Miracle-dz/UniFAR-FTUs huggingface dataset:
Ergodic Theorems for Polynomials in Nilpotent Groups

The principal results proved in this expository thesis are the IP polynomial Szemer\'edi theorem for nilpotent groups and the multiple term return times theorem with nilsequence weights. It also contains extensions of the convergence theorem for nilpotent polynomial multiple ergodic averages and the return times theorem to locally compact second countable amenable groups.
Using Deep Learning for Emotion Analysis of 18th and 19th Century German Plays

We present first results of the project “Emotions in Drama” in which we explore the annotation of emotions and the application of computational emotion analysis, predominantly deep learning-based methods, in the context of historical German plays of the time around 1800. We performed a pilot annotation study with five plays generating over 6,500 annotations for up to 13 sub-emotions structured in a hierarchical scheme. This emotion scheme includes common types like joy , anger or hate but also concepts that are specifically important for German literary criticism of this period like friend-ship , compassion or Schadenfreude . We evaluate the performance of various methods of emotion-based text sequence classification including lexicon-based methods, traditional machine learning, fastText as static word embedding, various transformer models based on BERT - or ELECTRA -architectures and pretrained with contemporary language, transformer-based methods pretrained or finetuned for historical and/or poetic language as well as the finetuning of BERT models via our own corpora and plays. We do achieve state-of-the-art results with hierarchical levels with two or three classes, i. e. the classification of valence (positive/negative). The best models are the transformer-based models gbert-large and gelectra-large by deepset pretrained on large corpora of contemporary German, which achieve accuracy values of up to 83%. Lexicon-based methods, traditional machine learning as well as static word embeddings are consistently outper-formed by transformer-based models. Models trained on historical texts show small and inconsistent improvements. The performance becomes significantly smaller for settings with multiple sub-emotions like 6 or 13 due to the general challenge and class imbalances in which the models achieve 57% and 47% respectively. We discuss how we intend to continue our annotations and how to improve the prediction results via various optimization techniques in future work.
UNTANGLING THE RECOMBINATION LINE EMISSION FROM H ii REGIONS WITH MULTIPLE VELOCITY COMPONENTS

H ii regions are the ionized spheres surrounding high-mass stars. They are ideal targets for tracing Galactic structure because they are predominantly found in spiral arms and have high luminosities at infrared and radio wavelengths. In the Green Bank Telescope H ii Region Discovery Survey (GBT HRDS), we found that > 30 % ? > of first Galactic quadrant H ii regions have multiple hydrogen radio recombination line (RRL) velocities, which makes determining their Galactic locations and physical properties impossible. Here we make additional GBT RRL observations to determine the discrete H ii region velocity for all 117 multiple-velocity sources within 18 ° < ℓ < 65 ° ? > . The multiple-velocity sources are concentrated in the zone 22 ° < ℓ < 32 ° ? > , coinciding with the largest regions of massive star formation, which implies that the diffuse emission is caused by leaked ionizing photons. We combine our observations with analyses of the electron temperature, molecular gas, and carbon recombination lines to determine the source velocities for 103 discrete H ii regions ( 88 % ? > of the sample). With the source velocities known, we resolve the kinematic distance ambiguity for 47 regions, and thus determine their heliocentric distances.
Discovery of a new Wolf-Rayet star and a candidate star cluster in the Large Magellanic Cloud with Spitzer

We report the first-ever discovery of a Wolf-Rayet (WR) star in the Large Magellanic Cloud via detection of a circular shell with the Spitzer Space Telescope. Follow-up observations with Gemini-South resolved the central star of the shell into two components separated from each other by a parts per thousand 2 arcsec (or a parts per thousand 0.5 pc in projection). One of these components turns out to be a WN3 star with H and He lines both in emission and absorption (we named it BAT99 3a using the numbering system based on extending the Breysacher et al. catalogue). Spectroscopy of the second component showed that it is a B0 V star. Subsequent spectroscopic observations of BAT99 3a with the du Pont 2.5-m telescope and the Southern African Large Telescope revealed that it is a close, eccentric binary system, and that the absorption lines are associated with an O companion star. We analysed the spectrum of the binary system using the non-LTE Potsdam WR (powr) code, confirming that the WR component is a very hot (a parts per thousand 90 kK) WN star. For this star, we derived a luminosity of log L/ L-aS (TM) = 5.45 and a mass-loss rate of 10(- 5.8) M-aS (TM) yr(- 1), and found that the stellar wind composition is dominated by helium with 20 per cent of hydrogen. Spectroscopy of the shell revealed an He iii region centred on BAT99 3a and having the same angular radius (a parts per thousand 15 arcsec) as the shell. We thereby add a new example to a rare class of high-excitation nebulae photoionized by WR stars. Analysis of the nebular spectrum showed that the shell is composed of unprocessed material, implying that the shell was swept-up from the local interstellar medium. We discuss the physical relationship between the newly identified massive stars and their possible membership of a previously unrecognized star cluster.
The Ubiquity of Supermassive Black Holes in the Hubble Sequence

We present the results of a study of a statistically significant sample of galaxies which clearly demonstrate that supermassive black holes are generically present in all morphological types. Our analysis is based on the quantitative morphological classification of 1.12 million galaxies in the SDSS DR7 and on the detection of black hole activity via two different methods, the first one based on their X-ray/radio emission and the second one based on their mid-infrared colors. The results of the first analysis confirm the correlation between black hole and total stellar mass for 8 galaxies and includes one galaxy classified as bulgeless. The results of our second analysis, consisting of 15,991 galaxies, show that galaxies hosting a supermassive black hole follow the same morphological distribution as the general population of galaxies in the same redshift range. In particular, the fraction of bulgeless galaxies, 1,450 galaxies or 9 percent, is found to be the same as in the general population. We also present the correlation between black hole and total stellar mass for 6,247 of these galaxies. Importantly, whereas previous studies were limited to primarily bulge-dominated systems, our study confirms this relationship to all morphological types, in particular, to 530 bulgeless galaxies. Our results indicate that the true correlation that exists for supermassive black holes and their host galaxies is between the black hole mass and the total stellar mass of the galaxy and hence, we conclude that the previous assumption that the black hole mass is correlated with the bulge mass is only approximately correct.
MAGNETIC ACTIVITY CYCLES IN THE EXOPLANET HOST STAR ϵ ERIDANI

The active K2 dwarf ϵ Eri has been extensively characterized both as a young solar analog and more recently as an exoplanet host star. As one of the nearest and brightest stars in the sky, it provides an unparalleled opportunity to constrain stellar dynamo theory beyond the Sun. We confirm and document the 3-year magnetic activity cycle in ϵ Eri originally reported by Hatzes and coworkers, and we examine the archival data from previous observations spanning 45 years. The data show coexisting 3-year and 13-year periods leading into a broad activity minimum that resembles a Maunder minimum-like state, followed by the resurgence of a coherent 3-year cycle. The nearly continuous activity record suggests the simultaneous operation of two stellar dynamos with cycle periods of 2.95 ± 0.03 years and 12.7 ± 0.3 years, which, by analogy with the solar case, suggests a revised identification of the dynamo mechanisms that are responsible for the so-called “active” and “inactive” sequences as proposed by Böhm-Vitense. Finally, based on the observed properties of ϵ Eri, we argue that the rotational history of the Sun is what makes it an outlier in the context of magnetic cycles observed in other stars (as also suggested by its Li depletion), and that a Jovian-mass companion cannot be the universal explanation for the solar peculiarities.
On the Benjamin–Lighthill conjecture for water waves with vorticity

We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an inviscid, incompressible fluid (say, water). The water motion is supposed to be rotational with a Lipschitz continuous vorticity distribution, whereas the flow of finite depth is assumed to be unidirectional. We verify the Benjamin–Lighthill conjecture for flows with values of Bernoulli’s constant close to the critical one. For this purpose it is shown that a set of near-critical waves consists only of Stokes and solitary waves provided their slopes are bounded by a constant. Moreover, the subset of waves with crests located on a fixed vertical is uniquely parametrised by the flow force, which varies between its values for the supercritical and subcritical shear flows of constant depth. There exists another parametrisation for this set; it involves wave heights varying between the constant depth of the subcritical shear flow and the height of a solitary wave.
TeV Gamma-Ray Observations of Mrk421 and H1426+428 with TACTIC Imaging Telescope

We have observed extragalactic sources Mrk421 (z=0.30) and H1426+428 (z=0.129) in very high energy gamma region using TACTIC telescope at Mount Abu, Rajasthan, India. Mrk421 was observed during 07 December 2005 to 18 April 2007 for a total of ~331hours while H1426+428 was observed for ~244 hours between 22 March 2004 and 11 June 2007. Detailed analysis of Mrk421 data revealed the presence of a gamma signal with the excess of (~951\pm 82) gamma like events corresponding to a statistical significance of ~12.0 \sigma in ~97 hours during 27 December 2005 to 07 February 2006. The combined average flux was measured to be ~(1.04\pm0.14) Crab units. Observed time averaged differential energy spectrum was found to be consistent with both a pure power law $d\Phi/dE=(4.66\pm0.46)\times 10^{-11}\,E^{(-3.11\pm0.11)}\,\,cm^{-2}\,s^{-1}\,TeV^{-1}$ and power law with an exponential cutoff functions $d\Phi/dE=f_0E^{-\Gamma}exp(-E/E_0)$ with $f_0=(4.88\pm0.38)\times10^{-11}\,cm^{-2}\,s^{-1}\,TeV^{-1}$, $\Gamma=2.51\pm0.26$ and $E_0=(4.7\pm2.1)TeV$. The later function fits the observed spectrum well with lower value of reduced $\chi^2$. However, during the observation period from 18 December 2006 to 18 April 2007, the source was found to be in a low emission state and we have placed an upper limit of $1.44\times\,10^{-12}\,photons\,cm^{-2}\,s^{-1}$ at $3\sigma$ level on the integrated \gam flux above $1\,TeV$. Detailed analysis of H1426+428 data does not indicate the presence of any statistically significant $TeV$ \gam signal. Accordingly we have placed an upper limit of $\leq1.18\times10^{-12}\,photons\,cm^{-2}\,s^{-1}$ on the integrated $\gamma$-ray flux above $1\,TeV$ at 3$\sigma$ significance level.
Mass–metallicity relation from z = 5 to the present: evidence for a transition in the mode of galaxy growth at z = 2.6 due to the end of sustained primordial gas infall

We analyze the redshift evolution of the mass-metallicity relation in a sample of 110 Damped Ly$\alpha$ absorbers spanning the redshift range $z=0.11-5.06$ and find that the zero-point of the correlation changes significantly with redshift. The evolution is such that the zero-point is constant at the early phases of galaxy growth (i.e. no evolution) but then features a sharp break at $z=2.6\pm 0.2$ with a rapid incline towards lower redshifts such that damped absorbers of identical masses are more metal rich at later times than earlier. The slope of this mass metallicity correlation evolution is $0.35 \pm 0.07$ dex per unit redshift. We compare this result to similar studies of the redshift evolution of emission selected galaxy samples and find a remarkable agreement with the slope of the evolution of galaxies of stellar mass log$(M_{*}/M_\odot) \approx 8.5$. This allows us to form an observational tie between damped absorbers and galaxies seen in emission. We use results from simulations to infer the virial mass of the dark matter halo of a typical DLA galaxy and find a ratio $(M_{vir}/M_{*}) \approx 30$. We compare our results to those of several other studies that have reported strong transition-like events at redshifts around $z=2.5-2.6$ and argue that all those observations can be understood as the consequence of a transition from a situation where galaxies were fed more unprocessed infalling gas than they could easily consume to one where they suddenly become infall starved and turn to mainly processing, or re-processing, of previously acquired gas.
Evidence of reduced surface electron-phonon scattering in the conduction band of Bi 2 Se 3 by nonequilibrium ARPES

The nature of the Dirac quasiparticles in topological insulators calls for a direct investigation of the electron-phonon scattering at the surface. By comparing time-resolved ARPES measurements of the topological insulator Bi2Se3 with different probing depths, we show that the relaxation dynamics of the electronic temperature of the conduction band is much slower at the surface than in the bulk. This observation suggests that surface phonons are less effective in cooling the electron gas in the conduction band.
Feeding compact bulges and supermassive black holes with low angular momentum cosmic gas at high redshift

We use cosmological hydrodynamical simulations to show that a significant fraction of the gas in high redshift rare massive haloes falls nearly radially to their very centre on extremely short time-scales. This process results in the formation of very compact bulges with specific angular momentum a factor of 5–30 smaller than the average angular momentum of the baryons in the whole halo. Such low angular momentum originates from both segregation and effective cancellation when the gas flows to the centre of the halo along well-defined cold filamentary streams. These filaments penetrate deep inside the halo and connect to the bulge from multiple rapidly changing directions. Structures falling in along the filaments (satellite galaxies) or formed by gravitational instabilities triggered by the inflow (star clusters) further reduce the angular momentum of the gas in the bulge. Finally, the fraction of gas radially falling to the centre appears to increase with the mass of the halo; we argue that this is most likely due to an enhanced cancellation of angular momentum in rarer haloes which are fed by more isotropically distributed cold streams. Such an increasingly efficient funnelling of low angular momentum gas to the centre of very massive haloes at high redshift may account for the rapid pace at which the most massive supermassive black holes grow to reach observed masses around 109 M⊙ at an epoch when the Universe is barely 1 Gyr old.
Silver and Silver Nanoparticles for the Potential Treatment of COVID-19: A Review

COVID-19 is an epizootic and life-threatening outbreak affecting millions of people globally. Coronavirus variants have emerged in different locations since their origin. Silver and its compounds, including silver nanoparticles (AgNPs), have been used in the medical field for a long period, especially in surgical treatments. The anti-microbial and anti-viral properties of silver are well documented. These properties depend on the size of the particles, concentration, precursor, method of preparation, and the presence of other benefiting compounds. Several experiments were conducted by researchers worldwide to prove the anti-bacterial and anti-viral properties of silver (Ag) and AgNPs, emphasizing that silver can be introduced to multiple organs in the human body and exhibit the expected antiviral characteristics. In this review article, use of silver nanoparticles to fight the COVID-19 pandemic according with the current information is discussed. The mechanisms involving antiviral activity and toxicity are discussed in detail. This article concludes that strong binding of AgNPs with SARS-CoV-2 virus prevents binding with the host cell, leading to the death of the virus. However, increased cytotoxic effect of the silver compounds at higher concentrations is a matter of concern.
Cyber Operations RangE [CORE]: Containerized Gaming Platform for Cyberoperations Competitions

Cybersecurity gaming is popularized through capture-the-flag (CTF) competitions, war games, and forensic challenges. Providing actual hands-on experience, the cybersecurity competitions have great potential to support classroom learning, professional skill development, and scenario testing. To capitalize this, the supporting gaming platforms need to overcome the following issues: i) A complex virtualized infrastructure that requires extensive resources and administration, ii) Lack of support for real-time cyberoperations within a competition environment, and iii) implementation of independent, real-time scoring system which tracks progress and determines results of the competitors. In response to these issues, we have developed Cyber Operations RangE (CORE) - a containerized cybersecurity gaming platform. This paper presents the design, implementation, and the application of the CORE platform for real-time cyberoperations competitions.
Burnout syndrome, anxiety, depression and occupational well-being among Peru hospital staff during the COVID-19 pandemic

Introduction: The COVID-19 pandemic has had serious consequences for the mental health of individuals, especially health care providers, who have experienced symptoms of stress, anxiety and depression that affect their personal, family and social lives. This situation has led health entities to evaluate the negative effects and to design interventions. Objective: To establish the relationship between burnout syndrome, anxiety, depression and work well-being, considering sociodemographic and work variables, including differences according to the type Results: The results indicated multiple relationships among burnout syndrome, anxiety, depression and work well-being (p <0.05). Likewise, these relationships were also presented considering some sociodemographic and labor variables (p <0.05). Conclusions: The variables studied have a significant relationship in the health care personnel examined. Based on these findings, it is possible to have a baseline of the mental health of health personnel to plan interventions that emphasize those variables and groups at risk that require special attention.
Anisotropic inflation reexamined: upper bound on broken rotational invariance during inflation

The presence of a light vector field coupled to a scalar field during inflation makes a distinct prediction: the observed correlation functions of the cosmic microwave background (CMB) become statistically anisotropic. We study the implications of the current bound on statistical anisotropy derived from the Planck 2013 CMB temperature data for such a model. The previous calculations based on the attractor solution indicate that the magnitude of anisotropy in the power spectrum is proportional to N2, where N is the number of e-folds of inflation counted from the end of inflation. In this paper, we show that the attractor solution is not necessarily compatible with the current bound, and derive new predictions using another branch of anisotropic inflation. In addition, we improve upon the calculation of the mode function of perturbations by including the leading-order slow-roll corrections. We find that the anisotropy is roughly proportional to [2(εH+4ηH)/3−4(c−1)]−2, where εH and ηH are the usual slow-roll parameters and c is the parameter in the model, regardless of the form of potential of an inflaton field. The bound from Planck implies that breaking of rotational invariance during inflation (characterized by the background homogeneous shear divided by the Hubble rate) is limited to be less than 𝒪(10−9). This bound is many orders of magnitude smaller than the amplitude of breaking of time translation invariance, which is observed to be 𝒪(10−2).
Numerical solution of the incompressible ﬂow using a domain decomposition method

The Ph.D. thesis is devoted to numerical simulations of the Navier-Stokes (N-S) equations for stationary incompressible ﬂow using Balancing Domain Decomposition by Constraints (BDDC) method. The Finite Element Method (FEM) is used for the discretization of the N-S equations. In the thesis, the multilevel BDDC method is introduced which is suitable for solving the large system of linear algebraic equations. This method and its theory are well known for the Poisson problem, for linear elasticity, and ﬂow problems described by Stokes equations. The thesis is devoted to an extension of the multilevel BDDC method to the nonsymmetric problem arising from the discretization of the N-S equations. The weights operators for this form of the BDDC method are discussed including my own one based on an upwind scheme suitable for ﬂow problems. Next, my geometric partitioner is presented which is suitable for these problems, especially for problems with dimensionally complex geometry. All new approaches presented are diﬀerent oil inside hydrostatic bearing.
Affine embeddings of Cantor sets and dimension of $\alpha\beta$-sets

Let $E, F\subset {\Bbb R}^d$ be two self-similar sets, and suppose that $F$ can be affinely embedded into $E$. Under the assumption that $E$ is dust-like and has a small Hausdorff dimension, we prove the logarithmic commensurability between the contraction ratios of $E$ and $F$. This gives a partial affirmative answer to Conjecture 1.2 in \cite{FHR14}. The proof is based on our study of the box-counting dimension of a class of multi-rotation invariant sets on the unit circle, including the $\alpha\beta$-sets initially studied by Engelking and Katznelson.
Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers

In this paper, we study the relation between topological orders and their gapped boundaries. We propose that the bulk for a given gapped boundary theory is unique. It is actually a consequence of a microscopic definition of a local topological order, which is a (potentially anomalous) topological order defined on an open disk. Using this uniqueness, we show that the notion of "bulk" is equivalent to the notion of center in mathematics. We achieve this by first introducing the notion of a morphism between two local topological orders of the same dimension, then proving that the bulk satisfying the same universal property as that of the center in mathematics. We propose a classification (formulated as a macroscopic definition) of $n+$1D local topological orders by unitary multi-fusion $n$-categories, and explain that the notion of a morphism between two local topological orders is compatible with that of a unitary monoidal $n$-functor in a few low dimensional cases. We also explain in some low dimensional cases that this classification is compatible with the result of "bulk = center". In the end, we explain that above boundary-bulk relation is only the first layer of a hierarchical structure which can be summarized by the functoriality of the bulk (or center). This functoriality also provides the physical meanings of some well-known mathematical results on fusion 1-categories. This work can also be viewed as the first step towards a systematic study of the category of local topological orders, and the boundary-bulk relation actually provides a useful tool for this study.