Optimal Dual Schemes for Adaptive Grid Based Hexmeshing

Hexahedral meshes are a ubiquitous domain for the numerical resolution of partial differential equations. Computing a pure hexahedral mesh from an adaptively refined grid is a prominent approach to automatic hexmeshing, and requires the ability to restore the all hex property around the hanging nodes that arise at the interface between cells having different size. The most advanced tools to accomplish this task are based on mesh dualization. These approaches use topological schemes to regularize the valence of inner vertices and edges, such that dualizing the grid yields a pure hexahedral mesh. In this article, we study in detail the dual approach, and propose four main contributions to it: (i) We enumerate all the possible transitions that dual methods must be able to handle, showing that prior schemes do not natively cover all of them; (ii) We show that schemes are internally asymmetric, therefore not only their construction is ambiguous, but different implementative choices lead to hexahedral meshes with different singular structure; (iii) We explore the combinatorial space of dual schemes, selecting the minimum set that covers all the possible configurations and also yields the simplest singular structure in the output hexmesh; (iv) We enlarge the class of adaptive grids that can be transformed into pure hexahedral meshes, relaxing one of the tight topological requirements imposed by previous approaches. Our extensive experiments show that our transition schemes consistently outperform prior art in terms of ability to converge to a valid solution, amount and distribution of singular mesh edges, and element count. Last but not least, we publicly release our code and reveal a conspicuous amount of technical details that were overlooked in previous literature, lowering an entry barrier that was hard to overcome for practitioners in the field.

A Proof of the Riemann Hypothesis Based on a New Expression of the Completed Zeta Function

The completed zeta function $\xi(s)$ is expanded in MacLaurin series (infinite polynomial), which can be further expressed as infinite product (Hadamard product) of quadratic factors by its complex conjugate zeros $\rho_i=\alpha_i +j\beta_i, \bar{\rho}_i=\alpha_i-j\beta_i, 0<\alpha_i<1, \beta_i\neq 0, i\in \mathbb{N}$ are natural numbers from 1 to infinity, $\rho_i$ are in order of increasing $|\rho_i|=\sqrt{\alpha_i^2+\beta_i^2}$, i.e., $|\rho_1|<|\rho_2|\leq|\rho_3|\leq |\rho_4|, \cdots$, together with $\beta_1<\beta_2\leq\beta_3\leq\beta_4, \cdots$. Then, according to the functional equation $\xi(s)=\xi(1-s)$, we have $$\xi(0)\prod_{i\in \mathbb{N}}\Big{(}\frac{\beta_i^2}{\alpha_i^2+\beta_i^2}+\frac{(s-\alpha_i)^2}{\alpha_i^2+\beta_i^2}\Big{)} =\xi(0)\prod_{i\in \mathbb{N}}\Big{(}\frac{\beta_i^2}{\alpha_i^2+\beta_i^2}+\frac{(1-s-\alpha_i)^2}{\alpha_i^2+\beta_i^2}\Big{)}$$ which, by Lemma 3, is equivalent to $$(s-\alpha_i)^2 = (1-s-\alpha_i)^2, i \in \mathbb{N}, \text{from 1 to infinity.}$$ with only valid solution $\alpha_i= \frac{1}{2}$ (another solution $s=\frac{1}{2}$ is invalid due to obvious contradiction). Thus, a proof of the Riemann Hypothesis is achieved.

From Seaweeds to Cosmeceutics: A Multidisciplinar Approach

Macroalgae are widespread on the coasts of all the globe and lead to a negative ecological impact, requiring expensive remediations. Therefore, the valorization of invasive seaweed as a renewable source of bioactive products could represent a valid solution. In this context, three algal biomasses, belonging to brown, green, and red families (Sargassum muticum, Ulva lactuca, Solieria filiformis), collected in the venetian Laguna, were investigated as a source of active compounds for the formulation of cosmeceutics. Microwave (MW) and ultrasound (US) were applied to enhance the algae extraction by means of a hydroalcoholic solution. According to total phenolic content (TPC) evaluation, MW demonstrated the best performing outcomes, resulting in 19.77, 22.02, and 16.94 mgGAE/gExtr (30 min at 90 °C) for brown, green, and red algae, respectively. Antioxidant activity was tested as well, showing comparable trends (49.19, 26.24, and 3.02 mmolTrolox eq./gExtr for brown, green, and red algae, respectively). Due to natural algae predisposition to absorb contaminants, the metal content analysis helped to screen the applicability of these extracts, identifying Ulva lactuca as the most suitable source of antioxidants for cosmetic formulations. This MW extract was then adopted to formulate two different preparations, namely a gel and an emulsion. Thermal and mechanical tests confirmed the stability of each formulation, together with neutral organoleptic characteristics. Finally, the actives release was investigated by means of a tape stripping essay, showing an efficient controlled release for gel formulation, even after 7 h of test. The produced cosmeceutics merged non-conventional extraction technologies with formulation expertise, offering a valuable alternative to solve the macroalgae disposal issue.

Digital Mobility Assessment for Regulatory and Clinical Endorsement in Hip Fracture Patients

Hip fracture is the most frequent non-intentional injury of older persons leading to hospital admission in Europe and North America. Until recently, in regulatory submissions no attention was given to patients’ mobility after sustaining/recovering from a hip fracture. To better evaluate efficacy and effectiveness of new drugs and treatments, it is necessary to develop mobility biomarkers since failure to recover and regain pre-fracture mobility is considered the single most important disability symptom experienced by hip fracture patients, often leading to care home admission. However, regularly used measures of mobility capacity are not representative of individuals’ performance in real life, intermittent in nature, and require visiting study centers. Digital technology has the potential to revolutionize mobility assessment in a real-life setting. With this presentation we build a case for a valid solution for real-world digital mobility assessment in hip fracture patients as carried out in the “Mobilise-D” clinical validation study.

Modeling, structural and cfd analysis of mobile robot for banana cultivation

The banana plantation is a popular cash crop in southern parts of India. Globally, India ranks first in banana production by producing about 14 million metric tons annually. Cultivation of which involves humongous manual tasks with moderate difficulty, often the tasks are accompanied by considerable spending towards accomplishing those tasks. More often than not it affects the earning prospects of the farmer thus, succumbing to a great loss of investment. A valid solution to this problem from the technological perspective is to provide low-cost automation for the hectic tasks in banana cultivation. Through this work, a baby step towards addressing the issues in banana cultivation is initiated. This paper deals with the design, structural, computational fluid dynamics simulation of an Agricultural field robot for aiding banana cultivation by producing a plantation hole for banana seedlings. The conceptualized idea is modeled in 3dimension using SolidWorks software with suitable dimensions, then by applying desired material properties to the individual components a static structural analysis is executed on the assembly. After the completion of structural analysis, subsequently, CFD analysis is carried out with an Ansys-Fluent workbench on the equivalent solid modal replica of the assembly modal, developed exclusively to analyze the wind effects.

A Graph-Based Ant Algorithm for the Winner Determination Problem in Combinatorial Auctions

Iterative combinatorial auctions are known to resolve bidder preference elicitation problems. However, winner determination is a known key bottleneck that has prevented widespread adoption of such auctions, and adding a time-bound to winner determination further complicates the mechanism. As a result, heuristic-based methods have enjoyed an increase in applicability. We add to the growing body of work in heuristic-based winner determination by proposing an ant colony metaheuristic–based anytime algorithm that produces optimal or near-optimal winner determination results within specified time. Our proposed algorithm resolves the speed versus accuracy problem and displays superior performance compared with 20 past state-of-the-art heuristics and two exact algorithms, for 94 open test auction instances that display a wide variety in bid-bundle composition. Furthermore, we contribute to the literature in two predominant ways: first, we represent the winner determination problem as one of finding the maximum weighted path on a directed cyclic graph; second, we improve upon existing ant colony heuristic–based exploration methods by implementing randomized pheromone updating and randomized graph pruning. Finally, to aid auction designers, we implement the anytime property of the algorithm, which allows auctioneers to stop the algorithm and return a valid solution to the winner determination problem even if it is interrupted before computation ends.

Sewage sludge enhances tomato growth and improves fruit-yield quality by restoring soil fertility

Among the various disposal strategies for sewage sludge (SS), soil application is the most suitable. This study was conducted to evaluate soil amendment with SS (0, 10, 20, 30 and 40 g/kg) and its impact on soil fertility and tomato (Solanum lycopersicum L.) growth. The SS significantly improved the agromorphological attributes, the number of produced fruits, and the fruit biomass of tomato plants. The 30 g/kg application of SS led to the highest growth rate and fruit yield. Considering the fruits, the best safe enrichment of metal nutrients was recorded at 30 g/kg, with a significant increase in the micronutrient metals Mn, Zn, Ni, Cu, and Fe with 624, 193, 125, 70, and 32%, respectively, compared to the control. The SS amendment enhanced soil fertility, and heavy metals were within the permissible ranges for agricultural soils. Bioaccumulation factors (BFs) indicated that SS application induced the accumulation of most of the studied metals in the roots, and the BF values of Zn, Cu, Ni, and Pb were > 1. The current study concluded that recirculating SS nutrient components to agricultural soils could offer a valid solution for the sustainable management of this organic waste and enhance plant-crop productivity.

THE PHILOSOPHICAL EXAMINATION ON INTEGRATION OF KNOWLEDGE AND WAYS FORWARD

The crisis of error and confusion of knowledge in cumulative today is inevitable as it has given birth to the false leaders who are incapable of making correct decision in their scope of responsibilities. Secularism as the poisoning ideology had inflicted chaos to the proper metaphysical realm of God with the subordination of existents in ranks through their corpus of so-called modern knowledge that have been rendered dominantly yet arguably as mainstream intellectualism. The nature of unified and hierarchical knowledge is mistreated and broken into fragmentation because the supreme, first principle of Tawhid as the soul of Islamic thought is suspended in knowledge production of modern science. As an antidote to this issue fast forward after the Islamization of knowledge was introduced, the idea of integration of knowledge was also brought into the picture to resolve the same brand crisis. However, the initiative of integration of knowledge as one of those has been grappling to present its philosophical underpinnings as in tandem with Islamic worldview as the valid solution to the knowledge crisis concerned. Therefore, this conceptual paper is esteemed to examine the philosophical structure of integration of knowledge idea as seen from Islamic mega scheme of knowledge. The data collection method involved in this writing was purely library search with the selection of literature from the advocates of integration of knowledge and some referenced from Islamic epistemology. The facts gathered were analyzed through content analysis technique with the approach of philosophical argumentation. The main findings of this writing were two-folded: i) The presentation of ontological, epistemological, axiological and methodological examination of integration of knowledge idea and its limitations. ii) The proposed integration of knowledge framework as a one of the methodologies of Islamic source in knowledge production and preservation. We contend that the contribution of this writing would further reframe the implementation of integration of knowledge in academic research endeavor in the institution advocating this epistemological idea.

Autotransplantation of the Third Molar: A Therapeutic Alternative to the Rehabilitation of a Missing Tooth: A Scoping Review

Introduction: Tooth autotransplantation is the repositioning of an erupted, partially erupted, or non-erupted autologous tooth from one site to another within the same individual. Several factors influence the success rate of the autotransplant, such as the stage of root development, the morphology of the tooth, the surgical procedure selected, the extraoral time, the shape of the recipient socket, the vascularity of the recipient bed, and the vitality of the cells of the periodontal ligament. The aim of this scoping review was to provide the most up-to-date information and data on the clinical principles of the third-molar autograft and thus provide clinical considerations for its success. Materials and methods: This review was conducted based on PRISMA-ScR (Preferred Reporting Items for Systematic reviews and Meta-Analyses extension for Scoping Reviews). The research was conducted by searching for keywords in three databases—PubMed, Scopus and Google Scholar—by two independent reviewers following the PRISMA protocol, from which 599 records were identified. Conclusions: Third-molar autotransplantation is a valid solution to replace missing teeth. The key to the success of this technique is the surgical procedure, which must be as atraumatic as possible to preserve the periodontal ligament of the tooth to be transplanted. The success rate is also linked to the stage of development of the root, with a worse prognosis in the case of a complete root.

The Effect of a Probiotic Complex on the Gut-Brain Axis: A Translational Study

<b><i>Background:</i></b> The gut-brain axis refers to the network of connections that involve multiple biologic systems, allowing bidirectional communication between the gut and the brain. This communication is mainly mediated by gut microbiota, thanks to its ability to modulate several processes like the production of neurotransmitters. As such, keeping a balanced gut microbiota through probiotic intake could be a valid solution in supporting the right gut-brain communications. <b><i>Methods:</i></b> A two-step in vitro screening of five different probiotic strains was carried out to select the best performers in the modulation of stress markers. A first selection on SK-N-DZ neuronal cell lines was performed to evaluate the inhibition of the epigenetic enzyme LSD1, promotion of GABA, and expression of serotonin. Three out of five strains were tested for their ability to promote serotonin synthesis in the Caco2 cell line. As a result, <i>Limosilactobacillus reuteri</i> PBS072 and <i>Bifidobacterium breve</i> BB077 were selected as the best performing strains. To confirm their effects in humans, a proof-of-concept trial was carried out to evaluate stress-related parameters for 28 days of product intake in a group of 30 stressed students. <b><i>Results:</i></b> A significant improvement of cognitive functions, in terms of short-term memory, attention, and executive performance, as well as of psychophysiological markers, such as salivary cortisol level, skin conductance, sleep quality, and anxiety, were observed. <b><i>Conclusions:</i></b> According to the results, <i>L. reuteri</i> PBS072 and <i>B. breve</i> BB077 are potential probiotic candidates for improving stress resilience, cognitive functions, and sleep quality.