Quantification of trabecular bone microdamage using the virtual internal bond model and the individual trabeculae segmentation technique To cite this Article Fang, Guanhui, Ji, Baohua, Liu, X. Sherry and Guo, X. Edward(2010) 'Quantification of trabecular bone microdamage using the virtual internal bond model and the individual trabeculae segmentation technique', Computer Methods in Trabecular bone microdamage has significant implications in the physiology and pathology of bone tissue such as in bone remodelling, aetiology of osteoporosis and agerelated fractures (Burr et al. 1997; Wachtel and Keaveny 1997; Burr 2003; . While moderate levels of microdamage may play an important role in the maintenance of structural bone integrity as an important stimulus providing spatial regulation of boneremodelling activity (Mori and Burr 1993 , Nagaraja et al. 2005 , Seeman 2008 ), excessive damage can not only reduce the elastic modulus (Liu et al. 2003) but also the strength of bone (Keaveny et al. 1994c; Burr et al. 1997; Wachtel and Keaveny 1997; Burr 2003) . At present, however, how the damage initiates and accumulates in trabecular bone tissue with the increase in external loading has not yet been fully understood (Burr 2003) . A quantitative study of the underlying mechanisms of this phenomenon may provide insight that can lead to the improvement of fracture risk assessment methods and to the development of therapeutic strategies to treat skeletal fragility diseases such as osteoporosis.. Many experimental studies have been dedicated to the understanding of the damage behaviours of trabecular bone. By combining the histological damage labelling technique and finite-element method (FEM) simulations, Nagaraja et al. (2005) found that damaged trabeculae possessed significantly higher local stresses and strains than did other trabeculae. Their numerical results showed that microdamage initiation occurred prior to the apparent yield of the bone samples, consistent with other studies (Keaveny et al. 1994c ; Moore and Gibson 2002) . Using synchrotron radiation micro-computed tomography (SRmCT), Thurner et al. (2006) studied the different failure behaviours of trabecular bone using both pre-fatigued and non-fatigued samples. They found that the fatigued sample failed in a burst-like fashion in contrast to a distinct failure band seen in the non-fatigued one. Wang and Niebur (2006) studied the microdamage propagation in trabecular bone due to changes in loading mode. They found that the propagating microcracks under mixed loading modes were, on average, longer than microcracks formed by a single-mode overload.. Theoretical and numerical methods used to model trabecular bone damage have also been developed (Guo et al. 1994; Vanrietbergen et al. 1995; Niebur et al. 2000 ; Moore and Gibson 2001; Yeh and Keaveny 2001; Makiyama et al. 2002; Stolken and Kinney 2003; Bevill et al. 2006; . Guo et al. (1994) modelled trabecular bone as a 2D hexagonal honeycomb. They assumed that the cracks in trabeculae grew according to a Paris law and trabeculae failed when the cracks reached a critical length beyond which the crack will propagate catastrophically according to the theory of fracture mechanics. Later, Makiyama et al. (2002) studied the crack growth in trabecular bone using a 3D random honeycomb, while in the work of Moore and Gibson (2001) , trabecular bone was modelled by the open-cell network (rod-like structure) and closed-cell network (plate-like structure). Yeh and Keaveny (2001) used a 3D lattice model to study the roles of microdamage and microfracture in trabecular damage. In their work, a strainbased modulus reduction rule was used to simulate the microdamage formation. In addition, a strain-based microfracture criterion was applied to remove fractured trabeculae from the model once the trabeculae's strain exceeded the critical value.. Although a lot of important progress has been made in previous studies, the underlying mechanisms of the initiation and accumulation of damage in trabecular bone still have not been fully understood because of unresolved difficulties in the numerical and experimental approaches. For instance, in previous numerical studies either ad hoc pre-microdamage had to be introduced in the model (Guo et al. 1994; Schaffner et al. 2000; Moore and Gibson 2001; Makiyama, et al. 2002) to explicitly simulate the evolution of damage, or phenomenological strain-based modulus reduction laws (Yeh and Keaveny 2001; had to be adopted to implicitly model the evolution of trabecular bone damage, but the parameters in these modulus reduction laws could not be obtained from experiments. Furthermore, due to the complexity of trabecular bone architecture, it is difficult for current experimental techniques to capture the details of the damage evolution, especially the initiation, in trabecular bone (Nagaraja et al. 2005) . Therefore, a physics-based numerical approach needs to be developed for studying the evolution of microdamage in trabecular bone tissue.. In this paper, a novel constitutive model, called the virtual internal bond (VIB) model Klein and Gao 1998) , is introduced to explore the behaviour of microdamage in trabecular bone. Compared with previous conventional models, the VIB model has unique advantages in modelling damage and fracture of materials. It can describe the mechanical behaviours of bone tissue not only at small deformations before the initiation of microdamage, but also at large deformations during damage accumulation. In particular, separate fracture criteria are no longer necessary. Therefore, it is a natural process for the VIB model to simulate the initiation and propagation of damage in trabecular bone without a pre-assumed ad hoc crack and fracture criterion in the simulation. In addition, a novel (3D) image analysis technique, named individual trabeculae segmentation (ITS), recently developed by the co-authors of this paper for the decomposition of trabecular bone microarchitecture into individual plates and rods (Liu et al. 2006 (Liu et al. , 2008 (Liu et al. , 2009 ) will be adopted to examine the microdamage behaviour in individual trabecular plates and rods. The combination of these two novel approaches, i.e. the VIB model and the ITS technique, will allow a quantitative study of the micromechanics of trabecular bone microdamage. In this study, we, for the first time, explicitly simulate the initiation and propagation of damage in trabecular bone using the VIB model. The main novelty of this study is that our simulations are able to capture the whole process of damage development in trabecular bone under an external load (Figures 2 and 3) . Different from previous studies in which the ad hoc microdamage needed to be assumed in the simulation with explicit models or a somewhat artificial strain-based modulus reduction criterion needed to be assumed to implicitly simulate the damage, our approach can explicitly simulate the initiation and accumulation of trabecular damage automatically without any pre-defined microcrack. A unique 3D image analysis technique ITS can be used to study the effects of microarchitecture on the damage behaviour of trabecular bone. The combination of the two novel methods provides a deeper understanding of the damage mechanics of trabecular bone on both trabecular and tissue levels by directly accessing the initiation and accumulation of damage as well as the effects of the microstructural parameters on the damage behaviour of trabecular bone. Consistent with previous studies (Yeh and Keaveny 2001; Moore and Gibson 2002; Nagaraja et al. 2005; Liu et al. 2009 ), our simulations show that the microdamage initiates at a very small apparent strain (Figure 4(a) ), ranging from 0.2 to 0.4%; however, microfracture of trabecula occurs at a much higher apparent strain, e.g. our results show that some thin transverse trabeculae are fractured around the apparent yield strain (Figure 2 ). Yeh and Keaveny (2001) showed that microdamage of trabeculae began around 0.2% strain and trabecular bone fracture began near the apparent yield point of samples in their studies. Nagaraja et al. (2005) also indicated that microdamage initiation occurred at about 0.2 -0.6% prior to the apparent yield when they studied the relationship between the amount of microdamage and the apparent strain of bovine trabecular bone with a combination of experiments and FEM simulations. Moore and Gibson (2002) showed that damage was initiated in the linear elastic region, but that the damage increases rapidly at the peak of the stress -strain curve.. We found that the damage behaviour has a close relationship with the yield properties of trabecular bone. Our simulations show that trabecular bone damage increases rapidly as the apparent strain approaches the yield strain (Figures 3 and 6 -8) . In recent studies of yield behaviour of vertebral trabecular bone, Liu et al. (2009) showed that the volume of yielded bone tissue increases rapidly near the apparent yield strain. This consistence suggests that microdamage might be the underlying mechanism of the yield behaviours of bone tissue. Liu et al. also showed that more longitudinal trabecular plates yielded than the oblique and transverse plates, whereas more transverse trabecular rods yielded than the oblique and longitudinal ones. These results are consistent with our findings about the roles of different microarchitectures in the damage behaviour of trabecular bone, i.e. the trabecular plates, especially the longitudinal ones, have a dominant role in the contribution to the damage behaviour of trabecular bone near apparent yield strain, which again demonstrates the important role that microdamage has in the yield properties of trabecular bone.. In the present study, we showed that aBV/TV is an important microstructural parameter for characterising the damage and yield behaviour of trabecular bone. The bone volume fraction, BV/TV, alone, is not sufficient for describing the damage and yield behaviour of trabecular bone. For instance, when two samples have similar BV/TVs, it is difficult to judge which one has higher yield strength ( Figure 5(c) ). The microarchitecture of the trabecular bone should also be considered. Previous studies (Jensen et al. 1990; Borah et al. 2000; Pothuaud et al. 2002; Liu et al. 2006 Liu et al. , 2008 Liu et al. , 2009 ) also saw the importance of microarchitecture when they studied the elastic modulus and strength of trabecular bone. Liu et al. defined the new parameter aBV/TV, called 'axial bone volume fraction', to characterise the microarchitecture of trabecular bone. They found that aBV/TV shows a better correlation with the axial elastic modulus when compared with BV/TV. We show that aBV/TV has a strong correlation with the yield strength of trabecular bone samples ( Figure 5(d) ). Furthermore, our results suggest that the longitudinal (axial) trabeculae take a dominant role in the damage behaviour of trabecular bone. The underlying mechanism is that large aBV/TV allows for more bone tissue to be sufficiently used for the stiffness and strength of trabecular bone.

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Numerical simulation of flood waves and calculation of exerted forces on the cylindrical piers in contraction channels with different cross section profiles A numerical model based on two-dimensional shallow water equations is presented. The depthaveraged velocity components with free-surface elevation have been used as independent variables in the model. The finite element technique is applied to discretize the spatial derivatives.Triangular elements with quadratic and linear interpolating functions are employed for two horizontal velocity components and the free-surface elevation, respectively. The standard Galerkin method is applied for discretization of the governing equations. Time discretization is performed using an implicit scheme. The resulting linear system of equations is solved by the GMRES method.The model is validated using three test cases and the results are compared with an analytical solution, the result of numerical work and experimental data, respectively. Favorable agreement was achieved in all three cases. Subsequently, the developed model is applied to simulate free-surface elevation through a channel contraction. The effects of width of the narrow section as well as the profile of the cross section of the channel on the wave forces exerted on a circular cylinder were studied. This was done in a channel with a quartic narrow section. Plots of time histories of the drag coefficient on the cylinder were produced, demonstrating the effects of the mentioned parameters.

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A Unified Approach for the Recursive Determination of Generalized Inverses Abstract--Using a unified approach, simple derivations for the recursive determination of different types of generalized inverses of a matrix are presented. These include results for the generalized inverse, the least-squares generalized inverse, the minimum-norm generalized inverse, and the MoorePenrose inverse of a matrix. The recursive determination of a generalized inverse of a matrix finds extensive applications in the fields of statistical inference [1] [2] [3] , filtering theory, estimation theory [4] , and system identification [5] . More recently, generalized inverses have found renewed applicability in the field of analytical dynamics [6, 7] . The reason for the extensive applicability of recursive relations is that they provide a systematic method to generate 'updates' whenever sequential addition of data or new information becomes available, and updated estimates which take into account this additional information are required.. The recursive scheme for the computation of the Moore-Penrose (MP) inverse [8, 9] of a matrix was ingeniously obtained in a famous paper by Greville in 1960 [2] . Because of its extensive applicability, Greville's result is widely stated in almost every book that touches on the subject of generalized inverses of matrices. Yet, because of the complexity of his solution technique, Greville's proof is seldom, if ever, quoted or outlined, even in specialized texts which deal solely with generalized inverses of matrices. For example, in books like [4, [10] [11] [12] ], Greville's result is stated, but no constructive proof is provided, most likely because of its perceived complexity.. In the same vein, Mitra and Bhimasankaram [13] provide several results for the recursive determination of generalized inverses of matrices; they state their results as several Ansatze and prove them by directly verifying their validity using a number of specialized results related to generalized inverses of matrices. Their results are equivalent to those presented here. However, they provide no constructive proofs for their results and their proofs for the various types of gen-0898-1221/98/$ -see front matter © 1998 Elsevier Science Ltd. All rights reserved. PII: S0898-1221 (98)00247-8. Typeset by ~4.h~-TEX eralized inverses have no underlying reasoning or thread running through them; only verifications of the various Ansatze are carried out. In this paper, we present a simple constructive approach inspired in part by Bellman's optimality principle, to the recursive determination of various generalized inverses of a matrix. The approach relies on a unified underlying theme and shows clearly why and how the differences in the recursive forms of the various generalized inverses arise. Thus, our results encompass those of Greville [2] , and our method of proof, being constructive, provides deeper insights into the nature of the recursive determination of generalized inverses.. For convenience, we introduce the following notation. Given a real matrix A, its MP-inverse G satisfies the following four conditions:. AG is symmetric, and (4) GA is symmetric.. We shall denote a matrix G which satisfies all four of these conditions by A {1'2'a'4}. Similarly, a matrix which satisfies only the first and fourth condition above shall be denoted as A {1,4} and shall be referred to as the {1,4}-inverse of A, etc.. The most commonly used generalized inverses of a matrix are the MP-inverse (also denoted here as the {1,2,3,4}-inverse), the {1,3}-inverse, the {1,4}-inverse, and the {1}-inverse because these inverses are relevant to the solution x of the matrix equation Ax = b or of the relation Ax ~ b. We shall begin by defining these generalized inverses (as in [12] ) in terms of the relevant linear relations which they help solve. The MP-inverse provides the minimum-length solution x = A{1'2's'a}b in the set of least-squares solutions of the possibly inconsistent equation Ax ~ b for any b, the {1,3}-inverse provides a least-squares solution A{1,S}b to the possibly inconsistent equation Ax ~ b for any b, the {1,4}-inverse provides a minimum-length solution A {1,4} b for any b for which the equation is consistent, and the {1}-inverse of A provides a solution A{1}b for any b for which the equation Ax = b is consistent. This paper is concerned with these four commonly used generalized inverses defined above, which we shall denote, in general, by A*. The solution x is then expressed, in general, as A*b. Their generalized forms are given in [14] .. Given a real m by k matrix Ak, one can partition it as [Ak-1 a] where Ak-1 consists of the first (k-1) columns of the matrix Ak and a is its last column. The column vector a comprises 'new' or additional information, while the matrix Ak-1 comprises accumulated past data. The generalized inverse A~ of the updated matrix Ak is then sought in terms of the generalized inverse A~_ 1 of the matrix Ak-1 which corresponds to past accumulated data, and the vector a containing new or additional information. The MP-inverse of a matrix A is unique. The other generalized inverses ~{1,4} which we shall deal with here are not in general unique, and so, in what follows, by say "'k-1 , we shall mean any one of the set of {1,4}-inverses of the matrix Ak-1. From equations (la) and (lb), notice that the form of the inverse A~_lis the same for c = 0 and for c ~ 0. We have used separate equations here only for convenience.. PROOF OF PART 1. We consider the solution of the least squares problem (6) where we have partitioned the vector x into the (k -1)-vector z and the scalar s. To determine the minimum-length-least-squares solution x of Akx ~ b, we consider all those pairs (z, s) which minimize J(z, s) = IIAk_lz + as -bll 2, and from these pairs select the one whose length zT z + s 2 is a minimum. We begin by setting s = so, where So is some fixed scalar. Thus, we have. Minimizing (7) such that ~7-~ is also a minimum from among all (k -1)wectors z, we obtain, from the definition of the MP-inverse,. Thus, for a given value of the scalar So, the (k-1)-vector ~ is a function of so. Using equation (8) in equation (7), we can now find so such that . is a minimum. Depending on c (I " ,U,2,3,4}, = -.'ik-l~k_l )a , we must now deal with two cases: the first when c ¢ 0; the second when c --0. The first case occurs when a does not lie in the column space of Ak-1; the second, when the vector a lies in the column space of the matrix Ak-1.. (i) For c ~ 0, the unique value of so which minimizes (9) is given by. C T C{1,2,3,4} b :. where in the first equality, we have used the fact that the matrix (I --.,"l.k_lZlk_ 1"4 A{1,2,3,4}\) is symmetric, and in the second equality, that it is idempotent. Having found the unique value so which minimizes (9), we now obtain from (8), the minimum-length-least-squares solution of Akx .~. b as. L So L uT J where the first equality follows by the definition of the MP-inverse. (ii) For c --0, we observe from equation (9) . ------/'.{1,2,3,4}~ T .{1,2,3,4}. Using equation (8) For a fixed so, we minimize. to yield a{1,3} (b -aso). for some {1,3}-inverse of the m by (k -1) matrix Ak-z. We next minimize. with respect to so and again need to consider two cases: when c ¢ 0 and where c = 0.. (i) For c ¢ 0, we obtain the unique value of so which minimizes (19) to be. cTc where we have again used the fact that the matrix (I -Ak_1A{kl'31 }) is symmetric and idempotent. Following the same sort of steps as before, we then obtain the required result for this case. . for some {1}-inverse of Ak-1. Again as in Parts 2 and 3 above, the {1}-inverse obtained from equations (la), (lb), and (5) can be used to obtain other {1}-inverses by adding to this {1}-inverse any matrix (L + R) where L is such that LAk = 0 and R is such that AkR = O. (See [14] .) | In this paper, we present a unified approach for obtaining recursive relations for several of the commonly used generalized inverses of an m by k matrix A. Part 1 of our main result which deals with the MP-inverse was obtained by Greville [2] , but in a more complex manner; our proof of this part is substantially simpler. The unifying theme used in this paper is brought about by defining generalized inverses in terms of the solution(s) x = A*b of the matrix equation Ax = b or of the relation Ax .~ b, and then using a procedure akin to dynamic programming. This results in similar lines of reasoning for obtaining recursive relations for the various types of generalized inverses, while providing insight into why and how the differences among them arise.

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


High Speed Architectures for Finding the First two Maximum/Minimum Values Abstract-High speed architectures for finding the first two maximum/minimum values are of paramount importance in several applications, including iterative (e.g., turbo and low-density-parity-check) decoders. In this brief, stemming from a previous work, based on radix-2 solutions, we propose higher and mixed radix implementations that improve the architecture latency. Post place and route results on a 180-nm CMOS standard cell technology show that the proposed architectures achieve lower latency than radix-2 solutions with a moderate area increase.Index Terms-Low-density-parity-check (LDPC) decoder, minimum values generator, tree structure approach, turbo decoder. Recently, several simplified algorithms for channel decoding have been proposed for low-density-parity-check (LDPC) [1] and turbo codes [2] . The -min algorithm [3] , min-sum, and its improved versions [4] , are widely used in LDPC decoders, [5] , [6] . Similarly, in [7] a novel multi-input max 3 approximation for turbo and turbo trellis-coded-modulation (TCM) coding is proposed. All these works share the need for finding the first two maximum/minimum (max/min) values in a set of M elements. As an example, in the min-sum algorithm [4] the magnitude of the i-th output of a check node having degree dc is given by the first min of the dc inputs' magnitudes, unless this equals the ith input's magnitude, in which case the second min is employed. In [7] , the Jacobian logarithm of n inputs is computed as the first max (max1) plus a correction term that depends on max1-max2, where max2 is the second max. A similar problem can be found also in K-best multiple-input-multiple-output (MIMO) detectors [8] - [10] , non-binary LDPC decoders [11] and turbo product codes [12] , [13] where the computation of the first W max/min values is required. For the sake of brevity the extension to the search of the first W max/min values is not investigated in this brief.. All the architectures proposed in [14] - [16] for finding the first two max/min values are based on radix-2 tree structures or a proper blend of radix-2 and radix-3 blocks. Even if these architectures are remarkably small in terms of area, they require a relevant number of stages (especially for large M ) which negatively affects the delay. However, some applications as iterative decoders (e.g., turbo codes [2] , [7] ), require high throughput and include feedback loops in the processing: in these cases pipelining does not provide any throughput improvement and different solutions are necessary.. In this brief, stemming from [16] we analyze the implementation of a generic radix-K solution and we further extend the design space considering mixed radix architectures (MRAs). In [17] a similar work is presented. However, it focuses only on using binary and trinary trees. On the contrary, this work offers a systematic treatment including MRAs and, to the best of our knowledge, it is the first work addressing MRAs for finding the first two max/min values. . Lately there has been intense interest in 3-D ICs in the semiconductor industry. 3-D integration is being hailed as a "Beyond Moore" driver which promises to provide further increase in integration density. A 3-D IC is made up of an IC stack with very short vertical interconnections between adjacent dies by means of through-silicon vias (TSVs). There are a lot of potential advantages to go 3-D including smaller footprint, reduced interconnect delay, higher system performance, and lower power consumption. Moreover, heterogeneous technologies can be comfortably integrated in a die stack. One can choose the most suitable process to manufacture each die to optimize the cost and performance. The simplest example is stacking memory and CPU. In this brief high speed architectures for finding the first two max/min values are presented. The proposed solution extends previous works based on radix-2 and radix-3 solutions to both higher and mixed radix solutions. As shown by experimental results MRAs achieve lower latency than radix-2 architectures with a limited area increase. Moreover, MRAs show better figures than other solutions proposed for LDPC decoders.

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


Polynomial-time homology for simplicial Eilenberg-MacLane spaces In an earlier paper ofČadek, Vokřínek, Wagner, and the present authors, we investigated an algorithmic problem in computational algebraic topology, namely, the computation of all possible homotopy classes of maps between two topological spaces, under suitable restriction on the spaces.We aim at showing that, if the dimensions of the considered spaces are bounded by a constant, then the computations can be done in polynomial time. In this paper we make a significant technical step towards this goal: we show that the Eilenberg-MacLane space K(Z, 1), represented as a simplicial group, can be equipped with polynomial-time homology (this is a polynomial-time version of effective homology considered in previous works of the third author and co-workers).To this end, we construct a suitable discrete vector field, in the sense of Forman's discrete Morse theory, on K(Z, 1). The construction is purely combinatorial and it can be understood as a certain procedure for reducing finite sequences of integers, without any reference to topology.The Eilenberg-MacLane spaces are the basic building blocks in a Postnikov system, which is a "layered" representation of a topological space suitable for homotopy-theoretic computations. Employing the result of this paper together with other results on polynomial-time homology, in another paper we obtain, for every fixed k, a polynomial-time algorithm for computing the kth homotopy group π k (X) of a given simply connected space X, as well as the first k stages of a Postnikov system for X, and also a polynomial-time version of the algorithm ofČadek et al. mentioned above. Recently our co-authors and we [ČKM + 11] have developed an algorithm for a problem in computational algebraic topology (more precisely, in computational homotopy theory), namely, computing all homotopy classes of maps between two topological spaces X and Y (given as finite simplicial complexes, say), under certain natural conditions on X and Y .. Our original motivation was understanding the computational complexity of the Z 2 -index of a given Z 2 -space, which is a quantity appearing in various applications of topology in combinatorics and geometry (e.g., topological lower bounds for the chromatic number of a graph, or an algorithm for testing the embeddability of a given simplicial complex into R d ). We hope to reach results in this direction in the future, and we also expect that the developed methods will be applicable for other natural problems (such as extendability of maps; as a concrete application, it was already possible to answer a question of Franek et al. [FRZ11] on testing nullhomotopy of maps into a sphere). For more information on this project we refer to [ČKM + 11,ČKM + 12,ČKM + 13].. Towards polynomial-time homology.. The implementation of some of the operations in the algorithm of [ČKM + 11] relies on the methods of effective homology, initiated by the third author in [Ser94] and further developed by him and his co-workers (see, e.g., [RS02, RRS06, RS12] ). These provide algorithmic solutions of many problems in algebraic topology, but so far no analysis of their running time was available, and for some parts the running time can actually be exponential.. One of our aims is to obtain polynomial-time algorithms for these tasks where possible, or alternatively, show computational hardness.. Let us stress that by "polynomial-time" we mean, throughout this paper, polynomial-time for every fixed dimension. Thus, assuming that the input to an algorithm is a space represented as a finite simplicial complex X, we want that the running time is polynomial in the number of simplices of X, but the polynomial may depend on the dimension k of X (and the dependence on k may be exponential or even worse). Of course, one could be even more ambitious and ask for a polynomial dependence on k as well; however, we do not expect such algorithms to exist, in view of computational hardness results [Ani89,ČKM + 13].. To integrate this effort with existing algorithms, we start with the framework of effective homology mentioned above, and we introduce an analogous definition of polynomial-time homology; see Section 2. In another paper [ČKM + 12], we show that various known constructions and operations on objects with effective homology have polynomial-time versions. With a repertoire of such operations, we also obtain a polynomial-time version of the algorithm of [ČKM + 11], as well as other algorithms, such as computing the higher homotopy group π k (X) in polynomial time for every fixed k, or computing the first k stages of a Postnikov system for X.

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


Evaluation of struggle strategy in Genetic Algorithms for ground stations scheduling problem Ground station scheduling problem arises in spacecraft operations and aims to allocate ground stations to spacecraft to make possible the communication between operations teams and spacecraft systems. The problem belongs to the family of satellite scheduling for the specific case of mapping communications to ground stations. The allocation of a ground station to a mission (e.g. telemetry, tracking information, etc.) has a high cost, and automation of the process provides many benefits not only in terms of management, but in economic terms as well. The problem is known for its high complexity as it is an over-constrained problem. In this paper, we present the resolution of the problem through Struggle Genetic Algorithms -a version of GAs that distinguishes for its efficiency in maintaining the diversity of the population during genetic evolution. We present some computational results obtained with Struggle GA using the STK simulation toolkit, which showed the efficiency of the method in solving the problem. Ground Station Scheduling is one of the most important problems in the field of Satellite-Scheduling. It consists in computing feasible planning of communications between satellites or spacecraft (SC) and operations teams of Ground Station (GS). The problem arises in many real life applications and projects, such as from ESA (European Space Agency) [7, 6, 2] (see Fig. 1 for ESA Tracking Network) and NASA [5] . In fact, there is a growing interest and need of the efficient resolution of the problem also from smaller projects from research institutions and universities.. Ground Station Scheduling is a very complex problem due to its overconstrained nature. Indeed, there are several restrictions that make the planning of even small problem instances too complex to deal with manually or by brute force search algorithms.. • The over-constrained nature: There is a large set of constraints. In fact, this is the first major difference between the problems of conventional scheduling and that of Ground Station scheduling. First, there are restrictions on the communication time required for each SC in a period of time. Secondly, there are restrictions on the visibility of each window on each Spacecraft Ground Station, i.e. the time at which each SC can communicate with each GS in a given time period. Resources are thus not available at all times for mission allocation.. • Communication time variables: The second major difference with other planning algorithms is that in the case of Ground-Station Scheduling, the length of the communication is variable, where it should be at least the required communication time and at most the maximum time within which the window visibility ends or the visibility window of another communication starts.. All scheduling variants, in their general formulations, are highly constrained problems and have been shown computationally hard [11, 9, 3, 13] .. In this paper, we propose the resolution of Ground-Station Scheduling using Struggle Genetic Algorithms. Struggle GA is a version of GAs, which aims to keep a diverse population of individuals. For that, Struggle GA creates a new generation by replacing only a portion of the population with newly generated individuals. A new individual replaces the individual that is genetically most similar to it only in case the new individual obtains a better fitness value than the one to be replaced. The aim is to avoid premature convergence and reach a better convergence point. Several similarity functions for individuals are considered (Hamming, Euclidean, Cosine and Hash-based functions) to identify the one that works best for the problem We have experimentally evaluated the Struggle GA using the STK simulation toolkit, by generating a family of instances of different sizes (small, medium, large) that tries to capture real features of the problem.. The rest of the paper is organized as follows. In Section 2 we describe the Ground-Station Scheduling. The different fitness types for the problem are formulated in Section 3. The Struggle GA is given in Section 4 and its experimental evaluation in Section 5. We end the paper in Section 6 with some conclusions and remarks for future work. Window time scheduling problems are well-known for their computational complexity due they are over-constrained scheduling problems. One such problem is that of Ground Station Scheduling, which arises in mission operations for the efficient management of satellite/space missions for communication of spacecrafts with ground stations. The problem is to efficiently allocate a large number of missions (tasks) to a rather small number of ground stations (resources). Given the computational hardness of the problem, meta-heuristics are resolution methods to cope in practice with its efficient resolution. In this paper we have presented the evaluation of Struggle Genetic Algorithms for the problem. Struggle GA is a version of GAs in which an individual replaces another individual of the population only if it has better fitness but additionally should be genetically similar to the individual to be replaced. The aim in Struggle GA is to control the convergence of the GA and avoid premature convergence. This is done by implementing several similarity measures, including some hash-based functions, which achieve high efficiency. We have evaluated the Struggle GA using the STK simulation toolkit. Three groups of different size instances are generated, namely, small, medium and large, aiming to simulate realistic features of the problem. The Struggle GA was able to compute high quality schedules in very short times.

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 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 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 B 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 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 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 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 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 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 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 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


Modeling of celiac disease immune response and the therapeutic effect of potential drugs Background: Celiac disease (CD) is an autoimmune disorder that occurs in genetically predisposed people and is caused by a reaction to the gluten protein found in wheat, which leads to intestinal villous atrophy. Currently there is no drug for treatment of CD. The only known treatment is lifelong gluten-free diet. The main aim of this work is to develop a mathematical model of the immune response in CD patients and to predict the efficacy of a transglutaminase-2 (TG-2) inhibitor as a potential drug for treatment of CD. Overall, the use of antibodies against IFN-γ, and IL-15, analogues of gluten peptides repressing IEC activation, and TG-2 inhibitor would not be efficient solutions to treat CD. The model indicates that the most efficient therapeutic agent is a product that acts on species involved in both the innate and the adaptive immune response, i.e. analogues of gluten peptides that arrest APC activation. This model could be applied in the pharmaceutical R&D arena for the design of drugs against autoimmune small intestine disorders and on the design of their corresponding clinical trials. CD is a complex autoimmune disorder with many unexplored aspects. Role and contribution of various possible mechanisms (disruption of "central", "peripheral" tolerances, T cell anergy, etc.) to oral tolerance breakdown, CD pathogenesis and severity is not established yet. There are different possible ways of gluten peptides transfer into the lamina propria [57] . They could cross the intestinal epithelium either via the paracellular route or via the transcellular route. In the first case this occurs as a consequence of an increased permeability, in the second case it occurs by using enterocytic vesicles that are able to cross the basal membrane allowing intact gluten peptides to have access to the lamina propria. It is known that one of the main cause of CD is the presence of HLA DQ2 and DQ8 molecules, but 1-2% of CD patients do not have DQ2 and/or DQ8 [51] . So there could be non DQ2/DQ8 ways of immune response stimulation. In our model the mechanism of oral tolerance breakdown has not been considered. We take into account only DQ2/DQ8 route of immune response stimulation and paracellular way of gluten peptides transfer into lamina propria. To describe healthy patients we use the assumption that there are no innate and adaptive immune responses in healthy subject (see section "Methods"). This approach allows us to simplify the equations of our model and to decrease the number of model parameters. The detailed description of mechanisms of IEL activation, transport of gluten peptides through intestine wall, interaction of peptides with non DQ2/DQ8 APC in healthy subjects could help to study and understand more clear the processes underlying the absence of immune responses in healthy subjects. This could be the next step for modeling of immune response in human.. The model described in this manuscript was able to predict that a TG-2 inhibitor can reduce the antibody levels down to zero if the deamidated peptides are more immunogenic than the native peptides, i.e. if the ЕС50 of deamidated peptides binding to APCs and B-cells is 80-fold lower or less than for native peptides. However, a TG-2 inhibitor would not significantly increase the villous area because the influence of antibodies on IEC death and inhibition of their maturation is insignificant. This is logical given that the villous area in a patient on a GFD was experimentally shown to be 50% of that in a healthy patient. It is known that in a patient following GFD the antibody levels are similar to the background antibody levels of a healthy patient (i.e. it equals to zero in the model). It follows from this that a 2-fold reduction in the villous area (from 100% to 50%) is due to IELs and IFN-γ, to a lesser extent, zonulin. After changing over from GFD to gluten-containing diet, the villous area decreases from 50% to 10%. This can be attributed to an increase in the levels of IELs and IFN-γ that trigger IEC apoptosis, as well as to the action of IL-21 and the antibodies. Overall, even if one suggests that the reduction from 50% to 10% only occurs through antibodies, then upon the condition that deamidated peptides are significantly more immunogenic than native ones (the ЕС50 ratio is 1:80 or greater), the TG-2 inhibitor induces a state similar to that of a GFD (in terms of both the antibody level and the villous area).. An evaluation of the efficacy of various potential drugs to treat CD suggests that the most efficient therapeutic agents would be analogues of immunogenic peptides that repress activation of APCs. This is logical as activated APCs play a key role in the adaptive immune response and maintenance of the activity of effectors of the innate immune response. Activated APCs release IL-15 that in turn arrests IELs death and at the same time induce their activation, i.e. stimulates differentiation of natural killers from IELs triggering apoptosis. As a conclusion, by arresting APC activation it seems that the synthesis of antibodies can be completely shut down and the concentrations of activated IELs, IFN-γ, and IL-21 significantly decreased, resulting in an increase of the villous area up to 51%.. One type of promising agents for CD therapy, the analogues of immunogenic peptides that repress IEC activation, appeared to be less efficient than GFD. These analogues arrest IEC activation, which represses the synthesis of zonulin and IL-15. However, this has no significant effect on effectors of the adaptive immune response. Activated APCs continue the synthesis of IL-15, activating IELs and T-cells, both of which trigger the release of IFN-γ and IL-21. The antibody level, which depend directly and exclusively on the number of activated T-cells and the amount of gluten peptides in the lamina propria, remain nearly the same as in the absence of peptide analogues. The villous area, increases only up to 14% due to the absence of zonulin, and a limited reduction in the concentration of activated IELs, IFN-γ and IL-21.. Significant reduction in IFN-γ and IL-15 level (resulted from administration of corresponding specific antibodies, for example) leads to the small decrease in antibody level. This can be explained in terms of auxiliary role of the cytokines in adaptive immune response. Indeed, IFN-γ is involved in T cells activation and elevation of IFN-γ results in increase in rate of T cells activation by some extent but even complete depletion of IFN-γ does not lead to stop in T cell activation. IL-15 is involved in differentiation of APCs from monocytes. Elevation in IL-15 is able to increase the rate of differentiation of APCs from monocytes but there is other IL-15 independent ways of replenishment of APC population. At the same time, decrease in IFN-γ and IL-15 levels results in significant increase of villous area (up to 40% and 46% respectively) because of the significant influence of IFN-γ and IL-21 on IEC apoptosis and strong stimulation effect of IL-15 on IEL activation.. The robustness of model predictions was analyzed in the following manner. We simulated villous area and antibody level during different treatments taking the value of model parameters from the confidential intervals identified using method described in section "Simulations on the range of parameter's confidential intervals" (Additional file 1). Results are presented in Additional file 1: Figure S15-24 . From the analysis we can conclude that model predictions of influence of TG-2 inhibitor, permeability inhibitor, DQ-2 blocking peptides on villous are and antibody level and IFN-γ, IL-15 antibodies on antibody level are quite robust to variation in model parameters. On the other hand, robustness of the model predictions for IFN-γ (Additional file 1: Figure S22 ) and IL-15 (Additional file 1: Figure S23 ) antibodies influence on villous area is not satisfactory. This can be explained in terms of lack of sufficient amount of available experimental data required for reliable identification of parameter values responsible for the processes associated with contribution of IFN-γ and IL-15 to immune response in CD. This pushes us to state that model of celiac disease developed in our manuscript can be applied to identify gaps in experimental and clinical data and to initiate more quantitative and rational exploration of the processes involved in CD pathogenesis. Taking these gaps in experimental/ clinical data in mind model can advise on optimal design of clinical study or experiment [58, 59] . Celiac disease (CD) is an autoimmune disorder caused by the gluten protein contained in many grains. Upon entry of gluten into the small intestine, a patient develops painful digestion disorders due to villi impairment and loss of absorption. CD is partially a heritable disease [1] . The gene implicated in predisposition to CD (HLA DQ2 and DQ8) has a worldwide prevalence of around 1%. At present there is no therapeutic agent to treat this disorder. The only approach able to minimize the CD symptoms and currently used as prophylaxis is the strict compliance to a gluten-free diet (GFD), which consists on the removal of all gluten containing products, such as starchy and pasta from the diet, or the exchange of these products for products with a reduced gluten content [2] . Similar to many other autoimmune diseases, CD involves innate and adaptive immune responses [3, 4] . The innate response causes a primary impairment of villi in the small intestine, increasing epithelial permeability allowing the entry of proteins from the lumen to the lamina propria [1] . The adaptive immune response involves the binding of peptides and/or proteins present in the intestinal lamina propia to antigen-presenting cells (APCs) which leads to antibody production [1] . These peptides can undergo deamidation by the enzyme tissue transglutaminase (TG-2) [1] , which in genetically predisposed individuals can boost the peptide immunogenicity [5, 6] . This deamidation process enables the APCs to take up not only immunogenic peptides but also TG-2-peptide complexes. As a consequence, antibodies are produced not only against gluten peptides but also against TG-2 [7] [8] [9] [10] . The two markers of CD are a decline in the villous area of the small intestine (i.e. villous breakdown), and the appearance of anti TG-2 antibody in plasma. This suggests that TG-2 is a key component of the disease and therefore a potential target candidate for CD therapy. Nevertheless, there are many unexplored aspects in CD pathogenesis such as breakdown of oral tolerance and non DQ2/DQ8 ways of adaptive immune response stimulation.. To describe all intra-and extracellular processes associated with a disease and integrate heterogeneous sets of experimental data, a Quantitative Systems Pharmacology (QSP) modeling approach can be employed. This approach enables the description of a general mechanism of the immune response and its integration into the regulatory mechanisms characteristic of a disease of interest, in the current case CD. In addition, the QSP modeling approach provides a way for integrating the experimental data into a model to appropriately describe the disease of interest; with the aim of evaluating the most important processes and predicting potential targets for therapy.. A mathematical model of CD or its immune response has not yet been described in the literature. However, the mathematical modeling of a general immune response has been extensively performed and described, in particular the adaptive immune response, i.e. antigen presentation, synthesis, and activity of antibodies. The majority of the examples in the literature only describe general trends of the adaptive immune response to an antigen, without taking into account the complex regulatory mechanisms associated to the specific disease [11] [12] [13] [14] . Just a limited number of publications focus on the adaptive immune response in the context of a disease mechanism in particular those induced by bacterial agents [15, 16] . The work presented here intends to fill in these gaps by constructing a model of the innate and adaptive immune responses in CD. This model integrates all the human in vitro, ex vivo and in vivo data available, enabling the prediction of the efficacy of a TG-2 inhibitor, as well as the effect of other possible therapeutic agents on the levels of anti-TG-2 antibodies in plasma, and on the villous area in the small intestine. Available experimental data, facts and assumptions used for model development zonulin level and number of IEC. Velocity of gluten peptides transport through intestine wall is equal to zero when there is no zonulin and level of IEC corresponds to healthy subject level. The influence of zonulin and IEC is described in additive manner (for more details see Additional file 1). e) To take into account a delay in antibody production caused by T cells activation [42] and affinity maturation of B cells [43] , a transient step in T-cell activation was introduced. f ) The arrival of gluten peptides into the lumen of healthy subjects and celiac disease patients on gluten-containing diet was considered constant rather than discrete and at a rate of 3 times per day, which would correspond to a normal daily food intake. It was set to the average inflow in a patient following a GFD diet, which according to the Codex Draft Revise Standard (2000) should contain less that 20 ppm of gluten for foodstuffs naturally gluten-free (GF) and less than 200 ppm for foodstuffs rendered gluten-free (GF) [44] .

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


Language Identification of Kannada, Hindi and English Text Words Through Visual Discriminating Features Language identification is an important topic in pattern recognition and image processing based automatic document analysis and recognition. The objective of language identification is to translate human identifiable documents to machine identifiable codes [1] . The world we live in, is getting increasingly interconnected, electronic libraries have become more pervasive [2] and at the same time increasingly automated including the task of presenting a text in any language as automatically translated text in any other language. Identification of the language in a document image is of primary importance for selection of a specific OCR system processing multi lingual documents [3] . Language identification may seem to be an elementary and simple issue for humans in the real world, but it is difficult for a machine, primarily because different scripts (a script could be a common medium for different languages) are made up of different shaped patterns to produce different character sets [4] . OCR is of special significance for a multi-lingual country like India, where the text portion of the document usually contains information in more than one language. A document containing text information in more than one language is called a multilingual document. For such type of multilingual documents, it is very essential to identify the text language portion of the document, before the analysis of the contents could be made. Although a great number of OCR techniques have been developed over years [5, 6] , almost all existing works on OCR make an important implicit assumption that the language of the document to be processed is known beforehand [2] . Individual OCR tools have been developed to deal best with only one specific language [7] . In an automated environment such document processing systems relying on OCR would clearly need human intervention to select the appropriate OCR package, which is certainly inefficient, undesirable and impractical [4] . A pre-OCR language identification system would enable the correct OCR system to be selected in order to achieve the best character interpretation of the document [7] . This area has not been very widely researched to date, despite its growing importance to the document image processing community and the progression towards the "paperless office" [7] . Keeping this drawback in mind, in this paper an attempt has been made to solve a more foundation problem of language identification of a text from a multilingual document, before its contents are automatically read. Language identification is one of the vision application problems. Generally human system identifies the language in a document using some visible characteristic features such as texture, horizontal lines, vertical lines, which are visually perceivable and appeal to visual sensation. This human visual perception capability has been the motivator for the development of the proposed system. With this context, in this paper, an attempt has been made to simulate the human visual system, to identify the type of the language based on visual clues, without reading the contents of the document. In a multi-lingual country like India (India has 18 regional languages derived from 12 different scripts; a script could be a common medium for different languages [8] ), documents like bus reservation forms, passport application forms, examination question papers, bank-challen, language translation books and money-order forms may contain text words in more than one language forms. For such an environment, multi lingual OCR system is needed to read the multilingual documents. To make a multi-lingual OCR system successful, it is necessary to separate portions of different language regions of the document before feeding to individual OCR systems. In this direction, multi lingual document segmentation has strong direct application potential, especially in a multilingual country like India. In the context of Indian languages, some amount of research work has been reported [2, 4, 8, 9] . Further there is a growing demand for automatically processing the documents in every state in India including Karnataka. Under the three language formulae [8] , adopted by most of the Indian states, the document in a state may be printed in its respective official regional language, the national language Hindi and also in English. Accordingly, a document produced in Karnataka, a state in India, may be printed in its official regional language Kannada, national language Hindi and also in English. For such an environment, multilingual OCR system is needed to read the multilingual documents. To make a multilingual-OCR system successful, it is necessary to develop the multilingual-OCR system that would work in two stages: (i) Identification and separation of different language portions of the document and (ii) Feeding of individual language regions to appropriate OCR system. In this paper, we focus on the first stage of the multilingual-OCR system and present procedures for identification and separation of Kannada, Hindi and English text portions of the multilingual document produced at Karnataka, an Indian state. In the present case, it could also be called as script or language identification, since the three languages Kannada, Hindi and English belong to three different scripts. In this paper, we have presented line-wise and wordwise identification models to identify Kannada, Hindi and English text words from Indian multilingual machine printed documents. The proposed models are developed based on the four visual discriminating features, which serve as useful visual clues for language identification. The methods help to accurately identify and separate different language portions of Kannada, Hindi, English and Hindu Arabic numerals and also to group the portion of the document in other than these three languages into a separate class called OTHERS.. The experimental results show that the two methods are effective and good enough to identify and separate the three language portions of the document, which further helps to feed individual language regions to specific OCR system. Our future work is to develop a system that can identify other Indian languages. From the literature survey, it has been revealed that some amount of work has been carried out in script/language identification. Peake and Tan [7] have proposed a method for automatic script and language identification from document images using multiple channel (Gabour) filters and gray level co-occurrence matrices for seven languages: Chinese, English, Greek, Korean, Malayalam, Persian and Russian. Tan [2] has developed rotation invariant texture feature extraction method for automatic script identification for six languages: Chinese, Greek, English, Russian, Persian and Malayalam. In the context of Indian languages, some amount of research work on script/language identification has been reported [8, 10, 11, 13] . Pal and Choudhuri [8] [9] have developed a character script class identification system for machine printed bilingual documents in English and Kannada scripts using probabilistic neural network. Pal and Choudhuri [10] have proposed an automatic separation of Bangla, Devanagari and Roman words in multilingual multiscript Indian documents. Nagabhushan et.al. [13] have proposed a fuzzy statistical approach to Kannada vowel recognition based on invariant moments. Pal et. al. [12] have suggested a word-wise script identification model from a document containing English, Devanagari and Telugu text. Chanda and Pal [11] have proposed an automatic technique for word-wise identification of Devanagari, English and Urdu scripts from a single document. Spitz [18] has proposed a technique for distinguishing Han and Latin based scripts on the basis of spatial relationships of features related to the character structures. Pal et al. [19] have developed a script identification technique for Indian languages by employing new features based on water reservoir principle, contour tracing, jump discontinuity, left and right profile. Ramachandra et al. [20] have proposed a method based on rotation-invariant texture features using multichannel Gabor filter for identifying six (Bengali, Kannada, Malayalam, Oriya, Telugu and Marathi) Indian languages. Hochberg et al. [21] have presented a system that automatically identifies the script form using cluster-based templates. Gopal et al. [22] have presented a scheme to identify different Indian scripts through hierarchical classification which uses features extracted from the responses of a multichannel log-Gabor filter. Our survey for previous research work in the area of document script/language identification shows that much of them rely on script/languages followed by other countries and few from our country, but hardly few attempts focus on these three languages Kannada, Hindi and English followed in Karnataka, an Indian state. In one of my earlier works [4] , it is assumed that a given document should contain the text lines in one of the three languages Kannada, Hindi and English. In one of my previous papers [14] , the results of detailed investigations were presented related to the study of the applicability of horizontal and vertical projections and segmentation methods to identify the language of a document considering specifically the three languages Kannada, Hindi and English. It is reasonably natural that the documents produced at the border regions of Karnataka may also be printed in the regional languages of the neighboring states like Telugu, Tamil, Malayalam and Urdu. The system [4] was unable to identify the text words for such documents having text words in Telugu, Tamil, Malayalam, Urdu languages and hence these text words were misclassified into any one among the three languages, whichever is nearer and similar in its visual appearance. For example, Telugu is misclassified as Kannada and Tamil is misclassified as English. If the document consists of text words in other than the anticipated languages, our previous algorithm fails to identify the type of the language by misclassifying the text words. Keeping the drawback of the previous method [15] in mind, we have proposed a system that would more accurately identify and separate different language portions of Kannada, Hindi and English documents and also to classify the portions of the document in other than these three languages into a fourth class category -OTHERS, as our intension is to identify only Kannada, Hindi and English. The system identifies the three languages in four stages: in the first stage Hindi is identified, in the second stage Kannada is identified, in the third stage English is identified and in the fourth and the last stage, languages other than Kannada, Hindi and English are grouped into fourth class category OTHERS without identifying the type of that language as our main aim is to focus only on Kannada, Hindi and English languages. This paper is organized as follows. Section 2 describes some discriminating features in the characters of Kannada, Hindi and English text words. In Section 3, two models proposed for identifying the three languages -Kannada, Hindi and English, have been discussed. The experimental details and the results obtained are presented in section 4. Conclusions are given in section 5.

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


DESIGN OF EXPERIMENTS ON NEURAL NETWORK'S PARAMETERS OPTIMIZATION FOR TIME SERIES FORECASTING IN STOCK MARKETS Abstract: Artificial neural network (ANN) model has been used for years to conduct research in stock price prediction for three reasons. First, it has a higher prediction accuracy rate in empirical research. Second, it is not subject to the assumption of having samples from a normal distribution. Third, it can deal with non-linear problems. Nevertheless, the accuracy of prediction relies on the parameter settings of neural network as well as the complexities of problems and the neural network architecture; the results of the analysis could be even more significant with the selection of optimal parameters and network architecture. Currently, as a way of setting parameters, most researchers employed the trial and error method. However, this method is very time-consuming and labor-intensive and may not result in the optimal parameters. Therefore, this research took advantage of a back propagation neural network (BPNN) for the purpose of parameter optimization through constructing a model of stock price prediction, applying design of experiment (DOE) to systematize experiment scheduling, and methods of main effects analysis and interaction analysis. The research used two datasets of financial ratios from 50 blue chip companies in Taiwanese stock market and 40 listed American banks in New York stock exchange as experimental samples. Research results showed that the correlation forecasting, root mean squared error (RMSE), and computing time, which can effectively increase the accuracy of stock price prediction, are better than traditional statistical methods and conventional neural network model. Among diversified financial products, stock is an investment tool which is public and easy to obtain information. Stock price movements mean profits or losses on investments, and the ultimate purpose of investment and financial management is to gain maximum profits through minimum costs. Regardless of the means of evaluation to predict price, the stock price movement has always been the focus of concern not only for individual or institutional investors, but also for academic research.. Generally speaking, financial statements include an income statement, a balance sheet, a statement of stockholders equity and a statement of cash flows. The result of utilizing financial statements to analyze past operations or to evaluate current financial performance for the purpose of determining company stability is predictable [1] . Moreover, the investment behavior of investors is easily affected by accounting information released by each company [2] . Many scholars have focused their research on the relationship between company profitability and stock returns, and the research results proved that accounting information can be a reference base for investors to understand more about the business operations of each company [3] [4] [5] [6] [7] . Consequently, financial statements can provide information about financial position, business results, profitability and growth capacity of a company for investors as references of decision-making and investment planning.. The financial ratios are used to understand a company's financial information, such as a company's solvency, operating performance, operating capacity, growth potential and corporate risk. A variety of investors and stock market analysts utilize financial ratios to analyze the value of potential investment in a company [8] [9] . However, there is often a non-linear relationship among related financial variables; unlike the analysis tools of artificial intelligence, traditional regression analysis cannot be used to more effectively simulate the non-linear relationship between financial variables. Nevertheless, for sales prediction [10] , consumer preference [11] , company financial diagnosis [12] [13] and stock trading prediction [14] [15] , artificial neural networks (ANN) has been proven effective by numerous researchers. In addition, discovered that in the application of predicting financial ratios, ANN has been proved to be more effective than traditional logistic regression and discriminant analysis methods [16] . Because of its effectiveness being applied to financial ratios, ANN has been used to determine the financial soundness of a company by many researchers [17] , such as the application of bankruptcy prediction. Moreover, concerning stock price prediction, Dunis and Jalilov (2002) used the neural network regression (NNR) to construct the financial forecasting models and financial trading models for international stock markets [18] . Enke and Thawornwong (2005) indicated that there is a non-linear relationship between financial variables and the financial markets, and thought that ANN can effectively explore the relationship [19] . Lipinski (2005) discovered stock buying, selling and holding strategies through self-organizing maps and the K-means algorithm [20] . Zhu (2008) used ANN to analyze the effect of stock trading volume on the predictive ability to short-term, medium-term and long-term stock investment [21] . Al-Qaheri et al. (2008) applied three methods, rough set, genetic algorithms and ANN, to predict the stock price [22] .. Empirical research has proven that ANN has a higher prediction accuracy rate, not being subject to the assumption of having samples from a normal distribution, and having no non-linear problems that variables have to deal with. Also, strengths of the ANN model include having less hypothesis restrictions and more capability of dealing with non-linear problems. However, the strength of the prediction function of ANN relies on the parameter settings, network architecture design, and the complexity of problem. If appropriate parameters and network architecture are selected, then the results are even more significant. Currently, most researchers manually adjusted the parameters to determine the optimal parameters of the neural network based on prior self-experience, recommendation settings in the literatures, or trial and error method adoption [23] . However, it may not be objective if the experimental parameters are determined merely by the experience of researchers. By doing so, only one factor variable can be changed at one time, the interaction between factors may not be able to be discussed, obtaining optimal parameters is very time and labor intensive, and the parameters found by the trial and error method may not be the optimal combination. Thus, instead of the traditional trial and error method which manually adjusts the parameters, this study employed the Design of Experiment (DOE) to establish a systematic research method for parameter design optimization, and developed a systematic prediction model to improve the accuracy of stock price prediction. The main purposes of this research are summarized as follows:. (1) in order to effectively increase the performance of back propagation neural network, this research took advantage of an experimental design to build a model for stock price prediction, and used financial indicators as research variables.. (2) in order to improve the weakness of the traditional trial and error method, specifically that manually adjusting the parameters is very time consuming, this research aims at assisting researchers in systematically conducting experiments through an experimental scheduling for saving time and costs, and conducting empirical research for the purpose of upgrading the prediction capacity of the model. Stock investment is an investment toll which is popular and commonly used in the world. Applying ANN on the prediction of stock price has been verified as an effective prediction tool. Most academic researchers have applied trial and error according to their experiences to get the optimization parameters' setting of ANN. This research can successfully find out the key factors through applying design of experiment systematically, and further find the optimal parameter combination. The empirical result shows a significant improvement for the correlation coefficient of ANN. In addition, the application of fractional factorial experiment will also allow a significant decrease of experiment frequency, and further save time and cost. The difference is that it can explore many factors during one experiment without going through the trial and error. Therefore, it can be seen that the proposed methodology is feasible. There are some researches can be worth to investigate. First, bio-inspired computing algorithms can be considered to integrating with SVM model. Second, the parameter optimization method proposed by this research only applies BPNN as the study object, future studies will be able to verify the predication performance of other neural network models. Third, this research defines the stock price on the 5 th business day after the publication date of the financial statement as the output variable. Future studies can explore towards a mid-term or long-term financial statement disclosure. Finally, this research recommends adding more experimental factors on design of experiment to improve the interpretability of reaction value.

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