Geometric Criteria Research Articles

Diffusion sampling schemes: A generalized methodology with nongeometric criteria.

The aim of this paper is to show that geometrical criteria for designing multishell -space sampling procedures do not necessarily translate into reconstruction matrices with high figures of merit commonly used in the compressed sensing theory. In addition, we show that a well-known method for visiting k-space in radial three-dimensional acquisitions, namely, the Spiral Phyllotaxis, is a competitive initialization for the optimization of our nonconvex objective function. We propose the gradient design method WISH (WeIghting SHells) which uses an objective function that accounts for weighted distances between gradients within M-tuples of consecutive shells, with ranging between 1 and the maximum number of shells . All the -tuples share the same weight . The objective function is optimized for a sample of these weights, using Spiral Phyllotaxis as initialization. State-of-the-art General Electrostatic Energy Minimization (GEEM) and Spherical Codes (SC) were used for comparison. For the three methods, reconstruction matrices of the attenuation signal using MAP-MRI were tested using figures of merit borrowed from the Compressed Sensing theory (namely, Restricted Isometry Property -RIP- and Coherence); we also tested the gradient design using a geometric criterion based on Voronoi cells. For RIP and Coherence, WISH got better results in at least one combination of weights, whilst the criterion based on Voronoi cells showed an unrelated pattern. The versatility provided by WISH is supported by better results. Optimization in the weight parameter space is likely to provide additional improvements. For a practical design with an intermediate number of gradients, our results recommend to carry out the methodology here used to determine the appropriate gradient table.

Stability and bifurcation analysis of a size-stage-structured cooperation model

In this paper, we propose a size-stage-structured cooperation model which has two distinct life stages in facultative cooperator. The primary feature of this model is to consider size structure, stage structure and obligate and facultative symbiosis at the same time in a cooperation system. We use the method of characteristic to show that this new model can be reduced to a threshold delay equations (TDEs) model, which can be further transformed into a functional differential equations (FDEs) model by a simple change of variables. Such simplification allows us to apply the classical theory of FDEs and establish a set of sufficient conditions to investigate the qualitative analysis of solutions of the FDEs model, including the global existence and uniqueness, positivity and boundedness. What’s more, we use the geometric criteria to get the conclusions about stability and Hopf bifurcation of positive equilibrium because the coefficients of the characteristic equation depend on the bifurcation parameter. Finally, numerical simulations are carried out as supporting evidences of our analytical results. Our results show that the presence of size structure and stage structure plays an important role in the dynamic behavior of the model.

Uncertainty Principle for Hermite Functions and Null-Controllability with Sensor Sets of Decaying Density

We establish a family of uncertainty principles for finite linear combinations of Hermite functions. More precisely, we give a geometric criterion on a subset Ssubset mathbb {R}^d ensuring that the L^2-seminorm associated to S is equivalent to the full L^2-norm on mathbb {R}^d when restricted to the space of Hermite functions up to a given degree. We give precise estimates how the equivalence constant depends on this degree and on geometric parameters of S. From these estimates we deduce that the parabolic equation whose generator is the harmonic oscillator is null-controllable from S. In all our results, the set S may have sub-exponentially decaying density and, in particular, finite volume. We also show that bounded sets are not efficient in this context.

EFFECT OF KEYFRAMES EXTRACTION FROM THERMAL INFRARED VIDEO STREAM TO GENERATE DENSE POINT CLOUD OF THE BUILDING'S FACADE

Abstract. Keyframes extraction is required and effective for the 3D reconstruction of objects from a thermal video sequence to increase geometric accuracy, reduce the volume of aerial triangulation calculations, and generate the dense point cloud. The primary goal and focus of this paper are to assess the effect of keyframes extraction from the thermal infrared video sequence on the geometric accuracy of the dense point cloud generated. The method of keyframes extraction of thermal infrared video presented in this paper consists of three basic steps. (A) The ability to identify and remove blur frames from non-blur frames in a sequence of recorded frames. (B) The ability to apply the standard baseline condition between sequence frames to establish the overlap condition and prevent the creation of degeneracy conditions. (C) Evaluating degeneracy conditions and keyframes extraction using Geometric Robust Information Criteria (GRIC). The performance evaluation criteria for keyframes extraction in the generation of the thermal infrared dense point cloud in this paper are to assess the increase in density of the generated three-dimensional point cloud and reduce reprojection error. Based on the results and assessments presented in this paper, using keyframes increases the density of the thermal infrared dense point cloud by about 0.03% to 0.10% of points per square meter. It reduces the reprojection error by about 0.005% of pixels (2 times).

Flexible-to-Stretchable Mechanical and Electrical Interconnects

Stretchable electronic devices that maintain electrical function when subjected to stress or strain are useful for enabling new applications for electronics, such as wearable devices, human-machine interfaces, and components for soft robotics. Powering and communicating with these devices is a challenge. NFC (near-field communication) coils solve this challenge but only work efficiently when they are in close proximity to the device. Alternatively, electrical signals and power can arrive via physical connections between the stretchable device and an external source, such as a battery. The ability to create a robust physical and electrical connection between mechanically disparate components may enable new types of hybrid devices in which at least a portion is stretchable or deformable, such as hinges. This paper presents a simple method to make mechanical and electrical connections between elastomeric conductors and flexible (or rigid) conductors. The adhesion at the interface between these disparate materials arises from surface chemistry that forms strong covalent bonds. The utilization of liquid metals as the conductor provides stretchable interconnects between stretchable and non-stretchable electrical traces. The liquid metal can be printed or injected into vias to create interconnects. We characterized the mechanical and electrical properties of these hybrid devices to demonstrate the concept and identify geometric design criteria to maximize mechanical strength. The work here provides a simple and general strategy for creating mechanical and electrical connections that may find use in a variety of stretchable and soft electronic devices.

Study of the conditional flexibility effect of compressed chord on the overall stability of corrugated beams

In this paper, the calculation of cut corrugated beams loaded with uniformly distributed load in the plane of the wall, with a wall height of 333 and 500 mm (54 sizes), chord width from 160 to 400 mm and chord thickness from 6 to 30 mm for general stability in accordance with Building Codes (BC) 294.1325800.2017 is made. A geometric criterion has been defined which defines the boundaries of the load-carrying capacity of Russian corrugated beams between the flat bending form stability and the strength of the normal section under the action of the bending moment in the plane of the wall.

Exploring the influence of graphene on antiaromaticity of pentalene.

Theoretical investigations on the influence of graphene fragments on the antiaromaticity of pentalene are conducted by employing multiple aromaticity descriptors based on magnetic, geometric and electronic criteria. NICS as a sole descriptor for analysing the antiaromaticity of pentalene on graphene fragments has to be carefully considered while looking through the other aromaticity indicators.

Density functional theory study of crown ether-magnesium complexes: from a solvated ion to an ion trap.

Metal ion detection rests on host-guest recognition. We propose a theoretical protocol for designing an optimal trap for a desired metal cation. A host for magnesium ions was sought for among derivatives of crown ethers 12-crown-4, 15-crown-5, and 18-crown-6. Mg-crown complexes and their hydrated counterparts with water molecules bound to the cation were optimized using density functional theory. Based on specific geometric criteria, Interacting quantum atoms analysis and density functional theory-based molecular dynamics of Mg-crown complexes immersed in water, crown ethers for optimal accommodation of Mg2+ in aqueous solution were identified. Selectivity of the chosen crowns towards Na+, K+, and Ca2+ ions is addressed.

On endomorphisms of projective varieties with numerically trivial canonical divisors

Let [Formula: see text] be a klt projective variety with numerically trivial canonical divisor. A surjective endomorphism [Formula: see text] is amplified (respectively, quasi-amplified) if [Formula: see text] is ample (respectively, big) for some Cartier divisor [Formula: see text]. We show that after iteration and equivariant birational contractions, a quasi-amplified endomorphism will descend to an amplified endomorphism. As an application, when [Formula: see text] is Hyperkähler, [Formula: see text] is quasi-amplified if and only if it is of positive entropy. In both cases, [Formula: see text] has Zariski dense periodic points. When [Formula: see text] is an abelian variety, we give and compare several cohomological and geometric criteria of amplified endomorphisms and endomorphisms with countable and Zariski dense periodic points (after an uncountable field extension).

Moment observability and output feedback stabilisation for linear stochastic impulsive systems

ABSTRACT This paper is concerned with the observability of linear stochastic impulsive systems with multiplicative noise. The concept of 2pth moment observability is first introduced. Then, to explore the moment observability, a deterministic expanded system is established for the linear stochastic impulsive systems by the generalised -representation technique. It shows that the linear stochastic impulsive system is 2pth moment observability if and only if the expanded system is completely observable. Subsequently, a series of algebraic criteria and geometric criteria for 2pth moment observability of linear stochastic impulsive systems are established by analysing the solution of the expanded system. The impulsive observer-based stabilisation problem for linear stochastic systems is further studied based on these observability criteria. Finally, two numerical examples illustrate the proposed theoretical results.

PatchIT: A Multipurpose Patch Creation Tool for Image Processing Applications

Patch-based approaches in image processing are often preferable to working with the entire image. They provide an alternative representation of the image as a set of partial local sub-images (patches) which is a vital preprocessing step in many image processing applications. In this paper, a new software tool called patchIT is presented, providing an integrated framework suitable for the systematic and automatized extraction of patches from images based on user-defined geometrical and spatial criteria. Patches can be extracted in both a sliding and random manner and can be exported either as images, MATLAB .mat files, or raw text files. The proposed tool offers further functionality, including masking operations that act as spatial filters, identifying candidate patch areas, as well as geometric transformations by applying patch value indexing. It also efficiently handles issues that arise in large-scale patch processing scenarios in terms of memory and time requirements. In addition, a use case in cartographic research is presented that utilizes patchIT for map evaluation purposes based on a visual heterogeneity indicator. The tool supports all common image file formats and efficiently processes bitonal, grayscale, color, and multispectral images. PatchIT is freely available to the scientific community under the third version of GNU General Public License (GPL v3) on the GitHub platform.

Computational prediction of ω-transaminase selectivity by deep learning analysis of molecular dynamics trajectories.

We previously presented a computational protocol to predict the enzymatic (enantio)selectivity of an ω-transaminase towards a set of ligands (Ramírez-Palacios et al. (2021) Journal of Chemical Information and Modeling 61(11), 5569-5580) by counting the number of binding poses present in molecular dynamics (MD) simulations that met a defined set of geometric criteria. The geometric criteria consisted of a hand-crafted set of distances, angles and dihedrals deemed to be important for the enzymatic reaction to take place. In this work, the MD trajectories are reanalysed using a deep-learning approach to predict the enantiopreference of the enzyme without the need for hand-crafted criteria. We show that a convolutional neural network is capable of classifying the trajectories as belonging to the 'reactive' or 'non-reactive' enantiomer (binary classification) with a good accuracy (>0.90). The new method reduces the computational cost of the methodology, because it does not necessitate the sampling approach from the previous work. We also show that analysing how neural networks reach specific decisions can aid hand-crafted approaches (e.g. definition of near-attack conformations, or binding poses).

A process optimization framework for laser direct energy deposition: Densification, microstructure, and mechanical properties of an Fe[sbnd]Cr alloy

Laser Direct Energy Deposition (DED) is a metal additive manufacturing technique with the ability to fabricate large and complex parts through deposition of metal powders. However, achieving high-density parts and targeted build heights using DED can be challenging due to the large number of highly sensitive process variables. This work proposes a robust fabrication parameter optimization framework to generate process maps for primary parameters in DED, including laser power, scan speed, mass flow rate, hatch spacing, and layer height. Simple single-track experiments were utilized to map out the parameter space, and a combination of geometric criteria for hatch spacing and layer height were proposed to determine parameter sets that achieve both targeted build heights and mitigate porosity formation. Using this framework, specimens with >99 % density and consistent mechanical properties were successfully fabricated over a wide range of process parameters for an Fe-9wt.%Cr (Fe9Cr) alloy, a surrogate for radiation damage-resistant reduced activation ferritic/martensitic (RAFM) steels. Processing these materials using DED is of particular interest in the development of plasma facing components for nuclear fusion applications. The microstructure and mechanical properties of as-printed Fe9Cr were characterized using optical and electron microscopy, X-ray diffraction, and uniaxial tensile tests. As-printed Fe9Cr displayed ~25 % elongation and ultimate tensile strengths of up to 475 MPa which is comparable to similar wrought alloys. The proposed framework will allow for accelerated DED parameter optimization for novel alloy systems, as well as open the possibility for local microstructure control while simultaneously mitigating defect formation.

A theoretical justification of the slip index concept in fretting analysis

Fretting in the partial-slip and gross-slip regimes under a constant normal load is considered. The tangential force—displacement relations for the forward and backward motions are described based the generalized Cattaneo—Mindlin theory of tangential contact and Masing’s hypothesis on modelling the force—displacement hysteretic loop. Besides the critical force and displacement parameters (characterizing the triggering of sliding), the model includes one dimensionless fitting parameter that tunes the tangential contact stiffness of the friction—contact interface. Explicit expressions are derived for the main tribological parameters of the fretting loop, including the slip index and the signal index. The presented phenomenological modelling approach has been applied to the analysis of two sets of experimental data taken from the literature. It has been shown that the experimentally observed simple relation of a rational type between the slip index and the slip ratio corresponds to the gross-slip asymptotics of the corresponding model-based predicted relation. The known quantitative criteria for the transition from the partial slip regime to the gross slip regime are expressed in terms of the stiffness parameter, and a novel geometric transition criterion is formulated.

Geometrically-driven generation of mechanical designs through deep convolutional GANs

Despite the freedom Additive Manufacturing (AM) offers when manufacturing organic shapes, it still requires some geometrical criteria to avoid a part's collapse during printing. The most synergetic design approach to AM is Topology Optimization (TO), which finds an optimal free-form given mechanical constraints. However, it is hard for TO to integrate these layout geometry-related constraints and it seldom proposes printable shapes. Therefore, this work leverages the Deep Learning (DL) capability to handle spatial correlations within the mechanical design process by integrating the layout and mechanical constraints at the conceptual level. It proposes a DL-layout-driven solution (DL-TO) trained via a triple-discriminator Generative Adversarial Network (GAN) framework. The DL-TO's performance is demonstrated by generating mechanically valid 2D designs conforming with layout constraints in a fraction of a second. DL-TO's creativity is illustrated by its capability to generate designs with unseen input constraints (passive/active elements) and to propose several shapes for the same input mechanical constraints, a task that is hard for a traditional TO to achieve.

Local normal forms of em-wavefronts in affine flat coordinates

In our previous work, we have generalized the notion of dually flat or Hessian manifold to quasi-Hessian manifold; it admits the Hessian metric to be degenerate but possesses a particular symmetric cubic tensor (generalized Amari-Centsov tensor). Indeed, it naturally appears as a singular model in information geometry and related fields. A quasi-Hessian manifold is locally accompanied with a possibly multi-valued potential and its dual, whose graphs are called the $e$-wavefront and the $m$-wavefront respectively, together with coherent tangent bundles endowed with flat connections. In the present paper, using those connections and the metric, we give coordinate-free criteria for detecting local diffeomorphic types of $e/m$-wavefronts, and then derive the local normal forms of those (dual) potential functions for the $e/m$-wavefronts in affine flat coordinates by means of Malgrange's division theorem. This is motivated by an early work of Ekeland on non-convex optimization and Saji-Umehara-Yamada's work on Riemannian geometry of wavefronts. Finally, we reveal a relation of our geometric criteria with information geometric quantities of statistical manifolds.

The Mechanism of Selective Recognition of Lipid Substrate by hDHHC20 Enzyme

S-acylation is a post-translational linkage of long chain fatty acids to cysteines, playing a key role in normal physiology and disease. In human cells, the reaction is catalyzed by a family of 23 membrane DHHC-acyltransferases (carrying an Asp-His-His-Cys catalytic motif) in two stages: (1) acyl-CoA-mediated autoacylation of the enzyme; and (2) further transfer of the acyl chain to a protein substrate. Despite the availability of a 3D-structure of human acyltransferase (hDHHC20), the molecular aspects of lipid selectivity of DHHC-acyltransferases remain unclear. In this paper, using molecular dynamics (MD) simulations, we studied membrane-bound hDHHC20 right before the acylation by C12-, C14-, C16-, C18-, and C20-CoA substrates. We found that: (1) regardless of the chain length, its terminal methyl group always reaches the "ceiling" of the enzyme's cavity; (2) only for C16, an optimal "reactivity" (assessed by a simple geometric criterion) permits the autoacylation; (3) in MD, some key interactions between an acyl-CoA and a protein differ from those in the reference crystal structure of the C16-CoA-hDHHS20 mutant complex (probably, because this structure corresponds to a non-native dimer). These features of specific recognition of full-size acyl-CoA substrates support our previous hypothesis of "geometric and physicochemical selectivity" derived for simplified acyl-CoA analogues.

A feature-based assembly information modeling method for complex products’ 3D assembly design

During the assembly design of complex products, the process data management is disordered and the data expression is not standardized, and depends mainly on the experience of technical personnel resulting in a lack of unified data source, low design efficiency, and low automation. This paper proposes a feature-based assembly information model to address these problem, providing standardized original design data for complex product 3D-assembly design. Taking the geometric feature of the mating faces as the study object, the overall structure of complex products and the information requirements of each assembly design stage were analyzed to construct the assembly feature information model. By focusing on the composition and expression form of information in the assembly feature information model, a geometric feature classification criterion applicable to assembly design is presented, and the matching rules of feature pairs, assembly relationship, and assembly constraint instructions are established. Based on these, assembly design information is extracted and expressed in a standardized form. As a validation, the modeling method was conducted on a marine diesel engine cylinder cap as a case study; the performance and applicability of the established rules and the extraction and expression methods were verified through the comparison with the assembly process of the cylinder cap.

How does electron exchange correlation influence reactivity of metallo-β-lactamase L1 against cephalosporin antibiotics

Cephalosporin hydrolysis by the metallo-β-lactamase L1 is a reaction where electron delocalization in the substrate-protein complex affects the reaction rate: the more cephalosporin lone pairs are localized on the N atom, the higher hydrolysis rates are. We show that high Fermi holevariability is responsible for the stipulation of the electron lone pairs’ localization.One-electron potentials reveal that higher lone pairs’ localization is expressed in the dominance of the static exchange correlation (reflected in theaverage Fermi hole depth) in theN atomvicinity. However, this dominance was found to be defined by the height of the kinetic exchange potential barriers (expressing the Fermi holevariability and the response of the exchange correlation hidden in the kinetic potential to electron density variations), rather than by the features of the static exchange correlation itself. The need to account both static and kinetic exchange correlations for the reliable description of the electron delocalization explains inapplicability of the simple geometric criteria for the chemical bonding study in the considered systems.

Accurate determination of active slip systems for improved geometrical criteria of basal-to-basal slip transfer at grain boundaries in pure Mg

Basal-to-basal slip transfer across grain boundaries was analyzed through the combination of slip trace analysis and electron back-scatterer diffraction in weakly-textured pure Mg specimens deformed in tension. Basal slip was the dominant deformation mechanism in many grains, and slip transfer/blocking was assessed at 103 grain boundaries. In addition, the actual active slip system(s) in 170 grains were determined through the analysis of the grain rotation as a result of plastic slip along the basal slip systems. Finally, the twist angle θ (formed between the traces of both active slip planes in the grain boundary plane) was determined in selected cases by the progressive removal of the material by a focus ion beam to measure the grain boundary orientation within the sample. It was found that the basal slip system with the highest global Schmid factor was the most active one in only 49.3% of the grains. In 25.7% of the grains, the basal slip system with the highest Schmid factor was not active. The analysis of basal-to-basal slip transfer/blocking showed that slip transfer is likely to occur if mαβ′ > 0.73. In the cases in which mαβ′ > 0.73 and slip transfer did not occur, it was found that the twist angle θ > 60°. Moreover, slip transfer is unlikely to take place if the trace of one of the active slip systems across the boundary is parallel to the grain boundary.