Relative Version Research Articles

Cloaking Rayleigh waves via symmetrized elastic tensors

In this work we propose a strategy based on coordinate transformation to cloak Rayleigh waves. Rayleigh waves are in-plane elastic waves which propagate along the free surface of semi-infinite media. They are governed by Navier equations that retain their form for an in-plane arbitrary coordinate transformation x=Ξ(X), upon choosing the specific kinematic relation U(Ξ(X))=u(x) between displacement fields in virtual, i.e. reference, (U) and transformed, i.e. cloaked, (u) domains. However, the elasticity tensor of the transformed domain is no longer fully symmetric, and thus, it is difficult to design with common materials. Motivated by this issue, we propose a symmetrization technique, based on the arithmetic mean, to obtain anisotropic, yet symmetric, elastic tensors for Rayleigh wave near-cloaking. In particular, by means of time-harmonic numerical simulations and dispersion analyses, we compare the efficiency of triangular and semi-circular cloaks designed with the original non-symmetric tensors and the related symmetrized versions. In addition, different coordinate transformations, e.g. linear, quadratic and cubic, are adopted for the semi-circular cloaks. Through the analyses, we show that a symmetrized semi-circular cloak, obtained upon the use of a quadratic transformation, performs better than the other investigated designs. Our study provides a step towards the design of feasible and efficient broadband elastic metamaterial cloaks for surface waves.

A relative version of the Turaev–Viro invariants and the volume of hyperbolic polyhedral 3‐manifolds

AbstractWe define a relative version of the Turaev–Viro invariants for an ideally triangulated compact 3‐manifold with nonempty boundary and a coloring on the edges, generalizing the Turaev–Viro invariants [36] of the manifold. We also propose the volume conjecture for these invariants whose asymptotic behavior is related to the volume of the manifold in the hyperbolic polyhedral metric [22, 23] with singular locus of the edges and cone angles determined by the coloring, and prove the conjecture in the case that the cone angles are sufficiently small. This suggests an approach of solving the volume conjecture for the Turaev–Viro invariants proposed by Chen–Yang [8] for hyperbolic 3‐manifolds with totally geodesic boundary.

Causes, Effects, and Mitigation Measures of Time and Cost Overruns in Water Supply Projects: Case of Tigrai Region, Northern Ethiopia

Project cost overrun and schedule delay are major and widespread problems in the construction industry. In Tigrai, most water supply construction projects are not completed within the predetermined contract time and planned budget. Hence, this research was carried out to investigate the causes and effects of time and cost overrun in water supply projects in Tigrai, northern Ethiopia and further recommend effective mitigation measures. A total of 87 questionnaires were distributed, 50 of them were collected, and desk study of 12 water supply projects were conducted. Data were analyzed using relative importance index and statistical software SPSS version 20. Results showed that the most important causes of time overrun were design errors and changes, lack of consistency between bill of quantities and drawings, and change order. Similarly, the most important causes of cost overrun were design errors and changes, lack of consistency between bill of quantities and drawings, and shortage of construction materials and electromechanical equipment in local market. The most effective mitigation measure of the overruns was complete and proper design. Time and cost overrun of the projects ranged between 0 and 203% and between 0 and 25%, respectively. The regression model showed that time overrun was estimated well (r2 = 0.95) using delays caused by design errors and changes and material import. Similarly, cost overrun was estimated well (r2 = 0.98) using factors that affect cost. Overall, the major cause for the overruns was design problem, hence clients and consultants should give due attention for the design process.

Relative homology of invariant group chains

Let Q be a finite group acting by automorphisms on a discrete group G. K. Knudson has introduced the homology of invariant group chains H⁎Q(G,A). A useful tool in homology is its relative version. In this paper we introduce the homology of Q-permutation representations as a generalization of the homology of permutation representations defined by Snapper. We prove the existence of a spectral sequence which converges to the homology of a Q-permutation representation. We also introduce a relative version of the homology of invariant group chains using the notion of Q-permutation representations following Adamson and give a topological interpretation of that relative homology.

Predicting Mechanical Complications After Adult Spinal Deformity Operation Using a Machine Learning Based on Modified Global Alignment and Proportion Scoring With Body Mass Index and Bone Mineral Density.

This study aimed to create an ideal machine learning model to predict mechanical complications in adult spinal deformity (ASD) surgery based on GAPB (modified global alignment and proportion scoring with body mass index and bone mineral density) factors. Between January 2009 and December 2018, 238 consecutive patients with ASD, who received at least 4-level fusions and were followed-up for ≥ 2 years, were included in the study. The data were stratified into training (n = 167, 70%) and test (n = 71, 30%) sets and input to machine learning algorithms, including logistic regression, random forest gradient boosting system, and deep neural network. Body mass index, bone mineral density, the relative pelvic version score, the relative lumbar lordosis score, and the relative sagittal alignment score of the global alignment and proportion score were significantly different in the training and test sets (p < 0.05) between the complication and no complication groups. In the training set, the area under receiver operating characteristics (AUROCs) for logistic regression, gradient boosting, random forest, and deep neural network were 0.871 (0.817-0.925), 0.942 (0.911-0.974), 1.000 (1.000-1.000), and 0.947 (0.915-0.980), respectively, and the accuracies were 0.784 (0.722-0.847), 0.868 (0.817-0.920), 1.000 (1.000-1.000), and 0.856 (0.803-0.909), respectively. In the test set, the AUROCs were 0.785 (0.678-0.893), 0.808 (0.702-0.914), 0.810 (0.710-0.910), and 0.730 (0.610-0.850), respectively, and the accuracies were 0.732 (0.629-0.835), 0.718 (0.614-0.823), 0.732 (0.629-0.835), and 0.620 (0.507-0.733), respectively. The random forest achieved the best predictive performance on the training and test dataset. This study created a comprehensive model to predict mechanical complications after ASD surgery. The best prediction accuracy was 73.2% for predicting mechanical complications after ASD surgery.

Patient-Centered Outcomes Following Prone Lateral Single-Position Approach to Same-Day Circumferential Spine Surgery.

Retrospective study. Evaluate surgical characteristics and postoperative 2-year results of the PL approach to spinal fusion. Prone-lateral(PL) single positioning has recently gained popularity in spine surgery due to lower blood loss and operative time but has yet to be examined for other notable outcomes, including realignment and patient-reported measures. We included circumferential spine fusion patients with a minimum one-year follow-up. Patients were stratified into groups based on undergoing PL approach versus same-day staged (Staged). Mean comparison tests identified differences in baseline parameters. Multivariable logistic regression, controlling for age, levels fused, and Charlson Comorbidity Index were used to determine the influence of the approach on complication rates, radiographic and patient-reported outcomes up to two years. One hundred twenty-two patients were included of which 72(59%) were same-day staged and 50(41%) were PL. PL patients were older with lower body mass index (both P <0.05). Patients undergoing PL procedures had lower estimated blood loss and operative time (both P <0.001), along with fewer osteotomies (63% vs. 91%, P <0.001). This translated to a shorter length of stay (3.8d vs. 4.9, P =0.041). PL procedures demonstrated better correction in both PT (4.0 vs. -0.2, P =0.033 and pelvic incidence and lumbar lordosis (-3.7 vs. 3.1, P =0.012). PL procedures were more likely to improve in GAP relative pelvic version (OR: 2.3, [1.5-8.8]; P =0.003]. PL patients suffered lesser complications during the perioperative period and greater improvement in NRS-Back (-6.0 vs. -3.3, P =0.031), with less reoperations (0.0% vs. 4.8%, P =0.040) by two years. Patients undergoing PL single-position procedures received less invasive procedures with better correction of pelvic compensation, as well as earlier discharge. The prone lateral cohort also demonstrated greater clinical improvement and a lower rate of reoperations by two years following spinal corrective surgery. Level-III.

Subgroups of continuous full groups and relative continuous orbit equivalences of one-sided topological Markov shifts

Let A be an irreducible non-permutation matrix with entries in {0,1}. We study a family ΓA,f of subgroups of the continuous full group ΓA of the one-sided topological Markov shift (XA,σA). The subgroup ΓA,f is indexed by an integer valued continuous function f on XA such that ΓA,0=ΓA the non-amenable continuous full group and ΓA,1=ΓAAF the amenable AF full group. We will first prove that a spatial realization theorem for the subgroups ΓA,f under certain conditions on the functions f. We will second introduce relative versions of continuous orbit equivalence to study classification of the subgroups ΓA,f related to their associated groupoids and C⁎-algebras.

Exponential fields and Conway’s omega-map

Inspired by Conway’s surreal numbers, we study real closed fields whose value group is isomorphic to the additive reduct of the field. We call such fields omega-fields and we prove that any omega-field of bounded Hahn series with real coefficients admits an exponential function making it into a model of the theory of the real exponential field. We also consider relative versions with more general coefficient fields.

Supersessionist Time and the Turn of Synagoga in the Northern Homily Cycle and Rawlinson Versions of the Theophilus Legend

This article explores three understudied Middle English versions of the popular anti-Judaic Marian miracle tale of Theophilus. I demonstrate how these versions of Theophilus draw upon widely known medieval imagery of Ecclesia and Synagoga to depict Theophilus's journey as one of soteriological regression. A comparative analysis of the two related Northern Homily Cycle versions of Theophilus demonstrates how Synagoga is evoked in the portrayal of Theophilus's despair, which is shown to be a supersessionist issue in his misunderstanding of the Holy Spirit and Trinitarian theology. These two versions then depict Theophilus engaging with Davidic lineage in relation to Marian power, the manner of which unsettles the Christian supersessionist project of the texts and, I argue, earns him physical retribution. I show how these insecurities are resolved in the later Rawlinson version of Theophilus with an invocation of Synagoga in her "return" to Christianity, taken from eschatological readings of Song of Songs 6:13.

Use of the Global Alignment and Proportion score to predict postoperative health-related quality of life in adult spinal deformity surgery.

The purpose of this study was to validate the Global Alignment and Proportion (GAP) score as a predictor of health-related quality of life (HRQOL) outcomes for patients undergoing adult spinal deformity (ASD) surgery. This was a retrospective cohort study of patients with ASD undergoing long-segment spine fusions (≥ 5 vertebrae fused) at a single institution over a 2-year period (n = 85). Radiographic parameters were measured at preoperative, 6-week postoperative, 1-year postoperative, and 2-year postoperative visits. GAP scores were calculated using 4 sagittal parameters: relative pelvic version, relative lumbar lordosis, lordosis distribution index, and relative spinopelvic alignment. Patients were stratified into 3 GAP categories at each time point: proportioned (score 0-2), moderately disproportioned (score 3-6), and severely disproportioned (score ≥ 7). HRQOL outcomes were collected at preoperative, 1-year postoperative, and 2-year postoperative visits; these measures included patient self-reported outcome measures (i.e., PROMIS), Scoliosis Research Society-22 spinal deformity questionnaire (SRS-22), and Oswestry Disability Index (ODI) scores. Overall, 42% of cases were revision surgeries and 96.5% of patients underwent fusion to the sacrum. The mean preoperative GAP score significantly improved from preoperative (7.84) to immediate postoperative (3.31) assessment (p < 0.001). Similarly, the percentage of patients categorized as proportioned improved from 9.4% at preoperative to 45.9% at immediate postoperative evaluation. The preoperative GAP score or category was not significantly associated with any preoperative HRQOL outcome metrics. The immediate postoperative GAP score was not correlated with any 1-year HRQOL outcomes. However, the immediate postoperative GAP score was significantly associated with 2-year SRS-22 outcomes, including SRS-22 function (r = -0.35, p < 0.01), self-image (r = -0.27, p = 0.044), and subtotal (r = -0.35, p < 0.01) scores. As compared to severely disproportioned patients, proportioned patients had better SRS-22 pain (4.08 vs 3.17, p = 0.04), satisfaction (4.40 vs 3.50, p = 0.02), and subtotal (4.01 vs 3.27, p = 0.036) scores. The immediate postoperative GAP score was also significantly associated with 2-year PROMIS outcomes, including PROMIS pain (r = 0.31, p = 0.023) and physical function (r = -0.35, p < 0.01) scores. As compared to severely disproportioned patients, proportioned patients had better PROMIS pain (53.18 vs 63.60, p = 0.025) and physical function (41.66 vs 34.18, p = 0.017) scores. Postoperative GAP score or category did not predict any ODI outcomes. The postoperative GAP score is a predictor of long-term HRQOL outcomes following ASD surgery, and proportioned patients are more likely to have less pain and be satisfied with their surgery. However, the postoperative GAP score does not predict outcomes as measured by ODI.

Mathematical analysis of generative adversarial networks based on complex picture fuzzy soft information

Generative Adversarial Networks (GANs) are the models that generate data samples from the statistical distribution of the data. It is one of the most well-known branches of machine learning and deep learning. Different techniques are involved in the processing and production of visual data, which sometimes gives rise to misperception uncertainties. Bearing this issue in mind, we define some solid mathematical concepts to model and resolve the stated problem named complex picture fuzzy soft relations (CPFSRs) which is defined by the Cartesian product (CP) of two complex picture fuzzy soft sets (CPFSSs). The major objective of this study is to develop some innovative and useful notions that may be used to handle difficult and inconsistent information in practical situations. The proposed notion is foremost and superior to the prevailing ideas, where the presented idea is the improved technique of two different theories, named picture fuzzy set (PFS) and soft set (SS). Additionally, it presents the picture fuzzy soft set (PFSS) in professional decision-making by reducing complexions. The evaluated CPFSRs are the improved versions of soft relations, fuzzy relations, complex soft relations, and complex fuzzy relations. Therefore, this paper provides modeling methodologies based on CPFSRs which are used for the analysis of electing the best GAN for effective working. In the process, the score functions are also formulated and analyzed. Finally, a comparative study of existing techniques has been done to show the validity of the proposed work.

Real Semi-Stable Degenerations, Real-Oriented Blow-Ups, and Straightening Corners

Abstract We study totally real semi-stable degenerations (and more generally, smooth semi-stable degenerations). Our goal is to describe the homeomorphism type of the real locus ${\textbf R} X_t$ of the general fibre in terms of the special fibre. We give a general homeomorphism statement via the real-oriented blow-up of the family. Using this, we give more explicit descriptions of ${\textbf R} X_t$ as a stratified space glued from (covers of) strata of the special fibre. We also give relative versions of the statements and consider the example of toric degenerations in order to link the technique to tropicalisation.

Morse theory of Bestvina–Brady type for posets and matchings

We introduce a Morse theory for posets of Bestvina–Brady type combining matchings and height functions. This theory generalizes Forman's discrete Morse theory for regular CW-complexes and extends previous results on Morse theory for $h$-regular posets to all finite posets. We also develop a relative version of Morse theory which allows us to compare the topology of a poset with that of a given subposet.

Amgen launches Humira competitor

After years of legal jousting by the companies involved, the first drug has launched to challenge AbbVie’s Humira as a biological treatment for inflammatory disease. Amgen’s Amjevita is the first in a string of nine biosimilars —closely related versions of a biologic drug that function comparably—from several firms that are becoming available in the coming year. Drug developers are watching closely: Amjevita’s sales performance in the next few months will indicate the market’s appetite for biosimilars across the US pharmaceutical industry, experts say. “This is probably the most important biosimilar launch in the past couple of years, and probably for the next few years,” says Andrew Mulcahy, a senior economist at the nonprofit research organization RAND Corporation. “This is the drug to watch.” Biosimilars are the biologic equivalent of generic versions of small-molecule drugs. One difference is that, like the original biologics, biosimilars are costly to develop and challenging to

Energy and entropy in the geometrical trinity of gravity

All energy is gravitational energy. That is the consequence of the equivalence principle, according to which gravity is the universal interaction. The physical charges of this interaction have remained undisclosed, but the advent of the geometrical trinity opened a new approach to this foundational problem. Here it is shown to provide a background-independent unification of the previous, noncovariant approaches of Bergmann-Thomson, Cooperstock, Einstein, von Freud, Landau-Lifshitz, Papapetrou, and Weinberg. First, the Noether currents are derived for a generic Palatini theory of gravity coupled with generic matter fields, and then the canonical, i.e., the unique charges, are robustly derived and analyzed, particularly in the metric teleparallel and the symmetric teleparallel versions of general Relativity. These results, and their application to black holes and gravitational waves, are new.

Generalized Harmonically Convex Fuzzy-Number-Valued Mappings and Fuzzy Riemann–Liouville Fractional Integral Inequalities

We propose the concept of up and down harmonically convex mapping for fuzzy-number-valued mapping as our main goal in this work. With the help of up and down harmonically fuzzy-number convexity and the fuzzy fractional integral operator, we also show the results for the Hermite–Hadamard (H–H) inequality, the Fejér type inequality, and some other related versions of inequalities. Moreover, some examples are also presented to discuss the validity of the main results. The results from the new technique show how the suggested scheme is accurate, adaptable, efficient, and user-friendly.

The (largest) Lebesgue number and its relative version

The (largest) Lebesgue number and its relative version

Unification of relative versions of some star-covering properties

Unification of relative versions of some star-covering properties

«СКАЗАНИЕ О ХОЛОПЬЕЙ ВОЙНЕ»: ЛИТЕРАТУРНАЯ ИСТОРИЯ И ПРОБЛЕМА ИСТОРИЧЕСКОЙ ОСНОВЫ

The purpose of the article is to restore the literary history and to determine the historical basis of the so-called «The Tale of the Kholop War». This plot of Russian historical literature of the late Middle Ages and Early Modern times has been pre-served in various similar, but textually not directly related versions of the 16th-17th centuries. The earliest among them is the story of the German diplomat Siegmund Herberstein; he presented it with reference to the Novgorod Chronicle. The oldest Russian versions known to science, however, date back to the end of the 17th century. These are «The Tale of Vyatka citizens» and «Historical and Ancient Description» by T. Kamenevich-Rvovsky. The article discusses possible literary sources of the Russian plot dating back to antiquity and proposes a reconstruction of the content of the original text known to Herberstein. As a result, the author comes to the conclusion that the origin of «The Tale» is linked to how the Nov-gorod elites feel after the loss of Novgorod's independence in the 15th century. At the same time, the plot of «The Tale» can also be based on elements of an oral tradition dating back to the times of the formation of the Old Russian state.

High Order Geometric Methods With Splines: An Analysis of Discrete Hodge-Star Operators

A new kind of spline geometric method approach is presented. Its main ingredient is the use of well established spline spaces forming a discrete de Rham complex to construct a primal sequence $\{X^k_h\}^n_{k=0}$, starting from splines of degree $p$, and a dual sequence $\{\tilde{X}^k_h\}_{k=0}^n$, starting from splines of degree $p-1$. By imposing homogeneous boundary conditions to the spaces of the primal sequence, the two sequences can be isomorphically mapped into one another. Within this setup, many familiar second order partial differential equations can be finally accommodated by explicitly constructing appropriate discrete versions of constitutive relations, called Hodge--star operators. Several alternatives based on both global and local projection operators between spline spaces will be proposed. The appeal of the approach with respect to similar published methods is twofold: firstly, it exhibits high order convergence. Secondly, it does not rely on the geometric realization of any (topologically) dual mesh. Several numerical examples in various space dimensions will be employed to validate the central ideas of the proposed approach and compare its features with the standard Galerkin approach in Isogeometric Analysis.