statistical hough transform the standard hough transform is a popular method in image processing and is traditionally estimated using histograms densities modeled with histograms in high dimensional space and or with few observations can be very sparse and highly demanding in memory in this paper we propose first to extend the formulation to continuous kernel estimates second when dependencies in between variables are well taken into account the estimated density is also robust to noise and insensitive to the choice of the origin of the spatial coordinates finally our new statistical framework is unsupervised all needed parameters are automatically estimated and flexible priors can easily be attached to the observations we show experimentally that our new modeling encodes better the alignment content of images

non markovian quantum dynamics correlated projection superoperators and hilbert space averaging the time convolutionless tcl projection operator technique allows a systematic analysis of the non markovian quantum dynamics of open systems we present a class of projection superoperators that project the states of the total system onto certain correlated system environment states it is shown that the application of the tcl technique to this class of correlated superoperators enables the nonperturbative treatment of the dynamics of system environment models for which the standard approach fails in any finite order of the coupling strength we demonstrate further that the correlated superoperators correspond to the idea of a best guess of conditional quantum expectations which is determined by a suitable hilbert space average the general approach is illustrated by means of the model of a spin that interacts through randomly distributed couplings with a finite reservoir consisting of two energy bands extensive numerical simulations of the full schrodinger equation of the model reveal the power and efficiency of the method

the quantum state diffusion model applied to open systems a model of a quantum system interacting with its environment is proposed in which the system is represented by a state vector that satisfies a stochastic differential equation derived from a density operator equation such as the bloch equation and consistent with it the advantages of the numerical solution of these equations over the direct numerical solution of the density operator equations are described the method is applied to the nonlinear absorber cascades of quantum transitions second harmonic generation and a measurement reduction process the model provides graphic illustrations of these processes with statistical fluctuations that mimic those of experiments the stochastic differential equations originated from studies of the measurement problem in the foundations of quantum mechanics the model is compared with the quantum jump model of dalibard 1992 carmichael and others which originated among experimenters looking for intuitive pictures and rules of computation

on detection of multiple object instances using hough transforms hough transform based methods for detecting multiple objects use nonmaxima suppression or mode seeking to locate and distinguish peaks in hough images such postprocessing requires the tuning of many parameters and is often fragile especially when objects are located spatially close to each other in this paper we develop a new probabilistic framework for object detection which is related to the hough transform it shares the simplicity and wide applicability of the hough transform but at the same time bypasses the problem of multiple peak identification in hough images and permits detection of multiple objects without invoking nonmaximum suppression heuristics our experiments demonstrate that this method results in a significant improvement in detection accuracy both for the classical task of straight line detection and for a more modern category level pedestrian detection problem

a hough transform based line recognition method utilizing both parameter space and image space hough transform ht is recognized as a powerful tool for graphic element extraction from images due to its global vision and robustness in noisy or degraded environment however the application of ht has been limited to small size images for a long time besides the well known heavy computation in the accumulation the peak detection and the line verification become much more time consuming for large size images another limitation is that most existing ht based line recognition methods are not able to detect line thickness which is essential to large size images usually engineering drawings we believe these limitations arise from that these methods only work on the ht parameter space this paper therefore proposes a new ht based line recognition method which utilizes both the ht parameter space and the image space the proposed method devises an image based gradient prediction to accelerate the accumulation introduces a boundary recorder to eliminate redundant analyses in the line verification and develops an image based line verification algorithm to detect line thickness and reduce false detections as well it also proposes to use pixel removal to avoid overlapping lines instead of rigidly suppressing the nxn neighborhood we perform experiments on real images with different sizes in terms of speed and detection accuracy the experimental results demonstrate the significant performance improvement especially for large size images

closed form line segment extraction using the hough transform this paper proposes a novel closed form solution to complete line segment extraction given a voting angle in image space the voting distribution is analyzed and two functional relationships are deduced regarding the corresponding column in hough space voting along the distance axis is considered as being a random variable and voting values in cells are considered as forming a probability distribution statistical characteristics of this distribution are used to fit a quadratic polynomial curve and a linear curve direction length and width of a line segment are simultaneously computed in a closed form based on coefficients of fitted quadratic polynomial curves the midpoint of a line segment is determined based on the fitted linear curve the method is tested on simulated and real world images results show that the proposed closed form solution is feasible in the presence of quantization errors or image noise highlightswe proposed a method for obtaining the complete set of line segment parameters the direction length and width of a line segment are extracted simul taneously in a closed form we provided a complete theoretical derivation of voting variance with respect to voting angle the midpoint of a line segment is determined by the coefficients of the fitted linear curve parallel crossing and aligned line segments are discussed by analysing events in image space and hough space

real time line detection through an improved hough transform voting scheme the hough transform ht is a popular tool for line detection due to its robustness to noise and missing data however the computational cost associated to its voting scheme has prevented software implementations to achieve real time performance except for very small images many dedicated hardware designs have been proposed but such architectures restrict the image sizes they can handle we present an improved voting scheme for the ht that allows a software implementation to achieve real time performance even on relatively large images our approach operates on clusters of approximately collinear pixels for each cluster votes are cast using an oriented elliptical gaussian kernel that models the uncertainty associated with the best fitting line with respect to the corresponding cluster the proposed approach not only significantly improves the performance of the voting scheme but also produces a much cleaner voting map and makes the transform more robust to the detection of spurious lines

operator correlations and quantum regression theorem in non markovian lindblad rate equations non markovian lindblad rate equations arise from alternative microscopic interactions such as quantum systems coupled to composite reservoirs where extra degrees of freedom mediate the interaction between the system and a markovian reservoir as well as from systems coupled to complex structured reservoirs whose action can be well approximated by a direct sum of markovian sub reservoirs budini in phys rev a 74 053815 2006 the purpose of this paper is two fold first for both kinds of interactions we find general expressions for the system operator correlations written in terms of the lindblad rate propagator secondly we find the conditions under which a quantum regression hypothesis is valid we show that a non markovian quantum regression theorem can only be granted in a stationary regime being a necessary condition the fulfillment of a detailed balance condition this result is independent of the underlying microscopic interaction providing a criterion for the validity of the regression hypothesis in non markovian lindblad like master equations as an example we study the correlations of a two level system coupled to different kind of reservoirs

line fitting in a noisy image the conventional least squared distance method of fitting a line to a set of data points is unreliable when the amount of random noise in the input such as an image is significant compared with the amount of data correlated to the line itself points which are far away from the line outliers are usually just noise but they contribute the most to the distance averaging skewing the line from its correct position the author presents a statistical method of separating the data of interest from random noise using a maximum likelihood principle

collinear segment detection using ht neighborhoods in this paper geometrical analysis is used to extract novel straight line segment features from the wings around the peaks of the hough transform ht based on these features a practical segment detection method is proposed which has the ability to determine complete straight line segment parameters including the location of the center length slope and the euclidean distance to the origin the proposed method does not rely on edge point verification in the image space i e the complete set of segment features are determined only using the information embodied in the ht data the proposed method can distinguish between highly collinear straight line segments segment detection is robust to disturbing edge points especially ones collinear with the object a predefined collinear segment resolution that provides a theoretical criterion to determine straight line contiguity is derived image processing and analysis experiments show consistent robust performance

positivity preserving non markovian master equations a general class of integrodifferential non markovian master equations is developed which is representative of the dynamics of small subsystems interacting with open reservoirs with memory conditions which guarantee positivity of the subsystem reduced density are established

old and new straight line detectors description and comparison straight line detection is important in several fields such as robotics remote sensing and imagery the objective of this paper is to present several methods old and new used for straight line detection we begin by reviewing the standard hough transform sht then three new methods are suggested the revisited hough transform rht the parallel axis transform pat and the circle transform ct these transforms utilize a point line duality to detect straight lines in an image the rht and the pat should be faster than the sht and the ct because they use line segments whereas the sht uses sinusoids and ct uses circles moreover the pat rht and ct use additions and multiplications whereas the sht uses trigonometric functions sine and cosine for calculation to compare the methods we analyze the distribution of the frequencies in the accumulators and observe the effect on the detection of false local maxima we also compare the robustness to noise of the four transforms finally an example with a real image is given

a continuous counting observation and posterior quantum dynamics a stochastic model for a continuous photon counting measurement is proposed an equation for the generating functional of the statistics of counts is found a stochastic linear equation for the unnormalised posterior state vector of atoms continuously collapsing without mixing is derived by using quantum stochastic calculus methods

jump diffusion unravelling of a non markovian generalized lindblad master equation the correlated projection technique has been successfully applied to derive a large class of highly non markovian dynamics the so called non markovian generalized lindblad type equations or lindblad rate equations in this article general unravelings are presented for these equations described in terms of jump diffusion stochastic differential equations for wave functions we show also that the proposed unraveling can be interpreted in terms of measurements continuous in time but with some conceptual restrictions the main point in the measurement interpretation is that the structure itself of the underlying mathematical theory poses restrictions on what can be considered as observable and what is not such restrictions can be seen as the effect of some kind of superselection rule finally we develop a concrete example and discuss possible effects on the heterodyne spectrum of a two level system due to a structured thermal like bath with memory

line detection in images through regularized hough transform the problem of determining the location and orientation of straight lines in images is of great importance in the fields of computer vision and image processing traditionally the hough transform a special case of the radon transform has been widely used to solve this problem for binary images in this paper we pose the problem of detecting straight lines in gray scale images as an inverse problem our formulation is based on use of the inverse radon operator which relates the parameters determining the location and orientation of the lines in the image to the noisy input image the advantage of this formulation is that we can then approach the problem of line detection within a regularization framework and enhance the performance of the hough based line detector through the incorporation of prior information in the form of regularization we discuss the type of regularizers that are useful for this problem and derive efficient computational schemes to solve the resulting optimization problems enabling their use in large applications finally we show how our new approach can be alternatively viewed as one of finding an optimal representation of the noisy image in terms of elements chosen from a dictionary of lines this interpretation relates the problem of hough based line finding to the body of work on adaptive signal representation

combining several ordinal measures in clinical studies in medical research it is rare that a single variable is sufficient to represent all relevant aspects of epidemiological risk genomic activity adverse events or clinical response since biological systems tend to be neither linear nor hierarchical in nature the assumptions of traditional multivariate statistical methods based on the linear model can often not be justified on theoretical grounds establishing concept validity through empirical validation is not only problematic but also time consuming this paper proposes the use of u statistics for scoring multivariate ordinal data and a family of simple non parametric tests for analysis the scoring method is demonstrated to be applicable to scoring clinical response profiles in the treatment of psoriasis and then to identifying genomic pathways that best correlate with these profiles

continuous time open quantum random walks and non markovian lindblad master equations a new type of quantum random walks called open quantum random walks has been developed and studied in attal et al open quantum random walks preprint and central limit theorems for open quantum random walks preprint in this article we present a natural continuous time extension of these open quantum random walks this continuous time version is obtained by taking a continuous time limit of the discrete time open quantum random walks this approximation procedure is based on some adaptation of repeated quantum interactions theory attal and pautrat in annales henri poincare physique theorique 7 59 104 2006 coupled with the use of correlated projectors breuer in phys rev a 75 022103 2007 the limit evolutions obtained this way give rise to a particular type of quantum master equations these equations appeared originally in the non markovian generalization of the lindblad theory breuer in phys rev a 75 022103 2007 we also investigate the continuous time limits of the quantum trajectories associated with open quantum random walks we show that the limit evolutions in this context are described by jump stochastic differential equations finally we present a physical example which can be described in terms of open quantum random walks and their associated continuous time limits

hough transform modified by line connectivity and line thickness a modified hough transform based on a likelihood principle of connectivity and thickness is proposed for line detection it makes short as well as thick line segments easier to detect in a noisy image certain desirable properties of the new method are justified by theory and simulations

generalized pairwise comparisons of prioritized outcomes in the two sample problem this paper extends the idea behind the u statistic of the wilcoxon mann whitney test to perform generalized pairwise comparisons between two groups of observations the observations are outcomes captured by a single variable possibly repeatedly measured or by several variables of any type e g discrete continuous time to event when several outcomes are considered they must be prioritized we show that generalized pairwise comparisons extend well known non parametric tests and illustrate their interest using data from two randomized clinical trials we also show that they lead to a general measure of the difference between the groups called the proportion in favor of treatment denoted which is related to traditional measures of treatment effect for a single variable

new memory and computation efficient hough transform for detecting lines the slope intercept hough transform siht is one of the two types of line detection methods however the disadvantage of the siht is its low memory utilization say 50 based on the affine transformation this paper presents a new method to improve the memory utilization of the siht from 50 to 100 according to the proposed affine transformation we first present a basic siht based algorithm for detecting lines instead of concerning floating point operations in the basic siht based algorithm an improved siht based algorithm which mainly concerns integer operations is presented besides the memory utilization advantage experimental results reveal that the improved siht based algorithm has more than 60 execution time improvement ratio when compared to the basic siht based algorithm and has more than 33 execution time improvement ratio when compared to another type of line detection methods such as the r based ht algorithm and its variant the detailed complexity analyses for all the related algorithms are also investigated and we show that the time complexity required in the improved siht based algorithm is the least

power and sample size calculations for the wilcoxon mann whitney test in the presence of death censored observations we consider a clinical trial of a potentially lethal disease in which patients are randomly assigned to two treatment groups and are followed for a fixed period of time a continuous endpoint is measured at the end of follow up for some patients however death or severe disease progression may preclude measurement of the endpoint a statistical analysis that includes only patients with endpoint measurements may be biased an alternative analysis includes all randomized patients with rank scores assigned to the patients who are available for the endpoint measurement on the basis of the magnitude of their responses and with worst rank scores assigned to those patients whose death precluded the measurement of the continuous endpoint the worst rank scores are worse than all observed rank scores the treatment effect is then evaluated using the wilcoxon mann whitney test in this paper we derive closed form formulae for the power and sample size of the wilcoxon mann whitney test when missing measurements of the continuous endpoints because of death are replaced by worst rank scores we distinguish two approaches for assigning the worst rank scores in the tied worst rank approach all deaths are weighted equally and the worst rank scores are set to a single value that is worse than all measured responses in the untied worst rank approach the worst rank scores further rank patients according to their time of death so that an earlier death is considered worse than a later death which in turn is worse than all measured responses in addition we propose four methods for the implementation of the sample size formulae for a trial with expected early death we conduct monte carlo simulation studies to evaluate the accuracy of our power and sample size formulae and to compare the four sample size estimation methods

semi automatic spline fitting of planar curvilinear profiles in digital images using the hough transform abstract we develop a novel method for the recognition of curvilinear profiles in digital images the proposed method semi automatic for both closed and open planar profiles essentially consists of a preprocessing step exploiting an edge detection algorithm and a main step involving the hough transform technique in the preprocessing step a canny edge detection algorithm is applied in order to obtain a reduced point set describing the profile curve to be reconstructed also to identify in the profile possible sharp points like cusps we additionally use an algorithm to find the approximated tangent vector of every edge point in the subsequent main step we then use a piecewisely defined hough transform to locally recognize from the point set a low degree piecewise polynomial curve the final outcome of the algorithm is thus a spline curve approximating the underlined profile image the output curve consists of polynomial pieces connected g 1 continuously except in correspondence of the identified cusps where the order of continuity is only c 0 as expected to illustrate effectiveness and efficiency of the new profile detection technique we present several numerical results dealing with detection of open and closed profiles in images of different type i e medical and photographic images

accurate and robust line segment extraction using minimum entropy with hough transform the hough transform is a popular technique used in the field of image processing and computer vision with a hough transform technique not only the normal angle and distance of a line but also the line segment s length and midpoint centroid can be extracted by analysing the voting distribution around a peak in the hough space in this paper a method based on minimum entropy analysis is proposed to extract the set of parameters of a line segment in each column around a peak in hough space the voting values specify probabilistic distributions the corresponding entropies and statistical means are computed the line segment s normal angle and length are simultaneously computed by fitting a quadratic polynomial curve to the voting entropies the line segment s midpoint and normal distance are computed by fitting and interpolating a linear curve to the voting means the proposed method is tested on simulated images for detection accuracy by providing comparative results experimental results on real world images verify the method as well the proposed method for line segment detection is both accurate and robust in the presence of quantization error background noise or pixel disturbances

extended hough transform for linear feature detection improving the accuracy of line segment detection reduces the complexity of subsequent high level processing common in cartographic feature detection we developed a new extension to the hough transform and reported on its application to building extraction we expanded the hough space by a third parameter the horizontal or vertical coordinate of the image space to provide incremental information as to the length of the lineal feature being sought using this extended ht transform allowed us to more accurately detect the true length of a line segment in addition we used a bayesian probabilistic approach to process our extended hough space that further increased the accuracy of our extended hough transform

the generalized radon transform sampling accuracy and memory considerations the generalized radon or hough transform is a well known tool for detecting parameterized shapes in an image the radon transform is a mapping between the image space and a parameter space the coordinates of a point in the latter correspond to the parameters of a shape in the image the amplitude at that point corresponds to the amount of evidence for that shape in this paper we discuss three important aspects of the radon transform the first aspect is discretization using concepts from sampling theory we derive a set of sampling criteria for the generalized radon transform the second aspect is accuracy for the specific case of the radon transform for spheres we examine how well the location of the maxima matches the true parameters we derive a correction term to reduce the bias in the estimated radii the third aspect concerns a projection based algorithm to reduce memory requirements

accurate and efficient curve detection in images the importance sampling hough transform the hough transform is a well known technique for detecting parametric curves in images we place a particular group of hough transforms the probabilistic hough transforms in the framework of importance sampling this framework suggests a way in which probabilistic hough transforms can be improved by specifying a target distribution and weighting the sampled parameters accordingly to make identification of curves easier we investigate the use of clustering techniques to simultaneously identify multiple curves in the image we also use probabilistic arguments to develop stopping conditions for the algorithm results from applying our method and two popular versions of the hough transform to both simulated and real data are shown

a novel hough transform based on eliminating particle swarm optimization and its applications hough transform ht is a well established method for curve detection and recognition due to its robustness and parallel processing capability however ht is quite time consuming in this paper an eliminating particle swarm optimization epso algorithm is employed to improve the speed of a ht the parameters of the solution after hough transformation are considered as the particle positions and the epso algorithm searches the optimum solution by eliminating the weakest particles to speed up the computation an accumulation array in hough transformation is utilized as a fitness function of the epso algorithm the experiments on numerous images show that the proposed approach can detect curves or contours of both noise free and noisy images with much better performance especially for noisy images it can archive much better results than that obtained by using the existing ht algorithms

robust line fitting in a noisy image by the method of moments the standard least squared distance method of fitting a line to a set of data points is known to be unreliable when the random noise in the input is significant compared with the data correlated to the line itself here we present a new statistical clustering method based on legendre moment theory and maximum entropy principle for line fitting in a noisy image we propose a new approach for estimating the underlying probability density function p d f of the data set the p d f is expanded in terms of legendre polynomials by means of the legendre moments the order of the expansion is selected according to the maximum entropy principle then the points corresponding to the maxima of the p d f will be the true points of the line to be extracted by a chaining algorithm this approach is directly generalized to multidimensional data the proposed algorithm was successfully applied to real and simulated noisy line images with comparison to some well known methods

quantum master equation for a system influencing its environment a perturbative quantum master equation is derived for a system interacting with its environment which is more general than the ones derived before our master equation takes into account the effect of the energy exchanges between the system and the environment and the conservation of energy in the finite total system this master equation describes relaxation mechanisms in isolated nanoscopic quantum systems in its most general form this equation is non markovian and a markovian version of it rules the long time relaxation we show that our equation reduces to the redfield equation in the limit where the energy of the system does not affect the density of state of its environment this master equation and the redfield one are applied to a spin environment model defined in terms of random matrices and compared with the solutions of the exact von neumann equation the comparison proves the necessity to allow energy exchange between the subsystem and the environment in order to correctly describe the relaxation in an isolated nanoscopic total system

analytic line fitting in the presence of uniform random noise abstract one of the most fundamental tasks in pattern recognition involves fitting a curve such as a line segment to a given set of data points using the conventional ordinary least squares ols method of fitting a line to a set of data points is notoriously unreliable when the data contain points coming from two different populations i randomly distributed points random noise ii points correlated with the line itself e g obtained by perturbing the line with zero mean gaussian noise points which lie far away from the line i e outliers usually belong to the random noise population since they contribute the most to the squared distances they skew the line estimate from its correct position in this paper we present an analytic method of separating the components of the mixture unlike previous methods we derive a closed form solution applying a variant of the method of moments mom to the assumed mixture model yields an analytic estimate of the desired line finally we provide experimental results obtained by our method

linear band detection based on the euclidean distance transform and a new line segment extraction method abstract a linear band which is a straight line segment with some width i e thickness is a more structured higher level feature compared to edge or line features in spite of the usefulness of linear bands as features papers dealing with their detection problem are rare in this paper we propose a new method for detecting linear bands in gray scale images we first talk about our opinion on what types of linear bands a desirable detector should be able to detect and then give a description on how we designed our detector to achieve the goal our method consists largely of two parts 1 extracting the candidate center line pixels of the linear bands contained in an input gray scale image sub parts edge detection euclidean distance transform ridge detection in a distance map and noisy ridge pixel removal 2 extracting line segments from the result of 1 using our new line segment detection method sub parts modified hough transform base line segment grouping redundant line segment removal and postprocessing experimental results show that our method is practical and robust

multiple time correlation functions for non markovian interaction beyond the quantum regression theorem we derive the dynamical equation of the reduced propagator an object that evolves state vectors of the system conditioned to the dynamics of its environment which is not necessarily in the vacuum state at the initial time such a reduced propagator is essential to obtain multiple time correlation functions mtcfs we also study the evolution of mtcfs within the weak coupling limit and show that the quantum regression theorem is in general not satisfied we illustrate the theory in two different cases first solving an exact model and second presenting the results of the numerical integration for a system coupled with a thermal environment through a nondiagonal interaction

lsd a fast line segment detector with a false detection control we propose a linear time line segment detector that gives accurate results a controlled number of false detections and requires no parameter tuning this algorithm is tested and compared to state of the art algorithms on a wide set of natural images

a probabilistic hough transform abstract the hough transform for straight line detection is considered it is shown that if just a small subset of the edge points in the image selected at random is used as input for the hough transform the performance is often only slightly impaired thus the execution time can be considerably shortened the performance of the resulting probabilistic hough transform is analysed the analysis is supported by experimental evidence

analysis of a clinical trial involving a combined mortality and adherence dependent interval censored endpoint clinical trials often involve a variety of clinical and laboratory measures that are used as endpoints and sometimes two of these measures are combined in one endpoint when the individual components of such a combined endpoint are time to event measurements the analysis is straightforward if each of the components is measured frequently and regularly over time however the analysis of the combined endpoint is more difficult when one component of the endpoint is right censored and the other is interval censored this paper describes a statistic based on a rank ordering of events for such a combined measure the power of the test statistic is explored

global rank tests for multiple possibly censored outcomes clinical trials often collect multiple outcomes on each patient as the treatment may be expected to affect the patient on many dimensions for example a treatment for a neurological disease such as als is intended to impact several dimensions of neurological function as well as survival the assessment of treatment on the basis of multiple outcomes is challenging both in terms of selecting a test and interpreting the results several global tests have been proposed and we provide a general approach to selecting and executing a global test the tests require minimal parametric assumptions are flexible about weighting of the various outcomes and are appropriate even when some or all of the outcomes are censored the test we propose is based on a simple scoring mechanism applied to each pair of subjects for each endpoint the pairwise scores are then reduced to a summary score and a rank sum test is applied to the summary scores this can be seen as a generalization of previously proposed nonparametric global tests e g o brien 1984 we discuss the choice of optimal weighting schemes based on power and relative importance of the outcomes as the optimal weights are generally unknown in practice we also propose an adaptive weighting scheme and evaluate its performance in simulations we apply the methods to analyze the impact of a treatment on neurological function and death in an als trial

what s in a set of points straight line fitting the problem of fitting a straight line to a planar set of points is reconsidered a parameter space computational approach capable of fitting one or more lines to a set of points is presented the suggested algorithm handles errors in both coordinates of the data points even when the error variances vary between coordinates and among points and can be readily made robust to outliers the algorithm is quite general and allows line fitting according to several useful optimality criteria to be performed within a single computational framework it is observed that certain extensions of the hough transform can be turned to be equivalent to well known m estimators thus allowing computationally efficient approximate m estimation

there is no quantum regression theorem the onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium it is here asserted that this hypothesis fails in the quantum case this is shown first by explicit calculation for the example of quantum brownian motion of an oscillator and then in general from the fluctuation dissipation theorem it is asserted that the correct generalization of the onsager hypothesis is the fluctuation dissipation theorem s0031 9007 96 00679 5

non markovian master equations from entanglement with stationary unobserved degrees of freedom we deduce a class of non markovian completely positive master equations which describe a system in a composite bipartite environment consisting of a markovian reservoir and additional stationary unobserved degrees of freedom that modulate the dissipative coupling the entanglement induced memory effects can persist for arbitrary long times and affect the relaxation to equilibrium as well as induce corrections to the quantum regression theorem by considering the extra degrees of freedom as a discrete manifold of energy levels strong non exponential behaviour can arise such as for example power law and stretched exponential decays