Geometric Regularity Research Articles

Geometric Regularity of Blow-up Limits of the Kähler-Ricci Flow

Geometric Regularity of Blow-up Limits of the Kähler-Ricci Flow

Mathematical Modeling of Forwarder Operation When Collecting Logs in the Forest Swath

Optimization of the machines allows you to increase their productivity and reduce the labor costs for performing individual elements of the technological cycle of their work in the forest. In this regard, the authors offer theoretical studies that take into account the peculiarities of the work of one of the most popular logging machines today, namely, a machine for collecting and forwarding logs (forwarder). The article discusses the technological features of the functioning of these machines, identifies ways to reduce the cost of collecting logs, justifies the rational width of apiaries, which allows collecting logs with a minimum number of movements between work positions. The main purpose of the study is to substantiate the mathematical dependence for determining the rational values of such interrelated parameters of the forwarder's operation as the distance between the working positions of collecting logs and the width of apiaries. The authors propose an analytical approach to solving the problem. On the basis of the standard technological scheme of the harvester's movement through the swath, geometric regularities of the trajectory of the manipulator movement, dimensional characteristics and location of the prepared logs are revealed. As a result of the work, mathematical dependencies are constructed that make it possible to determine the rational values of the desired parameters. The results can be used by research organizations in planning the production process of logging operations. The introduction of author's recommendations into production will contribute to improving the efficiency and operation of forestry equipment.

Static and Seismic Safety of the Inclined Tower of Portogruaro: A Preliminary Numerical Approach

Masonry towers are peculiar structures with complex structural behavior despite biased conclusions deriving from their geometrical regularity and simplicity. Their geometrical features and the epistemic uncertainty that masonry material bears strongly influence their static and seismic behavior. This paper investigates a remarkable and representative case study. The bell tower of Portogruaro (Italy) is a 57 m high tall construction, built in the XII-th century, and has a notable inclination. The Italian Guideline for the safety assessment of masonry towers is a key focus in this paper, highlighting the pros and cons of different suggested approaches. Some relevant proposals are presented in this paper in order to address the seismic safety assessment of masonry bell towers. The findings show that very slender structures do not meet the guidelines recommendations due to limitations in their current stress state. In addition, in similar cases, the recommended values for the mechanical properties of masonry material led to predicting non-withstanding structural behavior, questioning the correct choice of the adapted material properties. Advanced pushover analysis has been conducted in order to investigate the results of the simplified approach in terms of failure patterns and seismic safety estimation. The simulations are implemented for four different hypothetical scenarios of the existing masonry mechanical properties. The results obtained for the case study tower reflect a different perspective in the seismic assessment of masonry towers when specific approaches are defined. The preliminary results on the safety of Portogruaro Tower show a significant variability of seismic safety based on the adopted scenario, highlighting the necessity to pay attention to the preservation state of the present case and of similar ones.

An improved method for upscaling 2D images using adaptive edge sharpening and an optimized directional anisotropic diffusion filter

Image upscaling employs various polynomial techniques, including bicubic and Lanczos, to minimize computing load for various real-time applications. Polynomial interpolation, on the other hand, results in blurring artifacts in high resolution (HR) images due to edge degradation. Many other interpolation approaches, including edge-based and dictionary learning-based schemes, result in blurring in the image’s high frequency (HF) region. As a result, a novel post-processing technique is proposed that uses the Lanczos method to upscale the low resolution (LR) image. To eliminate blur along the image’s edge, the edge component of the interpolated image is retrieved. Adaptive sharpening is used to make the edges more prominent, as predicting pixels in the high variance region is challenging. After the edge is extracted, the smooth region is filtered with an optimized directional anisotropic diffusion (ODAD) filter to preserve texture details and geometric regularity. The sharpened edge image is aggregated with the ODAD filtered image to generate an improved HR (IHR) image. The IHR is then scaled up and down to reduce blurring even further, resulting in a blurred HR image (BHR). The residual image is obtained by subtracting the BHR from the IHR images, which represent the undetected HF. Finally, the residual image and the IHR image are combined to generate the final restored image, which includes all prediction loss details. The results of the experiments show that the proposed algorithm outperforms existing methodologies, particularly in terms of visuality and parameter-wise measurement.

Depth assisted novel view synthesis using few images

In this paper, we introduce a novel approach to improve the performance of Neural Radiance Fields (NeRF) from limited input views. NeRF has exhibited impressive capabilities in producing photo-realistic renderings when trained on dense input views, but its performance degrades as the number of training views decreases. Our key insight is that the original NeRF lacks geometric regularization and appearance information due to limited inputs, resulting in an over-fitting issue. To address this challenge, we present a novel method: first, a global sampling method with geometric regularization is employed by utilizing warped images as additional pseudo-views, which optimizes the multi-view consistency during the training. Second, we introduce a local patch sampling technique with perceptual regularization to ensure pixel correspondence in appearance. Furthermore, we incorporate depth information for explicit geometry regularization. We evaluate our method on the DTU dataset and LLFF dataset from a different number of inputs. Extensive evaluations demonstrate that our approach outperforms existing benchmarks across various metrics, achieving state-of-the-art results.

Optofluidic SERS based on Ag nanocubes with high sensitivity for detecting a prevalent water pollutant.

To enhance the integration and practical applicability of the Raman detection system, silver nanocubes (Ag NCs) were synthesized using a polyol method. A liquid-liquid interface approach was employed to transfer a monolayer of Ag NCs "film" onto a SiO2 substrate, resulting in the fabrication of a highly sensitive and uniform surface-enhanced Raman scattering (SERS) substrate denoted as "Ag NCs@SiO2." The electromagnetic field distribution of various dimers on the Ag NCs@SiO2 was analyzed using finite difference time domain (FDTD) software. The results reveal that the electromagnetic enhancement effect is most pronounced in cube-cube dimers, indicating that Ag NCs exhibit superior localized surface plasmon resonance (LSPR) response due to their well-defined geometric regularity and sharp geometric angles. For Rhodamine 6G (R6G) probe molecules, the Ag NCs@SiO2 shows ultrahigh sensitivity, with a limit of detection (LOD) of 10-12 mol/L, and the enhancement factor (EF) can reach 1.4 × 1010. The relative standard deviation (RSD) at the main characteristic peaks is below 10%, demonstrating good consistency in substrate performance. In addition, the Ag NCs@SiO2 modified with hexanethiol exhibits high sensitivity, uniformity, and repeatability in detecting for pyrene, with the LOD of 10-8 mol/L and a minimum RSD of 6.09% at the main characteristic peak, and effective recognition capabilities for pyrene and anthracene in mixed solutions. Finally, chemisorption and physisorption strategies were prepared in optofluidic channels and experimentally compared, enabling real-time detection of the pyrene solution. This method can achieve a rapid detection and precise differentiation of polycyclic aromatic hydrocarbons in a water pollutant.

Blueprinting extendable nanomaterials with standardized protein blocks

A wooden house frame consists of many different lumber pieces, but because of the regularity of these building blocks, the structure can be designed using straightforward geometrical principles. The design of multicomponent protein assemblies, in comparison, has been much more complex, largely owing to the irregular shapes of protein structures1. Here we describe extendable linear, curved and angled protein building blocks, as well as inter-block interactions, that conform to specified geometric standards; assemblies designed using these blocks inherit their extendability and regular interaction surfaces, enabling them to be expanded or contracted by varying the number of modules, and reinforced with secondary struts. Using X-ray crystallography and electron microscopy, we validate nanomaterial designs ranging from simple polygonal and circular oligomers that can be concentrically nested, up to large polyhedral nanocages and unbounded straight ‘train track’ assemblies with reconfigurable sizes and geometries that can be readily blueprinted. Because of the complexity of protein structures and sequence–structure relationships, it has not previously been possible to build up large protein assemblies by deliberate placement of protein backbones onto a blank three-dimensional canvas; the simplicity and geometric regularity of our design platform now enables construction of protein nanomaterials according to ‘back of an envelope’ architectural blueprints.

Geometric regularity criteria for the Navier–Stokes equations in terms of velocity direction

In this paper, we are inspired by a famous result by Constantin and Fefferman who proved that a simple geometrical assumption on the direction of the vorticity leads to the regularity of weak solutions of the 3D Navier–Stokes equations. We show that the same result can be achieved if the vorticity direction is replaced by the velocity direction. We further strengthen this result and prove that in fact it is not necessary to consider the velocity direction in all close space points but only in the points whose distance equals to a small positive number dependant on the data. In the second part of the paper, we extend a result by Berselli and C rdoba concerning the role of the helicity for the regularity of the weak solutions of the Navier–Stokes equations.

Application of ABAQUS Flow-Solid coupling model to evaluate sealing capability of sandstone formation interface based on the cracking behavior of cohesive force units

Estimating the sealing property of the cementing interface is vital for judging the quality of well cementing construction. The main methods currently used to evaluate the sealing property of the cementing interface (hydraulic cementing strength method and shear cementing strength method) are susceptible to the effects of specimen geometric regularity, interfacial cementing condition, and shear damage pressure source, and the measurement results are not stable, making it difficult to use them as effective methods to evaluate the real cementing interface sealing performance. In this paper, based on the cracking behavior of cohesive units, a method to evaluate the sealing performance of the cementing interface by simulating the cracking process of fluid breaking through the cementing interface in ABAQUSTM FEA software was investigated. The research process includes two parts: first, using a self-designed holding stretching device after eliminating the errors caused by non-interface displacement in the conventional stretching method by repeated stretching and subtraction. The real interfacial traction-separation curve and formation cohesion unit parameters were obtained. Secondly, the cohesive unit parameters obtained in the first step were input into ABAQUSTM FEA software to build a fluid–solid coupling model to simulate the cracking process in the interface region when the fluid breaks through the cementing interface, in which obtaining the solid interface cracking sealing pressure and evaluating its sealing performance are finished. And the accuracy and feasibility of this method were verified by a homemade physical sealing model of the cementing interface. In addition, the factors affecting the fluid pressure at the breakthrough of the cemented interface were investigated in this paper, and it was concluded that changing the elastic modulus of sandstone and cement sheath had a more significant effect on the fluid pressure at the breakthrough of the cemented interface than their Poisson's ratios. Furthermore, the results of this paper also indicate that when the permeability of cement sheath and sandstone is in the range of 0.001 mD–10 mD, the fluid pressure at the time of breaking the cemented interface decreases as the permeability of cement sheath and sandstone increases, and beyond this interval, the effect of the sudden change in permeability of cement sheath and sandstone on the fluid pressure at the time of breaking the cemented interface is no longer obvious.

Performance-based evaluation of reinforced concrete buildings at vertical geometric regularity limit

Performance-based evaluation of reinforced concrete buildings at vertical geometric regularity limit

Embedding Ontologies in the Description Logic ALC by Axis-Aligned Cones

This paper is concerned with knowledge graph embedding with background knowledge, taking the formal perspective of logics. In knowledge graph embedding, knowledge— expressed as a set of triples of the form (a R b) (“a is R-related to b”)—is embedded into a real-valued vector space. The embedding helps exploiting geometrical regularities of the space in order to tackle typical inductive tasks of machine learning such as link prediction. Recent embedding approaches also consider incorporating background knowledge, in which the intended meanings of the symbols a, R, b are further constrained via axioms of a theory. Of particular interest are theories expressed in a formal language with a neat semantics and a good balance between expressivity and feasibility. In that case, the knowledge graph together with the background can be considered to be an ontology. This paper develops a cone-based theory for embedding in order to advance the expressivity of the ontology: it works (at least) with ontologies expressed in the description logic ALC, which comprises restricted existential and universal quantifiers, as well as concept negation and concept disjunction. In order to align the classical Tarskian Style semantics for ALC with the sub-symbolic representation of triples, we use the notion of a geometric model of an ALC ontology and show, as one of our main results, that an ALC ontology is satisfiable in the classical sense iff it is satisfiable by a geometric model based on cones. The geometric model, if treated as a partial model, can even be chosen to be faithful, i.e., to reflect all and only the knowledge captured by the ontology. We introduce the class of axis-aligned cones and show that modulo simple geometric operations any distributive logic (such as ALC) interpreted over cones employs this class of cones. Cones are also attractive from a machine learning perspective on knowledge graph embeddings since they give rise to applying conic optimization techniques.

CIPS-3D++: End-to-End Real-Time High-Resolution 3D-Aware GANs for GAN Inversion and Stylization.

Style-based GANs achieve state-of-the-art results for generating high-quality images, but lack explicit and precise control over camera poses. Recently proposed NeRF-based GANs have made great progress towards 3D-aware image generation. However, the methods either rely on convolution operators which are not rotationally invariant, or utilize complex yet suboptimal training procedures to integrate both NeRF and CNN sub-structures, yielding un-robust, low-quality images with a large computational burden. On top of our open-source CIPS-3D framework 1https://github.com/PeterouZh/CIPS-3D, this paper presents an upgraded version called CIPS-3D++, aiming at high-robust, high-resolution and high-efficiency 3D-aware GANs. On the one hand, our basic model CIPS-3D, encapsulated in a style-based architecture, features a shallow NeRF-based 3D shape encoder as well as a deep MLP-based 2D image decoder, achieving robust image generation/editing with rotation-invariance. On the other hand, our proposed CIPS-3D++, inheriting the rotational invariance of CIPS-3D, together with geometric regularization and upsampling operations, encourages high-resolution high-quality image generation/editing with great computational efficiency. Trained on raw single-view images, without any bells and whistles, CIPS-3D++ sets new records for 3D-aware image synthesis, with an impressive FID of 3.2 on FFHQ at the 1024×1024 resolution. In the meantime, CIPS-3D++ runs efficiently and enjoys a low GPU memory footprint so that it can be trained end-to-end on high-resolution images directly, in contrast to previous alternate/progressive methods. Based on the infrastructure of CIPS-3D++, we propose a 3D-aware GAN inversion algorithm named FlipInversion, which can reconstruct the 3D object from a single-view image. We also provide a 3D-aware stylization method for real images based on CIPS-3D++ and FlipInversion. In addition, we analyze the problem of mirror symmetry suffered in training, and solve it by introducing an auxiliary discriminator for the NeRF network. Overall, CIPS-3D++ provides a strong base model that can serve as a testbed for transferring GAN-based image editing methods from 2D to 3D. Our open-source project as well as accompanying demo videos can be found online 2https://github.com/PeterouZh/CIPS-3Dplusplus.

Knowledge-driven inference for automatic reconstruction of indoor detailed as-built BIMs from laser scanning data

In spite of recent advances, a significant disparity between automatically reconstructed building information models (BIMs) and real scenes persists, particularly within complex indoor environments. With this objective in mind, a knowledge-driven as-built BIM reconstruction method is proposed, which employs laser scanning point clouds and panorama images. Initiation of the method involves the segmentation of 3D data into individual rooms through the application of wall constraints. Subsequently, geometric regularization of the rooms is performed, accompanied by the establishment of topological relations through the maintenance of rigid consistency among rooms. Finally, building frames and components embedded within walls are reconstructed and assembled to formulate comprehensive BIMs. The method was evaluated using indoor point cloud datasets (ISPRS and WUT), showing that it outperforms state-of-the-art techniques with room segmentation accuracy and completeness of 0.98 and 0.88, respectively, and achieving millimetre level accuracy on average.

Variability in parameter estimation for a tall steel-frame building

The between-event variability in identified shear wave velocities of fitted four-layer beam models in the response of a 54-story steel-frame building during nine earthquakes over a period of 27 years (1992–2019) is investigated. Recorded response and simulated response by its digital twin (linear finite element model with fixed base) were used as input, that is, the real structure and its digital twin were identified. Two surrogate models were fitted, a Timoshenko beam and a shear beam. The waveform inversion of impulse response functions method, developed earlier by the authors, was used to fit the beam models. The coefficients of variation (C.V.) of the between-events variability in the wave velocity estimates of the four layers were analyzed and compared for the different cases of data (real structure versus digital twin), different surrogate models, and different locations on the floor where the motions were observed. The results showed that the variability of the digital twin was affected by the contamination of the response by torsion, which is not accounted for in the beam models, by the degree of geometric regularity of the structure and by how closely the beam model represented the nature of the building deformation (balance of shear and bending deformation). These effects were minor in comparison to the nonlinear effects (recoverable nonlinearity and permanent stiffness degradation), which were not present in the digital twin response. The C.V. for the real structure (about 3%–5%) was comparable for both beam models fitted.

On the Importance of Chemical Precision in Organic Electronics: Fullerene Intercalation in Perfectly Alternating Conjugated Polymers

AbstractThe true structure of alternating conjugated polymers—the state‐of‐the‐art materials for many organic electronics—often deviates from the idealized picture. Homocoupling defects are in fact inherent to the widely used cross‐coupling polymerization methods. Nevertheless, many polymers still perform excellently in the envisaged applications, which raises the question if one should really care about these imperfections. This article looks at the relevance of chemical precision (and lack thereof) in conjugated polymers covering the entire spectrum from the molecular scale, to the micro and mesostructure, up to the device level. The different types of polymerization errors for the alkoxylated variant of the benchmark (semi)crystalline polymer poly[2,5‐bis(3‐tetradecylthiophen‐2‐yl)thieno[3,2‐b]thiophene (PBTTT) are identified, visualized, and quantified and a general strategy to avoid homocoupling is introduced. Through a combination of experiments and supported by simulations, it is shown that these coupling defects hinder fullerene intercalation and limit device performance as compared to the homocoupling‐free analog. This clearly demonstrates that structural defects do matter and should be generally avoided, in particular when the geometrical regularity of the polymer is essential. These insights likely go beyond the specific PBTTT derivatives studied here and are of general relevance for the wider organic electronics field.

Conceptual orthospaces—Convexity meets negation

Neural networks and in general subsymbolic learning approaches perform well on usual learning tasks, but they are black boxes lacking desired properties such as explainability or trustworthiness. Fully integrated symbolic/subsymbolic systems account for these properties, e.g., through the injection of symbolic information into a subsymbolic learning framework. Systems relying on embeddings can be considered as specific examples of such systems where facts, expressed in some logic, are embedded into a continuous space. Instances mentioned in the facts are mapped to points and the relations/concepts mentioned in the facts are mapped to a region in that space. This allows to exploit geometric regularities in order to tackle typical learning tasks such as link prediction. Embeddings provide the first step towards filling the gap between qualitative, Tarskian style semantics, which is used for deductive reasoning over the facts, and quantitative structures, which are used for representing objects, relations, and concepts for learning purposes. However, to enable meaningful reasoning, embeddings of relations and concepts are not allowed to be shaped arbitrarily. Especially, convex sets turned out to be appropriate due to their computational advantages and due to their foundation in cognition. Convexity can be defined with a ternary betweenness relation and concepts can be defined as betweenness-closed (= convex) sets. Though many interesting phenomena of cognitive reasoning can be explained in such a framework, it is at least not obvious how to use betweenness for other, more logico-formal aspects of reasoning that, e.g., require defining logical operators. In particular, for the logical operator of negation other mathematical structures such as the orthoframes of Goldblatt (1974) [13] have proven more useful. In this paper, we provide results on the connection between convexity and orthoframes. In particular, we investigate the construction of convex concepts equipped with an orthogonality relation. We give a universal construction of a betweenness relation over an orthoframe and show that based on Euclidean betweenness (thus using the classical notion of convexity) and under some natural restrictions, convex cones are the only structures capable of modeling such a space.

The mathematics of Almada Negreiros

In this paper, we deepen our study of the geometric work of Portuguese artist Almada Negreiros, who went beyond the usual practice of geometric abstractionists to find geometric regularities in ways that resemble the work of a mathematician.

RFMNet: Robust Deep Functional Maps for unsupervised non-rigid shape correspondence

In traditional deep functional maps for non-rigid shape correspondence, estimating a functional map including high-frequency information requires enough linearly independent features via the least square method, which is prone to be violated in practice, especially at an early stage of training, or costly post-processing, e.g. ZoomOut. In this paper, we propose a novel method called RFMNet (Robust Deep Functional Map Networks), which jointly considers training stability and more geometric shape features than previous works. We directly first produce a pointwise map by resorting to optimal transport and then convert it to an initial functional map. Such a mechanism mitigates the requirements for the descriptor and avoids the training instabilities resulting from the least square solver. Benefitting from the novel strategy, we successfully integrate a state-of-the-art geometric regularization for further optimizing the functional map, which substantially filters the initial functional map. We show our novel computing functional map module brings more stable training even under encoding the functional map with high-frequency information and faster convergence speed. Considering the pointwise and functional maps, an unsupervised loss is presented for penalizing the correspondence distortion of Delta functions between shapes. To catch discretization-resistant and orientation-aware shape features with our network, we utilize DiffusionNet as a feature extractor. Experimental results demonstrate our apparent superiority in correspondence quality and generalization across various shape discretizations and different datasets compared to the state-of-the-art learning methods.

Cult and Architecture in the Chalcolithic Period of the Southern Levant: The Case of En-Gedi and Teleilat Ghassul

We studied the architectural remains of two Chalcolithic (Ghassulian) cultic complexes at En-Gedi and Teleilat Ghassul Area E in order to trace aspects of the architectural planning principles and methods involved in their design and construction. Architectural Formal Analysis has brought to light hitherto unnoticed spatial relations between architectural elements that seem to have structured the ritual activity at the two sites. The discerned geometric regularities imply that specific mathematical knowledge and the same set of design principles and methods were used in the planning of both complexes. The emerging pictures of highly structured ritual and of the use of geometry in Ghassulian cultic production may be used to support suggestions regarding some sort of cultic establishment (priesthood) during the Chalcolithic Ghassulian.

Geodesic Models With Convexity Shape Prior.

The minimal geodesic models established upon the eikonal equation framework are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with geometric regularization terms, such as euclidean curve length or curvature-penalized length, for computing geodesic curves. In this paper, we take into account a more complicated problem: finding curvature-penalized geodesic paths with a convexity shape prior. We establish new geodesic models relying on the strategy of orientation-lifting, by which a planar curve can be mapped to an high-dimensional orientation-dependent space. The convexity shape prior serves as a constraint for the construction of local geodesic metrics encoding a particular curvature constraint. Then the geodesic distances and the corresponding closed geodesic paths in the orientation-lifted space can be efficiently computed through state-of-the-art Hamiltonian fast marching method. In addition, we apply the proposed geodesic models to the active contours, leading to efficient interactive image segmentation algorithms that preserve the advantages of convexity shape prior and curvature penalization.