Miracle-dz/UniFAR-FTUs huggingface dataset:
Minimal Transitive Factorizations of Permutations into Cycles

Abstract We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings, that is, we study the number ${{H}_{\alpha }}({{i}_{2}},{{i}_{3}},.)$ of ways a given permutation (with cycles described by the partition $\alpha $ ) can be decomposed into a product of exactly ${{i}_{2}}$ 2-cycles, ${{i}_{3}}$ 3-cycles, etc., with certain minimality and transitivity conditions imposed on the factors. The method is to encode such factorizations as planar maps with certain descent structure and apply a new combinatorial decomposition to make their enumeration more manageable. We apply our technique to determine ${{H}_{\alpha }}({{i}_{2}},{{i}_{3}},.)$ when $\alpha $ has one or two parts, extending earlier work of Goulden and Jackson. We also show how these methods are readily modified to count inequivalent factorizations, where equivalence is defined by permitting commutations of adjacent disjoint factors. Our technique permits us to generalize recent work of Goulden, Jackson, and Latour, while allowing for a considerable simplification of their analysis.
Explicit formula of a supersingular polynomial for rank-2 Drinfeld modules and applications

Rank-2 Drinfeld modules are a function-field analogue of elliptic curves, and the purpose of this paper is to investigate similarities and differences between rank-2 Drinfeld modules and elliptic curves in terms of supersingularity. Specifically, we provide an explicit formula of a supersingular polynomial for rank-2 Drinfeld modules and prove several basic properties. As an application, we give a numerical example of an asymptotically optimal tower of Drinfeld modular curves.
An immersed discontinuous Galerkin method for compressible Navier‐Stokes equations on unstructured meshes

We introduce an immersed high‐order discontinuous Galerkin method for solving the compressible Navier‐Stokes equations on non–boundary‐fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are advanced in time with an explicit time marching scheme. The discretisation meshes may contain simplicial (triangular or tetrahedral) elements of different sizes and need not be structured. On the discretisation mesh, the fluid domain boundary is represented with an implicit signed distance function. The cut‐elements partially covered by the solid domain are integrated after tessellation with the marching triangle or tetrahedra algorithms. Two alternative techniques are introduced to overcome the excessive stable time step restrictions imposed by cut‐elements. In the first approach, the cut‐basis functions are replaced with the extrapolated basis functions from the nearest largest element. In the second approach, the cut‐basis functions are simply scaled proportionally to the fraction of the cut‐element covered by the solid. To achieve high‐order accuracy, additional nodes are introduced on the element faces abutting the solid boundary. Subsequently, the faces are curved by projecting the introduced nodes to the boundary. The proposed approach is verified and validated with several two‐ and three‐dimensional subsonic and hypersonic low Reynolds number flow applications, including the flow over a cylinder, a space capsule, and an aerospace vehicle.
A Survey of Data Balancing Technique for Multi-Class Imbalanced Problem

: The imbalanced dataset contains skewed distribution of data. Such data distribution generates difficulties for machine learning algorithms. It may lead to generate false results in case of data imbalance. Various techniques proposed in a literature to balance a dataset using oversampling or under sampling methods. The study of these techniques is done independently. A little work has been done with the combined study of these two techniques. Some techniques have constraint on dataset type i
Long-time heat kernel estimates and upper rate functions of Brownian motion type for symmetric jump processes

Let $X$ be a symmetric jump process on $\R^d$ such that the corresponding jumping kernel $J(x,y)$ satisfies $$J(x,y)\le \frac{c}{|x-y|^{d+2}\log^{1+\varepsilon}(e+|x-y|)}$$ for all $x,y\in\R^d$ with $|x-y|\ge1$ and some constants $c,\varepsilon>0$. Under additional mild assumptions on $J(x,y)$ for $|x-y| 0$ is an upper rate function of the process $X$, which enjoys the same form as that for Brownian motions. The approach is based on heat kernel estimates of large time for the process $X$. As a by-product, we also obtain two-sided heat kernel estimates of large time for symmetric jump processes whose jumping kernels are comparable to $$\frac{1}{|x-y|^{d+2+\varepsilon}}$$ for all $x,y\in\R^d$ with $|x-y|\ge1$ and some constant $\varepsilon>0$.
Pointwise and ergodic convergence rates of a variable metric proximal ADMM

In this paper, we obtain global $\mathcal{O} (1/ \sqrt{k})$ pointwise and $\mathcal{O} (1/ {k})$ ergodic convergence rates for a variable metric proximal alternating direction method of multipliers(VM-PADMM) for solving linearly constrained convex optimization problems. The VM-PADMM can be seen as a class of ADMM variants, allowing the use of degenerate metrics (defined by noninvertible linear operators). We first propose and study nonasymptotic convergence rates of a variable metric hybrid proximal extragradient (VM-HPE) framework for solving monotone inclusions. Then, the above-mentioned convergence rates for the VM-PADMM are obtained essentially by showing that it falls within the latter framework. To the best of our knowledge, this is the first time that global pointwise (resp. pointwise and ergodic) convergence rates are obtained for the VM-PADMM (resp. VM-HPE framework).
KNOWLEDGE CREATION PRACTICES AND EMPLOYEE PERFORMANCE IN SELECTED PUBLIC TECHNICAL VOCATIONAL EDUCATION AND TRAINING INSTITUTIONS IN KENYA

Employee performance in technical vocational education and training institutions has been found to be poor. Poor performance among employees is exhibited through a high level of incompetence and lack of innovativeness among Technical Vocational Education and Training Institutions (TVET) graduates. This culminates in problems of graduate employability owing to a lack of required skills required by employers. This poor performance may be ascribed in part to deterioration in individual employee performance as a consequence of ineffective skills amongst employees and inadequate knowledge management practices inside the institutions. Globally, despite the fact that there exist many knowledge management practices in higher educational institutions in many countries, there is strong agreement amongst academics and researchers that knowledge imparted through higher institutions of learning falls short in providing youth with the appropriate and relevant skills needed to succeed in the labour market. Higher education institutions as ‘knowledge intensive’ organizations thrive on the creation and dissemination of knowledge and therefore rely heavily on the performance of its employees to facilitate and continually generate and disseminate knowledge. The study sought to investigate the influence of Knowledge Creation Practices on Employee Performance in public technical vocational education and training institutions in Kenya. The study was anchored on Unified Model of Dynamic Knowledge Creation propounded by Nonaka, Toyama & Konno in the year 2000. The study used a positivism philosophy and a descriptive survey research design. The target population comprised of 11 national polytechnics in Kenya. The unit of inquiry comprised of 265 administrators comprised of both academic and non-academic heads of department. Primary data was collected using structured self-administered questionnaires. The reliability of the research instrument was ascertained using Cronbach Alpha. Validity was established using content and construct validity. Quantitative data were analysed using descriptive and inferential statistics with aid of SPSS 26. Descriptive analysis used includes; frequencies, mean, standard deviation and percentages while inferential analysis involved correlation analysis and multiple linear regression analysis to test the hypothesis at a significance level of 0.05. Regression analysis indicated that knowledge creation (P=0.000) has a significant influence on employee performance. The study concluded that knowledge creation practices significantly influence employee performance in TVETs. The study recommends that managers should create a better atmosphere in their institutions that encourage their employees to express new ideas. They also should apply effective ways to manage knowledge workers better by creating policies that inculcate new knowledge which consequently should go a long way in continously improving employee performance. Article visualizations:
Robust procedures for converting among Lindblad, Kraus and matrix representations of quantum dynamical semigroups

Given a quantum dynamical semigroup expressed as an exponential superoperator acting on a space of N-dimensional density operators, eigenvalue methods are presented by which canonical Kraus and Lindblad operator sum representations can be computed. These methods provide a mathematical basis on which to develop novel algorithms for quantum process tomography—the statistical estimation of superoperators and their generators—from a wide variety of experimental data. Theoretical arguments and numerical simulations are presented which imply that these algorithms will be quite robust in the presence of random errors in the data.
The subarcsecond mid-infrared view of local active galactic nuclei – I. The N- and Q-band imaging atlas

We present the first subarcsecond-resolution mid-infrared (MIR) atlas of local active galactic nuclei (AGN). Our atlas contains 253 AGN with a median redshift of z = 0.016, and includes all publicly available MIR imaging performed to date with ground-based 8-m class telescopes, a total of 895 independent measurements. Of these, more than 60 per cent are published here for the first time. We detect extended nuclear emission in at least 21 per cent of the objects, while another 19 per cent appear clearly point-like, and the remaining objects cannot be constrained. Where present, elongated nuclear emission aligns with the ionization cones in Seyferts. Subarcsecond resolution allows us to isolate the AGN emission on scales of a few tens of parsecs and to obtain nuclear photometry in multiple filters for the objects. Median spectral energy distributions (SEDs) for the different optical AGN types are constructed and individual MIR 12 and 18 mu m continuum luminosities are computed. These range over more than six orders of magnitude. In comparison to the arcsecond-scale MIR emission as probed by Spitzer, the continuum emission is much lower on subarcsecond scales in many cases. The silicate feature strength is similar on both scales and generally appears in emission (absorption) in type I (II) AGN. However, the polycyclic aromatic hydrocarbon emission appears weaker or absent on subarcsecond scales. The differences of the MIR SEDs on both scales are particularly large for AGN/starburst composites and close-by (and weak) AGN. The nucleus dominates over the total emission of the galaxy only at luminosities greater than or similar to 10(44) erg s(-1). The AGN MIR atlas is well suited not only for detailed investigation of individual sources but also for statistical studies of AGN unification.
General approach to few-cycle intense laser interactions with complex atoms

A general ab initio and nonperturbative method to solve the time-dependent Schroedinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom, i.e., beyond the models of quasi-one-electron or quasi-two-electron targets, is described. The field-free Hamiltonian and the dipole matrices are generated using a flexible B-spline R-matrix method. This numerical implementation enables us to construct term-dependent, nonorthogonal sets of one-electron orbitals for the bound and continuum electrons. The solution of the TDSE is propagated in time using the Arnoldi-Lanczos method, which does not require the diagonalization of any large matrices. The method is illustrated by an application to the multiphoton excitation and ionization of Ne atoms. Good agreement with R-matrix Floquet calculations for the generalized cross sections for two-photon ionization is achieved.
The mass function of primordial rogue planet MACHOs in quasar nano-lensing

The recent Sumi et al (2010 Astrophys. J. 710 1641; 2011 Nature 473 349) detection of free roaming planet mass MACHOs in cosmologically significant numbers recalls their original detection in quasar microlening studies (Colley and Schild 2003 Astrophys. J. 594 97; Schild R E 1996 Astrophys. J. 464 125). We consider the microlensing signature of such a population, and find that the nano-lensing (microlensing) would be well characterized by a statistical microlensing theory published previously by Refsdal and Stabell (1991 Astron. Astrophys. 250 62) Comparison of the observed First Lens microlensing amplitudes with the theoretical prediction gives close agreement and a methodology for determining the slope of the mass function describing the population. Our provisional estimate of the power law exponent in an exponential approximation to this distribution is 2.98+1.0−0.5, where a Salpeter slope is 2.35.
Explicit counting of ideals and a Brun–Titchmarsh inequality for the Chebotarev density theorem

We prove a bound on the number of primes with a given splitting behavior in a given field extension. This bound generalizes the Brun–Titchmarsh bound on the number of primes in an arithmetic progression. The proof is set up as an application of Selberg’s Sieve in number fields. The main new ingredient is an explicit counting result estimating the number of integral elements with certain properties up to multiplication by units. As a consequence of this result, we deduce an explicit estimate for the number of ideals of norm up to [Formula: see text].
Psychological distress and metabolomic markers: A systematic review of posttraumatic stress disorder, anxiety, and subclinical distress

Psychological distress is a multifactorial construct that refers to non-specific symptoms of depression, anxiety, posttraumatic stress disorder (PTSD), or stress more generally. A systematic review of metabolomic markers associated with distress has the potential to reveal underlying molecular mechanisms linking distress to adverse health outcomes. The current systematic review extends prior reviews of clinical depressive disorders by synthesizing 39 existing studies that examined metabolomic markers for PTSD, anxiety disorders, and subclinical psychological distress in biological specimens. Most studies were based on small sets of pre-selected candidate metabolites, with few metabolites overlapping between studies. Vast heterogeneity was observed in study design and inconsistent patterns of association emerged between distress and metabolites. To gain a more robust understanding of distress and its metabolomic signatures, future research should include 1) large, population-based samples and longitudinal assessments, 2) replication and validation in diverse populations, 3) and agnostic metabolomic strategies profiling hundreds of targeted and nontargeted metabolites. Addressing these research priorities will improve the scope and reproducibility of future metabolomic studies of psychological distress.
Groups Satisfying the Two-Prime Hypothesis with a Composition Factor Isomorphic to PSL2(q) for q ⩾ 7

Let G be a finite group and write cd(G) for the degree set of the complex irreducible characters of G. The group G is said to satisfy the two-prime hypothesis if for any distinct degrees a, b 2 cd(G), the total number of (not necessarily different) primes of the greatest common divisor gcd(a, b) is at most 2. We prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to PSL2(q) for q ⩾ 7.
Nonperturbative Yukawa theory at finite density and temperature

In-medium Yukawa theory is part of the thermodynamics of the standard model of particle physics and is one of the main building blocks of most effective field theories of fermionic systems. By computing its pressure we investigate the nonperturbative thermodynamics at finite temperature and density using the optimized perturbation theory framework. Our calculations are valid for arbitrary fermion and scalar masses, temperature, chemical potential, and not restricted to weak coupling. The model is considered in the presence as well as in the absence of condensates. Comparison with nonperturbative results shows that second-order perturbation theory fails in the first case but performs rather well when condensates are absent, even at high-temperature regimes.
Splitting Algorithms for Rare Events of Semimartingale Reflecting Brownian Motions

We study rare event simulations of semimartingale reflecting Brownian motions (SRBMs) in an orthant. The rare event of interest is that a d-dimensional positive recurrent SRBM enters the set [Formula: see text] before hitting a small neighborhood of the origin [Formula: see text] as [Formula: see text] with a starting point outside the two sets and of order o(n). We show that, under two regularity conditions (the Dupuis–Williams stability condition of the SRBM and the Lipschitz continuity assumption of the associated Skorokhod problem), the probability of the rare event satisfies a large deviation principle. To study the variational problem (VP) for the rare event in two dimensions, we adapt its exact solution from developed by Avram, Dai, and Hasenbein in 2001. In three and higher dimensions, we construct a novel subsolution to the VP under a further assumption that the reflection matrix of the SRBM is a nonsingular [Formula: see text]-matrix. Based on the solution/subsolution, particle-based simulation algorithms are constructed to estimate the probability of the rare event. Our estimator is asymptotically optimal for the discretized problem in two dimensions and has exponentially superior performance over standard Monte Carlo in three and higher dimensions. In addition, we establish that the growth rate of the relative bias term arising from discretization is subexponential in all dimensions. Therefore, we can estimate the probability of interest with subexponential complexity growth in two dimensions. In three and higher dimensions, the computational complexity of our estimators has a strictly smaller exponential growth rate than the standard Monte Carlo estimators.
Vogel-Fulcher freezing in relaxor ferroelectrics

A physical mechanism for the freezing of polar nanoregions (PNRs) in relaxor ferroelectrics is presented. Assuming that the activation energy for the reorientation of a cluster of PNRs scales with the mean volume of the cluster, the characteristic relaxation time {tau} is found to diverge as the cluster volume reaches the percolation limit. Applying the mean field theory of continuum percolation, the familiar Vogel-Fulcher equation for the temperature dependence of {tau} is derived.
Therapeutic endoscopy in combined therapy of gastroduodenal ulcers

: The method of therapeutic endoscopy is a very important component in the complex treatment of chronic gastroduodenal ulcers. In 115 of 116 patients with gastric or duodenal ulcers who were treated by the authors the ulcer epithelialized and a cicatrix formed. When therapeutic endoscopy with the application of hippophae oil was added to the basic therapy, the period of the inpatient treatment reduced 1.5-2 times. The late results of the management of chronic gastroduodenal ulcers by this method were studied and confirmed its sufficiently high therapeutic efficacy (the results were positive in 93.7% of cases).
Resolving the extended stellar halos of nearby galaxies: the wide-field PISCeS survey†

Abstract In the wide-field Panoramic Imaging Survey of Centaurus and Sculptor (PISCeS), we investigate the resolved stellar halos of two nearby galaxies (the elliptical Centaurus A and the spiral Sculptor, D ~ 3.7 Mpc) out to a projected galactocentric radius of 150 kpc with Magellan/Megacam. The survey has led to the discovery of ~20 faint satellites to date, plus prominent streams and substructures in two environments that are substantially different from the Local Group, i.e. the Centaurus A group dominated by an elliptical and the loose Sculptor group of galaxies. These discoveries clearly attest to the importance of past and ongoing accretion processes in shaping the halos of these nearby galaxies, and provide the first census of their satellite systems down to an unprecedented MV < −8. The detailed characterization of the stellar content, shape and gradients in the extended halos of Sculptor, Centaurus A, and their dwarf satellites provides key constraints on theoretical models of galaxy formation and evolution.
A limit on the ABJ model

There is a large amount of evidence that the ABJM model is integrable in the planar limit. Less clear is whether or not the ABJ model is integrable. Here we investigate a limit of the ABJ model in the weak coupling limit where one 't Hooft parameter is much greater than the other. At the 4 loop level in the SU(2) × SU(2) sector the anomalous dimensions of single trace operators map to two Heisenberg spin chains with nearest neighbor interactions with an overall coefficient that is a function of one of the 't Hooft parameters. We conjecture the form of this function and show that is consistent with observations about the ABJ model concerning unitarity and parity, including strong coupling statements.
The IRAM-30 m line survey of the Horsehead PDR. III. High abundance of complex (iso-)nitrile molecules in UV-illuminated gas

Context. Complex (iso-)nitrile molecules, such as CH3CN and HC3N, are relatively easily detected in our Galaxy and in other galaxies. Aims: We aim at constraining their chemistry through observations of two positions in the Horsehead edge: the photo-dissociation region (PDR) and the dense, cold, and UV-shielded core just behind it. Methods: We systematically searched for lines of CH3CN, HC3N, C3N, and some of their isomers in our sensitive unbiased line survey at 3, 2, and 1 mm. We stacked the lines of C3N to improve the detectability of this species. We derived column densities and abundances through Bayesian analysis using a large velocity gradient radiative transfer model. Results: We report the first clear detection of CH3NC at millimeter wavelength. We detected 17 lines of CH3CN at the PDR and 6 at the dense core position, and we resolved its hyperfine structure for 3 lines. We detected 4 lines of HC3N, and C3N is clearly detected at the PDR position. We computed new electron collisional rate coefficients for CH3CN, andwe found that including electron excitation reduces the derived column density by 40% at the PDR position, where the electron density is 1-5 cm-3. While CH3CN is 30 times more abundant in the PDR (2.5 × 10-10) than in the dense core (8 × 10-12), HC3N has similar abundance at both positions (8 × 10-12). The isomeric ratio CH3NC/CH3CN is 0.15 ± 0.02. Conclusions: The significant amount of complex (iso-)nitrile molecule in the UV illuminated gas is puzzling as the photodissociation is expected to be efficient. This is all the more surprising in the case of CH3CN, which is 30 times more abundant in the PDR than in the dense core. In this case, pure gas phase chemistry cannot reproduce the amount of CH3CN observed in the UV-illuminated gas. We propose that CH3CN gas phase abundance is enhanced when ice mantles of grains are destroyed through photo-desorption or thermal-evaporation in PDRs, and through sputtering in shocks. Based on observations obtained with the IRAM-30 m telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany), and IGN (Spain). Appendices are available in electronic form at http://www.aanda. org