recognition of white matter bundles using local and global streamline based registration and clustering virtual dissection of diffusion mri tractograms is cumbersome and needs extensive knowledge of white matter anatomy this virtual dissection often requires several inclusion and exclusion regions of interest that make it a process that is very hard to reproduce across experts having automated tools that can extract white matter bundles for tract based studies of large numbers of people is of great interest for neuroscience and neurosurgical planning the purpose of our proposed method named recobundles is to segment white matter bundles and make virtual dissection easier to perform this can help explore large tractograms from multiple persons directly in their native space recobundles leverages latest state of the art streamline based registration and clustering to recognize and extract bundles using prior bundle models recobundles uses bundle models as shape priors for detecting similar streamlines and bundles in tractograms recobundles is 100 streamline based is efficient to work with millions of streamlines and most importantly is robust and adaptive to incomplete data and bundles with missing components it is also robust to pathological brains with tumors and deformations we evaluated our results using multiple bundles and showed that recobundles is in good agreement with the neuroanatomical experts and generally produced more dense bundles across all the different experiments reported in this paper recobundles was able to identify the core parts of the bundles independently from tractography type deterministic or probabilistic or size thus recobundles can be a valuable method for exploring tractograms and facilitating tractometry studies

new refinements of the jensen inequalities based on samples with repetitions abstract in this paper we give a refinement of the jensen inequality for any mid convex function f by arithmetic means of f evaluated at arithmetic means of samples with repetitions the case of samples without repetitions was treated by j e pecaric and v volenec osterreich akad wiss math natur kl sonderdruck sitzungsber 197 1988 463 467

inequalities of hadamard s type for lipschitzian mappings and their applications in this paper we give some inequalities of hadamard s type for m lipschitzian functions some applications which are connected with arithmetic mean geometric mean harmonic mean logarithmical mean identric mean etc for two positive numbers are also given

mixed mean inequalities for several positive definite matrices on basis of the geometric mean proposed recently by t ando chi kwong li and roy mathias in this paper we present several kinds of mixed means for three or more positive definite matrices and prove some related mixed mean inequalities

on weighted hermite hadamard inequalities abstract in this paper we give a weighted form of the hermite hadamard inequalities some applications of them are also derived the results presented here would provide extensions of those given in earlier works finally we pose two interesting problems

two mappings in connection to hadamard s inequalities w are known in the literature as hadamard s inequalities we note that j hadamard was not the first who discovered them as is pointed out by d s mitrinovic and i b laekovic 3 the inequalities 1 are due to c hermite who obtained them in 1883 ten years before j hadamard in this paper by the use of mappings 2 and 4 we shall establish some refinements of 1 for other inequalities in connection to hadamard s result see 1 2 51 where further references are given

design of a fuzzy servo controller a design method of a fuzzy servo controller for nonlinear plants has been presented the proposed method is an error feedback scheme where the controller also receives signals representing the plant operating points integrator is used in the control loop to ensure setpoint following low frequency disturbance rejection and to enhance the robustness of the closed loop system a training scheme for the fuzzy controller is derived that minimizes the output error between a reference model and the plant the training is conducted off line for a class of setpoints conforming to the normal operating condition of the plant results of simulation studies are also presented

towards quantitative connectivity analysis reducing tractography biases diffusion mri tractography is often used to estimate structural connections between brain areas and there is a fast growing interest in quantifying these connections based on their position shape size and length however a portion of the connections reconstructed with tractography is biased by their position shape size and length thus connections reconstructed are not equally distributed in all white matter bundles quantitative measures of connectivity based on the streamline distribution in the brain such as streamline count density average length and spatial extent volume are biased by erroneous streamlines produced by tractography algorithms in this paper solutions are proposed to reduce biases in the streamline distribution first we propose to optimize tractography parameters in terms of connectivity then we propose to relax the tractography stopping criterion with a novel probabilistic stopping criterion and a particle filtering method both based on tissue partial volume estimation maps calculated from a t1 weighted image we show that optimizing tractography parameters stopping and seeding strategies can reduce the biases in position shape size and length of the streamline distribution these tractography biases are quantitatively reported using in vivo and synthetic data this is a critical step towards producing tractography results for quantitative structural connectivity analysis

refinements and similar extensions of hermite hadamard inequality for fractional integrals and their applications in this paper we establish some new refinements and similar extensions of hermite hadamard inequality for fractional integrals and present several applications in the beta function

on some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula some inequalities are presented here for differentiable convex mappings using hermite hadamard s integral inequality holding for convex functions a parallel development is deduced for differentiable concave functions some applications to special means of real numbers are also given finally some error estimates for the midpoint formula are obtained

hermite hadamard inequality for fuzzy integrals in this paper we prove a hermite hadamard type inequality for fuzzy integrals some examples are given to illustrate the results

control of nonlinear dynamical systems using neural networks ii observability identification and control for pt i see ibid vol 4 1993 this paper considers the problems of regulation and tracking of a dynamical system when the state variables of the dynamical system are not accessible the existence of the nonlinear maps describing the identifier and controller are first established and the implications for neural network realizations are described simulation results are included to complement the theoretical discussions

segmentation of brain mr images through a hidden markov random field model and the expectation maximization algorithm the finite mixture fm model is the most commonly used model for statistical segmentation of brain magnetic resonance mr images because of its simple mathematical form and the piecewise constant nature of ideal brain mr images however being a histogram based model the fm has an intrinsic limitation no spatial information is taken into account this causes the fm model to work only on well defined images with low levels of noise unfortunately this is often not the the case due to artifacts such as partial volume effect and bias field distortion under these conditions fm model based methods produce unreliable results here the authors propose a novel hidden markov random field hmrf model which is a stochastic process generated by a mrf whose state sequence cannot be observed directly but which can be indirectly estimated through observations mathematically it can be shown that the fm model is a degenerate version of the hmrf model the advantage of the hmrf model derives from the way in which the spatial information is encoded through the mutual influences of neighboring sites although mrf modeling has been employed in mr image segmentation by other researchers most reported methods are limited to using mrf as a general prior in an fm model based approach to fit the hmrf model an em algorithm is used the authors show that by incorporating both the hmrf model and the em algorithm into a hmrf em framework an accurate and robust segmentation can be achieved more importantly the hmrf em framework can easily be combined with other techniques as an example the authors show how the bias field correction algorithm of guillemaud and brady 1997 can be incorporated into this framework to achieve a three dimensional fully automated approach for brain mr image segmentation

fuzzy systems as universal approximators an additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy an additive fuzzy system approximates the function by covering its graph with fuzzy patches in the input output state space and averaging patches that overlap the fuzzy system computes a conditional expectation e y x if we view the fuzzy sets as random sets each fuzzy rule defines a fuzzy patch and connects commonsense knowledge with state space geometry neural or statistical clustering systems can approximate the unknown fuzzy patches from training data these adaptive fuzzy systems approximate a function at two levels at the local level the neural system approximates and tunes the fuzzy rules at the global level the rules or patches approximate the function

inequalities of hadamard s type for lipschitzian mappings in this paper we establish several inequalities of hadamard s type for lipschitzian mappings

tract based morphometry for white matter group analysis we introduce an automatic method that we call tract based morphometry or tbm for measurement and analysis of diffusion mri data along white matter fiber tracts using subject specific tractography bundle segmentations we generate an arc length parameterization of the bundle with point correspondences across all fibers and all subjects allowing tract based measurement and analysis in this paper we present a quantitative comparison of fiber coordinate systems from the literature and we introduce an improved optimal match method that reduces spatial distortion and improves intra and inter subject variability of fa measurements we propose a method for generating arc length correspondences across hemispheres enabling a tbm study of interhemispheric diffusion asymmetries in the arcuate fasciculus af and cingulum bundle cb the results of this study demonstrate that tbm can detect differences that may not be found by measuring means of scalar invariants in entire tracts such as the mean diffusivity md differences found in af we report tbm results of higher fractional anisotropy fa in the left hemisphere in af caused primarily by lower 3 the smallest eigenvalue of the diffusion tensor in the left af and higher left hemisphere fa in cb related to higher 1 the largest eigenvalue of the diffusion tensor in the left cb by mapping the significance levels onto the tractography trajectories for each structure we demonstrate the anatomical locations of the interhemispheric differences the tbm approach brings analysis of dti data into the clinically and neuroanatomically relevant framework of the tract anatomy

an application of hayashi s inequality for differentiable functions abstract in this paper we offer an application of hayashi s generalization of steffensen s inequality for differentiable functions as well as its connections with the celebrated hermite hadamard s integral inequality for convex functions some applications for special means are also given

self tuning control of non linear armax models a control weighted self tuning minimum variance controller with a non linear difference equation structure is described an extended recursive least squares estimation algorithm is employed to provide the adaptiveness performance analysis of the controller is discussed in terms of a cumulative loss function and high order correlation functions of the system input output and residual sequences simulation results from an experiment using a model identified from a real system are also provided

registration atlas estimation and variability analysis of white matter fiber bundles modeled as currents this paper proposes a generic framework for the registration the template estimation and the variability analysis of white matter fiber bundles extracted from diffusion images this framework is based on the metric on currents for the comparison of fiber bundles this metric measures anatomical differences between fiber bundles seen as global homologous structures across subjects it avoids the need to establish correspondences between points or between individual fibers of different bundles it can measure differences both in terms of the geometry of the bundles like its boundaries and in terms of the density of fibers within the bundle it is robust to fiber interruptions and reconnections in addition a recently introduced sparse approximation algorithm allows us to give an interpretable representation of the fiber bundles and their variations in the framework of currents first we used this metric to drive the registration between two sets of homologous fiber bundles of two different subjects a dense deformation of the underlying white matter is estimated which is constrained by the bundles seen as global anatomical landmarks by contrast the alignment obtained from image registration is driven only by the local gradient of the image second we propose a generative statistical model for the analysis of a collection of homologous bundles this model consistently estimates prototype fiber bundles called template which capture the anatomical invariants in the population a set of deformations which align the geometry of the template to that of each subject and a set of residual perturbations the statistical analysis of both the deformations and the residuals describe the anatomical variability in terms of geometry stretching torque etc and texture fiber density etc third this statistical modeling allows us to simulate new synthetic bundles according to the estimated variability this gives a way to interpret the anatomical features that the model detects consistently across the subjects this may be used to better understand the bias introduced by the fiber extraction methods and eventually to give anatomical characterization of the normal or pathological variability of fiber bundles

some inequalities for differentiable convex mapping with application to weighted trapezoidal formula and higher moments of random variables abstract several inequalities for differentiable convex wright convex and quasi convex mapping are obtained respectively that are connected with the celebrated hermite hadamard integral inequality also some error estimates for weighted trapezoid formula and higher moments of random variables are given

tracking and disturbance rejection of mimo nonlinear systems with pi controller we study tracking and disturbance rejection of a class of mimo nonlinear systems with linear proportional plus integral pi compensator roughly speaking we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady state i o map then a simple pi compensator can be used to yield a stable unity feedback closed loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors

deterministic and probabilistic tractography based on complex fibre orientation distributions we propose an integral concept for tractography to describe crossing and splitting fibre bundles based on the fibre orientation distribution function odf estimated from high angular resolution diffusion imaging hardi we show that in order to perform accurate probabilistic tractography one needs to use a fibre odf estimation and not the diffusion odf we use a new fibre odf estimation obtained from a sharpening deconvolution transform sdt of the diffusion odf reconstructed from q ball imaging qbi this sdt provides new insight into the relationship between the hardi signal the diffusion odf and the fibre odf we demonstrate that the sdt agrees with classical spherical deconvolution and improves the angular resolution of qbi another important contribution of this paper is the development of new deterministic and new probabilistic tractography algorithms using the full multidirectional information obtained through use of the fibre odf an extensive comparison study is performed on human brain datasets comparing our new deterministic and probabilistic tracking algorithms in complex fibre crossing regions finally as an application of our new probabilistic tracking we quantify the reconstruction of transcallosal fibres intersecting with the corona radiata and the superior longitudinal fasciculus in a group of eight subjects most current diffusion tensor imaging dti based methods neglect these fibres which might lead to incorrect interpretations of brain functions

some inequalities involving means and their converses using an idea of j sandor and v e s szabo an inequality of ky fan and its generalizations are proved we also establish some converses of these inequalities as consequences some well known inequalities are obtained

reproducibility of superficial white matter tracts using diffusion weighted imaging tractography human brain connection map is far from being complete in particular the study of the superficial white matter swm is an unachieved task its description is essential for the understanding of human brain function and the study of pathogenesis triggered by abnormal connectivity in this work we automatically created a multi subject atlas of swm diffusion based bundles of the whole brain for each subject the complete cortico cortical tractogram is first split into sub tractograms connecting pairs of gyri then intra subject shape based fiber clustering performs compression of each sub tractogram into a set of bundles proceeding further with shape based clustering provides a match of the bundles across subjects bundles found in most of the subjects are instantiated in the atlas to increase robustness this procedure was performed with two independent groups of subjects in order to discard bundles without match across the two independent atlases finally the resulting intersection atlas was projected on a third independent group of subjects in order to filter out bundles without reproducible and reliable projection the final multi subject diffusion based u fiber atlas is composed of 100 bundles in total 50 per hemisphere from which 35 are common to both hemispheres

properties of h convex functions related to the hermite hadamard fejer inequalities in this paper we prove the hermite hadamard fejer inequalities for an h convex function and we point out the results for some special classes of functions also some generalization of the hermite hadamard inequalities and some properties of functions h and f which are naturally joined to the h convex function are given finally applications on p logarithmic mean and mean of the order p are obtained

refinements of hadamard type inequalities for quasi convex functions with applications to trapezoidal formula and to special means in this paper some inequalities of hadamard s type for quasi convex functions are given some error estimates for the trapezoidal formula are obtained applications to some special means are considered

automatic fiber bundle segmentation in massive tractography datasets using a multi subject bundle atlas this paper presents a method for automatic segmentation of white matter fiber bundles from massive dmri tractography datasets the method is based on a multi subject bundle atlas derived from a two level intra subject and inter subject clustering strategy this atlas is a model of the brain white matter organization computed for a group of subjects made up of a set of generic fiber bundles that can be detected in most of the population each atlas bundle corresponds to several inter subject clusters manually labeled to account for subdivisions of the underlying pathways often presenting large variability across subjects an atlas bundle is represented by the multi subject list of the centroids of all intra subject clusters in order to get a good sampling of the shape and localization variability the atlas composed of 36 known deep white matter bundles and 47 superficial white matter bundles in each hemisphere was inferred from a first database of 12 brains it was successfully used to segment the deep white matter bundles in a second database of 20 brains and most of the superficial white matter bundles in 10 subjects of the same database