Wolfram Research Research Articles

Regional features of the incidence of diseases of the musculoskeletal system and connective tissue during the COVID-19 pandemic in the Volga Federal District.

Diseases of the musculoskeletal system (MSMS) are highly common among the population, causing high rates of temporary and permanent disability in those affected. The problem is also determined by the wide age range of the sick — from young to elderly, which dictates the need to assess the prevalence and regional characteristics of musculoskeletal pathology among the population, including those of working age. The purpose of the study is to investigate the regional features of the primary incidence of the adult population of working age in the Volga Federal District (VFD) with diseases of class ICD-10 XIII (M00‑M99) «Diseases of the musculoskeletal system and connective tissue» during the COVID-19 pandemic in 2020–2021. Methods of descriptive and applied statistics were used in the research process. Statistical collections with information on the incidence of BCM in the adult population and the population over working age were studied. For a comparative assessment, we used the construction of a 95 % confidence interval for the average incidence value for the period 2012–2019. method of generating repeated samples (bootstrap). Growth rate ( %) of the incidence rate in 2020–2021. calculated to average values for 2012–2019. Using the non-parametric Wilcoxon test, the differences between the values of all studied indicators and primary incidence (PI) for 2020–2021 (p) were assessed. The variability of indicators was assessed using coefficients of variation (Cv). For statistical processing of the generated database, the Microsoft Excel program and the Wolfram Research Mathematica v.11.3 system were used. During the studied period, the adult population living in the Volga Federal District was characterized by a decrease in the incidence of diseases of the musculoskeletal system. Significant fluctuations in primary incidence were revealed. In 2020–2021 For most of the studied indicators, there was an increase in Cv of primary morbidity, differences in morbidity levels for individual nosological forms of diseases of the musculoskeletal system in the regions of the district. During the pandemic of the new coronavirus infection in the Volga Federal District, multidirectional changes in the levels of primary incidence of diseases of the musculoskeletal system were observed, which was most likely due to the limitation of the provision of specialized medical care in certain regions.

Формирование текстурных признаков хронического воспаления околоносовых пазух (экспериментальное исследование)

Relevance. Morphological examination of the solid phase of biological fluids for the purpose of diagnosing a pathological process is currently quite widely used in various fields of medicine. The current stage of development of the morphological study of human biological fluids is the use of new technology for computer statistical analysis of biological fluids at the stage of solid sediment. The technology is based on identifying structural markers of a pathological process in images of the solid phase of biological fluids. In previous studies based on the Mathematica 13 program (Wolfram Research), we discovered markers of disturbances in the structure of the solid phase of nasal secretions in chronic rhinosinusitis. A system of computer algorithms was created that revealed the main textural features of these structural markers in the pathology under study (entropy, fractal dimension, degree of homogeneity). In a previous study, we presented the statistical processing based on the use of a system of computer algorithms served as the basis for automated analysis of the solid phase of biological fluids for diagnosing the pathological process. However, to date, the process of formation of structures characteristic of normal and pathological conditions during dehydration of biological fluid has not been sufficiently studied. In this regard, conducting an experimental study of the process of formation of textural signs of chronic rhinosinusitis for the scientific substantiation of their diagnostic use in practical otorhinolaryngology is currently of undoubted relevance. Objective. To assess the dynamics of the formation of textural signs of chronic rhinosinusitis during dehydration of nasal secretions. Materials and methods. An experimental study was conducted on the dynamics of the formation of textural signs of chronic rhinosinusitis in the process of dehydration of the secretion of the nasal mucosa in 60 patients with this disease through a comparative morphological assessment of raster images of textures. Experimental, biophysical, statistical methods, conversion of liquids into the solid phase (wedge-shaped dehydration), video microscopy, and computer mathematical analysis of images were used. Results. The experimental studies made it possible to quantify the dynamics of the formation of textural features of the inflammatory process in the paranasal sinuses (entropy, fractal dimension, degree of homogeneity) during the systemic self-organization of nasal secretions using the wedge-shaped dehydration method in patients with chronic rhinosinusitis. Conclusion. The presented data indicate that the textural features obtained during statistical processing (entropy, fractal dimension, degree of homogeneity) represent objective characteristics of structural markers of the solid phase formed during dehydration of nasal secretions in chronic rhinosinusitis, which justifies the use of statistical analysis of textures of the solid phase of biological fluids in automated mode for diagnosing chronic rhinosinusitis in clinical otorhinolaryngological practice.

The Development and Adaptation of a Predictive Model of Full-Factor Optimisation of the Basic Probiotic Fermented Dairy Product Technological Process

Introduction: In the conditions of rapidly developing markets and the increasing needs of the population for new types of products with long shelf life, there is a need to expand their range, further improve their quality and biological value, and modernize traditional technologies. The main means of achieving these goals is to increase the efficiency and quality of scientific research and accelerate the introduction of scientific achievements in industry. The latter will make adjustments to accelerate the development of effective technologies of whole-milk products. The use of new methods of experiment planning in order to optimize technological processes will reduce the duration of research on the creation of new types of products.Purpose: The article is devoted to the research related to the development and adaptation of a predictive (mathematical) model for optimization of the technological process of probiotic fermented dairy product production. This approach will allow to ensure the design of a certain set of formulations for probiotic fermented dairy product, in which the relative biological value (RBV) will correspond to the maximum value at satisfactory given process parameters.Materials and Methods: The objects of research were: probiotic fermented dairy product manufactured in accordance with the developed mathematical model of the process. The search of specialized literature was carried out using electronic databases: E-library, Scopus, MDPI, Science Direct. Mathematical processing of experimental data for the development of the probiotic fermented dairy product model was carried out using Microsoft Excel 2010 (Microsoft Corporation, Ink.) with the "Solution Search" add-in, as well as specialized software packages TableCurve 2D v.5.01 (SYSTAT Software, Ink.) and Wolfram Mathematica 10.2 (Wolfram Research, Ink.).Results: A mathematical model for optimization of the technological process of probiotic fermented dairy product production was developed. A full-factor experiment (FFE) was conducted, in which the mass fraction of sucrose ( , %) and fat-protein index (r) - the ratio of the mass fraction of fat to the mass fraction of protein in the normalized mixture in the intervals from 0 to 10 and from 0 to 1.5%, respectively, were taken as independent factors. RBV was taken as the resultant factor. Based on the results of the research, a refined mathematical description of the dependence of RBV indicator on the mass fraction of sucrose and fat-protein index was obtained. The set of data on the influence of the mass fraction of sucrose on the dynamics of local maximum of RBV and the dynamics of the corresponding values of the mass fraction of fat showed that the maximum of RBV equal to 244.866% corresponded to the mass fraction of sucrose equal to 7.31%. The latter corresponded to the optimum fat-protein index of 1.241. In order to ensure maximum RBV, the lower limit of the mass fraction of fat had to correspond to 3.475%. The analysis of the FFE data showed the presence of additional corrective factors of RBV indicator dependence on fat and protein mass fraction indices. To refine the developed model taking into account additional factors, a correction factor (Q) was introduced into it.Conclusion: Approbation of the optimization model of the technological process of probiotic fermented dairy product production and the obtained mathematical dependencies can serve as a criterion for the formation of a set of formulations for the production of sugar-containing fermented dairy products with a high potential of relative biological value. It should be taken into account that the definition area of this approach is limited in terms of mass fraction of fat in the range from 0.06 to 4.84% and mass fraction of protein - from 2.8 to 3.9%. With this approach (model development) it is possible to analyze promising modes for the studied process, which in real conditions at the experimental stage are not always possible to obtain. The development of this model will significantly reduce the duration of research on the optimization of the technological process.

Effect of Temperature on the Radial Distribution Function of Atoms in the Silicate Glass 2sio2·PBO

In this article, results of investigation of the effect of temperature on radial distribution function of atoms in lead-silicate glass are reported. Radial distribution functions of atoms in the lead-silicate glass 2SiO2∙PbO were calculated via Mathematica 5.1 Wolfram Research from high-temperature X-ray diffraction patterns. It turned out that in the range of 773-973 K mainly variations of the location of atoms in the third coordination sphere have observed, while in the range of 973-1123 K, changes in the first and second coordination spheres take place.

Machine Learning Algorithm to Perform the American Society of Anesthesiologists Physical Status Classification.

The American Society of Anesthesiologists (ASA) Physical Status (PS) Classification System defines perioperative patient scores ranging from 1 to 6 (healthy to brain dead, respectively).The scoring is performed and used by physician anesthesiologists and providers to classify surgical patients based on co-morbidities and various clinical characteristics. There is potentially a variability in scoring stemming from individual biases.The biases impact the prediction of operating times, length of stay in the hospital, anesthetic management, and billing.This study's purpose was to develop an automated system to achieve reproducible scoring. A machine learning (ML) model was trained on already assigned ASA PS scores of 12,064 patients. The ML algorithm was automatically selected by Wolfram Mathematica (Wolfram Research, Champaign, IL) and tested with retrospective records not used in training. Manual scoring was performed by the anesthesiologist as part of the standard preoperative evaluation.Intraclass correlation coefficient (ICC) in R (version 4.2.2; R Development Core Team, Vienna, Austria) was calculated to assess the consistency of scoring. An ML model was trained on the data corresponding to 12,064 patients. Logistic regression was chosen automatically, with an accuracy of 70.3±1.0% against the training dataset. The accuracy against 1,999 patients (the test dataset) was 69.6±1.0%. The ICC for the comparison between ML and the anesthesiologists' ASA PS scores was greater than 0.4 ("fair to good"). We have shown the feasibility of applying ML to assess the ASA PS score within an oncology patient population. Though our accuracy was not very good, we feel that, as more data are mined, a valid foundation for refinement to ML will emerge.

Automated Gaze-Based Identification of Students’ Strategies in Histogram Tasks through an Interpretable Mathematical Model and a Machine Learning Algorithm

As a first step toward automatic feedback based on students’ strategies for solving histogram tasks we investigated how strategy recognition can be automated based on students’ gazes. A previous study showed how students’ task-specific strategies can be inferred from their gazes. The research question addressed in the present article is how data science tools (interpretable mathematical models and machine learning analyses) can be used to automatically identify students’ task-specific strategies from students’ gazes on single histograms. We report on a study of cognitive behavior that uses data science methods to analyze its data. The study consisted of three phases: (1) using a supervised machine learning algorithm (MLA) that provided a baseline for the next step, (2) designing an interpretable mathematical model (IMM), and (3) comparing the results. For the first phase, we used random forest as a classification method implemented in a software package (Wolfram Research Mathematica, ‘Classify Function’) that automates many aspects of the data handling, including creating features and initially choosing the MLA for this classification. The results of the random forests (1) provided a baseline to which we compared the results of our IMM (2). The previous study revealed that students’ horizontal or vertical gaze patterns on the graph area were indicative of most students’ strategies on single histograms. The IMM captures these in a model. The MLA (1) performed well but is a black box. The IMM (2) is transparent, performed well, and is theoretically meaningful. The comparison (3) showed that the MLA and IMM identified the same task-solving strategies. The results allow for the future design of teacher dashboards that report which students use what strategy, or for immediate, personalized feedback during online learning, homework, or massive open online courses (MOOCs) through measuring eye movements, for example, with a webcam.

Application Research of Mathematica Software in Calculus Teaching

Abstract Under the background of teaching in the new era, image recognition, operation, and processing of experimental data are still the focus of calculus teaching. Mathematica has powerful functions as mathematical software and was developed by Wolfram Research. Aiming at the complex symbols and data operation problems in many fields, the software flexibly combines mathematics branches such as geometry and algebra, dramatically simplifying the operation process. This paper takes Mathematica’s existing mathematical software as a reference to discuss whether the addition of such software helps improve the effectiveness of daily teaching. The study found that using this software can stimulate students’ interest and enhance the quality of education.

AscotraceR: An R Package Resource to Simulate the Spatiotemporal Spread of Ascochyta Blight in a Chickpea Field Over a Growing Season.

ascotraceR: An R Package Resource to Simulate the Spatiotemporal Spread of Ascochyta Blight in a Chickpea Field Over a Growing Season.

Longitudinal progression of diabetes mellitus in Wolfram syndrome: The Washington University Wolfram Research Clinic experience.

(1) Describe the progression of diabetes mellitus over time in an observational study of Wolfram syndrome, a rare, genetic, neurodegenerative disorder, which often includes diabetes mellitus and is typically diagnosed during childhood or adolescence. (2) Determine whether C-peptide could be used as a marker of diabetes progression in interventional trials for Wolfram syndrome. N=44 (25F/19M) participants with genetically confirmed Wolfram syndrome attended the Washington University Wolfram Research Clinic annually from 2010 to 2019. Medical history, physical examinations, blood sampling, and questionnaires were used to collect data about diabetes mellitus and other components of Wolfram syndrome. Beta-cell function was assessed by determination of C-peptide during a mixed meal tolerance test. Random coefficients models evaluated the rate of progression of C-peptide over time, and power analyses were used to estimate the number of subjects needed to detect a change in C-peptide decline during an intervention trial. 93.2% of patients had diabetes mellitus. Mean HbA1c across all study visits was 7.9%. C-peptide significantly decreased with increasing duration of diabetes mellitus (p< 0.0001); an optimal break point in C-peptide decline was identified to occur between 0.1 and 2.3 years after diabetes mellitus diagnosis. Twenty patients per group (active vs. control) were estimated to be needed to detect a 60% slowing of C-peptide decline during the first 2.3 years following diabetes diagnosis. C-peptide declines over time in Wolfram syndrome and could potentially be used as a marker of diabetes progression in interventional studies for Wolfram syndrome, especially within the first 2 years after diabetes diagnosis.

Bankruptcy or Success? The Effective Prediction of a Company’s Financial Development Using LSTM

There is no doubt that the issue of making a good prediction about a company’s possible failure is very important, as well as complicated. A number of models have been created for this very purpose, of which one, the long short-term memory (LSTM) model, holds a unique position in that it generates very good results. The objective of this contribution is to create a methodology for the identification of a company failure (bankruptcy) using artificial neural networks (hereinafter referred to as “NN”) with at least one long short-term memory (LSTM) layer. A bankruptcy model was created using deep learning, for which at least one layer of LSTM was used for the construction of the NN. For the purposes of this contribution, Wolfram’s Mathematica 13 (Wolfram Research, Champaign, Illinois) software was used. The research results show that LSTM NN can be used as a tool for predicting company failure. The objective of the contribution was achieved, since the model of a NN was developed, which is able to predict the future development of a company operating in the manufacturing sector in the Czech Republic. It can be applied to small, medium-sized and manufacturing companies alike, as well as used by financial institutions, investors, or auditors as an alternative for evaluating the financial health of companies in a given field. The model is flexible and can therefore be trained according to a different dataset or environment.

TripleK: A Mathematica package for evaluating triple-K integrals and conformal correlation functions

I present a Mathematica package designed for manipulations and evaluations of triple-K integrals and conformal correlation functions in momentum space. Additionally, the program provides tools for evaluation of a large class of 2- and 3-point massless multi-loop Feynman integrals with generalized propagators. The package is accompanied by five Mathematica notebooks containing detailed calculations of numerous conformal 3-point functions in momentum space. Program summaryProgram Title: TripleKCPC Library link to program files:http://dx.doi.org/10.17632/5sz4bt28vr.1Developer’s repository link:https://triplek.hepforge.org/Licensing provisions: GNU General Public License v3.0Programming language: Wolfram Language [1] (Mathematica 10.0 or higher)Supplementary material: The package includes five Mathematica notebooks containing bulk of the results regarding the structure of conformal 3-point functions.Nature of problem: Triple-K integrals were introduced in [2] as a convenient tool for the analysis of conformal 3-point functions in momentum space. All 3-point functions of scalar operators, conserved currents and stress tensor can be expressed in terms of triple-K integrals. Furthermore, a large class of 2- and 3-point massless multi-loop Feynman integrals with generalized propagators is expressible in terms of triple-K integrals as well. Since the expressions are usually long and unwieldy, an automated tool is essential for efficient manipulations.Solution method: In [3] an effective reduction algorithm was provided for expressing a large class of triple-K integrals in terms of master integrals. The presented package implements this reduction scheme. As far as the multi-loop Feynman integrals are concerned, the conversion to multiple-K integrals proceeds by means of Schwinger parameterization.Additional comments including restrictions and unusual features: Despite extensive testing, this package is a one man job, therefore bugs are unavoidable. Please, report all issues at adam.bzowski@physics.uu.se or abzowski@gmail.com. [1] Wolfram Research Inc., Mathematica, Version 11.2, 12.0, Champaign, IL, 2020 [2] A. Bzowski, P. McFadden, K. Skenderis, Implications of conformal invariance in momentum space, JHEP 03 (2014) 111. http://arxiv.org/abs/1304.7760arXiv:1304.7760, https://doi.org/10.1007/JHEP03(2014)111doi:10.1007/JHEP03(2014)111 [3] A. Bzowski, P. McFadden, K. Skenderis, Evaluation of conformal integrals, JHEP 02 (2016) 068. http://arxiv.org/abs/1511.02357arXiv:1511.02357, https://doi.org/10.1007/JHEP02(2016)068doi:10.1007/JHEP02(2016)068

2278-PUB: Longitudinal Progression of Diabetes Mellitus in Wolfram Syndrome

Wolfram Syndrome (WFS) is a rare, genetic, neurodegenerative disorder with associated features of diabetes mellitus (DM), diabetes insipidus, deafness, and optic atrophy. In order to design intervention studies, concrete markers of disease progression are required. DM in WFS is believed to be due to endoplasmic reticulum stress-induced failure of insulin secretion. Therefore, progressive loss of insulin production may be a viable marker of disease progression. The purpose of this study was to examine progression of DM, measured by beta-cell function, in WFS patients over time. N=44 (25F/19M) participants with genetically confirmed WFS attended the Washington University Wolfram Research Clinic from 2010-2019. A mixed meal tolerance test was administered to assess beta cell function (i.e., C-peptide). A hierarchical random coefficients model was used to relate C-peptide as a function of DM duration. Most patients (91%) had DM at time of study enrollment (N=39) or developed DM during the study (N=1). There was a significant association between C-peptide and DM duration, such that C-peptide decreased over time (F= 39.44, p=&amp;lt;0.0001). Given the high prevalence and easily dated onset of DM in WFS, deterioration in C-peptide could potentially be used as a biomarker to assess disease progression in intervention trials for WFS, particularly in those with duration of DM &amp;lt; 10 years as they may be less likely to experience a C-peptide floor effect. Disclosure M. Ray: None. T. Hershey: None. L. Chen: None. N.H. White: None. B.A. Marshall: None. Funding Washington University (HD070855, U54HD087011); Clinical and Translational Science Award (UL1RR024992); National Institute on Drug Abuse (5T32DA007261-27); Diabetes Research Center (DK020579); Snow Foundation, George Decker and Julio V. Santiago Pediatric Diabetes Research Fund; Mallinckrodt Institute of Radiology; McDonnell Center for Systems Neuroscience

Stability of an anisotropic dielectric elastomer plate

A variety of methods have been proposed to improve the performance of dielectric elastomer transducers, which lead to the anisotropic electromechanical behavior of the material. This paper theoretically analyzes the effect of material anisotropy on the diffuse modes of instability in dielectric elastomer plates. As a first step, a transversely isotropic material is considered in the present study. The linearized incremental theory is used and the plate thickness is considered in the stability analysis. The bifurcation equations are solved with Wolfram Mathematica (Wolfram Research, Inc., 2019) [1] to obtain the critical stretches under different electric field. It is found that, compared to the isotropic material, material anisotropy results in larger unstable regions and higher critical stretches above which the plate is stable. It is also shown that material anisotropy has a stronger influence on a thinner plate. As the plate thickness increases, the influence decreases.

Impact of Mechanical Circulatory Support and Heart Transplantation on Survival of the Population of Transplant Eligible Advanced Heart Failure Patients - A Computer Simulation Study

Long term survival after heart transplantation is better than after implantation of VAD, however, the reported survival curves do not represent the whole population of transplant eligible patients, where some die while waiting for the transplantation and do not include the time on the waiting list. The aim of the present study was to use computer simulation model to assess the impact of left ventricular assist device implantation, heart transplantation and combination of both on the overall survival of a group of transplant eligible patients. A computer model was made in Mathematica v12.0 (Wolfram Research, Champaign, IL, USA) to simulate overall survival of a group of virtual patients eligible for heart transplantation in different scenarios, by using Seattle heart failure model score to define baseline survival and published survival curves after heart transplantation, ventricular assist device implantation and time to transplantation to generate individual survival times for each virtual patient. Computer generated data were compared with survival of the transplant eligible patients treated at the University Medical Center Ljubljana, Slovenia. Kaplan-Meier survival curves are presented for baseline, combined waiting list and heart transplantation, waiting list, combined waiting list and high-risk ventricular assist device implantation and combined ventricular assist device implantation and heart transplantation survival. The model has shown that overall group survival after heart transplantation only is much worse than published post-transplant survival due to waiting list mortality. Waiting list mortality is lower than true baseline mortality due to informative censoring. Ventricular assist device implantation is beneficial in higher risk patients but can do more harm in lower risk patients. The combined use of ventricular assist device implantation and heart transplantation has the greatest impact on survival, by decreasing early mortality with ventricular assist device and increasing the long-term survival with transplantation.

Call for papers: BCCE 2020

Abstracts are being accepted for the 26th Biennial Conference on Chemical Education, which will be held at Oregon State University July 18–23. The meeting theme is “Chemistry Is Paramount.” The program will feature 186 technical symposia, 137 workshops, two poster sessions, four plenary sessions, and an exhibition. Plenary speakers include Geraldine Richmond of the University of Oregon, Peter Mahaffy of the King’s University in Alberta, and Theodore Gray of Wolfram Research. There will be a social and dance on Wednesday night with live music from Al D. Hyde and the Key Tones, a classic rock-and-roll band with a horn section made up exclusively of chemistry educators. Abstracts are due by Feb. 24. For more information or to submit an abstract, visit bcce2020.org.

Computational Models of Building Structures. Visualization and Intelligent Content Design

On the basis of the author’s methodology using Wolfram Research technology received and presented science-intensive, adaptive content, which is the result of research in solving problems of modeling, calculation, analysis and visualization of building structures. The article reviewed the main elements, examples of hook up of functions and options of the system Wolfram Mathematica, which provides an extension and addition of electronic resources by means of intelligent computing and interactive visualization.

Spinal Cord Tolerance Guided by Stereotactic Radiosurgical Treatment of Intramedullary Arteriovenous Malformations

Spinal cord toxicity resulting in neurological deficits remains the most feared complication of spinal region stereotactic radiosurgery (SRS). In treating vertebral body disease, a radiation dose gradient can typically be established between tumor and spinal cord. This is difficult for intramedullary spinal cord arteriovenous malformations (iSCAVMs), which can be integrated throughout the cord. Here we report outcomes of cord tolerance in treatment of integrated iSCAVMs. A retrospective cohort of 17 consecutive patients with integrated iSCAVMs treated once with frameless robotic surgery, SRS between 2007 and 2018 was accrued. Clinical outcomes, dose prescriptions, and target dose-volume histogram (DVH) parameters were acquired. Volumes of interest (VOIs) comprising the proper AVM and cord were registered on treatment planning software. A cord minus AVM (CmA) structure representing independent spinal cord was generated by Boolean subtraction of the respective proper AVM from the cord. Various dose quantifiers were extracted from DVHs, statistical univariate analysis was performed, and Task Group 101 (TG101) constraints were interpolated to two-fraction regimens with α/β of 2-3 Gray (Gy) using Wolfram Mathematica (Wolfram Research, Champaign, IL). Among the 17 patients analyzed (eight male and nine female), all had CmA volumes smaller than cord, confirming the integrated nature of their iSCAVMs. Nine had a nidus in the C-spine; six in the T-spine; and two in the L-spine or lower. Median age at diagnosis was 23, ranging from 9 to 56 years. Nine patients had no prior intervention, while eight had prior embolization(s) and/or microsurgery. Median follow-up time was 40 months. Ten patients (59%) experienced Grade (G) 0 neurological toxicity post-treatment, seven (41%) experienced G1, and zero experienced G2+. Three patients were prescribed three fractions to 21 or 24 Gy. The rest received two fractions (20-22 Gy). Max dose (Dmax) to cord and CmA ranged from 2278-2874 cGy and 2000-2659 cGy, respectively. All patients had Dmax to cord and CmA greater than TG101 constraints. All patients received minimum dose to hottest 0.03 cc volume (D0.03) to cord greater than constraints; 15 patients (88%), to CmA. All patients received minimum dose to hottest 0.35 cc volume (D0.35) to cord greater than threshold; 13 patients (76%), to CmA. At significant level of 0.05, one-tailed binomial test suggests max monthly G2+ toxicity rate of 0.4% in exceeding tolerances. No neurologic toxicity beyond Grade 1 was experienced by any patient, all of whom received Dmax to spinal cord tissue (both independent and integrated with AVM) beyond recommended constraints. Further, all patients exceeded volumetric constraints to cord. Most exceeded volumetric constraints to CmA, as well. Novel tolerance data from rare iSCAVMs may influence current cord constraints to avoid limiting appropriate treatment of more common vertebral metastases.

Classical general relativity effects to second order in mass, spin, and quadrupole moment

In this contribution, we calculate the light deflection, perihelion shift, time delay and gravitational redshift using an approximate metric that contains the Kerr metric and an approximation of the Erez-Rosen spacetime. The results were obtained directly using (Mathematica 2018 Wolfram Research, Inc., Version 11.3, Champaign). The results agree with the ones presented in the literature, but they are extended until second order terms of mass, angular momentum and mass quadrupole. The inclusion of the mass quadrupole is done by means of the metric; no expansion of the gravitational potential as in the parameterized post-Newtonian is required.

On calibrated weights in stratified sampling

In this paper, we propose a calibration estimator of population mean in stratified sampling using the known mean and variance information from multi-auxiliary variables. The problem of determining the optimum calibrated weights is formulated as a Nonlinear Programming Problem (NLPP) that is solved using the Lagrange multiplier technique. Numerical example with real data is presented to illustrate the computational details of the proposed estimator. A comparison study is also carried out using real and simulated data to evaluate the performance and the usefulness of the proposed estimator. The study reveals that the proposed estimator with multi-auxiliary information is more efficient estimator of the population mean as it provides least estimated variance and highest gain in relative efficiency (RE). References Jean Claude Deville and Carl Erik Sarndal. Calibration estimators in survey sampling. Journal of the American statistical Association, 87(418):376–382, 1992. doi:10.1080/01621459.1992.10475217 . Victor M Estevao and Carl Erik Sarndal. Survey estimates by calibration on complex auxiliary information. International Statistical Review, 74(2):127–147, 2006. doi:110.1111/j.1751-5823.2006.tb00165.x Patrick J Farrell and Sarjinder Singh. Model-assisted higher-order calibration of estimators of variance. Australian and New Zealand Journal of Statistics, 47(3):375–383, 2005. doi:10.1111/j.1467-842X.2005.00402.x Wolfram Research, Inc. Mathematica, Version 11.3. Champaign, IL, 2018. Jong Min Kim, Engin A Sungur, and Tae Young Heo. Calibration approach estimators in stratified sampling. Statistics and probability letters, 77(1):99–103, 2007. doi:10.1016/j.spl.2006.05.015 Phillip S Kott. Using calibration weighting to adjust for nonresponse and coverage errors. Survey Methodology, 32(2):133, 2006. Dinesh K Rao. Mathematical programing in stratified random sampling. PhD thesis, School of Computing, Information and Mathematical Sciences, The University of the South Pacific, Fiji, February 2017. Dinesh K. Rao, Tokaua. Tekabu, and Mohammad G M Khan. New calibration estimators in stratified sampling. In Proceedings of Asia-Pacific World Congress on Computer Science and Engineering, pages 66–70. IEEE, 2016. Gurmindar K Singh, Dinesh K Rao, and Mohammed GM Khan. Calibration estimator of population mean in stratified random sampling. In Proceedings of Asia-Pacific World Congress on Computer Science and Engineering (APWC on CSE), pages 1–5. IEEE, 2014. Sarjindar Singh, Stephen Horn, and Frank Yu. Estimation of variance of general regression estimator: Higher level calibration approach. Survey Methodology, 24:41–50, 1998. Sarjinder Singh. Advanced Sampling Theory With Applications: How Michael Selected Amy, volume I and II. Kluwer Academic Publishers, Netherlands, 2003. Sarjinder Singh. On the calibration of design weights using a displacement function. Metrika, 75(1):85–107, 2012. doi:10.1007/s00184-010-0316-6 Sarjinder Singh, Stephen Horn, Sadeq Chowdhury, and Frank Yu. Theory and methods: Calibration of the estimators of variance. Australian and New Zealand Journal of Statistics, 41(2):199–212, 1999. doi:10.1111/1467-842X.00074 D S Tracy, S Singh, and R Arnab. Note on calibration in stratified and double sampling. Survey Methodology, 29(1):99–104, 2003. Changbao Wu and Randy R Sitter. A model-calibration approach to using complete auxiliary information from survey data. Journal of the American Statistical Association, 96(453):185–193, 2001. doi:10.1198/016214501750333054

(Invited) Elucidating the Micro Phase-Separation of Mixed Kappa and Iota Carrageenan Gels Using Multiple Particle Tracking

Carrageenan is a family of linear sulfated polysaccharides extracted from seaweeds. Among the different types of carrageenan, kappa carrageenan (KC) and iota carrageenan (IC) are widely used in industries due to its gelling behavior. Because of its importance in industries, KC and IC as well as its mixtures have been extensively studied using different methods. However, it is still unclear whether mixed KC:IC undergo a phase separated network structure of IC-rich and KC-rich or interpenetrated network structure. In this report, the network structure and gelation mechanism of KC, IC and its mixture were elucidated using multiple particle tracking. Sodium-type κ- and ι- carrageenan powder was purchased from Tokyo Chemical Industry Co., Ltd. (Tokyo, Japan). All samples were dialyzed against NaCl solution and subsequently against deionized water, to obtain Na+ type carrageenan solutions. Samples were prepared by diluting carrageenan and KCl solutions and heated for 30 min at 70 °C under vigorous stirring. The prepared solutions were mixed using vortex to obtain 1.5% w/w carrageenan with 10 mM KCl and heated at 90 °C for 20 min. Fluorescently labelled 0.1 μm particles (Green, ThermoScientific) were added at a concentration of ~0.01% (v/w) at 90 °C and stirred for another 5 min to assure homogenous dispersion. Mixture of KC and IC was prepared at different volume fraction of IC. Movies of the diffusing particles were recorded at a frame rate of 7.5 frames per second for 110 seconds. In cooling experiments, particle tracking was performed at different sample temperatures from 50 °C to 10 °C. In storage experiments, hot solutions of carrageenan were cooled down from 50 °C to 5 °C at a rate of 1 °C/min in a temperature-controlled incubator to form a gel. The gelled sample was stored at 5 °C prior to experiment and particle tracking was performed at 5 °C. Particle tacking was implemented in Mathematica 10 (Wolfram Research, Inc., USA). The temperature dependence of the mean square displacement (MSD) of particles in KC, IC and mixed KC:IC gels were carried out to quantify the dynamics of the evolving network structure on cooling as shown in Figure 1. In mixed KC:IC, a two-step decrease in MSD was observed. The onset of the observed decrease is close to the decrease in pure KC and IC gels. This trend is consistent with the observed increase in the viscoelastic modulus in dynamic viscoelasticity measurements. The decrease in the MSD with decreasing temperature is due to the steric hindrance created by the formation of clusters of IC and KC chain aggregates. This suggests that KC and IC chains formed aggregates independently on cooling. In pure carrageenan, IC gels formed weak entanglement among clusters of IC chain that allowed diffusion of particles through crevices of the entangled clusters while KC gels rapidly formed thick aggregates of interconnected clusters that confined the particles. On the other hand, in mixed KC:IC, the presence of IC clusters decreased the mobility of KC chains at low temperature thus slowed the formation of stable clusters of KC. With storage time, a broad distribution of MSD was observed for the mixed gels. This suggests that an inhomogeneous solution was formed as KC and IC clusters continue to rearrange to form a stable network. The degree of heterogeneity in the mixed gels is reflected in the corresponding van Hove distribution of particle displacement and the distribution of MSD as a function of slope. In the van Hove distribution, a bimodal Gaussian form with a broad and narrow Gaussian width fit well on the distribution suggests a mobile and immobile fraction of particle at each mixing ratios. In the distribution of MSD as a function of slope, the mobile and immobile particles were identified and clustered accordingly. This suggests that the presence of mobile particles was due to the existence of IC-rich domains that allowed diffusion of particles and the immobile particles was due to the confinement of particles in KC-rich domains as shown in the graphical representation in Figure 1. This is consistent with the proposed gelation mechanism of a local phase separation into IC-rich and KC-rich domains. As the volume fraction of IC was increased, the number of mobile particles increased consequently and suggests a phase transition from a sea-island (80%KC:20%IC) to a bi-continuous (50%KC:50%IC) to an island-sea (30%KC:70%IC) network structure is likely to occur. Figure 1