Miracle-dz/UniFAR-FTUs huggingface dataset:
A NEW DP-MINIMAL EXPANSION OF THE INTEGERS

Abstract We consider the structure $({\Bbb Z}, + ,0,|_{p_1 } , \ldots ,|_{p_n } )$, where $x|_p y$ means $v_p \left( x \right) \leqslant v_p \left( y \right)$ and vp is the p-adic valuation. We prove that this structure has quantifier elimination in a natural expansion of the language of abelian groups, and that it has dp-rank n. In addition, we prove that a first order structure with universe ${\Bbb Z}$ which is an expansion of $({\Bbb Z}, + ,0)$ and a reduct of $({\Bbb Z}, + ,0,|_p )$ must be interdefinable with one of them. We also give an alternative proof for Conant’s analogous result about $({\Bbb Z}, + ,0, < )$.
Bulk behaviour of Schur-Hadamard products of symmetric random matrices

We develop a general method for establishing the existence of the Limiting Spectral Distributions (LSD) of Schur–Hadamard products of independent symmetric patterned random matrices. We apply this method to show that the LSD of Schur–Hadamard products of some common patterned matrices exist and identify the limits. In particular, the Schur–Hadamard product of independent Toeplitz and Hankel matrices has the semi-circular LSD. We also prove an invariance theorem that may be used to find the LSD in many examples.
Continued fractions in function fields: polynomial analogues of McMullen's and Zaremba's conjectures

We examine the polynomial analogues of McMullen's and Zaremba's conjectures on continued fractions with bounded partial quotients. It has already been proved by Blackburn that if the base field is infinite, then the polynomial analogue of Zaremba's conjecture holds; we will prove this again with a different method and examine some known results for finite base fields. Translating to the polynomial setting a result of Mercat, we will prove that the polynomial analogue of McMullen's conjecture holds over infinite algebraic extensions of finite fields and that, over finite fields, it would be a consequence of the polynomial analogue of Zaremba's conjecture. We will then prove that the polynomial analogue of McMullen's conjecture holds over uncountable base fields, over $\overline{\mathbb Q}$ (thanks to the theory of reduction of a formal Laurent series modulo a prime) and over number fields. For this purpose, we will examine the connection between the continued fractions of polynomial multiples of $\sqrt D$ and pullbacks of generalized Jacobians of the hyperelliptic curve $U^2=D(T)$.
Evaluating the Prevent–Teach–Reinforce Model for High School Students With Autism Spectrum Disorder

This study evaluated the use of the Prevent–Teach–Reinforce (PTR) model as an intensive individualized behavior intervention. Three educators and three high school students with autism spectrum disorder participated in the study. A concurrent multiple baseline design across participants was used to demonstrate the outcomes. The results indicated that the educators implemented the PTR intervention plans with high levels of fidelity, and their implementation of the intervention plans led to decreases in problem behavior and increases in replacement behavior across all three participating students with autism spectrum disorder. The educators demonstrated using the Individualized Behavior Rating Scale Tool effectively as designed to monitor student progress, and the educators and students found the PTR intervention to be acceptable and satisfactory. All three educators expressed interest in continuing to implement the PTR intervention after the completion of the study. Implications and areas for future research are discussed.
Flow intermittency affects structural and functional properties of macroinvertebrate communities in alpine streams

1. Flow regime is a major determinant of the structure and functioning of aquatic ecosystems. Under climate change, flow intermittency is becoming more prevalent in glaciated alpine catchments, but the effects of increasing dryness on aquatic biodiversity remain largely unknown. 2. We characterised flow intermittency patterns in 30 streams of a glaciated alpine catchment over 15 months and separated these streams into four intermittency categories: perennial streams, winter- drying streams, moderately intermittent streams with occasional drying in summer, and periodically intermittent streams with extensive dry periods throughout the year. We then examined how these drying patterns affected structural and functional properties of benthic macroinvertebrate communities, and whether these changes were primarily deterministic or stochastic. 3. At the does functional and how do changes in community structure with drying affect functional rates (e.g., OM in alpine stream networks?
A multi-wavelength study of z = 3.15 Lyman-α emitters in the GOODS south field

Context. Ly�-emitters have proven to be excellent probes of faint, star- forming galaxies in the high redshift universe. However, although the sample of known emitters is increasingly growing, their nature (e.g. stellar masses, ages, metallicities , star-formation rates) is still poorly constrained. Aims. We aim to study the nature of Ly�-emitters, to find the properties of a typical Ly �-emitting galaxy and to compare these properties with the properties of other galaxies at similar redshift, in particular Lyman-break galaxies.
Lowland rivers: Geomorphology, human impacts, and management

Lowland rivers are unique geomorphic and hydrologic settings that support distinctive environmental processes and a range of human activities. Lowland rivers often have broad valleys and deltas characterized by multiple raised channel belts and distributaries separated by expansive flood basins. These result in unique floodplain architectural elements that serve as important secondary controls on the fluvial environment, specifically patterns of inundation, sediment dispersal, and riparian biogeochemical and ecosystem processes (Lewin & Ashworth, 2014; Park & Latrubesse, 2017). The societal importance of fluvial lowlands is vastly disproportionate to their areal extent over Earth’s land surface, which is about 5.0% in total (Overeem & Syvitski, 2009) and merely 0.5% for deltas (Science, 14 May 2021). The combination of their relatively small global areal extent and high population concentration results in many lowland rivers having been adversely impacted by human activities, including upstream land use, dams, and hard engineering structures in support of flood control, navigation, settlement and agriculture. These problems are accentuated towards the coast where fluvial-deltaic landscapes are being drowned by sea level rise exacerbated by sediment starvation and land subsidence, which is also influenced by hydraulic infrastructure and groundwater withdrawal for agriculture and industry (Best & Darby, 2020; Giosan et al., 2014; Minderhoud et al., 2020; Syvitski et al., 2012). This special issue of Earth Surface Processes & Landforms provides a contemporary view of the dynamics and management of lowland rivers from a fluvial geomorphic perspective. The issue draws upon case studies from a broad longitudinal range of settings and includes empirical approaches that combine field and geographic information system and remote sensing (GIS and RS)-based analyses. The 10 special issue contributions herein reviewed concern important fundamental and applied topics within lowland river science, specifically highlighting three key themes. These include ‘natural’ river channel dynamics within settings that vary from the standard body of knowledge (Guha et al., 2022; Rogério et al., 2022; Sinha et al., 2022), geomorphic response to channel engineering (Mossa & Chen, 2022; Marteau et al., 2022; Tang et al., 2022; Wu et al., 2022), and flood basin management in response to environmental change (Keim et al., 2022; Phillips, 2022; Valentine et al., 2022). The categories are not mutually exclusive, and most contributions have linkages across multiple themes.
Constructions of Maximum Few-Distance Sets in Euclidean Spaces

A finite set of vectors $\mathcal{X}$ in the $d$-dimensional Euclidean space $\mathbb{R}^d$ is called an $s$-distance set if the set of mutual distances between distinct elements of $\mathcal{X}$ has cardinality exactly $s$. In this paper we present a combined approach of isomorph-free exhaustive generation of graphs and Gröbner basis computation to classify the largest $3$-distance sets in $\mathbb{R}^4$, the largest $4$-distance sets in $\mathbb{R}^3$, and the largest $6$-distance sets in $\mathbb{R}^2$. We also construct new examples of large $s$-distance sets in $\mathbb{R}^d$ for $d\leq 8$ and $s\leq 6$, and independently verify several earlier results from the literature.
The Hardy–Littlewood conjecture and rational points

Abstract Schinzel’s Hypothesis (H) was used by Colliot-Thélène and Sansuc, and later by Serre, Swinnerton-Dyer and others, to prove that the Brauer–Manin obstruction controls the Hasse principle and weak approximation on pencils of conics and similar varieties. We show that when the ground field is $\mathbb{Q}$ and the degenerate geometric fibres of the pencil are all defined over $\mathbb{Q}$, one can use this method to obtain unconditional results by replacing Hypothesis (H) with the finite complexity case of the generalised Hardy–Littlewood conjecture recently established by Green, Tao and Ziegler.
MAJORITY-VOTE MODEL ON (3, 4, 6, 4) AND (34, 6) ARCHIMEDEAN LATTICES

On Archimedean lattices, the Ising model exhibits spontaneous ordering. Two examples of these lattices of the majority-vote model with noise are considered and studied through extensive Monte Carlo simulations. The order/disorder phase transition is observed in this system. The calculated values of the critical noise parameter are qc = 0.091(2) and qc = 0.134(3) for (3, 4, 6, 4) and (34, 6) Archimedean lattices, respectively. The critical exponents β/ν, γ/ν and 1/ν for this model are 0.103 (6), 1.596 (54), 0.872 (85) for (3, 4, 6, 4) and 0.114 (3), 1.632 (35), 0.98 (10) for (34, 6) Archimedean lattices. These results differs from the usual Ising model results and the majority-vote model on so-far studied regular lattices or complex networks. The effective dimensionalities of the system [Deff (3, 4, 6, 4) = 1.802(55) and Deff (34, 6) = 1.860(34)] for these networks are reasonably close to the embedding dimension two.
Village Fund Allocation Information System Design

Village development has a very important and strategic role in the context of National Development and Regional Development. In village development, the village government is located as a subsystem of the government administration system in Indonesia, so that the village has the authority, duties and obligations to regulate and manage the interests of its own community. In carrying out the authority, duties, and obligations of the village in the administration of government and development, a source of village income is needed. In the process of managing the Village (Gampong) Fund Allocation, Peukan Bada District, Aceh Besar District, the village government is faced with the condition of the community's education level being still weak. Based on previous research, this research has a purpose, namely to describe and analyze the Management of Village Fund Allocation in empowering rural communities; the driving and inhibiting factors for the management of Village Fund Allocation in empowering rural communities in Peukan Bada District, Aceh Besar District. The objectives to be achieved from this research are; create an online budget data processing information system design, and improve all aspects of data forms or expand the relationship or relationship of each data. The design method used is the waterfall model taking basic activities such as specification, development, validation, and evolution and representing them as phases such as requirements specification, software design, implementation, testing and so on. Based on the results of the analysis and design of the village fund allocation information system, it can be seen that until now it is still done manually. The author can conclude including; the design of the village fund allocation application can provide convenience in carrying out the implementation process of gampong development, and the use of a system that is still manual has limitations in the data storage process, data search and report generation process.
Moments of random multiplicative functions and truncated characteristic polynomials

We give an asymptotic formula for the $2k$th moment of a sum of multiplicative Steinhaus variables. This was recently computed independently by Harper, Nikeghbali and Radziwi\l\l. We also compute the $2k$th moment of a truncated characteristic polynomial of a unitary matrix. This provides an asymptotic equivalence with the moments of Steinhaus variables. Similar results for multiplicative Rademacher variables are given.
The Ideation Compass: supporting interdisciplinary creative dialogues with real time visualization

ABSTRACT This study presents the potential of live topic visualization in supporting creative dialogs during remote idea generation. We developed a novel Creativity Support Tool (CST) to explore the effects of the live topic visualization. The tool emphasizes the interdisciplinary knowledge background of participants. Using Natural Language Processing (NLP) and topic modeling, the tool provides users with a live visual mapping of the domains and topics being orally discussed. To understand the tool’s user perceived effects, we conducted evaluation sessions and interviews with participants (N = 10) from two different disciplinary backgrounds: design and bioscience. The findings show that live visualization of domains and topics supported self-reflection during individual and collaborative creativity and encouraged a balanced discussion, which can mitigate discipline-based fixation in ideation.
BerezinToeplitz quantization on Khler manifolds

Abstract We study BerezinToeplitz quantization on Khler manifolds. We explain first how to compute various associated asymptotic expansions, then we compute explicitly the first terms of the expansion of the kernel of the BerezinToeplitz operators, and of the composition of two BerezinToeplitz operators. As an application, we estimate the norm of Donaldson's Q-operator.
Minimality for unions of 2-dimensional minimal cones with non-isolated singularities

In this article we prove that for a large class of 2-dimensional minimal cones (including almost all 2-dimensional minimal cones that we know), the almost orthogonal union of any two of them is still a minimal cone. Comparing to existing results for minimality of almost orthogonal union of planes \cite{2p,2ptopo}, here we are dealing with unions of cones with non isolated singularities, which results in a series of essential difficulties, and new ideas are required. The proof in this article can be generalized to other types of minimalities, e.g. topological minimality, Reifenberg minimality, etc.
Structure-Preserving Model Reduction of Forced Hamiltonian Systems

This paper reports a development in the proper symplectic decomposition (PSD) for model reduction of forced Hamiltonian systems. As an analogy to the proper orthogonal decomposition (POD), PSD is designed to build a symplectic subspace to fit empirical data. Our aim is two-fold. First, to achieve computational savings for large-scale Hamiltonian systems with external forces. Second, to simultaneously preserve the symplectic structure and the forced structure of the original system. We first reformulate d'Alembert's principle in the Hamiltonian form. Corresponding to the integral and local forms of d'Alembert's principle, we propose two different structure-preserving model reduction approaches to reconstruct low-dimensional systems, based on the variational principle and on the structure-preserving projection, respectively. These two approaches are proven to yield the same reduced system. Moreover, by incorporating the vector field into the data ensemble, we provided several algorithms for energy preservation. In a special case when the external force is described by the Rayleigh dissipative function, the proposed method automatically preserves the dissipativity, boundedness, and stability of the original system. The stability, accuracy, and efficiency of the proposed method are illustrated through numerical simulations of a dissipative wave equation.
Characterization of Epithelial-Mesenchymal Transition Identifies a Gene Signature for Predicting Clinical Outcomes and Therapeutic Responses in Bladder Cancer

Purpose The complex etiological variables and high heterogeneity of bladder cancer (BC) make prognostic prediction challenging. We aimed to develop a robust and promising gene signature using advanced machine learning methods for predicting the prognosis and therapy responses of BC patients. Methods The single-sample gene set enrichment analysis (ssGSEA) algorithm and univariable Cox regression were used to identify the primary risk hallmark among the various cancer hallmarks. Machine learning methods were then combined with survival and differential gene expression analyses to construct a novel prognostic signature, which would be validated in two additional independent cohorts. Moreover, relationships between this signature and therapy responses were also identified. Functional enrichment analysis and immune cell estimation were also conducted to provide insights into the potential mechanisms of BC. Results Epithelial-mesenchymal transition (EMT) was identified as the primary risk factor for the survival of BC patients (HR=1.43, 95% CI: 1.26-1.63). A novel EMT-related gene signature was constructed and validated in three independent cohorts, showing stable and accurate performance in predicting clinical outcomes. Furthermore, high-risk patients had poor prognoses and multivariable Cox regression analysis revealed this to be an independent risk factor for patient survival. CD8+ T cells, Tregs, and M2 macrophages were found abundantly in the tumor microenvironment of high-risk patients. Moreover, it was anticipated that high-risk patients would be more sensitive to chemotherapeutic drugs, while low-risk patients would benefit more from immunotherapy. Conclusions We successfully identified and validated a novel EMT-related gene signature for predicting clinical outcomes and therapy responses in BC patients, which may be useful in clinical practice for risk stratification and individualized treatment.
The exact power law for Buffon’s needle landing near some random Cantor sets

In this paper, we study the Favard length of some random Cantor sets of Hausdorff dimension 1. We start with a unit disk in the plane and replace the unit disk by $4$ disjoint subdisks (with equal distance to each other) of radius $1/4$ inside and tangent to the unit disk. By repeating this operation in a self-similar manner and adding a random rotation in each step, we can generate a random Cantor set ${\cal D}(\omega)$. Let ${\cal D}_n$ be the $n$-th generation in the construction, which is comparable to the $4^{-n}$-neighborhood of ${\cal D}$. We are interested in the decay rate of the Favard length of these sets ${\cal D}_n$ as $n\to\infty$, which is the likelihood (up to a constant) that "Buffon's needle" dropped randomly will fall into the $4^{-n}$-neighborhood of ${\cal D}$. It is well known in [P. Mattila, Orthogonal projections, Riesz capacities, and Minkowski content, Indiana Univ. Math. J. 39 (1990), no. 1, 185-198] that the lower bound of the Favard length of ${\cal D}_n(\omega)$ is constant multiple of $n^{-1}$. We show that the upper bound of the Favard length of ${\cal D}_n(\omega)$ is $C n^{-1}$ for some $C>0$ in the average sense. We also prove the similar linear decay for the Favard length of ${\cal D}^d_n(\omega)$ which is the $d^{-n}$-neighborhood of a self-similar random Cantor set with degree $d$ greater than $4$. Notice in the non-random case where the self-similar set has degree greater than $4$, the best known result for the decay rate of the Favard length is $e^{-c\sqrt {\log n}}$.
FREE ACTIONS OF SOME COMPACT GROUPS ON MILNOR MANIFOLDS

Abstract In this paper, we investigate free actions of some compact groups on cohomology real and complex Milnor manifolds. More precisely, we compute the mod 2 cohomology algebra of the orbit space of an arbitrary free ℤ2 and $\mathbb{S}^1$-action on a compact Hausdorff space with mod 2 cohomology algebra of a real or a complex Milnor manifold. As applications, we deduce some Borsuk–Ulam type results for equivariant maps between spheres and these spaces. For the complex case, we obtain a lower bound on the Schwarz genus, which further establishes the existence of coincidence points for maps to the Euclidean plane.
From local Torelli to global Torelli

We introduce the notions of strong local Torelli and T-class for polarized manifolds, and prove that strong local Torelli implies global Torelli theorem on the Torelli spaces for polarized manifolds in the T-class. We discuss many new examples of projective manifolds for which such global Torelli theorem holds. As applications we prove that, in these cases, a canonical completion of the Torelli space is a bounded pseudoconvex domain in complex Euclidean space, and show that generic Torelli implies global Torelli on moduli space with certain level structure.
Rheological Investigation of Welding Waste-Derived Graphene Oxide in Water-Based Drilling Fluids

Throughout the world, the construction industry produces significant amounts of by-products and hazardous waste materials. The steel-making industry generates welding waste and dusts that are toxic to the environment and pose many economic challenges. Water-based drilling fluids (WBDF) are able to remove the drill cuttings in a wellbore and maintain the stability of the wellbore to prevent formation damage. To the best of our knowledge, this is the first study that reports the application of welding waste and its derived graphene oxide (GO) as a fluid-loss additive in drilling fluids. In this research, GO was successfully synthesized from welding waste through chemical exfoliation. The examination was confirmed using XRD, FTIR, FESEM and EDX analyses. The synthesized welding waste-derived GO in WBDF is competent in improving rheological properties by increasing plastic viscosity (PV), yield point (YP) and gel strength (GS), while reducing filtrate loss (FL) and mud cake thickness (MCT). This study shows the effect of additives such as welding waste, welding waste-derived GO and commercial GO, and their amount, on the rheological properties of WBDF. Concentrations of these additives were used at 0.01 ppb, 0.1 ppb and 0.5 ppb. Based on the experiment results, raw welding waste and welding waste-derived GO showed better performance compared with commercial GO. Among filtration properties, FL and MCT were reduced by 33.3% and 39.7% with the addition of 0.5 ppb of raw welding-waste additive, while for 0.5 ppb of welding waste-derived GO additive, FL and MCT were reduced by 26.7% and 20.9%, respectively. By recycling industrial welding waste, this research conveys state-of-the-art and low-cost drilling fluids that aid in waste management, and reduce the adverse environmental and commercial ramifications of toxic wastes.
Amibes de sommes d’exponentielles

Résumé L’objectif de cet article est d’étudier la notion d’amibe au sens de Favorov pour les systèmes finis de sommes d’exponentielles à fréquences réelles et de montrer que, sous des hypothèses de généricité sur les fréquences, le complémentaire de l’amibe d’un système de $(k\,+\,1)$ sommes d’exponentielles à fréquences réelles est un sous-ensemble $k$ -convexe au sens d’Henriques.