Use Of Sum Research Articles

A proposal to clarify the use of Sum of Bases in the Brazilian Remineralizer Regulation and in Soil Science

The term Sum of Bases has different meanings in Soil Science and the Remineralizer Regulations. This issue may cause misunderstandings in communication, particularly between the agricultural community and the mining community, becoming an obstacle to the advancement of the use of this soil amendment. In this scientific note we propose the use of subscript “R” (SBR), standing for Rock, in English, and Rocha, in Brazilian Portuguese, and “S” (SBS) standing for Soil in English and Solo in Brazilian Portuguese. [...]

On the Unification of Schemes and Software for Wavelets on the Interval

We revisit the construction of wavelets on the interval with various degrees of polynomial exactness, and explain how existing schemes for orthogonal- and Spline wavelets can be extended to compactly supported delay-normalized wavelets. The contribution differs substantially from previous ones in how results are stated and deduced: linear algebra notation is exploited more heavily, and the use of sums and complicated index notation is reduced. This extended use of linear algebra eases translation to software, and a general open source implementation, which uses the deductions in this paper as a reference, has been developed. Key features of this implementation is its flexibility w.r.t. the length of the input, as well as its generality regarding the wavelet transform.

Abstract 763: Understanding of cancer clinical trial data and statistical opportunities

Abstract Purpose: The study aims to discuss various types of cancer clinical trial data with potential statistical solutions. Background: Cancer clinical trial allows researchers discovering new strategies to prevent, detect, diagnose, or treat cancer. Each trial collects many types of patient data to evaluate various treatment characteristics, such as tumor response data, adverse event (AE) data, demographic data, and follow-up data. Each data type is often stored in a multi-dimensional and irregularly longitudinal layout with potential hierarchical structure, therefore generating ‘big data' phenomena. Such complexities often scare away researchers and lead to use naïve descriptive statistics for analysis. As a result, it loses valuable information and becomes a major hurdle to advance cancer precision medicine. Here we share our thoughts for two primary data types: tumor response data and safety data. Tumor Response Data: Tumor response data is a key component to evaluate treatment efficacy in clinical trial for solid tumor. Response Evaluation Criteria for Solid Tumors (RECIST) has been a standard tool to assess treatment effect. RECIST measures three types of lesion to determine treatment efficacy: target lesion, non-target lesion, and new lesion. Target lesion is the primary lesion to determine response (tumor shrinkage), progression (tumor outgrowth), or stable disease. However, studies have raised issues regarding RECIST being applied for incorrect determination of response, which resulted in premature termination of therapy and imprecise efficacy. One key limitation of RECIST is the use of sum of all target lesion sizes for clinical decision-making. While this approach is straightforward for calculation, it fails to address lesion variability of tumor growth in an individual patient. Statistical mixed effect model could be a powerful tool to fully utilize all lesion data to provide overall assessment of treatment effect and individual lesion variability. Safety Data: Safety data is a critical component of clinical trial to protect patients from unnecessary risk and to develop safety profile of the drug for benefit-risk assessment. The safety data contains many types of AE to monitoring drug toxicity. Evaluation metrics include grade, duration, and likelihood of the treatment attribution; therefore it forms a giant complicated structure. However, safety report in clinical trials is often presented in summary descriptive statistics, such as yes/no of occurrence or frequency of occurrence for each AE. This type of report has been challenged due to inadequate information or lack of details. Statistical opportunities include integration of various safety metrics to generate more useful toxicity variables, such as AE duration adjusted with different grade. Conclusion: Clinical trial collects valuable big data and statistical methods have potential to transform the rich but complicated data into informative evidence. Citation Format: Dung-Tsa Chen, Ben Creelan, Trevor Rose, Wenyaw Chan. Understanding of cancer clinical trial data and statistical opportunities [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 763.

Two-Module Weight-Based Sum Code in Residue Ring Modulo M=4

The paper describes research results of features of error detection in data vectors by sum codes. The task is relevant in this setting, first of all, for the use of sum codes in the implementation of the checkable discrete systems and the technical means for the diagnosis of their components. Methods for sum codes constructing are described. A brief overview in the field of methods for sum codes constructing is provided. The article highlights codes for which the values of all data bits are taken into account once by the operations of summing their values or the values of the weight coefficients of the bits during the formation of the check vector. The paper also highlights codes that are formed when the data vectors are initially divided into subsets, in particular, into two subsets. An extension of the sum code class obtained by isolating two independent parts in the data vectors, as well as weighting the bits of the data vectors at the stage of code construction, is proposed.
 The paper provides a generalized algorithm for two-module weighted codes construction, and describes their features obtained by weighing with non-ones weight coefficients for one of data bits in each of the subvectors, according to which the total weight is calculated. Particular attention is paid to the two-module weight-based sum code, for which the total weight of the data vector in the residue ring modulo M = 4 is determined. It is shown that the purpose of the inequality between the bits of the data vector in some cases gives improvements in the error detection characteristics compared to the well-known two-module codes. Some modifications of the proposed two-module weighted codes are described. A method for calculating the total number of undetectable errors in the two-module sum codes in the residue ring modulo M = 4 with one weighted bit in each of the subsets is proposed. Detailed characteristics of error detection by the considered codes both by the multiplicities of undetectable errors and by their types (unidirectional, symmetrical and asymmetrical errors) are given. The proposed codes are compared with known codes. A method for the synthesis of two-module sum encoders on a standard element base of the single signals adders is proposed. The classification of two-module sum codes is presented.

A systematic framework for formulating convex failure envelopes in multiple loading dimensions

The failure envelope approach is widely used to assess the ultimate capacity of shallow foundations for combined loading, and to develop foundation macro-element models. Failure envelopes are typically determined by fitting appropriate functions to a set of discrete failure load data, determined either experimentally or numerically. However, current procedures to formulate failure envelopes tend to be ad hoc, and the resulting failure envelopes may not have the desirable features of being convex and well-behaved for the entire domain of interest. This paper describes a new systematic framework to determine failure envelopes – based on the use of sum of squares convex polynomials – that are guaranteed to be convex and well-behaved. The framework is demonstrated by applying it to three data sets for failure load combinations (vertical load, horizontal load and moment) for shallow foundations on clay. An example foundation macro-element model based on the proposed framework is also described.

Enforcing necessary non-negativity constraints for common diffusion MRI models using sum of squares programming

In this work we investigate the use of sum of squares constraints for various diffusion-weighted MRI models, with a goal of enforcing strict, global non-negativity of the diffusion propagator. We formulate such constraints for the mean apparent propagator model and for spherical deconvolution, guaranteeing strict non-negativity of the corresponding diffusion propagators. For the cumulant expansion similar constraints cannot exist, and we instead derive a set of auxiliary constraints that are necessary but not sufficient to guarantee non-negativity. These constraints can all be verified and enforced at reasonable computational costs using semidefinite programming. By verifying our constraints on standard reconstructions of the different models, we show that currently used weak constraints are largely ineffective at ensuring non-negativity. We further show that if strict non-negativity is not enforced then estimated model parameters may suffer from significant errors, leading to serious inaccuracies in important derived quantities such as the main fiber orientations, mean kurtosis, etc. Finally, our experiments confirm that the observed constraint violations are mostly due to measurement noise, which is difficult to mitigate and suggests that properly constrained optimization should currently be considered the norm in many cases.

Incremental [formula omitted]-gain stability of piecewise-affine systems with piecewise-polynomial storage functions

This paper concerns the incremental L2-gain stability of piecewise-affine (PWA) systems. We propose sufficient conditions derived from dissipativity theory to compute an upper bound on the incremental L2-gain. This is achieved by constructing piecewise-polynomial storage functions through the use of sum of squares (SOS) relaxations. The constraints are expressed as linear matrix inequalities (LMIs), which can be solved numerically in an efficient way. The proposed conditions are verified to be less conservative than previous results found in the literature by means of a numerical example.

New LMI conditions for admissibility analysis of time-varying descriptor systems

This paper presents new admissibility analysis conditions for discrete-time descriptor systems. Firstly, it proposes an extension, expressed as necessary and sufficient admissibility conditions, of admissibility criteria developed in the literature for linear time-invariant systems in order to incorporate the time-varying case. This extension exploits time-varying slack variables and uses the linear matrix inequality (LMI) formulation. Then, this extension is applied to the case of polytopic descriptor systems with bounded time-varying parameters. The use of sum of squares polynomials allows to eliminate the criteria parametric dependence and to provide new admissibility analysis conditions expressed as a LMIs feasibility problem. This new admissibility analysis result uses parameter-dependent slack variables and may be less conservative than the results already proposed in the literature as sustained by our numerical evaluation.

Traffic quality Index to intersections considering fuel efficiency

The environmental conditions of urban areas are directly affected by the operation in their road intersections and by the amount of vehicles and its dispersion throughout the day. To measure these conditions, the present study aims to propose a Traffic Quality Index (TQI) applicable to urban intersections and for comparing traffic performance, bringing a comprehensive methodology about the parameters involved in intersection quality. To prepare the TQI, it was used the Delphi methodology, through opinion of traffic experts. The results supported the selection of a group containing five parameters, namely: delay per vehicle; stops per vehicle; average speed; fuel efficiency and queue size. The formulation of the TQI has been established based on the values of parameters scored and their respective weights and evaluated for use of sum or product. Aiming at its validation, the TQI was applied to four intersections (two of them non-signalized and the other two signalized), simulated by Synchro Studio 9 software, and the results were compared with those obtained by the HCM (Highway Capacity Manual) and ICU (Intersection Capacity Utilization). It was found that the TQI product is more sensitive to roads changes and is a tool to assist the development and evaluation of urban road design and traffic planning, and that its use is complementary to the HCM and ICU methodologies.

Alternative Methods to Make Efficient Use of Two Decks of Cards in Randomized Response Sampling

In this article, alternative randomized response models are proposed, which make use of sum of quantitative scores generated from two decks of cards being used in a survey. The proposed methods are compared to the Odumade and Singh and Singh and Grewal models through a simulation study. It is shown that the modified methods can be used more efficiently than those both models.

Predicting the development of critical biological stages of Sunn pest,Eurygaster integriceps Put. (Hemiptera: Scutelleridae), by using sumof degree-days for timing its chemical control in wheat*

This investigation was carried out for possible use of sum of degree-days (total effective temperatures) in order to predict the critical biological stages in chemical control of Sunn pest, Eurygaster integriceps Put. (Hemiptera: Scutelleridae), in 28 wheat fields of Adiyaman, Diyarbakir, and Sanliurfa provinces from 2007 to 2010, and in climate chamber conditions. Development threshold temperature (°C) of Sunn pest in terms of the life span, starting from egg to new generation of adults, was found as 13.30 °C. Sums of degree-days starting from 1 January to appearance of the eggs, first-stage nymphs (n 1 ), second-stage nymphs (n 2 ), and fourth-stage nymphs (n 4 ) were found with the averages of 44.6, 84.4, 123.3, and 223.1 degree-days, respectively. The results from the field studies reflected that developmental biological data on sum of degree-days as a predictive tool could be useful in better decision making to start chemical applications as soon as the appearance of n 1 until n 4 for Sunn pest control.

Usefulness of Sum of ST-Segment Elevation on Electrocardiograms (Limb Leads) for Predicting In-Hospital Complications in Patients With Stress (Takotsubo) Cardiomyopathy

Although the prognosis of patients with stress (takotsubo) cardiomyopathy is relatively favorable, serious complications occur in some patients. It is generally accepted that electrocardiography is an essential tool for the diagnosis of stress cardiomyopathy, with findings highly suggestive of the characteristics of myocardial damage. We tested the hypothesis that the quantitative analysis of electrocardiograhic changes can predict complications in stress cardiomyopathy. The study subjects were 85 patients with stress cardiomyopathy. A total of 34 patients developed ≥1 in-hospital complications (heart failure, intraventricular pressure gradient [>30 mm Hg], cardiogenic shock, ventricular tachycardia/fibrillation, and embolism). Patients with complications were likely to have a higher heart rate (96 ± 25 vs 76 ± 17 beats/min, p <0.001), larger sum of ST-segment elevation in 12 leads (median 10.5 mm; interquartile range 5.0 to 17.5 vs 3.0 mm, interquartile range 0 to 7.0; p <0.001) and extension of ST-segment elevation to limb leads (50% vs 12%, p <0.001) than those without complications. Multivariate logistic regression analysis identified heart rate (odds ratio 1.05, 95% confidence interval 1.02 to 1.07, p = 0.001) and sum of ST-segment elevation in 12 leads (odds ratio 1.24, 95% confidence interval 1.11 to 1.39, p <0.001) as significant and independent predictors of complications. Receiver operating characteristic analysis selected 5.5 mm as the best cutoff value of sum of ST-segment elevation in 12 leads for the prediction of complications, with a sensitivity and specificity of 74% and 73%, respectively, and area under the curve of 0.81 (95% confidence interval 0.72 to 0.90, p <0.001). The results suggest that the extent and magnitude of ST-segment elevation on the electrocardiogram are potentially useful predictors of in-hospital complications in patients with stress cardiomyopathy.

Usefulness of sum of the thickness of plaque in the carotid artery for predicting the presence and the extent of the coronary artery disease in patients with type 2 diabetes mellitus without known coronary artery disease

AimsThe usefulness of the sum of plaque thickness in the carotid artery (plaque score; PS), as a prediction of coronary artery disease (CAD) was investigated in patients with type 2 diabetes mellitus. MethodsB mode ultrasonographic scanning of the carotid artery and multislice computed tomography (MSCT) coronary angiography were performed in 227 diabetic patients without known cardiac disease. ResultsThe PS was useful to predict the presence of diseased [nonobstructive and obstructive] CAD (≧3 segments) and obstructive (≧50%) CAD with cut-off value of 3.5mm (area under curve: 0.745 and 0.782, respectively), according to a receiver operating characteristics curve analysis. A multivariate logistic analysis of baseline risk factors showed that the PS was independent risk factor for the prediction of diseased and obstructive coronary artery disease (R2=0.2165, p<0.0001 and R2=0.2265, p<0.0001, respectively). The PS was most significant predictor of the number of diseased and obstructive segments of the coronary artery in a multiple regression analysis (R2=0.2022, p<0.0001 and R2=0.2209, p<0.0001, respectively). ConclusionsThe PS in the carotid artery was useful for the prediction of the presence and the extent of CAD, and was most important as a screening test for the identification of a high risk group of asymptomatic diabetic patients.

Minimal driving of hippocampal theta by the supramammillary nucleus during water maze learning

Previous studies have shown only modest effects of supramammillary nucleus (SuM) dysfunction on theta frequency and learning in the water maze (WM), with larger effects in other tasks. However, theta recorded from SuM, and used to trigger the production of theta-like oscillations in the hippocampus, produced reversal of the deficit in WM learning produced by theta blocking. We explored this apparent inconsistency by analyzing the relationship between SuM and hippocampal theta in the control group of this theta-blocking experiment using coherence, phase analysis, and the directed transfer function. We found little evidence of an influence of SuM on the hippocampus in the bulk of WM learning-with some possibility of SuM becoming involved briefly later in learning. A learning-related increase in coherence was observed in conjunction with gradual phase reorganization of hippocampal theta in relation to SuM theta. This change in phase dynamics between the two structures was also correlated with a relative increase of the estimated direction of theta propagation from the SuM to the hippocampus. These results are consistent with the previous weak effects of SuM lesions and suggest that the use of SuM as a source to trigger hippocampal theta and recover function is likely to be due to coherence between SuM and some other structure that normally controls hippocampal theta during WM learning.

Stability and robustness analysis of nonlinear systems via contraction metrics and SOS programming

A wide variety of stability and performance questions about linear dynamical systems can be reformulated as convex optimization problems involving linear matrix inequalities (LMIs). These techniques have been recently extended to nonlinear systems with polynomial or rational dynamics through the use of sum of squares (SOS) programming. In this paper we further extend the class of systems that can be analyzed with convexity-based methods. We show how to analyze the robust stability properties of uncertain nonlinear systems with polynomial or rational dynamics, via contraction analysis and SOS programming. Since the existence of a global contraction metric is a sufficient condition for global stability of an autonomous system, we develop an algorithm for finding such contraction metrics using SOS programming. The search process is made computationally tractable by relaxing matrix definiteness constraints, the feasibility of which indicates the existence of a contraction metric, to SOS constraints on polynomial matrices. We illustrate our results through examples from the literature and show how our contraction-based approach offers advantages when compared with traditional Lyapunov analysis.

Joint Use of Sum and Delta Channels for Multiple Radar Target DOA Estimation

This paper deals with the problem of estimating the parameters, i.e., complex amplitudes, directions of arrival (DOAs), and Doppler frequencies, of multiple radar targets present in the same range-azimuth resolution cell of a surveillance radar, by joint processing the sum and delta channel data. The AML-RELAX (asymptotically maximum likelihood) estimator previously derived by the authors is extended to a two-channel system scenario. Both the cases of targets having the same Doppler frequencies and different Doppler frequencies are considered. Performance is numerically investigated through Monte Carlo simulation and compared with that of the single channel estimator, which exploits knowledge of the sum antenna main beam only. Performance of the AML-RELAX estimator is also compared with that of two monopulse estimators for single and multiple target scenarios.

A continuous sampling plan using sums of conforming run‐lengths

AbstractA continuous sampling plan, CSP‐SUM, is proposed based on the use of sums of run‐lengths of conforming items for deciding when to switch between the phases of sampling inspection and 100% inspection. The conventional measures of performance of CSPs such as the average outgoing quality, average fraction inspected, and the proportion passed under sampling inspection are evaluated for CSP‐SUM. Using these and other measures, comparisons with some standard CSPs are provided and indicate better performance for CSP‐SUM. Comparisons are also made with a recently‐proposed CSP utilizing CUSUMs, termed CSP‐CUSUM, and indicate that the performance of CSP‐SUM can be close to that of CSP‐CUSUM. A table is provided to aid the choice of parameters for the operation of CSP‐SUM. It is recommended that a conforming run‐length control chart be maintained in parallel with CSP‐SUM to detect significant upward shifts in the fraction defective of the process. Copyright © 2003 John Wiley &amp; Sons, Ltd.

Large Second-Order Optical Nonlinearities in Open-Shell Chromophores. Planar Metal Complexes and Organic Radical Ion Aggregates

Attempts to discover molecular chromophores with large hyperpolarizabilities have largely focused on closed-shell organic species. This contribution explores the use of sum over states (SOS) perturbation theory and the computationally efficient intermediate neglect of differential overlap (INDO) model Hamiltonian, combined with single configuration interaction (SCI) techniques, to calculate frequency-dependent quadratic molecular hyperpolarizabilities of both coordination complexes and organic radical ion chromophore aggregates having open-shell doublet ground state electronic structures. The correct evaluation of the lowest-lying excited states has been tested by comparison with experimental optical spectra. In the cases considered here, the INDO/SCI-SOS method provides both a good description of linear optical transitions and an adequate prediction of second-order nonlinearity. It is seen that the larger second-order nonlinearities of systems having open-shell electronic states, as compared to those having analogous closed-shell structures, are a consequence of accessible lower-lying charge-transfer excited electronic states. The INDO/SCI-SOS model is attractive for designing new, highly efficient open-shell second-order nonlinear optical chromophores.

Upconverting time gate for imaging through highly scattering media

We report the use of sum- and difference-frequency generation for two-dimensional upconversion time gating. Using difference-frequency generation, which can provide gain as well as upconversion (as an optical parametric amplifier), we have imaged through a scattering medium with an attenuation of exp(−25), using 1 mJ of energy from a single laser pulse.

Hinging hyperplanes for regression, classification, and function approximation

A hinge function y=h(x) consists of two hyperplanes continuously joined together at a hinge. In regression (prediction), classification (pattern recognition), and noiseless function approximation, use of sums of hinge functions gives a powerful and efficient alternative to neural networks with computation times several orders of magnitude less than is obtained by fitting neural networks with a comparable number of parameters. A simple and effective method for finding good hinges is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>