Statistical Computations on Biological Rhythms I: Dissecting Variable Cycles and Computing Signature Phases in Activity-Event Time Series

We propose a computational methodology to compute and extract circadian rhythmic patterns from an individual animal’s activity-event time series. This lengthy dataset, composed of a sequential event history, contains an unknown number of latent rhythmic cycles of varying duration and missing waveform information. Our computations aim at identifying the onset signature phase which individually indicates a sharp event intensity surge, where a subject-night ends and a brand new cycle’s subject-day begins, and collectively induces a linearity manifesting the individual circadian rhythmicity and information about the average period. Based on the induced linearity, the least squares criterion is employed to choose an optimal sequence of computed onset signature phases among a finite collection derived from the hierarchical factor segmentation (HFS) algorithm. The multiple levels of coding schemes in the HFS algorithm are designed to extract contrasting patterns of aggregation against sparsity of activity events along the entire temporal axis. This optimal sequence dissects the whole time series into a sequence of rhythmic cycles without model assumptions or ad hoc behavioral definitions regarding the missing waveform information. The performance of our methodology is favorably compared with two popular approaches based on the periodogram in a simulation study and in real data analyses. The computer code and data used in this article are available on the JCGS webpage.     

On a Variational Model for Selective Image Segmentation of Features with Infinite Perimeter

Variational models provide reliable formulation for segmentation of features and their boundaries in an image, following the seminal work of Mumford-Shah (1989, Commun. Pure Appl. Math.) on dividing a general surface into piecewise smooth sub-surfaces. A central idea of models based on this work is to minimize the length of feature’s boundaries (i.e., H1 Hausdorff measure). However there exist problems with irregular and oscillatory object boundaries, where minimizing such a length is not appropriate, as noted by Barchiesi et al. (2010, SIAM J. Multiscale Model. Simu.) who proposed to miminize L2 Lebesgue measure of the γ-neighborhood of the boundaries. This paper presents a dual level set selective segmentation model based on Barchiesi et al. (2010) to automatically select a local feature instead of all global features. Our model uses two level set functions: a global level set which segments all boundaries, and the local level set which evolves and finds the boundary of the object closest to the geometric constraints. Using real life images with oscillatory boundaries, we show qualitative results demonstrating the effectiveness of the proposed method.     

Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set

The work reported in this paper addresses the challenge of the efficient and accurate defuzzification of discretised interval type-2 fuzzy sets. The exhaustive method of defuzzification for type-2 fuzzy sets is extremely slow, owing to its enormous computational complexity. Several approximate methods have been devised in response to this bottleneck. In this paper we survey four alternative strategies for defuzzifying an interval type-2 fuzzy set: (1) The Karnik–Mendel Iterative Procedure, (2) the Wu–Mendel Approximation, (3) the Greenfield–Chiclana Collapsing Defuzzifier, and (4) the Nie–Tan Method.We evaluated the different methods experimentally for accuracy, by means of a comparative study using six representative test sets with varied characteristics, using the exhaustive method as the standard. A preliminary ranking of the methods was achieved using a multi-criteria decision making methodology based on the assignment of weights according to performance. The ranking produced, in order of decreasing accuracy, is (1) the Collapsing Defuzzifier, (2) the Nie–Tan Method, (3) the Karnik–Mendel Iterative Procedure, and (4) the Wu–Mendel Approximation.Following that, a more rigorous analysis was undertaken by means of the Wilcoxon Nonparametric Test, in order to validate the preliminary test conclusions. It was found that there was no evidence of a significant difference between the accuracy of the Collapsing and Nie–Tan Methods, and between that of the Karnik–Mendel Iterative Procedure and the Wu–Mendel Approximation. However, there was evidence to suggest that the collapsing and Nie–Tan Methods are more accurate than the Karnik–Mendel Iterative Procedure and the Wu–Mendel Approximation.In relation to efficiency, each method’s computational complexity was analysed, resulting in a ranking (from least computationally complex to most computationally complex) as follows: (1) the Nie–Tan Method, (2) the Karnik–Mendel Iterative Procedure (lowest complexity possible), (3) the Greenfield–Chiclana Collapsing Defuzzifier, (4) the Karnik–Mendel Iterative Procedure (highest complexity possible), and (5) the Wu–Mendel Approximation.     

NMR Studies of Drugs. Applications of Achiral and Chiral Lanthanide Shift Reagents to a 5-Substituted-4-thiazolidinone

The 60 MHz ¹H NMR spectra of racemic 5-[[3,5-bis(1,1-dimethylethyl)-4-hydroxyphenyl]methyl]-4-thiazolidinone, 1, have been studied in CDCl₃ solution at 28° with the achiral lanthanide shift reagent (LSR), tris (6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedionato)europium (III), 2, and the chiral LSRs, tris[3-(heptafluoropropylhydroxymethylene)- (+)-camphoratojeuropium(III), 3, and tris[3-(trifluoromethylhydroxymethylene-(+) -camphorato]europium (III), 4, Significant enantiomeric shift differences were observed in the presence of added 3, for the aryl protons of 1 that should permit direct determination of enantiomeric excess. Relative magnitudes of lanthanide-induced shift for the different nuclei of 1 with the three LSRs are compared and discussed in terms of preferred LSR binding sites. A favored conformation of 1 with respect to rotation about the C(5)-CH₂ bond is suggested.     

The perturbed laplacian matrix of a graph

For a graph G, we define its perturbed Laplacian matrix as D?A(G) where A(G) is the adjacency matrix of G and D is an arbitrary diagonal matrix. Both the Laplacian matrix and the negative of the adjacency matrix are special instances of the perturbed Laplacian. Several well-known results, contained in the classical work of Fiedler and in more recent contributions of other authors are shown to be true, with suitable modifications, for the perturbed Laplacian. An appropriate generalization of the monotonicity property of a Fiedler vector for a tree is obtained. Some of the results are applied to interval graphs.     

The extended QUALIFLEX method for multiple criteria decision analysis based on interval type-2 fuzzy sets and applications to medical decision making

QUALIFLEX, a generalization of Jacquet-Lagreze’s permutation method, is a useful outranking method in decision analysis because of its flexibility with respect to cardinal and ordinal information. This paper develops an extended QUALIFLEX method for handling multiple criteria decision-making problems in the context of interval type-2 fuzzy sets. Interval type-2 fuzzy sets contain membership values that are crisp intervals, which are the most widely used of the higher order fuzzy sets because of their relative simplicity. Using the linguistic rating system converted into interval type-2 trapezoidal fuzzy numbers, the extended QUALIFLEX method investigates all possible permutations of the alternatives with respect to the level of concordance of the complete preference order. Based on a signed distance-based approach, this paper proposes the concordance/discordance index, the weighted concordance/discordance index, and the comprehensive concordance/discordance index as evaluative criteria of the chosen hypothesis for ranking the alternatives. The feasibility and applicability of the proposed methods are illustrated by a medical decision-making problem concerning acute inflammatory demyelinating disease, and a comparative analysis with another outranking approach is conducted to validate the effectiveness of the proposed methodology.     

Exact approaches for solving robust prize-collecting Steiner tree problems

In the Prize-Collecting Steiner Tree Problem (PCStT) we are given a set of customers with potential revenues and a set of possible links connecting these customers with fixed installation costs. The goal is to decide which customers to connect into a tree structure so that the sum of the link costs plus the revenues of the customers that are left out is minimized. The problem, as well as some of its variants, is used to model a wide range of applications in telecommunications, gas distribution networks, protein–protein interaction networks, or image segmentation.     

Supervised Domain Adaptation for Automated Semantic Segmentation of the Atrial Cavity

Atrial fibrillation (AF) is the most common cardiac arrhythmia. At present, cardiac ablation is the main treatment procedure for AF. To guide and plan this procedure, it is essential for clinicians to obtain patient-specific 3D geometrical models of the atria. For this, there is an interest in automatic image segmentation algorithms, such as deep learning (DL) methods, as opposed to manual segmentation, an error-prone and time-consuming method. However, to optimize DL algorithms, many annotated examples are required, increasing acquisition costs. The aim of this work is to develop automatic and high-performance computational models for left and right atrium (LA and RA) segmentation from a few labelled MRI volumetric images with a 3D Dual U-Net algorithm. For this, a supervised domain adaptation (SDA) method is introduced to infer knowledge from late gadolinium enhanced (LGE) MRI volumetric training samples (80 LA annotated samples) to a network trained with balanced steady-state free precession (bSSFP) MR images of limited number of annotations (19 RA and LA annotated samples). The resulting knowledge-transferred model SDA outperformed the same network trained from scratch in both RA (Dice equals 0.9160) and LA (Dice equals 0.8813) segmentation tasks.     

酶促水解法拆分布洛芬乙酯的工艺研究

以布洛芬乙酯为反应底物,探索了酶促水解法拆分布洛芬的工艺。以曲拉通X-100为表面活性剂,利用南极假丝酵母脂肪酶B（CAL-B）催化拆分外消旋布洛芬乙酯,并对表面活性剂含量、有机溶剂种类和添加量、酶量、缓冲溶液pH、温度及时间等反应条件进行了优化;得到的最佳反应条件为：在pH为9.0的缓冲溶液中,添加80 mg曲拉通X-100、50 μL二氯甲烷和15 mg CAL-B,于30℃下反应48 h;在该条件下,S-布洛芬乙酯的剩余率（C）为65%,布洛芬乙酯的对映体过量值（ees）为94%。     

A Clustering Approach for the Separation of Touching Edges in Particle Images

The occurrence of touching objects in images of particulate systems is very common especially in the absence of dispersion methods during image acquisition. The separation of these touching particles is essential before accurate estimation of particle size and shape can be achieved from these images. In the current work, clustering approaches based on the fuzzy C‐means algorithm are employed to identify the touching particle regions. Firstly, clustering in the multidimensional space of image features, e.g., standard deviation, gradient and range calculated in a certain neighborhood of each pixel, is performed to trap the touching regions. Then, in a novel proposed method, the clustering of pixel intensity itself into two fuzzy clusters is performed and a feature, referred to as the ‘Fuzzy Range', is calculated for each pixel from its membership values in both clusters and is presented as a distinguishing feature of the touching regions. Both approaches are compared and the superiority of the latter method in terms of the non‐necessity of neighborhood based calculations and minimum disfiguration is elucidated. The separation methods presented herein do not make any assumption about the shape of the particle as is undertaken in many methods reported elsewhere. The technique is proven to minimize greatly the deleterious effects of over‐segmentation, as is the case with traditional watershed segmentation techniques, and consequently, it results in a superior performance.