We give a topological condition for a generic sliced space to be globally hyperbolic, without any hypothesis on the lapse function, shift function and spatial metric.

Recent advances in differential topology single out four-dimensions as being special, allowing for vast varieties of exotic smoothness (differential) structures, distinguished by their handlebody decompositions, even as the coarser algebraic topology is fixed. Should the spacetime we reside in takes up one of the more exotic choices, and there is no obvious reason why it shouldn't, apparent pathologies would inevitably plague calculus-based physical theories assuming the standard vanilla structure, due to the non-existence of a diffeomorphism and the consequent lack of a suitable portal through which to transfer the complete information regarding the exotic physical dynamics into the vanilla theories. An obvious plausible consequence of this deficiency would be the uncertainty permeating our attempted description of the microscopic world. We tentatively argue here, that a re-inspection of the key ingredients of the phenomenological particle models, from the perspective of exotica, could possibly yield interesting insights. Our short and rudimentary discussion is qualitative and speculative, because the necessary mathematical tools have only just began to be developed.

In previous studies, the authors utilized a single-dimensional operationalization of species density that implies induction of hierarchy and time with certain topologies. For further clarification of induced fractals including the relation to renormalization in physics, here a theoretical development is proposed based on a newly identified fact, namely that scaling parameters for magnetization exactly correspond to imaginary parts of Riemann zeta nontrivial zeros. An analogy to magnetization and accompanying Fake Monster Algebra is invoked to lend support to this theory, along with empirical species density data for a wild Dictyostelia community. A master torus and a Lagrangian/Hamiltonian are derived expressing fractal structures as a solution for diminishing divergent terms in renormalization.

Machines for direct digital inkjet printing on cylindrical containers are a new technology out on the market. Their commercialization in the industrial sector has been affected by their high precision. This leads to the use of mechanisms with narrow manufacturing tolerances and to the search for topologies that have the least accumulated error without affecting quality. Machines with topologies to work on flat substrates have printing and productivity problems working on cylindrical substrates. This research paper presents the qualitative design of a direct digital inkjet printer working over cylindrical substrates comparing five mechanical topologies; three topologies with radial distribution and two topologies with parallel distribution. The aim of these topologies is to find the precision, quality and efficiency of the printer taking into account the restrictions present in its construction. Each topology has separate constitutive mechanisms, it is analyzed the tolerance ranges between the print head and the substrate whose cumulative error maximizes the inkjet print resolution to determine precision. From five Topologies, number 1, 2 and 5 meet the requirements. the topology 2 meets the requirements but it is not able to be developed due to current technological limitations.

Recent methodological advances have enabled researchers to track the network structure of the human brain over time. Together, these studies provide novel insights into effective brain function, highlighting the importance of the systems-level perspective in understanding the manner in which the human brain organizes its activity to facilitate behavior. Here, we review a range of recent fMRI and electrophysiological studies that have mapped the relationship between inter-regional communication and network structure across a diverse range of brain states. In doing so, we identify both behavioral and biological axes that may underlie the tendency for network reconfiguration. We conclude our review by providing suggestions for future research endeavors that may help to refine our understanding of the functioning of the human brain.

In Functional Analysis as well as Topology, we frequently encounter sets, say $X$, that contain elements close to each other. These sets display a defining "finite-ness" property: for all open cover $\mathcal{O}$ of $X$, there exists a finite subcollection $\mathcal{U}\subseteq\mathcal{O}$ such that $\mathcal{U}$ covers $X$. Such spaces $X$ are called $\textbf{compact}$, and the above "finite-ness" property afford us great convenience, because we can always investigate $X$ by investigating its finite open cover $\mathcal{U}$Arzela-

An essential step in solving any topology optimization problem is determining the sensitivities of the objective function and optimization constraints. Unfortunately, these sensitivities are usually derived and implemented manually. Nontrivial objective functions and constraints, especially with the involvement of material and geometric nonlinearities, need strenuous mathematical derivation, leading to error-prone implementation. Another intriguing approach to finding sensitivities is automatic differentiation. This paper uses the automatic differentiation and adjoint method to find the sensitivities for two multiphysics topology optimization problems: 1) thermoelasticity and 2) piezoelectricity. This approach is not limited to these examples and can be easily extended to other single- or multi-physics topology optimization problems.

Geometry deals both with analogical thinking and physical/biological observables. Naïve, common-sense descriptions of objects’ shapes and systems’ trajectories in geometric phase spaces may help experimental investigation. For example, very different biological dynamics, as the developmental growth patterns of the oldest known animal (the extinct Dickinsonia) and the human brain electric oscillations, display a striking analogy: when encompassed in abstract geometric spaces, their paths describe the same changes in curvature: from convex, to flat, to concave and vice versa. This dynamical behavior, anticipated by Nicholas de Cusa in his analogical account of “coincidentia oppositorum” (1440), helps to describe widespread biological paths in the manageable terms of concave, flat and convex curves on donut-like structures. Every trajectory taking place on such toroidal manifolds can be located, through a topological technique called Hopf fibration, into a four-dimensional space. We discuss how the correlation between Hopf fibration and Navier-Stokes equations allows us to treat the above-mentioned biological and neuroscientific curved paths in terms of flows taking place into a viscous fluid medium that can be experimentally assessed and quantified.

Additive Manufacturing (AM) provides an opportunity to fundamentally redesign components previously limited by conventional manufacturing techniques. A new process for this workflow of design, manufacture by Powder Bed Fusion (PBF) and validation is presented, to which a case study of a crank for a high performance racing bicycle is applied. Topology optimisation generated conceptually ideal geometry from which a functional design was interpreted. Design for AM considerations were employed to reduce build time, material usage and post-processing labour. PBF was employed to manufacture the parts, and the build quality assessed using Computed Tomography (CT). Static and dynamic functional testing was performed and compared to a Finite Element Analysis (FEA). CT confirmed good build quality of tall, complex geometry with no significant geometrical deviation from CAD over 0.5 mm. Static testing proved performance close to current market leaders, although failure under fatigue occurred after just 2495 ± 125 cycles, the failure mechanism was consistent in both its form and location. These physical results were representative of those simulated, thus validating the FEA. This research demonstrates a complete workflow from design, manufacture, post-treatment and validation of a highly loaded PBF manufactured component, offering practitioners with a validated approach to the application of PBF.

In this study, we define the concept of pseudo-prime subhypermodules of hypermodules as a generalization of the prime hyperideal of commutative hyperrings in [17]. Firstly we examine the spectrum of the Zariski topology, which we built on the element of the pseudo-prime subhypermodules of a class of hyper-modules, then we give some relevant properties of the hypermodule in this topological hyperspace.

A single tree topology is a commonly employed topology for wireless sensor networks (WSN) to connect sensors to one or more remote gateways. However, its many-to-one traffic routing pattern imposes heavy burden on downstream nodes, as the same routes are repeatedly used for packet transfer, from one or more upstream branches. The challenge is how to choose the most optimal routing paths that minimizes energy consumption across the entire network. This paper proposes a proactive energy awareness-based many-to-one traffic routing scheme to alleviate the above said problem referred to as Energy Balance-Based Energy Hole Alleviation in tree topology (EBEHA-T). This protocol combines updated status of variations in energy consumption pattern around sink-hole zones and distribution of joint nodes among the trees. With this approach, EBEHA-T proactively prevents sink-hole formation instead of just a reactive response after they have occurred. Performance evaluation of EBEHA-T against benchmark method RaSMaLai shows increased energy saving across the entire network and a marked improvement in energy consumption balance in energy-hole zones. This precludes energy hole formation and the consequent network partitioning, leading to improved network lifetime beyond that of the RasMaLai. OMNET++ network simulation software has been used for the evaluation.

Topology optimization is a pioneering design method that can provide various candidates with high mechanical properties. However, the high-resolution for the optimum structures is highly desired, normally in turn leading to computationally intractable puzzle, especially for the famous Solid Isotropic Material with Penalization (SIMP) method. In this paper, an efficient and high-resolution topology optimization method is proposed based on the Super-Resolution Convolutional Neural Network (SRCNN) technique in the framework of SIMP. The SRCNN includes four processes, i.e. refining, path extraction & representation, non-linear mapping, and reconstruction. The high computational efficiency is achieved by a pooling strategy, which can balance the number of finite element analysis (FEA) and the output mesh in optimization process. To further reduce the high computational cost of 3D topology optimization problems, a combined treatment method using 2D SRCNN is built as another speeding-up strategy. A number of typical examples justify that the high-resolution topology optimization method adopting SRCNN has excellent applicability and high efficiency for 2D and 3D problems with arbitrary boundary conditions, any design domain shape, and varied load.

In this paper, the concept of fuzzy locally convex spaces generated by a family of fuzzy seminorms is introduced. We prove that a Minkowski functional of zero neighborhoods generates a seminorm and finally deduce that the topology generated by the family of seminorms coincides with that of the Minkowski functional.

Type-2 fuzzy sets were introduced by L. Zadeh aiming at modelling some settings in which fuzzy sets (usually called type-1 fuzzy sets) are not sufficient to reflect certain uncertainty degrees - loosely speaking, they are fuzzy sets whose membership degrees are ordinary fuzzy sets. On the other hand, fiber bundles are topological entities of extreme importance in Mathematics itself and many other scientific areas, like Physics (General Relativity, Field Theory etc.), finance modelling, and statistical inference. The present work introduces a conceptual link between the two ideas and conjectures about the potential mutual benefits that can be obtained from this viewpoint.As an objective and usable product of the presented ideas, it is described a framework for defining type-2 fuzzy hedges, proper to operate on interval type-2 fuzzy sets.

A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes' Theorem, global charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields D, H to possess a gauge freedom, just as the electromagnetic scalar and vector potentials $\varphi$ and A do. This has implications for the treatment of electromagnetism in spacetimes where black holes both form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of D, H we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional (effective) charge on the wormhole's mouth.

One new La (III) based coordination polymer , namely, [La(1,4-bdc)(H2O)].(H2O) (1) (tpa = terephthalic acid) has been synthesized through the solvothermal synthesis using terephthalic acid. Structural analysis reveals that compound 1 has a 3-D network with a cube topology. The solid state photolumienescence study shows that compound 1 has a strong emission peak at 680 nm upon excitation at 220 nm . The emission peak is characteristic of the red light emission in the visible region of the electromagnetic spectrum.

The necessity of the dark energy and dark matter in the present universe could be a consequence of the antimatter elimination assumption in the early universe. In this research, I derive a new model to obtain the cosmic horizon radius and the potential cosmic topology utilising a new construal of space geometry inspired by large-angle correlations of the cosmic microwave background (CMB). A version of the Big Bounce theory is utilised to avoid the Big Bang singularity and inflationary constraints, and to tune the initial conditions of the curvature density. The mathematical derivation of a positively curved universe governed by only gravity revealed two cosmic horizon solutions. Although the positive horizon is conventionally associated with the evolution of the matter universe, the negative horizon solution could imply additional evolution in the opposite direction. This possibly suggests that the matter and antimatter could be evolving in opposite directions as distinct sides of the universe, as in the visualised Sloan Digital Sky Survey. The cosmic horizon radius is found to be accountable for the universal space curvature. By implementing this model, we find a decelerated stage of expansion during the first 10 Gyr, which is followed by a second stage of an accelerated expansion; potentially matching the tension in Hubble parameter measurements. In addition, the model predicts a final time-reversal stage of spatial contraction leading to the Big Crunch of a cyclic universe. The predicted density is 1.14. Other predictions are (1) a calculable flow rate of the matter side towards the antimatter side at the accelerated stage; conceivably explaining the dark flow observation, (2) a time-dependent spacetime curvature over horizon evolution, which could influence the galactic rotational speed; possibly explaining the high speed of stars, and (3) evolvable spacetime internal voids at the accelerated stage, which could contribute in continuously increasing the matter and antimatter densities elsewhere in both sides respectively. These findings may indicate the existence of the antimatter as a distinct side, which influences the evolution of the universe instead of the dark energy or dark matter.

This paper provides an overview of the new CPAM Project on Additive Manufacturing (AM) in design and simulation, focusing on topology & lattice structure optimization for a light-weighting advantage. This industry/academia collaboration project aims to utilize existing hardware and software tools, and investigate the practical limits of the technologies, providing eventual guidelines for general use. This will provide a solid foundation for the practical use of metal AM optimized solid and latticed structures especially for Ti6Al4V parts. Two case studies are demonstrated here, one a purely topology optimized design, and one also incorporating lattice optimized design, both from Ti6Al4V and load-bearing components, to be utilized in the Nelson Mandela University (NMU) Eco-Car Project in competition, late in 2018. This paper presents the Design for Additive Manufacturing (DfAM) process, the challenges met iro applying a DfAM design mindset, and a unique final voxel-based smoothing step finishing off the design process. Detailed structural integrity assessment of these parts are included - the question remains: can Additive Manufacturing help win the race?

In wireless sensor networks, there is no a central controller to enforce cooperation between nodes. Therefore, nodes may generate selfish behavior to conserve their energy resources. In this paper, we address the problems of transmission power minimization and energy balance in wireless sensor networks using a topology control algorithm. We considered the energy efficiency and energy balance of the nodes, and an improved optimization-integrated utility function is designed by introducing the Theil index. Based on this, a topological control game model of energy balance is established, and it is proved that the topological game model is an ordinal potential game with Pareto optimality. Additionally, an energy-balanced topology control game algorithm (EBTG) is proposed to construct topologies. The simulation and comparison show that, compared with other topological control algorithms based on game theory, the EBTG algorithm can improve energy balance and energy efficiency while reducing the transmitting power of nodes, thus prolonging the network lifetime.

Starting from the tenets of human imagination, i.e., the concepts of lines, points and infinity, we provide a biological demonstration that the skeptical claim “human beings cannot attain knowledge of the world” holds true. We show that the Euclidean account of the point as “that of which there is no part” is just a conceptual device, untenable in our physical/biological realm: terms like “lines, surfaces and volumes” label non-existent, arbitrary properties. We also elucidate the psychological and neuroscientific features hardwired in our brain that lead us humans to think to points and lines as truly occurring in our environment. Therefore, our current scientific descriptions of objects’ shapes, graphs and biological trajectories in phase spaces need to be revisited, leading to a proper portrayal of the real world’s events. In order to provide also a positive account, we view miniscule bounded physical surface regions as the basic objects in a biological context in a traversal of spacetime instead of the usual Euclidean points. Our account makes it possible to erase a painstaking problem that causes many theories to break down and/or being incapable of describing extreme events: the unwanted occurrence of infinite values in equations, such as singularity in the description of black holes. We propose a novel approach, based on point-free geometrical standpoints, that banishes infinitesimals and leads to a tenable physical/biological geometry. We conclude that points, lines, volumes and infinity do not describe the world, rather they are fictions introduced by ancient surveyors of land surfaces.

A number of experimental tests of time orientability are described as well as clear experimental signatures from non time orientability (time reversal). Some tests are well known, while others are based on more recent theoretical work. Surprisingly, the results all suggest that time is not orientable at a microscopic level; even definitive tests are positive. At a microscopic level the direction of time can reverse and a consistent forward time direction cannot be defined. That is the conclusion supported by a range of well-known experiments. The conflict between quantum theory and local realism; electrodynamics with electric charges; and spin half transformation properties of fermions; can all be interpreted as evidence of time reversal. While particle-antiparticle annihilation provides a definitive test. It offers both a new view of space-time and an novel interpretation of quantum theory with the potential to unify classical and quantum theories.

The continuous nature of space and time is a fundamental tenet of many scientific endeavours. That digital representation imposes granularity is well recognized but whether it is possible to address space completely remains unanswered. Part 1 argues that Hales’ proof of Keppler’s conjecture on the packing of hard spheres suggests the answer to be ‘no’, providing examples of why this matters in GIS generally and spatio-temporal GIS in particular. Part 2 seeks to resolve the dichotomy between continuous and granular space, showing how a continuous space may be emergent over a random graph. However, its projection into 3D/4D imposes granularity. Perhaps surprisingly, representing space and time as locally conjugate may be key to addressing a ‘smooth’ spatial continuum. This insight leads to the suggestion of Face Centered Cubic Packing as a space-time topology but also raises further questions for spatio-temporal representation.

In this paper we establish a topological framework of τ-structures to quantify the evolutionary transitions between two RNA sequence-structure pairs. τ-structures developed here consist of a pair of RNA secondary structures together with a non-crossing partial matching between the two backbones. The loop complex of a τ-structure captures the intersections of loops in both secondary structures. We compute the loop homology of τ-structures. We show that only the zeroth, first and second homology groups are free. In particular, we prove that the rank of the second homology group equals the number γ of certain arc-components in a τ-structure, and the rank of the first homology is given by γ−χ+1, where χ is the Euler characteristic of the loop complex.

Abstract: To describe the feeder topology and information exchange between intelligent electronic devices (IEDs) for Internet of Things (IoT), it is necessary to extend IEC 61850 and add a logical model. The feeder model described in IEC 61970 is then extended in IEC 61850 to serve as a container for the equipment along the distribution line. For the physical connections in the electrical equipment, both terminal and connectivity node logical models are added. Taking logical node XCBR as the example, its attributes for the terminals are added to the electrical equipment. The logical node LCNN is then further added in order to describe the connectivity node. By next adding the logical node LTPN to describe the topological node, and FTPA to describe the results of the topology analysis, we can efficiently describe the topology analysis results. Based on these new logical nodes, the exchange of topology information between intelligent terminals no longer relies on configuration files, but only requires logical nodes. Through the above expansion, the topology description and information exchange of medium and low voltage feeders are realized.

Over the past 150 million years, the hyperarid core of the Atacama Desert has been transformed by geologic and atmospheric conditions into one of the most unique and inhospitable landscapes on the planet. This makes it an ideal Mars analog that has been explored for decades as preliminary studies on the space life discovery. However, two heavy rainfalls that occurred in the Atacama in 2015 and 2017 provide a unique opportunity to study the response of resident extremophiles to rapid environmental change associated with excessive water and salt shock. Here we combine geochemical analyses with molecular biology to study the variations in salts and microbial communities along an aridity gradient, and to examine the reshuffling of hyperarid microbiomes before and after the two rainfall events. Analysis of microbial community composition revealed that soils within the southern desert were consistently dominated by Actinobacteria, Proteobacteria, Acidobacteria, Planctomycetes, Chloroflexi, Bacteroidetes, Gemmatimonadetes, and Verrucomicrobia; soils within the hyperarid sites were dominated by Aquificae and Deinococcus-Thermus before heavy rainfalls, while these organisms almost totally diminished after rainfall, and the hyperarid microbial consortia and metabolisms transformed to a more southern desert pattern along with increased biodiversity. Salts at the shallow subsurface were dissolved and leached down to a deeper layer, both benefitting and challenging indigenous microorganisms with the excessive input of water and ions. Microbial viability was found to change with aridity and rainfall events but correlated with elevation, pH, conductivity, chloride, nitrate, sulfate, and soil organic matters (SOM). Metagenomic functional pathways related to stressor responses also increased in post-rainfall hyperarid soils. Our findings contribute to the primary goal of Atacama Mars analog research for understanding the microbial community structure and adaptations: this study sheds light on the structure of xerophilic, halophilic, and radioresistant microbiomes in hyperarid environments, and their response to changes in water availability.

Cloud infrastructure provides computing services where computing resources can be adjusted on-demand. However, the adoption of cloud infrastructures brings concerns like reliance on the service provider network, reliability, compliance for service level agreements (SLAs), etc. Software-defined networking (SDN) is a networking concept that suggests the segregation of a network’s data plane from the control plane. This concept improves networking behavior. In this paper, we present an SDN-enabled resource-aware topology framework. The proposed framework employs SLA compliance, Path Computation Element (PCE) and shares fair loading to achieve better topology features. We also present an evaluation, showcasing the potential of our framework.

Topological Data Analysis (TDA) refers to a collection of methods that find the structure of shapes in data. Although recently, TDA methods have been used in many areas of data mining, it has not been widely applied to text mining tasks. In most text processing algorithms, the order in which different entities appear or co-appear is being lost. Assuming these lost orders are informative features of the data, TDA may play a significant role in the resulted gap on text processing state of the art. Once provided, the topology of different entities through a textural document may reveal some additive information regarding the document that is not reflected in any other features from traditional text processing methods. In this paper, we introduce a novel approach that hires TDA in text processing in order to capture and use the topology of different same-type entities in textural documents. First, we will show how to extract some topological signatures in the text using persistent homology-i.e., a TDA tool that captures topological signature of data cloud. Then we will show how to utilize these signatures for text classification.

Due to the demands of personal travels and entertainments, light airplanes and small business aircrafts are developing rapidly. Light airplane structure is simple; however, it lacks crashworthiness design, especially the considerations on the impact of energy absorption. Therefore, in an event of accident, significant damage to passengers will be usually incurred. Airplanes made of composite materials structurally have high specific strength and good aerodynamic configuration. These materials have become the primary choice for new airplane development. This study mainly explores the topology optimization analysis of the light aircraft’s cockpit made of carbon fiber reinforced composites. This paper compares the compression amounts in the original models of composite material and aluminum alloy fuselages with the models after optimization during the crash-landing, in order to investigate the safety of fuselages made of different materials after structural optimization under the dynamic crashing. This study found that the energy absorbed by the aluminum alloy fuselage during crash-landing is still higher than that by the carbon fiber reinforced composites fuselage. On the other hand, the aluminum alloy fuselage after topology optimization could have an energy absorption capability enhanced by 40%, as compared to the that of the original model of aluminum alloy fuselage.

Background: Visceral leishmaniasis affects approximately 12 million people worldwide. Current existing drugs cause several side effects and resistance, the identification of new therapeutic targets for the development of new drugs is necessary. The vesicular trafficking in the parasite flagellar pocket is essential for parasite survival and proliferation, but little is known about the proteins involved in the endocytic/secretory pathways. In this work, we are describing the characterization of a transporter cargo protein SFT-2/Got-1 like in Leishmania infantum. Material and Methods: Using bioinformatics tools, the putative Got-1 protein A4HSK3 was characterized structurally and phylogenetically. Molecular biology was used to clone and express the protein and confocal fluorescence to determine its subcellular localization. Results: The Got-1 like protein presents four alpha helix TM conserved domains (aa38-aa147) characteristics of the Got-1/SFT-2 family proteins and an important Pen-2 conserved motif LGDYXXF located in the extracellular loop. Confocal microscopy suggests that Got-1/SFT-2 like is localized in the flagellar pocket, and is partially co-localized with the L. infantum presenilin-like protein. Phylogenetically, the Leishmania sp Got-1 like is contained in a subgroup of proteins clearly detached from the other Trypanosomatidae, such as T. cruzi and T. brucei. Conclusions: Our data show the presence of an important transported proteins, and its colocalization with the presenilin aspartyl protease in the flagellar pocket of the L. infantum open new perspectives to identify novel targets, which can be an alternative therapeutic strategy against leishmaniasis.

This hypothesis is the result of my conviction that science will oneday prove everything in space and time is part of a unification. In "A Brief History of Time", Stephen Hawking wrote, "If everything in the universe depends on everything else in a fundamental way, it might be impossible to get close to a full solution (of the universe's puzzles) by investigating parts of the problem (such as general relativity and quantum mechanics) in isolation." The goal: to establish a “proof of concept” to which equations can be added. It’s concluded the Steady State, Big Bang, Inflation and Multiverse theories all ultimately fail and a topological model including bits (binary digits), Mobius strips, figure-8 Klein bottles and Wick rotation works better. The failed cosmologies have impressive points leading to the idea that they’re all necessary stepping-stones. For example, the Big Bang is seen here as violation of the 1st Law of Thermodynamics but its supposed origin from quantum fluctuations is reminiscent of bits switching between 1 and 0. The topological hypothesis has potential to explain dark matter, dark energy, and electromagnetic-gravitational union. Finally, the article introduces what is called vector-tensor-scalar geometry - and extensions of Einstein's Gravity and Maxwell's Electromagnetism.

3D city models are being extensively used in applications such as evacuation scenarios and energy consumption estimation. The main standard for 3D city models is the CityGML data model which can be encoded through the CityJSON data format. CityGML and CityJSON use polygonal modelling in order to represent geometries. True topological data structures have proven to be more computationally efficient for geometric analysis compared to polygonal modelling. In a previous study, we have introduced a method to topologically reconstruct CityGML models while maintaining the semantic information of the dataset, based solely on the combinatorial map (C-Map) data structure. As a result of the limitations of C-Map's semantic representation mechanism, the resulting datasets could suffer either from semantic information loss or the redundant repetition of them. In this article, we propose a solution for a more efficient representation of both geometry, topology and semantics by incorporating the C-Map data structure in the CityGML data model and implementing a CityJSON extension to encode the C-Map data. In addition, we provide an algorithm for the topological reconstruction of CityJSON datasets to append them according to this extension. Finally, we apply our methodology to three open datasets in order to validate our approach when applied to real-world data. Our results show that the proposed CityJSON extension can represent all geometric information of a city model in a lossless way, providing additional topological information for the objects of the model.

By combing continuum topology optimization (TO) method and lattice structure technique, a sandwich aircraft spoiler with a high stiffness-to-weight is designed. TO method is served to produce the shell of the aircraft spoiler and the lattice structure, used as cores, is employed to support the shell. TO problem is established as maximizing the stiffness of the structure with limited material volume. Density-based method is utilized to achieve a 0/1 solution. We then empirically replace the core of the aircraft spoiler by using 3D kagome lattice structure. Two different materials, i.e., aluminum alloy and titanium alloy, are synthetically applied to further reduce the weight and simultaneously improve the strength of the aircraft spoiler. Numerical simulations are conducted to show that the designed aircraft spoiler can meet the service environment with a reduction of its weight by approximately 80% when compared with that of the initial design model. Finally, we have fabricated the designed model with photosensitive resin by using 3D printing technique.

The unexploited unification of quantum physics, general relativity and biology is a keystone that paves the way towards a better understanding of the whole of Nature. Here we propose a mathematical approach that introduces the problem in terms of group theory. We build a cyclic groupoid (a nonempty set with a binary operation defined on it) that encompasses the three frameworks as subsets, representing two of their most dissimilar experimental results, i.e., 1) the commutativity detectable both in our macroscopic relativistic world and in biology; 2) and the noncommutativity detectable both in the microscopic quantum world and in biology. This approach leads to a mathematical framework useful in the investigation of the three apparently irreconcilable realms. Also, we show how cyclic groupoids encompassing quantum mechanics, relativity theory and biology might be equipped with dynamics that can be described by paths on the twisted cylinder of a Möbius strip.

This work investigates centered polygonal lacunary functions restricted from the unit disk onto symmetry angle space which is defined by the symmetry angles of a given centered polygonal lacunary function. This restriction allows for one to consider only the p-sequences of the centered polygonal lacunary functions which are bounded, but not convergent, at the natural boundary. The periodicity of the $p$-sequences naturally gives rise to a convergent subsequence, which can be used as a grounds for decomposition of the restricted centered polygonal lacunary functions. A mapping of the unit disk to the sphere allows for the study of the line integrals of restricted centered polygonal that includes analytic progress towards closed form representations. Obvious closures of the domain obtained from the spherical map lead to four distinct topological spaces of the "broom topology'' type.

We present a new computing package Flagser, designed to construct the directed flag complex of a finite directed graph, and compute persistent homology for flexibly defined filtrations on the graph and the resulting complex. The persistent homology computation part of Flagser is based on the program Ripser [2], but is optimised specifically for large computations. The construction of the directed flag complex is done in a way that allows easy parallelisation by arbitrarily many cores. Flagser also has the option of working with undirected graphs. For homology computations Flagser has an Approximate option, which shortens compute time with remarkable accuracy. We demonstrate the power of Flagser by applying it to the construction of the directed flag complex of digital reconstructions of brain microcircuitry by the Blue Brain Project and several other examples. In some instances we perform computation of homology. For a more complete performance analysis, we also apply Flagser to some other data collections. In all cases the hardware used in the computation, the use of memory and the compute time are recorded.

In this paper we review a proposal to represent the geometric degrees of freedom of the gravitational field as a branched covering space, and introduce a new application of this in which the branch loci are 1- or 2-knots. This allows one to construct arbitrary smooth, closed 3- and 4-manifolds with enough geometric and topological information to write down a partition function and calculate statistical quantities in the thermodynamic limit. Further, we find clear evidence for a dimensional reduction of the spacetime geometry from four to two. As an example, we choose a family of smooth 4-manifolds presented in this way, and calculate the entropy of the system.

Structural system design is the process of giving form to a set of interconnected components subjected to loads and design constraints while navigating a complex design space. While safe designs are relatively easy to develop, optimal designs are not. Modern computational optimization approaches employ population based metaheuristic algorithms to overcome challenges with the system design optimization landscape. However, the choice of the initial population, or ground structure, can have an outsized impact on the resulting optimization. This paper presents a new method of generating such ground structures, using a combination of topology optimization (TO) and a novel system extraction algorithm. Since TO generates monolithic structures, rather than systems, its use for structural system design and optimization has been limited. In this paper, truss systems are extracted from topologies through morphological analysis and artificial intelligence techniques. This algorithm, and its assessment, constitutes the key contributions of this paper. The structural systems obtained are compared with ground truth solutions to evaluate the performance of the algorithms. The generated structures are also compared against benchmark designs from the literature. The results indicate that the presented truss generation algorithm produces structures comparable to those generated through metaheuristic optimization, while mitigating the need for assumptions about initial ground structures.

This paper outlines a tool developed with the purpose of creating a simple configurable emulated network environment that can be used in cyber defence exercises. Research has been conducted into the various related subject areas: cyber defence exercises, network threats, network emulation, network traffic replay, network topologies, and common network services. From this research a requirements specification was produced to encapsulate the features required to create this tool. A network, containing many of the aspects researched, was designed and implemented using Netkit-NG to act as a blueprint for the tool and to further knowledge in the construction of an emulated network. Following this the tool was developed and tested to ensure requirements were met.

We create a model universe by equipping a topological surface (system) with compact dimensions insulated by an information blocking horizon. The insulated compact WF can produce entanglement independent of distance. Interaction between the system and the WF changes the curvature of the first and the quantum state (frequency) of the second in an interconnected relationship. Thus, the field curvature measures the evolution of the particle WF as time. Positive field curvature creates pressure, whereas negative field curvature generates a vacuum, satisfying the Borsuk-Ulam Theorem and the Page and Wootters mechanism of static time. The accumulation of pressure or vacuum generates poles with contrasting dimensionalities, two-dimensional black hole horizons (time infinite), and four-dimensional cosmic voids (time zero). The orthogonality of the field and the compact WF give rise to global self-regulation that fine-tunes the cosmic parameters and can promote fractal topology. The four-dimensional vacuum in cosmic voids can produce an accelerating expansion without dark energy. When gravity effects are eliminated, we find a new, so far unexplored, order-increasing side of entropy. The verifiable and elegant hypothesis satisfies Mach's principle.

This work proposes a systematic topology optimization approach to simultaneously design the morphing functionality and actuation in three-dimensional wing structures. The actuation is assumed to be a linear strain-based expansion in the actuation material and a three-phase material model is employed to represent structural and actuating materials, and void. To ensure both structural stiffness with respect to aerodynamic loading and morphing capabilities, the optimization problem is formulated to minimize structural compliance while morphing functionality is enforced by constraining a morphing error between actual and target wing shape. Moreover, a feature mapping approach is utilized to constrain and simplify actuator geometries. A trailing edge wing section is designed to validate the proposed optimization approach. Numerical results demonstrate that three-dimensional optimized wing sections utilize a more advanced structural layout to enhance structural performance while keeping morphing functionality than two-dimensional wing ribs. The work presents the first step towards systematic design of three-dimensional morphing wing sections.

We give an exact mathematical construction of a spacelike order $<$, which is dual to the standard chronological order $\ll$ in the $n$-dimensional Minkowski space $M^n$ and we discuss its order-theoretic, geometrical as well as its topological implications, conjecturing a possible extension to curved spacetimes.

Proper identification of oriented knots and 2-component links requires a precise link nomenclature. Motivated by questions arising in DNA topology, this study aims to produce a nomenclature unambiguous with respect to link symmetries. For knots, this involves distinguishing a knot type from its mirror image. In the case of 2-component links, there are up to sixteen possible symmetry types for each topology. The study revisits the methods previously used to disambiguate chiral knots and extends them to oriented 2-component links with up to nine crossings. Monte Carlo simulations are used to report on writhe, a geometric indicator of chirality. There are ninety-two prime 2-component links with up to nine crossings. Guided by geometrical data, linking number and the symmetry groups of 2-component links, a canonical link diagram for each link type is proposed. All diagrams but six were unambiguously chosen ( $8_1^{2}5$ , $9_5^2$ , $9_3^{2}4$ , $9_3^{2}5$ , $9_3^{2}9$ , and $9_4^{2}1$ ). We include complete tables for prime knots with up to ten crossings and prime links with up to nine crossings. We also prove a result on the behavior of the writhe under local lattice moves.

The aim of this research is forwarded for assessment of provision possibilities of the multi-componential and heterogeneous services in the fast-changing topology of cargo transportation processes. The mobile intelligent services in nowadays transport means require the development of complex infrastructure for multi-compositional service support. Our objectives are related to the investigation in data-transfer capabilities for heterogeneous service support, by offering some improvements for developing the infrastructure of transportation of vehicles by helping in the administration of transport processes. This research aims to develop an approach for assessment of infrastructure for sustainable management of cargo transportation processes by roads. Such assessment is multi-layered by including the management possibilities of cargo transportation logistic processes and electronic (smart, mobile) services by implementing of nowadays innovative software and hardware of information communication technologies (ICT). Special attention is paid for road safety, more environment cleanable, and paperless management by assessing the integration of potentials and prospects of wireless, vehicle Ad-hoc communication networks (VANET), and other communication possibilities. Some requirements are revealed for such type of infrastructure for the provision of heterogeneous services. The results of the development of infrastructure demonstrate the capacities of the potential of wireless networks for the provision of high-level of multi-component, heterogeneous services.

A topological quantum interplay between the magnetic flux and the mass has been investigated, for the case of an electron, by evaluating a gauge-invariant phase factor (a Wilson loop) linked to the electromagnetic gauge field of the particle. In particular, from this phase factor and the quantization of the magnetic flux variations, a relationship between the mass at rest of the electron and its self-energy , arising from radiative corrections, has been obtained also within a QED approach. Besides, a formulation of an energy scale comparable to the energy at rest of an electron-positron pair is proposed. Remarkably, a reckoning of the Bohr energy of a W⁺ W^- pair is compatible with constants and parameters usually employed within the electroweak theory and comparable to the energy at rest of an electron-positron pair.

An existing power grid is going through a massive transformation. Smart grid technology is a radical approach for improvisation in prevailing power grid. Integration of electrical and communication infrastructure is inevitable for the deployment of Smart grid network. Smart grid technology is characterized by full duplex communication, automatic metering infrastructure, renewable energy integration, distribution automation and complete monitoring and control of entire power grid. Wireless sensor networks (WSNs) are small micro electrical mechanical systems which are accomplished to collect and communicate the data from surroundings. WSNs can be used for monitoring and control of smart grid assets. Security of wireless sensor based communication network is a major concern for researchers and developers. The limited processing capabilities of wireless sensor networks make them more vulnerable to cyber-attacks. The countermeasures against cyber-attacks must be less complex with an ability to offer confidentiality, data readiness and integrity. The address oriented design and development approach for usual communication network requires a paradigm shift to design data oriented WSN architecture. WSN security is an inevitable part of smart grid cyber security. This paper is expected to serve as a comprehensive assessment and analysis of communication standards, cyber security issues and solutions for WSN based smart grid infrastructure.

Prereactive complexes in noncovalent organocatalysis are sensitive to the relative chirality of the binding partners and to hydrogen bond isomerism. Both effects are present when a transiently chiral alcohol docks on a chiral α-hydroxy ester, turning such 1:1 complexes into elementary, non-reactive model systems for chirality induction in the gas phase. With the help of linear infrared and Raman spectroscopy in supersonic jet expansions, conformational preferences are investigated for benzyl alcohol in combination with methyl lactate, also exploring p-chlorination of the alcohol and the achiral homolog methyl glycolate to identify potential London dispersion and chirality effects on the energy sequence. Three of the four combinations prefer barrierless complexation via the hydroxy group of the ester (association). In contrast, the lightest complex shows predominantly insertion into the intramolecular hydrogen bond, like the analogous lactate and glycolate complexes of methanol. The experimental findings are rationalized with computations and a uniform helicality induction in the alcohol by the lactate is predicted, independent on insertion into or association with the internal lactate hydrogen bond. p-Chlorination of benzyl alcohol has a stabilizing effect on association, because the insertion motif prevents a close contact between the chlorine and the hydroxy ester. After simple anharmonicity and substitution corrections, the B3LYP-D3 approach offers a fairly systematic description of the known spectroscopic data on alcohol complexes with α-hydroxy esters.

We present the real number system as a natural generalization of the natural numbers. First, we prove the co-finite topology, $Cof(\mathbb N)$, is isomorphic to the natural numbers. Then, we generalize these results to describe the continuum $[0,1]$. Then we prove the power set $2^{\mathbb Z}$ contains a subset isomorphic to the non-negative real numbers, with all its defining structure of operations and order. Finally, we provide two different constructions of the entire real number line. We see that the power set $2^{\mathbb N}$ can be given the defining structure of $\mathbb R$. The constructions here provided give simple rules for calculating addition, multiplication, subtraction, division, powers and rational powers of real numbers, and logarithms. The supremum and infimum are explicitly constructed by means of a well defined algorithm that ends in denumerable steps. In section 5 we give evidence our construction of $\mathbb N$ and $\mathbb R$ are canonical; these constructions are as natural as possible. In the same section, we propose a new axiomatic basis for analysis. In the last section we provide a series of graphic representations and physical models that can be used to represent the real number system. We conclude that the system of real numbers is completely defined by the order structure of $\mathbb N$.}

In this paper, some characterizations of fuzzifying strong compactness are given, including characterizations in terms of nets and pre -subbases. Several characterizations of locally strong compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other. According to Kepler’s 1^st Law, “orbit of a planet with respect to the Sun is an ellipse, with the Sun at one of the two foci.” Orbit of the Moon with respect to Earth is also distinctly elliptical, but this ellipse has a varying eccentricity as the Moon comes closer to and goes farther away from the Earth in a harmonic style along a full cycle of this ellipse. In this paper, our research results are summarized, where it is first mathematically shown that the “distance between points around any two different circles in three dimensional space” is equivalent to the “distance of points around a vector ellipse to another fixed or moving point, as in two dimensional space”. What is done is equivalent to showing that bodies moving on two different circular orbits in space vector wise behave as if moving on an elliptical path with respect to each other, and virtually seeing each other as positioned at an instantaneously stationary point in space on their relative ecliptic plane, whether they are moving with the same angular velocity, or different but fixed angular velocities, or even with different and changing angular velocities with respect to their own centers of revolution. This mathematical revelation has the potential to lead to far reaching discoveries in physics, enabling more insight into forces of nature, with a formulation of a new fundamental model regarding the motions of bodies in the Universe, including the Sun, Planets, and Satellites in the Solar System and elsewhere, as well as at particle and subatomic level. Based on the demonstrated mathematical analysis, as they exhibit almost fixed elliptic orbits relative to one another over time, the assertion is made that the Sun, the Earth, and the Moon must each be revolving in their individual circular orbits of revolution in space. With this expectation, individual orbital parameters of the Sun, the Earth, and the Moon are calculated based on observed Earth to Sun and Earth to Moon distance data, also using analytical methods developed as part of this research to an approximation. This calculation and analysis process have revealed additional results aligned with observation, and this also supports our assertion that the Sun, the Earth, and the Moon must actually be revolving in individual circular orbits.

Causal relationships lie at the very core of our scientific description of biophysical phenomena. Nevertheless, observable facts such as chaotic dynamics, symmetry breaks, long-range collisionless neural interactions, zero-value energy singularities, particle/wave duality, ecological approaches to visual perception elude cause effect inductive explanations. We illustrate how simple topological claims, seemingly useless and far away from scientific inquiry (e.g., “given at least some wind on Earth, there must at all times be a cyclone or anticyclone somewhere”; “if one stirs to dissolve a lump of sugar in a cup of coffee, it appears there is always a point without motion”; “at any moment, there is always a pair of antipodal points on the Earth’s surface with equal temperatures and barometric pressures”) describe a real world, made of projections and mappings unsupplied with causality. Unavoidable, necessary, passive, spontaneous changes in systems’ shapes, dimensions and symmetries incarnate biophysical quantifiable counterparts of abstract mathematical concepts. Real features arising from topological mechanisms do not require causal powers to be produced, because are independent of exerted physical forces, energetic fields’ actions and thermodynamic constraints. Providing examples that shed novel interpretative light on phenomena such as double slit experiments, cellular mechanisms and brain function, we conclude as follows: countless scientific matters can be accessed through methodological weapons which not just break causality, replace temporal correlations and probabilistic a priori knowledge of previous cases, but also permit augments in available information devoid of entropy increases and energy losses.

Additive manufacturing (AM) of high strength Al alloys promises to enhance the performance of critical components related to various aerospace and automotive applications. The key advantage of AM is its ability to generate lightweight, robust, and complex shapes. However, the characteristics of the as-built parts may represent an obstacle to satisfy the part quality requirements. The current study investigates the influence of selective laser melting (SLM) process parameters on the quality of parts fabricated from different Al alloys. A design of experiment (DOE) is used to analyze relative density, porosity, surface roughness, and dimensional accuracy according to the interaction effect between the SLM process parameters. The results show a range of energy densities and SLM process parameters for the AlSi10Mg and Al6061 alloys needed to achieve “optimum” values for each performance characteristic. A process map is developed for each material by combining the optimized range of SLM process parameters for each characteristic to ensure good quality of the as-built parts. The second part of this study investigates the effect of SLM process parameters on the microstructure and mechanical properties of the same Al alloys. This comprehensive study is also aimed at reducing the amount of post-processing needed.

In this paper, we investigate the use of fat tissue as a communication channel between in-body, implanted devices at R-band frequencies (1.7–2.6 GHz). The proposed fat channel is based on an anatomical model of the human body. We propose a novel probe that is optimized to efficiently radiate the R-band frequencies into the fat tissue. We use our probe to evaluate the path loss of the fat channel by studying the channel transmission coefficient over the R-band frequencies. We conduct extensive simulation studies and validate our results by experimentation on phantom and ex-vivo porcine tissue, with good agreement between simulations and experiments. We demonstrate a performance comparison between the fat channel and similar waveguide structures. Our characterization of the fat channel reveals propagation path loss of 1.4 dB and 3.8 dB per 20 mm for phantom and ex-vivo porcine tissue, respectively. These results demonstrate that fat tissue can be used as a communication channel for high data rate intra-body networks.

We propose a non-invasive approach to control the quality of spheroids and their fusion into a complex bioconstruct. The proposed method is based on the union of the nutrient concentration change calculated using Fick's law and the "reaction-diffusion" equations, taking into account absorption coefficient with specifying the exact fusion geometry using implicit Function Repre-sentation (FRep) functions. The proposed approach allows us to analyze the viability of cells within the spheroid, predict the fusion of spheroids, and accurately model complex heteroge-neous biostructures as a future task for our research. These results will significantly accelerate the development of such a promising field of additive biotechnologies as 3D bioprinting.

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other, whereas objects follow parabolic escape orbits while moving away from Earth and bodies asserting a gravitational pull, and some comets move in near-hyperbolic orbits when they approach the Sun. In this article, it is first mathematically proven that the “distance between points on any two different circles in three-dimensional space” is equivalent to the “distance of points on a vector ellipse from another fixed or moving point, as in two-dimensional space.” Then, it is further mathematically demonstrated that “distance between points on any two different circles in any number of multiple dimensions” is equivalent to “distance of points on a vector ellipse from another fixed or moving point”. Finally, two special cases when the “distance between points on two different circles in multi-dimensional space” become mathematically equivalent to distances in “parabolic” or “near-hyperbolic” trajectories are investigated. Concepts of “vector ellipse”, “vector hyperbola”, and “vector parabola” are also mathematically defined. The mathematical basis derived in this Article is utilized in the book “Everyhing Is A Circle: A New Model For Orbits Of Bodies In The Universe” in asserting a new Circular Orbital Model for moving bodies in the Universe, leading to further insights in Astrophysics.

This paper establishes methods that quantify the structure of statistical interactions within a given data set using the characterization of information theory in cohomology by finite methods, and provides their expression in terms of statistical physic and machine learning. Following [1–3], we show directly that k multivariate mutual-informations (I_k) are k-coboundaries. The k-cocycles are given by I_k = 0, which generalize statistical independence to arbitrary dimension k. The topological approach allows to investigate Shannon’s information in the multivariate case without the assumptions of independent identically distributed variables. We develop the computationally tractable subcase of simplicial information cohomology represented by entropy H_k and information I_k landscapes. The I₁ component defines a self-internal energy functional U_k, and (−1)^k I_k,k≥2 components define the contribution to a free energy functional G_k of the k-body interactions. The set of information paths in simplicial structures is in bijection with the symmetric group and random processes, provides a topological expression of the 2nd law and points toward a discrete Noether theorem (1st law). The local minima of free-energy, related to conditional information negativity and the non-Shannonian cone of Yeung [4], characterize a minimum free energy complex. This complex formalizes the minimum free-energy principle in topology, provides a definition of a complex system, and characterizes a multiplicity of local minima that quantifies the diversity observed in biology. Finite data size effects and estimation bias severely constrain the effective computation of the information topology on data, and we provide simple statistical tests for the undersampling bias and for the k-dependences following [5]. We give an example of application of these methods to genetic expression and cell-type classification. The maximal positive I_k identifies the variables that co-vary the most in the population, whereas the minimal negative I_k identifies clusters and the variables that differentiate-segregate the most. The methods unravel biologically relevant I₁₀ with a sample size of 41. It establishes generic methods to quantify the epigenetic information storage and a unified epigenetic unsupervised learning formalism.

In 1999, Molodtsov initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the notion of soft topological spaces, also defining and investigating many new soft properties as generalization of the classical ones. In this paper, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Lemma to the class of soft topological spaces.

In this study, we present the concept of interval-valued fuzzy soft point and then introduce the notions of neighborhood and quasi-neighbourhood of it in interval-valued fuzzy soft topological spaces. Separation axioms in interval-valued fuzzy soft topology, so-called $q$-$T_{i}$ for $ i=0,1,2,3,4 ,$ is introduced and some of its basic properties are also studied.

Vibration suppression in a field of frequencies and the creation of band gaps which do not allow the propagation of the waves is studied in this paper by means of microstructures designed through topology optimization. Topology optimization is formulated in frequency domain. Band gap design is based on Floquet-Bloch theory and genetic optimization. The result is appealing in view of modern 3D printing techniques.