Geometric Classification Research Articles

The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras

This paper is devoted to the complete algebraic and geometric classification of complex 4-dimensional nilpotent weakly associative, complex 4-dimensional symmetric Leibniz algebras, and complex 5-dimensional nilpotent symmetric Leibniz algebras. In particular, we proved that the variety of complex 4-dimensional symmetric Leibniz algebras has no Vergne–Grunewald–O'Halloran Property (there is an irreducible component formed by only nilpotent algebras), but on the other hand, it has Vergne Property (there are no rigid nilpotent algebras).

Satellite constructions and geometric classification of Brunnian links

We study satellite operations on Brunnian links. First, we find two special satellite operations, both of which can construct infinitely many distinct Brunnian links from almost every Brunnian link. Second, we give a geometric classification theorem for Brunnian links, characterize the companionship graph defined by Budney in [JSJ-decompositions of knot and link complements in [Formula: see text], Enseign. Math. 3 (2005) 319–359], and develop a canonical geometric decomposition, which is simpler than JSJ-decomposition, for Brunnian links. The building blocks of Brunnian links then turn out to be Hopf [Formula: see text]-links, hyperbolic Brunnian links, and hyperbolic Brunnian links in unlink-complements. Third, we define an operation to reduce a Brunnian link in an unlink-complement into a new Brunnian link in [Formula: see text] and point out some phenomena concerning this operation.

Geology of Bajalia Anticline of the Low Folded Zone of Iraq

Bajalia Anticline is located about 60km northeast of central Amarah city in Al-Teeb area near Iraq-Iran border. Field and laboratory works were conducted to study topography, geomorphology, stratigraphy, and structural geology of Bajalia Anticline. The Anticline has a longitudinal shape with about 29km in length and 5-7km in width. Injana, Mukdadiya, and Bai Hassan formations are the three formations that were recognized in the study area. The geometrical structural analysis depicts that the Anticline is non-cylindrical, asymmetrical, close, sub-horizontal, steeply inclined, and linear fold. Most of the fractures in the Anticline are joints. These joints were classified based on the tectonics axes, which are a, b, and c, into ac, bc, and hol. A major reverse fault is located at the margin of the southwestern limb parallel to the fold axis with about 25km length. This fault is responsible on the vergence of the Anticline and overturned part of the southwestern limb. The Anticline was formed as a result of the collision between the Arabian and Iranian plates during the Late Tertiary. The maximum stress axis, which is caused by collision, is perpendicular to the hinge line. The geometrical and genetic classification indicates that the Anticline was formed by the high folding intensity and with a role of evaporites layers.

Geometric Interpretation and General Classification of Three-Dimensional Polarization States through the Intrinsic Stokes Parameters

In contrast with what happens for two-dimensional polarization states, defined as those whose electric field fluctuates in a fixed plane, which can readily be represented by means of the Poincaré sphere, the complete description of general three-dimensional polarization states involves nine measurable parameters, called the generalized Stokes parameters, so that the generalized Poincaré object takes the complicated form of an eight-dimensional quadric hypersurface. In this work, the geometric representation of general polarization states, described by means of a simple polarization object constituted by the combination of an ellipsoid and a vector, is interpreted in terms of the intrinsic Stokes parameters, which allows for a complete and systematic classification of polarization states in terms of meaningful rotationally invariant descriptors.

DEVELOPMENT OF 3D CADASTRE IN NEW SOUTH WALES THROUGH E-PLAN LODGEMENT

Abstract. With rapid growth of urban environments worldwide, there is an increasing need to develop more innovative and efficient land administration systems. In Australia, various jurisdictions are currently in the process of implementing 3D cadastre to support better land administration services to the wider community. The ‘Cadastre 2034 Strategy’ published by the Intergovernmental Committee on Surveying and Mapping (ICSM) for Australia in 2014 indicates that a digital cadastre will be implemented as part of that strategy. As part of development of 3D cadastre, State of New South Wales has used the ePlan model based on LandXML for digital lodgement and validation of cadastral plans. This initiative aims to replace PDF cadastral plans with the digital format of LandXML. However, with the introduction of LandXML as the chosen formats for digital cadastral plans in NSW, there has been a significantly low level of Strata Plan digital capture and submission in LandXML format by the surveying industry. The research aims to identify the main challenges and explore a suitable method to improve the adoption of the digital format for Strata Plan submission and development of 3D cadastre in NSW. In this research paper, a mixed method research approach has been used by integrating both qualitative and quantitative data. The primary data was collected using online questionnaires and surveys of different stakeholders from government and the private surveying industry. The data allowed for the assessment of the effectiveness and implications of the digital system currently maintained by the NSW LRS (Land Registry Services). A case study was used for the creation, validation and lodgement of an existing strata plan using LandXML format. This paper demonstrates that implementation of 3D digital cadastral plans needs to be more structured in order to satisfy all stakeholders involved. More investment into the representation of complex 3D geometric models and classification for validation will improve the uptake by surveyors. The paper concludes with a discussion on the implications of the proposed strata plan implementation strategy and proposes future research within the topic of strata plan validation in NSW, Australia.

Advanced Deep Learning-Based Supervised Classification of Multi-Angle Snowflake Camera Images

AbstractWe present improvements over our previous approach to automatic winter hydrometeor classification by means of convolutional neural networks (CNNs), using more data and improved training techniques to achieve higher accuracy on a more complicated dataset than we had previously demonstrated. As an advancement of our previous proof-of-concept study, this work demonstrates broader usefulness of deep CNNs by using a substantially larger and more diverse dataset, which we make publicly available, from many more snow events. We describe the collection, processing, and sorting of this dataset of over 25,000 high-quality multiple-angle snowflake camera (MASC) image chips split nearly evenly between five geometric classes: aggregate, columnar crystal, planar crystal, graupel, and small particle. Raw images were collected over 32 snowfall events between November 2014 and May 2016 near Greeley, Colorado and were processed with an automated cropping and normalization algorithm to yield 224x224 pixel images containing possible hydrometeors. From the bulk set of over 8,400,000 extracted images, a smaller dataset of 14,793 images was sorted by image quality and recognizability (Q&R) using manual inspection. A presorting network trained on the Q&R dataset was applied to all 8,400,000+ images to automatically collect a subset of 283,351 good snowflake images. Roughly 5,000 representative examples were then collected from this subset manually for each of the five geometric classes. With a higher emphasis on in-class variety than our previous work, the final dataset yields trained networks that better capture the imperfect cases and diverse forms that occur within the broad categories studied to achieve an accuracy of 96.2% on a vastly more challenging dataset.

The algebraic and geometric classification of nilpotent right alternative algebras

We present algebraic and geometric classifications of the $4$-dimensional complex nilpotent right alternative algebras. Specifically, we find that, up to isomorphism, there are only $9$ non-isomorphic nontrivial nilpotent right alternative algebras. The corresponding geometric variety has dimension $13$ and it is determined by the Zariski closure of $4$ rigid algebras and one one-parametric family of algebras.

Classification Systems in Rotator Cuff Tears

Rotator cuff pathology is one of the most common conditions affecting the shoulder joint. Several classification systems have been used to describe rotator cuff tears in orthopedic literature. However, no comprehensive classification inclusive of all types and characteristics currently exists. Rotator cuff tears are classified based on various parameters. These include: 1. Tear depth 2. Tear Size/Extent 3. Tear Retraction 4. Tendon Quality 5. Tear Progression 6. Arthroscopic Classification. This review article aims to establish an algorithm based on the various existing classification systems so as to arrive at the best surgical or non-surgical solution as well as prognosticate the patient regarding the outcome. Special consideration needs to be made for massive tears which are irreparable. Keywords: Rotator cuff tears; Rotator cuff tear classification; Massive irreparable rotator cuff tears; Partial rotator cuff tears; Subscapularis tears; Geometric Classification; Arthroscopic Classification; Rotator cuff retraction; Rotator cuff tendon quality; Prognosis for Rotator Cuff tears.

Natural History of Rotator Cuff Tears

Rotator cuff tears are a frequent phenomenon with an increasing incidence when the patient gets older. A considerable number of tears remain asymptomatic during a lifetime. However, still, a substantial number of asymptomatic tears become symptomatic. There is, at present evolving evidence that surgical treatment of small to medium-sized tears does better than conservative treatment, even after a long term follow-up. A treatment algorithm is suggested to help the clinician in decision making, where tear size and age are important factors in the prognosis of surgical treatment. Keywords: Rotator cuff; Ruptures; Natural historyf tears; Partial rotator cuff tears; Subscapularis tears; Geometric Classification; Arthroscopic Classification; Rotator cuff retraction; Rotator cuff tendon quality; Prognosis for Rotator Cuff tears.

Wavelet Transform and Fractal Theory for Detection and Classification of Self-extinguishing and Fugitive Power Quality Disturbances

In this paper, fractal theory and wavelet transform are combined to detect and classify self-extinguishing and fugitive scenarios of power quality disturbances (PQDs). After deciding whether the disturbance is simple or complex, the additional voltage is denoised through Discrete Wavelet Transform (DWT); the denoising process is adapted according to whether the distorted voltage contains oscillatory transients or not. At the detection stage, the grille fractal dimension of the DWT decomposition detail is computed. Then, a threshold is deduced to detect the start and end moments of the disturbance. The results reveal that the proposed detection scheme yields accurate location of PQDs even in the presence of high oscillatory transients. An algorithm based on geometric and statistical approaches is developed at the classification stage to recognize PQDs automatically. The geometric classification is based on Continuous Wavelet Transform (CWT), whereas the statistical classification is based on Multifractal Detrended Fluctuations Analysis (MFDFA) and an energy metric. The results prove that the combination of geometric and statistical classification can serve as an effective discrimination tool for PQDs. The major strength of the proposed approach is its ability to interpret the impact of each disturbance on the multifractal behavior of the nominal voltage, thus giving the possibility to draw the necessary generalizations for real-time applications.

Geometrical Classification of Folds in the Bozdağlar Massif (Konya, Central Anatolia)

Bu çalışmada Bozdağlar Masifi’ndeki (Konya Kuzeyi) deforme kayaçlarda gözlenen kıvrımların geometrik sınıflamaları ve oluşum mekanizması açısından birbirleriyle karşılaştırılması amaçlanmıştır. Altınekin, Meram-Dereköy ve Sarayönü bölgelerindeki Paleozoyik yaşlı metamorfik kayaçlarda gelişen toplamda yüze yakın kıvrım analiz edilerek eğim izogonları ve kanatlar arası açıya göre sınıflandırılmıştır. Dikey kalınlık grafikleri oluşturulan kıvrımlar için yassılma oranları hesaplanmıştır. Çalışma alanlarında yapılan geometrik sınıflamalarla, bölgede yassılmış paralel kıvrımların egemen olduğu ve kompetent tabakaların sınıf 1C, inkompetent tabakaların sınıf 2 ve sınıf 3 türü kıvrımlar oluşturacak şekilde kıvrımlandıkları görülmüştür. Altınekin bölgesindeki yassılmış sınıf 1C türü kıvrımlara ait yassılma oranları ( ) kompetent (dayanımlı) tabakalar için 0.4-0.8, inkompetent (dayanımsız) tabakalar için 0.3-0.8, Meram-Dereköy bölgesindeki yassılmış sınıf 1C türü kıvrımlara ait yassılma oranı ( ) kompetent tabakalar için 0.5-0.8, Sarayönü bölgesindeki yassılmış sınıf 1C türü kıvrımlara ait yassılma oranı ( ) kompetent tabakalar için 0.7-0.9 aralığındadır. Yapılan Fleuty sınıflamasına göre ise yassılma oranlarıyla uyumlu olarak kıvrımların her üç bölgede benzer şekilde açık, dar ve sıkışık kıvrımlar olarak geliştiği, sadece Meram-Dereköy bölgesinde açık kıvrım gelişmediği belirlenmiştir.

The algebraic and geometric classification of nilpotent left-symmetric algebras

This paper is devoted to the complete algebraic and geometric classification of complex 4-dimensional nilpotent left-symmetric algebras. The corresponding geometric variety has dimension 15 and decomposes into 3 irreducible components determined by the Zariski closures of two one-parameter families of algebras and a two-parameter family of algebras (see Theorem B). In particular, there are no rigid 4-dimensional complex nilpotent left symmetric algebras.

Repair Tension During Arthroscopic Rotator Cuff Repair is Correlated With Preoperative Tendon Retraction and Postoperative Rotator Cuff Integrity

This study aimed to examine the correlation of repair tension during arthroscopic rotator cuff repair (ARCR) with preoperative factors and to evaluate whether measuring tension during ARCR is effective for predicting rotator cuff integrity after ARCR. Patients who underwent ARCR from May 2014 to June 2017 were enrolled in this study. Inclusion criteria were patients with medium or larger-sized tears and with a minimum of 6 months' follow-up. Patients with a partial repair were excluded. Intraoperative repair tension was measured according to Davidson's method. Correlation of repair tension with preoperative factors was evaluated with Pearson and Spearman correlation coefficient tests. Logistic regression analysis was performed on intraoperative factors, including repair tension, to identify independent predictors of retear after ARCR. Receiver operating characteristic (ROC) curve was used to determine the cutoff value of repair tension for retear. One-hundred twenty patients met the inclusion criteria. Mean repair tension was 26.6±12.6 N, and retear was found in 29 shoulders (24.2%). Among the preoperative factors, tear size in the mediolateral (P < .001) and anteroposterior (P < .001) directions, DeOrio and Cofield's classification (P <0.001), geometric classification (P <.001), and fatty infiltration of supraspinatus (P= .006) and infraspinatus (P= .003) were significantly correlated with repair tension. However, multivariable logistic regression analysis identified only tear size in the mediolateral direction as an independent predictor of repair tension (P= .036). Logistic regression analysis showed that repair tension (P= .02) and geometric classification (P < .001) are significant factors affecting rotator cuff integrity after ARCR. ROC curve analysis showed the cutoff value of repair tension of large to massive tears for retear to be 35.6 N. This study demonstrated that intraoperative repair tension is strongly correlated with tear size in the mediolateral direction based on preoperative magnetic resonance imaging and that measuring tension during ARCR is effective for predicting rotator cuff integrity after ARCR. Level IV, prognostic study.

The normal stiffness of the edentulous alveolar process

The normal stiffness of the jawbone is seldom considered, as opposed to the mechanical properties of its individual cortical and trabecular components. Our standpoint is essentially structural, rather than purely material-oriented, as the jawbone is considered as a natural load-bearing structure. Throughout the work, 3 representative sections in the mandible and the maxilla are modelled and compared. Specifically, we evaluate the sections' elastic structural stiffness numerically, according to the recent geometrical classification proposed by Shemtov Yona (2021). Each case is modelled using two extreme configurations for the cortical-trabecular interaction, namely bonded and unbonded. Those two configurations reflect extreme interfacial conditions, though the bonded one is more physical. For the unbonded cases, the structural stiffness is the sum of the individual stiffnesses of the components. By sharp contrast, the bonded case results in a much larger stiffness than that obtained by the simple sum of the individual stiffnesses, indicating a strong synergistic stiffening effect between the components through their interface. We also investigate the role of the elastic moduli, whose reported values vary widely in the literature, emphasizing the role of the trabecular Poisson's coefficient, whose stiffening effect is evidenced when it exceeds about 0.3. The bone's structural stiffness shown here complements the geometrical classification of the jawbone types with a fundamental mechanical/structural property delineating the coupling between the mechanical properties and the geometry. The adopted approach is not limited to the jawbone and applies in principle to other bone types. From a clinical standpoint, the results presented here complement not only the basic mechanical aspects of the geometrical characterization, but also provide a starting point for future studies on dental implant placement and stability, the latter being directly related to the structural stiffness.

Measuring Bayesian Robustness Using Rényi Divergence

This paper deals with measuring the Bayesian robustness of classes of contaminated priors. Two different classes of priors in the neighborhood of the elicited prior are considered. The first one is the well-known ϵ-contaminated class, while the second one is the geometric mixing class. The proposed measure of robustness is based on computing the curvature of Rényi divergence between posterior distributions. Examples are used to illustrate the results by using simulated and real data sets.

3D Classification of Cold-Water Coral Reefs: A Comparison of Classification Techniques for 3D Reconstructions of Cold-Water Coral Reefs and Seabed

Cold-water coral (CWC) reefs are complex structural habitats that are considered biodiversity “hotspots” in deep-sea environments and are subject to several climate and anthropogenic threats. As three-dimensional structural habitats, there is a need for robust and accessible technologies to enable more accurate reef assessments. Photogrammetry derived from remotely operated vehicle video data is an effective and non-destructive method that creates high-resolution reconstructions of CWC habitats. Here, three classification workflows [Multiscale Geometrical Classification (MGC), Colour and Geometrical Classification (CGC) and Object-Based Image Classification(OBIA)] are presented and applied to photogrammetric reconstructions of CWC habitats in the Porcupine Bank Canyon, NE Atlantic. In total, six point clouds, orthomosaics, and digital elevation models, generated from structure-from-motion photogrammetry, are used to evaluate each classification workflow. Our results show that 3D Multiscale Geometrical Classification outperforms the Colour and Geometrical Classification method. However, each method has advantages for specific applications pertinent to the wider marine scientific community. Results suggest that advancing from commonly employed 2D image analysis techniques to 3D photogrammetric classification methods is advantageous and provides a more realistic representation of CWC habitat composition.

Geometric cycles and characteristic classes of manifold bundles

We produce new cohomology for non-uniform arithmetic lattices \Gamma &lt; \mathrm {SO}(p,q) using a technique of Millson–Raghunathan. From this, we obtain new characteristic classes of manifold bundles with fiber a closed 4k -dimensional manifold M with indefinite intersection form of signature (p,q) . These classes are defined on finite covers of B Diff (M) and are shown to be nontrivial for M=\#_g(S^{2k}\times S^{2k}) . In this case, the classes produced live in degree g and are independent from the algebra generated by the stable (i.e. MMM) classes. We also give an application to bundles with fiber a K3 surface.

Updating the Matrix Approach to Creating a Parametric Balance of Technological Process

Currently, the feed industry uses a large number of different types of feed mixers. The preparation of feed mixtures with different ingredients, with frequently changing compositions, must comply with such condition as uniformity. Basically, any prepared multicomponent mass should be distributed uniformly throughout the volume of each recipe element.The mixtures homogeneity can be achieved by using various equipment, which, unfortunately, is not always efficient and cost-effective. The selection of a technological line from equipment that provides a low-cost production cycle is a very time-consuming task, since the use of an experimental base of changing types of mixing machines implies unforeseen economic expenditures.Often when starting a certain production cycle of dry or wet mixtures, a preliminary forecast of the process effectiveness which can be achieved by creating a mathematical model of mixing is needed. All kinds of technological units designs, their geometric components classification, physico-mechanical and rheological indicators, operating-kinematic characteristics of the process can be used in the mathematical model.Having studied the mixing process we came to the conclusion that a high degree of mixing uniformity can be obtained with the same geometric particle sizes. But such a phenomenon is quite rare. Thus, an ideal mixture can be obtained by forcibly selecting process parameters.The effectiveness of this process can be based on a matrix approach. The process matrix will contain the dominant most significant indicators which have interconnections in the intermatrix space that create a certain parametric balance.It is advisable to divide the mathematical interpretation of the homogeneous feed mixtures creating process into several stages:- the first stage includes loading into the software model of the characteristics displaying the specific features of the process in question;- the second stage includes empirical patterns description;- the third stage creates an opportunity for searching for optimal tasks solutions.When studying the graphical dependences of the influence of process parameters on the output of quality energy indicators, the optimal solutions region is determined, each point of which allows to effectively carry out the mixing process in a screw-blade mixer.

Novel geometric classification of 3D seismic and its application to the Habshan clinoforms of Western Oman

The principles and benefits of seismic sequence stratigraphy have withstood the test of time, but the application of seismic sequence stratigraphy is still carried out mostly manually. Several tool kits have been developed to semiautomatically extract dense stacks of horizons from seismic data, but they stop short of exploiting the full potential of seismo-stratigraphic models. We introduce novel geometric seismic attributes that associate relative geologic age models with seismic geomorphological models. We propose that a relative sea level curve can be derived from the models. The approach is demonstrated on a case study from the Lower Cretaceous Kahmah Group in the northwestern part of Oman where it helps in sweet-spotting and derisking elusive stratigraphic traps.

Moves on k-graphs preserving Morita equivalence

AbstractWe initiate the program of extending to higher-rank graphs (k-graphs) the geometric classification of directed graph $C^*$ -algebras, as completed in Eilers et al. (2016, Preprint). To be precise, we identify four “moves,” or modifications, one can perform on a k-graph $\Lambda $ , which leave invariant the Morita equivalence class of its $C^*$ -algebra $C^*(\Lambda )$ . These moves—in-splitting, delay, sink deletion, and reduction—are inspired by the moves for directed graphs described by Sørensen (Ergodic Th. Dyn. Syst. 33(2013), 1199–1220) and Bates and Pask (Ergodic Th. Dyn. Syst. 24(2004), 367–382). Because of this, our perspective on k-graphs focuses on the underlying directed graph. We consequently include two new results, Theorem 2.3 and Lemma 2.9, about the relationship between a k-graph and its underlying directed graph.