ShantanuT01/DACTYL-Pretraining huggingface dataset:
As the reviewer have pointed out, the proof of Roelke Conjecture contains an error.   For cofinite groups, we obtain a formula connecting the discrete spectrum of Laplace operator and the resonance spectrum. Using this formula, we give a proof of the Roelke conjecture. In this version, we make several corrections in Theorem 1 and Lemma 5.
The halo spin flip refers to the phenomenon that the spin axes of dark matter halos with masses above a certain threshold tend to be preferentially aligned perpendicular to the hosting large-scale filaments, while low-mass halos tend to have their spin axes aligned parallel to such structures. Extensive work has so far been conducted to understand this phenomenon under the assumption of cold dark matter and suggested that its origin should be closely related to the nonlinear evolution of the halo angular momentum in the anisotropic cosmic web. We present, for the first time, a numerical examination of this phenomenon assuming the presence of massive neutrinos, finding a clear and robust dependence of the threshold mass for the spin flip on the total neutrino mass. Our physical explanation is that the presence of more massive neutrinos retard the nonlinear evolution of the cosmic web, which in turn allows the halo spin vectors to better retain their memories of the initial tidal interactions in the nonlinear regime. Our finding implies that the statistical alignment of halo spins with the large-scale structures can be in principle used as a probe of the total neutrino mass.
We want to estimate whether the positrons produced by the beta plus decay of 26Al, 44Ti and 56Ni synthesised in massive stars and supernovae are sufficient to explain the 511 keV annihilation emission observed in our Galaxy. Such a possibility has often been put forward in the past. We developed a Monte Carlo Galactic propagation code for ~MeV positrons in which the Galactic interstellar medium, the Galactic magnetic field (GMF) and the propagation are finely described. This code allows us to simulate the spatial distribution of the 511 keV annihilation emission. We test several GMFs models and several positron escape fractions from type-Ia supernova for 56Ni positrons. We consider the collisional ballistic transport mode and then compare the simulated 511 keV intensity spatial distributions to the INTEGRAL/SPI data. Whatever the GMF configuration and the escape fraction chosen for 56Ni positrons, the 511 keV intensity distributions are very similar. The main reason is that ~MeV positrons do not propagate very far away from their birth sites in our model. The direct comparison to the data does not allow us to constrain the GMF configuration and the escape fraction for 56Ni positrons. In any case, nucleosynthesis positrons produced in steady state cannot explain the full annihilation emission. The comparison to the data shows that: (a) the annihilation emission from the Galactic disk can be accounted for; (b) the strongly peaked annihilation emission from the inner Galactic bulge can be explained by positrons annihilating in the central molecular zone but this seems to require more positron sources than the population of massive stars and type Ia supernovae usually assumed for this region; (c) the more extended emission from the Galactic bulge cannot be explained. We show that a transient source at the GC, such as a starburst episode, could explain this extended component.
The application of the conventional theory of macroparameter fluctuations has been shown to go beyond the framework of the thermodynamic description in a number of cases. The principles of the theory of quantum-thermal fluctuations of effective macroparameters and their correlations have been formulated. The theory satisfies the applicability conditions of equilibrium thermodynamics and is based on effective macroparameters, which take the integral stochastic action of the environment into account at any temperatures. The correlator of conjugate macroparameters, namely, the effective entropy and the effective temperature, has been calculated. The correlator was found to be proportional to the effective action which characterizes the stochastic environment. The pair correlators for the conjugate effective parameters entropy-temperature and coordinate-momentum have been demonstrated to depend linearly on the effective action, with their minimum values being determined by Planck's constant.
Highly sophisticated synthesis methods and experimental techniques allow for precise measurements of magnetic properties of nanoparticles that can be reliably reproduced using theoretical models. Here, we investigate the magnetic properties of ferrite nanoparticles by using theoretical techniques based on Monte Carlo methods. We introduce three stages of sophistication in the macromagnetic model. First, by using tailor-made hamiltonians we study single nanoparticles. In a second stage, the internal structure of the nanoparticle is taken into consideration by defining an internal (core) and external (shell) region, respectively. In the last stage, an assembly of core/shell NPs are considered. All internal magnetic couplings such as inter and intra-atomic exchange interactions or magnetocrystalline anisotropies have been estimated. Moreover, the hysteresis loops of the aforementioned three cases have been calculated and compared with recent experimental measurements. In the case of the assembly of nanoparticles, the hysteresis loops together with the zero-field cooling and field cooling curves are shown to be in a very good agreement with the experimental data. The current model provides an important tool to understand the internal structure of the nanoparticles together with the complex internal spin interactions of the core-shell ferrite nanoparticles.
We derive a high-resolution formula for the quantization and entropy coding approximation quantities for fractional Brownian motion, respective to the supremum norm and L^p[0,1]-norm distortions. We show that all moments in the quantization problem lead to the same asymptotics. Using a general principle, we conclude that entropy coding and quantization coincide asymptotically. Under supremum-norm distortion, our proof uses an explicit construction of efficient codebooks based on a particular entropy constrained coding scheme. This procedure can be used to construct close to optimal high resolution quantizers.
In this paper, we introduce the notion of variational free boundary problem. Namely, we say that a free boundary problem is variational if its solutions can be characterized as the critical points of some shape functional. Moreover, we extend the notion of nondegeneracy of a critical point to this setting. As a result, we provide a unified functional-analytical framework that allows us to construct families of solutions to variational free boundary problems whenever the shape functional is nondegenerate at some given solution. As a clarifying example, we apply this machinery to construct families of nontrivial solutions to the two-phase Serrin's overdetermined problem in both the degenerate and nondegenerate case.
A generic semiclassical superconducting nanostructure connected to multiple superconducting terminals hosts a quasi-continuous spectrum of Andreev states. The spectrum is sensitive to the superconducting phases of the terminals. It can be either gapped or gapless depending on the point in the multi-dimensional parametric space of these phases. Special points in this space correspond to setting some terminals to the phase 0 and the rest to the phase of $\pi$. For a generic nanostructure, three distinct spectra come together in the vicinity of a special point: two gapped phases of different topology and a gapless phase separating the two by virtue of topological protection.   In this paper, we show that a weak interaction manifesting as quantum fluctuations of superconducting phases drastically changes the spectrum in a narrow vicinity of a special point. We develop an interaction model and derive a universal generic quantum action that describes this situation. The action is complicated by incorporating a non-local in time matrix order parameter, and its full analysis is beyond the scope of the present paper. Here, we identify and address two limits: the semiclassical one and the quantum one, concentrating on the first-order interaction correction in the last case.   In both cases, we find that the interaction squeezes the domain of the gapless phase in the narrow vicinity of the point so the gapped phases tend to contact each other immediately, defying the topological protection. We identify the domains of strong coupling where the perturbation theory does not work. In the gapless phase, we find the logarithmic divergence of the first-order corrections. This leads us to an interesting hypothesis: weak interaction might induce an exponentially small gap in the formerly gapless phase.
A short Reply to the Comment of Brankov, Tonchev and Zagrebnov, quant-ph/0506207, is given.
A hybrid model is presented for hadron polarization that is based on perturbative QCD subprocesses and the recombination of polarized quarks to form polarized hadrons. The model, originally applied to polarized $\Lambda$'s that were inclusively produced by proton beams, is extended to include pion beams and polarized $\Lambda_c$'s. The resulting polarizations are calculated as functions of $x_F$ and $p_T$ for high energies and are found to be in fair agreement with recent experiments.
We study decay of unstable D-branes in string theory in the presence of electric field, and show that the classical open string theory results for various properties of the final state agree with the properties of closed string states into which the system is expected to decay. This suggests a duality between tree level open string theory on unstable D-branes and closed strings at high density.
The Gell-Mann $\lambda$ matrices for Lie algebra su(3) are the natural basis for the Hilbert space of Hermitian operators acting on the states of a three-level system(qutrit). So the construction of EWs for two-qutrit states by using these matrices may be an interesting problem. In this paper, several two-qutrit EWs are constructed based on the Gell-Mann matrices by using the linear programming (LP) method exactly or approximately. The decomposability and non-decomposability of constructed EWs are also discussed and it is shown that the $\lambda$-diagonal EWs presented in this paper are all decomposable but there exist non-decomposable ones among $\lambda$-non-diagonal EWs.
Morphing attacks have posed a severe threat to Face Recognition System (FRS). Despite the number of advancements reported in recent works, we note serious open issues such as independent benchmarking, generalizability challenges and considerations to age, gender, ethnicity that are inadequately addressed. Morphing Attack Detection (MAD) algorithms often are prone to generalization challenges as they are database dependent. The existing databases, mostly of semi-public nature, lack in diversity in terms of ethnicity, various morphing process and post-processing pipelines. Further, they do not reflect a realistic operational scenario for Automated Border Control (ABC) and do not provide a basis to test MAD on unseen data, in order to benchmark the robustness of algorithms. In this work, we present a new sequestered dataset for facilitating the advancements of MAD where the algorithms can be tested on unseen data in an effort to better generalize. The newly constructed dataset consists of facial images from 150 subjects from various ethnicities, age-groups and both genders. In order to challenge the existing MAD algorithms, the morphed images are with careful subject pre-selection created from the contributing images, and further post-processed to remove morphing artifacts. The images are also printed and scanned to remove all digital cues and to simulate a realistic challenge for MAD algorithms. Further, we present a new online evaluation platform to test algorithms on sequestered data. With the platform we can benchmark the morph detection performance and study the generalization ability. This work also presents a detailed analysis on various subsets of sequestered data and outlines open challenges for future directions in MAD research.
The main result of this paper is a proof that there are examples of spatially compact solutions of the Einstein-dust equations which only exist for an arbitrarily small amount of CMC time. While this fact is plausible, it is not trivial to prove. It is necessary to obtain a lower bound for the lapse function of a CMC foliation in a suitable class of inhomogeneous spacetimes. This bound, which shows that in these spacetimes the lapse cannot collapse in finite CMC time, may be of independent interest. This fact is contrasted with the positive results previously obtained for other matter models, e.g. collisionless matter or wave maps.
We investigate the effects of Supergiant Shells (SGSs) and their interaction on dense molecular clumps by observing the Large Magellanic Cloud (LMC) star forming regions N48 and N49, which are located between two SGSs, LMC 4 and LMC 5. $^{12}$CO ($J$=3-2, 1-0) and $^{13}$CO ($J$=1-0) observations with the ASTE and Mopra telescopes have been carried out towards these regions. A clumpy distribution of dense molecular clumps is revealed with 7 pc spatial resolution. Large velocity gradient analysis shows that the molecular hydrogen densities ($n({\rm H}_2)$) of the clumps are distributed from low to high density ($10^3$-$10^5$ cm$^{-3}$) and their kinetic temperatures ($T_{\rm kin}$) are typically high (greater than $50$ K). These clumps seem to be in the early stages of star formation, as also indicated from the distribution of H$\alpha$, young stellar object candidates, and IR emission. We found that the N48 region is located in the high column density HI envelope at the interface of the two SGSs and the star formation is relatively evolved, whereas the N49 region is associated with LMC 5 alone and the star formation is quiet. The clumps in the N48 region typically show high $n({\rm H}_2)$ and $T_{\rm kin}$, which are as dense and warm as the clumps in LMC massive cluster-forming areas (30 Dor, N159). These results suggest that the large-scale structure of the SGSs, especially the interaction of two SGSs, works efficiently on the formation of dense molecular clumps and stars.
Suppose $X$ is a hyperelliptic curve of genus $g$ defined over an algebraically closed field $k$ of characteristic $p=2$. We prove that the de Rham cohomology of $X$ decomposes into pieces indexed by the branch points of the hyperelliptic cover. This allows us to compute the isomorphism class of the $2$-torsion group scheme $J_X[2]$ of the Jacobian of $X$ in terms of the Ekedahl-Oort type. The interesting feature is that $J_X[2]$ depends only on some discrete invariants of $X$, namely, on the ramification invariants associated with the branch points. We give a complete classification of the group schemes which occur as the $2$-torsion group schemes of Jacobians of hyperelliptic $k$-curves of arbitrary genus.
We present a study of the scaling behavior of the R\'{e}nyi entanglement entropy (REE) in SU($N$) spin chain Hamiltonians, in which all the spins transform under the fundamental representation. These SU($N$) spin chains are known to be quantum critical and described by a well known Wess-Zumino-Witten (WZW) non-linear sigma model in the continuum limit. Numerical results from our lattice Hamiltonian are obtained using stochastic series expansion (SSE) quantum Monte Carlo for both closed and open boundary conditions. As expected for this 1D critical system, the REE shows a logarithmic dependence on the subsystem size with a prefector given by the central charge of the SU($N$) WZW model. We study in detail the sub-leading oscillatory terms in the REE under both periodic and open boundaries. Each oscillatory term is associated with a WZW field and decays as a power law with an exponent proportional to the scaling dimension of the corresponding field. We find that the use of periodic boundaries (where oscillations are less prominent) allows for a better estimate of the central charge, while using open boundaries allows for a better estimate of the scaling dimensions. For completeness we also present numerical data on the thermal R\'{e}nyi entropy which equally allows for extraction of the central charge.
We examine to which extent correlated realistic nucleon-nucleon interactions, derived within the Unitary Correlation Operator Method (UCOM), can describe nuclear collective motion in the framework of first-order random-phase approximation (RPA). To this end we employ the correlated Argonne V18 interaction in calculations within the so-called "Extended" RPA (ERPA) and investigate the response of closed-shell nuclei. The ERPA is a renormalized RPA version which considers explicitly the depletion of the Fermi sea due to long-range correlations and thus allows us to examine how these affect the excitation spectra. It is found that the effect on the properties of giant resonances is rather small. Compared to the standard RPA, where excitations are built on top of the uncorrelated Hartree-Fock (HF) ground state, their centroid energies decrease by up to 1 MeV, approximately, in the isovector channel. The isoscalar response is less affected in general. Thus, the disagreement between our previous UCOM-based RPA calculations and the experimental data are to be attributed to other effects, mainly to a residual three-body force and higher-order configurations. Ground-state properties obtained within the ERPA are compared with corresponding HF and perturbation-theory results and are discussed as well. The ERPA formalism is presented in detail.
We present a new approach to capturing the broad diversity of emission line and continuum properties in quasar spectra. We identify populations of spectrally similar quasars through pixel-level clustering on 12,968 high signal-to-noise spectra from the Sloan Digital Sky Survey (SDSS) in the redshift range of $1.57<z<2.4$. Our clustering analysis finds 396 quasar spectra that are not assigned to any population, 15 misclassified spectra, and six quasars with incorrect redshifts. We compress the quasar populations into a library of 684 high signal-to-noise composite spectra, anchored in redshift space by the Mg II emission line. Principal component analysis on the library results in an eigenspectrum basis spanning 1067 to 4007 $\r{A}$. We model independent samples of SDSS quasar spectra with the eigenbasis, allowing for a free redshift parameter. Our models achieve a median reduced chi-squared on non-BAL quasar spectra that is reduced by 8.5% relative to models using the eigenspectra from the SDSS spectroscopic pipeline. A significant contribution to the relative improvement is from the ability to reconstruct the range of emission line variation. The redshift estimates from our model are consistent with the Mg II emission line redshift with an average offset that displays 51.4% less redshift-dependent variation relative to the SDSS eigenspectra. Our method for developing quasar spectra models can improve automated classification and predict the intrinsic spectrum in regions affected by intervening absorbers such as Ly$\alpha$, C IV, and Mg II, thus benefiting studies of large-scale structure.
The combined effects of hole doping and magnetic dilution on a lamellar Heisenberg antiferromagnet are studied in the framework of the frustration model. Magnetic vacancies are argued to remove some of the frustrating bonds generated by the holes, thus explaining the increase in the temperature and concentration ranges exhibiting three dimensional long range order. The dependence of the Neel temperature on both hole and vacancy concentrations is derived quantitatively from earlier renormalization group calculations for the non--dilute case, and the results reproduce experimental data with no new adjustable parameters.
Spectral-timing products of kilohertz quasi-periodic oscillations (kHz QPOs) in low-mass X-ray binary (LMXB) systems, including energy- and frequency-dependent lags, have been analyzed previously in 4U 1608-52, 4U 1636-53, and 4U 1728-34. Here, we study the spectral-timing properties of the lower kHz QPO of the neutron star LMXB Aquila X-1 for the first time. We compute broadband energy lags, as well as energy-dependent lags and the covariance spectrum using data from the Rossi X-ray Timing Explorer (RXTE). We find very similar characteristics to other previously studied systems, including soft lags of $\sim$30 $\mu$s between the 3.0 - 8.0 keV and 8.0 - 20.0 keV energy bands at the average QPO frequency. We also find lags that show a nearly monotonic trend with energy, with the highest energy photons arriving first. The covariance spectrum of the lower kHz QPO is well fit by a thermal Comptonization model, though we find a higher seed photon temperature compared to the mean spectrum, which was also seen in Peille et al., (2015), and indicates the possibility of a composite boundary layer emitting region. Lastly, we see in one set of observations, an Fe K component in the covariance spectrum at 2.4-$\sigma$ confidence which may raise questions about the role of reverberation in the production of lags.
We construct surface measures in a Hilbert space endowed with a probability measure $\nu$. The theory fits for invariant measures of some stochastic partial differential equations such as Burgers and reaction--diffusion equations. Other examples are weighted Gaussian measures and special product measures $\nu$ of non Gaussian measures; in this case we exhibit a Markov process having $\nu$ as invariant measure. In any case we prove integration by parts formulae on sublevel sets of good functions (including spheres and hyperplanes) that involve surface integrals.
This paper presents an approach for automatic detection of Munro's Microabscess in stratum corneum (SC) of human skin biopsy in order to realize a machine assisted diagnosis of Psoriasis. The challenge of detecting neutrophils in presence of nucleated cells is solved using the recent advances of deep learning algorithms. Separation of SC layer, extraction of patches from the layer followed by classification of patches with respect to presence or absence of neutrophils form the basis of the overall approach which is effected through an integration of a U-Net based segmentation network and a capsule network for classification. The novel design of the present capsule net leads to a drastic reduction in the number of parameters without any noticeable compromise in the overall performance. The research further addresses the challenge of dealing with Mega-pixel images (in 10X) vis-a-vis Giga-pixel ones (in 40X). The promising result coming out of an experiment on a dataset consisting of 273 real-life images shows that a practical system is possible based on the present research. The implementation of our system is available at https://github.com/Anabik/CapsDeMM.
There are multiple techniques to determine the chemical composition of the ultra-high-energy cosmic rays. While most of the methods are primarily sensitive to the average atomic mass, it is challenging to discriminate between the two lightest elements: proton and helium. In this paper, the proton-to-helium ratio in the energy range $10^{18.0} \mbox{eV}$ to $10^{19.3} \mbox{eV}$ is estimated using the tail of the distribution of the depth of the shower maximum $X_{\mathrm{max}}$. Using the exponential decay scale $\Lambda$ measured by the Pierre Auger Observatory and the Telescope Array experiment we derive the 68\%\,CL constraints on the proton-to-helium ratio $\mathrm{p}/\mathrm{He} > 7.3 $ and $\mathrm{p}/\mathrm{He} > 0.43 $ for $10^{18.0} < E < 10^{18.5}$ eV and $10^{18.3} < E < 10^{19.3}$ eV correspondingly. It is shown that the result is conservative with respect to the admixture of heavier elements. We evaluate the impact of the hadronic interaction model uncertainty. The implications for the astrophysical models of the origin of cosmic rays and the safety of the future colliders are discussed.