multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

co registration and distortion correction of diffusion and anatomical images based on inverse contrast normalization diffusion mri provides quantitative information about microstructural properties which can be useful in neuroimaging studies of the human brain echo planar imaging epi sequences which are frequently used for acquisition of diffusion images are sensitive to inhomogeneities in the primary magnetic b0 field that cause localized distortions in the reconstructed images we describe and evaluate a new method for correction of susceptibility induced distortion in diffusion images in the absence of an accurate b0 fieldmap in our method the distortion field is estimated using a constrained non rigid registration between an undistorted t1 weighted anatomical image and one of the distorted epi images from diffusion acquisition our registration framework is based on a new approach inversion inverse contrast normalization for very simple registration which exploits the inverted contrast relationship between t1 and t2 weighted brain images to define a simple and robust similarity measure we also describe how inversion can be used for rigid alignment of diffusion images and t1 weighted anatomical images our approach is evaluated with multiple in vivo datasets acquired with different acquisition parameters compared to other methods inversion shows robust and consistent performance in rigid registration and shows improved alignment of diffusion and anatomical images relative to normalized mutual information for non rigid distortion correction

the monadic second order logic of graphs ix machines and their behaviours abstract we establish that every monadic second order property of the behaviour of a machine transition systems and tree automata are typical examples of machines is a monadic second order property of the machine itself in this way we clarify the distinction between dynamic properties of machines i e properties of their behaviours and their static properties i e properties of the graphs or relational structures representing them it is important for program verification that the dynamic properties that one wants to verify can be formulated statically in the simplest possible way as a corollary of our main result we also obtain that the monadic theory of an algebraic tree is decidable

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

parameterized and approximation complexity of partial vc dimension abstract we introduce the problem partial vc dimension that asks given a hypergraph h x e and integers k and l whether one can select a set c x of k vertices of h such that the set e c e e of distinct hyperedge intersections with c has size at least l the sets e c define equivalence classes over e partial vc dimension is a generalization of vc dimension which corresponds to the case l 2 k and of distinguishing transversal which corresponds to the case l e the latter is also known as test cover in the dual hypergraph we also introduce the associated fixed cardinality maximization problem max partial vc dimension that aims at maximizing the number of equivalence classes induced by a solution set of k vertices we study the algorithmic complexity of partial vc dimension and max partial vc dimension both on general hypergraphs and on more restricted instances in particular neighborhood hypergraphs of graphs

hitting forbidden subgraphs in graphs of bounded treewidth we study the complexity of a generic hitting problem h subgraph hitting where given a fixed pattern graph h and an input graph g we seek for the minimum size of a set x v g that hits all subgraphs of g isomorphic to h in the colorful variant of the problem each vertex of g is precolored with some color from v h and we require to hit only h subgraphs with matching colors standard techniques e g courcelle s theorem show that for every fixed h and the problem is fixed parameter tractable parameterized by the treewidth of g however it is not clear how exactly the running time should depend on treewidth for the colorful variant we demonstrate matching upper and lower bounds showing that the dependence of the running time on treewidth of g is tightly governed by h the maximum size of a minimal vertex separator in h that is we show for every fixed h that on a graph of treewidth t the colorful problem can be solved in time 2 mathcal o t mu h cdot v g but cannot be solved in time 2 o t mu h cdot v g o 1 assuming the exponential time hypothesis eth furthermore we give some preliminary results showing that in the absence of colors the parameterized complexity landscape of h subgraph hitting is much richer

existential second order logic over graphs charting the tractability frontier fagin s theorem the first important result of descriptive complexity asserts that a property of graphs is in np if and only if it is definable by an existential second order formula in this article we study the complexity of evaluating existential second order formulas that belong to prefix classses of existential second order logic where a prefix class is the collection of all existential second order formulas in prenex normal form such that the second order and the first order quantifiers obey a certain quantifier pattern we completely characterize the computational complexity of prefix classes of existential second order logic in three different contexts 1 over directed graphs 2 over undirected graphs with self loops and 3 over undirected graphs without self loops our main result is that in each of these three contexts a dichotomy holds that is to say each prefix class of existential second order logic either contains sentences that can express np complete problems or each of its sentences expresses a polynomial time solvable problem although the boundary of the dichotomy coincides for the first two cases it changes as one moves to undirected graphs without self loops the key difference is that a certain prefix class based on the well known ackermann class of first order logic contains sentences that can express np complete problems over graphs of the first two types but becomes tractable over undirected graphs without self loops moreover establishing the dichotomy over undirected graphs without self loops turns out to be a technically challenging problem that requires the use of sophisticated machinery from graph theory and combinatorics including results about graphs of bounded tree width and ramsey s theorem

obtaining planarity by contracting few edges the planar contraction problem is to test whether a given graph can be made planar by using at most k edge contractions this problem is known to be np complete we show that it is fixed parameter tractable when parameterized by k

distortion correction in fetal epi using non rigid registration with a laplacian constraint geometric distortion induced by the main b0 field disrupts the consistency of fetal echo planar imaging epi data on which diffusion and functional magnetic resonance imaging is based in this paper we present a novel data driven method for simultaneous motion and distortion correction of fetal epi a motion corrected and reconstructed t2 weighted single shot fast spin echo ssfse volume is used as a model of undistorted fetal brain anatomy our algorithm interleaves two registration steps estimation of fetal motion parameters by aligning epi slices to the model and deformable registration of epi slices to slices simulated from the undistorted model to estimate the distortion field the deformable registration is regularized by a physically inspired laplacian constraint to model distortion induced by a source free background b0 field our experiments show that distortion correction significantly improves consistency of reconstructed epi volumes with ssfse volumes in addition the estimated distortion fields are consistent with fields calculated from acquired field maps and the laplacian constraint is essential for estimation of plausible distortion fields the epi volumes reconstructed from different scans of the same subject were more consistent when the proposed method was used in comparison with epi volumes reconstructed from data distortion corrected using a separately acquired b0 field map

single shot compensation of image distortions and bold contrast optimization using multi echo epi for real time fmri abstract functional magnetic resonance imaging fmri is most commonly based on echo planar imaging epi with higher field strengths gradient performance and computational power real time fmri has become feasible that is brain activation can be monitored during the ongoing scan however epi suffers from geometric distortions due to inhomogeneities of the magnetic field especially close to air tissue interfaces thus functional activations might be mislocalized and assigned to the wrong anatomical structures several techniques have been reported which reduce geometric distortions for example mapping of the static magnetic field b0 or the point spread function for all voxels yet these techniques require additional reference scans and in some cases extensive computational time moreover only static field inhomogeneities can be corrected because the correction is based on a static reference scan we present an approach which allows for simultaneous acquisition and distortion correction of a functional image without a reference scan the technique is based on a modified multi echo epi data acquisition scheme using a phase encoding pe gradient with alternating polarity the images exhibit opposite distortions due to the inverted pe gradient after adjusting the contrast of the images acquired at different echo times this information is used for the distortion correction we present the theory implementation and applications of this single shot distortion correction significant reduction in geometric distortion is shown both for phantom images and human fmri data moreover sensitivity to the blood oxygen level dependent bold effect is increased by weighted summation of the undistorted images

unwarping of unidirectionally distorted epi images echo planar imaging epi is a fast nuclear magnetic resonance imaging mri method unfortunately local magnetic field inhomogeneities induced mainly by the subject s presence cause significant geometrical distortion predominantly along the phase encoding direction which must be undone to allow for meaningful further processing so far this aspect has been too often neglected in this paper the authors suggest a new approach using an algorithm specifically developed for the automatic registration of distorted epi images with corresponding anatomically correct mri images they model the deformation field with splines which gives us a great deal of flexibility while comprising the affine transform as a special case the registration criterion is least squares interestingly the complexity of its evaluation does not depend on the resolution of the control grid the spline model gives the authors good accuracy thanks to its high approximation order the short support of splines leads to a fast algorithm a multiresolution approach yields robustness and additional speedup the algorithm was tested on real as well as synthetic data and the results were compared with a manual method a wavelet based sobolev type random deformation generator was developed for testing purposes a blind test indicates that the proposed automatic method is faster more reliable and more precise than the manual one

multi tissue constrained spherical deconvolution for improved analysis of multi shell diffusion mri data constrained spherical deconvolution csd has become one of the most widely used methods to extract white matter wm fibre orientation information from diffusion weighted mri dw mri data overcoming the crossing fibre limitations inherent in the diffusion tensor model it is routinely used to obtain high quality fibre orientation distribution function fodf estimates and fibre tractograms and is increasingly used to obtain apparent fibre density afd measures unfortunately csd typically only supports data acquired on a single shell in q space with multi shell data becoming more and more prevalent there is a growing need for csd to fully support such data furthermore csd can only provide high quality fodf estimates in voxels containing wm only in voxels containing other tissue types such as grey matter gm and cerebrospinal fluid csf the wm response function may no longer be appropriate and spherical deconvolution produces unreliable noisy fodf estimates the aim of this study is to incorporate support for multi shell data into the csd approach as well as to exploit the unique b value dependencies of the different tissue types to estimate a multi tissue odf the resulting approach is dubbed multi shell multi tissue csd msmt csd and is compared to the state of the art single shell single tissue csd ssst csd approach using both simulations and real data we show that msmt csd can produce reliable wm gm csf volume fraction maps directly from the dw data whereas ssst csd has a tendency to overestimate the wm volume in voxels containing gm and or csf in addition compared to ssst csd msmt csd can substantially increase the precision of the fodf fibre orientations and reduce the presence of spurious fodf peaks in voxels containing gm and or csf both effects translate into more reliable afd measures and tractography results with msmt csd compared to ssst csd

a bayesian approach to robust adaptive beamforming an adaptive beamformer that is robust to uncertainty in source direction of arrival doa is derived using a bayesian approach the doa is assumed to be a discrete random variable with a known a priori probability density function pdf that reflects the level of uncertainty in the source doa the resulting beamformer is a weighted sum of minimum variance distortionless response mvdr beamformers pointed at a set of candidate doas where the relative contribution of each mvdr beamformer is determined from the a posteriori pdf of the doa conditioned on previously observed data a simple approximation to the a posteriori pdf results in a straightforward implementation performance of the approximate bayesian beamformer is compared with linearly constrained minimum variance lcmv beamformers and data driven approaches that attempt to estimate signal characteristics or the steering vector from the data

counting modulo quantifiers on finite structures we give a combinatorial method for proving elementary equivalence in first order logic fo with counting modulo n quantifiers dn inexpressibility results for fo dn with built in linear order are also considered for instance the class of linear orders of length divisible by n 1 cannot be expressed in fo dn using this result we prove that comparing cardinalities or connectivity of ordered graphs are not definable in fo dn we also show that the height of complete n ary trees cannot be expressed in fo dn with linear order interpreting the predicate y nx as a complete n ary tree we show that the predicate y px cannot be defined in fo dn with linear order whenever p has a prime factor that does not divide n this solves the problem raised by niwi ski and stolboushkin lics 93 we also discuss a connection between our results and the well known open problem in circuit complexity theory whether acc nc1

calibration free b0 correction of epi data using structured low rank matrix recovery we introduce a structured low rank algorithm for the calibration free compensation of field inhomogeneity artifacts in echo planar imaging epi mri data we acquire the data using two epi readouts that differ in echo time using time segmentation we reformulate the field inhomogeneity compensation problem as the recovery of an image time series from highly undersampled fourier measurements the temporal profile at each pixel is modeled as a single exponential which is exploited to fill in the missing entries we show that the exponential behavior at each pixel along with the spatial smoothness of the exponential parameters can be exploited to derive a 3 d annihilation relation in the fourier domain this relation translates to a low rank property on a structured multi fold toeplitz matrix whose entries correspond to the measured k space samples we introduce a fast two step algorithm for the completion of the toeplitz matrix from the available samples in the first step we estimate the null space vectors of the toeplitz matrix using only its fully sampled rows the null space is then used to estimate the signal subspace which facilitates the efficient recovery of the time series of images we finally demonstrate the proposed approach on spherical mr phantom data and human data and show that the artifacts are significantly reduced

simultaneous multi scale diffusion estimation and tractography guided by entropy spectrum pathways we have developed a method for the simultaneous estimation of local diffusion and the global fiber tracts based upon the information entropy flow that computes the maximum entropy trajectories between locations and depends upon the global structure of the multi dimensional and multi modal diffusion field computation of the entropy spectrum pathways requires only solving a simple eigenvector problem for the probability distribution for which efficient numerical routines exist and a straight forward integration of the probability conservation through ray tracing of the convective modes guided by a global structure of the entropy spectrum coupled with a small scale local diffusion the intervoxel diffusion is sampled by multi b shell multi q angle diffusion weighted imaging data expanded in spherical waves this novel approach to fiber tracking incorporates global information about multiple fiber crossings in every individual voxel and ranks it in the most scientifically rigorous way this method has potential significance for a wide range of applications including studies of brain connectivity

towards fixed parameter tractable algorithms for abstract argumentation abstract argumentation frameworks have received a lot of interest in recent years most computational problems in this area are intractable but several tractable fragments have been identified in particular dunne showed that many problems can be solved in linear time for argumentation frameworks of bounded tree width however these tractability results which were obtained via courcelle s theorem do not directly lead to efficient algorithms the goal of this paper is to turn the theoretical tractability results into efficient algorithms and to explore the potential of directed notions of tree width for defining larger tractable fragments as a by product we will sharpen some known complexity results

maximally robust capon beamformer the standard capon beamformer scb achieves the maximum output signal to interference plus noise ratio in the error free case however estimation errors of the signal steering vector and the array covariance matrix can result in severe performance deteriorations of the scb especially if the training data contains the desired signal component a popular technique to improve the robustness against model errors is to compute the capon beamformer with the maximum output power considering an uncertainty set for the signal steering vector however maximizing the total beamformer output power may result in an insufficient suppression of interferers and noise as an alternative approach to mitigate the detrimental effect of model errors we propose to compute the capon beamformer with the minimum sensitivity considering the uncertainty set for the signal steering vector the proposed maximally robust capon beamformer mrcb is at least as robust as the maximum output power capon beamformer with the same uncertainty set for the signal steering vector we show that the mrcb can be implemented efficiently using lagrange duality simulation results demonstrate that the mrcb outperforms state of the art robust adaptive beamformers in many scenarios

an algebraic theory of graph reduction we show how membership in classes of graphs definable in monadic second order logic and of bounded treewidth can be decided by finite sets of terminating reduction rules the method is constructive in the sense that we describe an algorithm which will produce from a formula in monadic second order logic and an integer k such that the class defined by the formula is of treewidth k a set of rewrite rules that reduces any member of the class to one of finitely many graphs in a number of steps bounded by the size of the graph this reduction system corresponds to an algorithm that runs in time linear in the size of the graph

beamforming via nonconvex linear regression impulsive processes frequently occur in many fields such as radar sonar communications audio and speech processing and biomedical engineering in this paper we propose a nonconvex linear regression nlr based minimum dispersion beamforming technique for impulsive signals to achieve significant performance improvement over the conventional minimum variance beamformer the proposed beamformer minimizes the ell p norm of the output with p subject to a linear distortionless response constraint resulting in a difficult nonconvex and nonsmooth optimization problem the constrained optimization problem is first reduced to a multivariate linear regression via constraint elimination as a major contribution of this paper a coordinate descent algorithm cda is devised for solving the resultant nlr problem of ell p minimization with p at a computational complexity of cal o mn 2 where m is the number of sensors and n is the sample size at each inner iteration of the cda an efficient algorithm is designed to find the global minimum of each subproblem of univariate linear regression the convergence of the cda is analyzed the nlr beamformer with a single constraint is further generalized to the case of multiple linear constraints which is robust against model mismatch simulation results demonstrate the superior performance of nonconvex optimization based beamformer

high dimensional image registration using symmetric priors this paper is about warping a brain image from one subject the object image so that it matches another the template image a high dimensional model is used whereby a finite element approach is employed to estimate translations at the location of each voxel in the template image bayesian statistics are used to obtain a maximum a posteriori map estimate of the deformation field the validity of any registration method is largely based upon the constraints or in this instance priors incorporated into the model describing the transformations in this approach we assume that the priors should have some form of symmetry in that priors describing the probability distribution of the deformations should be identical to those for the inverses i e warping brain a to brain b should not be different probabilistically from warping b to a the fundamental assumption is that the probability of stretching a voxel by a factor of n is considered to be the same as the probability of shrinking n voxels by a factor of n 1 in the bayesian framework adopted here the priors are assumed to have a gibbs form where the gibbs potential is a penalty function that embodies this symmetry the penalty function of choice is based upon the singular values of the jacobian having a lognormal distribution this enforces a continuous one to one mapping a gradient descent algorithm is presented that incorporates the above priors in order to obtain a map estimate of the deformations we demonstrate this approach for the two dimensional case but the principles can be extended to three dimensions a number of examples are given to demonstrate how the method works

hitting minors on bounded treewidth graphs ii single exponential algorithms abstract for a finite collection of graphs f the f m deletion resp f tm deletion problem consists in given a graph g and an integer k decide whether there exists s v g with s k such that g s does not contain any of the graphs in f as a minor resp topological minor we are interested in the parameterized complexity of both problems when the parameter is the treewidth of g denoted by tw and specifically in the cases where f contains a single connected planar graph h we present algorithms running in time 2 o tw n o 1 called single exponential when h is either p 3 p 4 c 4 the paw the chair and the banner for both h m deletion and h tm deletion and when h k 1 i with i 1 for h tm deletion some of these algorithms use the rank based approach introduced by bodlaender et al 2015 7 this is the second of a series of articles on this topic and the results given here together with other ones allow us in particular to provide a tight dichotomy on the complexity of h m deletion in terms of h

size and treewidth bounds for conjunctive queries this article provides new worst case bounds for the size and treewith of the result q d of a conjunctive query q applied to a database d we derive bounds for the result size q d in terms of structural properties of q both in the absence and in the presence of keys and functional dependencies these bounds are based on a novel coloring of the query variables that associates a coloring number c q to each query q intuitively each color used represents some possible entropy of that variable using this coloring number we derive tight bounds for the size of q d in case i no functional dependencies or keys are specified and ii simple functional dependencies keys are given these results generalize recent size bounds for join queries obtained by atserias et al 2008 in the case of arbitrary compound functional dependencies we use tools from information theory to provide lower and upper bounds establishing a close connection between size bounds and a basic question in information theory our new coloring scheme also allows us to precisely characterize both in the absence of keys and with simple keys the treewidth preserving queries the queries for which the treewidth of the output relation is bounded by a function of the treewidth of the input database finally we give some results on the computational complexity of determining the size bounds and of deciding whether the treewidth is preserved

dr tamas diffeomorphic registration for tensor accurate alignment of anatomical structures in this work we propose dr tamas diffeomorphic registration for tensor accurate alignment of anatomical structures a novel framework for intersubject registration of diffusion tensor imaging dti data sets this framework is optimized for brain data and its main goal is to achieve an accurate alignment of all brain structures including white matter wm gray matter gm and spaces containing cerebrospinal fluid csf currently most dti based spatial normalization algorithms emphasize alignment of anisotropic structures while some diffusion derived metrics such as diffusion anisotropy and tensor eigenvector orientation are highly informative for proper alignment of wm other tensor metrics such as the trace or mean diffusivity md are fundamental for a proper alignment of gm and csf boundaries moreover it is desirable to include information from structural mri data e g t1 weighted or t2 weighted images which are usually available together with the diffusion data the fundamental property of dr tamas is to achieve global anatomical accuracy by incorporating in its cost function the most informative metrics locally another important feature of dr tamas is a symmetric time varying velocity based transformation model which enables it to account for potentially large anatomical variability in healthy subjects and patients the performance of dr tamas is evaluated with several data sets and compared with other widely used diffeomorphic image registration techniques employing both full tensor information and or dti derived scalar maps our results show that the proposed method has excellent overall performance in the entire brain while being equivalent to the best existing methods in wm

complexity of conflict free colorings of graphs we consider conflict free colorings of graph neighborhoods each vertex of the graph must be assigned a color so that for each vertex v there is at least one color appearing exactly once in the neighborhood of v the goal is to minimize the number of used colors we consider both the case of closed neighborhoods when the neighborhood of a node includes the node itself and the case of open neighborhoods when a node does not belong to its neighborhood in this paper we study complexity aspects of the problem we show that the problem of conflict free coloring of closed neighborhoods is np complete moreover we give non approximability results for the conflict free coloring of open neighborhoods from a positive point of view both problems become tractable if parameterized by the vertex cover number or the neighborhood diversity number of the graph we present simple algorithms which improve on existing results

parameterized algorithms for conflict free colorings of graphs abstract in this paper we study the conflict free coloring of graphs induced by neighborhoods a coloring of a graph is conflict free if every vertex has a uniquely colored vertex in its neighborhood the conflict free coloring problem is to color the vertices of a graph using the minimum number of colors such that the coloring is conflict free we consider both closed neighborhoods where the neighborhood of a vertex includes itself and open neighborhoods where a vertex does not include in its neighborhood we study the parameterized complexity of conflict free closed neighborhood coloring and conflict free open neighborhood coloring problems we show that both problems are fixed parameter tractable fpt when parameterized by the cluster vertex deletion number of the input graph this generalizes the result of gargano and rescigno theoretical computer science 2015 that conflict free coloring is fpt parameterized by the vertex cover number also we show that both problems admit an additive constant approximation algorithm when parameterized by the distance to threshold graphs we also study the complexity of the problem on special graph classes for split graphs we give a polynomial time algorithm for closed neighborhood conflict free coloring problem whereas we show that open neighborhood conflict free coloring is np complete for cographs we show that conflict free closed neighborhood coloring can be solved in polynomial time and conflict free open neighborhood coloring need at most three colors we show that interval graphs can be conflict free colored using at most four colors

extended hybrid space sense for epi off resonance and eddy current corrected joint interleaved blip up down reconstruction abstract introduction geometric distortions along the phase encode direction caused by off resonant spins are still a major issue in epi based functional and diffusion imaging if the off resonance map is known it is possible to correct for distortions most correction methods operate as a post processing step on the reconstructed magnitude images theory and methods here we present an algebraic reconstruction method hybrid space sense that incorporates a physics based model of off resonances phase inconsistencies between k space segments and t2 decay during the acquisition the method can be used to perform a joint reconstruction of interleaved acquisitions with normal blip up and inverted blip down phase encode direction which results in reduced g factor penalty results a joint blip up down simultaneous multi slice sms reconstruction for sms factor 4 in combination with twofold in plane acceleration leads to a factor of two decrease in maximum g factor penalty while providing off resonance and eddy current corrected images conclusion we provide an algebraic framework for reconstructing diffusion weighted epi data that in addition to the general applicability of hybrid space sense to 2d epi sms epi and 3d epi with arbitrary k space coverage along z allows for a modeling of arbitrary spatio temporal effects during the acquisition period like off resonances phase inconsistencies and t2 decay the most immediate benefit is a reduction in g factor penalty if an interleaved blip up down acquisition strategy is chosen which facilitates eddy current estimation and ensures no loss in k space encoding in regions with strong off resonance gradients

the recognizability of sets of graphs is a robust property once the set of finite graphs is equipped with an algebra structure arising from the definition of operations that generalize the concatenation of words one can define the notion of a recognizable set of graphs in terms of finite congruences applications to the construction of efficient algorithms and to the theory of context free sets of graphs follow naturally the class of recognizable sets depends on the signature of graph operations we consider three signatures related respectively to hyperedge replacement hr context free graph grammars to vertex replacement vr context free graph grammars and to modular decompositions of graphs we compare the corresponding classes of recognizable sets we show that they are robust in the sense that many variants of each signature where in particular operations are defined by quantifier free formulas a quite flexible framework yield the same notions of recognizability we prove that for graphs without large complete bipartite subgraphs hr recognizability and vr recognizability coincide the same combinatorial condition equates hr context free and vr context free sets of graphs inasmuch as possible results are formulated in the more general framework of relational structures

parallel algorithms with optimal speedup for bounded treewidth we describe the first parallel algorithm with optimal speedup for constructing minimum width tree decompositions of graphs of bounded treewidth on n vertex input graphs the algorithm works in o log n 2 time using o n operations on the erew pram we also give faster parallel algorithms with optimal speedup for the problem of deciding whether the treewidth of an input graph is bounded by a given constant and for a variety of problems on graphs of bounded treewidth including all decision problems expressible in monadic second order logic on n vertex input graphs the algorithms use o n operations together with o log n log n time on the erew pram or o log n time on the crcw pram

compatibility of unrooted phylogenetic trees is fpt a collection of t1 t2 tk of unrooted leaf labelled phylogenetic trees all with different leaf sets is said to be compatible if there exists a tree t such that each tree ti can be obtained from t by deleting leaves and contracting edges determining compatibility is np hard and the fastest algorithm to date has worst case complexity of around nk time n being the number of leaves here we present an o nf k algorithm proving that compatibility of unrooted phylogenetic trees is fixed parameter tractable fpt with respect to the number k of trees

the monadic second order logic of graphs xiv uniformly sparse graphs and edge set quantifications we consider the class usk of uniformly k sparse simple graphs i e the class of finite or countable simple graphs every finite subgraph of which has a number of edges bounded by k times the number of vertices we prove that for each k every monadic second order formula intended to express a graph property that uses variables denoting sets of edges can be effectively translated into a monadic second order formula where all set variables denote sets of vertices and that expresses the same property of the graphs in usk this result extends to the class of uniformly k sparse simple hypergraphs of rank at most m for any k and m it follows that every subclass of usk consisting of finite graphs of bounded clique width has bounded tree width clique width is a graph complexity measure similar to tree width and relevant to the construction of polynomial algorithms for np complete problems on special classes of graphs

large scale robust beamforming via ell _ infty minimization in this paper linearly constrained and robust ell infty norm beamforming techniques are proposed for non gaussian signals a conventional approach for ell infty minimization needs to solve a linear programming lp or second order cone programming socp however this strategy is computationally prohibitive for big data because the existing algorithms for lp or socp such as simplex method or interior point method can only solve small or medium scale problems in this paper the alternating direction method of multipliers admm is devised for large scale ell infty beamforming problems where the core subproblems can be formulated concisely as a linearly or second order cone constrained least squares and the proximity operator of the ell infty norm in each iteration remarkably a linear time complexity algorithm is devised that efficiently computes the ell infty norm proximity operator simulation results verify the high efficiency of the admm and the superiority of the ell infty norm beamforming techniques over several representative beamformers indicating that its performance can approach the optimal upper bound

image distortion correction in fmri a quantitative evaluation a well recognized problem with the echo planar imaging epi technique most commonly used for functional magnetic resonance imaging fmri studies is geometric distortion caused by magnetic field inhomogeneity this makes it difficult to achieve an accurate registration between a functional activation map calculated from an epi time series and an undistorted high resolution anatomical image a correction method based on mapping the spatial distribution of field inhomogeneities can be used to reduce these distortions this approach is attractive in its simplicity but requires postprocessing to improve the robustness of the acquired field map and reduce any secondary artifacts furthermore the distribution of the internal magnetic field throughout the head is position dependent resulting in an interaction between distortion and head motion therefore a single field map may not be sufficient to correct for the distortions throughout a whole fmri time series in this paper we present a quantitative evaluation of image distortion correction for fmri at 2t we assess i methods for the acquisition and calculation of field maps ii the effect of image distortion correction on the coregistration between anatomical and functional images and iii the interaction between distortion and head motion assessing the feasibility of using field maps to reduce this effect we propose that field maps with acceptable noise levels can be generated easily using a dual echo time epi sequence and demonstrate the importance of distortion correction for anatomical coregistration even for small distortions using a dual echo time series to generate a unique field map at each time point we characterize the interaction between head motion and geometric distortion however we suggest that the variance between successively measured field maps introduces additional unwanted variance in the voxel time series and is therefore not adequate to correct for time varying distortions

an inverse problem approach to the correction of distortion in epi images magnetic resonance imaging using the echo planar imaging epi technique is particularly sensitive to main b sub 0 field inhomogeneities the primary effect is geometrical distortion in the phase encoding direction here the authors present a method based on the conjugate gradient algorithm to correct for this geometrical distortion by solving the epi imaging equation two versions are presented one that attempts to solve the full four dimensional 4 d imaging equation and one that independently solves for each profile along the blip encoding direction results are presented for both phantom and in vivo brain epi images and compared with other proposed correction methods

uniform and nonuniform recognizability deterministic and nondeterministic finite state recognizability over finite structures are introduced in an algebraic setting avoiding detailed computational conventions as needed in the definition of finite state acceptors for deterministic recognizability the classical approach is adopted using a uniform homomorphism from the input domain consisting of terms into a finite algebra for the nondeterministic case we refer to relational input structures and to an acceptance via relational homomorphisms which are applied nonuniformly since they depend on the input structures we show how this approach encompasses known models of nondeterministic automata over finite words trees pictures and graphs and present some elementary metaresults connecting uniform recognizability nonuniform recognizability and monadic second order logic

the monadic second order logic of graphs x linear orderings graphs are finite and handled as relational structures we give some answers to the following general questions 1 1 for which classes of graphs c is it possible to specify a linear ordering of the set of vertices of each graph of c by fixed monadic second order formulas 2 2 for which classes of graphs c does there exist an extension l of monadic second order logic such that a subclass l of c is recognizable if and only if it is the class of graphs in c that satisfy a formula of l in this paper recognizability is understood in an algebraic sense relative to a finite set of graph operations and basic graphs that generate all graphs of c 3 3 for which classes of graphs c is it possible to construct in every graph of the class and by fixed formulas of a suitable extension of monadic second order logic its hierarchichal structure i e a finite term written with the operations and basic graphs of 2 that defines the considered graph applications concern dependency graphs of partially commutative words partial k paths cographs and graphs the modular decomposition of which uses prime graphs of bounded size

equivalences and transformations of regular systems applications to recursive program schemes and grammars abstract this work presents a unified theory of recursive program schemes context free grammars grammars on arbitrary algebraic structures and in fact recursive definitions of all kind by means of regular systems the equivalences of regular systems associated with either all their solutions or their least solutions in all domains of appropriate type satisfying a set of algebraic laws expressed by equations are systematically investigated and characterized in some cases in terms of system transformations by folding unfolding and rewriting according to the equational algebraic laws grammars are better characterized in terms of polynomial systems which are regular systems involving the operation of set union and the same questions are raised for them we also examine conditions insuring the uniqueness of the solution of a regular or of a polynomial system this theory applies to grammars of many kinds which generate trees graphs etc we formulate some classical transformations of context free grammars in terms of correct transformations which only use folding unfolding and algebraic laws and we immediately obtain their correctness

increasing the minimum degree of a graph by contractions abstract the degree contractibility problem is to test whether a given graph g can be modified to a graph of minimum degree at least d by using at most k contractions we prove the following three results first degree contractibility is np complete even when d 14 second it is fixed parameter tractable when parameterized by k and d third it is w 1 hard when parameterized by k we also study its variant where the input graph is weighted i e has some edge weighting and the contractions preserve these weights the weighted degree contractibility problem is to test if a weighted graph g can be contracted to a weighted graph of minimum weighted degree at least d by using at most k weighted contractions we show that this problem is np complete and that it is fixed parameter tractable when parameterized by k in addition we pinpoint a relationship with the problem of finding a minimal edge cut of maximum size in a graph and study the parameterized complexity of this problem and its variants

functional density and edge maps characterizing functional architecture in individuals and improving cross subject registration population level inferences and individual level analyses are two important aspects in functional magnetic resonance imaging fmri studies extracting reliable and informative features from fmri data that capture biologically meaningful inter subject variation is critical for aligning and comparing functional networks across subjects and connecting the properties of functional brain organization with variations in behavior cognition and genetics in this study we derive two new measures which we term functional density map and edge map and demonstrate their usefulness in characterizing the function of individual brains specifically using data from the human connectome project hcp we show that 1 both functional maps capture intrinsic properties of the functional connectivity pattern in individuals while exhibiting large variation across subjects 2 functional maps derived from either resting state or task evoked fmri can be used to accurately identify subjects from a population and 3 cross subject alignment using these functional maps considerably reduces functional variation and improves functional correspondence across subjects over state of the art multimodal registration algorithms our results suggest that the proposed functional density and edge maps are promising features in characterizing the functional architecture in individuals and provide an alternative way to explore the functional variation across subjects

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

deformable templates using large deformation kinematics a general automatic approach is presented for accommodating local shape variation when mapping a two dimensional 2 d or three dimensional 3 d template image into alignment with a topologically similar target image local shape variability is accommodated by applying a vector field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth globally positive definite jacobian smoothness is guaranteed without specifically penalizing large magnitude deformations of small subvolumes by constraining the transformation on the basis of a stokesian limit of the fluid dynamical navier stokes equations this differs fundamentally from quadratic penalty methods such as those based on linearized elasticity or thin plate splines in that stress restraining the motion relaxes over time allowing large magnitude deformations kinematic nonlinearities are inherently necessary to maintain continuity of structures during large magnitude deformations and are included in all results after initial global registration final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability

the role of planarity in connectivity problems parameterized by treewidth for some years it was believed that for connectivity problems such as hamiltonian cycle algorithms running in time 2 o tw n o 1 called single exponential existed only on planar and other topologically constrained graph classes where tw stands for the treewidth of the n vertex input graph this was recently disproved by cygan et al 3 focs 2011 bodlaender et al 1 icalp 2013 and fomin et al 11 soda 2014 who provided single exponential algorithms on general graphs for most connectivity problems that were known to be solvable in single exponential time on topologically constrained graphs in this article we further investigate the role of planarity in connectivity problems parameterized by treewidth and convey that several problems can indeed be distinguished according to their behavior on planar graphs known results from the literature imply that there exist problems like cycle packing that cannot be solved in time 2 o tw log tw n o 1 on general graphs but that can be solved in time 2 o tw n o 1 when restricted to planar graphs our main contribution is to show that there exist natural problems that can be solved in time 2 o tw log tw n o 1 on general graphs but that cannot be solved in time 2 o tw log tw n o 1 even when restricted to planar graphs furthermore we prove that planar cycle packing and planar disjoint pathscannot be solved in time 2 o tw n o 1 the mentioned negative results hold unless the eth fails we feel that our results constitute a first step in a subject that can be further exploited

a linear time algorithm for finding tree decompositions of small treewidth in this paper we give for constant k a linear time algorithm that given a graph g v e determines whether the treewidth of g is at most k and if so finds a tree decomposition of g with treewidth at most k a consequence is that every minor closed class of graphs that does not contain all planar graphs has a linear time recognition algorithm another consequence is that a similar result holds when we look instead for path decompositions with pathwidth at most some constant k

performance of dmi and eigenspace based beamformers the performance of the direct matrix inversion dmi method for antenna arrays of arbitrary geometry is analyzed by asymptotic statistical techniques the effects of eigenspace disturbance caused by finite samples on the output interference and noise powers are examined under the unit gain constraint in the direction of the desired signal the results show that the performance of the dmi method is degraded mostly by the disturbed noise subspace that suggests the use of an eigenspace based beamformer in which the weight vector is computed by using the signal plus interference subspace component of the sample correlation matrix convergence properties of the eigenspace based beamformer are evaluated for the cases in which the source number is known and in which it is overestimated theoretical analyses validated by computer simulations indicate that the eigenspace based beamformer has faster convergence rate than the dmi method

the monadic second order logic of graphs vii graphs as relational structures abstract relational structures form a unique framework in which various types of graphs and hypergraphs can be formalized and studied we define operations on structures that are compatible with monadic second order logic and that are powerful enough to represent context free graph and hypergraph grammars of various types namely the so called hyperedge replacement c ednce and separated handle rewriting grammars several results concerning monadic second order properties of the generated sets are obtained in a uniform way we also give a logical characterization of the equational sets of structures that generalizes the ones obtained by engelfriet and courcelle for hyperedge replacement and c ednce sets of graphs

syntactic recognizability of graphs with fuzzy attributes abstract we present a syntactic recognition theory for graphs with fuzzy edges and fuzzy nodes by employing the algebraic structure of magmoids several examples are illustrated and it is proved that the cut of a recognizable set of fuzzy graphs is not always recognizable as a set of crisp graphs the described theory is then applied for the recognition of fuzzy cognitive maps and the recognizability of interesting examples of sets of fuzzy cognitive maps is examined

second order cone programming second order cone programming socp problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the cartesian product of second order lorentz cones linear programs convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as socp problems as can many other problems that do not fall into these three categories these latter problems model applications from a broad range of fields from engineering control and finance to robust optimization and combinatorial optimization on the other hand semidefinite programming sdp that is the optimization problem over the intersection of an affine set and the cone of positive semidefinite matrices includes socp as a special case therefore socp falls between linear lp and quadratic qp programming and sdp like lp qp and sdp problems socp problems can be solved in polynomial time by interior point methods the computational effort per iteration required by these methods to solve socp problems is greater than that required to solve lp and qp problems but less than that required to solve sdp s of similar size and structure because the set of feasible solutions for an socp problem is not polyhedral as it is for lp and qp problems it is not readily apparent how to develop a simplex or simplex like method for socp while socp problems can be solved as sdp problems doing so is not advisable both on numerical grounds and computational complexity concerns for instance many of the problems presented in the survey paper of vandenberghe and boyd vb96 as examples of sdps can in fact be formulated as socps and should be solved as such in 2 3 below we give socp formulations for four of these examples the convex quadratically constrained quadratic programming qcqp problem problems involving fractional quadratic functions rutcor rutgers university e mail alizadeh rutcor rutgers edu research supported in part by the u s national science foundation grant ccr 9901991 ieor columbia university e mail gold ieor columbia edu research supported in part by the department of energy grant de fg02 92er25126 national science foundation grants dms 94 14438 cda 97 26385 and dms 01 04282

a model based method for retrospective correction of geometric distortions in diffusion weighted epi the self diffusion tensor may be calculated from several echo planar image acquisitions preceded by different diffusion gradients unfortunately these diffusion gradients cause geometric distortion that must be corrected before estimation of the tensor in the present paper we suggest and implement a method for retrospective correction of these distortions firmly based on a physical model for the diffusion weighted images this method simultaneously estimates subject movement and distortion parameters by finding the set of parameters that minimizes residual error when fitting data to the diffusion tensor model we show how this notion can be formalized as a quadratic form thereby facilitating the implementation of a rapid algorithm in addition we suggest models for how distortions vary with slice position and gradient direction that allow us to substantially reduce the dimensionality of the parameter space our results indicate that we are able to estimate both eddy current induced distortion and subject movement directly from the data without need of any additional measurements

the monadic second order logic of graphs i recognizable sets of finite graphs abstract the notion of a recognizable set of finite graphs is introduced every set of finite graphs that is definable in monadic second order logic is recognizable but not vice versa the monadic second order theory of a context free set of graphs is decidable

a novel adaptive beamformer based on semidefinite programming sdp with magnitude response constraints a novel robust adaptive beamformer formulated as a semidefinite programming sdp problem is proposed in this paper with new constraints on the magnitude response the beamwidth and response ripple of the robust response region can be well controlled moreover only a small part of these inequality constraints on the magnitude response are active during optimization so that few degrees of freedom dofs of the adaptive beamformer are consumed consequently the resultant beamformer has significant improvement on signal to interference plus noise ratio sinr an important problem in the proposed beamformer is how to generate the array weight vector from the optimal semidefinite matrix in this paper a method utilizing the extended spectral factorization method is proposed to solve this problem simple implementation flexible performance control as well as significant sinr enhancement support the practicability of the proposed method

robust minimum variance beamforming this paper introduces an extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response sources of this uncertainty include imprecise knowledge of the angle of arrival and uncertainty in the array manifold in our method uncertainty in the array manifold is explicitly modeled via an ellipsoid that gives the possible values of the array for a particular look direction we choose weights that minimize the total weighted power output of the array subject to the constraint that the gain should exceed unity for all array responses in this ellipsoid the robust weight selection process can be cast as a second order cone program that can be solved efficiently using lagrange multiplier techniques if the ellipsoid reduces to a single point the method coincides with capon s method we describe in detail several methods that can be used to derive an appropriate uncertainty ellipsoid for the array response we form separate uncertainty ellipsoids for each component in the signal path e g antenna electronics and then determine an aggregate uncertainty ellipsoid from these we give new results for modeling the element wise products of ellipsoids we demonstrate the robust beamforming and the ellipsoidal modeling methods with several numerical examples

dr buddi diffeomorphic registration for blip up blip down diffusion imaging method for correcting echo planar imaging distortions we propose an echo planar imaging epi distortion correction method dr buddi specialized for diffusion mri which uses data acquired twice with reversed phase encoding directions often referred to as blip up blip down acquisitions dr buddi can incorporate information from an undistorted structural mri and also use diffusion weighted images dwi to guide the registration improving the quality of the registration in the presence of large deformations and in white matter regions dr buddi does not require the transformations for correcting blip up and blip down images to be the exact inverse of each other imposing the theoretical blip up blip down distortion symmetry may not be appropriate in the presence of common clinical scanning artifacts such as motion ghosting gibbs ringing vibrations and low signal to noise the performance of dr buddi is evaluated with several data sets and compared to other existing blip up blip down correction approaches the proposed method is robust and generally outperforms existing approaches the inclusion of the dwis in the correction process proves to be important to obtain a reliable correction of distortions in the brain stem methods that do not use dwis may produce a visually appealing correction of the non diffusion weighted images but the directionally encoded color maps computed from the tensor reveal an abnormal anatomy of the white matter pathways

local search is a ptas for feedback vertex set in minor free graphs abstract we show that an extremely simple local search gives a ptas for the feedback vertex set fvs problem in minor free graphs it keeps exchanging a constant number of vertices to improve the current solution until a local optimum is reached the previous ptas by fomin lokshtanov raman and saurabh 1 despite theoretical efficiency is much more complicated in the sense that it combines many advanced algorithmic tools such as contraction decomposition framework by demaine and hajiaghayi 2 courcelle s theorem 3 and the robertson and seymour decomposition 4 our main technical contribution is to show that the local optimum only differs the global optimum by a 1 factor we do so by introducing steiner points those who are not in the local and optimal solutions to the standard analysis of local search we believe that our technique is of independent interest

block matching distortion correction of echo planar images with opposite phase encoding directions by shortening the acquisition time of mri echo planar imaging epi enables the acquisition of a large number of images in a short time compatible with clinical constraints as required for diffusion or functional mri however such images are subject to large local distortions disrupting their correspondence with the underlying anatomy the correction of those distortions is an open problem especially in regions where large deformations occur we propose a new block matching registration method to perform epi distortion correction based on the acquisition of two epi with opposite phase encoding directions ped it relies on new transformations between blocks adapted to the epi distortion model and on an adapted optimization scheme to ensure an opposite symmetric transformation we present qualitative and quantitative results of the block matching correction using different metrics on a phantom dataset and on in vivo data we show the ability of the block matching to robustly correct epi distortion even in strongly affected areas

an axiomatic definition of context free rewriting and its application to nlc graph grammars abstract an abstract notion of context free grammar is introduced it deals with abstract objects that can be words trees graphs or other combinatorial objects it is applied to nlc graph grammars introduced by rozenberg and janssens the monadic second order theory of a context free nlc set of graphs is decidable

monadic second order evaluations on tree decomposable graphs abstract every graph generated by a hyperedge replacement graph grammar can be represented by a tree namely the derivation tree of the derivation sequence that produced it certain functions on graphs can be computed recursively on the derivation trees of these graphs by using monadic second order logic and semiring homomorphisms we describe in a single formalism a large class of such functions polynomial and even linear algorithms can be constructed for some of these functions we unify similar results obtained by takamizawa 1982 bern 1987 arnborg 1991 and habel 1989

efficient computation of representative families with applications in parameterized and exact algorithms let m e i be a matroid and let s ls1 str be a family of subsets of e of size p a subfamily s s is q representative for s if for every set y e of size at most q if there is a set x s disjoint from y with x y i then there is a set x s disjoint from y with x y i by the classic result of bollobas in a uniform matroid every family of sets of size p has a q representative family with at most p qp sets in his famous two families theorem from 1977 lovasz proved that the same bound also holds for any matroid representable over a field f we give an efficient construction of a q representative family of size at most p qp in time bounded by a polynomial in p qp t and the time required for field operations we demonstrate how the efficient construction of representative families can be a powerful tool for designing single exponential parameterized and exact exponential time algorithms the applications of our approach include the following in the l ong d irected c ycle problem the input is a directed n vertex graph g and the positive integer k the task is to find a directed cycle of length at least k in g if such a cycle exists as a consequence of our 6 75k o k no 1 time algorithm we have that a directed cycle of length at least log n if such a cycle exists can be found in polynomial time in the m inimum e quivalent g raph meg problem we are seeking a spanning subdigraph d of a given n vertex digraph d with as few arcs as possible in which the reachability relation is the same as in the original digraph d we provide an alternative proof of the recent results for algorithms on graphs of bounded treewidth showing that many connectivity problems such as h amiltonian c ycle or s teiner t ree can be solved in time 2o t n on n vertex graphs of treewidth at most t for the special case of uniform matroids on n elements we give a faster algorithm to compute a representative family we use this algorithm to provide the fastest known deterministic parameterized algorithms for k p ath k t ree and more generally k s ubgraph i somorphism where the k vertex pattern graph is of constant treewidth

the monadic second order logic of graphs xii planar graphs and planar maps we prove that we can specify by formulas of monadic second order logic the unique planar embedding of a 3 connected planar graph if the planar graph is not 3 connected but given with a linear order of its set of edges we can also define a planar embedding by monadic second order formulas we cannot do so in general without the ordering even for 2 connected planar graphs the planar embedding of a graph can be specified by a relational structure called a map which is a graph enriched with a circular ordering of the edges incident with each vertex this circular ordering called a rotation system represents a planar embedding of the neighbourhood of each vertex for each connected map one can define a linear order on its vertices by formulas of monadic second order logic hence we have for planar graphs some kind of equivalence between linear orderings and planar embeddings

a family of generalized constant modulus algorithms for blind equalization by generalizing the definition of complex modulus this letter presents a family of generalized constant modulus algorithms whose special examples includes not only the well known constant modulus algorithm but also the recently proposed sign godard algorithm square contour algorithm sca generalized sca and sign sca

how to correct susceptibility distortions in spin echo echo planar images application to diffusion tensor imaging diffusion tensor imaging is often performed by acquiring a series of diffusion weighted spin echo echo planar images with different direction diffusion gradients a problem of echo planar images is the geometrical distortions that obtain near junctions between tissues of differing magnetic susceptibility this results in distorted diffusion tensor maps to resolve this we suggest acquiring two images for each diffusion gradient one with bottom up and one with top down traversal of k space in the phase encode direction this achieves the simultaneous goals of providing information on the underlying displacement field and intensity maps with adequate spatial sampling density even in distorted areas the resulting dt maps exhibit considerably higher geometric fidelity as assessed by comparison to an image volume acquired using a conventional 3d mr technique

boundary classes for graph problems involving non local properties abstract we continue the study of boundary classes for np hard problems and focus on seven np hard graph problems involving non local properties hamiltonian cycle hamiltonian cycle through specified edge hamiltonian path feedback vertex set connected vertex cover connected dominating set and graph vc con dimension our main result is the determination of the first boundary class for feedback vertex set we also determine boundary classes for hamiltonian cycle through specified edge and hamiltonian path and give some insights on the structure of some boundary classes for the remaining problems

robust adaptive beamforming for general rank signal models the performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment sources or sensor array this is especially true when the desired signal components are present in the beamformer training data snapshots because in this case the adaptive array performance is very sensitive to array and model imperfections the similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly but the training sample size is small we propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary type mismatches of the desired signal array response our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank one point source and higher rank scattered source fluctuating wavefront desired signal models the proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst case performance optimization simple closed form solutions to the considered robust adaptive beamforming problems are derived our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms while at the same time offer a significantly improved robustness and faster convergence rates

quantitative evaluation of image based distortion correction in diffusion tensor imaging a statistical method for the evaluation of image registration for a series of images based on the assessment of consistency properties of the registration results is proposed consistency is defined as the residual error of the composition of cyclic registrations by combining the transformations of different algorithms the consistency error allows a quantitative comparison without the use of ground truth specifically it allows a determination as to whether the algorithms are compatible and hence provide comparable registrations consistency testing is applied to evaluate retrospective correction of eddy current induced image distortion in diffusion tensor imaging of the brain in the literature several image transformations and similarity measures have been proposed generally showing a significant reduction of distortion in side by side comparison of parametric maps before and after registration transformations derived from imaging physics and a three dimensional affine transformation as well as mutual information mi and local correlation lc similarity are compared to each other by means of consistency testing the dedicated transformations could not demonstrate a significant difference for more than half of the series considered lc similarity is well suited for distortion correction providing more consistent registrations which are comparable to mi

quadratically constrained minimum dispersion beamforming via gradient projection a quadratically constrained minimum dispersion qcmd beamformer that is robust against model uncertainties is devised for non gaussian signals different from the minimum variance based beamformers the qcmd beamformer minimizes the ell p norm p geq 1 of the output while constraining the magnitude response of any steering vector within a spherical uncertainty set to exceed unity a gradient projection algorithmic framework is proposed to efficiently solve the resulting convex optimization problem instead of directly applying the standard optimization algorithm which has a high computational complexity in each iteration the gradient projection updates the solution along the gradient direction and projects it back to the constraint set importantly a closed form expression of the projection onto the constraint set is derived which only needs a low complexity of cal o m with m being the sensor number therefore the proposed algorithm is much faster and simpler to implement compared with the standard method in addition the robust constant modulus beamformer rcmb is also discussed as a special case of the qcmd beamformer simulation results demonstrate the efficiency of the gradient projection algorithm and superiority of the qcmd beamformer over several representative robust beamformers indicating that it can approach the optimal performance bound

new robust 3 d phase unwrapping algorithms application to magnetic field mapping and undistorting echoplanar images abstract the phase as well as the magnitude of mri images can carry useful information it may be used to encode flow or temperature or to map the magnetic field for the undistorting of epis and automated shimming in all cases we measure the extra spin given to nuclei unfortunately we can only measure the final phase of the spins the rotation is wrapped into the range and to obtain a measure of the parameter of interest the missing multiples of 2 must be replaced a process known as phase unwrapping while simple in principle standard phase unwrapping algorithms fail catastrophically in the presence of even small amounts of noise here we present a new algorithm for robust three dimensional phase unwrapping in which unwrapping is guided so that it initially works on less noisy regions we test the algorithm on simulated phase data and on maps of magnetic field which were then used to successfully undistort epi images the unwrapping algorithm could be directly applied to other kinds of phase data

on the parameterized complexity of recognizing well covered r l graph an r ell partition of a graph g is a partition of its vertex set into r independent sets and ell cliques a graph is r ell if it admits an r ell partition a graph is well covered if every maximal independent set is also maximum a graph is r ell well covered if it is both r ell and well covered in this paper we consider two different decision problems in the r ell well covered graph problem r ell wcg for short we are given a graph g and the question is whether g is an r ell well covered graph in the well covered r ell graph problem wc r ell g for short we are given an r ell graph g together with an r ell partition of v g into r independent sets and ell cliques and the question is whether g is well covered we classify most of these problems into p conp complete np complete np hard or conp hard only the cases wc r 0 g for r ge 3 remain open in addition we consider the parameterized complexity of these problems for several choices of parameters such as the size alpha of a maximum independent set of the input graph its neighborhood diversity or the number ell of cliques in an r ell partition in particular we show that the parameterized problem of deciding whether a general graph is well covered parameterized by alpha can be reduced to the wc 0 ell g problem parameterized by ell and we prove that this latter problem is in xp but does not admit polynomial kernels unless mathsf conp subseteq mathsf np mathsf poly

correction for direction dependent distortions in diffusion tensor imaging using matched magnetic field maps diffusion tensor imaging dti has seen increased usage in clinical and basic science research in the past decade by assessing the water diffusion anisotropy within biological tissues e g brain researchers can infer different fiber structures important for neural pathways a typical dti data set contains at least one base image and six diffusion weighted images along non collinear encoding directions the resultant images can then be combined to derive the three principal axes of the diffusion tensor and their respective cross terms which can in turn be used to compute fractional anisotropy fa maps apparent diffusion coefficient adc maps and to construct axonal fibers the above operations all assume that dti images along different diffusion weighting directions for the same brain register to each other without spatial distortions this assumption is generally false as the large diffusion weighting gradients would usually induce eddy currents to generate diffusion weighting direction dependent field gradients leading to mis registration within the dti data set traditional methods for correcting magnetic field induced distortions do not usually take into account these direction dependent eddy currents unique for dti and they are usually time consuming because multiple phase images need to be acquired in this report we describe our theory and implementation of an efficient and effective method to correct for the main field and eddy current induced direction dependent distortions for dti images under a unified framework to facilitate the daily practice of dti acquisitions

convexity constrained and nonnegativity constrained spherical factorization in diffusion weighted imaging diffusion weighted imaging dwi facilitates probing neural tissue structure non invasively by measuring its hindrance to water diffusion analysis of dwi is typically based on generative signal models for given tissue geometry and microstructural properties in this work we generalize multi tissue spherical deconvolution to a blind source separation problem under convexity and nonnegativity constraints this spherical factorization approach decomposes multi shell dwi data represented in the basis of spherical harmonics into tissue specific orientation distribution functions and corresponding response functions without assuming the latter as known thus fully unsupervised in healthy human brain data the resulting components are associated with white matter fibres grey matter and cerebrospinal fluid the factorization results are on par with state of the art supervised methods as demonstrated also in monte carlo simulations evaluating accuracy and precision of the estimated response functions and orientation distribution functions of each component in animal data and in the presence of oedema the proposed factorization is able to recover unseen tissue structure solely relying on dwi as such our method broadens the applicability of spherical deconvolution techniques to exploratory analysis of tissue structure in data where priors are uncertain or hard to define

robust beamforming by linear programming in this paper a robust linear programming beamformer rlpb is proposed for non gaussian signals in the presence of steering vector uncertainties unlike most of the existing beamforming techniques based on the minimum variance criterion the proposed rlpb minimizes the l norm of the output to exploit the non gaussianity we make use of a new definition of the lp norm 1 p of a complex valued vector which is based on the lp modulus of complex numbers to achieve robustness against steering vector mismatch the proposed method constrains the l modulus of the response of any steering vector within a specified uncertainty set to exceed unity the uncertainty set is modeled as a rhombus which differs from the spherical or ellipsoidal uncertainty region widely adopted in the literature the resulting optimization problem is cast as a linear programming and hence can be solved efficiently the proposed rlpb is computationally simpler than its robust counterparts requiring solution to a second order cone programming we also address the issue of appropriately choosing the uncertainty region size simulation results demonstrate the superiority of the proposed rlpb over several state of the art robust beamformers and show that its performance can approach the optimal performance bounds

integrated sense dti with correction of susceptibility and eddy current induced geometric distortions diffusion tensor imaging dti is vulnerable to geometric distortions caused by subject dependent susceptibility effects and diffusion weighting direction dependent eddy currents although the introduction of sensitivity encoding sense has reduced the overall distortions for the same imaging matrix size this benefit is offset by the increasing demand for higher spatial resolution thus significant distortions remain or are exacerbated in high resolution sense dti acquisitions while the susceptibility induced distortions cause global spatial misregistration the direction dependent eddy current induced distortions cause misregistration among different diffusion weighted images leading to errors in the derivation of the diffusion tensor in virtually all voxels and consequently in resulting diffusion parameters as well as in fiber tracking here we apply a comprehensive approach that corrects for both susceptibility and eddy current induced distortions to high resolution sense dti acquisitions and demonstrate its effectiveness efficiency and reliability in vivo as well as its advantages over a twice refocused spin echo sequence this method should find increased use in modern dti experiments where sense acquisitions are commonly used