Deep brain implantable microelectrode arrays for detection and functional localization of the subthalamic nucleus in rats with Parkinson’s disease

The subthalamic nucleus(STN)is considered the best target for deep brain stimulation treatments of Parkinson’s disease(PD).It is difficult to localize the STN due to its small size and deep location.Multichannel microelectrode arrays(MEAs)can rapidly and precisely locate the STN,which is important for precise stimulation.In this paper,16-channel MEAs modified with multiwalled carbon nanotube/poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate)(MWCNT/PEDOT:PSS)nanocomposites were designed and fabricated,and the accurate and rapid identification of the STN in PD rats was performed using detection sites distributed at different brain depths.These results showed that nuclei in 6-hydroxydopamine hydrobromide(6-OHDA)-lesioned brains discharged more intensely than those in unlesioned brains.In addition,the MEA simultaneously acquired neural signals from both the STN and the upper or lower boundary nuclei of the STN.Moreover,higher values of spike firing rate,spike amplitude,local field potential(LFP)power,and beta oscillations were detected in the STN of the 6-OHDA-lesioned brain,and may therefore be biomarkers of STN localization.Compared with the STNs of unlesioned brains,the power spectral density of spikes and LFPs synchronously decreased in the delta band and increased in the beta band of 6-OHDA-lesioned brains.This may be a cause of sleep and motor disorders associated with PD.Overall,this work describes a new cellular-level localization and detection method and provides a tool for future studies of deep brain nuclei.

Function and Chromosomal Localization of Differentially Expressed Genes Induced by Marssonina brunnea f.sp.multigermtubi in Populus deltoides

A total of 1,160 differentially expressed genes induced by Marssonina brunnea f. sp. muhigermtubi were identified in Populus deltoides cv. ＇Lux＇ （1-69/55） with two-colour cDNA microarray including 2,952 cDNAs from two cDNA libraries constructed with 72 h inoculated poplar leaves. Functional analysis showed that 1,160 genes were classified into 11 functional categories that are involved in metabolism （15.9%）, signal transduction （9.5%）, transcription and replication （8.7%）, and cell rescue and defense （7.8%）. Among them, 926 genes were sporadically localized on 19 linkage groups. Chromosome 2 contained 102 （11%） differentially expressed genes, followed by chromosome 1 which contains 93 genes （10%）, and chromosome 17 had the least number of differentially expressed genes. Clustering of expressed sequence tags （ESTs） in poplar genome was observed at the terminal regions of several chromosomes. The relationship between cluster of genes and plant defense response would be further studied.

Differentiability of Convex Functions in Locally Convex Spaces（Ⅰ）──Continuous Convex Functions and Gateaux Differentiability

The aim of this paper is to investigate the differentiability(Gateaux differentiabllity and subdifferentiability) of continuous convex functions on locally convex spaces and to study the behaviour of some important results for this research area in locally convex spaces.

A STUDY ON THE WEIGHT FUNCTION OF THE MOVING LEAST SQUARE APPROXIMATION IN THE LOCAL BOUNDARY INTEGRAL EQUATION METHOD

The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.

Abnormal Local Activity and Functional Dysconnectivity in Patients with Schizophrenia Having Auditory Verbal Hallucinations

Auditory verbal hallucination(AVH)is emphasized as a pathological hallmark of schizophrenia.Neuroimaging studies provide evidence linking AVH to overlapping functional abnormalities in distributed networks.However,no clear conclusion has still been reached.This study aimed to further explore the brain activity of patients with schizophrenia having AVH from both local activity(LA)and functional connectivity(FC)insights,while excluding confounding factors from other positive symptoms.A total of 42 patients with AVH(AVH patients group,APG),26 without AVH(non-AVH patients group,NPG),and 82 normal controls(NC)underwent resting-state functional magnetic resonance imaging(fMRI).LA measures,including regional homogeneity(ReHo)and fractional amplitude of low-frequency fluctuations(fALFF),and FC measures were evaluated to understand the neuroimaging mechanism of AVH.APG showed increased ReHo and fALFF in the bilateral putamen(Put)compared with NPG and NC.FC analysis(using bilateral putamen as seeds)revealed that all patients showed abnormal FC of multiple resting state network regions,including the anterior and post cingulate cortex,middle frontal gyrus,inferior parietal gyrus,and left angular gyrus.Interestingly,APG showed significantly decreased FC of insula extending to the superior temporal gyrus and inferior frontal gyrus compared with NPG and NC.The present findings suggested a significant correlation of abnormal LA and dysfunctional putamen-auditory cortical connectivity with the neuropathological mechanism of AVH,providing evidence for the functional disconnection hypothesis of schizophrenia.

Functional anatomical hepatectomy guided by indocyanine green fluorescence imaging in patients with localized cholestasis:Report of four cases

BACKGROUND Liver cancer is a malignant tumor with a high incidence.At present,the most effective treatment is laparoscopic hepatectomy(LH).Indocyanine green fluorescence imaging(ICG-FI)has become an important tool in LH,and the most common fluorescent types of tumors are total fluorescence,partial fluorescence,and rim fluorescence.CASE SUMMARY We presented four cases of LH guided by ICG-FI in which we also observed the fourth special fluorescent type.When the tumor or intrahepatic stone compresses the adjacent bile duct to cause local cholestasis,the liver segment or subsegment with obstructed bile drainage will show strong fluorescence.Complete removal of the lesion together with the fluorescent liver parenchyma may help reduce the risk of tumor or stone recurrence.CONCLUSION This type of partial fluorescence can indicate local biliary compression,and the resection method is related to bile drainage,which may be called functional anatomical hepatectomy and ensures radical resection of the lesion.

LOCAL C-SEMIGROUPS AND LOCAL C-COSINE FUNCTIONS

This paper is concerned with the local C-semigroups and local C-cosine functions without the assumption that the image of C is dense in a Banach space X, First, the sufficient and necessary conditions for a local C-semigroup and a C-cosine function to be the restriction of a global C-semigroup and a global C-cosine function to an interval are given, respectively, Secondly, it is characterized for a closed operator to be the generator of a local C-semigroup and a local C-cosine function, respectively.

Extended Kantorovich method for local stresses in composite laminates upon polynomial stress functions

The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress functions. The stress fields are initially assumed by means of the Lekhnitskii stress functions under the plane strain state. Applying the principle of complementary virtual work,the coupled ordinary differential equations are obtained in which the solutions can be obtained by solving a generalized eigenvalue problem. Then an iterative procedure is established to achieve convergent stress distributions. It should be noted that the stress function based extended Kantorovich method can satisfy both the traction-free and free edge stress boundary conditions during the iterative processes. The stress components near the free edges and in the interior regions are calculated and compared with those obtained results by finite element method（FEM）. The convergent stresses have good agreements with those results obtained by three dimensional（3D） FEM. For generality, various layup configurations are considered for the numerical analysis. The results show that the proposed polynomial stress function based extended Kantorovich method is accurate and efficient in predicting the local stresses in composite laminates and computationally much more efficient than the 3D FEM.

MULTI-SCALE COHERENT STRUCTURES IN TURBULENT BOUNDARY LAYER DETECTED BY LOCALLY AVERAGED VELOCITY STRUCTURE FUNCTIONS

The time sequence of longitudinal velocity component at different vertical locations in turbulent boundary layer was finely measured in a wind tunnel. The concept of coarse_grained velocity structure functions, which describes the relative motions of straining and compressing for multi_scale eddy structures in turbulent flows, was put forward based on the theory of locally multi_scale average. Based on the consistency between coarse_grained velocity structure function and Harr wavelet transformation,detecting method was presented, by which the coherent structures and their intermittency was identified by multi_scale flatness factor calculated by locally average structure function. Phase_averaged evolution course for multi_scale coherent eddy structures in wall turbulence were extracted by this conditional sampling to educe scheme. The dynamics course of multi_scale coherent eddy structures and their effects on statistics of turbulent flows were studied.

Functionally Graded Cellular Structure Design Using the Subdomain Level Set Method with Local Volume Constraints

Functional graded cellular structure(FGCS)usually shows superiormechanical behaviorwith lowdensity and high stiffness.With the development of additivemanufacturing,functional graded cellular structure gains its popularity in industries.In this paper,a novel approach for designing functionally graded cellular structure is proposed based on a subdomain parameterized level set method(PLSM)under local volume constraints(LVC).In this method,a subdomain level set function is defined,parameterized and updated on each subdomain independently making the proposed approach much faster and more cost-effective.Additionally,the microstructures on arbitrary two adjacent subdomains can be connected perfectly without any additional constraint.Furthermore,the local volume constraint for each subdomain is applied by virtue of the augmented Lagrange multiplier method.Finally,several numerical examples are given to verify the correctness and effectiveness of the proposed approach in designing the functionally graded cellular structure.From the optimized results,it is also found that the number of local volume constraints has little influence on the convergence speed of the developed approach.

Construction Theory of Function on Local Fields

We establish the construction theory of function based upon a local field Kp as underlying space. By virture of the concept of pseudo-differential operator, we introduce ＂fractal calculus＂ （or, p-type calculus, or, Gibbs-Butzer calculus）. Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D（C Kp） and locally compact group Kp^＋-（= Kp）, so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type, and equivalent approximation theorems on the HOlder-type space C^σ（Kp）, σ 〉0, are proved; then the equivalent approximation theorem on Sobolev-type space Wr（Kp）, σ≥0, 1≤r 〈∞, is shown.

The nonlocal solution of two parallel cracks in functionally graded materials subjected to harmonic anti-plane shear waves

In this paper, the dynamic interaction of two parallel cracks in functionally graded materials （FGMs） is investigated by means of the non-local theory. To make the analysis tractable, the shear modulus and the material density are assumed to vary exponentially with the coordinate vertical to the crack. To reduce mathematical difficulties, a one-dimensional non-local kernel is used instead of a twodimensional one for the dynamic problem to obtain stress fields near the crack tips. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present at the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips. The present result provides theoretical references helpful for evaluating relevant strength and preventing material failure of FGMs with initial cracks. The magnitude of the finite stress field depends on relevant parameters, such as the crack length, the distance between two parallel cracks, the parameter describing the FGMs, the frequency of the incident waves and the lattice parameter of materials.

AN ALGORITHM TO MINIMIZED LOCALLY LIPSCHITZIAN FUNCTION

This paper gives a method of descent for the locally Lipschitzian function. It is assumed that the generalized subgradient set of the differentiable point is a singleton point. We introduce an implementable algorithm which is globally convergent. Numerical examples show the implementation and efficiency of the algorithm .

Functional localization of the cortical motor area in the brain Electrocorticogram analysis

The method for rapidly, precisely and non-invasively localizing functional regions of the brain is a problem in neuromedicine research. Cortical electrostimulation is the optimal localization method during brain surgery, with a degree of accuracy of approximately 5 mm. However, electrostimulation can damage the cerebral cortex, trigger epilepsy, and extend the operation time. Studies are required to determine whether cortical motor regions can be localized by wavelet analysis from electrocorticograms. In this study, based on wavelet analysis of electrocorticograms, a selection of algorithms for classification of the mu rhythm in the motor regions utilizing experimental data was verified. Results demonstrated that a characteristic quantity of energy ratio in the reconstructed signal was filtered in the d6 （7.81-15.62 Hz） band prior to and following motion events. A characteristic threshold was considered to be 40%. The accuracy of localization detection was 93%. The degree of accuracy was less than 5 mm. The present study avoided the problems of cerebral cortex injury and epilepsy onset, with an operation time of 60 seconds. Therefore, wavelet analysis on electrocorticogram is feasible for localizing cortical motor regions. Furthermore, this localization technique is accurate, safe and rapid.

REPRESENTATION OF ADDITIVE FUNCTIONALS AND LOCAL TIMES FOR JUMP MARKOV PROCESSES AND THEIR FUNCTIONAL LIMIT THEOREM

The representation of additive functionals and local times for jump Markov processes are obtained. The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.

Coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions

In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation function, Filippov solution of the neural network is defined. Based on Brouwer's fixed point theorem and definition of Mittag–Leffler stability, sufficient criteria are established to ensure the existence of (2k + 3)~n (k ≥ 1) equilibrium points, among which (k + 2)~n equilibrium points are locally Mittag–Leffler stable. Compared with the existing results, the derived results cover local Mittag–Leffler stability of both fractional-order and integral-order recurrent neural networks. Meanwhile discontinuous networks might have higher storage capacity than the continuous ones. Two numerical examples are elaborated to substantiate the effective of the theoretical results.

LOCAL MEDIAN ESTIMATION OF VARIANCE FUNCTION

This paper considers local median estimation in fixed design regression problems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong convergence rates of the proposed estimators are obtained. Simulation results are given to show the performance of the proposed methods.

CHAINS OF FUNCTION SPACES OVER EUCLIDIAN SPACES AND LOCAL FIELDS

The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function spaces' over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields.

The Theory of Vector-Valued Function in Locally Convex Space

In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and Cauchy integral formula are extended to the locally convex space.

Local Polynomial Estimation of Distribution Functions

Under the condition that the total distribution function is continuous and bounded on （ -∞,∞ ）, we constructed estimations for distribution and hazard functions with local polynomial method, and obtained the rate of strong convergence of the estimations.