Boundary properties of the inconsistency of pairwise comparisons in group decisions This paper proposes an analysis of the effects of consensus and preference aggregation on the consistency of pairwise comparisons. We define some boundary properties for the inconsistency of group preferences and investigate their relation with different inconsistency indices. Some results are presented on more general dependencies between properties of inconsistency indices and the satisfaction of boundary properties. In the end, given three boundary properties and nine indices among the most relevant ones, we will be able to present a complete analysis of what indices satisfy what properties and offer a reflection on the interpretation of the inconsistency of group preferences. In a wide range of decision making problems, it occurs that an expert, or a group of experts, is asked to rate some alternatives. Selecting the best alternative is trivial when the number of considered alternatives is very small, but complexity arises as the number of alternatives, and criteria with respect to which alternatives are judged, grows. Techniques based on pairwise comparisons allow the expert to discriminate between two alternatives at a time, thus decomposing the problem into more simple and easily tractable sub-problems. The Analytic Hierarchy Process (AHP) by Saaty (1977 Saaty ( , 1980 is probably the best known among all the methods using pairwise comparisons. In a recent survey by Ishizaka and Labib (2011) on the latest developments of the AHP, consistency of preferences and group decisions have been considered hot topics, and the possibility of estimating inconsistency been regarded as a valuable asset for techniques adopting pairwise comparison matrices.. Consistency has been widely regarded as a desirable, yet hardly ever achievable, property of preferences in decision making problems. Following the thesis of Irwin (1958) , which links the concepts of preference and discrimination, being consistent in expressing preferences means being rational in discriminating between alternatives. Although one might argue that consistency does not necessarily imply expertise of the decision maker (consistent preferences could possibly be obtained randomly), it is undebatable that a good expert should always be able to state his preferences in a non-contradictory way. Hence, although consistency alone does not guarantee the expertise of a decision maker, the existence of inconsistencies should be symptomatic of the decision maker's scarce preparation or lack of knowledge of the problem. Going back in time, even in the fundamental contribution by Savage (1972) consistency of preferences was regarded as a desideratum. More recently, Gass (2005) recalled that also Luce and Raiffa (1957) and Fishburn (1991) regarded transitivity of preferences, and consequently their consistency, as an auspicable, but not necessary, condition for the preferences of a decision maker.. Note that the use of the concept of consistency has not been limited to the quantification of inconsistency. For example, just to cite the most recent results, it has been used to improve consistency of preferences in the framework of a model based on Hadamard product between matrices , to detect the most inconsistent comparisons (Ergu et al., 2011) , and to derive the priority vector by means of a geometric similarity measure (Kou and Lin, 2014) . On the other hand, also the concept of group decisions with pairwise comparisons has been studied; for example Altuzarra et al. (2010) proposed a statistical model for consensus in the AHP including assumptions on group consistency, and Bernasconi et al. (2014) studied, from the empirical point of view, different aggregation methods for preferences.. Consistency has been a widely studied research topic in decision sciences, but, in spite of the growing effort in studying group decisions, most of the research on consistency of preference relations has focused on the reliable assessment of the degree of inconsistency of single pairwise comparison matrices. Only few, and more recent, studies (Escobar et al., 2004; Grošelj and Zadnik Stirn, 2012; Lin et al., 2008; Liu et al., 2012) have tried to extend the issue of inconsistency quantification to the case with multiple decision makers by examining single measures of inconsistency but never proposing a more general reasoning on the matter. Furthermore, very few studies have in-vestigated the connection between consensus and consistency. In a qualitative study, Weiss and Shanteau (2004) highlighted how consensus alone does not necessarily lead to better decisions and, instead, emphasized the fundamental role of the expertise of decision makers, which they called consistency.. In this paper we will provide further results on the connection between group decisions and inconsistency, in particular on how the former affects the latter. More specifically we shall define some general boundary properties for the inconsistency of a group of decision makers and see whether different inconsistency indices satisfy them or not. In doing so, we shall be able to derive and use some more general results starting from some axiomatic properties of inconsistency indices (Brunelli and Fedrizzi, 2013) .. The paper is outlined as follows. In Section 2 we recall the definitions of pairwise comparison matrices and inconsistency, and we summarize the axioms which were proposed to characterize inconsistency indices. In Section 3 we define the boundary properties and, within the same section, in Subsections 3.1 and 3.2 we study the satisfaction of lower and upper boundary properties. In Section 4 we discuss the implications of the results, and in Section 5 we draw the conclusions. From our investigation on the connection between consensus and inconsistency, we can summarize some relevant findings. First, the effect of the preference aggregation among different decision makers on the inconsistency of the group preferences depends crucially on the inconsistency index that is used. More precisely, we proved that a certain number of already known indices satisfy the upper boundary property and/or the strong upper boundary property. As a consequence, for some indices the inconsistency of the aggregated preferences is always lower than a weighted mean of the inconsistencies of the original preference relations. This effect can be synthesized by saying that preference aggregation is consistency improving. On the other hand, if the inconsistency is evaluated by means of other indices, then the opposite result can be obtained. Therefore, as pointed out in Brunelli and Fedrizzi (2013) , a suitable choice of an inconsistency index is a crucial phase in decision-making processes, since the use of different methods for measuring consistency can lead to different conclusions and can affect the decision outcome in practical applications. Interestingly, some more general results have been derived from the axiomatic system proposed by Brunelli and Fedrizzi (2013) . If it is true that one of the merits of an axiomatic system is its fertility, i.e. the capacity to produce propositions, then Propositions 1 and 2 and Corollaries 1 and 2 are positive signs in this direction and seem to indicate that the axiomatic system can be used to derive interesting results. Hence, we believe that future research on inconsistency of pairwise comparisons (i) can build upon the axiomatic system A1-A5 and (ii) further investigate the relation between consensus and consistency, perhaps clarifying the open issues exposed in the previous section. In the previous section we analyzed some boundary properties and whether they are respected or not by some well-known inconsistency indices. To do so, we also related these new properties with the axioms A1-A5 introduced by Brunelli and Fedrizzi (2013) and discussed some implications. One result is that the inconsistency of a combination of pairwise comparison matrices cannot be lower bounded by the value of inconsistency of the least inconsistent matrix. We have in fact shown that an inconsistency index satisfying A1 is never lower bounded with respect to the aggregation of the preferences of different decision makers. Moreover, results show that, more often than not, inconsistency indices are, instead, upper bounded. Table 1 summarizes the results obtained in the previous section. Comparing the results summarized in Table 1 with the satisfaction of the axioms A1-A5, it appears that all the indices which satisfy the axioms A1-A5 are also upper bounded. From this, it is only natural to hypothesize that the axioms A1-A5 mathematically imply the satisfaction of the upper boundary condition. However, this is not true and can be formalized in the following proposition.

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


Simultaneous correction of ghost and geometric distortion artifacts in EPI using a multiecho reference scan Abstract-A computationally efficient technique is described for the simultaneous removal of ghosting and geometrical distortion artifacts in echo-planar imaging (EPI) utilizing a multiecho, gradient-echo reference scan.Nyquist ghosts occur in EPI reconstructions because odd and even lines of -space are acquired with opposite polarity, and experimental imperfections such as gradient eddy currents, imperfect pulse sequence timing, field inhomogeneity, susceptibility, and chemical shift result in the even and odd lines of -space being offset by different amounts relative to the true center of the acquisition window. Geometrical distortion occurs due to the limited bandwidth of the EPI images in the phase-encode direction. This distortion can be problematic when attempting to overlay an activation map from a functional magnetic resonance imaging experiment generated from EPI data on a high-resolution anatomical image.The method described here corrects for geometrical distortion related to inhomogeneity, gradient eddy currents, radio-frequency pulse frequency offset, and chemical shift effect. The algorithm for removing ghost artifacts utilizes phase information in two dimensions and is, thus, more robust than conventional one-dimensional methods. An additional reference scan is required which takes approximately 2 min for a matrix size of 64 64 and a repetition time of 2 s. Results from a water phantom and a human brain at 3 T demonstrate the effectiveness of the method for removing ghosts and geometric distortion artifacts. Echo-planar imaging (EPI) has become a common acquisition method for high temporal resolution applications such as functional magnetic resonance imaging (fMRI) and diffusion-weighted imaging (DWI). EPI suffers from two major sources of artifacts: N=2 or Nyquist ghosts, and geometric distortion. The ghosts degrade image quality and signal-to-noise ratio (SNR), and the geometric distortion makes it difficult to co-register EPI images with conventionally acquired anatomical images. These artifacts become more apparent at higher magnetic field strengths where local variations in magnetic field caused by susceptibility gradients cause severe phase distortions in the nuclear magnetic resonance (NMR) signal. For example, in a typical EPI fMRI brain scan, the magnetic field inhomogeneity in the nasal sinuses is on the order of 1 ppm (125 Hz. at 3 T). Since the spins will have de-phased by 4 revolutions over the 32-ms acquisition time, the magnitude of the geometrical distortion in this area will be approximately 4 pixels for a 64 2 64 matrix with a 125-kHz bandwidth. The resulting misregistration of the EPI scans relative to high-resolution anatomical images can lead to misinterpretation of functional activation maps. Furthermore, misregistration of activation maps with anatomical images can be dangerously misleading when fMRI is used for presurgical planning. The ghost artifacts can also lead to inaccurate calculations of the apparent diffusion coefficient in DWI experiments. Methods proposed to correct for the ghost artifact include one-dimensional phase correction using nonphase encoded or phase-encoded reference scans [1] , [2] , and two-dimensional (2-D) correction using the phase information from the EPI image [3] . Methods to correct for geometric distortion involve collecting conventional gradient echo, offset spin-echo, or EPI images at different values of echo time (TE) in order to estimate the B 0 field inhomogeneity [4] - [6] . A method using a multiecho reference scan was recently proposed by Chen and Wyrwicz [7] . However, that method is very computationally intensive. In clinical applications of DWI or fMRI, where viewing of the results is desired within a short time frame, the method of Chen and Wyrwicz may not be feasible. In research fMRI applications, it is often desirable to process the data before the subject leaves the scanner to check for motion artifacts and subject compliance and to redo the fMRI scan if necessary. Online processing is particularly useful in pediatric applications, the focus of research in our center, where failure rates due to motion or subject noncompliance are higher than in adults [8] . While it is possible to estimate subject motion directly from the k-space EPI data [9] , the availability of online activation maps is still useful in order to monitor for subject compliance and to make a judgment on whether the scan needs to be repeated.. In this paper we propose a method to simultaneously correct for ghosting artifacts and geometric distortion with use of the multiecho reference scan. The distorted EPI images are first corrected for ghosting based on the method proposed by Chen and Wyrwicz [10] , and then for geometric distortion based on the phase images generated from the reference scan. For a 64 2 64 matrix the multiecho reference scan can be acquired in 128 s with a 2-s repetition time, and may be easily run as a multislice experiment, provided the repetition time (TR) time allows.. The algorithms used to perform the ghost correction and distortion correction were implemented in Interactive Data Language (Research Systems, Inc., Boulder, CO). 1 The parameters needed for these corrections are calculated from the reference scan, and these parameters may then be used to correct all EPI scans subsequently acquired during an imaging session, as long as the subject does not move. Once the necessary parameters are calculated from the multiecho reference scan, the only added computational costs required to apply the corrections to subsequent scans are an additional Fourier transform, multiplication, and addition for the ghost correction, and a sinc interpolation for the geometric distortion correction. These corrections, therefore, add minimal computational time at no cost in SNR. We have implemented an easy and time-efficient method for correcting for ghosting and geometric distortion simultaneously by using a multiecho reference scan. The multiecho reference scan can be obtained in approximately 2 min with a 2-s TR if there are 64 lines in the phase-encode direction. This scan can be used to simultaneously correct for both Nyquist ghost artifacts and for geometric distortion. Once the appropriate parameters are calculated from the reference scan, the corrections can be implemented with minimal cost in computational time and no cost in SNR. The correction can then be applied to all EPI data sets subsequently acquired during an imaging session, as long as the subject does not move. As advanced imaging methods are implemented at increasingly higher magnetic field strengths, applying corrections such as described here becomes increasingly important.. EPI images of both a ball of water and a human brain at 3 T were acquired and the method described above effectively corrected for both the ghosting and the geometric distortion in those images. The parameters needed for the corrections were computed in approximately 1 s for each 64 2 64 slice on a Dell 933-MHz Pentium III workstation running Windows NT. The total time needed to reconstruct each slice, including both the ghost and geometric distortion correction, was approximately 0.012 s. For a typical fMRI dataset consisting of 24 slices and 100 time points for a total of 2400 images, the correction parameters may be computed in under 30 s, during which time the first fMRI task may be performed by the subject. The entire fMRI dataset may then be reconstructed in approximately 30 s, allowing for the images to be viewed before the subject leaves the scanner. The method allows, however, for the later use of the correction method of Chen [7] , should it be so desired, as the same reference data is acquired. (1) where (1) is the Dirac delta function, is the projection angle, r and are polar coordinates, and = x cos + y sin and = 0x sin +y cos define a rotated coordinate system. In this paper, we will consider R as a compact operator between the spaces L 2 (D) and L 2 (Z ; w 01 ) [1] , where Z = [01; 1] 2[0; 2) , and w() = 1 0 2 . In the absence of data noise or errors, the inverse Radon transform R 01 can be calculated and used to recover the object f exactly. However, the presence of data noise or errors generally renders the inverse problem ill-posed.. Range conditions for the Radon transform have been widely studied [2] , [3] . While of obvious theoretical importance, the exploitation of range conditions may also have significant practical implications. Forcing an inconsistent data function to satisfy the range conditions is operationally equivalent to projecting the data function onto the range of the imaging transform. Because projecting to the range removes the inconsistent component of the data function, it may reduce statistical noise and deterministic artifacts that may, in turn, improve the quality of the reconstructed image. Of course, projecting the data function to the range of the imaging transform also ensures that a solution to the inverse problem exists.. The filtered backprojection (FBP) algorithm is a widely used reconstruction algorithm for inverting the 2-D Radon transform [2] , [4] . In the absence of data noise and errors, the FBP algorithm can exactly invert the Radon transform. In this paper, we examine the processing of a Publisher Item Identifier S 0278-0062(01)04409-3.. 0278-0062/01$10.00 ©2001 IEEE

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


Quantum Error Correction beyond the Bounded Distance Decoding Limit Abstract-In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density paritycheck codes defined over Galois field of size 2 p . The proposed quantum error correcting codes are based on the binary quasicyclic CSS (Calderbank, Shor and Steane) codes. The resulting quantum codes outperform the best known quantum codes and surpass the performance limit of the bounded distance decoder. By increasing the size of the underlying Galois field, i.e., 2 p , the error floors are considerably improved. In 1963, Gallager invented low-density parity-check (LDPC) codes [1] . Due to the sparseness of the code representation, LDPC codes are efficiently decoded by the sum-product algorithm. By a powerful optimization method density evolution [2] , developed by Richardson and Urbanke, messages of sum-product decoding can be statistically evaluated. The optimized LDPC codes exhibit error correcting performance very close to the Shannon limit [3] . Recently, LDPC codes have been generalized from a point of view of Galois fields, i.e. non-binary LDPC codes are proposed. Non-binary LDPC codes were invented by Gallager [1] . Davey and MacKay [4] found that non-binary LDPC codes can outperform binary ones.. Quantum LDPC codes, which are quantum error-correcting codes, have been developed in a similar manner to (classical) LDPC codes. By the discovery of CSS (Calderbank, Shor and Steane) codes [5] , [6] and stabilizer codes [7] , the notion of parity-check measurement, which is a generalized notion of parity-check matrix, is introduced to quantum information theory. In particular, a parity-check measurement for a CSS code is characterized by a pair of parity-check matrices which satisfy the following condition: the product of one of the pair and the transposed other is subjected to be a zero-matrix.. Quantum LDPC codes were first introduced by Postol in [8] . The above CSS constraint on the parity-check matrices makes the design of the quantum LDPC codes difficult. MacKay et al. proposed the bicycle codes [9] and Cayley graph based CSS codes [10] . In [11] , Poulin et al. proposed serial turbo codes for the quantum error correction. These codes can be decoded by an efficient iterative decoder. To the best of the authors' knowledge, these codes [9] , [10] , [11] are the best known quantum error correcting codes among efficiently decodable quantum LDPC codes so far. In [12] , Hagiwara and Imai proposed a construction method of CSS code pair that has quasi-cyclic (QC) parity-check matrices with arbitrary regular even row weight L ≥ 4 and column weight J such that L/2 ≥ J ≥ 2. However, the resulting codes do not outperform the codes proposed by MacKay el al. [9] , [10] .. Generally, LDPC CSS codes tend to have poor minimum distance. The minimum distance of an LDPC CSS code is upper-bounded by the row weight of the parity-check matrix. This is due to the dual and sparse constraint on the paritycheck matrices. When the LDPC CSS codes are used with large code length, the poor minimum distance leads to high error floors. Therefore, it is desired to establish the construction method of quantum LDPC codes with large minimum distance. We should note that it is important to study quantum LDPC codes with large minimum distance which grows with code length [13] for constructing quantum LDPC codes with vanishing decoding error probability.. Non-binary LDPC codes are defined as codes over GF(2 p ) with p > 2. The parity-check matrices of non-binary LDPC codes are given as sparse matrices over GF(2 p ). In this paper, we investigate non-binary LDPC codes for quantum error correction. It is empirically known that the best classical nonbinary LDPC codes have column weight J = 2 from a point of view of error-correcting performance [14] . Moreover, due to the sparse representation of non-binary parity-check matrices of column weight J = 2, the non-binary LDPC codes are efficiently decoded by FFT-based sum-product algorithm [15] .. In this paper, we propose a construction method of a binary CSS code which can be viewed also as a pair of nonbinary LDPC codes. More precisely, the proposed construction method produces a binary code pair (C, D) such that C ⊃ D ⊥ , and C and D are also defined by non-binary sparse paritycheck matrices over GF(2 p ) of column weight J = 2. This satisfies the constraint of CSS codes. To this end, we first construct P J × P L binary QC parity-check matrix pair (Ĥ C ,Ĥ D ) with column weight J = 2 and row weight L such thatĤ CĤ T D = 0 by the method developed in [12] . Solving some linear equations on Z 2 p −1 , we get P J × P L non-binary parity-check matrix pair (H Γ , H ∆ ) with column weight J = 2 and row weight L such that H Γ H T ∆ = 0. It is known that a natural linear map from GF(2 p ) to GF (2) p×p is given so that through this map, the non-binary LDPC matrix pair (H Γ , H ∆ ) can be viewed as a binary LDPC matrix pair. Numerical experiments show the resulting CSS codes outperform the best known quantum error correcting codes and surpass the performance limit of the bounded distance decoder. By increasing the size of the underlying Galois field, i.e., 2 p , the error floors are The rest of this paper is organized as follows. Section II describes the construction method of a non-binary twisted LDPC parity-check matrix pair (HG, H ∆ ) of column weight J = 2. Section III describes the decoding algorithm of the binary twisted code pair (C, D). Section IV demonstrates the decoding performance of the proposed codes. We proposed a novel construction method of CSS codes. The resulting CSS codes can be viewed as non-binary LDPC codes over GF(2 p ). Due to the sparse representation of the parity-check matrices, the proposed codes are efficiently decoded. The simulation results over the depolarizing channels show that the proposed codes outperform the other quantum error correcting codes which exhibited the best decoding performance so far. The error floors are lowered by increasing the size of the underlying Galois field, i.e., 2 p .

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


Extended Gabor approach applied to classification of emphysematous patterns in computed tomography Abstract Chronic obstructive pulmonary disease (COPD) is a progressive and irreversible lung condition typically related to emphysema. It hinders air from passing through airpaths and causes that alveolar sacs lose their elastic quality. Findings of COPD may be manifested in a variety of computed tomography (CT) studies. Nevertheless, visual assessment of CT images is time-consuming and depends on trained observers. Hence, a reliable computer-aided diagnosis system would be useful to reduce time and interevaluator variability. In this paper, we propose a new emphysema classification framework based on complex Gabor filters and local binary patterns. This approach simultaneously encodes global characteristics and local information to describe emphysema morphology in CT images. Kernel Fisher analysis was used to reduce dimensionality and to find the most discriminant nonlinear boundaries among classes. Finally, classification was performed using the k-nearest neighbor classifier. The results have shown the effectiveness of our approach for quantifying lesions due to emphysema and that the combination of descriptors yields to a better classification performance. COPD describes a collection of lung diseases that are characterized by parenchymal destruction and gradual limitation of airflow. Although it may manifest as emphysema, chronic bronchitis, or both, the former is the most common pathophysiological manifestation and is mainly attributable to tobacco smoking [2] . Studies of the World Health Organization report that over 65 million people have COPD worldwide and predict that it will be responsible for 10 % of the world's mortality by 2030 [22] . Therefore, in order to prevent other health complications such as pneumothorax and respiratory infections, the accurate characterization of emphysema is required for developing efficient treatments.. The literature recognizes three types of emphysema [26] : (1) Paraseptal (PS) also known as distal acinar emphysema is characterized by destruction of distal airway structures, alveolar ducts, and alveolar sacs. It is localized around the pleura; (2) Panlobular (PL) or panacinar emphysema destroys uniformly alveoli and prevails in the lower half of the lungs; and (3) Centrilobular (CL) or centriacinar emphysema is the most common type of pulmonary emphysema. It begins in the respiratory bronchioli and spreads peripherally. Most of the damage is usually contained to the upper half of the lungs.. Attenuation values in CT images, which are expressed in the Hounsfield unit (HU) scale, have been used to identify pathological changes in lung parenchyma because they are linked to physical density of lung tissue [14] . Hayhurst et al. [9] showed that attenuation values in patients who had CL differed from healthy patients with normal tissue (NT).. Density mask is a common technique used to quantify emphysema. It describes the amount of air presented in a CT image and computes the percentage of pixel values smaller than a previously selected threshold. Routinely, -910 HU is taken as a standard threshold but recently Madani et al. [12] observed that if the threshold lies somewhere between -960 to -980, HU then the correlation with emphysema is larger. Mean lung density [25] is another objective measure of the extent of macroscopic emphysema; it is defined as the percentage of tissue lung below -950 HU. All these metrics consider that emphysema causes an abnormal enlargement of air spaces; thus, the air-tissue ratio in an emphysematous lung should increase, whereas the density should decrease proportionally to the amount of emphysema. Nevertheless, such methods are sensitive to scanner calibration and noise. In addition, they cannot distinguish emphysema patterns due to averaging effect.. On the other hand, texture analysis in lung CT images may provide new insights toward the construction of a reliable computer-aided diagnosis system because it is capable of identify changes in lung parenchyma and abnormalities associated with emphysema. For instance, Sørensen et al. [24] combined textural features using local binary patterns (LBPs) to classify three classes of emphysema. In [3] , fractal analysis was proposed to classify 3258 emphysema patches of size 64 9 64 pixels. A simpler alternative based on the density estimation of local histograms was introduced in [13] . A different approach was presented in [23] where the authors used metadata to label lung samples. A technique based on the embedded probabilistic PCA was proposed in [29] to classify interstitial lung abnormalities that include emphysema as one class, whereas in [5] , the Riesz transform was used to obtain features of lung abnormalities.. In this study, we propose a novel approach that exploits the advantages of complex Gabor filters (CGF) such as the strong correlation with the human visual system and simultaneously encodes local intensity information provided by LBPs. The former are global descriptors, whereas the latter are local operators. Since the low-attenuation areas in lung CT images describe different emphysema patterns, the discrimination problem was focused on the characterization of local intensities and global spatial variations. Our approach considers these aspects and provides a robust representation for each type of emphysema. Therefore, an improvement in the classification rate can be attained. We used a methodology composed of three stages to assign a given patch to one of several patterns: (1) feature extraction, (2) dimensionality reduction using kernel Fisher discriminant analysis (KFDA), and (3) classification using k-nearest neighbor (k-NN) classifier. This paper is organized as follows: In Sect. 2, we described the construction of the feature vectors. In Sect. 3, we explained the procedure to reduce dimensionality. The data are presented in Sect. 4 . The experiments and results are detailed in Sect. 5. Finally, our work is summarized in Sect. 6. In this paper, we proposed a new approach to quantify up to six emphysema patterns based on complex Gabor filters and local binary patterns. This joint model allows to encode global texture characteristics with local information simultaneously. We presented the complex Gabor model and summarized its properties related to the human visual system. Since Gabor-based methods transform images into a high-dimensional feature vectors, we applied kernel Fisher discriminant analysis via the kernel trick to avoid computing a mapping function and to find discriminant boundaries among classes. Then, we performed tenfold cross-validation and leave-one-patient-out cross-validation to assess our approach. We also included a comparison between complex and real Gabor filters. The difference is that in the frequency, domain real Gabor filters are represented by two real-valued Gaussians symmetrically placed on each side of the origin, whereas complex Gabor filters are represented with a single Gaussian on the positive side of the spectrum. Therefore, real filters contain more redundant information than complex filters. However, redundant information does not always allow greater discrimination ability. This suggests that the next step to improve the classification should be a sparse model that performs a deeper analysis of the redundant information.. In general, the extended descriptors increased precision rates around 15 % in the BW dataset. Concerning the BWH dataset, our method achieved a F 1 score of 70.32, which means 10 % above any single descriptor. Theses results were mainly influenced by the misclassified severity levels of CL, most of the errors occurred between moderate and severe emphysema that could indicate a limitation of the BWH database.. It seems that only the distribution of attenuation values in PS is clearly different from the rest of the classes. Since we consider that the main limitation of filter approaches is that the information from each coefficient is represented with a few moments causing loss of information in terms of orientation and distribution, we used LBPs to overcome this limitation and characterize the distributions of local patterns. Most of the errors using GFV occurred between NT and CL patterns but the precision rates of such patterns increase around 30 % when EGFV 16;2 is used. These results have shown that the proposed approach is a promising technique that yields a good performance in Table 6 Comparison rates using the BWH dataset and leave-one-patient-out cross-validation

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


Three-dimensional encoding/two-dimensional decoding of medical data We propose a fully three-dimensional (3-D) wavelet-based coding system featuring 3-D encoding/two-dimensional (2-D) decoding functionalities. A fully 3-D transform is combined with context adaptive arithmetic coding; 2-D decoding is enabled by encoding every 2-D subband image independently. The system allows a finely graded up to lossless quality scalability on any 2-D image of the dataset. Fast access to 2-D images is obtained by decoding only the corresponding information thus avoiding the reconstruction of the entire volume. The performance has been evaluated on a set of volumetric data and compared to that provided by other 3-D as well as 2-D coding systems. Results show a substantial improvement in coding efficiency (up to 33%) on volumes featuring good correlation properties along the z axis. Even though we did not address the complexity issue, we expect a decoding time of the order of one second/image after optimization. In summary, the proposed 3-D/2-D multidimensional layered zero coding system provides the improvement in compression efficiency attainable with 3-D systems without sacrificing the effectiveness in accessing the single images characteristic of 2-D ones.

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A design for adaptive web service evolution In this paper, we define the problem of simultaneously deploying multiple versions of a web service in the face of independently developed unsupervised clients. We then propose a solution in the form of a design technique called Chain of Adapters and argue that this approach strikes a good balance between the various requirements. The Chain of Adapters technique is particularly suitable for self-managed systems since it makes many versionrelated reconfiguration tasks safe, and thus subject to automation. Version management of deployed software has always been a tricky business. In this age of foreshortened development cycles, direct unsupervised links between independently developed applications, and increasingly self-managing systems, the complexity of evolving "live" applications is becoming a critical issue. In this paper, we explore the problem and propose a design technique that makes managing version evolution simpler-whether for human administrators or self-managing systems.. Since easing version management is an overly broad target, we focus specifically on versioning of web services-broadly understood as applications whose functionality is exposed to third-party clients over a network. Our goal is to permit the evolution of a service's interface and implementation while remaining backwards-compatible with clients written to comply with previous versions. Section 2 lists all our requirements in detail and demonstrates why a number of common versioning strategies are inappropriate in this context.. Our solution, which we call Chain of Adapters and present in Section 3, is a design technique that can be applied by the service developer and imposes no requirements on clients or server infrastructure. While it is simple enough to be applied manually, we also describe a prototype tool we have built to automate some of its more repetitive aspects. It is well suited to deployment in selfmanaging systems since it affords the manager a larger number of safe configuration options. Section 4 discusses related work, and Section 5 concludes with a summary and future research directions. In this paper, we laid out our requirements for a solution to the web service version management problem, and illustrated a number of unsatisfactory yet popular approaches. We then presented our own solution called Chain of Adapters, which is a simple design technique that can be applied by the developer to achieve backwards compatibility. Our technique provides a good tradeoff between satisfying the various requirements, with particular strength in the area of version untangling.. The Chain of Adapters can prove useful in self-configuration scenarios. By decomposing a long update/roll-back transaction into a sequence of independent smaller transactions, the response time is affected to a smaller degree and the end user won't notice a discontinuity in service.. Though we implemented an Eclipse plug-in that helps apply this technique to WSDL/SOAP web services and tested it on a few small applications, it is not clear whether the design would scale to large web services. Further evaluation along these lines is needed, as well as further research into independent re-inventions of this design technique in hope of an eventual promotion to a full-fledged design pattern. The effectiveness of this approach in self-configuration scenarios is also subject to further work. Vinoski [18] and Stuckenholz [17] provide rather bleak overviews of the state of the art in middleware versioning. Within the realm of web services, Ponnekanti and Fox's work [15, 14] is the closest to ours, proposing to chain interface adapters to achieve compatibility. However, they focus on using third party adapters to match clients with independently developed web services rather than on including the development of such adapters in the web service evolutionary cycle. Brown and Ellis [2] , on the other hand, advocate having one service support multiple interfaces (cf. Figure 5 but without the inheritance) and advertising the fact through UDDI. Irani [8] covers the subject at a high level, and seems to advocate running multiple versions in parallel (cf. Figure 3 ) at a single endpoint, with a broker in the server engine dispatching calls appropriately. Finally, Kalali et al. [9] assume that clients can adapt automatically to changing interfaces if they are but notified that they have indeed changed.. For web services defined using WSDL and XML Schema, another promising avenue of approach is to look specifically at the extensibility of XML languages. Most of the work is centered around the W3C, with unfinished proposals that range from XML Schema extensibility details [11, 12, 13] to general versioning principles [14] such as "must understand" and "must ignore" rules. Wilde [19] has looked at applying some of these ideas to web services, along with additional declarative semantics to describe extensions to a service's vocabulary. While some of these ideas look promising and may yet come to fruition, they are not yet distilled enough to be employed by web service developers without further research.. Finally, the present work was inspired by (and its name derived from) the Adapter and Chain of Responsibility design patterns from Gamma et al. [5] . We later discovered that a design technique essentially identical to Chain of Adapters had been suggested by Hallberg [7] for Haskell modules under the name "Eternal Compatibility in Theory"; we do not know whether his proposal was adopted by that community. Hallberg hints that the idea may have been floated much earlier by Stroustrup, and we also have anecdotal reports of the technique being used informally Figure 11 . Reconfiguring an application piece-by-piece in other object-oriented systems. If so, it may well be a design pattern just waiting to be discovered.

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Introducing k-point parallelism into VASP For many years ab initio electronic structure calculations based upon density functional theory have been one of the main application areas in high performance computing (HPC). Typically, the Kohn–Sham equations are solved by minimisation of the total energy functional, using a plane wave basis set for valence electrons and pseudopotentials to obviate the representation of core states. One of the best known and widely used software for performing this type of calculation is the Vienna Ab initio Simulation Package, VASP, which currently offers a parallelisation strategy based on the distribution of bands and plane wave coefficients over the machine processors. We report here an improved parallelisation strategy that also distributes the k-point sampling workload over different processors, allowing much better scalability for massively parallel computers. As a result, some difficult problems requiring large k-point sampling become tractable in current computing facilities. We showcase three important applications: dielectric function of epitaxially strained indium oxide, solution energies of tetravalent dopants in metallic VO2, and hydrogen on graphene. This document is a report for the dCSE-funded project that introduces k-point parallelism into VASP v5.2.2 on HECToR. In what follows I will briefly show why the performance of VASP is important on HECToR, how it is parallelized, and then I shall discuss the introduction of k-point parallelism into VASP and how I implemented what I will call k-point parallelized version of VASP. I shall then present the results of the k-point parallelized code and finally discuss the improvements in VASP that my work delivers. The k-point parallelized codes can certainly provide more efficient use of computation cycles as it can be demonstrated in tests cases (2.1)-(2.2) and application 4.1. There are also other cases, where either the original code does not scale at all to larger number of cores -see test cases (2.3),(2.5) , or the original code does not even work on large number of cores (see test case (2.4)) or exterior limitations such as the 12 hour queue on HECToR in application (4.2) do not allow large simulations. In all these cases we demonstrated the calculations could be achieved with the k-point parallelized code. • Dr Ian J. Bush for the constant support and the fruitful discussions and corrections during the code development process, the proof-reading and corrections on this report and all the presentations relevant to this work. He should be thanked also for the coordination of the successful collaboration with the HPC Materials Chemistry Consortium.

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In silico description of cobalt and nickel assimilation systems in the genomes of methanogens Abstract Methanogens are a diverse group of organisms that can live in a wide range of environments. Herein, cobalt and tungsten assimilation pathways have proposed to be established in the genomes of Methanococcus maripaludies C5 and Methanosarcina mazei Go1, respectively. All of the proteins involved in the proposed pathways were identified from public domain databases and then complied manually to reconstruct the pathways. The function of proteins with unknown function was assigned by a combined prediction approach. Totally, 17 proteins were identified to cobalt transport and assimilation processes whereas 7 proteins reported to tungsten assimilation system. Phylogenetic analysis of this study revealed that heavy metal transporter of methanogens could be evolved from closely related members in the different genera of methanogens. Nevertheless, genes encoding for metal resistance proteins could be originated from thermophilic and sulfur reducing bacteria. Many metalloenzymes in methanogens were very unique to the species of methanogens. It implied that these metal ions were utilized to produce the precursors for energy driven processes of methanogens. This study suggested that in combination of systems models and evolutionary inference can only correlate metabolic fluxes and physiological changes in methanogens. In silico models of this study will provide insights to design experiments for heavy metal assimilation processes of methanogens growing under heavy metal-rich environments and or in a laboratory condition. A huge quantity of heavy metal ions have been deposited in the environment due to a general global increase in industrial activity over the past few decades (Silver and Phung 1996) . Although transition metals cobalt and tungsten, essential components of many enzymes, are taken up by specific transport systems of several different types. All metals are toxic at higher concentrations, because they cause oxidative stress by formation of free radicals (Berti and Jacobs 1996) . The transport of ions into the cytoplasm is generally a tightly controlled process mediated by membrane transport proteins. It is more regulated due to the selectively permeable plasma membrane of the cells, which usually has a large negative resting potential. This membrane potential provides a strong electrochemical gradient for the inward movement of metal ions. Most metal ions enter cells by an energy dependent saturable process via specific or generic metal ion carriers or channels (Bubb and Lester 1991) . Metal chelate complexes may also be transported across the plasma membrane via specialized carriers (Cunningham and Berti 1993; Chellapandi 2011) .. The transition metals cobalt and tungsten are essential cofactors for a number of prokaryotic enzymes involved in a variety of metabolic processes. Methanogens are of particular interest for bioremediation purpose since they can exist under heavy metals contaminated ecosystems. Florencio et al. (1994) studied the effect of cobalt on the growth rate and activity of different microorganisms involved in the anaerobic degradation of methanol. They reported that only methylotrophic methanogens and acetogens are stimulated by cobalt. Park et al. (2010) emphasized the importance of supplementing trace metals such as iron, cobalt, and nickel for maximum methanogenic activity, there is no evidence whether such supplements, even at relatively low concentration, could perturb anaerobic biomass. It strongly suggested that acetoclastic methanogens stressed due to reduced hydraulic/solids retention time may be susceptible to trace metal addition. Formate dehydrogenase, formyl methanufuran dehydrogenase, acetylene hydratase, and a class of phylogenetically related oxidoreductases are tungstoenzymes that catalyze the reversible oxidation of aldehydes (Kletzin and Adams 1996) . Kessler et al. (1997) reported that tungsten has specifically to inhibit diazotrophic growth of Methanococcus maripaludis in the presence of molybdenum. The mechanism of nickel and cobalt uptake in many bacteria and most archaea is not known, although, for instance in methanogenes, Ni-and Co-containing enzymes are essential for energy metabolism and anabolism (Rodionov et al. 2006 ). Moreover, a little effort has been made on investigating the cellular systems of methanogens for controlling uptake and distribution of metal ions prevent toxic accumulation and subsequent oxidative damage of macromolecules.. Combining the relevant metabolic and genomic information of an organism allows for metabolic comparisons to be performed between various species of the same organisms as well as between different organisms (Francke et al. 2005) . It also manifests the additional information of cellular and physiological processes of organisms (Vothknecht and Tumbula 1999) . Proteomic investigations of methanogens in their native environments provide the most realistic information about their function but also pose the greatest experimental and bioinformatics challenges (Lacerda and Reardon 2009). Systems biology approaches have often been used to gain insights into the physiological responses of microorganisms to heavy metal stresses (Mergeay et al. 2003; Marrero et al. 2004; Baker-Austin et al. 2005; Rohlin and Gunsalus 2010) . In this perspective, the present study was aimed to elucidate the cell function and physiology of methanogens in response to transport and assimilation processes of cobalt and tungsten ions using computational systems biology approach. Heavy metal toxicity on cellular metabolism of methanogens is still being a major problem for commodity production using industrial effluents containing heavy metals incorporation (Pedone et al. 2004 ). Since, in silico description has revealed on understanding cobalt and tungsten assimilation behaviors of methanogens. The rate evolution of a gene remains the same as long as the biological function does not change (Kimura 1983 ). The identification of orthologous genes among many species is the shortest way to predict functions of sequenced genomes (Razia et al. 2010 ). Initially, orthologs of known nickel and cobalt transporter genes in available prokaryotic genomes were identified by similarity search. A combined functional prediction (sequence similarity search, phylogenetic interface, structure-function relationship) was employed for assigning function of missing proteins with unknown function. Perhaps, such approach can provide more biological reliability, when the predicted proteins incorporated in the proposed systems. Cobalt ions are imported into the cell through a membrane complex formed by a protein assembly cbiAM-NOQS located in the membrane of M. maripaludies. CobW is associated czcD to form the first efflux system while cbiO1PT with corA assembled to form second efflux system. Transport of cobalt ions against their concentration gradient through membrane may be derived by copper transporting P-type ATPase (copP). Apart from the metal transporter systems, it assumed five possible ways to utilize cobalt ions in the cytoplasm; (1) a cobalt ion incorporated with sirohydrochlorin can be converted cobalt-sirohydrochlorin reversibly by enzyme cbiX; (2) cob (II)yrinic acid a,c-diamide and hydrogen ion are produced from hydrogenobyrinic acid a,c-diamide and cobalt by enzyme cbiA; (3) cbiE, a cobalt-dependent enzyme, is used for synthesis of precorrin-8X and carbon dioxide; (4) carbon monoxide dehydrogenase is contributed to produce carbon dioxide from carbon monoxide that can be activated in presence of cobalt ion; (5) 3-dehydroquinate and phosphate are final products of enzyme reaction catalyzed by aorB. As the consequence of these reactions, hydrogen ions and CO 2 are produced that can be served as substrates for methane biosynthesis. It suggested that cobalt ions can take an account to indirectly regulate the methanogenesis of methanogens, particularly hydrogen utilizing methanogens. Cobalt ion is required for nitrogen metabolism because of 3-dehydroquinate synthase activity dependent on the concentration of cobalt ions. The proposed cobalt assimilation systems is accorded with earlier investigations (Lorowitz et al. 1992; Bhattacharya et al. 1995; Brindley et al. 2003) .. Tungsten is the heaviest atom and the only third-row transition element that exhibits biological activity in enzymes (Bevers et al. 2008) . Tungsten-specific transporter (torBP) is occurred in the membrane of M. maripaludies, which is functionally identical to tungsten transport protein A (wtpA) of hyperthermophilic archaeon Pyrococcus furiosus (Bevers et al. 2006) . The presence of tungstendependent enzymes (fwdD, fpoI, aor2) in this genome suggested that methanogenic archaea are utilizing tungsten as one of the key metals for their energy-driven process. Concentration gradient energy driven process can be activated on pumping tungsten ions across the cell membrane and excessive or accumulated ions can be indirectly utilized for catalytic activities of these enzymes. As similar to cobalt assimilation systems, carbon dioxide is evolved as Fig. 5 Phylogenetic tree of aor2 and cdh2/coxA families in the genome of M. mazei Go1 constructed by NJ algorithm with similarity sequences of closely related organisms end-products that may be served as a substrate of the methane biosynthesis. Thus, it revealed the physiological importance of tungsten ions in methanogens for their energetic metabolisms.. ABC transporter plays a crucial role in substrate uptake, export, and osmoregulation in methanogens (Nies 2003) . Many bacterial species possess transporters from only one family, and few species have a redundant set of nickel/ cobalt transporters from different families (Rodionov et al. 2006) . Methanogens have typical transporter for capable and selective transport of these metal ions. Even if metal transporter can be evolved from closely related members in the different genera of methanogens, metal resistance proteins may be originated from thermophilic and sulfur reducing bacteria. Protein superfamilies of methanogens for metal transport process have a reasonable sequence similarity to closely related protein families of proteobacteria. It may be reasonable due to unique genomic and evolutionary features and ancient metabolic adaptation. Nevertheless, these protein families can be evolved into present bacterial lineages at a slow evolution rate (Ranea et al. 2004; Dupont et al. 2010) . It suggests that methanogens have typical metal transporter as compared to present bacterial system.. Metalloenzymes are very unique to the species of methanogens. CbiX/cbiN, coxA, cdh2, and aor2 families show a phylogenetic proximity between methanogens and thermophilic archaea in accordance to earlier report (Itoh 2003) . A close evolutionary resemblance is noted between methanogens and acidogenic bacteria for cbix/cbiN. It may possibly occur when such proteins of these organisms shared for energetic metabolisms in a microbial consortium (Lee et al. 2008; Henderson et al. 2010) . AroB family of methanogens has phylogenetically corresponded with sulfur utilizing archaea as a result of sulfur cycling and methanogenesis are primarily drive microbial colonization (Borin et al. 2009 ). Hence, it revealed the phylogenetic and metabolic relatedness for heavy metal assimilation pathways can likely be established among methanogens, sulfur utilizing archaea and methylotrophs, which is agreed with earlier works (Boetius et al. 2000; Thomsen et al. 2001; Orphan et al. 2001 Orphan et al. , 2003 Teske et al. 2003; Caldwell et al. 2008) . Nonetheless, in silico representation should couple with an experimental program that may provide valuable information including genetic and metabolic regulatory systems of methanogens. The present pathway models will thus provide a simple idea to understand the heavy metal assimilation behaviors of methanogens. The text mining results implied that M. maripaludies C5 genome has more number of protein sequence entries for cobalt utilization whereas Methanosarcina mazei Go1genome possessed a good established system to tungsten assimilation. Other methanogens have only limited number of protein entries in the database.. Cobalt assimilation system in M. maripaludies. The genome of M. maripaludies is comprised of 10 protein coding genes (cbiS, cbiQ, cbiT, cbiP, cbiO1, cbiN, cbiM, corA, cobW, czcD) for cobalt transport and export processes, and 7 protein coding genes (cbiA, cbiN, cbiD, cbiB, cbiE, coxA, aroB) for cobalt-dependent biochemical reactions involved in the different metabolic pathways (Table 1) . Among these, the function of proteins cbiP and cobW were predicted in this study. Cobalt ABC transporter, inner membrane subunit and predicted cobalt ABC transporter, permease have similar conserved domain (cbiQ; e-value 3.70 9 10 -34 ), showing the functional In silico description of cobalt and nickel 107 resemblance for transporting cobalt ions across the cell membrane. Apart from cation diffusion facilitator family protein, this genome has a protein cobW that is functionally corresponded to Ni/Co exporter as the results of the conserved domain similarity (Ras-like GTPase superfamily; e-value 1.98 9 10 -19 ) and other sequence and structural likeliness. This study shows that it has four ABC transporters (cbiPQST) and in addition to that, four transporter proteins (cbiMNO1 and corA) existed to increase the cobalt transport rate of this organism. Cation facilitator family protein (czcD) along with predicted Ni/Co exporter can regulate the cobalt ion export from cytoplasm of the cell. Cobalt assimilation process in the cell may be raised by the incorporation of cobalt ions into the enzymes, such as cbiA, cbiN aoxA and aroB. Cobalt ions can also contribute in photorespiration process indirectly by synthesizing precursors as the result of occurring enzymes cbiBDE. As represented in Fig. 1 , cobalt ion export rate mediated by a protein complex (cobW-czcD) is lower than cobalt transport rate carried out by a transporter assembly (cbiAMNOQS). A transporter assembly cbiO1PT-corA is supported to increase the cobalt transport rate, which is rather than that of enzymatic detoxification processes.

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Automatic Moderation of Online Discussion Sites Online discussion sites (ODS) are plagued with various types of unwanted content such as spam, obscene and malicious contents. Prevention and detection-based techniques have been proposed to filter inappropriate content (IC) out from ODS. But, while prevention techniques have been widely adopted, detection of IC remains mostly a manual task. Existing detection techniques, which are divided into rule-based and statistical techniques, suffer from various limitations. Rule-based techniques usually consist of manually crafted rules or blacklists of keywords. Both are time-consuming to create and tend to generate too many false-positives and false-negatives. Statistical techniques typically use corpora of labeled examples to train a classifier to tell "good" and "bad" messages apart. Although statistical techniques are generally more robust than rule-based techniques, they are difficult to deploy because of the prohibitive cost of manually labeling examples.In this paper, we describe a novel classification technique to train a classifier from a partially labeled corpus and use it to moderate IC in ODS. Partially labeled corpora are much easier to produce than completely labeled corpora, as they are only made 1 up with unlabeled examples and examples labeled with a single class (e.g. "bad").We implemented and tested this technique on a corpus of messages posted on a stock message board and compared it with two baseline techniques. Results show that our method outperforms the two baselines and that it can be used to significantly reduce the number of messages that need to be reviewed by human moderators. Like many other social media sites, online discussion sites (ODS) are plagued with various types of unwanted content such as spam, or obscene and malicious messages. ODS encompasses a variety of systems that enable users to engage in conversations online or offline, publicly or privately. Examples of ODS are forums, commenting systems, review sites, chatrooms, etc. Characterized by a low editorial control, and offering amazing opportunities to engage with people and disseminate information quickly, ODS make an attractive target for spammers and other fraudsters. In addition, as the role of social media in the digital marketing mix of organizations continues to grow, they have also become more exposed to the publication of inappropriate content such as defamation, information leakage or stock ramping. According to the security firm Websense, spam and malicious comments alone account for 95% of all user-generated comments to blogs 1 . This paper addresses the problem of moderating ODS and it presents a novel technique for automatically identifying contributions not complying with a site's terms of use.. Prevention and detection-based techniques have been proposed to filter out inappropriate content (IC) from ODS. But, while prevention techniques, such as CAPTCHAs 2 or account fees have been widely adopted, detection of IC remains mostly a manual task. Indeed, existing detection techniques, which are divided into rule-based and statistical techniques, suffer from various limitations. Rule-based techniques, such as whitelists of senders or blacklists of keywords, usually consist of manually crafted rules [16] . For instance, Kontostathis et al.. recently developed a rule-based system to detect cyberpredators in Internet Relay Chat [16] .. One of the main problems with these techniques is that building and maintaining rules is generally time-consuming and laborious. Moreover, they tend to generate too many falsepositives and false-negatives. In other words, they can easily consider a message containing objectionable keywords in an appropriate context as inappropriate or, conversely, they can consider a message containing malicious content expressed with acceptable terms as appropriate. Statistical techniques are usually based on machine-learning. They use corpora of labeled examples to train a classifier to separate "good" from "bad" messages [25, 34] . For instance, Pendar compared SVM with kNN classifiers to separate predator communication from victim communication based on the content of the messages [25] . Statistical techniques, like rule-based techniques, are often similar to spam identification techniques. But, although statistical techniques have been broadly adopted for spam filtering, they are seldom used to moderate ODS because of the lack of labeled examples and of the prohibitive cost of labeling a large-enough number of examples.. In this paper, we present a novel classification-based technique for moderating ODS that can train a classifier from a partially labeled corpus. Typically, a partially labeled data set is made up with a certain number of examples labeled as "bad" and a large amount of unlabeled data potentially containing both "good" and "bad" examples. Therefore, they are faster and cheaper to generate than completely labeled corpora required by other classification-based 4 techniques. The technique has been implemented and compared with two baseline techniques in an evaluation on a large corpus of messages posted in a stock message board. Results show that our method outperforms the two baselines and that it can be used to drastically reduce the number of messages that need to be reviewed by human moderators. At this stage, the method can effectively be used in a semi-automated system for moderating IC but not in a completely automated system as the proportion of false-positive is still too significant. In the last section, we discuss some of the main challenges that need to be addressed to build a completely automated moderation system.. The remainder of the paper is organized as follows. Section 2 provides background information about inappropriate content in ODS and discusses the limitations of existing humanbased approaches to moderation. Section 3 reviews the literature on automatic filtering of inappropriate content in ODS and overviews related work on classification from partiallylabeled data. In Section 4, we present our approach and the implementation of our filtering technique. Section 5 describes the dataset used for our experiments. Experimental results are presented in Section 6, and finally, in Section 7, we give some concluding remarks and future work. Our approach is based on a measure of correlation, known as the Interest factor [29] or Lift. . Given a vocabulary of words V , a set of positive documents p, and a set of unlabeled documents u, the Lift L measures the probability of a subset of words v ∈ V occurring in p against the probability of occurring in the entire sample.. If L is greater than 1, the probability of v occurring in the positive class is higher than that of the entire sample. Hence, the occurrence of v is considered to be positively correlated to the positive class. On the other hand, if L is less than 1, it suggests that the occurrence of v is negatively correlated to the positive class. If L is equal to 1 then the occurrence of v is independent of the class of the document. This can be summarized as follows: . In other words, if v is positively correlated to p. Let v = {v 1 , v 2 , ...v k }. As in Naive Bayes classifier [20] , assuming that the occurrence of a word v i is statistically independent of the occurrence of any other word in v, we can re-write condition 3 as:. Condition 4 forms the basis of our approach. Given a document in the form of a word vector, we calculate the probability of the occurrence of the given word vector in the positive class (left-hand side of condition 4), and the probability of occurrence in the entire data (righthand side of condition 4). If the LHS is greater than the RHS, the document is predicted to be positive. Otherwise, it is predicted to be negative.. As discussed in the previous section, the major advantage of our approach is that it does not need any estimate of the negative class distribution for the class prediction. In this paper, we have presented a novel classification technique to train a classifier from a partially labeled corpus and use it to moderate IC in ODS. We implemented and tested this technique on a corpus of messages posted on a stock message board and compared it with two baseline techniques. Results show that our method outperforms the baselines, and it can effectively be used to identify messages that are likely to contain inappropriate material.. Thus, the method can be used in a semi-automated context to support the moderation task by reducing the number of messages that need to be reviewed by moderators. However, the number of misclassification errors remains too significant for the method to be used in a completely automated context.. The fact that a high number of acceptable messages are classified as inappropriate is not specifically due to the proposed classification technique. Most messages are misclassified because they contain features which are wrongly considered as representative of the positive class. Indeed, our current attribute selection technique consists in selecting words occurring in at least one of the instances in the positive class. This results in too many words being selected and words being improperly considered as significantly discriminant of the positive class. In addition, the method also has some cases of false-negative the number of which could be reduced with a better attribute selection technique. For example, some messages are acceptable on the surface (i.e. lexically) but their content may be harmful to forum users. A possible solution to address this problem is to rely on contextual features that can be extracted from the same thread as the message. The following examples show user reactions to messages that are likely to contain inappropriate content.. • Drunk your an idiot....keep ramping and see what happens. (. . . ). • Puket So stop manipulating the SP from where you are (. . . ). • oman Your comments are the type I take offence at (. . . ). Contextual features may be very useful to semantically characterize the content of a target message using lexical processing [5] . In future work, our main goal is to address these issues by coming up with a better attribute selection technique for partially labeled data. This table reports Similarly to PNB [7] and PrTFIDF [36] , PULL is based on the Naive Bayes classification model. However, it differs from these approaches for two main reasons. First, PULL does not need an estimate of the proportion of positive instances in the labeled data (p). In [7] , this probability is supposed to be given while in [36] , the probability is estimated by maximizing a performance function. Using a different performance measure would give a different estimate. Second, PULL uses a different technique to estimate the probability of a feature in the negative class P (v|N ). In PULL, P (v|N ) is estimated by P (v) while PNB and PrTFIDF use 1 − p to estimate it. In PNB and PrTFIDF, the estimate of P (v|N ) may. have negative values because of the way it is calculated. The greater the estimate p is, the greater the probability of P (w|N ) to be negative is. To overcome this problem, the estimate of P (v|N ) needs to be smoothen which may significantly alter the natural distribution of P (v|N ), consequently affecting the classifier accuracy. Inappropriate content (IC) pervades online discussion sites such as forums, newsgroups and chatrooms. There are basically three main types of content that can be particularly damaging for a site's reputation and trust. In addition, as demotion techniques are mostly intended to ranking systems, detection techniques are the main approaches to fight IC in online discussion sites.. Most existing websites rely on manual moderation to detect IC. In the classic approach, user contributions are moderated by a group of special users called moderators. These users have moderation privileges that allow them to accept/reject and delete messages from other users. Moderators intervene either before or after publication of messages. In the case of pre-moderation, all submissions remain pending until they are approved by the moderators.. The advantage of this approach is that all published material has been moderated; the main drawback is that the publication delay can be long due to moderation delays (MD), thus refraining users from using the service. Therefore, most systems implement a post-moderation strategy, where submissions are immediately published but can be verified and removed any time after publication. Post-moderation enables the removal of publication delays, but it has no impact on moderation delays. Moreover, the proportion of published contributions that have been verified, or moderation coverage (MC), is often small in case of post-moderation.. Alternative strategies to centralized moderation have been designed to reduce MD and increase MC using community feedback. For example, in a distributed moderation system, all users are given moderation privileges to enable the community to self-moderate. Reactive moderation system is a hybrid approach between centralized and distributed moderation where moderation is performed by moderators, but the user community has the ability to alert them when they find IC. Although reactive and distributed moderation enable the verification of more messages and more quickly, in a system with a large number of contributions, The key step in implementing our approach is to calculate the word probabilities for the positive class P (v i |p), and for the entire sample P (v i ). As in a Naive Bayes classifier, we estimate the word probabilities by counting the word occurrences in the respective class as follows:. where n is the set of all instances, p is the set of labeled positive instances, N (v i , x) is the number times the word v i occurs in the set x, and N (x) is the total number of word occurrences in set x. Assuming that the unlabeled data is generated according to the underlying generative model, and the word distribution in the unlabeled positive documents is the same as the labeled positive documents, Equation 6 can be re-written as:. where u is the set of unlabeled instances.. Re-writing the prediction condition of our approach given by 4, using Equations 5 and 7, we obtain:. As in a Naive Bayes classifier, we need to apply Laplace correction in order to avoid condition 8 resulting in zero, when a word frequency is zero in given set. Hence, in our implementation we use the following formula:. where |v| is the number of words from the vocabulary that occur in the given instance, and e is a constant. e is usually set to 1, however, for highly imbalanced classes this value tends to biaised towards the minority class. Hence, in our experiments, we set e to 0.5.

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


Analysis of patent activity in the field of quantum information processing This paper provides an analysis of patent activity in the field of quantum information processing. Data from the PatentScope database from the years 1993-2011 was used. In order to predict the future trends in the number of filed patents time series models were used. Quantum information science studies the application of quantum mechanics to processing, storing and transmitting information. The main trends of research involving theoretical aspects of quantum computing are: quantum information theory, quantum computation, quantum cryptography, quantum communication and quantum games. The origins of the field date back to the first decades of the twentieth century, when the bases of quantum mechanics were formulated. The beginnings of quantum information theory can be traced back to von Neumann [1] , but the first established research in this area was conducted by Holevo [2] and Ingarden [3] .. In the last two decades of the twentieth century, the groundwork for quantum computing was laid. First in the eighties, Bennett and Brassard [4] , then seven years later Ekert [5] discovered quantum key distribution (QKD) protocols. These research achievements gave rise to the whole new field of quantum cryptography. The Feynman's idea of quantum simulators [6] and Deutsch's work [7] on the universal quantum computer, followed by the discovery of the first quantum algorithms by Shor [8] and Grover [9] in the nineties of the twentieth century created the whole new field of research on quantum computing and quantum algorithms. One of the promising areas of quantum information processing is quantum game theory initiated by Meyer [10] and then followed by Eisert, Wilkens and Lewenstein [11] at the turn of the century. Its application to quantum auctions was proposed later by Piotrowski and Sładkowski [12] .. At present it is hard to tell which specific physical system will be applied for the implementation of quantum information processing [13] . Among the most promising physical implementations one can point out cavity quantum electrodynamics [14, 15, 16] , trapped ions [17, 18] , quantum optical lattices [19, 20, 21] , nitrogen-vacancy centers [22, 23] and various realizations based on superconducting qubits [24, 25, 26, 27, 28, 29] . However, it is believed that realistic systems capable of processing information according to the rules of quantum theory will be composed of diverse physical systems interacting with each other [30] . For this reason a significant amount of research has been dedicated to engineering the building blocks of quantum networks [31, 32, 33] . We have provided an analysis of patent activity in the field of quantum information processing. One can notice an increase in patent activity in the years [2001] [2002] [2003] [2004] [2005] [2006] [2007] [2008] [2009] . In subsequent years the activity sharply decreased. In order to predict the future activity we have used several models to estimate the number of patents to be filed until the year 2015. Both models with low error -SVR and ARMA(1,2) -predict that around 15 patents will be filed in 2015. Figure 2 presents the number of reported patents in years from 1993 to 2011. The above mentioned models were fitted to the data and an extrapolation was made to the year 2015.

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