MATHEMATICAL FOUNDATION OF A NEW COMPLEXITY MEASURE

For many continuous bio-medieal signals with both strong nonlinearity and non-stationarity, two criterions were proposed for their complexity estimation ： （1） Only a short data set is enough for robust estimation; （2） No over-coarse graining preproeessing, such as transferring the original signal into a binary time series, is needed. Co complexity measure proposed by us previously is one of such measures. However, it lacks the solid mathematical foundation and thus its use is limited. A modified version of this measure is proposed, and some important properties are proved rigorously. According to these properties, this measure can be considered as an index of randomness of time series in some senses, and thus also a quantitative index of complexity under the meaning of randomness finding complexity. Compared with other similar measures, this measure seems more suitable for estimating a large quantity of complexity measures for a given task, such as studying the dynamic variation of such measures in sliding windows of a long process, owing to its fast speed for estimation.

Complexity analyses of multi-wing chaotic systems

The complexities of multi-wing chaotic systems based on the modified Chen system and a multi-segment quadratic function are investigated by employing the statistical complexity measure （SCM） and the spectral entropy （SE） algorithm. How to choose the parameters of the SCM and SE algorithms is discussed. The results show that the complexity of the multi-wing chaotic system does not increase as the number of wings increases, and it is consistent with the results of the Grassberger-Procaccia （GP） algorithm and the largest Lyapunov exponent （LLE） of the multi-wing chaotic system.

Photodynamic diagnostics of early gastric cancer:Complexity measures of gastric microcirculation and new model of metastatic adenocarcinoma of rat stomach

The detection of early gastric cancer that often develops asymptomatically is crucial for improving patient survival.The photodynamic diagnosis(PDD)of gastric cancer using 5-aminolevulinic acid/protoporphyrin IX(5-ALA/PpIX)has been reported in several studies.However,the selectivity of PDD of gastric tumor is poor with often false-positive results that require the development of new methods to improve PDD for early gastric cancer.Therefore,a measure of the complexity of gastric microcirculation(multi-scale entropy,MSE)and the detrendedfluctuation analysis(DFA)were applied as additional tools to detect early gastric cancer in rats.In this experimental study,we used our original model of metastatic adenocarcinoma in the stomach of a rat.To induce a gastric tumor,we used a long-term combination(for 9 months,which is 1/2 of the life of rats)of two natural factors,such as chronic stress(overpopulation being typical for modern cities)and the daily presence of nitrites in food and drinks,which are common ingredients added to processed meat andfish to help preserve food.Our results clearly show that both methods,namely,PDD using 5-ALA/PpIX and complexity/correlation analysis,can detect early gastric cancer,which was confirmed by histological analysis.Pre-cancerous areas in the stomach were detected as an intermediatefluorescent signal or MSE level between normal and malignant lesions of the stomach.However,in some cases,PDD with 5-ALA/PpIX produced a false-positivefluorescence of exogenousfluorophores due to its accumulation in benign and inflammatory areas of the mucosa.This fact indicates that the PDD itself is not sufficient for the correct diagnosis of gastric cancer,and the use of additional characteristics,e.g.,complexity measures or scaling exponents,can significantly improve the diagnostic accuracy of PDD of gastric cancer that should be confirmed in further clinical studies and applications.

Cyclomatic Complexity-Based Encapsulation, Data Hiding, and Separation of Concerns

Three design principles are prominent in software development-encapsulation, data hiding, and separation of concerns. These principles are used as subjective quality criteria for both procedural and object-oriented applications. The purpose of research is to quantify encapsulation, data hiding, and separation of concerns is quantified using cyclomatic-based metrics. As a result of this research, the derived design metrics, coefficient of encapsulation, coefficient of data hiding, and coefficient of separation of concerns, are defined and applied to production software indicating whether the software has low or high encapsulation, data hiding, and separation of concerns.

Banach Space Valued Martingales with Respect to Complex Measure and Their Inequalities

Let d μ=ψ d ν be a complex valued measure where ν is a non negative measure and ψ is a complex valued function which satisfies b + p or b + ∞∩a 1 condition. We prove some basic martingale inequalities such as B G inequalities, weak ( p,p) and strong (p,p) type inequalities for Banach space valued martingale with respect to complex measure μ .

Hydrothermal Reaction, Structure and Magnetic Properties of a Binuclear Cobalt Complex with N-donor Ligand:2-Methyldipyrido[3,2-f:2ˊ3ˊ-h]quinoxaline

One complex [Co1.5（C6H5CHCHCOO）3（Medpq）]·H2O（C6H5CHCHCOO = cinnamic acid, Medpq = 2-methyldipyrido[3,2-f：2,3-h]quinoxaline） 1 has been hydrothermally synthesized and structurally characterized by elemental analysis, IR spectrum, TG, single-crystal X-ray diffraction and magnetic susceptibility measurements. Complex 1 crystallizes in the triclinic system, space group P1, with a = 10.224（5）, b = 14.572（5）, c = 15.139（5）A, α = 112.704（5）, β = 97.168（5）, γ = 109.749（5）, V = 1871.8（13） 3 and Z = 2（at 293（2） K）. In the crystal structure, the Co（1） ion is hexa-coordinated with six atoms from three different cinnamic acid ligands and the symmetric three different cinnamic acid ligands; the Co（2） center adopts a coordination environment with two nitrogen atoms from Medpq ligand and four oxygen atoms from two different cinnamic ligands, assuming a slightly distorted octahedral geometry, respectively. The negative value of the Weiss constant indicates antiferromagnetic exchange interactions between the Co ions.

SOLUTIONS AND STABILITY OF A GENERALIZATION OF WILSON'S EQUATION

In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.

Spectral entropy analysis of different alpha band rhythms in relation to hand motor imagery

The event-related desynchronization/synchronization(ERD/ERS) time courses of lower and upper alpha band rhythms during hand motor imagery are investigated respectively by Fourier Sectral Entropy (FSE) in this paper. By analyzing one group of BCI competition data, it was found that FSE within upper alpha band displays a pronounced increase and decrease over contralateral and ipsilateral brain areas respectively at the onset of hand motor imagery, which is corresponding to the antagonistic ERD/ERS patterns in previous studies. Different from the upper alpha activity pattern, FSE within lower alpha band displays a consistent increase over both two hemispheres hand representative areas. The preliminary results show that FSE could disclose the different behaviors of the upper and lower alpha band rhythms so that a new idea with the complexity measure is provided to characterize functional dissociation of lower and upper frequency alpha rhythms in relation to hand motor imagery.

Complexity Measure Based on ProgramSlicing and Its Validation

The popular single-factor complexity measure cannot comprehensively reflect program complexity and the existing hybrid complexity measure cannot express the interactive behaviors of programs. To treat these problems, in this paper, we propose a complexity measure based on program slicing（CMBPS）. CMPBS not only can evaluate factors which affect program complexity such as the length of the program, control flow, data flow and data types of output variables, but also can give expression of the interactive relation between programs. And we also prove that CMBPS satisfies all of Weyuker properties. Compared with the popular complexity measures, CMBPS is a well-structured complexity measure.

Deep learning for complex displacement field measurement

Traction force microscopy(TFM)is one of the most successful and broadly-used force probing technologies to quantify the mechanical forces in living cells.The displacement recovery of the fluorescent beads within the gel substrate,which serve as the fiducial markers,is one of the key processes.The traditional methods of extracting beads displacements,such as PTV,PIV,and DIC,persistently suffer from mismatching and loss of high-frequency information while dealing with the complex deformation around the focal adhesions.However,this information is crucial for the further analysis since the cells mainly transmit the force to the extracellular surroundings through focal adhesions.In this paper,we introduced convolutional neural network(CNN)to solve the problem.We have generated the fluorescent images of the non-deformable fluorescent beads and the displacement fields with different spatial complexity to form the training dataset.Considering the special image feature of the fluorescent images and the deformation with high complexity,we have designed a customized network architecture called U-DICNet for the feature extraction and displacement estimation.The numerical simulation and real experiment show that U-DICNet outperforms the traditional methods(PTV,PIV,and DIC).Particularly,the proposed U-DICNet obtains a more reliable result for the analysis of the local complex deformation around the focal adhesions.

3D shape measurement of larger complex objects based on fringe cycle correction

The grating fringe on the reference plane is broadened in the intersecting axis system because of oblique-angle projection. In order to solve this problem, we study the theoretical model of the temporal phase unwrapping method based on the fringe cycle correction. We also study the 3D shape measurement theoretical model of the larger complex objects after considering the coordinate deviation and lens distortion. Experimental results demonstrate that the fringe cycle on the reference plane can be corrected to a constant value, the lens distortion can be corrected, and 3D shape of larger complex objects can be accurately measured.