ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper is based on a course given by the author at the University of Rome ``La Sapienza'' in the Academic year 2000/2001. The intended aim of the course was to rapidly introduce, although not in an exhaustive way, the non-expert PhD student to deformations of compact complex manifolds, from the very beginning to some recent (i.e. at that time not yet published) results. The goal of these lectures is to give a soft introduction to extended deformation theory. In view of the aim (and the hope) of keeping this paper selfcontained, user friendly and with a tolerating number of pages, we consider only deformations of compact complex manifolds. Anyhow, most part of the formalism and of the results that we prove here will apply to many other deformation problems.
The detection of gravitational waves (GWs) and an accompanying electromagnetic (E/M) counterpart have been suggested as a future probe for cosmology and theories of gravity. In this paper, we present calculations of the luminosity distance of sources taking into account inhomogeneities in the matter distribution that are predicted in numerical simulations of structure formation. In addition, we show that inhomogeneities resulting from clustering of matter can mimic certain classes of modified gravity theories, or other effects that dampen GW amplitudes, and deviations larger than $\delta \nu \sim \mathcal{O}(0.1)\ (99\%\ \rm{C.L.})$ to the extra friction term $\nu$, from zero, would be necessary to distinguish them. For these, we assume mock GWs sources, with known redshift, based on binary population synthesis models, between redshifts $z=0$ and $z=5$. We show that future GW detectors, like Einstein Telescope or Cosmic Explorer, will be needed for strong constraints on the inhomogeneity parameters and breaking the degeneracy between modified gravity effects and matter anisotropies by measuring $\nu$ at $5 \%$ and $1 \%$ level with $100$ and $350$ events respectively.
We present a two-dimensional (2-D) fitting algorithm (GALFIT, Version 3) with new capabilities to study the structural components of galaxies and other astronomical objects in digital images. Our technique improves on previous 2-D fitting algorithms by allowing for irregular, curved, logarithmic and power-law spirals, ring and truncated shapes in otherwise traditional parametric functions like the Sersic, Moffat, King, Ferrer, etc., profiles. One can mix and match these new shape features freely, with or without constraints, apply them to an arbitrary number of model components and of numerous profile types, so as to produce realistic-looking galaxy model images. Yet, despite the potential for extreme complexity, the meaning of the key parameters like the Sersic index, effective radius or luminosity remain intuitive and essentially unchanged. The new features have an interesting potential for use to quantify the degree of asymmetry of galaxies, to quantify low surface brightness tidal features beneath and beyond luminous galaxies, to allow more realistic decompositions of galaxy subcomponents in the presence of strong rings and spiral arms, and to enable ways to gauge the uncertainties when decomposing galaxy subcomponents. We illustrate these new features by way of several case studies that display various levels of complexity.
We report a search for H2O megamasers in 274 SDSS type-2 AGNs (0.3 < z < 0.83), half of which can be classified as type-2 QSOs from their [OIII] 5007 luminosity, using the Robert C. Byrd Green Bank Telescope (GBT) and the Effelsberg 100-m radio telescope. Apart from the detection of the extremely luminous water vapor megamaser SDSS J080430.99+360718.1, already reported by Barvainis & Antonucci (2005), we do not find any additional line emission. This high rate of non-detections is compared to the water maser luminosity function created from the 78 water maser galaxies known to date and its extrapolation towards the higher luminosities of "gigamasers" that we would have been able to detect given the sensitivity of our survey. The properties of the known water masers are summarized and discussed with respect to the nature of high-z type-2 AGNs and megamasers in general. In the appendix, we list 173 additional objects (mainly radio galaxies, but also QSOs and galaxies) that were observed with the GBT, the Effelsberg 100-m radio telescope, or Arecibo Observatory without leading to the detection of water maser emission.
We present a spectral study of the evolution matrix of the totally asymmetric exclusion process on a ring at half filling. The natural symmetries (translation, charge conjugation combined with reflection) predict only two fold degeneracies. However, we have found that degeneracies of higher order also exist and, as the system size increases, higher and higher orders appear. These degeneracies become generic in the limit of very large systems. This behaviour can be explained by the Bethe Ansatz and suggests the presence of hidden symmetries in the model.   Keywords: ASEP, Markov matrix, symmetries, spectral degeneracies, Bethe Ansatz.
We present a new proof of a fundamental result concerning cycles of random permutations which gives some intuition for the connection between Touchard polynomials and the Poisson distribution. We also introduce a rather novel permutation statistic and study its distribution. This quantity, indexed by $m$, is the number of sets of size $m$ fixed by the permutation. This leads to a new and simpler derivation of the exponential generating function for the number of covers of certain multisets.
A residue formula which evaluates any correlation function of topological $SU_n$ Yang-Mills theory with arbitrary magnetic flux insertion in two dimensions are obtained. Deformations of the system by two form operators are investigated in some detail. The method of the diagonalization of a matrix valued field turns out to be useful to compute various physical quantities. As an application we find the operator that contracts a handle of a Riemann surface and a genus recursion relation.
Organic Zener diodes with a precisely adjustable reverse breakdown from -3 V to -15 V without any influence on the forward current-voltage curve are realized. This is accomplished by controlling the width of the charge depletion zone in a pin-diode with an accuracy of one nanometer independently of the doping concentration and the thickness of the intrinsic layer. The breakdown effect with its exponential current voltage behavior and a weak temperature dependence is explained by a tunneling mechanism across the HOMO-LUMO gap of neigh- boring molecules. The experimental data are confirmed by a minimal Hamiltonian model approach, including coherent tunneling and incoherent hopping processes as possible charge transport pathways through the effective device region.
Training deep object detectors requires significant amount of human-annotated images with accurate object labels and bounding box coordinates, which are extremely expensive to acquire. Noisy annotations are much more easily accessible, but they could be detrimental for learning. We address the challenging problem of training object detectors with noisy annotations, where the noise contains a mixture of label noise and bounding box noise. We propose a learning framework which jointly optimizes object labels, bounding box coordinates, and model parameters by performing alternating noise correction and model training. To disentangle label noise and bounding box noise, we propose a two-step noise correction method. The first step performs class-agnostic bounding box correction by minimizing classifier discrepancy and maximizing region objectness. The second step distils knowledge from dual detection heads for soft label correction and class-specific bounding box refinement. We conduct experiments on PASCAL VOC and MS-COCO dataset with both synthetic noise and machine-generated noise. Our method achieves state-of-the-art performance by effectively cleaning both label noise and bounding box noise. Code to reproduce all results will be released.
The mobility of an overdamped particle, in a periodic potential tilted by a constant external field and moving in a medium with periodic friction coefficient is examined. When the potential and the friction coefficient have the same periodicity but have a phase difference, the mobility shows many interesting features as a function of the applied force, the temperature, etc. The mobility shows stochastic resonance even for constant applied force, an issue of much recent interest. The mobility also exhibits a resonance like phenomenon as a function of the field strength and noise induced slowing down of the particle in an appropriate parameter regime.
Nano oils comprising Graphene nanoflakes and CNTs have been experimentally observed for the first time to exhibit augmented dielectric breakdown strengths compared to the base transformer oils. Variant nano oils comprising different Gr and CNT samples suspended in two different grades of transformer oils have yielded consistent and high degrees of enhancement in the breakdown strength. The apparent counter intuitive phenomenon of enhancing insulating caliber of fluids utilizing nanostructures of high electronic conductance has been shown to be physically consistent thorough theoretical analysis. The crux mechanism has been pin pointed as efficient charge scavenging leading to hampered streamer growth and development, thereby delaying probability of complete ionization. The mathematical analysis presented provides a comprehensive picture of the mechanisms and physics of the electrohydrodynamics involved in the phenomena of enhanced breakdown strengths. Furthermore, the analysis is able to physically explain the various breakdown characteristics observed as functions of system parameters, such as, nanostructure type, size distribution, relative permittivity, base fluid dielectric properties, nanomaterial concentration and nano oil temperature. The mathematical analyses have been extended to propose a physically and dimensionally consistent analytical model to predict the enhanced breakdown strengths of such nano oils from involved constituent material properties and characteristics. The model has been observed to accurately predict the augmented insulating property, thereby rendering it as an extremely useful tool for efficient design and prediction of breakdown characteristics of nanostructure infused insulating fluids.
Context. Stars can maintain their observable magnetic activity from the PMS to the tip of the red giant branch. However, the number of known active giants is much lower than active stars on the main sequence since on the giant branch the stars spend only about 10% of their main sequence lifetime. Due to their rapid evolution it is difficult to estimate the stellar parameters of giant stars. A possibility for obtaining more reliable stellar parameters of an active giant arises when it is a member of an eclipsing binary system.   Aims. We have discovered EPIC 211759736, an active spotted giant star in an eclipsing binary system during the Kepler K2 Campaign 5. The eclipsing nature allows us to much better constrain the stellar parameters than in most cases of active giant stars. Method. We have combined the K2 data with archival HATNet and DASCH photometry, new spectroscopic radial velocity measurements, and a set of follow-up ground-based BVRI photometric observations, to find the binary system parameters as well as robust spot models for the giant at two different epochs.   Results. We determined the physical parameters of both stellar components and provide a description of the rotational and long-term activity of the primary component. The temperatures and luminosities of both components were examined in the context of the HR diagram. We find that both the primary and the secondary components deviate from the evolutionary tracks corresponding to their masses in the sense that the stars appear in the diagram at lower masses than their true masses.   Conclusions. We further evaluate the proposition that active giants have masses that are found to be generally higher by traditional methods than are indicated by stellar evolution tracks in the HR diagram. A possible reason for this discrepancy could be a strong magnetic field, since we see greater differences in more active stars.
Active regions are the source of the majority of magnetic flux rope ejections that become Coronal Mass Ejections (CMEs). To identify in advance which active regions will produce an ejection is key for both space weather prediction tools and future science missions such as Solar Orbiter. The aim of this study is to develop a new technique to identify which active regions are more likely to generate magnetic flux rope ejections. The new technique will aim to: (i) produce timely space weather warnings and (ii) open the way to a qualified selection of observational targets for space-borne instruments. We use a data-driven Non-linear Force-Free Field (NLFFF) model to describe the 3D evolution of the magnetic field of a set of active regions. We determine a metric to distinguish eruptive from non-eruptive active regions based on the Lorentz force. Furthermore, using a subset of the observed magnetograms, we run a series of simulations to test whether the time evolution of the metric can be predicted. The identified metric successfully differentiates active regions observed to produce eruptions from the non-eruptive ones in our data sample. A meaningful prediction of the metric can be made between 6 to 16 hours in advance. This initial study presents an interesting first step in the prediction of CME onset using only LOS magnetogram observations combined with NLFFF modelling. Future studies will address how to generalise the model such that it can be used in a more operational sense and for a variety of simulation approaches.
We present the spatially resolved star formation history (SFH) of the Carina dwarf spheroidal galaxy, obtained from deep, wide-field g,r imaging and a metallicity distribution from the literature. Our photometry covers $\sim2$ deg$^2$, reaching up to $\sim10$ times the half-light radius of Carina with a completeness higher than $50\%$ at $g\sim24.5$, more than one magnitude fainter than the oldest turnoff. This is the first time a combination of depth and coverage of this quality has been used to derive the SFH of Carina, enabling us to trace its different populations with unprecedented accuracy. We find that Carina's SFH consists of two episodes well separated by a star formation temporal gap. These episodes occurred at old ($>10$ Gyr) and intermediate ($2$-$8$ Gyr) ages. Our measurements show that the old episode comprises the majority of the population, accounting for $54\pm5\%$ of the stellar mass within $1.3$ times the King tidal radius, while the total stellar mass derived for Carina is $1.60\pm0.09\times 10^{6} M_{\rm{\odot}}$, and the stellar mass-to-light ratio $1.8\pm0.2$. The SFH derived is consistent with no recent star formation which hints that the observed blue plume is due to blue stragglers. We conclude that the SFH of Carina evolved independently of the tidal field of the Milky Way, since the frequency and duration of its star formation events do not correlate with its orbital parameters. This result is supported by the age/metallicity relation observed in Carina, and the gradients calculated indicating that outer regions are older and more metal poor.
Contextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck's constant, $\hbar$, can also be used to characterize the classical-quantum divide by expanding quantities of interest in powers of $\hbar$---all orders higher than $\hbar^0$ can be interpreted as quantum corrections to the order $\hbar^0$ term. We show that contextual measurements in finite-dimensional systems have formulations within the Wigner-Weyl-Moyal (WWM) formalism that require higher than order $\hbar^0$ terms to be included in order to violate the classical bounds on their expectation values. As a result, we show that contextuality as a resource is equivalent to orders of $\hbar$ as a resource within the WWM formalism. This explains why qubits can only exhibit state-independent contextuality under Pauli observables as in the Peres-Mermin square while odd-dimensional qudits can also exhibit state-dependent contextuality. In particular, we find that qubit Pauli observables lack an order $\hbar^0$ contribution in their Weyl symbol and so exhibit contextuality regardless of the state being measured. On the other hand, odd-dimensional qudit observables generally possess non-zero order $\hbar^0$ terms, and higher, in their WWM formulation, and so exhibit contextuality depending on the state measured: odd-dimensional qudit states that exhibit measurement contextuality have an order $\hbar^1$ contribution that allows for the violation of classical bounds while states that do not exhibit measurement contextuality have insufficiently large order $\hbar^1$ contributions.
Electronic structure descriptors are computationally efficient quantities used to construct qualitative correlations for a variety of properties. In particular, the oxygen p-band center has been used to guide material discovery and fundamental understanding of an array of perovskite compounds for use in catalyzing the oxygen reduction and evolution reactions. However, an assessment of the effectiveness of the oxygen p-band center at predicting key measures of perovskite catalytic activity has not been made, and would be highly beneficial to guide future predictions and codify best practices. Here, we have used Density Functional Theory at the PBE, PBEsol, PBE+U, SCAN and HSE06 levels to assess the correlations of numerous measures of catalytic performance for a series of technologically relevant perovskite oxides, using the bulk oxygen p-band center as an electronic structure descriptor. We have analyzed correlations of the calculated oxygen p-band center for all considered functionals with the experimentally measured X-ray emission spectroscopy oxygen p-band center and multiple measures of catalytic activity, including high temperature oxygen reduction surface exchange rates, aqueous oxygen evolution current densities, and binding energies of oxygen evolution intermediate species. Our results show that the best correlations for all measures of catalytic activity considered here are made with PBE-level calculations, with strong observed linear correlations with the bulk oxygen p-band center (R2 = 0.81-0.87). This study shows that strong linear correlations between numerous important measures of catalytic activity and the oxygen p-band bulk descriptor can be obtained under a consistent computational framework, and these correlations can serve as a guide for future experiments and simulations for development of perovskite and related oxide catalysts.
Defects usually play an important role in tuning and modifying various properties of semiconducting or insulating materials. Therefore we study the impact of point and line defects on the electronic structure and optical properties of MoS2 monolayers using density-functional methods. The different types of defects form electronic states that are spatially localized on the defect. The strongly localized nature is reflected in weak electronic interactions between individual point or line defect and a weak dependence of the defect formation energy on the defect concentration or line defect separation. In the electronic energy spectrum the defect states occur as deep levels in the band gap, as shallow levels very close to the band edges, as well as levels in-between the bulk states. Due to their strongly localized nature, all states of point defects are sharply peaked in energy. Periodic line defects form nearly dispersionless one-dimensional band structures and the related spectral features are also strongly peaked. The electronic structure of the monolayer system is quite robust and it is well preserved for point defect concentrations of up to 6%. The impact of point defects on the optical absorption for concentrations of 1% and below is found to be very small. For higher defect concentrations molybdenum vacancies were found to quench the overall absorption and sulfur defects lead to sharp absorption peaks below the absorption edge of the ideal monolayer. For line defects, we did not find a considerable impact on the absorption spectrum. These results support recent experiments on defective transition metal chalcogenides.
We propose a numerical method which embeds the variational non-Gaussian wavefunction approach within exact diagonalization, allowing for efficient treatment of correlated systems with both electron-electron and electron-phonon interactions. Using a generalized polaron transformation, we construct a variational wavefunction that absorbs entanglement between electrons and phonons into a variational non-Gaussian transformation; exact diagonalization is then used to treat the electronic part of the wavefunction exactly, thus taking into account high-order correlation effects beyond the Gaussian level. Keeping the full electronic Hilbert space, the complexity is increased only by a polynomial scaling factor relative to the exact diagonalization calculation for pure electrons. As an example, we use this method to study ground-state properties of the two-dimensional Hubbard-Holstein model, providing evidence for the existence of intervening phases between the spin and charge-ordered states. In particular, we find one of the intervening phases has strong charge susceptibility and binding energy, but is distinct from a charge-density-wave ordered state, while the other intervening phase displays superconductivity at weak couplings. This method, as a general framework, can be extended to treat excited states and dynamics, as well as a wide range of systems with both electron-electron and electron-boson interactions.
A systematic derivation of Boltzmann equation is presented in the framework of closed-time-path formalism. Introducing a new type of probe, the expectation value of number operator is calculated as a functional of source. Then solving for the source by inverting the relation, the equation of motion for number is obtained when the source is removed, and it turns out to be the Boltzmann equation. The inversion formula is used in the course of derivation.
We investigate the non-linear evolution of spherical density and velocity perturbations of dark matter and dark energy in the expanding Universe. For that we have used the conservation and Einstein equations to describe the evolution of gravitationally coupled inhomogeneities of dark matter, dark energy and radiation from linear stage in the early Universe to the non-linear one at the current epoch. The simple method of the numerical integration of the system of non-linear differential equations for evolution of the central part of halo is proposed. The results are presented for halo of cluster ($k=2$ Mpc$^{-1}$) and supercluster scales ($k=0.2$ Mpc$^{-1}$) and show that quintessential scalar field dark energy with small value of effective speed of sound $c_s<0.1$ can give noticeable impact on the formation of large scale structures in the expanding Universe.
We study theoretically the electron transport properties in carbon nanotubes under the influence of an external electric field E(t) using Boltzmann's equation. The current-density equation is derived. Negative differential conductivity is predicted when {\omega}{\tau}<<1 (quasi-static case). We observed this in the neighbourhood where the constant electric field E_o is equal to the amplitude of the AC electric field E_1 and the peak decreases with increasing E_1. This phenomenon can also be used for the generation of terahertz radiation without electric current instability.