Basis Elements Research Articles

An Adaptive Model Reduction Method Leveraging Locally Supported Basis Functions

We propose a new method, the continuous Galerkin method with globally and locally supported basis functions (CG-GL), to address the parametric robustness issues of reduced-order models (ROMs) by incorporating solution-based adaptivity with locally supported finite element basis functions. The CG-GL method combines the accuracy of locally supported basis functions with the efficiency of globally supported data-driven basis functions. Efficient output-based dual-weighted residual error estimates are derived and implemented for the CG-GL method and used to drive efficient online trial space adaptation. An empirical quadrature procedure is introduced for rapid evaluation of nonlinear terms that does not require retraining throughout the adaptation process. Two numerical experiments demonstrate the potential of the CG-GL method to produce accurate approximations with limited training and its tunable trade-off between accuracy and computational cost.

OPTIMIZATION AND EVALUATION THE EFFECTIVENESS OF IMMEDIATE PROSTHETIC APPROACHES FOR PATIENTS AFTER TEETH EXTRACTION AND MAXILLOFACIAL SURGERY

Surgical interventions in the dentoalveolar system and maxillofacial area inevitably lead to the formation of long-term healing postoperative wounds or acquired jaw defects. An accessible method of choice for early rehabilitation is considered to be direct removable dentures, however, traditional approaches to this type of treatment can lead to postoperative inflammatory complications. At the Department of Orthopedic Dentistry and Orthodontics of Ryazan State Medical University carried out orthopedic treatment in 120 patients aged from 21 to 89 years after teeth extraction and surgical interventions in the maxillofacial area during the period from 2021 to 2023. The proposed approach to treatment was to manufacture structures of immediate dentures depending on the type of oral mucosa of the prosthetic bed using additive manufacturing technologies and the creation of elastic elements of dentures bases with dynamic control of inflammatory postoperative complications using an improved Schiller-Pisarev test. The effectiveness of the proposed approach was compared with the traditional immediate dentures. According to the results of the study, it was found that the proposed protocol for treatment and diagnosis made it possible to achieve a reduction in the area of wound healing by 50% and a decrease in the area of inflammation by 78% faster compared to the traditional method. Normalization of the microcirculatory activity of the wound healing zones was achieved in the period from 10 to 20 days of observation, with the traditional method, insufficient microcirculatory activity was noted by the 30th day of observation.

Italian World War I Veterans as an Element of the Social Basis of a Totalitarian State

Italian World War I Veterans as an Element of the Social Basis of a Totalitarian State

Multistage fluorite mineralization in the southern Black Forest, Germany: evidence from rare earth element (REE) geochemistry

Abstract. The Black Forest hosts a wide range of hydrothermal mineralization, including fluorite–barite vein deposits. In a detailed investigation of the Finstergrund and Tannenboden deposits in the Wieden mining district (southern Black Forest), the diversity, geochemical evolution and relative chronology of multistage fluorite precipitation is tracked on the basis of rare earth element (REE) geochemistry, geologic field relationships and crystal zoning. Geochemical discrimination and mathematical λ coefficients suggest a total of seven fluorite REE groups, at least three distinguishable post-Variscan fluid mobilization events and independent formation histories for the deposits despite their spatial proximity. Fluorite vein mineralization at the Finstergrund deposit evolved over three fluid generations, was derived from gneissic source aquifers and comprises five distinct fluorite REE groups: the first fluid generation is characterized by fluorite precipitation above 200 ∘C (“group III”), below 200 ∘C (“group I”) and after fractional crystallization (“group IV”); the second generation comprises remobilized fluorite (“group II”); and the third generation revealed fluorite precipitation by meteoric water mixing (“group V”). Fluorite vein formation at the Tannenboden deposit is associated with two distinct fluorite REE patterns derived from the same fluid generation: fluorite precipitation above 200 ∘C (“group VII”) and after cooling below 200 ∘C (“group VI”). Its fluid source aquifer lithology best matches migmatites contrary to previous models that suggest either gneissic or granitic aquifer rocks for fluorite vein precipitation in the Black Forest. The decoupled formation history between the deposits is tectonically controlled as suggested by a new genetic model for the Wieden mining district. The model argues for a change in the local fluid percolation network and the termination of hydrothermal activity at the Tannenboden deposit after the first fluid mobilization event. The geochemical evolution of multistage fluorite mineralization, as exemplified by the Tannenboden and Finstergrund deposits in combination with other fluorite mineralizations in the Black Forest, provides unique insights into the lithospheric origin and precipitation behaviour of fluorite by various fluid–rock interaction processes occurring in large hydrothermal systems. The local diversity of REE patterns emphasizes the need for detailed investigations of individual hydrothermal vein deposits.

Julie Andrews: from the myth of the androgyne to gender fluidity

ABSTRACT Julie Andrews’s character in The Sound of Music (Robert Wise 1965) is in many ways the embodiment of an androgynous ideal that can be found in the mythical origins of numerous traditions. This is evident in the actress’s childish and clumsy body movements, in her ambiguous anatomy, and in the dialogue she maintains with the Alpine landscape, which she engages with repeatedly in the film as if it were a kind of primordial environment for her. This article explores the evolution of the idea of androgyny over the course of Andrews’s career, culminating nearly twenty years after the release of The Sound of Music with Victor/Victoria (Blake Edwards 1982), a film that foreshadows the contemporary notion of gender fluidity. Adopting a methodological discourse related to star studies and drawing on concepts from feminism and queer theory, this article dives into Andrews’s filmography in an effort to clarify this narrative line and its development on the basis of key elements of her performance, such as the use of her body, gestures and the gaze.

On a wider class of prior distributions for graphical models

AbstractGaussian graphical models are useful tools for conditional independence structure inference of multivariate random variables. Unfortunately, Bayesian inference of latent graph structures is challenging due to exponential growth of $\mathcal{G}_n$ , the set of all graphs in n vertices. One approach that has been proposed to tackle this problem is to limit search to subsets of $\mathcal{G}_n$ . In this paper we study subsets that are vector subspaces with the cycle space $\mathcal{C}_n$ as the main example. We propose a novel prior on $\mathcal{C}_n$ based on linear combinations of cycle basis elements and present its theoretical properties. Using this prior, we implement a Markov chain Monte Carlo algorithm, and show that (i) posterior edge inclusion estimates computed with our technique are comparable to estimates from the standard technique despite searching a smaller graph space, and (ii) the vector space perspective enables straightforward implementation of MCMC algorithms.

Basis-Finding Algorithm for Decoding Fountain Codes for DNA-Based Data Storage

In this paper, we consider the decoding of fountain codes where the received symbols may have errors. It is motivated by the application of fountain codes in DNA-based data storage systems where the inner code decoding, which generally has undetectable errors, is performed before the outer fountain code decoding. We propose a novel and efficient decoding algorithm, namely basis-finding algorithm (BFA), followed by three implementations. The key idea of the BFA is to find a basis of the received symbols, and then use the most reliable basis elements to recover the source symbols with the inactivation decoding. Gaussian elimination is used to find the basis and to identify the most reliable basis elements. As a result, the BFA has polynomial time complexity. For random fountain codes, we are able to derive some theoretical bounds for the frame error rate (FER) of the BFA. Extensive simulations with Luby transform (LT) codes show that, the BFA has significantly lower FER than the belief propagation (BP) algorithm except for an extremely large amount of received symbols, and the FER of the BFA generally decreases as the average weight of basis elements increases.

ИНЖЕКЦИОННО-ПОЛЕВАЯ СТРУКТУРА, ВЫПОЛНЕННАЯ ДВОЙНОЙ ДИФФУЗИЕЙ ПРИМЕСЕЙ

In the 80s of the last century, integrated injection logic (I2L) was widely used as an elementbase. Somewhat later, in the development of I2L, injection-field logic (IPL) appeared for the constructionof VLSI. Both element bases are close in the degree of integration on a chip. An increase inthe degree of integration into VLSI can be achieved using self-displacement of regions, in which theintroduction of impurities of different types is carried out using a single boundary of the maskingmaterial. In this paper, this principle is used to create a vertical channel of a key field-effect transistorof IPL logic. In a p-type epitaxial film deposited on an n+-type substrate, an n-type region with adepth greater than the thickness of the epitaxial film is sequentially created first, and then impuritydiffusion is performed in the same window with the creation of a region p-type. The gap betweenthese n-type regions is the channel of the field-effect transistor being formed. Next, a shallow n+-typeregion is created that overlaps the channel, which is the drain region of a key field-effect transistorwith a vertical channel, the p-type diffusion region is a gate, and the uniformly alloyed region of theepitaxial film performs the function of an injector. Branching along the outlet in this IPL structure isprovided by placing several drains along the perimeter of the channel. Due to this geometry, thestructure has a greater reproducibility of parameters compared to the basic design of the IPL. Topologicalvariants of the implementation of the IPL cell and schemes based on it are considered:schemes 6 OR-NOT and Dt-trigger. The proposed design and technological version of the IPL cellcan be recommended for creating VLSI of a high degree of integration

On quantum complexity

The ETH ansatz for matrix elements of a given operator in the energy eigenstate basis results in a notion of thermalization for a chaotic system. In this context for a certain quantity - to be found for a given model - one may impose a particular condition on its matrix elements in the energy eigenstate basis so that the corresponding quantity exhibits linear growth at late times. The condition is to do with a possible pole structure the corresponding matrix elements may have. Based on the general expectation of complexity one may want to think of this quantity as a possible candidate for the quantum complexity. We note, however, that for the explicit examples we have considered in this paper, there are infinitely many quantities exhibiting similar behavior.

Automation Strategies for the Photogrammetric Reconstruction of Pipelines

A responsible use of energy resources is currently more important than ever. For the effective insulation of industrial plants, a three-camera measurement system was, therefore, developed. With this system, the as-built geometry of pipelines can be captured, which is the basis for the production of a precisely fitting and effective insulation. In addition, the digital twin can also be used for Building Information Modelling, e.g. for planning purposes or maintenance work. In contrast to the classical approach of processing the images by calculating a point cloud, the reconstruction is performed directly on the basis of the object edges in the image. For the optimisation of the, initially purely geometrically calculated components, an adjustment approach is used. In addition to the image information, this approach takes into account standardised parameters (such as the diameter) as well as the positional relationships between the components and thus eliminates discontinuities at the transitions. Furthermore, different automation approaches were developed to facilitate the evaluation of the images and the manual object recognition in the images for the user. For straight pipes, the selection of the object edges in one image is sufficient in most cases to calculate the 3D cylinder. Based on the normalised diameter, the missing depth can be derived approximately. Elbows can be localised on the basis of coplanar neighbouring elements. The other elbow parameters can be determined by matching the back projection with the image edges. The same applies to flanges. For merging multiple viewpoints, a transformation approach is used which works with homologous components instead of control points and minimises the orthogonal distances between the component axes in the datasets.

An efficient numerical method on modified space-time sparse grid for time-fractional diffusion equation with nonsmooth data.

In this paper, we focus on developing a high efficient algorithm for solving d-dimension time-fractional diffusion equation (TFDE). For TFDE, the initial function or source term is usually not smooth, which can lead to the low regularity of exact solution. And such low regularity has a marked impact on the convergence rate of numerical method. In order to improve the convergence rate of the algorithm, we introduce the space-time sparse grid (STSG) method to solve TFDE. In our study, we employ the sine basis and the linear element basis for spatial discretization and temporal discretization, respectively. The sine basis can be divided into several levels, and the linear element basis can lead to the hierarchical basis. Then, the STSG can be constructed through a special tensor product of the spatial multilevel basis and the temporal hierarchical basis. Under certain conditions, the function approximation on standard STSG can achieve the accuracy order with degrees of freedom (DOF) for and DOF for , where J denotes the maximal level of sine coefficients. However, if the solution changes very rapidly at the initial moment, the standard STSG method may reduce accuracy or even fail to converge. To overcome this, we integrate the full grid into the STSG, and obtain the modified STSG. Finally, we obtain the fully discrete scheme of STSG method for solving TFDE. The great advantage of the modified STSG method can be shown in the comparative numerical experiment.

DEEPENING THE PRINCIPLES OF MEDIA EDUCATION BASED ON THE GENERAL SYSTEMS THEORY

The purpose of the article is to generalize and deepen the principles of media education (as a system-building basis for creating the theory and practice of media education) based on Yu. A. Urmantsev’s general systems theory. To achieve the goal, the following methodological tools are used: the philosophical principle of the unity of the world as the methodological basis of the research; the method of theoretical analysis of the problem field of the research; the general systems theory, which made it possible to generalize and deepen some principles of media education.
 In the article, the principles of the Concept of implementing media education in Ukraine were generalized and somewhat deepened, that is, they received a systemic meaning being based on certain meaningful elements of the general systems theory. This made it possible to carry out a systematic correlation of the principles of media education and some pedagogical phenomena on the basis of meaningful elements of the general systems theory.
 It is shown that the principles of media education, the elements of the model of a school as a social institution, and the elements of the model of a man as a subject of psychology are in system-correlation relations, which realizes the philosophical principle of the unity of the world and testifies to the fact that the procedure of systematic generalization of the principles of media education is adequate to the theoretical and methodological principles both the general systems theory, and the pedagogical teaching about the school as a social institution and about media education as its essential aspect.
 The table developed by the author "Systemic correlation of the principles of media education and some pedagogical phenomena being based on the meaningful elements of the general theory of systems" allows to deepen the formulation of such principle of media education as "aesthetic elevation in the context of media education".
 The task of systematic analysis and deepening each of the seven systemically presented principles of media education belongs to the promising areas of development of the principles of media education.

Analytic Semiroots for Plane Branches and Singular Foliations

The analytic moduli of equisingular plane branches has the semimodule of differential values as the most relevant system of discrete invariants. Focusing in the case of cusps, the minimal system of generators of this semimodule is reached by the differential values attached to the differential 1-forms of the so-called standard bases. We can complete a standard basis to an extended one by adding a last differential 1-form that has the considered cusp as invariant branch and the “correct” divisorial order. The elements of such extended standard bases have the “cuspidal” divisor as a “totally dicritical divisor” and hence they define packages of plane branches that are equisingular to the initial one. These are the analytic semiroots. In this paper we prove that the extended standard bases are well structured from this geometrical and foliated viewpoint, in the sense that the semimodules of differential values of the branches in the dicritical packages are described just by a truncation of the list of generators of the initial semimodule at the corresponding differential value. In particular they have all the same semimodule of differential values.

Learning Block Structured Graphs in Gaussian Graphical Models

A prior distribution for the underlying graph is introduced in the framework of Gaussian graphical models. Such a prior distribution induces a block structure in the graph’s adjacency matrix, allowing learning relationships between fixed groups of variables. A novel sampling strategy named Double Reversible Jumps Markov chain Monte Carlo is developed for learning block structured graphs under the conjugate G-Wishart prior. The algorithm proposes moves that add or remove not just a single edge of the graph but an entire group of edges. The method is then applied to smooth functional data. The classical smoothing procedure is improved by placing a graphical model on the basis expansion coefficients, providing an estimate of their conditional dependence structure. Since the elements of a B-Spline basis have compact support, the conditional dependence structure is reflected on well-defined portions of the domain. A known partition of the functional domain is exploited to investigate relationships among portions of the domain and improve the interpretability of the results. Supplementary materials for this article are available online.

Numerical modeling investigation of cross-laminated timber connections consisting of multiple glued-in rods

Glued-in rods are stiff and high-capacity connections that are used in timber structures. Regardless of the many advantages of glued-in rods, research on the glued-in rods in CLT is limited, especially on numerical modeling. This paper provides the numerical modeling principles, validation details, and parametric studies of glued-in rods embedded on the edge of CLT. The numerical modeling was performed on a 3D finite element basis, and the cohesive surface method was used to define the bond lines along the rods. To validate the numerical models, 24 replica experiments were performed and investigated the effect of the rod diameter and of the embedment length on the pull-out strength of rods embedded perpendicular, parallel, and on the boundary of two cross-wised layers. The numerical models were validated according to the maximum load, stiffness, as well as the failure mode of the glued-in rods. The numerical models showed high reliability in simulating the experiments and predicted the strength of the glued-in rods with a maximum of 4% difference. After validation of the numerical models, the parametric study covered the pull-out strength investigation of rods with 20, 24, and 30 mm diameter and anchorage lengths of 250, 350, and 450 mm embedded in the perpendicular, parallel, and on the boundary of cross-wised layers on the edge of 5 and 7 layer CLT panels. The findings showed that increasing the embedment length and rod diameter enhanced the pull-out strength of the glued-in rods, regardless of where the rod was positioned on the CLT's edge. Rods embedded perpendicular to the grain showed the highest pull-out strength, and two rods with 30 mm diameter and 450 mm embedment lengths reached 961 kN pull-out strength. Numerical models showed that for the same diameter and embedment length of two rods embedded on the parallel and on the boundary of two cross-wised layers reached 836 and 738 kN pull-out strength, respectively. Finally, A design equation is provided to determine the pull-out strength of the glued-in rods embedded in CLT based on the shear strength of the bondline.

Application of Hi-C technology in three-dimensional genomics research and disease pathogenesis analysis.

3D genomics aims to investigate the spatial structure of chromatin in the nucleus on the basis of genomic sequences, gene structures and relevant regulatory elements. The spatial organization of chromosomes is fundamental for gene expression regulation. Recent advances of high-throughput chromosome conformation capture (Hi-C) technology and its derivatives, has enabled capture of chromatin architecture with high resolution. In this review, we summarize the development and applications of various technologies of 3D genomes in disease research, particularly in the elucidation of pathogenic mechanisms in cancers and other systemic disorders.

Determining the Most Appropriate Material Substitution by Upcycling and Recycling Methods for The Management of Waste Printed Circuit Boards

In this study, the material substitutions that would be achieved by upcycling and recycling methods that can be applied to waste printed circuit boards were compared through the sequential application of Streamlined Life Cycle Assessment (S-LCA) and Multi-Criteria Decision-Making (MCDM) techniques. Substitutions by upcycling methods were determined as gold mine, bronze mine, lead mine, activated carbon, and copper mine. And, portland cement, aggregate, sawdust, fiberglass and styrene butadiene rubber were determined as the substituted materials that can be obtained by recycling methods. At the S-LCA stage, CML-IA baseline and ReCiPe 2016 methods were used for the characterization. For the MCDM study, environmental, technical, and economic criteria were determined. Remarkable characterization results of S-LCA were used as the environmental criteria of MCDM. The Entropy method was used for the weighting of the criteria. TOPSIS method was used to compare the alternatives on the basis of weighted criteria. LCA study shows that impact categories of Abiotic Depletion Potential (element basis), Total Ecotoxicity Potential, and Human Toxicity Potential are the major impact categories. MCDM study shows that gold (0.9845) and styrene butadiene rubber (SBR) (0.7361) are the most appropriate substitutions that can be obtained by upcycling and recycling methods, respectively.

Non-Parametric Regression and Riesz Estimators

In this paper, we consider a non-parametric regression model relying on Riesz estimators. This linear regression model is similar to the usual linear regression model since they both rely on projection operators. We indicate that Riesz estimator regression relies on the positive basis elements of the finite-dimensional sub-lattice generated by the rows of some design matrix. A strong motivation for using the Riesz estimator model is that the data of explanatory variables may come from categorical variables. Calculations related to Riesz estimator regression are very easy since they arise from the measurability in finite-dimensional probability spaces. Moreover, we show that the fitted model of Riesz estimators is an ordinary least squares model. Any vector of some Euclidean space is supposed to be a rendom variable under the objective probability values, being used in expected utility theory and its applications. Finally, the reader may notice that goodness-of-fit measures are similar to those defined for the usual linear regression. Due to the fact that this model is non-parametric, it may include samples relevant to finance and actuarial science variables.

Efficiency Analysis of Concurrent Error-Detection Circuits on the Basis of Assessment by Belonging of Calculated Functions to Self-Dual Class and Preliminary Compression of Signals Using Linear Codes

A method is described for checking of calculations on whether functions belong to the class of self-dual with using well-known linear codes for preliminary compression of signals from the outputs of combinational devices in order to reduce the number of controlled signals. A generalized structure for organizing the checking of calculations with signal compression using arbitrary separable codes is proposed, which complements the well-known structures of self-dual check of parity calculations («self-dual parity») and self-dual check with duplication of each function («self-dual duplication))). In the concurrent error-detection circuit according to the presented method, all devices, except for the self-dual complement block, are standardized (typical). Therefore, to synthesize the concurrent error-detection circuit, it is necessary to obtain only the structure of this block in the selected elemental basis. The article presents a technique for synthesizing a block of self-dual complement when organizing the checking of calculations using arbitrary separable codes. Examples of the implementation of devices with concurrent error-detection circuits based on well-known linear codes — parity codes, Hamming codes and their modifications are given. Some results of mod­eling devices with concurrent error-detection circuits are given, noting the advantages and disadvantages of using each of the codes considered. The results obtained in the study can be applied in the development of self-checking computing devices and systems.

Resolvability in Subdivision Graph of Circulant Graphs

Circulant networks are a very important and widely studied class of graphs due to their interesting and diverse applications in networking, facility location problems, and their symmetric properties. The structure of the graph ensures that it is symmetric about any line that cuts the graph into two equal parts. Due to this symmetric behavior, the resolvability of these graph becomes interning. Subdividing an edge means inserting a new vertex on the edge that divides it into two edges. The subdivision graph G is a graph formed by a series of edge subdivisions. In a graph, a resolving set is a set that uniquely identifies each vertex of the graph by its distance from the other vertices. A metric basis is a resolving set of minimum cardinality, and the number of elements in the metric basis is referred to as the metric dimension. This paper determines the minimum resolving set for the graphs Hl[1,k] constructed from the circulant graph Cl[1,k] by subdividing its edges. We also proved that, for k=2,3, this graph class has a constant metric dimension.