Miracle-dz/UniFAR-FTUs huggingface dataset:
E(K/k) and other arithmetical invariants for finite Galois extensions

Let k be an algebraic number field and K be a finite extension of k. Recently, T. Ono defined positive rational numbers E(K/k) and E′(K/k) for K/k. In [7], he investigated some relations between E(K/k) and other cohomological invariants for K/k. He obtained a formula when K is a normal extension of k. In our paper [3], we obtained a similar formula for E′(K/k) in the case of normal extensions K/k. Both proofs essentially use Ono’s results on the Tamagawa number of algebraic tori, on which the formulae themselves do not depend. Hence, in [8], T. Ono posed a problem to give direct proofs of these formulae.
Myocardial Infarction-Induced INSL6 Decrease Contributes to Breast Cancer Progression

Myocardial infarction (MI) induces early-stage breast cancer progression and increases breast cancer patients' mortality and morbidity. Insulin-like peptide 6 (INSL6) overexpression can impede cardiotoxin-induced injury through myofiber regeneration, playing a significant role in MI progression. To investigate the diverse significance of INSL6 in a variety of malignant tumors, we explored INSL6 through MI GEO dataset and multiple omics data integrative analysis, such as gene expression level, enriched pathway analysis, protein-protein interaction (PPI) analysis, and immune subtypes as well as diagnostic value and prognostic value in pancancer. INSL6 expression was downregulated in the MI group, and overall survival analysis demonstrated that INSL6 could be the prognostic biomarkers in the overall survival of breast cancer (BRCA). INSL6 expression differs significantly not only in most cancers but also in different molecular and immune subtypes of cancers. INSL6 might be a potential diagnostic and prognostic biomarker of cancers due to the high accuracy in diagnostic and prognostic value. Furthermore, we focused on BRCA and further investigated INSL6 from the perspective of the correlations with clinical characteristics, prognosis in different clinical subgroups, coexpression genes, and differentially expressed genes (DEGs) and PPI analysis. Overall survival and disease-specific survival analysis of subgroups in BRCA demonstrated that lower INSL6 expression had a worse prognosis. Therefore, INSL6 aberrant expression is associated with the progression and immune cell infiltration of the tumor, especially in KIRP and BRCA. Therefore, INSL6 may serve as a potential prognostic biomarker and the crosstalk between MI and tumor progression.
Subsampling quantile estimators and uniformity criteria

Several asymptotically equivalent quantile estimators recently have been proposed as alternative to the conventional sample quantile. A variety of weight functions have been obtained either by subsampling considerations or by a kernel approach, analogous to density estimation techniques. Focusing on the former approach, a unified treatment of quantile estimators derived by subsampling is developed. Closely related to the generalized Harrell-Davis (HD) and Kaigh-Lachenbruch (KL) estimators, a new statistic performed well in Monte Carlo effiency comparisons presented here. Moreover, the new estimator shares certain desirable computational and finite-sample theeoretical properties with the KL estimator to yield convenient components representations for tests of uniformity and goodness-of-fit criteria. Similar analytic treatment for the HD statistics and kernel quantile estimators, however, is precluded by intractable eigenvalue problems.
Motion of Two Point Vortices in a Circular Domain

Motion of point vortices in a circular domain is studied. Especially the case of two vortices with equal strength is presented. The motion is described by a Hamiltonian as well as when they are in an infinite region. Though the system is integrable in the sense of Liouville, there is a wide variety of motion according to initial conditions. Classification of the motion can be made by considering two integrals and two parameters.
Interstellar gas, dust and diffuse bands in the SMC

Aims. In order to gain new insight into the unidentified identity of the diffuse interstellar band (DIB) carriers, this paper describes research into possible links between the shape of the interstellar extinction curve (including the 2175 A bump and far-UV rise), the presence or absence of DIBs, and physical and chemical conditions of the diffuse interstellar medium (gas and dust) in the Small Magellanic Cloud (SMC). Methods. We searched for DIB absorption features in VLT/UVES spectra of early-type stars in the SMC whose reddened lines-ofsight probe the diffuse interstellar medium of the SMC. Apparent column density profiles of interstellar atomic species (Na i ,K i ,C aii and Ti ii) are constructed to provide information on the distribution and conditions of the interstellar gas. Results. The characteristics of eight DIBs detected toward the SMC wing target AzV 456 are studied and upper limits are derived for the DIB equivalent widths toward the SMC stars AzV 398, AzV 214, AzV 18, AzV 65 and Sk 191. The amount of reddening is derived for these SMC sightlines, and, using RV and the H i column density, converted into a gas-to-dust ratio. From the atomic column density ratios we infer an indication of the strength of the interstellar radiation field, the titanium depletion level and a relative measure of turbulence/quiescence. The presence or absence of DIBs appears to be related to the shape of the extinction curve, in particular with respect to the presence or absence of the 2175 A feature. Our measurements indicate that the DIB characteristics depend on the local physical conditions and chemical composition of the interstellar medium of the SMC, which apparently determine the rate of formation (and/or) destruction of the DIB carriers. The UV radiation field (via photoionisation and photo-destruction) and the metallicity (i.e. carbon abundance) are important factors in determining diffuse band strengths which can differ greatly both between and within galaxies.
Cainozoic evolution of the state of stress and style of tectonism of the Basin and Range province of the western United States

Cainozoic evolution of the modern plate boundary along the western United States from subduction to a predominantly transform boundary coincided with a change from compressional to extensional deformation in the western United States. Extensions tectonism responsible for the modern Basin and Range province appears to represent a unique late-stage episode of a much longer period of extension initiated in an ‘in tra -arc ’ setting contemporaneously with calc-alkaline magmatism. Basin-range extension is distinguished from early extension on the basis of angular unconformities, differences in fault trends and spacing, and associated magmatism (basaltic). Prebasin-range extension (i.e. extension preceding the break-up of the region into ranges resembling the modern ones) was under way locally by at least 30 Ma and is now recognized by faulted and highly tilted strata exposed in uplifted range blocks, by large regions of the crust underlain by passively emplaced subvolcanic batholiths, and by the thickness and distribution of stratigraphic units. Locally, high strain rates that accompanied early extensions of as much as 50-100 % are implied. Data on preferentially orientated dyke swarms and fault slip vectors indicate a strikingly uniform WSW -ENE least principal stress orientation in the period ca. 20-10 Ma, during this early extension. The change from early extension to basin-range style faulting of the upper 15 km of crust, which resulted in broadly spaced ranges (25-35 km crest-crest spacing), was time-transgressive and probably not abrupt; locally both types occurred concurrently. Southern Basin and Range block faulting occurred largely in the period 13-10 Ma, in response to a stress field orientated similarly to that responsible for the early extension. In contrast, northern Basin and Range block faulting developed after 10 Ma and continues to the present in response to a stress field orientated approximately 45° clockwise to the earlier stress field. This modern stress field, with a WNW -ESE to E-W directed least principal stress, characterizes the entire modern Basin and Range province and Rio Grande rift region. The 45° change in least principal stress orientation is consistent with superposition of dextral shear associated with the development of the San Andreas transform fault. Inclusion of pre-basin-range extension may help resolve the discrepancy between estimates of 15-30% for basin-range block faulting and total extension estimates of 100-300 % for the Basin and Range province.
FOIST: Fluid–object interaction subcomputation technique

Our target is to develop computational techniques for studying aerodynamic interactions between multiple objects. The computational challenge is to predict the dynamic behavior and path of the object, so that separation (the process of objects relatively falling or moving away from each other) is safe and effective. This is a very complex problem because it has an unsteady, 3D nature and requires the solution of complex equations that govern the fluid dynamics (FD) of the object and the aircraft together, with their relative positions changing in time. Large-scale 3D FD simulations require a high computational cost. Not only must one solve the time-dependent Navier–Stokes equations governing the fluid flow, but also one must handle the equations of motion of the object as well as the treatment of the moving domain usually treated as a type of pseudo-solid. These costs include mesh update methods, distortion-limiting techniques, and remeshing and projection tactics. To save computational costs, point force calculations have been performed in the past. This paper presents a hybrid between full mesh-moving simulations and the point force calculation. This mesh-moving alternative is called FOIST: fluid–object subcomputation interaction technique. Copyright © 2009 John Wiley & Sons, Ltd.
Gauge-invariant time-dependent perturbation theory. II. degenerate case

For pt.I see ibid., vol.15, p.1201 (1982). The author formulates a manifestly gauge-invariant time-dependent perturbation theory for a nonrelativistic spinless charged particle interacting with a classical external electromagnetic radiation field. The treatment of the degenerate bound states and the states in the continuum is considered. It is found that the gauge-invariant and the conventional perturbative solutions agree on the net transition rates but disagree on the transition amplitudes and transition probabilities. The treatment of a realistic physical system can be obtained by combining the treatment here with that for a nondegenerate system.
Algorithms for Modular Elliptic Curves

This book presents a thorough treatment of many algorithms concerning the arithmetic of elliptic curves with remarks on computer implementation. It is in three parts. First, the author describes in detail the construction of modular elliptic curves, giving an explicit algorithm for their computation using modular symbols. Second, a collection of algorithms for the arithmetic of elliptic curves is presented; some of these have not appeared in book form before. They include: finding torsion and nontorsion points, computing heights, finding isogenies and periods, and computing the rank. Finally, an extensive set of tables is provided giving the results of the author's implementations of the algorithms. These tables extend the widely used "Antwerp IV Tables" in two ways, the range of conductors (up to 1000) and the level of detail given for each curve. In particular the quantities relating to the Birch-Swinnerton-Dyer conjecture have been computed in each case and are included.
THE ORBIT AND COLORS OF THE CEPHEID S MUSCAE

A new orbit has been computed for the binary Cepheid S Mus combining new data from Mount John Observatory with previous data. Corrections to the colors and reddening due to the light from the companion are derived. The spectral type determined from IUE low-dispersion spectra is used for these corrections. The corrections are small, even though the companion is one of the hottest (B5 V) known for a Cepheid.
Robust low-rank image representations by deep matrix decompositions

A novel approach based on low-rank representations (LRRs) for image representations is proposed. LRR seeks the lowest-rank representations among all the coefficient matrices that represent the images as linear combinations of the basis in the given dictionary. Unlike LRR methods of enforcing additional constraints on the representation and dictionary, an iterative process in which the low-rank decomposition is performed on the coefficient matrices has been developed. The rank of the representation matrices will be lower and lower with the iterations, termed as the deep low-rank (DLR) method. Extensive experiments were conducted to verify the state-of-the-art performance for classification tasks of the DRL method.
Fundamentals of semigroup theory

1. Introductory ideas 2. Green's equivalences regular semigroups 3. 0-simple semigroups 4. Completely regular semigroups 5. Inverse semigroups 6. Other classes of regular semigroups 7. Free semigroups 8. Semigroup amalgams References List of symbols
The Sum of Log-Normal Probability Distributions in Scatter Transmission Systems

The long-term fluctuation of transmission loss in scatter propagation systems has been found to have a logarithmicnormal distribution. In other words, the scatter loss in decibels has Gaussian statistical distribution. Therefore, in many important communication systems (e.g., FM), the noise power of a radio jump, or hop, has log-normal statistical distribution. In a multihop system, the noise power of each hop contributes to the total noise. The resulting noise of the system is therefore the statistical sum of the individual noise distributions. In multihop scatter systems and others, such as multichannel speech-transmission systems, the sum of several log-normal distributions is needed. No exact solution to this problem is known. The following discussion presents an approximate solution which is satisfactory in most practical cases. For tactical multihop scatter systems, a further approximation is proposed, which reduces significantly the necessary computation. An example of the computation is given.
Modeling of Stark Profiles in a Fluctuating Edge Tokamak Plasma

We present a model for the spectroscopic density diagnostic of a recombining divertor plasma, by retaining the fluctuations of charged particles due to low frequency turbulence. A Stark broadening model for hydrogen isotopes is used for the local line shape, and in accordance with our model, averaged over a density fluctuation PDF for obtaining the apparent line shape. We present the results of our model for the Balmer 10 → 2 line and compare to an experimental spectrum observed in the JET divertor. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An efficient synthesis approach for electromagnetic near‐ and far‐field contoured patterns using alternative narrow‐beam field functions transformed from the radiations of linearly excited array antennas with least computational complexity

This paper presents an effective scheme to accelerate the computational efficiency in synthesizing the electromagnetic contoured patterns spanned by the radiations of phased array antennas, which is applicable to synthesize both the near‐ and far‐field patterns. The core concept is to adapt/create closed‐form and simple formulations with least computational unknowns to be used in the iterative synthesis procedure. The efficiency is assured by avoiding the cumbersome numerical integration/summation for the radiation fields in the synthesis procedure. Thus, the scheme first transforms the conventional field basis functions (FBFs) defined by the radiations of every array elements into a set of global FBFs arising from the radiations of a set of overlapped virtual arrays, where each of the virtual arrays is properly excited by a Gaussian taper to avoid the ray caustic problems encountered in the asymptotic evaluations. The new FBFs (NFBFs) created by this transformation have radiation fields focused in narrow spans in contrast to the wide patterns of conventional FBFs and may reduce the number of FBFs in the computation if a small coverage area is considered. Furthermore, the closed‐form formulations of global NFBFs are obtained by asymptotic evaluation and may dramatically reduce the computational time. This approach is implemented with the use of successive projection method, which also provides closed‐form formulations to update the excitations in each iterative step, to synthesize the near‐ and far‐field contoured patterns to demonstrate the feasibility and efficiency.
Single‐lobed far‐field radiation pattern from surface‐emitting complex‐coupled distributed‐feedback diode lasers

Theoretical analysis of surface‐emitting complex‐coupled distributed‐feedback (SE‐CC‐DFB) lasers with a second‐order grating reveals that operation in a single‐lobed, orthonormal beam can be fundamentally favored. This happens when the modal‐gain difference between symmetric and antisymmetric modes due to the optical‐field (longitudinal) overlap with the gain/loss grating overcomes the modal‐gain difference based on radiation losses. The analysis is performed for a simple three‐layer structure with gain placed in the high‐index regions (i.e., in‐phase, second‐order CC‐DFB). Lasing at or near the Bragg frequency provides essentially uniform near‐field patterns, thus immunizing the device to gain spatial hole burning. The results and their implications are discussed.
Effects of cattle on vector-borne disease risk to humans: A systematic review

Vector-borne diseases (VBDs) may be transmitted among humans, domestic animals, and wildlife, with cattle in particular serving as an important source of exposure risk to humans. The close associations between humans and cattle can facilitate transmission of numerous VBDs which can impact nations public health and economic security. Published studies demonstrate that cattle can influence human exposure risk positively, negatively or have no effect. There is a critical need to synthesize the information in the scientific literature on this subject, in order to illuminate the various ecological mechanisms that can affect the risk of humans contracting VBDs from cattle. Therefore, the aim of this systematic review was to review the scientific literature, provide a synthesis of the possible effects of cattle on VBD risk to humans, and propose future directions for research. This study was performed according to the PRISMA 2020 extension guidelines for systematic review. After screening 470 peer-reviewed articles published between 1999 - 2019 using the databases Web of Science Core Collection, PubMed Central, CABI Global Health, and Google Scholar, and utilizing forward and backward search techniques, we identified 127 papers that met inclusion criteria. Results of the systematic review indicate that cattle can be beneficial or harmful to human health with respect to VBDs depending on vector and pathogen ecology and livestock management practices. Cattle can increase risk of exposure to infections transmitted by tsetse flies and ticks, followed by sandflies and mosquitoes, through a variety of mechanisms. However, cattle can have a protective effect when the vector prefers to feed on cattle instead of humans and when chemical control measures (e.g., acaricides/insecticides), semio-chemicals, and other integrated vector control measures are utilized in the community. We highlight that further research is needed to determine ways in which these mechanisms may be exploited to reduce VBD risk in humans.
The Sun, the Earth, and Near-Earth Space: A Guide to the Sun-Earth System

In a world of warmth and light and living things we soon forget that we are surrounded by a vast universe that is cold and dark and deadly dangerous, just beyond our door. On a starry night, when we look out into the darkness that lies around us, the view can be misleading in yet another way: for the brightness and sheer number of stars, and their chance groupings into familiar constellations, make them seem much nearer to each other, and to us, that in truth they are. And every one of them--each twinkling, like a diamond in the sky--is a white-hot sun, much like our own. The nearest stars in our own galaxy--the Milky Way-- are more than a million times further away from us than our star, the Sun. We could make a telephone call to the Moon and expect to wait but a few seconds between pieces of a conversation, or but a few hours in calling any planet in our solar system.
Investigations into Satisfiability Search

In this dissertation we investigate theoretical aspects of some practical approaches used in solving and understanding search problems. We concentrate on the Satisfiability problem, which is a strong representative from search problem domains. The work develops general theoretical foundations to investigate some practical aspects of satisfiability search. This results in a better understanding of the fundamental mechanics for search algorithm construction and behaviour. A theory of choice or branching heuristics is presented, accompanied by results showing a correspondence of both parameterisations and performance when the method is compared to previous empirically motivated branching techniques. The logical foundations of the backtracking mechanism are explored alongside formulations for reasoning in relevant logics which results in the development of a malleable backtracking mechanism that subsumes other intelligent backtracking proof construction techniques and allows the incorporation of proof rearrangement strategies. Moreover, empirical tests show that relevant backtracking outperforms all other forms of intelligent backtracking search tree construction methods. An investigation into modelling and generating world problem instances justifies a modularised problem model proposal which is used experimentally to highlight the practicability of search algorithms for the proposed model and related domains.