Geometric Standpoint Research Articles

Comprehensive Geographic Networks Analysis: Statistical, Geometric and Algebraic Perspectives

Using complex network analysis methods to analyze the internal structure of geographic networks is a popular topic in urban geography research. Statistical analysis occupies a dominant position in the current research on geographic networks. This perspective mainly focuses on node connectivity, while other perspectives, such as geometric and algebraic perspectives, can provide additional insights into network structure. Using 11 different real-world geographic networks as examples, this study examines geographic networks from statistical, geometric, and algebraic perspectives. The following are some of the paper’s new findings: (1) When viewed statistically, geometrically, and algebraically, geographic networks have completely different properties. The statistical perspective describes both local and global connectivity; the Ricci curvature in the geometric perspective can assess the network’s development potential as well as describe its transmission capability, and the algebraic perspective can capture the global network topology other than connectivity; (2) Networks are qualitatively and quantitatively classified from three perspectives. The classification results are in accordance with the topological robustness experiment results, which indicate that an analysis from many angles has a lot of practical relevance; (3) Statistical indicators are better than Ricci curvature in identifying essential nodes in networks from a geometric standpoint, whereas the latter is better at detecting significant edges. Overall, studying geographic networks from various perspectives may provide new insights into their understanding.

Front Cover: Interactive Competition Between Individual Diffusion Layers during Cyclic Voltammetry at Random Arrays of Band and Disk Electrodes: A Thorough Analysis Based on Global Simulations (ChemElectroChem 13/2021)

The Front Cover illustrates that while electrochemical arrays of electroactive sites may be extremely random from a geometric standpoint, as the beige array with its Voronoi tessellated unit cells shown at the left, their voltammetric responses become almost indistinguishable from those of fully periodic ones, idealized by the green honeycomb matrix at the right. This occurs as soon as peak-shaped voltammograms are observed due to full interactions of the diffusion layers generated by individual active sites. This justifies why the theory proposed by Amatore and Savéant almost 40 years ago to describe the behavior of electrochemical networks has always provided solid outcomes even for random ones. More information can be found in the Article by G. Pireddu et al.

Design for metal powder bed fusion: The geometry for additive part selection (GAPS) worksheet

In industry, Design for Additive Manufacturing (DfAM) is currently synonymous with expert knowledge and external consultants for many companies. Particularly in higher cost technologies, such as metal powder bed fusion, component design requires extensive additive manufacturing (AM) knowledge. If a part is improperly designed, then it can cause thousands of dollars of lost time and material through a failed print. To avoid this situation, specialists must be consulted throughout the printing process; however, the shortage of trained personnel familiar with AM can create a bottleneck during design. In order to help businesses identify candidate parts for Powder Bed Fusion (PBF) AM, this paper presents a DfAM worksheet to help engineers, drafters, and designers select good part candidates with little prior knowledge of the specific technology. This worksheet uses data from the literature to support the values used for design guidance. Example components are shown to demonstrate the worksheet process. Ratings of these components are then compared with expert raters’ assessments of their suitability for fabrication with PBF from a geometric standpoint. In addition to introducing the worksheet, preliminary user feedback about the worksheet is presented, and future work is discussed.

La geometría en los edificios de la Ciutat de les Arts i les Ciències de Valencia

La importancia de la utilización de la geometría en el diseño de Arquitectura, y más en concreto el uso de las superficies geométricas como configuradoras del espacio arquitectónico, es el tema central del presente artículo. En él se pone en valor el uso de estas formas geométricas definidas como elemento de control formal en la fase de diseño de los edificios y que a su vez ayuda a mantener una coherencia con el comportamiento estructural y una mayor facilidad tanto en la ejecución como en la materialización constructiva. Se ha realizado un caso práctico de análisis formal geométrico, la “Ciutat de les Arts i les Ciències” de Valencia, que constituye uno de los ejemplos de aplicación más claros de las formas geométricas en la Arquitectura actual. Los análisis son fundamentalmente de generación de las superficies, pero también recogen la vertiente estructural y constructiva estudiada desde el punto de vista geométrico.

한국 초등학교 수학교과서에 제시된 각(角)의 정의에 대한 고찰

The present research work considers that there are many contradictory elements in the way ‘angle’ is defined and presented in the Korean elementary mathematics textbooks (KEMT). Henceforth, an effort has been made to systematically analyze the problems and seek solutions from the past KEMT. All the textbooks from the starting to the recent curriculum were collected and definitions and subsequent activities of angle, right angle, and angle measure from the books were analyzed. Based on the analysis, it was apparent that KEMT had commonly defined angle as a geometric standpoint, but illustrations of angle and views on the 'sides of angle' included in the definitions of angle were significantly different between curriculums. In addition, contradictory elements were continuously found in the definitions of the angle, between the definitions of angle and right angle, and between the definitions of angle and subsequent activities. Accordingly, it is proposed to reconsider the way angle is defined and design subsequent activities so as not to reveal the contradictory elements in the futuristic development of textbooks.

In silico structure-based approaches to discover protein-protein interaction-targeting drugs.

A core concept behind modern drug discovery is finding a small molecule that modulates a function of a target protein. This concept has been successfully applied since the mid-1970s. However, the efficiency of drug discovery is decreasing because the druggable target space in the human proteome is limited. Recently, protein-protein interaction (PPI) has been identified asan emerging target space for drug discovery. PPI plays a pivotal role in biological pathways including diseases. Current human interactome research suggests that the number of PPIs is between 130,000 and 650,000, and only a small number of them have been targeted as drug targets. For traditional drug targets, in silico structure-based methods have been successful in many cases. However, their performance suffers on PPI interfaces because PPI interfaces are different in five major aspects: From a geometric standpoint, they have relatively large interface regions, flat geometry, and the interface surface shape tends to fluctuate upon binding. Also, their interactions are dominated by hydrophobic atoms, which is different from traditional binding-pocket-targeted drugs. Finally, PPI targets usually lack natural molecules that bind to the target PPI interface. Here, we first summarize characteristics of PPI interfaces and their known binders. Then, we will review existing in silico structure-based approaches for discovering small molecules that bind to PPI interfaces.

Kernel Method for Voice Activity Detection in the Presence of Transients

Voice activity detection in the presence of transient interferences is a challenging problem since transients are often detected incorrectly as speech by existing detectors. In this paper, we deviate from traditional approaches and take a geometric standpoint, in which the key element in obtaining an accurate voice activity detection is finding a metric that appropriately distinguishes between speech and transients. For example, speech and transients may often appear similar through the Euclidean distance when represented, e.g., by the Mel-frequency cepstral coefficients, thereby resulting in incorrect speech detection. To address this challenge, we propose to use a metric based on the statistics of the signal in short temporal windows and justify its use by modeling speech and transients by their latent generating variables. These latent variables may be related to physical constraints controlling the generation of the signal, and, as such, they accurately represent the content of the signal - speech or transient. We show that the Euclidean distance between the latent variables is approximated by the proposed metric. Then, by incorporating this metric into a kernel-based manifold learning method, we devise a measure of voice activity and show it leads to improved detection scores compared with competing detectors.

Non-equilibrium statistical approach to friction models

A geometric approach to the friction phenomena is presented. It is based on the holographic view which has recently been popular in the theoretical physics community. We see the system in one-dimension-higher space. The heat-producing phenomena are most widely treated by using the non-equilibrium statistical physics. We take 2 models of the earthquake. The dissipative systems are here formulated from the geometric standpoint. The statistical fluctuation is taken into account by using the (generalized) Feynman׳s path-integral.

Geometry and the quantum: basics

Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M_2(H) and M_4(C) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume >4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these representations give a seductive model of the "particle picture" for a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model emerge from Quantum Mechanics. Physical applications of this quantization scheme will follow in a separate publication.

Simulation and Experimental Characterization of Microscopically Accessible Hydrodynamic Microvortices

Single-cell studies of phenotypic heterogeneity reveal more information about pathogenic processes than conventional bulk-cell analysis methods. By enabling high-resolution structural and functional imaging, a single-cell three-dimensional (3D) imaging system can be used to study basic biological processes and to diagnose diseases such as cancer at an early stage. One mechanism that such systems apply to accomplish 3D imaging is rotation of a single cell about a fixed axis. However, many cell rotation mechanisms require intricate and tedious microfabrication, or fail to provide a suitable environment for living cells. To address these and related challenges, we applied numerical simulation methods to design new microfluidic chambers capable of generating fluidic microvortices to rotate suspended cells. We then compared several microfluidic chip designs experimentally in terms of: (1) their ability to rotate biological cells in a stable and precise manner; and (2) their suitability, from a geometric standpoint, for microscopic cell imaging. We selected a design that incorporates a trapezoidal side chamber connected to a main flow channel because it provided well-controlled circulation and met imaging requirements. Micro particle-image velocimetry (micro-PIV) was used to provide a detailed characterization of flows in the new design. Simulated and experimental results demonstrate that a trapezoidal side chamber represents a viable option for accomplishing controlled single cell rotation. Further, agreement between experimental and simulated results confirms that numerical simulation is an effective method for chamber design.

Study of mechanical properties of RF MEMS switches by nanoindentation: characterization and modeling of electro-mechanical behavior

This paper presents a thorough methodology to evaluate the mechanical properties of RF MEMS switches. It includes an analytical electro-mechanical model and nanoindentation characterizations which allow explaining the electrostatic behavior of the MEMS switches. Experimental and theoretical aspects are compared through two runs of ohmic electrostatic switches which are different from geometric and process flow standpoint. The switch is modeled as a clamped-clamped beam with mobile vertical loads, two stretching axial forces and two reaction moments in the anchors. The mechanical properties are characterized by nanoindentation technique; specific test protocol for measuring very low stiffness has been specially implemented with an adapted continuous stiffness measurement method. The measured values of the stiffness at the membrane center are respectively 79 and 137 N/m for the two runs, and they remain in good agreement with the theoretical model. The difference between these two runs is explained by the difference of the tensile residual stress. Moreover, the nanoindentation data turn out to be useful to evaluate the contact quality: dimple deformation due to twisting of the beam (contact in multiple steps), or inhomogeneous surface (stiffness is increasing while in contact). The fitted model is also used to approximate the restoring and contact forces and to point out the influence of the mechanical properties on the electrostatic behavior. A simple model with two parallel-plate capacitors in parallel, used for calculation of the up- and down-state capacitances, shows no discrepancy with experimental values. Finally, it may be concluded that the electrostatic behavior of the switches (pull-in voltage, up- and down-state capacitances, and probability of stiction) can be better understood thanks to the mechanical characterizations made by nanoindentation.

Blur and Disparity Provide Complementary Distance Information for Human Vision

Disparity is generally considered the most precise cue to depth, while blur is considered a coarse, qualitative cue. Depth from disparity and depth from blur have similar underlying geometries: one is based on triangulation between images collected by different eyes and the other is based on triangulation between images collected through different parts of the pupil. Thus, from a geometric standpoint, they provide complementary distance information. Physiologically, the two cues have very different sensitivities. Disparity thresholds, expressed as just-noticeable differences in depth, are low near fixation, but increase rapidly away from fixation. In contrast, blur thresholds are relatively large and do not vary significantly with position relative to fixation. Thus, one might expect disparity to determine depth discrimination near fixation and blur to determine discrimination away from fixation. We tested this expectation in a psychophysical experiment. Observers were presented a reference and test stimulus on each trial. The two stimuli were either both in front of fixation or both behind fixation. After each trial, observers indicated which stimulus appeared more distant. We used a novel volumetric display (Love et al., 2009) to present stimuli that contained 1) only disparity information (Gaussian dot viewed binocularly), 2) only blur information (a disk with 1/f noise viewed monocularly), or 3) both disparity and blur information (1/f disk viewed binocularly). As expected, thresholds were lower in the disparity-only condition than in the blur-only condition and the two-cue thresholds were similar to the disparity-only thresholds when the reference and test were near fixation. The situation reversed, however, behind fixation where blur thresholds were lower than disparity thresholds and two-cue thresholds were similar to blur-only thresholds. Thus, disparity and blur are complementary sources of information with disparity providing the best depth information near fixation and blur providing the best information away from fixation.

Geometric Theory of Lattice Vibrations and Specific Heat

We discuss, from a geometric standpoint, the specific heat of a solid. This is a classical subject in solid state physics which dates back to a pioneering work by Einstein (1907) and its refinement by Debye (1912). Using a special quantization of crystal lattices and calculating the asymptotic of the integrated density of states at the bottom of the spectrum, we obtain a rigorous derivation of the classical Debye $T^3$ law on the specific heat at low temperatures. The idea and method are taken from discrete geometric analysis which has been recently developed for the spectral geometry of crystal lattices.

Some notes on the relativistic Doppler effect

The properties of the analytical formula of the relativistic Doppler-effect are discussed from the geometric standpoint. It is shown, in particular, that, contrary to the widely accepted view, as the observer and the source of electromagnetic radiation approach one another, in addition to the violet shift also a zero and a red shift (z ≥ 0) can be observed depending on the angle θ between the vector of relative velocity β and the observation direction.

Unraveling the Mysteries of Proprietary Connections

The purpose of this article is to provide some insight into the potential users of proprietary connections and to facilitate a rational selection process and procurement procedure. First, it must be noted that the standard and commonly used API casing connections [short, round thread casing and coupling (STC); long, round thread casing and coupling (LTC); buttress thread casing and coupling (BTC)] and API tubing connection EUE-8R (external upset ends, eight round thread tubing and coupling) can provide reliable service for the vast majority of well drilled and completed. Proprietary connections can and have been misapplied at considerable expense; for example, 9 5/8 drilling (intermediate/protective) casing. API BTC works more than adequately in drilling-mud environments. There is no need to use a proprietary connection for such service. In fact, pin nose metal-to-metal seal proprietary connections in this type of service can be less reliable than the API BTC connection since the metal-to-metal seal is much more damage prone than the thread seal of API BTC. Also, very reliable leak resistance, even to gas, is obtained with tin plated BTC couplings.

World geodetic system 1984: A modern and accurate global reference frame

Abstract The Defense Mapping Agency (DMA) has developed World Geodetic System (WGS) 1984, and starting from its earlier versions, viz., WGS 60, WGS 66, and WGS 72, the latest system is a state‐of‐the‐art, accurately defined, global reference frame. In its development, full advantage was derived from the advancement in theory, recent sophistication in computer technology, and the availability of new and more extensive data sets. The new system represents DMA's modeling of the earth from a geometric, geodetic, and gravitational standpoint, using data, techniques, and technology available through early 1984. This paper presents details about the WGS 84 defining parameters, reference frame definition, gravitational model, gravity formula, and its relationship with various local/regional geodetic datums. It also briefly outlines various advantages and applications to improve Mapping, Charting, and Geodetic (MC&G) products globally.