Number Of Facets Research Articles

Simplicial Complexes with Many Facets are Vertex Decomposable

Suppose $\Delta$ is a pure simplicial complex on $n$ vertices having dimension $d$ and let $c = n-d-1$ be its codimension in the simplex. Terai and Yoshida proved that if the number of facets of $\Delta$ is at least $\binom{n}{c}-2c+1$, then $\Delta$ is Cohen-Macaulay. We improve this result by showing that these hypotheses imply the stronger condition that $\Delta$ is vertex decomposable. We give examples to show that this bound is optimal, and that the conclusion cannot be strengthened to the class of matroids or shifted complexes. We explore an application to Simon's Conjecture and discuss connections to other results from the literature.

Optimal representation of tree foliage for local urban climate modeling

Trees impact the local urban climate, notably at street level by intercepting solar radiation and providing shading. Evapotranspiration in foliage may reduce the air temperature although it may increase relative humidity and leaf drag may reduce wind speed, affecting thermal comfort. To document and quantify this impact, microclimate modeling with Computational Fluid Dynamics (CFD) simulations requires explicit information of the urban configuration, including trees. However, trees are complex individuals with a variety of shapes and a variety of foliage distribution. This study aims to investigate the sensibility to the tree modeling of the urban climate simulations. Starting with terrestrial LiDAR data from trees of different species, ages, and forms, we propose a systematic evaluation of the optimal representation of arboreal configurations in terms of local urban comfort. One way to represent the foliage of trees accurately is to apply Delaunay triangulation on the LiDAR data, which yields a convex envelope model. The resulting foliage shape is very close to the actual tree, but includes a high number of facets leading to complex objects to model numerically. Comparing four species and three maturity level of trees with this method, the paper shows that the size of the zone shadowed by a tree is the parameter with the largest impact on thermal comfort, as the ability of trees to absorb solar radiation is the main asset to improve thermal comfort. The UTCI could be up to 2.1°C lower for a mature ACPL than for a sapling, mainly because the zone covered by the tree is larger. In addition, polyhedron shape rhombicuboctahedron (RBC) produces accurate shadowed zones. Mostly, in literature, tree canopies are modeled with cubic representations while we see that they overestimate the size of the shadowed zone. To have reliable compromise between accuracy and time for conception and computational time, this paper shows that the RBC is the best alternative to common tree models. Despite requiring a good knowledge of the canopy geometry, RBC provides a strong capacity for accurately modelling complex canopy shapes of most tree species and offers large benefits in reduced complexity. We show that the RBC shape, thanks to its simple but flexible geometry, is an efficient and accurate methodological approach to model trees and allows savings in computational time (up to 15% faster than the convex envelope) and costs; and we expect that this method will improve the modeling of further parametric studies on vegetation impact on thermal urban comfort.

On dihedral angle sums and number of facets for product polytopes

In this paper we present a method for computing the dihedral angle sums (and their two-sided estimates) of cartesian and skew product polytopes provided the sums of dihedral angles (or their estimates) are known for the factors. In addition, a formula for computing the number of facets of such product polytopes is derived. The method proposed is very universal and illustrated by several examples. The estimates are in a full agreement with known results for prisms and hexahedra.

New Therapeutic Strategies for the Inflammatory Rheumatoid Arthritis Disease: Emphasizing Mesenchymal Stem Cells and Associated exo-miRNA or exo-lncRNA.

The most prevalent inflammatory arthritis and a leading contributor to disability is rheumatoid arthritis (RA). Although it may not have arrived in Europe until the 17th century, it was present in early Native American communities several thousand years ago. Exosomes released by mesenchymal stem cells (MSCs) are highly immunomodulatory due to the origin of the cell. As a cell-free therapy, MSCs-exosomes are less toxic and elicit a weakened immune response than cell-based therapies. Exosomal noncoding RNAs (ncRNAs) are closely associated with a number of biological and functional facets of human health, especially microRNAs (miRNAs) and long noncoding RNAs (lncRNAs). Various exo-miRNAs and lncRNAs such as HAND2-AS1, miR-150-5p, miRNA-124a, and miR-320a lodged with MSC could be appropriate therapeutic ways for RA treatment. These MSC-derived exosomes affect RA disorders via different molecular pathways such as NFK-β, MAPK, and Wnt. The purpose of this review is to review the research that has been conducted since 2020 so far in the field of RA disease treatment with MSC-loaded exo-miRNAs and exo-lncRNAs.

Biexciton Emission in CsPbBr3 Nanocrystals: Polar Facet Matters.

The metal halide perovskite nanocrystals exhibit a remarkable tolerance to midgap defect states, resulting in high photoluminescence quantum yields. However, the potential of these nanocrystals for applications in display devices is hindered by the suppression of biexcitonic emission due to various Auger recombination processes. By adopting single-particle photoluminescence spectroscopy, herein, we establish that the biexcitonic quantum efficiency increases with the increase in the number of facets on cesium lead bromide perovskite nanocrystals, progressing from cube to rhombic dodecahedron to rhombicuboctahedron nanostructures. The observed enhancement is attributed mainly to an increase in their surface polarity as the number of facets increases, which reduces the Coulomb interaction of charge carriers, thereby suppressing Auger recombination. Moreover, Auger recombination rate constants obtained from the time-gated photon correlation studies exhibited a discernible decrease as the number of facets increased. These findings underscore the significance of facet engineering in fine-tuning biexciton emission in metal halide perovskite nanocrystals.

On Pisot units and the fundamental domain of Galois extensions of [formula omitted]

Let K be a number field that is Galois over Q with unit group of rank d. We obtain an upper bound on the number of facets of the reduction domain (and therefore the fundamental domain) of K of O(((d+1)ρ∞(ΛK)+log⁡(d2))d(d+1)!), where ρ∞(ΛK) is the covering radius of the log-unit lattice in the infinity norm. As a side-result, we also show that the Weil height of the shortest Pisot unit in the number field can be no greater than γ[K:Q]((d+1)ρ∞(ΛK)+dϵ) where γ=1 if K is totally real or 2 otherwise and ϵ>0 is some arbitrarily small constant.

Development and initial validation of a yes/no vocabulary test for North Sámi

Abstract This paper accounts for the development and initial validation of a yes/no vocabulary test of North Sámi called North Sámi Vocabulary Test (NSVT). North Sámi (NS) is an Indigenous language spoken in northern Scandinavia. Being an endangered language, NS is in need of revitalisation efforts. One contribution is the provision of proficiency assessment tools. We administered a 75-item NSVT version (50 real verbs and 25 pseudoverbs) to users of North Sámi in Sweden and Norway (N = 289). Evidence of high item- and person-based reliability and separation indices were observed, as well as support for a number of validity facets. High correlations existed between NSVT scores and self-reported and rated spoken proficiency. The NSVT provides quick and reliable assessment of vocabulary knowledge and an indication of overall language proficiency in North Sámi.

Misorientation Angle Study on Cleavage Fracture Propagation Surfaces of a Grade a Ship Steel, through Charpy and Four-Point Double-Notch Bend Tests

Misorientation Angle Study on Cleavage Fracture Propagation Surfaces of a Grade a Ship Steel, through Charpy and Four-Point Double-Notch Bend Tests

De-projecting the EFThedron

The space of Wilson coefficients of EFT that can be UV completed into consistent theories was recently shown to be described analytically by a positive geometry, termed the EFThedron. However, this geometry, as well as complementary numerical methods of semi-definite programming, have so far focused on the positivity of the partial wave expansion, which allows bounding only ratios of couplings. In this paper we describe how the unitarity upper bound of the partial waves can be incorporated. This new problem can be formulated in terms of the well known L-moment problem, which we generalize and solve from a geometrical perspective. We find the non-projective generalization of the EFThedron has an infinite number of non-linear facets, which in some cases have remarkably simple descriptions. We use these results to derive bounds on single couplings, finding that the leading derivative operators are bounded by unity, when normalized by the cut-off scale and loop factors. For general operators of mass dimension 2k we find the upper bound is heavily suppressed at large k, with an 1/k fall-off.

Atomistic study of CoCrCuFeNi high entropy alloy nanoparticles: Role of chemical complexity

High entropy alloy nanoparticles are envisaged as one of the most interesting materials compared to monoatomic materials due to their modulated properties in terms of their convenient surface-to-volume ratio. However, studies are still missing to unveil how composition or nanoparticle size can influence nanoparticle morphology. Based on molecular dynamics simulations, we perform a structural characterization as a function of nanoparticle size and the chemical composition of high entropy alloy nanoparticles subject to multiple annealing cycles. After the multiple thermal loads, we observe a substantial migration of copper atoms towards the np surface, consistent with the experimental results of Cu-based high entropy alloys. The resulting high entropy alloy nanoparticle behaves as a core–shell nanostructure with a rich fcc phase on the surface (50% of Cu) and 5% fcc phase in the nanoparticle core. Inspecting the nanoparticle surface, it is observed that high entropy alloy nanoparticles have a lack of surface facets, leading to a more spherical shape, quite different from mono-metallic nanoparticles with a high number of facets. Performing an average atoms simulation, it showed that nanoparticles are prone to form 111 surface facets independent of the nanoparticle size, suggesting that for high entropy alloy nanoparticles, the chemical complexity avoids the formation of surface facets. The latter can be explained in terms of the lattice distortion inducing tensile/compressive stress that drives the surface reconstruction. All in all our results match extremely well with experimental evidence of FeNiCrCoCu nanocrystalline materials, explaining the Cu segregation in terms of surface energy and mixing enthalpy criteria. We believe that our results provide a detailed characterization of high entropy nanoparticles focusing on how chemical complexity induces morphological changes compared to mono-crystalline nanoparticles. Besides, our findings are valuable for experimental works aimed at designing the shape and composition of multicomponent nanoparticles.

Facet Dependent Photoluminescence Blinking from Perovskite Nanocrystals.

Photoluminescence (PL) blinking of nanoparticles, while detrimental to their imaging applications, may benefit next-generation displays if the blinking is precisely controlled by reversible electron/hole injections from an external source. Considerable efforts are made to create well-characterized charged excitons within nanoparticles through electrochemical charging, which has led to enhanced control over PL-blinking in numerous instances. Manipulating the photocharging/discharging rates in nanoparticles by surface engineering can represent a straightforward method for regulating their blinking behaviors, an area largely unexplored for perovskite nanocrystals (PNCs). This work shows facet engineering leading to different morphologies of PNCs characterized by distinct blinking patterns. For instance, examining the PL intensity trajectories of single PNCs, representing the instantaneous photon count rate over time, reveals that the OFF-state population significantly increases as the number of facets increases from six to twenty-six. This study suggests that extra-faceted PNCs, owing to their polar facets and expanded surface area, render them more susceptible to photocharging, which results in larger OFF-state populations. Furthermore, the fluorescence correlation spectroscopy (FCS) study unveils that the augmented propensity for photocharging in extra-faceted PNCs can also originate from their greater tendency to form complexes with neighboring molecules.

Rockfall Analysis from UAV-Based Photogrammetry and 3D Models of a Cliff Area

The application of Unmanned Aerial Vehicles (UAVs), commonly known as drones, in geological, geomorphological, and geotechnical studies has gained significant attention due to their versatility and capability to capture high-resolution data from challenging terrains. This research uses drone-based high-resolution photogrammetry to assess the geomechanical properties and rockfall potential of several rock scarps within a wide area of 50 ha. Traditional methods for evaluating geomechanical parameters on rock scarps involve time-consuming field surveys and measurements, which can be hazardous in steep and rugged environments. By contrast, drone photogrammetry offers a safer and more efficient approach, allowing for the creation of detailed 3D models of a cliff area. These models provide valuable insights into the topography, geological structures, and potential failure mechanisms. This research processed the acquired drone imagery using advanced geospatial software to generate accurate orthophotos and digital elevation models. These outputs analysed the key factors contributing to rockfall triggering, including identifying discontinuities, joint orientations, kinematic analysis of failures, and fracturing frequency. More than 8.9 × 107 facets, representing discontinuity planes, were recognised and analysed for the kinematic failure modes, showing that direct toppling is the most abundant rockfall type, followed by planar sliding and flexural toppling. Three different fracturation grades were also identified based on the number of planar facets recognised on rock surfaces. The approach used in this research contributes to the ongoing development of fast, practical, low-cost, and non-invasive techniques for geomechanical assessment on vertical rock scarps. In particular, the results show the effectiveness of drone-based photogrammetry for rapidly collecting comprehensive geomechanical data valid to recognise the prone areas to rockfalls in vast regions.

Modulating surface zinc species via facet engineering for efficient electroreduction of CO2 to CO

Zn-based catalysts have attracted widespread interest in electrocatalytic reduction of CO2 to CO, but they struggle to achieve large current densities and high product selectivity. Herein, we develop two kinds of faceted ZnO nanorods with subtle changes in crystallography and surface composition, simply by adjusting thermal annealing conditions. The ZnO nanorods with high numbers of (101) facets (ZnO (101)) and a reorganized Zn-rich surface exhibit higher catalytic performance compared to conventional ZnO nanorods with more (002) crystal planes and an oxygen-rich surface. The ZnO (101) catalyst shows superior FECO (>90 %) over a broad potential range, and an attractive CO partial current density of − 215.3 mA cm−2 in flow cells. DFT results further reveal that CO2 molecules are more easily activated on the reorganized surface of the ZnO (101), which significantly facilitates the formation of *COOH and inhibits the hydrogen evolution reaction, leading to remarkable activity and selectivity.

Facets of High-Dimensional Gaussian Polytopes

We study the number of facets of the convex hull of n independent standard Gaussian points in Rd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}^d$$\\end{document}. In particular, we are interested in the expected number of facets when the dimension is allowed to grow with the sample size. We establish an explicit asymptotic formula that is valid whenever d/n→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d/n\\rightarrow 0$$\\end{document}. We also obtain the asymptotic value when d is close to n.

An outer approximation algorithm for generating the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems

In this paper, we present an outer approximation algorithm for computing the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems (MOMILPs). It produces the extreme points (i.e., the vertices) as well as the facets of the Edgeworth–Pareto hull. We note that these extreme points are the extreme supported non-dominated points of a MOMILP. We also show how to extend the concept of geometric duality for multi-objective linear programming problems to the Edgeworth–Pareto hull of MOMILPs and use this extension to develop the algorithm. The algorithm relies on a novel oracle that solves single-objective weighted-sum problems and we show that the required number of oracle calls is polynomial in the number of facets of the convex hull of the extreme supported non-dominated points in the case of MOMILPs. Thus, for MOMILPs for which the weighted-sum problem is solvable in polynomial time, the facets can be computed with incremental-polynomial delay—a result that was formerly only known for the computation of extreme supported non-dominated points. Our algorithm can be an attractive option to compute lower bound sets within multi-objective branch-and-bound algorithms for solving MOMILPs. This is for several reasons as (i) the algorithm starts from a trivial valid lower bound set then iteratively improves it, thus at any iteration of the algorithm a lower bound set is available; (ii) the algorithm also produces efficient solutions (i.e., solutions in the decision space); (iii) in any iteration of the algorithm, a relaxation of the MOMILP can be solved, and the obtained points and facets still provide a valid lower bound set. Moreover, for the special case of multi-objective linear programming problems, the algorithm solves the problem to global optimality. A computational study on a set of benchmark instances from the literature is provided.

Surface Reconstructions in II-VI Quantum Dots.

Although density functional theory (DFT) calculations have been crucial in our understanding of colloidal quantum dots (QDs), simulations are commonly carried out on QD models that are significantly smaller than those generally found experimentally. While smaller models allow for efficient study of local surface configurations, increasing the size of the QD model will increase the size or number of facets, which can in turn influence the energetics and characteristics of trap formation. Moreover, core-shell structures can only be studied with QD models that are large enough to accommodate the different layers with the correct thickness. Here, we use DFT calculations to study the electronic properties of QDs as a function of size, up to a diameter of ∼4.5 nm. We show that increasing the size of QD models traditionally used in DFT studies leads to a disappearance of the band gap and localization of the HOMO and LUMO levels on facet-specific regions of the QD surface. We attribute this to the lateral coupling of surface orbitals and the formation of surface bands. The introduction of surface vacancies and their a posteriori refilling with Z-type ligands leads to surface reconstructions that widen the band gap and delocalize both the HOMO and LUMO. These results show that the surface geometry of the facets plays a pivotal role in defining the electronic properties of the QD.

PID-5-SRF online administration: psychometric indicators and measurement invariance between different formats of data collection.

The PID-5 is a tool used to assess maladaptive personality traits according to the DSM-5 Alternative Model. Objective: The objective is to seek evidence of the validity and reliability of the Personality Inventory for DMS-5 (PID-5-SRF) admin-istered online and assess its measurement invariance compared to the paper-and-pencil administration. A sample of 274 individuals from the general population (73.4% of women; 34.76 years old ±11.6) completed the instrument online after the study was dissemi-nated on social media and among the authors' contacts. Internal consistency (facets α≥0.70; domains α≥0.89) and test-retest reliability (15 to 30 days: facets ICC≥0.63; domains ICC≥0.82) were satisfactory, but a floor effect was found in almost all the items. A large number of facets (N=9) showed better fit to a bifactorial structure, and the Exploratory Factor Analysis suggested that a six-factor model better fits the data. Measurement invariance between the online and paper-and-pencil administrations was not attested at a configural level. The results revealed satisfactory psychometric indicators when the instrument was applied online, confirming its feasibility in collecting data. However, the in-strument's structure is not invariant, and caution must be adopted when compar-ing and interpreting data collected through different formats.

Acarbose ameliorates western diet‐induced metabolic and cognitive impairments in the 3xTg mouse model of Alzheimer’s disease

AbstractBackgroundMany age‐related diseases are major risk factors of Alzheimer’s disease (AD), such as type II diabetes mellitus and cardiovascular disease. As such, there is a growing body of interest in determining if already in use geroprotective interventions for these disorders may also be beneficial in AD. One such intervention is acarbose, an anti‐diabetic drug that improves glucose homeostasis, reduces risk of myocardial infarction, and extends lifespan in various mouse models.MethodWe administered either a western diet or a western diet containing acarbose to diet‐induced obese male and female 3xTg mice starting at 6 months of age. Over the following 6 months, we examined a number of facets of metabolic health and analyzed cognitive function using Barnes maze. After sacrificing mice at 12 months of age, we analyzed aspects of AD pathology in the brain using Western blotting and immunohistochemistry.ResultBoth male and female 3xTg mice treated with acarbose exhibited decreased body weight and adiposity despite increased food consumption. Acarbose‐treated mice also had an overall improvement in glycemic control and increased energy expenditure. Female mice showed dramatic improvements in cognition and AD pathology, and males exhibited minor improvements as well. Preliminary data also suggest that there is increased gliosis in mice fed a western diet, which may be ameliorated by acarbose.ConclusionIn the context of a western diet, acarbose has dramatic benefits on metabolic health, cognitive health, and AD pathology. This suggests that there is potential for already in use geroprotective pharmaceuticals such as acarbose to ameliorate AD pathology.

How Many Raters Can Be Enough: G Theory Applied to Assessment and Measurement of L2 Speech Perception

This paper extends the use of Generalizability Theory to the measurement of extemporaneous L2 speech through the lens of speech perception. Using six datasets of previous studies, it reports on G studies–a method of breaking down measurement variance–and D studies–a predictive study of the impact on reliability when modifying the number of raters, items, or other facets that assist the field in adopting measurement designs that include comprehensibility, accentedness, and intelligibility. When data from a single audio sample per learner were subjected to D-studies, we find that both semantic differential and rubric scales for comprehensibility were reliable at the .90 level with about 15 trained raters or 50 untrained crowdsourced raters. In order to offer generalizable and dependable evaluations, empirically informed recommendations are given, including considerations for the number of speech samples rated, or the granularity of the scales for various assessment and research purposes.

Impact of the Number of Needle Tip Bevels on the Exerted Forces and Energy in Insulin Pen Injections.

Patients affected with type 1 diabetes and a non-negligible number of patients with type 2 diabetes are insulin dependent. Both the injection technique and the choice of the most suitable needle are fundamental for allowing them to have a good injection experience. The needles may differ in several parameters, from the length and diameter, up to the forces required to perform the injection and to some geometrical parameters of the needle tip (e.g., number of facets or bevels). The aim of the research is to investigate whether an increased number of bevels could decrease forces and energy involved in the insertion-extraction cycle, thus potentially allowing patients to experience lower pain. Two needle variants, namely, 31 G × 5 mm and 32 G × 4 mm, are considered, and experimental tests are carried out to compare 3-bevels with 5-bevels needles for both the variants. The analysis of the forces and energy for both variants show that the needles with 5 bevels require a statistically significant lower drag or sliding force (p-value = 0.040 for the 31 G × 5 mm needle and p-value < 0.001 for 32 G × 4 mm), extraction force (p-value < 0.001 for both variants), and energy (p-value < 0.001 for both variants) during the insertion-extraction cycle. As a result, 3-bevels needles do not have the same functionality of 5-bevels needles, show lower capacity of drag and extraction, and can potentially be related to more painful injection experience for patients.