Miracle-dz/UniFAR-FTUs huggingface dataset:
The Analysis of the Mode of Community E-commerce Platform about The Small Red Book

In recent years, with the rapid development of Internet data communication and network technology, big data technology has penetrated into all walks of life, and also has a crucial impact on the future development of new media, an emerging industry. The integration of new media into all aspects of people's life deeply affects people's behaviors and habits, and its development is closely related to the life of individuals and even the development of the country. Taking Small red book as an example, this paper uses 4Ps and SWOT analysis to analyze its brand positioning, APP marketing status and existing problems, and focuses on the development strategy of new media Small red book from the perspective of big data. The research results show that Small red book has its unique development advantages due to its unique and effective business model, making its strength remarkable in the same industry. This research has certain practical significance for developers of community e-commerce platforms.
Poset Topology: Tools and Applications

These lecture notes for the IAS/Park City Graduate Summer School in Geometric Combinatorics (July 2004) provide an overview of poset topology. These notes include introductory material, as well as recent developments and open problems. Some of the topics covered are: subspace arrangements, graph complexes, group actions on poset homology, shellability, recursive techniques, and fiber theorems.
Foliations and webs inducing Galois coverings

We introduce the notion of Galois holomorphic foliation on the complex projective space as that of foliations whose Gauss map is a Galois covering when restricted to an appropriate Zariski open subset. First, we establish general criteria assuring that a rational map between projective manifolds of the same dimension defines a Galois covering. Then, these criteria are used to give a geometric characterization of Galois foliations in terms of their inflection divisor and their singularities. We also characterize Galois foliations on $\mathbb P^2$ admitting continuous symmetries, obtaining a complete classification of Galois homogeneous foliations.
Attributed relational graph matching by neural-gas networks

In the past, the neural-gas (NG) network has been commonly used for clustering, classification and vector quantization of feature vectors. In this paper, a modified NG network is used to perform pattern recognition by matching attributed relational graphs. The ARG matching is formulated as an optimisation problem and the modified NG network is applied to solve it. As every scene vertex is matched to the best matching model vertex, there are some spurious matches in the mapping generated by the NG network. A pose clustering algorithm is used to eliminate these spurious mappings and to estimate the pose parameters. We present experimental results to demonstrate the proposed procedure.
Strong Orthogonality between the Möbius Function and Nonlinear Exponential Functions in Short Intervals

Let $\mu(n)$ be the M\"obius function, $e(z) = \exp(2\pi iz)$, $x$ real and $2\leq y \leq x$. This paper proves two sequences $(\mu(n))$ and $(e(n^k \alpha))$ are strongly orthogonal in short intervals. That is, if $k \geq 3$ being fixed and $y\geq x^{1-1/4+\varepsilon}$, then for any $A>0$, we have \[ \sum_{x< n \leq x+y} \mu(n) e\left(n^k \alpha \right) \ll y(\log y)^{-A} \] uniformly for $\alpha \in \mathbb{R}$.
Genus 3 mapping class groups are not Kähler

We prove that finite index subgroups of genus 3 mapping class and Torelli groups that contain the group generated by Dehn twists on bounding simple closed curves are not Kähler. These results are deduced from explicit presentations of the unipotent (aka, Malcev) completion of genus 3 Torelli groups and of the relative completions of genus 3 mapping class groups. The main results follow from the fact that these presentations are not quadratic. To complete the picture, we compute presentations of completed Torelli and mapping class in genera at least 4 ; they are quadratic. We also show that groups commensurable with hyperelliptic mapping class groups and mapping class groups in genera at most 2 are not Kähler.
Systolic Surfaces of Arithmetic Hyperbolic 3-Manifolds

In this paper we examine the geometry of minimal surfaces of arithmetic hyperbolic 3-manifolds. In particular, we give bounds on the totally geodesic 2-systole, construct infinitely many incommensurable manifolds with the same initial geometric genus spectrum in which volume and 1-systole are controlled, and analyze the growth of the genera of minimal surfaces across commensurability classes. These results have applications to the study of how Heegard genus grows across commensurability classes.
Monoid-like definitions of cyclic operads

Guided by the microcosm principle of Baez and Dolan and by the algebraic definitions of operads given by Kelly and Fiore, we introduce two "monoid-like" definitions of cyclic operads, one for the "exchangable-output" characterisation and the other for the alternative "entries-only" characterisation, both within the framework of Joyal's theory of species of structures. Relying on a result of Lamarche coming from the descent theory for species, we use these "monoid-like" definitions to prove the equivalence between the "exchangable-output" and "entries-only" points of view on cyclic operads.
Quantum symmetric states on free product C*-algebras

We introduce symmetric states and quantum symmetric states on universal unital free product C*-algebras an arbitrary unital C*-algebra A with itself infinitely many times, as a generalization of the notions of exchangeable and quantum exchangeable random variables. We prove existence of conditional expectations onto tail algebras in various settings and we define a natural C*-subalgebra of the tail algebra, called the tail C*-algebra. Extending and building on the proof of the noncommutative de Finetti theorem of Koestler and Speicher, we prove a de Finetti type theorem that characterizes quantum symmetric states in terms of amalgamated free products over the tail C*-algebra, and we provide a convenient description of the set of all quantum symmetric states on the free product C*-algebra in terms of C*-algebras generated by homomorphic images of A and the tail C*-algebra. This description allows a characterization of the extreme quantum symmetric states. Similar results are proved for the subset of tracial quantum symmetric states, though in terms of von Neumann algebras and normal conditional expectations. The central quantum symmetric states are those for which the tail algebra is in the center of the von Neumann algebra, and we show that the central quantum symmetric states form a Choquet simplex whose extreme points are the free product states, while the tracial central quantum symmetric states form a Choquet simplex whose extreme points are the free product traces.
Recycling Phosphorus from Agricultural Streams: Grey and Green Solutions

Many intensively farmed soils show high phosphorus (P) contents compared to the thresholds required for agricultural production; 0.084 Mt of P year−1 is leaving the European terrestrial system. This paper focuses mainly on non-point flows of P and provides an overview of the most promising and sustainable solutions for P recycling, centred on waste materials from agriculture. Given the global shortage of the primary resource of P, its management is critical for its efficient use. Nowadays, wastage and loss at every stage of the P cycle raise concerns about future supplies and especially about the resulting environmental problems, such as the eutrophication of surface water bodies and the reduction of biodiversity. Recovering P costs more than EUR 640 per tonne depending on the type of technique used. The opportunity for P recovery with green and sustainable technology is, therefore, a great challenge for the next years. Waste materials or by-products of agricultural processing have been considered ecologically safe, low-cost, and highly selective with high pollutant adsorption capacities, which would enable sustainable P recovery, both environmentally and economically. A realistic threshold for considering the reuse of P sustainably at the farm level is EUR 320 per tonne.
Improving visualization of intracranial arteries at the skull base for CT angiography with calcified plaques

Bony structures at the skull base were the main obstacle to detection and estimation of arterial stenoses and aneurysms for CT angiography in the brain. Direct subtraction and the matched mask bone elimination (MMBE) have become two standard methods for removing bony structures. However, clinicians regularly find that calcified plaques at or near the carotid canal cannot be removed satisfactorily by existing methods. The blood-plaque boundary tends to be blurred by subtraction operation while plaque size is constantly overestimated by the bone mask dilation operation in the MMBE approach. In this study, we propose using the level of enhancement to adjust the MMBE bone mask more intelligently on the artery- and tissue-bone/plaque boundaries. The original MMBE method is only applied to the tissue-bone boundary voxels; while the artery-bone/blood-plaque boundary voxels, identified by a higher enhancement level, are processed by direct subtraction instead. A dataset of 6 patients (3 scanned with a regular dose and 3 scanned with a reduced dose) with calcified plaques at or near the skull base is used to examine our new method. Preliminary results indicate that the visualization of intracranial arteries with calcified plaques at the skull base can be improved effectively and efficiently.
The local symbol complex of a Reciprocity Functor

For a reciprocity functor $\mathcal{M}$ we consider the local symbol complex $\mathcal{M}\otimes^{M}\mathbb{G}_{m}(\eta_{C})\to\oplus_{P\in C}\mathcal{M}(k)\to\mathcal{M}(k)$, where $C$ is a smooth complete curve over an algebraically closed field $k$ with generic point $\eta_{C}$ and $\otimes^{M}$ is the product of Mackey functors. We prove that if $\mathcal{M}$ satisfies certain conditions, then the homology of the above complex is isomorphic to the $K$-group of reciprocity functors $T(\mathcal{M},\underline{CH}_{0}(C)^{0})(Spec k)$.
Multicoloured Random Graphs: Constructions and Symmetry

This is a research monograph on constructions of and group actions on countable homogeneous graphs, concentrating particularly on the simple random graph and its edge-coloured variants. We study various aspects of the graphs, but the emphasis is on understanding those groups that are supported by these graphs together with links with other structures such as lattices, topologies and filters, rings and algebras, metric spaces, sets and models, Moufang loops and monoids. The large amount of background material included serves as an introduction to the theories that are used to produce the new results. The large number of references should help in making this a resource for anyone interested in beginning research in this or allied fields.
Intrinsic half-metallicity in hydrogenated boron-nitride nanoribbons

We have investigated the structural and electronic characteristics of fully hydrogenated boron-nitride (BN) layer and zigzag-edged nanoribbons using dispersion-corrected density-functional calculations. In the fully hydrogenated BN structure, the hydrogen atoms adsorb on top of the B and N sites, alternating on both sides of the hexagonal BN-plane in a specific periodic manner. Among various low-energy hydrogenated membranes referred to as chair, boat, twist-boat, and stirrup, the stirrup conformation is the most energetically favorable one. The zigzag-edged BN nanoribbon, prominently fabricated in experiments, possesses intrinsic half-metallicity with full hydrogenation. The half-metallicity can be tuned by applying a transverse electric bias, thereby providing a promising route for spintronics device applications.
Geração Automática de Variantes de Léxicos do Português Brasileiro para Sistemas de Reconhecimento de Fala

—In this paper, we propose a strategy for automatically generating a lexicon of pronunciation variants, independent of speaker, to be used in a speech recognition system for Brazilian Portuguese. The variants described are referred to the phonological processes inherent in natural languages, such as insertion or deletion of segments, segmental assimilation, and syllabic structure. Intra-and inter-word variants have been taken into account. The number and the types of variants obtained by automatically generated transcriptions are compared with the ones performed by an expert linguist. We have verified a very good agreement between both results (almost 100%)
Additive decompositions for rings of modular forms

We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for the full modular group. In many cases these modules are free or decompose at least into well-understood pieces. We apply this to characterize which rings of modular forms are Cohen--Macaulay and to prove finite generation results. These theorems are based on decomposition results about vector bundles on the compactified moduli stack of elliptic curves.
0-Efficient Triangulations of 3-Manifolds

efficient triangulations of 3-manifolds are defined and studied. It is shown that any triangulation of a closed, orientable, irreducible 3-manifold M can be modified to a 0-efficient triangulation orM can be shown to be one of the manifolds S 3 , RP 3 or L(3,1). Similarly, any triangulation of a com- pact, orientable, irreducible, @-irreducible 3-manifold can be modified to a 0-efficient triangulation. The notion of a 0-efficient ideal tr is de- fined. It is shown if M is a compact, orientable, irreducible, @-irreducible 3-manifold having no essential annuli and distinct from the 3-cell, then ◦ M admits an ideal triangulation; furthermore, it is shown that any ideal trian- gulation of such a 3-manifold can be modified to a 0-efficient ideal triangula- tion. A 0-efficient triangulation of a closed manifold has only one vertex or the manifold is S 3 and the triangulation has precisely two vertices. 0-efficient tri- angulations of 3-manifolds with boundary, and distinct from the 3-cell, have all their vertices in the boundary and then just one vertex in each bound- ary component. As tools, we introduce the concepts of barrier surface and shrinking, as well as the notion of crushing a triangulation along a normal sur- face. A number of applications are given, including an algorithm to construct an irreducible decomposition of a closed, orientable 3-manifold, an algorithm to construct a maximal collection of pairwise disjoint, normal 2-spheres in a closed 3-manifold, an alternate algorithm for the 3-sphere recognition prob- lem, results on edges of low valence in minimal triangulations of 3-manifolds, and a construction of irreducible knots in closed 3-manifolds.
The Significance of Simple Invariant Solutions in Turbulent Flows

Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. One of the significant advances in this respect has been the numerical discovery of simple invariant sets, such as nonlinear equilibria and periodic solutions, in well-resolved Navier--Stokes flows. This review describes some fundamental and practical aspects of dynamical systems theory for the investigation of turbulence, focusing on recently found invariant solutions and their significance for the dynamical and statistical characterization of low-Reynolds-number turbulent flows. It is shown that the near-wall regeneration cycle of coherent structures can be reproduced by such solutions. The typical similarity laws of turbulence, i.e. the Prandtl wall law and the Kolmogorov law for the viscous range, as well as the pattern and intensity of turbulence-driven secondary flow in a square duct can also be represented by these simple invariant solutions.
Substrate integrated waveguide (SIW) filter with hexagonal resonator

A novel substrate integrated waveguide (SIW) hexagonal resonator structure and its applications to bandpass filters are presented. Based on the SIW techniques, the resonance characteristic of proposed resonator is investigated. The hexagonal SIW resonators, which can combine flexibility of rectangular cavities and performance of circular cavities, are convenient for bandpass filters design. Since any of the six sides of a hexagonal resonator can be utilized for coupling, the filter configurations are flexible and adaptable. By changing the coupling sides of the hexagonal resonators, two types of experimental circuit configuration at the same central frequency of 10 GHz but with different fractional bandwidths of 3 and 6%, including third-order Chebyshev and crossed-coupling trisection, are constructed, fabricated, and measured. Measured results show a good agreement with simulated ones and validate the proposed configurations.
Adaptive manifold‐mapping using multiquadric interpolation applied to linear actuator design

Purpose – This work aims to present a multilevel optimization strategy based on manifold‐mapping combined with multiquadric interpolation for the coarse model construction.Design/methodology/approach – In the proposed approach the coarse model is obtained by interpolating the fine model using multiquadrics in a small number of points. As the algorithm iterates the response surface model is improved by enriching the set of interpolation points.Findings – This approach allows to accurately solve the TEAM Workshop Problem 25 using as little as 33 finite element simulations. Furthermore, it allows a robust sizing optimization of a cylindrical voice‐coil actuator with seven design variables.Research limitations/implications – Further analysis is required to gain a better understanding of the role that the initial coarse model accuracy plays in the convergence of the algorithm. The proposed model allows to carry out such analysis by varying the number of points included in the initial response surface model. Th.
Multi-Parameter Criticality in Chua's Circuit at Period-Doubling Transition to Chaos

Investigation of non-Feigenbaum types of period-doubling universality is undertaken for a single Chua's circuit and for two systems with a unidirectional coupling. Some codimension-2 critical situations are found numerically that were known earlier for bimodal 1D maps. However, the simplest of them (tricritical) does not survive in a strict sense when the exact dynamical equations are used instead of the 1D map approximation. In coupled systems double Feigenbaum's point and bicritical behavior are found and studied. Scaling properties that are the same as in two logistic maps with a unidirectional coupling are illustrated.
Herbivory damage but not plant disease under experimental warming is dependent on weather for three subalpine grass species

Both theory and prior studies predict that climate warming should increase attack rates by herbivores and pathogens on plants. However, past work has often assumed that variation in abiotic conditions other than temperature (e.g. precipitation) do not alter warming responses of plant damage by natural enemies. Studies over short time periods span low variation in weather, and studies over long time‐scales often neglect to account for fine‐scale weather conditions. Here, we used a 20+ year warming experiment to investigate if warming affects on herbivory and pathogen disease are dependent on variation in ambient weather observed over 3 years. We studied three common grass species in a subalpine meadow in the Colorado Rocky Mountains, USA. We visually estimated herbivory and disease every 2 weeks during the growing season and evaluated weather conditions during the previous 2‐ or 4‐week time interval (2‐week average air temperature, 2‐ and 4‐week cumulative precipitation) as predictors of the probability and amount of damage. Herbivore attack was 13% more likely and damage amount was 29% greater in warmed plots than controls across the focal species but warming treatment had little affect on plant disease. Herbivory presence and damage increased the most with experimental warming when preceded by wetter, rather than drier, fine‐scale weather, but preceding ambient temperature did not strongly interact with elevated warming to influence herbivory. Disease presence and amount increased, on average, with warmer weather and more precipitation regardless of warming. Synthesis. The effect of warming over reference climate on herbivore damage is dependent on and amplified by fine‐scale weather variation, suggesting more boom‐and‐bust damage dynamics with increasing climate variability. However, the mean effect of regional climate change is likely reduced monsoon rainfall, for which we predict a reduction in insect herbivore damage. Plant disease was generally unresponsive to warming, which may be a consequence of our coarse disease estimates that did not track specific pathogen species or guilds. The results point towards temperature as an important but not sufficient determinant and regulator of species interactions, where precipitation and other constraints may determine the affect of warming.
Experience conflicts with and undermines instruction and its legacy: examples from two-dimensional motion

Dynamic and static representations of two-dimensional motion serve to illustrate the possession of persistently incorrect views about Newtonian mechanics among adolescents and adults alike. Several aspects of these views are demonstrated to be strikingly similar to historically held theories, and to arise from perceptual features of motion that clearly pose a formidable obstacle to an acquisition of proper mechanics understanding. Suggestions for instructionally effective approaches to teaching are offered, with an eye on the larger implications for the development of scientific literacy.
Anti reflection coatings in semiconductor lasers: effects on power emission and external cavity lasing

Parameters controlling light generation and emission in semiconductor lasers were analyzed. Effects of facet reflectivity on laser emission and the overall power dissipation were studied. It is shown with typical values that, optimized conditions of facet coating can reduce the laser power dissipation by several hundred milliwatts for optical output levels on the order of 10 mw. A mathematical model was developed for external cavity lasing of semiconductor lasers. Effects of threshold shift and changes in slope efficiency for external cavity operation, as reported in the literature, are explained by our model. Our model also explains reported observations of residual Fabry-Pérot modes of oscillation in external cavity operation. It is shown that anti reflection coating plays the most significant role in decreasing the threshold current in external cavity mode compared to that of Fabry Pérot lasing. It is estimated that a coating reflectivity of 10-5 with an external grating efficiency of 50% can result in a shift of threshold current by more than 50 mA. The effects of grating efficiency and facet reflectivity on increasing the window of feasible external cavity laser operation with reduced competition from residual modes were studied.
Geometric classification of simple graph algebras

Inspired by Franks' classification of irreducible shifts of finite type we provide a short list of allowed moves on graphs that preserves the stable isomorphism class of the associated C*-algebras. We show that if two graphs have stably isomorphic and simple unital algebras then we can use these moves to transform one into the other.