Hierarchical projection regression for online estimation of elbow joint angle using EMG signals Abstract Exoskeletons offer great facilities to the elderly and disabled people with respect to extending their moving ranges and reacting to certain physical activities. Electromyogram (EMG) signals, which are derived from the neuromuscular system, provide an important access to the human-robot interface. On one hand, EMG signals can be used for real-time estimation of the motion intention of human body, e.g., the current joint angle status. On the other hand, however, the process of the mass EMG data, which are captured instantaneously from skin surface, challenges the state-of-the-art technology. Because its nonstationary and randomness, it is difficult to extract the valuable and stable features from the raw EMG signals. This paper investigates into the learning process of high dimensional EMG signals with a hierarchical mechanism that projects the original data into a lower feature space to achieve a local refined mapping from the EMG signals to the motion states of the human body. This hierarchically projected regression algorithm constructs incrementally a tree-based knowledge library, whose components represent local regression models. The components will be retrieved online efficiently and contribute to the estimation of the motion states. A great number of experiments are carried out to evaluate the accuracy of this novel algorithm. Exoskeletons, as a kind of wearable robot, recently get extensively researched and applied in the domain of physical assistive support in home, rehabilitation in medical field and stress powering in military. Whatever the role of wearable robot is, it is necessary for exoskeleton robots to interpret the intention of human motion in advance of the actual movement [1] . The electromyogram (EMG) signal, generated from the surface muscles' contraction, can be directly detected through sensors attached to the surface skin of the users. In this scenario, EMG signals provide rich information in real time that can serve as the interface of the human-machine system. By using EMG signals, wearable robots achieve desired flexibility because the inherent consciousness of human can be maintained to the utmost extent.. However, EMG signal is a kind of bio-signal which is very weak and can probably be affected by various noises. One of the greatest challenges in understanding EMG signals is their non-stationary and nonlinear characteristics. The EMG features, extracted from the raw signals, should be steady and valuable when they serve as the commands of exoskeletons, although the extracting process is intractable. Raw signals are usually sampled at a constant frequency. Therefore, the human motion estimation becomes a difficult issue due to its high dimensional inputs, i.e., a segment of time series. For example, the muscles are often modeled firstly by identifying several parameters before the actual modeling proceeds, such as Huxley model and Hill model for muscle activation and joint movements [2] [3] [4] [5] [6] . Many researchers analyzed the relations between the joint movement and the EMG statistics, first or second order [7] , and other features. Their studies show the strong nonlinearity of the relations. Based on the obtained features, the manipulators can be controlled to move according to the muscle movement of the users and enable to support the daily activities. For example, Kiguchi et al. [8] and Sato and Yagi [9] developed an exoskeleton for human upper-limb motion assistance based on EMG signal. In their work, root mean square is extracted to serve as the control command straightaway. However, the underlying knowledge is poorly explained by this naïve feature because a large amount of information is ignored. To remedy this, several nonlinear regression formulations have been proposed and tested [5, 10, 11] . Some latest methods are Gaussian process regression [12] , which can learn the inverse dynamics of a seven degrees-of-freedom SARCOS anthropomorphic robot arm, and Bayesian regression [13] , which can be used to predict EMG activities from neural firing. Unfortunately, the above traditional methods did not discuss the variety of the subjects, and their accuracy is unsatisfactory when it comes to estimate the continuous motion.. There are some researchers who have tried to map the EMG signals directly to the output, i.e., the joint angle states, without the steps of modeling and parameter identification. These are data-driven approaches, such as Artificial Neural Network (ANN). ANN is one of the black-box models dealing with mapping from multi-inputs to multioutputs, which is a combination of many nonlinear functions. Wang and Buchanan [5] designed a four-layer neural network that includes two hidden layers, to estimate the activation of ten muscles and proposed an algorithm named adjusted back-propagation to conquer the immeasurability of supervised information. Gopura and Kiguchi [11] proposed a fuzzy-neuron mapping from EMG signal to joint torque. Bu et al. [14] used a neural network to predict the movement and its occurrence probability. However, the prediction accuracy depends on the context information of a task. In general, ANN is not satisfactory in terms of realtime processing, especially for high dimensional training dataset. It cannot be applied in conditions where online training and updating are required. Another black-box state-space model was proposed in [15] for joint angle estimation based on EMG signal. This method needs position tracking system for tracking the joint movement to avoid estimation drifting.. The method proposed in this paper, named hierarchical projected regression (HPR), focuses on the high dimensional EMG data learning. By using HPR, the joint angle of human elbow can be estimated online. During the training stage, the HPR algorithm constructs a tree-based knowledge library, whose components represent local regression models. When it comes to the real-time operation stage, the joint angle can be retrieved online from the HPR tree using the EMG signals. At both the training stage and the real-time operation stage, the EMG signal is recorded and a sliding time-window is used to infer the stable features. In addition, in the training phase, the real angle of the human elbow is measured by an inertial measurement unit (IMU).. The remainder of the paper is arranged as follows. Experimental configuration and data acquisition are described in Sect. 2. Section 3 presents hierarchical projected regression algorithm in details. Section 4 describes the experimental results and the corresponding analysis. Section 5 discusses some extensions. A concise conclusion is drawn in Sect. 6. Electromyogram signals are extensively used in the field of wearable robots. Because of the non-stationary and uncertain natures of EMG signals, it is a challenging task to extract the valid and steady features from the raw signals. Fig. 11 A drinking task was carried out to evaluate the HPR. The user took the cup to his chest and then returned it back to the table. The motion of the elbow was estimated online. Meanwhile, the estimation was implemented by the manipulator that was mounted on a platform This paper proposed a hierarchical projected regression method to exploit the human motion intention hidden in the EMG signals. HPR is a tree-based algorithm where each node of the tree represents a cluster that can be separated from its parent node using k-Means approach. The child node will be divided recursively until the statistical criteria of the node are satisfied. In order to extract optimal lower dimensional features, a projecting matrix is derived in each spawning node. Finally, the leaf nodes of HPR tree are the representation of micro regression models. As the retrieval task takes places, the nearest branches in each level of HPR are traversed consecutively until the leaf node is reached. At the leaf node, the nearest point is found by nearest neighbor searching.. Hierarchical projected regression algorithm was validated by several experiments where different subjects with different loads and tasks were taken into consideration, and elbow motion was estimated online. The results have shown that HPR maps the high dimensional EMG signals to the elbow movement with satisfying accuracy. On the other hand, a robotic arm is driven to move following the estimated elbow movement. A great number of experiments have indicated that the algorithm we proposed is effective. Fig. 12 The comparison between the real angle and its estimation as the drinking task is carried out. The thin blue curve stands for the user's elbow angle that is detected by the IMU. The estimation from HPR is drawn with thick red curves. The average error is about 10.33°, which is small as can be see from the live video for drinking task (color figure online) In this section, all the reported experiments of motion estimation, according to the ethical standards, were carried out in order to evaluate the regression performance of the proposed method. Two subjects, A and B, participated in the experiments. First, subject A performs four trials with the loads of 1.54 kg. Data of these trials were used to train HPR. Then, both A and B were assigned to test our algorithm online. In the testing stage, they were assigned to move the elbow following the same task as in the training procedures. Five trials with 1.54 and 1.92 kg, respectively, were performed for the evaluating purpose.. In our experiments, a manipulator was employed to simulate the human elbow. The estimated angle is transferred to the manipulator as the commands for movement.. The manipulator is driven in the velocity mode which has the maximum velocity of 35°per second.

B I I O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Algorithms for symbolic/numeric control of affine dynamical systems We consider a general linear dynamical system and want to control its behavior. The goal is to reach a given target by minimizing a cost function. We provide a new generic algorithm with together exact, symbolic and numerical modules. In particular new efficient methods computing a block Kalman canonical exact decomposition and the optimal solutions are presented. We also propose a new numerical algorithm under-approximating the controllable domain in view of its analytical resolution in the context of singular sub-arcs. Aerospace engineering, automatics and other industries provide a lot of optimization problems, which can be described by optimal control formulations: change of satellites orbits, flight planning, motion coordination [7] ( [16] for more applications in aerospace industry). Optimal control has so become a more and more challenging domain and its theory has been extensively developed for many years. Nevertheless, the problem of synthesis of optimal feedback is not solved, even for linear systems. In some specific cases like time-optimal control problems, adequate solutions have been found [18, §3] , [2, 17, 16] . Also, control * Work partially supported by the Region Rhône-Alpes (Calcel project).. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. theory lacks generic algorithms, specially when singular subarcs appear [14, 19, 2] . Furthermore, in "real-life", optimal control problems are fully nonlinear. Therefore most of the algorithms presented here have been developed towards their application to the hybrid control of nonlinear dynamical systems: in [20] , we propose a piecewise affine approximation by way of a hybrid automaton. In each cell, the local optimal control problem is affine and techniques developed here will be applied. In this paper we consider a linear dynamical system: We have presented an algorithm for solving general linear optimal control problems. First we propose an explicit method to transform any problem into a canonical one by the way of a block Kalman decomposition. We have also developed generic algorithms solving the canonical problem even when complex boundaries occur. Yet, two important new features of our algorithms are that we give a full generic implementation and that they are mainly symbolic. Also,all the algorithms presented here have been implemented in Maple and work in high dimensions 2 .

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Generalizing the h- and g-indices We introduce two new measures of the performance of a scientist. One measure, referred to as the hα-index, generalizes the well-known h-index or Hirsch index. The other measure, referred to as the gα-index, generalizes the closely related g-index. We analyze theoretically the relationship between the hα- and gα-indices on the one hand and some simple measures of scientific performance on the other hand. We also study the behavior of the hα- and gα-indices empirically. Some advantages of the hα- and gα-indices over the h- and g-indices are pointed out. In 2005, Jorge Hirsch proposed a new measure of the performance of a scientist. This measure, which is referred to as the h-index or the Hirsch index, is based on the number of times the papers of a scientist have been cited. A scientist has h-index h if h of his n papers have at least h citations each and the other n − h papers have fewer than h + 1 citations each [15] . After its introduction, the h-index received a lot of attention in the scientific community (e.g., [2] ; for an overview, see [6] ) and quickly gained popularity. Nowadays, the h-index is a widely accepted measure of scientific performance. The automatic calculation of h-indices has even become a built-in feature of major bibliographic databases such as Web of Science and Scopus.. Apart from the h-index, there are of course many other ways to measure the performance of a scientist based on the number of times his papers have been cited. Hirsch [15] discussed a number of performance measures. As he pointed out, some measures have the disadvantage that they depend on a parameter with an arbitrarily chosen value. This is for example the case if the performance of a scientist is measured by counting the number of his papers with more than y citations. The value of the parameter y is arbitrary, and the performance of a scientist relative to his colleagues may increase or decrease when y is changed. A similar problem occurs if the performance of a scientist is measured by counting the number of citations of each of his q most cited papers. The value of the parameter q is arbitrary, and the relative performance of a scientist may increase or decrease when q is changed. Hirsch argued that the h-index has an advantage over performance measures like those mentioned above because it does not depend on a parameter with an arbitrarily chosen value. Although most researchers seem to have accepted this argument (e.g., [10, 11, 12, 17, 25] ; for an exception, see [21, 22] ), it is in fact not correct. Hirsch We have introduced the h α -and g α -indices, which generalize the h-and g-indices proposed. by Hirsch [15] and Egghe [10, 11] . The h-index can be obtained from the h α -index by setting the parameter α to 1. We have pointed out that setting α to 1 is arbitrary. In the literature, no theoretical or empirical arguments have been given why the value 1 would be better than other values. Hence, even though the h-index has been reported to work quite well in practical applications (e.g., [5, 15, 16, 26] ), the measure lacks a rigorous justification. A similar comment applies to the g-index.. Empirical research is needed to find out whether in practical applications the h α -and g α -indices provide better results than the h-and g-indices. An obvious question is whether the parameter α has a substantial effect on the way in which the h α -and g α -indices rank scientists.. If the effect of α is small, the use of the h-and g-indices seems fine. If, on the other hand, the effect of α is quite large, the h α -and g α -indices should be used instead of the h-and g-indices and a careful choice of α is necessary. In this paper, we have presented the results of a limited empirical study. The overall effect of α turned out to be relatively small in this study. However, it was also found that the rankings of some individual scientists relative to their colleagues depended quite strongly on α. More elaborate empirical research is needed to get a better idea of the sensitivity of the h α -and g α -indices to the parameter α.. Empirical research may also address the question what value of α is most appropriate for measuring scientific performance using the h α -and g α -indices. Since citation practices differ widely between fields, the answer to this question is most likely field-dependent. In some empirical studies [8, 9, 27] , it has been argued that the h-index tends to undervalue selective scientists. This seems to indicate that, at least in some fields, α can best be set to a value greater than 1.. We further note that a large number of performance measures have been proposed that are closely related to the h-index. Apart from the g-index [10, 11] , these measures include, for example, the A-, R-, and AR-indices [18, 19] , the h I -index [4] , the h m -index [24] , the h Tindex [1] , the h w -index [13] , the m-index [7] , and the w-index [29] . All these measures can be generalized in a similar way as we have shown for the h-index.. Finally, we note that the h α -and g α -indices introduced in this paper may be generalized even further. This can be done by first applying a monotone transformation to the number of citations of a paper and by then employing the transformed number of citations in the calculation of the indices (cf [21, 22] ). The h(2)-index proposed in [20] can be regarded as an example of this approach.

O O O O O O O O O O O O O O O O O O O O O O O O O O B O B I O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B I O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Predicting HIV-1 broadly neutralizing antibody epitope networks using neutralization titers and a novel computational method Background: Recent efforts in HIV-1 vaccine design have focused on immunogens that evoke potent neutralizing antibody responses to a broad spectrum of viruses circulating worldwide. However, the development of effective vaccines will depend on the identification and characterization of the neutralizing antibodies and their epitopes. We developed bioinformatics methods to predict epitope networks and antigenic determinants using structural information, as well as corresponding genotypes and phenotypes generated by a highly sensitive and reproducible neutralization assay. 282 clonal envelope sequences from a multiclade panel of HIV-1 viruses were tested in viral neutralization assays with an array of broadly neutralizing monoclonal antibodies (mAbs: b12, PG9,16, PGT121 -128, PGT130 -131, PGT135 -137, PGT141 -145, and PGV04). We correlated IC 50 titers with the envelope sequences, and used this information to predict antibody epitope networks. Structural patches were defined as amino acid groups based on solvent-accessibility, radius, atomic depth, and interaction networks within 3D envelope models. We applied a boosted algorithm consisting of multiple machine-learning and statistical models to evaluate these patches as possible antibody epitope regions, evidenced by strong correlations with the neutralization response for each antibody.We identified patch clusters with significant correlation to IC 50 titers as sites that impact neutralization sensitivity and therefore are potentially part of the antibody binding sites. Predicted epitope networks were mostly located within the variable loops of the envelope glycoprotein (gp120), particularly in V1/V2. Site-directed mutagenesis experiments involving residues identified as epitope networks across multiple mAbs confirmed association of these residues with loss or gain of neutralization sensitivity. Conclusions: Computational methods were implemented to rapidly survey protein structures and predict epitope networks associated with response to individual monoclonal antibodies, which resulted in the identification and deeper understanding of immunological hotspots targeted by broadly neutralizing HIV-1 antibodies. Despite the limitations, the thick patch analysis method can provide a useful tool to rapidly and automatically scan protein structures and identify epitope network regions associated with neutralization response. Our novel in-silico prediction method narrows down the search space for immunological hotspots to key variable regions. These regions are then good candidates for further evaluation by experimental studies as HIV-1 neutralizing antibody epitopes. Furthermore, this method can be adapted into other disease areas, particularly for predicting epitopes of highly variable viruses. We describe here a novel multi-modal method for predicting antibody-specific epitope networks, utilizing antigen structure models, viral genotypes, neutralization assay results, and data mining techniques, together in a pipeline called thick patch analysis (THIPA). The goal of this study was to identify epitope networks of HIV-1 broadly neutralizing antibodies (nAbs). The predicted epitope networks are clusters of antigenic residues significantly associated with binding and neutralization activity. We aimed to identify both conformational and linear epitopes by systematic mapping of the genotypic information onto 3D structural models and correlating that with the neutralization phenotype. For this purpose, we utilized the IC50 measurements of 21 monoclonal antibodies against a panel of 282 clonal HIV-1 viruses of various subtypes, co-receptor tropism, and neutralization sensitivity. Patches with a particular thickness and radius were identified on the HXB2 gp120 theoretical structure, and the genotype of each virus was mapped onto these models. The viral sequence located in each patch was captured as a binary (0/1) vector, representing presence (1) or absence (0) of a mutation as compared to HXB2. We then correlated these vectors with the IC 50 data by performing multiple statistical and machine-learning methods, and identified residues and patches significantly associated with the neutralization response to each antibody. Finally, we evaluated the significant patches detected by the data mining tools, and predicted epitope networks for HIV-1 monoclonal antibodies (mAbs).. The THIPA pipeline attempts to identify regions within the viral envelope that are likely to be targeted by Figure 3 Predicted Epitope Networks for all mAbs in 3D. Predicted epitope networks are indicated in red for each antibody. The 3D models represent a theoretical view of full-length HXB2 gp120 monomer by the CPHmodels program [46] . Model is rotated for each antibody to show the best view of network residues. Visualizations were generated using UCSF Chimera [49] . INSET: General location of the variable regions V1, V2, and V3 are indicated. Notably, the most overlapping residues between the predicted epitope networks of different mAbs were predominantly located within the variable loops V1/V2 of gp120.. nAbs, and therefore are critical to be studied for successful vaccine design. This computational method scans the gp120 molecule through patches with a probable size for an antibody footprint, and as such, it not only allows the examination to be applied in a structurally meaningful way, but also narrows down the search dimension to smaller area that is more computationally feasible to survey. The process utilizes sequences of naturally circulating S158, S162 , I165, R166, G167, K168, V169, Q170, K171, E172, Y173, A174, F175, F176, Y177, K178, D185, D187, T188, V200, I201 A B C D Predicted PG9 / gp120 Interacting Residues S158, S162 , G167, K168, V169, Q170, K171, E172, Y173, A174, F175, F176, Y177, K178, D185, D187, T188, V200, I201, N300, N301, N302, G312, F317, V318 [4] are colored blue. Overlap between predicted and published residues is indicated by blue residues which are also shown in ball-and-stick representation. The 3D models represent a theoretical view of full-length HXB2 gp120 as generated by the CPHmodels program [46] . A and B depict a hypothetical trimer seen from the top and side respectively, while C and D represent a monomer representation seen from the front and back respectively. Correct orientation of trimer subunits was obtained by aligning the Cα backbone of the predicted models with the corresponding chains of the trimer structure (PDB ID: 2NY7). Visualizations were generated using UCSF Chimera [49] .. viruses, rather than lab strains, which are more likely to be exposed to nAbs and thus, could elicit their escape mechanism. Additionally, this method allows the study of genotypic patterns and their impact on neutralization in context of co-occurring mutations [52] . One of the major data components included in this method is derived from a cell-based neutralization assay that determines the phenotype of the antibody in presence of a given virus. Consequently, residues that are identified as significant can elicit mechanisms of viral escape from the immune response. Another key aspect in the design of this method is the implementation of a boosted technique, which utilizes an ensemble of statistical and machine-learning models, each with unique set of strengths, allowing us to evaluate the network of information from different angles. Notably, since our purpose of applying these models was to discover potential immunological hotspots, and not to build a predictive algorithm, no fine-tuning of the model parameters was necessary. In particular, SVM accuracy cutoff of 70% using a linear kernel and default parameters allowed successful identification of significant patches without further parameter adjustment.. In order to examine the validity of our results and ensure that the identified residues are in-fact related to the neutralization activity, we performed site-directed mutagenesis (SDM) experiments using clones that differed in the residues identified to be part of the predicted epitope networks of a group of mAbs. The SDM results confirmed significant associations between a set of residues we investigated and the antibody response, suggesting that the THIPA method was able to correctly identify key residues out of many mutations. This is also remarkable given that there were many other sites that differed between the clones. The inclusion of mutation 169R in the envelope protein of a neutralizationresistant virus greatly increased the sensitivity to PG9 and PG16, suggesting that the normally shielded regions of the protein were made accessible to the antibody by this change. The mutation 169 K resulted in an either enhanced or reduced susceptibility to a number of mAbs. The reverse mutations K169Q and Y173S had much more dramatic effect on the neutralization activity against PG9 and PG16 mAbs than the Q169K and S173Y mutants. This might be due to the presence of Glutamine and Serine that help shield the neutralizing epitopes in the specific backbone. Although positions 178 and 185 were predicted to be significant for a group of mAbs, introducing mutations at these sites didn't affect the IC50 titers significantly suggesting that additional sites have to be involved in the antibody binding. One possibility is that multiple amino acid changes might modify the overall shape of the envelope protein, thus exposing Comparing the predicted neutralization sensitivity of the SVM models using only the significant sites within gp120 as input, to the measured antibody response. We obtained sensitivity and specificity for detection of resistance to the particular antibody. Overall accuracy of the predictions in the whole dataset as well as within each subtype was determined. Standard-deviation of % accuracy across those subtypes is shown in the last column.. normally hidden regions in the HIV-1 envelope protein to the antibodies. Additional experimental studies would be required in order to confirm the impact of the newly identified residues. For validating our results, we also developed computational models based only on the subset of significant residues. As shown by the high predictive accuracy of these models in Table 1 , the identified residues were found to substantially impact the neutralization sensitivity of the respective antibody. Predictive accuracy was also shown to be high across the different subtype groups, suggesting that subtype was not a confounder with respect to the quality of the predictions.. Additionally, we evaluated the structural implications of our results and compared them with the published literature. We demonstrated that this method can accurately identify previously published epitope regions of three HIV-1 mAbs (PG9, PG16, and PGV04), and provide information on other regions that may contribute to neutralization response or the corresponding escape mechanism. The predicted epitope network residues for PG9 and PG16 together with their published epitopes depicted on the trimer structure are shown in Figure 4 . The trimer view is provided since both nAbs PG9 and PG16 belong to the family of quaternary-structurespecific antibodies [53] .. It should be noted that the structural component of the THIPA process is fairly robust with regard to the structural model used. We compared the patch lists derived from the truncated gp120 monomer structure (PDB ID: 3JWD) and those derived from our full length predicted monomer structure (data not shown). Excluding sequence regions that are clipped in the 3JWD structure, there was a high degree of agreement in the patch definitions. We would predict that the differences in specifics of loop structure prediction would not significantly change patch definitions because they would always be defined as surface residues. However, if two core structures with different conformations were used (e.g. prefusion gp120 vs . postfusion gp120), then we would predict some unique patches would arise from that and potentially change epitope network prediction outcomes slightly.. Since the goal of this process was to maximize the ability to detect disparate potential antigen binding sites, it is critical to use diverse viruses with naturally occurring variants. We used 282 clones that differ widely in neutralization sensitivity, co-receptor tropism, and subtype. However, there remain residues that are conserved across all clones, so their impact as antigenic determinants could not be evaluated. Accordingly, a caveat of utilizing a limited set of viruses for the THIPA method is that the data mining processes are unable to find potential epitope network residues if there are no mutations in any of the sequences at that particular position.. For example, b12 and PGV04 are known to rely on making a salt-bridge with D368 [54] but that position is completely conserved in our virus panel and therefore could not be identified for either antibody. We recognize that our method is relevant for identifying highly variable regions associated with antibody neutralization (Additional file 1: Figure S3 ). Another limitation of this method is in detecting binding sites where low level mutations can be tolerated by the antibody, and therefore, may not be associated with a significant change in IC 50 .. There may be other viral properties, such as number of glycosylation sites [42] , that can impact the neutralization response and haven't yet been explored by this method. Including a broad spectrum of viral sequences and all possible genotypic determinants into the analysis is likely to increase the accuracy of the results. Also noteworthy is the fact that we used a theoretical model in our study in order to overcome the barrier of truncated variable loops in the available x-ray structures. Although the chosen model had minor deviations from the actual crystal structure (Additional file 1: Figure S2) , and it is a reasonable assumption that the variable loops can be flexible in space and thus not requiring to conform to a fixed structure, it will be beneficial and interesting to repeat the study using full-length crystal structures as they become available. An example of the risk associated with using a theoretical model is N332 for PGT121 which was reported by Julien et al. [55] . In the theoretical model, the angle of the N332 is rotated inward and only the tip of the residue presents a surface, so the site didn't make the depth cutoff in our method. Notably, other regions do overlap between our predictions and the reported PGT121 epitope, particularly regions in V3, for instance N301. In this paper, we present a novel method called thick patch analysis (THIPA) for predicting antibody epitope networks by correlating neutralization phenotype to the genotype and the antigen structure. We define an epitope network as a patch of residues that are antigenic determinants and have significant association with the neutralization response. Neutralization sensitivity for 21 HIV-1 monoclonal antibodies (b12, PG9,16, PGT121 -128, PGT130 -131, PGT135 -137, PGT141 -145, and PGV04) was determined by Monogram's neutralization assay [9] and was captured as IC 50 titers against a panel of 282 clonal viruses. Viral gp120 sequences were mapped onto structural patches and were then correlated with the neutralization response of these antibodies. Using data mining techniques, we identified residues that significantly impact neutralization activity, and are therefore considered to be potential antibody targets. For validating this method, we performed sitedirected mutagenesis (SDM) experiments using the residues predicted to be part of the epitope network of multiple nAbs. Additionally, we used the identified set of significant residues as input, and built SVM models to perform prediction of the neutralization response, and evaluated the accuracy of the predictions. The predicted epitope networks were also compared with the available literature on PG9, PG16 and PGV04. To date, the design of an effective vaccine against Human Immunodeficiency Virus-1 (HIV-1) remains a challenge and has failed to produce broad and effective neutralization responses [1] [2] [3] [4] [5] [6] [7] [8] . The design of protective immunogens is especially challenging due to the high viral escape rate from immune control [9] [10] [11] . Ongoing HIV-1 vaccine research efforts include finding and characterizing broadly neutralizing antibodies (nAbs), and the epitopes they target [12, 13] . Identification of the antigenic targets of nAbs along with mapping the immunologically important residues of known epitopes that affect neutralization is therefore a major goal of current HIV-1 vaccine research. The HIV-1 envelope is highly variable, and as a consequence, identification of key residues that affect neutralization can be complex. In some instances, lack of neutralization can be explained by amino acid changes in the known epitopes, but in other cases epitope conservation does not ensure neutralization [14] . In addition, many regions outside of the known epitopes have been shown to affect neutralization sensitivity [15] . The aim of this study is to develop a computational method for discovering and evaluating "epitope networks" that we define here as groups of interacting and variable residues that affect antibody binding.. A key element in successful immune response is the interaction between foreign antigens and antibodies produced by the B-cells. The ability to identify and characterize epitopes on antigen surfaces is important for vaccine design, the development of antibody therapeutics, and immunodiagnostic tests. In the last decade, significant effort has been invested to understand the nature and characteristics of linear epitopes with the goal of developing reliable methods for predicting them. Many tools of varying utility were produced and have been reviewed [16] . One significant outcome was the realization that there is no single measurable feature about protein-protein interactions that is able to reliably predict antibody binding sites. More recently, studies have been performed to address conformational epitope identification and prediction which resulted in several useful tools. These have been reviewed in detail by El-Manzalawy [17] . In general, existing methods for predicting conformational B-cell epitopes can be grouped into three categories: those that rely upon antigen protein structure alone [18] [19] [20] , those that use antigen structure in combination with the antibody peptide sequence [21, 22] and those that map peptide "mimics", mimotopes, derived from random peptide libraries to the antigen structure's surface [23] [24] [25] [26] .. In this paper, we describe a novel method that utilizes the antigen protein structure together with neutralization titers measured by Monogram Biosciences' neutralization assay [9] to predict functional B-cell epitope networks and key protein-protein interacting residues. Data generated from Monogram's neutralization assay has been previously used by researchers utilizing alanine scanning and various other lab techniques to characterize monoclonal antibodies (mAbs) [3, 4, 14, 27] . Our goal was to develop a rigorous computational method that incorporates neutralization sensitivity data from a panel of naturally occurring viruses, in combination with sequence and protein structure information, and applies an ensemble of data mining techniques to enable rapid and accurate prediction of antibody epitope networks. We aimed to investigate residues that can interact with antibodies as a network, and in a structurally meaningful way. We therefore evaluated envelope sequences grouped into patches of amino acid sites. These patches were then examined to discover networks of variable residues that significantly impact neutralization sensitivity.. Patch analysis has been previously suggested and performed to predict protein-protein interaction sites [28, 29] . To identify potential HIV-1 antibody epitope network residues on the antigen surface, we started with the common concept of a surface patch, as previously described [30] . Surface patches are typically defined by determining the accessible surface area (ASA) of each residue and taking those positioned above a certain threshold. These values can be calculated by a number of tools (DSSP [31] and NACCESS [32] for example) which use tables of maximum solvent accessibility for each amino acid in a Gly-X-Gly or Ala-X-Ala tripeptide configuration in solution. However, work by Singh et al. [33] in which they examined the surface accessibility of over 18,000 structures in the protein data bank (PDB), showed that observed surface accessibility often differed significantly from the values found in traditionally used tables [34, 35] and that occasionally the use of these values in a real-world calculation produced a result where an amino acid had a predicted ASA value of more than 100%. To address this, Singh et al. developed a table of highest observed accessibility (HOA) values and suggested normalizing ASA by HOA to obtain a more meaningful relative surface accessibility (RSA) [33] .. The concept of residue interaction networks (RIN) has been discussed recently in several publications [36, 37] . The principle is based upon the fact that proteins are not rigid bodies, as in a crystal structure, but rather that they are for the most part flexible and can change in response to their immediate environment. Likewise, in a protein-protein interaction, the orientation of an interacting residue can be influenced by other, buried, residues that are immediately below it as well as the residues located deeper underneath to some extent. Residue depth has been correlated with several protein properties, such as stability, and conservation of amino acids and their types [38] . Pintar et al. [39] defined atom depth as the distance in angstroms (Å) of a nonhydrogen buried atom from its closest solvent accessible protein neighbor. Using this definition, the residue depth (DPR) of surface residues is defined as 0, and >0 for all those that are buried. In an examination of structures in the PDB, it was found that buried atoms tend to cluster into discrete layers [39] . The first inner layer has a maximum DPR of ≈ 1.50 Å, with a second inner layer having a maximum DPR of ≈ 2.50 Å. It is then possible to use the mean residue DPR to construct "thick" surface patches in an attempt to capture key residues from the RIN that are important in defining a functional epitope.. In this study, we determined relative solvent accessibility according to the method of Singh et al. [33] when examining the structural information. Additionally, we took the RIN data into account by exploring thick patches with several thresholds for DPR. We generated structural patches considering the complete information according to these parameters, and systematically tested each patch for its ability to determine neutralization response. Our goal was to identify epitope networks which correspond to immunogenic regions recognized by nAbs.. We were able to build a bioinformatics process, called "thick patch analysis" (THIPA), that combines viral sequence and structural information as well as neutralization titers against viruses with a range of HIV-1 subtypes, and applies an ensemble of machine learning and statistical models to predict antibody epitope networks. In this paper, we describe the computational method, and the predicted epitope networks for 21 HIV-1 mAbs, as well as the results from the lab experiments we performed in order to validate the algorithm.

O O O O O B I O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B O O O O O O O O O O O B I I O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O B I O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O B I O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B I O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O B O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O


Improved Demons Technique with Orthogonal Gradient Information for Medical Image Registration Accurate registration is crucial for medical image analysis. In this letter, we proposed an improved Demons technique (IDT) for medical image registration. The IDT improves registration quality using orthogonal gradient information. The advantage of the proposed IDT is assessed using 14 medical image pairs. Experimental results show that the proposed technique provides about 8% improvement over existing Demons-based techniques in terms of registration accuracy. key words: medical image processing, image registration, optical flow, demons algorithm Image registration is an important technique to find a deformation field that aligns an source image I s with a target image I t . The deformation field defines how each pixel in image I s gets mapped to the space of image I t . In medical applications, registration technique is very important for images collected at different times or using different imaging modalities. Several intensity-based techniques have been proposed for medical image registration. Free-form deformation is a popular technique, where control points are defined in a grid overlaid on the image, and techniques differ on the way the intermediate points are interpolated from the control points [1] . Thirion [2] proposed Demons technique (DT) which is very efficient for medical image registration. The schematic of the DT is shown in Fig. 1 , where I s (x 0 ) and I t (x 0 ) are initial intensity of images. Note that x denotes the 2-D coodinate (x, y), and I s (x n ) is the nth updated version of image I s (x 0 ). The basic idea of DT is to make I t fixed, and move every pixel in I s iteratively guided by the deformation force (DF) until the difference between I s and I t reaches a minimal value.. Recently, Wang et al [3] proposed the symmetric Demons technique (SDT) to improve the convergence speed. Both DT and SDT techniques estimate the displacement for every pixel in the image based on the gradient information (GI). The DT and SDT are efficient if the deformation is in the direction of gradient. However, if the ground truth deformation is not parallel to the direction of the gradient, the DT and SDT cannot provide good performance. In this letter, we propose an improved Demons technique (IDT) which provides superior performance compared to the SDT by incorporating the orthogonal gradient information (OGI). In this letter, we proposed an improved Demons technique which combined symmetric gradient information with the OGI to obtain a more accurate displacement field calculation. Experimental results with medical images show that the proposed technique provides a significantly better registration performance than existing Demons-based techniques.

O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I B I B I B I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Enabling social interactions through real-time sketch-based communication We present UbiSketch, a tool for ubiquitous real-time sketchbased communication. We describe the UbiSketch system, which enables people to create doodles, drawings, and notes with digital pens and paper and publish them quickly and easily via their mobile phones to social communication channels, such as Facebook, Twitter, and email. The natural paperbased social interaction enabled by UbiSketch has the potential to enrich current mobile communication practices. With people constantly on the go and social communities spread out, people need quick, easy ways to exchange information. A range of applications on mobile devices now support communication nearly anywhere and anytime. Despite the need for fast access to these communication tools, the typical interaction workflow is tedious, demanding time and attention (taking the device out, switching it on, using an application, switching it off, putting it away).. In addition to the mobile phones, pens are still commonly carried, since they provide a simple way to make notes and annotate paper documents. The ubiquity of this pair of devices speaks to their usefulness. Paper documents have important properties that have yet to be achieved by digital media, including portability, flexibility, readability, and high resolution [7] . Pen and paper are widely used, especially in comparison to digital tools [8] , for note taking and doodling during lectures and meetings, and informal communication via sketching. Paper-based interfaces that digitize input enable users to exploit the affordances of digital media (e.g., search, storage, modification and distribution) in a mixed paper-digital environment.. We present UbiSketch, a mixed paper-digital system integrating Anoto Digital Pen and Paper technology 1 and 3G smart phones. UbiSketch exploits the affordances of pen and paper to support quick, easy, informal, sketch-based communication on mobile phones. We describe how the system enables Copyright is held by the owner/author(s). hand-written or drawn notes to be shared via social communication channels, such as Facebook, Twitter, or email. UbiSketch enables people to publish paper-based sketches to online channels with minimal effort, in real-time. We leverage current practices for mobile communication and penand-paper interaction to create a resource for self-expression and informal social interaction. The infrastructure we have developed is extensible, and could easily support additional communication channels. UbiSketch shows promise as a mechanism for lightweight visual communication, exploiting the affordances of pen and paper, mobile phones, and online social networks. We plan to conduct a field study to observe naturalistic usage practices. As Buxton observed [1] , sketches are quick to make, timely (provided when needed), inexpensive, disposable, and show the peculiarities of individuals' handwriting. Like spoken and written language, sketches are a form of communication with self and others, and they externalize ideas for remembering and sharing [10] . Although sketching with pen and paper is inexpensive, intuitive, and quick, paper-based sketches can be difficult to re-access, rearrange, or share [3] . Digital tablets or boards can enable digital input and interactive feedback [9, 5] , yet the experience and feeling of sketching differs from that of sketching on paper, and users often have to adjust their drawing techniques accordingly [2] . Various research projects have demonstrated the effectiveness of digital pen and paper technology for harnessing the affordances of paper and digital media [4, 12, 11] .

O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O


Automatic Detection of White Matter Hyperintensities in Healthy Aging and Pathology Using Magnetic Resonance Imaging: A Review Abstract White matter hyperintensities (WMH) are commonly seen in the brain of healthy elderly subjects and patients with several neurological and vascular disorders. A truly reliable and fully automated method for quantitative assessment of WMH on magnetic resonance imaging (MRI) has not yet been identified. In this paper, we review and compare the large number of automated approaches proposed for segmentation of WMH in the elderly and in patients with vascular risk factors. We conclude that, in order to avoid artifacts and exclude the several sources of bias that may influence the analysis, an optimal method should comprise a careful preprocessing of the images, be based on multimodal, complementary data, take into account spatial information about the lesions and correct for false positives. All these features should not exclude computational leanness and adaptability to available data. According to the STandards for Reporting Vascular changes on nEuroimaging (STRIVE), signal abnormality of variable size in cerebral white matter (WM) that appear hyperintense on T 2 -weighted magnetic resonance imaging (MRI) without cavitation (signal different from cerebrospinal fluid) are defined as white matter hyperintensities (WMH) of presumed vascular origin ). These abnormalities have been commonly found on MRI of clinically healthy elderly people; furthermore, they have been associated with various neurological and geriatric disorders (Kim et al. 2008; Debette and Markus 2010) .. MRI is highly sensitive to the changes affecting cerebral WM. Damaged white matter usually has a prolonged T 2 relaxation time due to increased tissue water content and to degradation of the macromolecular structure of myelin. Therefore, WMH are well depicted with conventional proton density (PD) and T 2 -weighted spin echo or fast spin echo sequences, but are even more conspicuous on fluid-attenuated inversion recovery (FLAIR) images.. The presence, shape and severity of WMH might provide further insight into healthy aging and pathophysiology of various disorders. Unfortunately, since WMH patterns are heterogeneous, ranging from large confluent periventricular WMH to punctate ones in deep WM, their classification is not straightforward. It has been shown that different visual rating scales, such as the Scheltens scale or the Fazekas scale (Scheltens et al. 1998) , are seldom comparable (van Straaten et al. 2006) , are inappropriate when examining longitudinal progression of WMH (Prins et al. 2004) , show poor sensitivity to clinical group differences (Mäntylä et al. 1997) , originate high intra-subject and inter-subject variability (van den Heuvel et al. 2006 ) and significant ceiling/floor effects (van Straaten et al. 2006; Gao et al. 2011) , therefore leading to inconsistencies between WMH studies. As an alternative to a qualitative rating scale, the manual delineation and quantification of WMH areas is a more reliable way to assess WM abnormalities, but the whole process, which is cumbersome and time-consuming for the neuroradiologist, shows high intra-rater and inter-rater variability (Grimaud et al. 1996) .. For all these reasons, given the increased interest in brain research and in the context of clinical studies involving a high number of subjects, an automated approach to detection of WMH is desirable. Although several fully automated methods have been proposed for WMH segmentation, no one clearly outperformed the others. Each of the methods described in the literature has strengths and weaknesses, mainly associated with the imaging modalities used and the abnormalities detected. Several methods have been designed for lesion detection in MS patients (García-Lorenzo et al. 2013; Lladó et al. 2012) , an issue that is similar to that of WMH segmentation. In practice, techniques originally trained on MS patients perform only moderately well when applied to geriatric patients (Admiraal-Behloul et al. 2005 ) and this happens for two main reasons. First, the contrast between gray matter (GM) and WM in MR images decreases with age. Second, the boundaries of MS lesions are sharper than those of WMH.. In this paper we describe the automated methods proposed specifically for WMH segmentation, which were applied to MR images of clinically healthy elderly people and patients with cardiovascular risk factors. Our aim is to compare the advantages and disadvantages of each algorithm, and to discuss the desirable features that should characterize an optimal detection method. In this paper we reviewed the principal approaches to segmentation of WMH from MR images of healthy elderly subjects and patients with vascular pathologies. The need for a fast, accurate and fully automated approach has been underpinned by the efforts that are continuously made to compare and standardize the assessment of WMH load. Currently, qualitative assessment of WMH is achieved through the use of visual rating scales, although Mantyla and colleagues, by comparing 13 different scales, concluded that their heterogeneous properties resulted in inconsistencies in previous studies (Mäntylä et al. 1997) , pointing out that inter-rater variability, along with time consuming procedures, made a true quantitative method superior to any visual rating scale.. Despite the number of proposed methods, an optimal algorithm has not yet been identified. This is probably due to the intrinsic complexity of the problem, as well as to the small samples upon which the majority of methods has been validated, leading to some sort of overfitting. In a recent study (Klöppel et al. 2011) , supervised kNN and SVM performances (Anbeek et al. 2004; Lao et al. 2008 ) outperformed an unsupervised threshold approach, with SVM obtaining the best performance. It is worth pointing out that the unsupervised approach used in this study relied upon FLAIR signal intensity only, without taking into account spatial information or multispectral data. This review has presented several more sophisticated unsupervised methods that have been shown to perform as well as supervised one, without the need for a manually segmented training set.. In order to correctly validate a segmentation method, a ground truth is needed. The majority of studies exploited quantitative measures of WMH load, such as the DSC, while in others (Maillard et al. 2008; Wu et al. 2006; Kruggel et al. 2008; Valdés Hernández et al. 2010; Payne et al. 2002 ) the ground truth was represented by visual rating scores. For completeness, it should be noted that the DSC does not give information about over-or under-segmentation, nor provides any notion about the consistency across disease severity, as the volume correlation does. In addition, WMH in some anatomical regions are more complicated to segment than others, an issue not addressed by global measures like DSC or correlation coefficients. Hence, multiple complementary metrics are needed, and reporting the location of errors would provide a better understanding of the performance of the proposed methods.. The use of multimodal information to perform WMH segmentation has been proved to perform better than the use of a single sequence (Anbeek et al. 2004; Dyrby et al. 2008; Beare et al. 2009; Samaille et al. 2012; Valdés Hernández et al. 2010; Sheline et al. 2008) , since it allows integration of spatial information, extracted from volumetric sequences, thus facilitating elimination of CSF artifacts (Anbeek et al. 2004; Dyrby et al. 2008; Gibson et al. 2010; Samaille et al. 2012; Jeon et al. 2011) . Furthermore, multi-spectral segmentation also allows volume acquisition of lesion subtypes such as lacunar/ subcortical infarcts and Virchow-Robin spaces (for a complete overview of lesion subtypes see Wardlaw et al. 2013) . In particular, Virchow-Robin space segmentations are typically based on T 2 and T 1 CSF intense voxels (for a review see Valdés Hernández et al. 2013) .. Redundant information is provided by PD, T 2 and FLAIR images: in fact, WM abnormalities appear hyperintense in all three sequences. However, the extent of WMH may not look the same on the different sequences (Filippi et al. 1996a, b) , and it was shown that FLAIR imaging present some limitations: it is less sensitive in the posterior fossa (Gawne-Cain et al. 1998 ) and for thalamic lesions (Bastos Leite et al. 2004 ), may overestimate WMH load and has a higher inter-vendor variability (Filippi et al. 1996a (Filippi et al. , b, 1999 Bastianello et al. 1997; Rovaris et al. 1999) . Furthermore, FLAIR may present hyperintense artifacts that can lead to an increase in false positives. This alternating behavior of FLAIR, i.e., losing sensitivity or specificity according to the spatial location of the lesion, might have a biological, albeit still unclear, explanation. A recent study (Haller et al. 2013 ) hypothesized that WMH identified by FLAIR despite the relatively mild demyelination, shown by histopathological comparison, could depend on a relatively high concentration of interstitial water in periventricular/perivascular regions, due, in turn, to agerelated modifications in blood-brain-barrier and plasma properties. On the other hand, the lack of sensitivity in the thalamus and in infratentorial regions could reflect different relaxation characteristics of both normal-appearing and abnormal tissue, accompanied by age-related changes in relaxation times (Bastos Leite et al. 2004) . Finally, during the acquisition of the FLAIR sequence, even a slight spatial inhomogeneity of the inversion pulse profile could influence the sensitivity of FLAIR to WMH in different spatial locations. For all these reasons, the combination of FLAIR with a redundant source (i.e., T 2 ) will increase the certainty of the WMH delineation and reduce false positives.. The accuracy of an automated WMH segmentation procedure is also limited by the scarce knowledge about the spatial distribution of the hyperintensities. Although it is well known that certain locations are more relevant than others (i.e., periventricular watershed), the exact probability of finding a WMH in a specific region is unknown. At the moment, the automatic spatial subdivision of WMH according to their distance from the ventricles has been developed in several methods (Anbeek et al. 2004; Maillard et al. 2008; Brickman et al. 2011; Jeon et al. 2011; Payne et al. 2002; Ramirez et al. 2011) , but further exploration of WMH topographic distribution is required.. In summary, whether supervised or not, from a methodological point of view a good segmentation method should:. -Rely on a good pre-processing stage, in order to be robust to noise; -Be computationally lean; -Use multimodal, complementary data. Anyway, since multimodal images are not always acquired in clinical practice, a good method should be adaptable to the data available in the specific context; -Consider spatial information, both in terms of tissue classes and known topology of WMH; -Be reproducible and applicable to data acquired at different times from different scanners; -Rely on a good, automated method for removing false positives.. In conclusion, advances in new algorithms, as well as new developments in MRI acquisition protocols, should help neuroradiologists to improve the evaluation of WMH, both in clinical studies, investigating their relationship with normal aging and pathology, and in every-day clinical practice.

O O O B I I O O B O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O


A Novel Interface for Interactive Exploration of DTI Fibers Visual exploration is essential to the visualization and analysis of densely sampled 3D DTI fibers in biological speciments, due to the high geometric, spatial, and anatomical complexity of fiber tracts. Previous methods for DTI fiber visualization use zooming, color-mapping, selection, and abstraction to deliver the characteristics of the fibers. However, these schemes mainly focus on the optimization of visualization in the 3D space where cluttering and occlusion make grasping even a few thousand fibers difficult. This paper introduces a novel interaction method that augments the 3D visualization with a 2D representation containing a low-dimensional embedding of the DTI fibers. This embedding preserves the relationship between the fibers and removes the visual clutter that is inherent in 3D renderings of the fibers. This new interface allows the user to manipulate the DTI fibers as both 3D curves and 2D embedded points and easily compare or validate his or her results in both domains. The implementation of the framework is GPUbased to achieve real-time interaction. The framework was applied to several tasks, and the results show that our method reduces the user's workload in recognizing 3D DTI fibers and permits quick and accurate DTI fiber selection. Diffusion tensor imaging (DTI) is a non-invasive magnetic resonance imaging (MRI) technique that measures the speed and direction of water diffusion in biological tissues. The characteristics of water diffusion in a biological structure (e.g., heart) can be mathematically summarized by a diffusion tensor field. By tracking the trajectories of the fastest diffusion in a diffusion tensor field with streamline methods [2] , a DTI dataset can be represented with a set of fiber tracts, or three-dimensional pathways. This process, called tractography, shows the connectivity and distribution of the fibers and has been widely used in visualization and analysis of DTI datasets [15, 18, 27] .. Exploring and analyzing fiber tracts in the three-dimensional space is challenging due to the visual clutter caused by the complexity of the geometry. For example, a fiber model for white matter may contain more than ten thousand fibers, making it difficult to derive useful insights from the dataset. A number of fiber clustering techniques [5, 18, 20, 24, 26] have been used to group similar fibers (i.e., fibers that lie close to one another and follow similar trajectories through the tensor field) into automatically representative fiber bundles. Graphical representations of such fiber bundles reduce the visual complexity of the dataset thereby facilitating a user's exploration of the data and allow him or her to more quickly gain insights into the structural integrity and connectivity of the fibers [6, 23] . However, renderings of clustered bundles can still suffer from occlusion (i.e., one cluster obscuring another) that impedes the perception of the DTI fibers or the selection of specific fibers [3] for further analysis.. The ability for scientists to interactively explore and select DTI fibers for inspection or for use in statistical analysis is critical for DTI research. The difficulty of interacting with DTI fiber models highlights the need for better visual representations and more convenient user interfaces. Existing solutions attempt to solve the problem by employing new visual forms or novel interaction methods such as interactive selection schemes [1, 3] , dynamic query [23] , geometric simplification [6, 10] , color-mapping [9, 8] , texture patterning of fiber dissimilarity [13] , and uncertainty visualization [11] . These methods have greatly improved 3D DTI fiber visualization. Nevertheless, most of them operate in the three-dimensional space, where the geometry is often occluded after being projected to a 2D viewport. To achieve satisfactory results, a user must be trained to perform careful and efficient exploration of the fiber model and to make anatomically correct fiber tract selections: a learning curve that can be steep and time consuming.. The current situation in visualizing complex DTI fiber models is analogous to the difficulty in exploring and visualizing volume datasets. Transfer function design and statistical analysis tools [25] have revolutionized volume rendering by facilitating user interactions and promoting useful insights about the data. The reason behind the success of the transfer functions in volume rendering includes the clarity and simplicity of a 2D representation and its direct coupling with 3D representation. However, to our knowledge, a similar interaction method has not been applied to DTI fiber tracts.. In this paper, we describe a novel DTI fiber exploration scheme that builds upon recent methods for DTI data analysis and fiber exploration techniques. The main contributions include:. • An effective interaction mode that combines 3D, 2D, and statistical views to broaden the user's exploratory space; • A coherent local-dimensional embedding algorithm that preserves the spatial relationships of the fiber tracts and provides the user with an uncluttered 2D representation of the data; and • A set of visualization, manipulation, and statistical analysis tools that reduces the user time and mental workload in recognizing 3D DTI fibers. Figure 1 shows a screen-shot of the main interface of our system. Our integrated system is GPU-accelerated and achieves interactive performance. The rest of this paper is organized as follows. Section 2 provides a brief summary of related work; Section 3 and Section 4 describe the details of our method and its implementation; Section 5 demonstrates the efficiency of the new interface with several case studies and a user evaluation; and Section 6 presents our conclusions. We have presented a novel interface that allows for effective representation and intuitive exploration of fiber tracts. At the core of our work is the embedding of the DTI fiber tracts to a 2D space that preserves the characteristics of the fiber tracts. The users can interact with DTI fibers in this 2D space and view, validate, and compare the results of the interaction in both views. Several case studies have verified the efficiency and reliability of the proposed approach. DTI fibers are usually integrated along the longest eigenvectors in a tensor field [2] . They can be represented and displayed as streamlines [15] , streamtubes and streamsurfaces [27] . The geometric shape of a set of fibers can be further simplified to a more abstractive visual form such as wrapped streamlines [10] or topological simplification [22] or by using hierarchical principal curves [6] . A novel set of interaction techniques introduced in Sherbondy et al. [23] allows for exploring brain connectivity and interpreting pathways. In [23] , the key operation offered to neuroscientists is the placement and manipulation of box-shaped or ellipsoid-shaped regions in coordination with a simple and flexible query language. A similar selection scheme is presented in Blaas et al. [3] . A clinical study shows that this approach is highly reproducible for fractional anisotropy (FA) calculated over the selected fiber bundles. To visually differentiate pathways, four different pattern styles are used to encode the local dissimilarity information of fibers, yielding an online navigation tool for fiber connectivity [13] . The dissimilarity within a group of fibers may be illustrated in cross section with an appropriate coloring scheme [9, 8] , making it easy to discern a cluster by color. Other features derived from the fibers could also be identified and visualized, such as the uncertainty arising from noise and partial volume effects [11] . Most of these schemes focus on the representation of DTI fibers in 3D space, limiting the amount of information that can be shown and explored before excessive visual clutter occurs. A recent work [14] proposes to link an embedding in the plane and a hierarchical clustering tree with the 3D fiber tracts, facilitating navigation through complex fiber tracts.. One application for our approach is DTI fiber clustering. By measuring the proximity among fibers, a fiber set can be grouped into anatomically meaningful fiber bundles. Different proximity measures have been proposed such as the single-linkage hierarchical clustering method. This method is based on the mean distance [26] and yields excellent results in practice [18] . Various clustering schemes can be chosen. Unsupervised partitions can be created by leveraging graph theory like the normalized cut [5] . In addition, a manifold learning scheme [24] can be used to construct proximity measures that capture the neighborhood structures in the high-dimensional data space. Supervised clustering is an alternative choice. Possible approaches include the identification of regions of interest (ROIs), fine-tuning of clustering parameters, or direct manipulations of fiber tracts [3, 23] . To reduce user interaction time, a clustered atlas model can be employed to rapidly construct a set of clusters for a new dataset. The clusters in the atlas model are augmented with expert anatomical labels and are transferred to new models by spectral learning [20] or affine registration [16] . The key idea is that a useful coordination between a simplified feature space view of fibers and the exact geometry in a standard 3D view and the interaction between them is essential for exploring DTI fibers. Many approaches have employed manifold learning algorithms to define a low-dimensional embedding of the fiber tracts that preserves the neighborhood structures in the high-dimensional space [24] . These embedding schemes have been mostly applied to DTI fiber clustering [20] . However, the clarity and efficiency of these techniques have rarely been exploited in other aspects of DTI fiber study such as userdrive interactive fiber tract selection. Our method makes use of both the simplicity of the low-dimensional embedding and the fidelity of the 3D fibers to enhance interaction, visualization, and exploration. We implemented the user interface with Microsoft Visual C++ 2008 and OpenGL and tested it in a PC equipped with an Intel Core 2 Duo 2.4 GHz CPU, 2G host memory, and a Nvidia GTX 280 graphics card.. In the interface, a single view is divided into multiple viewports to support multiple views in a single window. The fiber selection is achieved with the pick and selection features of OpenGL. The rendering of DTI fibers utilized a GPU-accelerated illuminated line algorithm [17] . The visualization, manipulation, and navigation of DTI fibers are in real-time. The implementation of the semisupervised clustering is adequately rapid for interactions: it takes only 1 second for a model with 4,000 fibers. However, computing the distance matrix and the MDS configuration is much more time consuming. Considering the data-parallel nature of matrix multiplications involved in these computations, a parallel acceleration scheme was employed by using the CUDA BLAS language [19] . The acceleration achieved for the construction of the distance matrix and the solving of MDS is more than 5 folds, as shown in Table 2 In addition to the tractography, other DT-MRI visualization schemes were incorporated into the 3D view of our interface, including the ellipsoidal glyphs [15] , streamtube [27] , and HyperLIC [28] representations. The streamtube representation has the same 2D embedding as the streamline representation, while the other two cannot.

O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B I O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Affine

equivalence

of

quartic

monomial

rotation

symmetric

Boolean

functions

in

prime

power

dimension

In

this

paper

we

analyze

and

exactly

compute

the

number

of

affine

equivalence

classes

under

permutations

for

quartic

monomial

rotation

symmetric

functions

in

prime

and

prime

power

dimensions.Published

by

Elsevier

Inc.

An

n-variable

Boolean

function

f

is

a

map

from

the

n

dimensional

vector

space

F

n

¼

n

into

the

two-element

field

F

that

is,

an

n-variable

Boolean

function

f

is

a

multivariate

polynomial

over

F

Denoting

the

addition

operator

over

F

by

a

Boolean

function

can

be

thought

as

a

multivariate

polynomial,

called

the

algebraic

normal

form

(ANF).

a

ij

x

i

x

j

þ

þ

a

x

x

x

n

where

the

coefficients

a

a

ij

a

F

The

maximum

number

of

variables

in

a

monomial

is

called

the

(algebraic)

degree,

and

it

is

denoted

by

degðf

Þ.

If

all

monomials

in

its

ANF

have

the

same

degree,

the

Boolean

function

is

said

to

be

homogeneous..

Functions

of

degree

at

most

one

are

called

affine

functions.

An

affine

function

with

constant

term

equal

to

zero

is

called

a

linear

function.

Define

the

scalar

product

of

x

¼

ðx

x

n

Þ;

y

¼

ðy

y

n

Þ

both

in

F

n

by

x

Á

y

¼

P

n

x

i

y

i

The

(Hamming)

weight,

denoted

by

wtðxÞ,

of

a

binary

string

x

is

the

number

of

ones

in

x,

and

the

Hamming

distance

dðx;

yÞ

between

x

and

by

Elsevier

Inc.

B I O O O O O B I O O O O O O O O O O O O O O O B I O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O