (MB-FCN) for face detection, which considers both efficiency and effectiveness in the design process. Our MB-FCN detector can deal with faces at all scale ranges with only a single pass through the backbone network. As such, our MB-FCN model saves computation and thus is more efficient, compared to previous methods that make multiple passes. For each branch, the specific skip connections of the convolutional feature maps at different layers are exploited to represent faces in specific scale ranges. Specifically, small faces can be represented with both shallow fine-grained and deep powerful coarse features. With this representation, superior improvement in performance is registered for the task of detecting small faces. We test our MB-FCN detector on two public face detection benchmarks, including FDDB and WIDER FACE. Extensive experiments show that our detector outperforms state-of-the-art methods on all these datasets in general and by a substantial margin on the most challenging among them (e.g. WIDER FACE Hard subset). Also, MB-FCN runs at 15 FPS on a GPU for images of size 640 x 480 with no assumption on the minimum detectable face size.
We present the first results of a new spectroscopic survey of the cluster Abell 85 targeting 1466 candidate cluster members within the central $\sim$1 deg$^2$ of the cluster and having magnitudes $m_r < 20.5$ using VIMOS/VLT and HYDRA/WIYN. A total of 520 galaxies are confirmed as either relaxed cluster members or part of an infalling population. A significant fraction are low mass; the median stellar mass of the sample is $10^{9.6} M_{\odot} $, and 25% have stellar masses below $10^9 M_{\odot}$ (i.e. 133 dwarf galaxies). We also identify seven active galactic nuclei (AGN), four of which reside in dwarf host galaxies. We probe the evolution of star formation rates, based on H$\alpha$ emission and continuum modeling, as a function of both mass and environment. We find that more star forming galaxies are observed at larger clustercentric distances, while infalling galaxies show evidence for recently enhanced star forming activity. Main sequence galaxies, defined by their continuum star formation rates, show different evolutionary behavior based on their mass. At the low mass end, the galaxies have had their star formation recently quenched, while more massive galaxies show no significant change. The timescales probed here favor fast quenching mechanisms, such as ram-pressure stripping. Galaxies within the green valley, defined similarly, do not show evidence of quenching. Instead, the low mass galaxies maintain their levels of star forming activity, while the more massive galaxies have experienced a recent burst.
Bulk metallic glass forms when liquid metal alloys solidify without crystalization. In the search for Iron-based bulk glass-forming alloys of the metal-metalloid type (Fe-B- and Fe-C-based), crystals based on the structural prototype C6Cr23 often preempt the amorphous phase. Destabilizing this competing crystal structure could enhance glass-formability. We carry out first-principles total energy calculations of enthalpy of formation to identify third elements that can effectively destabilize C6Cr23. Yttrium appears optimal among transition metals, and rare earths also are suitable. Atomic size is the dominant factor.
In this paper we remark that Shannon entropy can be expressed as a function of the self-information (i.e. the logarithm) and the inverse of the Lambert $W$ function. It means that we consider that Shannon entropy has the trace form: $-k \sum_{i} W^{-1} \circ \mathsf{ln}(p_{i})$. Based on this remark we define a generalized entropy which has as a limit the Shannon entropy. In order to facilitate the reasoning this generalized entropy is obtained by a one-parameter deformation of the logarithmic function.   Introducing a new concept of independence of two systems the Shannon additivity is replaced by a non-commutative and non-associative law which limit is the usual addition. The main properties associated with the generalized entropy are established, particularly those corresponding to statistical ensembles. The Boltzmann-Gibbs statistics is recovered as a limit. The connection with thermodynamics is also studied. We also provide a guideline for systematically defining a deformed algebra which limit is the classical linear algebra. As an illustrative example we study a generalized entropy based on Tsallis self-information. We point out possible connections between deformed algebra and fuzzy logics. Finally, noticing that the new concept of independence is based on t-norm the one-parameter deformation of the logarithm is interpreted as an additive generator of t-norms.
We obtained an exact solution for a uniformly accelerated Unruh-DeWitt detector interacting with a massless scalar field in (3+1) dimensions which enables us to study the entire evolution of the total system, from the initial transient to late-time steady state. We find that the Unruh effect as derived from time-dependent perturbation theory is valid only in the transient stage and is totally invalid for cases with proper acceleration smaller than the damping constant. We also found that, unlike in (1+1)D results, the (3+1)D uniformly accelerated Unruh-DeWitt detector in a steady state does emit a positive radiated power of quantum nature at late-times, but it is not connected to the thermal radiance experienced by the detector in the Unruh effect proper.
Face recognition of realistic visual images has been well studied and made a significant progress in the recent decade. Unlike the realistic visual images, the face recognition of the caricatures is far from the performance of the visual images. This is largely due to the extreme non-rigid distortions of the caricatures introduced by exaggerating the facial features to strengthen the characters. The heterogeneous modalities of the caricatures and the visual images result the caricature-visual face recognition is a cross-modal problem. In this paper, we propose a method to conduct caricature-visual face recognition via multi-task learning. Rather than the conventional multi-task learning with fixed weights of tasks, this work proposes an approach to learn the weights of tasks according to the importance of tasks. The proposed multi-task learning with dynamic tasks weights enables to appropriately train the hard task and easy task instead of being stuck in the over-training easy task as conventional methods. The experimental results demonstrate the effectiveness of the proposed dynamic multi-task learning for cross-modal caricature-visual face recognition. The performances on the datasets CaVI and WebCaricature show the superiority over the state-of-art methods.
Parameters of recent neural networks require a huge amount of memory. These parameters are used by neural networks to perform machine learning tasks when processing inputs. To speed up inference, we develop Partition Pruning, an innovative scheme to reduce the parameters used while taking into consideration parallelization. We evaluated the performance and energy consumption of parallel inference of partitioned models, which showed a 7.72x speed up of performance and a 2.73x reduction in the energy used for computing pruned layers of TinyVGG16 in comparison to running the unpruned model on a single accelerator. In addition, our method showed a limited reduction some numbers in accuracy while partitioning fully connected layers.
Applications of the integrable system techniques to the non-equilibrium transport problems are discussed. We describe one-dimensional electrons tunneling through a point-like defect either by the s-d exchange (Kondo) mechanism, or via the resonanse level (Anderson) mechanism. These models are potential candidates to be solved exactly in the presence of arbitrary external bias. We draw attention also to several mesoscopical systems which can be tackled by the massless form-factor approach, as perturbations of integrable models. The basic unperturbed model is the massless sine-Gordon model with the interaction (cosine) term restricted to one point, which is integrable. It is being perturbed by the second interaction term, which destroys integrability. Quasi-exact results can be obtained by making use of the basis of massless quasiparticles of the sine-Gordon model.