An extended range of stable-symmetric-conservative Flux Reconstruction correction functions The Flux Reconstruction (FR) approach offers an efficient route to achieving high-order accuracy on unstructured grids. Additionally, FR offers a flexible framework for defining a range of numerical schemes in terms of so-called FR correction functions. Recently, a one-parameter family of FR correction functions were identified that lead to stable schemes for 1D linear advection problems. In this study we develop a procedure for identifying an extended range of stable, symmetric, and conservative FR correction functions. The procedure is applied to identify ranges of such correction functions for various orders of accuracy. Numerical experiments are undertaken, and the results found to be in agreement with the theoretical findings. High-order methods for computational aerodynamics on unstructured grids offer the promise of increased accuracy at reduced cost, within the vicinity of complex engineering geometries. As such they have garnered continued interest over the past decades. However, to-date, their 'real-world' adoption in both industry and academia remains limited [1] . In 2007 Huynh proposed the Flux Reconstruction (FR) approach to high-order methods [2] . Based on a differential form of the governing system, it is hoped FR (also referred to as Lifting Collocation Penalty [3] or Correction Procedure via Reconstruction [4] ) will facilitate adoption of high-order methods amongst a wider community of fluid dynamicists.. Various properties of FR schemes, including their dispersion and dissipation characteristics [5, 6] , their associated Courant-Friedrichs-Lewy (CFL) limit [2, 5] , and their fundamental stability [7] , are all determined in full or in part by the form of their associated FR correction functions. These correction functions act to lift inter-element flux jumps from the boundary into the interior of each element. Building on the work of Huynh [2] and Jameson [8] , Vincent, Castonguay and Jameson recently identified a one-parameter family of correction functions that lead to stable FR schemes for 1D linear advection problems [7] . Identification of these correction functions, henceforth referred to as Vincent-Castonguay-Jameson-Huynh (VCJH) correction functions, provided significant insight into stability properties various FR schemes. However, further work is required in order to determine a full specification of the necessary and sufficient conditions that should be imposed on correction functions in order to guarantee stability.. In this study we develop a procedure for identifying an extended range of stable, symmetric, and conservative FR correction functions. The procedure is applied to identify ranges of such correction functions for various orders or accuracy. In all cases the original one-parameter VCJH correction functions are found to be a sub-set of the extended ranges. Numerical experiments are undertaken in order to verify the theoretical findings. FR schemes are similar to nodal DG schemes, which are arguably the most popular type of unstructured high-order method (at least in the field of computational aerodynamics). Like nodal DG schemes, FR schemes utilise a high-order (nodal) polynomial basis to approximate the solution within each element of the computational domain, and like nodal DG schemes, FR schemes do not explicitly enforce inter-element solution continuity. However, unlike nodal DG schemes, FR methods are based solely on the governing system in a differential form. A description of the FR approach in 1D is presented below. For further information see the original paper of Huynh [2] . For all k, correction functions defined by Eqs. (3.12) and (3.13) will be stable, symmetric and conservative provided the conditions defined by Eqs. . and Building on the work of Huynh [2] and Jameson [8] , Vincent, Castonguay and Jameson recently identified a one-parameter family of VCJH correction functions that lead to stable FR schemes for 1D linear advection problems [7] . In this study we developed a procedure for identifying an extended range of stable, symmetric, and conservative FR correction functions. The procedure was applied to identify ranges of such correction functions for various orders of accuracy. In all cases the original one-parameter VCJH correction functions were found to be a subset of the extended ranges. Numerical experiments were undertaken, and the results found to be in agreement with the theoretical findings. Future studies should extend the approach presented here to simplex elements in 2D and 3D. From an implementation perspective, it is advantageous to transform each Ω n to a standard element Ω S = {x|−1 ≤ x ≤ 1} via the mappinĝ. which has the inverse. Having performed such a transformation, the evolution of u δ n within any individual Ω n (and thus the evolution of u δ within Ω) can be determined by solving the following transformed equation within the standard element Ω S ∂û δ ∂t + ∂f δ ∂x = 0, (2.6). is a polynomial of degree k,. is a polynomial of degree k + 1, and. The FR approach to solving Eq. (2.6) within the standard element Ω S can be described in five stages. The first stage involves representingû δ in terms of a nodal basis as follows:. where l i are Lagrange polynomials defined as. 10). The second stage of the FR approach involves constructing a degree k polynomialf δ D =f δ D (x, t), defined as the approximate transformed discontinuous flux within Ω S . Specifically,f δ D is obtained via a collocation projection at the k + 1 solution points, and can hence be expressed aŝ. are simply values of the transformed flux at each solution pointx i (evaluated directly from the approximate solution). The fluxf δ D is termed discontinuous since it is calculated directly from the approximate solution, which is in general discontinuous between elements.. The third stage of the FR approach involves evaluating the approximate solution at either end of the standard element Ω S (i.e. atx = ±1). These values, in conjunction with analogous information from adjoining elements, are then used to calculate numerical interface fluxes. The exact methodology for calculating such numerical interface fluxes will depend on the nature of the equations being solved. For example, when solving the Euler equations one may use a Roe type approximate Riemann solver [9] , or any other two-point flux formula that provides for an upwind bias. In what follows the numerical interface fluxes associated with the left and right hand ends of Ω S (and transformed appropriately for use in Ω S ) will be denotedf δ I L andf δ I R respectively. The penultimate stage of the FR approach involves constructing the degree k + 1 polynomialf δ , by adding a correction fluxf δC =f δC (x, t) of degree k + 1 tof δ D , such that their sum equals the transformed numerical interface flux atx = ±1, yet in some sense followsf δ D within the interior of Ω S . In order to definef δC such that it satisfies the above requirements, consider first defining degree k +1 correction functions g L = g L (x) and g R = g R (x) to approximate zero (in some sense) within Ω S , as well as satisfying. A suitable expression forf δC can now be written in terms of g L and g R aŝ. . Using this expression, the degree k + 1 approximate transformed total fluxf δ within Ω S can be constructed from the discontinuous and correction fluxes as follows:. The final stage of the FR approach involves evaluating the divergence off δ at each solution pointx i using the expression. These values can then be used to advanceû δ in time via a suitable temporal discretisation of the following semidiscrete expression

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


Atom-Atom-Path similarity and Sphere Exclusion clustering: tools for prioritizing fragment hits Background: After performing a fragment based screen the resulting hits need to be prioritized for follow-up structure elucidation and chemistry. This paper describes a new similarity metric, Atom-Atom-Path (AAP) similarity that is used in conjunction with the Directed Sphere Exclusion (DISE) clustering method to effectively organize and prioritize the fragment hits. The AAP similarity rewards common substructures and recognizes minimal structure differences. The DISE method is order-dependent and can be used to enrich fragments with properties of interest in the first clusters.Results: The merit of the software is demonstrated by its application to the MAP4K4 fragment screening hits using ligand efficiency (LE) as quality measure. The first clusters contain the hits with the highest LE. The clustering results can be easily visualized in a LE-over-clusters scatterplot with points colored by the members' similarity to the corresponding cluster seed. The scatterplot enables the extraction of preliminary SAR. Conclusions: The detailed structure differentiation of the AAP similarity metric is ideal for fragment-sized molecules. The order-dependent nature of the DISE clustering method results in clusters ordered by a property of interest to the teams. The combination of both allows for efficient prioritization of fragment hit for follow-ups. We have described the implementation and use of AAP similarity coupled with DISE clustering as a tool to organize fragment hits. The presorting of the hits by decreasing LE ensures that the most interesting clusters appear at the top, thus, drawing the attention of the review team to the most promising compounds. While we have used LE in the discussion here, in principle the dataset can be presorted and re-clustered based on other properties or efficiency indices. The detailed description of atom neighborhoods used in the AAP similarity allows for the differentiation of even small changes in molecular structure. The combination of the AAP similarity and DISE clustering has also been successfully applied to prioritize high throughput screening hits [31] . The code for this software is available in Additional file 3. Screening of low-affinity and low-molecular weight fragments has become a powerful approach to identify lead matter and to initiate medicinal chemistry programs [1] . It has been shown that binding affinity does not increase linear with the molecular size [2] . Fragments are more likely to bind with high ligand efficiencies [3, 4] and can reveal important interactions required in more mature drug-like molecules. Choosing fragment hits for structure determination and chemical follow-up involves the evaluation of many project-specific parameters. Ligand efficiency (LE) is often used as one measure for assessing the quality of initial fragment hits.. Due to the generally higher hit rates of fragment screens (1-10%) most campaigns on libraries of 1,000-5,000 compounds will produce more hits, than downstream structural biology and chemistry resources can absorb for hit-to-lead development. To increase the chance of success, careful prioritization of the initial hits by a group of experienced specialists from different areas of drug discovery is important for advancing the most promising fragment hits. Fragment hit triage in advance of a structure determination typically weighs the LE parameter. However, many other properties including affinity, selectivity, and most importantly the chemical structure of the compound need critical consideration. In addition, fragment libraries often contain related molecules providing initial SAR and confidence in scaffold types. Clustering hit sets helps bring related molecules and features together for consideration, but the cluster order is usually determined by the algorithm and is independent of other factors such as LE. This results in a functional randomization of the order of the experimental data making trends harder to identify. To direct the attention of the specialists to the most promising hits we have employed a directed clustering method using a new similarity algorithm, to group hits with respect to both structure and data.. The Directed Sphere Exclusion (DISE) algorithm [5] used for the fragment clustering is an extension of the Sphere Exclusion (SE) algorithm [6, 7] . The first step consists of ordering input molecules by a non-structural parameter such as LE, which is followed by a diverse subset selection using the SE algorithm. The selected molecules are considered as cluster seeds. In the final step, the remaining molecules are assigned to the cluster seeds. The investigator has the choice of two assigning rules: Assign the remaining molecules to (a) the first cluster seed whose similarity to the candidate molecule is within the specified threshold or (b) the most similar cluster seed.. Sorting the input molecules according to decreasing LE ensures that fragments having the highest LE are evaluated first in the cluster seed selection. Assigning the remaining molecules to the cluster seeds using rule (a) yields clusters with decreasing maximum LE while using rule (b) produces clusters that are structurally more consistent. In either case, the DISE clustering places the fragment clusters with favorable LE on top of the list, thus, directing the focus of the review team to the most promising clusters. Consequently, molecules with low LE (LE < 0.3, typically 30-50% of hits in most screens) are either moved towards the bottom of the list or included in clusters with a higher LE compound as cluster seeds, and therefore do not distract the team from clusters that are of higher interest. To our knowledge there are no other clustering methods that allow the clustering to be influenced by a target property. Frequently used clustering methods in chemical informatics [8] include hierarchical clustering, Jarvis Patrick clustering and k-means clustering. They are either order independent or aim to minimize the order dependency (k-means clustering). This means that their results depend only on the similarity matrix and cannot be influenced by external target properties.. Equally important is the choice of similarity metric. Many similarity metrics have been published in the past [9] [10] [11] [12] [13] [14] [15] . For fragment hit clustering, the similarity metric should meet the following requirements: (1) To satisfy the perception of the medicinal chemists, the similarity metric should put a high weight on common substructures. (2) The similarity metric should be sensitive to small changes in substitution. The latter is important because fragments are small in comparison to High Throughput Screening (HTS) compounds. Therefore, small changes have a strong effect on similarity in fragments.. Fingerprint based similarity methods generate fingerprints by systematically recording patterns present in compounds. Generally linear or circular patterns originating from each atom are used. The similarity of two compounds is then computed by comparing the patterns present or absent in each [9] [10] [11] [12] [13] [14] [15] [16] [17] . Their relative orientation is not stored while recording the patterns. Consequently, the relative orientation of the patterns in the compounds is not taken into consideration when computing the similarity. When comparing compound 1a using linear fingerprints to 1b a low similarity is found due to the difference of the central atom on the piperidine/piperazine ring as noted by Stahl et al. [15] . When using circular fingerprints compounds 1a and 1b are nearest neighbors. However, because circular fingerprints have a small pattern size and do not encode any information on the relative position of the patterns, the closest compound to 2a is 1b.. Graph based similarity methods such as Maximum Common Substructure (MCSS) [12, 18] and Maximum Overlapping Set (MOS) [15] similarity based methods put a high weight on the common substructure. The similarity is computed from the ratio of the number of atoms and bonds in the MCSS or MOS to the total number of atoms and bonds. Because the similarity calculation is based on the integer counts, it is not sensitive to differences in substitution patterns. Stahl et al. introduced two empirical correction terms to mitigate this problem: one to penalize different arrangements of common substructures and the second to increase the similarity value if the two molecules have a substructure in common that exceeds 70% of the smaller molecule [15] . When comparing the compounds in Figure 1 the pairs 1a/ 1b and 2a/2b constitute nearest neighbors in agreement with chemical intuition.. For clustering fragment hits we have developed a new similarity metric: the Atom-Atom-Path (AAP) similarity metric that does not need empirical terms. AAP, too, puts a high weight on the common substructures. In the case of the compounds in Figure 1 it correctly recognizes the pairs 1a/1b and 2a/2b as nearest neighbors. The calculation of the AAP similarity of two molecules A and B consists of four steps. In the first step, each atom is described by the set of linear paths originating from it. In the second step, the atom-to-atom similarity of each atom in A to each atom in B is computed. This similarity matrix is used in the third step to map each atom in the smaller molecule to a unique atom in the other. The final step consists of computing the AAP similarity from the atom-to-atom similarities of the mapped atom pairs.. Because the set of atom paths encodes the neighborhood of the given atom, the more similar the sets of paths of two atoms are, the larger the atom-to-atom similarity is. An atom-to-atom similarity of 1 indicates that the two atoms are embedded in a large substructure present in both molecules. As a result, the AAP similarity of a molecule pair increases with the size of the common substructures. The change of a single atom affects the atom-to-atom similarities of neighboring atoms. The AAP similarity is sensitive to very small changes in substitution. Hence, we found that molecules with AAP similarities as low as 0.3 still share many common features. The similarity distribution of AAP as well as circular and linear fingerprint similarities for the full pairwise comparison of 4000 compounds from the Novartis-GNF Malaria Box data [19] sets is shown in Additional file 1: Figure S3 . The distributions show how the AAP similarities are generally much lower than the fingerprint based similarities.. Similarity for use to organize chemical compounds for medicinal chemists is highly subjective [20] . During repeated use at Genentech we have found that clustering using AAP similarity consistently gives results that are in agreement with medicinal chemists' perception. The mapping of atoms ensures that each atom is considered equally and the description of the atoms ensures a fine grained weighting through their environment. This results in clusters in which ring systems have a high weight avoiding the formation of clusters with large differences in scaffolds. To provide a comparison with Tanimoto similarity using linear and circular fingerprints we have included the clustering of a random subset of the Novartis-GNF Malaria Box dataset using three similarity metrics as Additional file 2. All programs required to cluster molecules using the DISE method and the AAP similarity are available in Additional file 3. Clustering using the DISE algorithm is performed by applying two command line programs to the input data, i.e. sdfSorter.csh and sdfCluster.pl ( Figure 2 ). sdfSorter.csh sorts records in SDF files by the value of one or more fields that must be present in the records. sdfCluster.pl performs the SE clustering by internally executing the sequence of command line programs shown in Figure 2 . The programs sdfMCSSSphereExclusion.csh and sdfMCSSNNFinder.csh use the AAP similarity for finding the cluster seeds and for assigning the cluster members to the closest seed. Below we describe the algorithm to compute the AAP similarity.

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


Using CSIM to model complex systems Simulation models of complex systems, defined here to be systems with large number of activities or resources or with activities which exhibit complex behavior patterns, make severe requirements on simulation packages. These requirements are in the form of expressiveness (can you express the complexity in the language of the model?) and in the form of accommodation (can the runtime environment handle the large number of simulation objects?). This paper describes CSIM, a process-oriented simulation language based on C, and the features of CSIM which make it useful in developing and executing models of complex systems. Process-oriented simulation (Franta 1977 , Saydam 1985 is a form of discrete event simulation which lets the model implementer focus on the activities being processed by a system, as opposed to the systems events which are the focus of event oriented simulation. Several languages have been designed to support process-oriented simulation, including GPSS (Gordon 1978) , Simula @ah1 and Nygaard 1967), SLAM I1 (Pritsker and Pegden 1979) . Simscript 11.5 (Law and Kelton, 1982) , ASPOL (MacDougall and McAlpine 1973 , MacDougall 1974 , and MacDougall 1975 RFSQ (Sauer and MacNair 1983) and PAWS (IRA 1987) . More recently, another process-oriented simulation language, called CSIM, has been introduced (Schwetman 1986 ).. Whenever a new simulation language or package appears, several questions naturally arise, questions such as:. 1. How is this language similar to and, also, different from other such languages? and

O O O B O B B O O O B O O O O B O O O O O O O O O O O O O B O O O B O B O O B O O O O O O O O B O B O O B O O B O O O O O O O O B O O O O O O B O O B O O O O B B O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O B O O O O O O O O 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 B B O O O O O O O O O O O B B O O O O O O O O O O O O O O B O O O O O O O O O O


13C metabolic flux analysis shows that resistin impairs the metabolic response to insulin in L6E9 myotubes Background: It has been suggested that the adipokine resistin links obesity and insulin resistance, although how resistin acts on muscle metabolism is controversial. We aimed to quantitatively analyse the effects of resistin on the glucose metabolic flux profile and on insulin response in L6E9 myotubes at the metabolic level using a tracer-based metabolomic approach and our in-house developed software, Isodyn. Several studies have identified positive correlations between resistin levels and IR in vivo [24] and in vitro [19] [20] [21] [22] . Overall, our results showed that resistin significantly alters glucose metabolism in L6E9 myotubes and their response to insulin. Of the whole set of metabolic changes induced by resistin in L6E9 myotubes, the imbalance in PDC and PC fluxes as well as the higher acetyl-CoA output flux for fatty-acid synthesis and other metabolic processes should be emphasized. Resistin impairs the normal metabolism of insulin, and the metabolism is directed to try to maintain the imbalance between the PDC and PC fluxes. In this way, L6E9 reduces TCAcycle fluxes and acetyl-CoA output fluxes, which leads to an important metabolic imbalance in the central carbon metabolic pathways of L6E9 myotubes.. It has been reported that IR in skeletal muscle, liver and adipose tissue is usually accompanied by glucose intolerance and hypertriglyceridemia [24] . In this way, our results showed the importance of the balance of PDC and PC in glucose metabolism.. Our results support the idea that metabolic disorders such as T2DM are caused by complex multi-molecular interactions that cannot be explained readily by an alteration in expression of a single gene or gene product, or even alteration of a single enzymatic cascade. The robustness of results obtained on the effects of insulin on L6E9 metabolism found by combining tracer-based metabolomic data and flux analyses using Isodyn showed that this approach is a suitable tool to study the effects of hormones on the central carbon metabolism network in myocytes. After the discovery of several adipocyte-secreted molecules (including lipid metabolites and adipokines), adipocytes were recognized as part of endocrine tissue [9, 11, 37] . These molecules enable adipocytes to communicate with other tissues and organs, and to regulate: the metabolism of lipids and glucose; energy balance; insulin action; cell proliferation. Resistin was identified as an adipokine, and it was suggested that it might link obesity and IR [12, 13] . However, the role of resistin in the pathophysiology of IR in humans and animals, and how it acts in muscle, liver and fat, is controversial [15, 16] .. Here, we investigated the effect of resistin on basal and insulin-stimulated glucose metabolism in L6E9 rat myotubes. We used tracer-based metabolomics and our in-house Isodyn software to analyse quantitatively metabolic flux distribution in this cell line under different incubation conditions. The response to insulin and other hormone stimuli in L6E9 cells is similar to that observed in skeletal muscle in vivo [38] . Hence, L6E9 cells are considered to be suitable models for analyses of the effect of resistin on glucose metabolism and on the metabolic response of muscle cells to insulin.. Analyses with Isodyn data provided an overview of the central carbon metabolism of L6E9 skeletal muscle cells. Analyses were undertaken assuming a metabolic steady state (though not assuming an isotopic steady state), and rapid mixing of isotopic isomers of the same metabolite throughout different intracellular compartments. Incubation with a large excess of glucose ensured the required glucose uptake throughout the incubation. The other conditions of incubation did not change, so the assumption of a metabolic steady state seemed reasonable. Rapid mixing of isotopic isomers of the same species throughout the cell is accepted for analyses of data of stable isotopes [39] . Fitting of experimental data in the framework of these assumptions suggested a set of metabolic fluxes underlying the measured distributions of isotopic isomers.. The effect of insulin on L6E9 myotubes increases glycolysis, PPP, and incorporation of pyruvate to the TCA cycle through PDC and fatty-acid synthesis Our results suggested that L6E9 myotubes were highly glycolytic, with active synthesis and degradation of glycogen, and showed TCA-cycle activity and acetyl-CoA output. Oxidative PPP was weakly active in this cell type. Furthermore, use of the same tools revealed that insulin activated the uptake and phosphorylation of glucose, glycolysis and lactate production, the oxidative branch of the PPP, pyruvate incorporation towards the TCA cycle and increased acetyl-CoA output (which is used for fatty-acid synthesis). We observed that insulin altered the ratio between PDC and PC fluxes by increasing the PDC flux (See figure on previous page.) Figure 2 Gene expression of enzymes related to pyruvate homeostasis. L6E9 myotubes were treated (Res+) or not treated (Res-) with 100 nM resistin for 8 h and then incubated for 6 h with 10 mM glucose in the absence (Ins-) or presence (Ins+) of 100 nM insulin. RT-qPCR monitoring of mRNA levels of pyruvate carboxylase (Pc) (A), pyruvate kinase muscle isozyme (Pkm2) (B), pyruvate dehydrogenase E1 alpha 1 (Pdha1) (C), pyruvate dehydrogenase kinase isozyme 2 (Pdk2) (D), pyruvate dehydrogenase kinase isozyme 4 (Pdk4) (E), cytosolic NADP-isocitrate dehydrogenase (Idh1) (F), NADP-dependent malic enzyme (Me1) (G) and cytosolic phosphoenolpyruvate carboxykinase 1 (Pck1) (H) are shown. Results from three experiments are expressed as the mean ± S.E.M. (*) indicates p < 0.05 and (**) p < 0.01 compared with the condition of neither resistin nor insulin. (#) indicates p < 0.05 and (##) p < 0.01 compared with L6E9 myotubes treated only with resistin.. through an increase of levels of Pdha1 and decrease of Pdk2 and Pdk4 mRNA. The effects of insulin on the metabolic flux distribution of L6E9 myotubes reported in the present study correlate with the known activation of PDC by profound suppression of Pdk4 expression in skeletal muscle [40] , inhibition of expression of the Pck1 gene, and the increase in glucose uptake and lactate production observed using other approaches [38, 41] .. The effect of resistin on L6E9 myotubes increases glycolysis and fatty-acid synthesis and alters the ratio between PDC and PC, tilting it towards direct incorporation of pyruvate through PDC Our results revealed that, in the absence of insulin, resistin activated glucose phosphorylation and the glycolytic pathway. Also, resistin did not affect the glycogen content in skeletal muscle. Even though enrichment of the glycogen label (reflected in the m2 values of the glycogen molecule) was not significantly different to the control condition, the tendency was for glycogen-related fluxes to be lower, a result that was in accordance with other works [22] . Furthermore, our approach showed that, even though many of the TCA-cycle fluxes remained unchanged, the ratio between the PDC and PC fluxes was significantly altered, effectively increasing the incorporation of pyruvate through PDC into mitochondria (as suggested by the reduction observed in levels of Pdk4 mRNA). PC activity is finely regulated by mechanisms such as allosteric activation by acetyl carnitine, which was not tested in this study. The acetyl-CoA output for fatty-acid synthesis was also increased after resistin treatment, which would explain the higher flux towards the TCA cycle. For analyses of the effect of resistin on glucose metabolism and on the metabolic response of muscle cells to insulin, L6E9 myotubes were pretreated for 8 h with or without resistin (100 nM). After preincubation, myotubes were incubated for a further 6 h with glucose (10 mM) that was 50% enriched in [1,2-13 C 2 ]-glucose in the absence or presence of 100 nM insulin and in the continued presence or absence of resistin.. After 6 h of incubation, glucose consumption, lactate production, intracellular levels of glycogen and glucose-6-phosphate (G6P) were determined (Table 1) , as were the mass-isotopomer distributions in glucose and lactate from the incubation medium, as well as glycogen glucose and ribose isolated from RNA in cell pellets ( Table 2) . Analyses of the obtained data by Isodyn determined the distribution of the metabolic flux profile of L6E9 myotubes under various incubation conditions (Table 3 ). Figure 1 summarises the qualitative changes in metabolites and fluxes. Obesity is increasing to epidemic proportions [1, 2] , starting from young ages [3, 4] , and is associated with an increase in the prevalence of type-2 diabetes mellitus (T2DM) throughout the world [2, 5] . In recent years, active participation of immune cells in obesity and T2DM has become evident [6, 7] . This chronic activation of the innate immune system can lead to insulin resistance (IR), impaired tolerance to glucose and, eventually, T2DM [8, 9] .. Adipose tissue produces a vast array of adipocytederived factors ("adipokines") that regulate the metabolism, inflammation and body mass [10, 11] . One of these adipokines, resistin, belongs to a family of cysteine-rich proteins shown to be involved in inflammation and altered insulin sensitivity in rodents [12, 13] . Resistin is produced from adipose tissue in rodents whereas, in humans, it is secreted by the mononuclear lymphocytes and stromal cells within adipose tissue [14, 15] . Studies in humanised resistin mice suggest that, even though the site of resistin production differs between species, human resistin exacerbates inflammation in white adipose tissue and contributes to IR, thereby impairing its normal effects [16, 17] .. IR is defined as the genetic or learned inability of target tissues to respond normally to the action of circulating hormones. It has been described in skeletal muscle but also in liver and adipose tissues [18] . Some studies have shown that resistin affects glucose transport and insulin-stimulated oxidation of glucose in L6 skeletal muscle cells [19] [20] [21] [22] . It also decreases the uptake and oxidation of long-chain fatty acids [23] and glycogen synthase kinase-3-β, as well as insulin-stimulated insulin receptor substrate-1 (IRS-1) tyrosine phosphorylation [19, 22] in the same cell line. Furthermore, high levels of resistin in rats leads to IR involving impaired insulin signalling in skeletal muscle, liver and adipose tissues, resulting in glucose intolerance, hyperinsulinemia and hypertriglyceridemia [24] . These observations link resistin in muscle-cell metabolism to IR.. Changes in the metabolome (i.e., the whole set of metabolites) have been described as the "ultimate" response of an organism to various events, such as genetic alterations as well as disease-based or environmental influences [25] . However, the metabolome is dynamic and metabolites are transformed continuously in the cell. Comprehensive characterisation of the metabolic networks and their functional states requires quantitative knowledge of intracellular metabolic fluxes. These intracellular fluxes can be quantified by analysing incorporation of labelled substrates in metabolic products using appropriate bioinformatic tools [26] .. Skeletal muscle is considered to be the main tissue involved in the maintenance of glucose homeostasis because its contribution to glucose uptake is ≈ 75% of the total contribution of peripheral tissues [27] , and it is the main tissue responsible for insulin-dependent glucose use. Also, pyruvate homeostasis-related fluxes in skeletal muscle play a critical part in glucose homeostasis [28] [29] [30] [31] [32] . A better understanding of how these fluxes work together in muscle cells is needed to understand this process.. The aim of the present study was to examine the effect of resistin on the central carbon metabolic network of rat skeletal muscle cells, and to ascertain how resistin alters the response of muscle cells to insulin at the metabolic level. We used [1, [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] C 2 ]-glucose as a tracer, analysed isotopomer distributions by gas cromatography (GC) coupled with mass spectrometry (MS), and quantified metabolic fluxes using Isodyn software [26, [33] [34] [35] [36] . In the model of the glucose metabolic network in skeletal muscle we included the glycolytic pathway and pentose phosphate pathway (PPP). Pyruvate dehydrogenase complex (PDC)-, phosphoenolpyruvate carboxykinase (PEPCK)-and pyruvate carboxylase (PC)-catalysed reactions were also included to account for pyruvate homeostasis-related fluxes. Resistin-induced alterations in the profile of metabolic fluxes of rat skeletal muscle cells were identified, and were complemented by analyses of the expression of certain genes.. The study presented here offers a wider vision than previously published of the metabolic reorganisation that resistin induces in rat skeletal muscle cells and in the metabolic response of these cells to insulin. Our observations provide new data for a more precise understanding of the effect of resistin on metabolic-network adaptations of skeletal muscle cells, and help to explain the role of resistin in the IR described in myocytes. Our work reveals the importance of tackling the study of complex biological systems from a systems-biology point of view to fully understand multifactorial diseases and identify new therapeutic targets.

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


An improved multipath MANET routing using link estimation and swarm intelligence Routing in ad hoc networks is challenging as nodes are mobile and links are continuously created and broken. Current on-demand ad hoc routing algorithms start route discovery after path break, incurring high cost to detect the disconnection and to establish a new route. Specifically, when a path is liable to break, the source is warned about the likelihood of disconnection. The source then starts path discovery avoiding disconnection entirely. A path is likely to break when link availability decreases. Since routing is nondeterministic polynomial (NP) hard, this work proposes an improved ad hoc on-demand multipath distance vector (AOMDV) based on link availability, neighboring node's queuing delay, node mobility, and bit error rate. The optimal path is selected using BAT meta-heuristic optimization. Simulation shows improved performance compared to AOMDV. With emerging mobile applications [1] [2] [3] , mobile ad hoc networks (MANETs) have attracted research from various groups due to its flexibility and usability in diverse applications. A MANET is a self-configuring temporary network of mobile nodes which are independent with each other and do not have any fixed infrastructure. MANETs do not control or regulate traffic [4] within the network but utilize the intermediate node's routing capability. Since source and destination nodes use intermediate nodes as routers, a routing path must be established for actual communication. Routing protocols are the key to MANET success and are an active area for MANET research [5] [6] [7] [8] [9] .. Many routing protocols have been proposed for ad hoc networks in literature which find a route based on given criteria for packet delivery from source to destination. In literature, routing protocols are broadly classified as table-driven protocols and on-demand protocols. In the former, also called proactive routing protocols, every node maintains a table of data containing routing information such that source can reach any node in the destination if a route exists. Popular table-driven protocols include optimized link state routing (OLSR) and destination sequenced distance vector (DSDV). In ondemand routing protocols, routes are created as and when needed. They are also called as reactive protocols, and the source invokes route discovery process when data has to be transmitted. A route is valid till destination is reached or until route is not required. Popular existing on-demand routing protocols include dynamic source routing (DSR) and ad hoc on-demand distance vector AODV [10, 11] protocol.. In AODV, [12, 13] a source node broadcasts route request (RREQ) to its neighbors. When adjacent nodes received RREQ with source node and target node addresses, it judges if it is the target. If yes, it sends a route reply (RREP); otherwise, it checks if it has active route to the destination in its table. If it has a fresh route, then it sends RREP to the source or it continues flooding by sending RREQ. AODV protocol discovers neighborhood nodes through regular broadcast of hello messages. When a link breaks, it sends route error message while deleted/broken records are repaired.. Ad hoc on-demand multipath distance vector (AOMDV) [14] is an AODV extension for computing multiple loopfree and link-disjoint paths. The routing table for destination includes a list of next hops and the number of hops to reach the destination. In AOMDV, all the available nexthop neighbors are assigned the same sequence numbers. A node maintains advertised hop count for every destination, and this hop count sends destination route advertisements. Every duplicate route advertisement that has been broadcasted and received by a node defines an alternative destination path.. A node accepts an alternative destination path-to ensure loop freedom-only when the hop count it has is lower than advertised hop count. To locate disjoint routes, a node does not reject duplicate RREQs immediately. Every RREQ has an additional field called first hop indicating its first hop. Also, a node maintains a firsthop list for every RREQ to track list of neighbors of source through which a RREQ copy was received. To ensure link disjoints in RREP's first hop, destination replies only to RREQs arriving through unique neighbors. Every RREP trajectory may intersect at an intermediate node, but each goes on a different reverse path to source ensuring link disjointness [15] . This work proposed improvements in AOMDV based on Link Quality. A link estimation algorithm-based AOMDV was proposed (LQ-AOMDV). The proposed LQ-AOMDV was optimized to obtain optimal solutions. A novel objective function was proposed to balance the load across the network and improve the network performance. Simulations results show that PDR of proposed BAT-AOMDV improved when compared to AOMDV and LQ-AOMDV. Average BAT-AOMDV values increased by 10.2 % when compared to AOMDV and increased by 2.17 % when compared to LQ-AOMDV. Further investigation is necessary to lower end-to-end delay. A multipath routing protocol proposed by Obaidat et al. [16] is a variant of single-path AODV routing protocol. The proposed method established node-disjoint paths with lowest delays based on interaction of factors from various layers. The proposed protocol's performance was investigated and compared to single-path AODV and multipath AOMDV protocols using Operations Network (OPNET). Results show improved performance of the proposed method in terms of throughput and end-toend delay.. Adaptive multi-metric (AM)-AOMDV, an improved AOMDV based on multiple metrics, was proposed by Khimsara et al., [17] . AM-AOMDV extends AOMDV by including many route metrics, a new local route update, and route maintenance algorithm. The latter uses onehop information exchange between one-hop nodes to improve route longevity. The modified technique improved packet delivery ratio and decreased end-to-end delay. Significant improvement was also found in route discovery frequency and routing overhead during node mobility. Multiple metrics ensure routing scheme convergence to most efficient route during transmission and avoided creation of hotspots.. Mallapur and Patil [18] proposed a Stable Backbonebased Multipath Routing Protocol (SBMRP). In the proposed protocol, candidate nodes were selected based on available bandwidth, link quality, node mobility, and available power. Source-destination paths were established through candidate nodes, to form a routing backbone. When a candidate node fails in a path due to lack measure values, another candidate node is used to create an alternate path. Simulation proved that the new technique reduced overhead, packet drop, and energy while increasing packet delivery rate.. Yu et al. [19] proposed Link Effective Available Time (LEAT). The method aimed to locate a link available time during epoch through measurement of distances between a mobile link's two nodes rather than using localization information. A new routing link cost was proposed which lowered link breakage. Routing was formulated as an optimal routing problem based on new cost, using a heuristic algorithm. Simulation shows that LEAT improved network performance in delay, hop counts, and throughput when compared to present routing algorithms.. Yu and Bao [20] proposed a new link cost to reduce breakages during data service. To reduce implementation complexity, the authors used only ranging information in link availability and avoided localization information. Routing was formulated, based on new metrics, as an optimal routing problem, needing a heuristic algorithm. Simulation proved that RBLAR improved link connectivity by reducing link breaks and improved network performance. Considering link reliability in route choice was proposed by Yelemou [21] . Route request procedure was modified to enable reliable paths using bit error rate (BER). Simulations showed the proposed system outperformed AOMDV even in conditions like mobility and multi-communication.. Chen et al., [22] extended AOMDV routing protocol to accommodate channel fading. The new channelaware AOMDV (CA-AOMDV) used channel average nonfading duration as routing metric to choose stable links for path discovery applying a pre-emptive handoff strategy to ensure reliable connection. Using this information, paths when available were reused and not discarded. The proposed system ensured lower downtime. The authors also showed via simulations common network performance measures, with good insights into differences in performance between CA-AOMDV and AOMDV.. Link availability estimation was used to select most stable route from alternate paths was proposed by Mazumdar et al. [23] and was implemented in AOMDV for route selection. Results show that selecting stable route leads to a higher throughput in dynamic network topologies.. Node mobility is a major factor link stability in MANETs. Cai and Liu [24] suggested Prediction of Link Stability-AOMDV (PLS-AOMDV) based on AOMDV multipath routing protocol that periodically predicted link stability by considering both node mobility and energy consumption to choose a high stability link. Simulation shows that PLS-AOMDV improved packet delivery rate.. Energy-efficient (EE)-AODV routing protocol that is an enhancement of current AODV routing protocol was proposed by Singh and Gupta [25] . Routing algorithm adopted by EE-AODV enhanced RREQ and RREP process to save mobile devices energy. EE-AODV considers a threshold energy level as minimum energy which must be available with a node for use as an intermediary node. When node energy reaches the threshold level, it would not be considered an intermediary node unless alternative paths are unavailable. Simulation shows that network life increased in EE-AODV compared to AODV.. Gunes et al. [26] proposed a swarm intelligence-based multipath routing protocol using ant colony optimization. The proposed algorithm reduced the routing overheads compared to traditional multipath routing protocol. Liu and Feng [27] used ant colony optimization metaheuristic on the node-disjoint multipath routing problem. The proposed algorithm concurrently sends data via multiple paths. Ziane and Melouk [28] extensively investigated multipath routing for multimedia data using swarm intelligence. Meta-heuristic techniques have been extensively used in wired and wireless networks including wireless sensor network, multicast routing [29] [30] [31] .. Yen et al. [32] proposed a multi-constrained quality of service (QoS) multicast routing method using genetic algorithm. The proposal will be flooding-limited using the available resources and minimum computation time in a dynamic environment. By selecting the appropriate values for parameters such as crossover, mutation, and population size, the genetic algorithm improves and tries to optimize the routes. Simulation results indicate its better performances compared to other methods.. Song et al. [33] exploited a biological model of Physarum to design a novel biology-inspired optimization algorithm for minimal exposure problem (MEP). First, formulate MEP and the related models and then convert MEP into the Steiner problem by discretizing the monitoring field to a large-scale weighted grid. Inspired by the path-finding capability of Physarum, the authors developed a biological optimization solution to find the road-network with minimal exposure among multiple points of interest. POA can also be used for solving the general Steiner problem. Extensive simulations demonstrate that the proposed models and algorithm are effective for finding the road-network with minimal exposure and feasible for the Steiner problem [34] .. Li et al. [35] proposed a reliable multicast protocol, called CodePipe, with advanced performance in terms of energy efficiency, throughput, and fairness in lossy wireless networks. Built upon opportunistic routing and random linear network coding, CodePipe not only simplifies transmission coordination between nodes but also improves the multicast throughput significantly by exploiting both intra-batch and inter-batch coding opportunities. In particular, four key techniques, namely LP-based opportunistic routing structure, opportunistic feeding, fast batch moving, and inter-batch coding, are proposed to offer substantial improvement in throughput, energy efficiency, and fairness. CodePipe was evaluated on NS2 simulator by comparing with other two state-of-the-art multicast protocols, MORE and Pacifier. Simulation results show that CodePipe significantly outperforms both of them.. The importance of routing in disruptive tolerant network, cognitive network, mesh network, and wireless sensor network has been extensively discussed in [33, [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] . From literature survey, it can be observed that link quality plays a very important role for obtaining better QOS in multipath routing protocols. Routing being nondeterministic polynomial (NP) hard, various meta-heuristic-based routing algorithms have also been proposed in literature using swarm intelligence metaheuristic. Popular meta-heuristic algorithms including genetic algorithm and particle swarm optimization (PSO) have shown to have drawbacks when the solution to be found is multimodal. In this work, it is proposed to investigate an improved AOMDV algorithm based on link quality and BAT meta-heuristic which has been shown to perform well for multimodal optimization problems. This work uses BAT optimization to find optimal route for AOMDV based on link quality and neighboring node queuing delay. In this section, the technique used for predicting link availability and queuing delay is presented. Since the problem is multi objective, BAT meta-heuristic is used to find optimal routes. For link availability estimation, the basic assumptions used are similar to that used in literature [49] [50] [51] [52] [53] [54] . The movement of a node from one location to another at a constant speed and direction is called epoch. The mobility of the nodes is comprised of multiple epochs which need not be same. The different epoch size used in this work is different from the same epoch length used in literature. Assuming each epoch is exponentially distributed with mean λ. The node mobility among different nodes is uncorrelated. Assuming all nodes have the same average epoch length, it is possible to predict the link availability between two nodes for duration T p using equation (2). In case the node velocity changes between two epochs and the distance between the nodes is less than the maximum transmission range of the node, the link availability can be computed using equation (3) .. Since movement among nodes are independent and based on the assumption of exponential distribution it can be shown that. It is possible to find the direction of node movement and whether two nodes are moving towards each other or away from each other using received signal strength indication (RSSI). The link quality degrades the square of the distance between the nodes, as the nodes move from each other. Alternatively, the change between a fixed epoch length can be computed by assuming a random variable ω which is a value smaller than t 0 + T p , and assuming both nodes are moving away from each other, the link quality can be given by. The average L s (ω) can be computed by equation (6) . Where f(w) ≥ 0 is given by. Substitute L s (ω) and f(w) with equation (3), we obtain equation (7). In a multihop network, the average delay to deliver a packet from source to destination is dependent on the number of hops to the destination. Delay cumulatively increase based on the data processing time, queuing time, and transmission time. Propagation delay in an ideal medium can be assumed to be minimal as the transmission distance is not substantial in MANETs. Decreasing queuing delay load balances the network. For a given route, let P i,j (t) be the number of packets available between node i and nodej . For the time interval [0, 1] , let the number of packets that arrive be given by α(t). If the time taken for the packet to leave node i and reach node j is T i, then the load in the link between i and j is given by equation (8). P T changes with time and reaches a steady state as t increases and can be given by equation (9) P ¼ lim. Using Little's theorem, equation (9) can be solved and a probability-based model can also be derived. If routes are selected based only on link quality, load balancing becomes a major issue. For a given source to destination, multiple routes are discovered using the link metric in AOMDV by modifying the route discovery process. To maintain a balance between the network load and QoS, the objective is to minimize. where PLR is the packet loss rate, L e is the estimated link, P e is the estimated load, d t is the delay threshold, and d is the delay in route. In this work, the BAT meta-heuristic is used to select the optimal route such that the objective is minimized. Xing-She Yang proposed BAT algorithm (BA) [55] , which imitates micro bat's echolocation behavior. Bats are the only mammals that fly and have advanced echolocation capabilities using short-frequency modulated signals which help it to identify obstructions. Micro bat is an example though all species use echolocation extensively. Bats emit a loud sound pulse and listen to resulting echo which bounces back from surrounding objects. The algorithm is based on the way micro bats fly to find food and avoid objects. The process of BAT algorithm is given by:. From the pseudo code, it can be seen that initial n random solutions, which are feasible routes between source and destination, are defined. For the frequency and pulse rate, compute the objective for each solution. Find the best route and generate local solutions based on the best route. Fig. 1 shows an example of how a local solution is created.. Random solution created can be S → N3 → N4 → N5 → D Based on network parameters, the best solution obtained is the route S → N1 → N4 → D, then a local search is initiated such that part of the route tree is changed. For example, a feasible solution obtained from local search can be represented by S → N1 → N6 → D Since the solution space is very large, new solutions are also created randomly every iteration. The BAT parameters used in this work is given in Table 1 .

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B O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O 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 B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O 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 B I O O 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Fuzzy data mining and management of interpretable and subjective information Fuzzy set theory offers an important contribution to data mining leading to fuzzy data mining. It enables the management of interpretable and subjective information in both input and output of the data mining process. In this paper, we discuss the notion of interpretability in fuzzy data mining and we present some references on the management of emotions as a particular kind of subjective information. Since its introduction by Lotfi Zadeh fifty years ago, fuzzy set theory has been fruitfully used in many domains. Data mining is one of the important fields of application, introduced in the 1990s as a particular step in knowledge discovery from database (KDD): "The data-mining component of KDD currently relies heavily on known techniques from machine learning, pattern recognition, and statistics to find patterns from data in the data-mining step of the KDD process" [1] . Early after the appearance of data mining, several works have proposed the use of fuzzy set theory to this domain.. The contributions of fuzzy sets in data mining are various: increasing the interpretability, enhancing the robustness of the process and managing unclear information, in particular subjective and emotional information. Both are provided by the introduction of fuzzy set theory to build up fuzzy data mining, offering to that process the capacity to mine complex information difficult to treat in a classic environment, considering the particular case of emotions.. Interpretability is the focus of this paper and it is discussed hereafter. Robustness of the process enables it to produce similar results when facing only small changes in the data (for instance, in the presence of noise). Robustness of fuzzy systems has been extensively studied and is well-known even in non-machine learning domains. Section 1 presents fuzzy data mining. In Section 2, interpretability in fuzzy data mining is discussed. In Section 3, the particular case of handling subjective information, such as emotions, is studied. Lastly, a conclusion and some future works are presented.

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


Vector mixed quasi complementarity problems in Banach spaces In this paper, we introduce a new class of set-valued vector implicit quasi complementarity problems with corresponding set-valued implicit quasi variational inequality problems. By means of the Fan-KKM theorem, we investigate the nonemptiness and compactness of solution sets of these problems. Our work generalizes and improves some results appeared recently in the literature. The complementarity theory introduced by Lemke [1] and Cottle and Dantzig [2] is a new domain of applied mathematics and it has many applications in optimization, economics, finance, engineering, mechanics and game theory; see for example [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] and the references therein. It is well known that some complementarity problems are equivalent to the related variational inequalities under certain conditions. There have been many discussions on the relations between the solution sets to complementarity problems and the solution sets to the corresponding variational inequality problems; see for example [3] [4] [5] [6] [8] [9] [10] [11] [12] [13] .. Recently Farajzadeh et al. [5] introduced mixed quasi complementarity problems in a topological vector space and established the existence result for mixed quasi variational inequality problems. They showed that the mixed quasi complementarity problems are equivalent to the mixed quasi variational inequality problems.. Very recently Khan [9] introduced and studied the following generalized vector implicit quasi complementarity problem (GVIQCP): find x ∈ K such that ⟨N(Ax, Tx), g(x)⟩ + F (g(x), g(x)) = 0 and ⟨N(Ax, Tx), h(y)⟩ + F (h(y), g(x)) ∈ P(x), ∀y ∈ K , and the following generalized vector implicit quasi variational inequality problem (GVIQVIP): find x ∈ K such that ⟨N(Ax, Tx), h(y) − g(x)⟩ + F (h(y), g(x)) − F (g(x), g(x)) ∈ P(x), ∀y ∈ K , where K ⊆ X be a nonempty closed and convex subset of a Banach space X ,. He investigated the nonemptiness and closeness of solution sets of these problems and proved that solution sets of both the problems are equivalent to each other under some suitable conditions.. Motivated by the recent work going in this direction, in this work we introduce a class of set-valued vector implicit quasi variational inequality problems and corresponding set-valued vector implicit quasi complementarity problems in real Banach spaces. Further by using the Fan-KKM theorem, we investigated the nonemptiness and compactness of solution sets of these problems. Furthermore, we establish equivalence between them under certain conditions. The results presented in this paper improve and generalize some recent results due to Khan [9] , Farajzadeh et al. [5] , Lee et al. [11] and Li and Huang [12] .

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


Existential witness extraction in classical realizability and via a negative translation Abstract. We show how to extract existential witnesses from classical proofs using Krivine's classical realizability-where classical proofs are interpreted as λ-terms with the call/cc control operator. We first recall the basic framework of classical realizability (in classical second-order arithmetic) and show how to extend it with primitive numerals for faster computations. Then we show how to perform witness extraction in this framework, by discussing several techniques depending on the shape of the existential formula. In particular, we show that in the Σ 0 1 -case, Krivine's witness extraction method reduces to Friedman's through a well-suited negative translation to intuitionistic second-order arithmetic. Finally we discuss the advantages of using call/cc rather than a negative translation, especially from the point of view of an implementation. Extracting an existential witness (i.e. an object t such that A(t)) from a proof of the formula ∃x A(x) is now a well-understood technique in intuitionistic logic. The simplest way to do it is to normalize the proof and retrieve the witness from the premise of its normal form. Through the Brouwer-Heyting-Kolmogorov interpretation, one can also read the proof as a functional program that reduces to a pair whose first component is the desired witness. Such techniques are implemented in proof-assistants based on intuitionistic systems [29, 20, 27] .. Extracting a witness from a classical proof of an existential formula is much more difficult, since classical logic is known not to enjoy the witness property. Such an extraction is actually not always feasible: for instance, we cannot expect to extract a witness from the obvious classical proof of the formula ∃x ((x = 1 ∧ C) ∨ (x = 0 ∧ ¬C)) in general-think of C being undecidable or, say, Riemann's conjecture.

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Avoiding unfairness of Owen allocations in linear production processes This paper deals with cooperation situations in linear production problems in which a set of goods are to be produced from a set of resources so that a certain benefit function is maximized, assuming that resources not used in the production plan have no value by themselves. The Owen set is a well-know solution rule for the class of linear production processes. Despite their stability properties, Owen allocations might give null payoff to players that are necessary for optimal production plans. This paper shows that, in general, the aforementioned drawback cannot be avoided allowing only allocations within the core of the cooperative game associated to the original linear production process. In this paper a new solution set named EOwen is introduced. For any player whose resources are needed in at least one optimal production plan, the EOwen set contains at least one allocation that assigns a strictly positive payoff to such player. A benefit cooperative game is a pair (N, v) , where N = {1, 2, ..., n} is the set of players and v : 2 N → R is the characteristic function assigning to every coalition S ⊂ N the maximum benefit that the cooperation between players in S would yield. For a complete introduction on cooperative game theory see for instance Owen (1995) or Forgó et al. (1999) . Assuming that the game is superadditive, that is v(S) + v(T ) ≤ v(S ∪ T ), ∀ S, T ⊂ N, cooperation among all players is beneficial and, therefore, the grand coalition N is to form.. One of the main questions in cooperative game theory is how to distribute the benefit obtained by the grand coalition N among the players.. An allocation is a vector α ∈ R n , such that α i is the payoff of player i and n i=1 α i = v(N). One well-accepted way of allocating v(N) among the players is to find allocations in the core. The core of a game (N, v) , denoted by Core (N, v) , is the set of allocations satisfying that no coalition of players can obtain a better payoff by acting separately from the rest of players. That is, Core(N, v) = {α ∈ R n : v(S) ≤ α(S) ∀ S ⊂ N, v(N) = α(N)},. where α(S) = i∈S α i , ∀ S ⊂ N. In principle, the core has at least two problems: the core of a game might be empty, that is, there are games for which no core allocations exist, and finding a core allocation might be a NPhard problem. Along the years, many other allocation rules have appeared in the literature. One of the most used allocation rules is the Shapley value, which has attracted a lot of interest for its many applications, see Moretti and Patrone (2008) .. A linear production problem is a situation in which certain goods that can be sold in a market are to be produced from a set of available distinct. resources. An implicit feature of the linear production problems we deal with in this paper is that the resources not used in the production plan have no value at all. Situations like this may arise when the resources are perishable and, if not used in the next production plan, they are wasted.. Another example of this situation is found in some industries in developed countries that give their excesses to underdeveloped countries, to charity organizations, or even to other companies within the same area as long as they are not competing ones. This is beneficial for both parties: the donor party gets rid of excesses which, if not used, must be eliminated at certain cost, and the receiving party only has to pay for the shipping costs, which is usually cheaper than having to buy the material.. In this paper we study a new set of allocations for linear production processes (LP processes for short), which arise when a bunch of players N = {1, . . . , n} with conflicting objectives control the resources of a LP problem.. A cooperative game, called LP game, can be associated to each LP process.. (Note that different LP processes may generate the same LP game.) An early reference to LP games can be found in Owen (1975) . LP games are totally balanced games, so every subgame of a LP game has a non-empty core. By solving the dual problem of the underlying linear production problem we can obtain a set of allocations for LP processes known as Owen allocations (see Owen (1975) ), which has been well-studied in the literature. One of its main properties is that Owen allocations are always core allocations, and are easily computed. More recently, Van Gellekom et al. (2000) provided an axiomatic characterization of this solution set. In this paper we show that, despite their stability properties, Owen allocations do not always yield a fair distribution of the benefit obtained. For instance, a player whose resources are necessary for any optimal plan may receive a null payoff from Owen allocations. Such drawback is discussed in this paper, and an alternative allocation set is proposed.. Since the pioneering work by Owen, several generalizations of LP games have appeared in the literature. Dubey and Shapley (1984) study a game in which players have partial control over the constraints of a general mathematical programming problem. Granot (1986) introduces another generalization in which the resources owned by a coalition are not restricted to be the sum of the resources of players in the coalition. Curiel et al. (1989) introduce LP games with committee control, obtaining results on the balancedness of these games, whose core has been more recently studied by Molina and Tejada (2004) .. The goal of this paper is to introduce a new set of allocations for linear production processes that avoid some of the aforementioned drawbacks of the Owen set. To this end, the rest of the paper is structured as follows. Section 2 gives a short introduction to LP processes and a motivation of the studied problem. Some definitions and technical results are given in Section 3. The allocation set proposed in this paper is introduced and analyzed in Section 4.. An axiomatic characterization and some of its properties are given, as well as a discussion about the impossibility of finding core allocations that avoid the unfairness problem of the Owen allocations we address in this paper. In this work we have introduced the EOwen set, a new solution rule on the class of linear production processes which overcomes certain drawbacks of the well-known Owen set, in the sense that one can always find an allocation that gives a strictly positive payoff to players whose resources are needed for (at least) one optimal production plan. Some examples in the paper show that Owen allocations do not satisfy this property.. EOwen is defined as the union, over all possible optimal production plans and all possible reduced matrices, of the Owen sets over the corresponding reduced LP processes, in which players get rid of the leftovers in their resources according to a reduced matrix. Several theoretical properties and an axiomatic characterization of this new solution rule are given. By means of an example we also prove that, in general, it is not possible to find allocations that give non-null payoffs to players that are necessary in order to achieve the optimal value of v(N) by restricting to the core.. We note that two types of players have been involved in this paper: group T1, consisting of players such that some of the resources they own are needed for (at least) one optimal production plan; and group T2, consisting of players whose resources are never completely used in any of the optimal production plans. Theorem 1 ensures that players in T1 can always find an allocation in. EOwen that gives them a strictly positive payoff. Examples have shown that players in T2 may receive only zero payoffs from Owen allocations. Players in both T1 and T2 are of special interest, since they receive strictly positive payoffs from EOwen allocations, and may only receive zero payoffs from. Owen allocations (see for instance examples 1 and 2).. Further research on this topic will focus on methods to find allocations with particular extra properties in the EOwen set, as well as efficient algorithms for obtaining them.

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A constraint programming approach for a batch processing problem with non-identical job sizes This paper presents a constraint programming approach for a batch processing machine on which a finite number of jobs of non-identical sizes must be scheduled. A parallel batch processing machine can process several jobs simultaneously and the objective is to minimize the maximal lateness. The constraint programming formulation proposed relies on the decomposition of the problem into finding an assignment of the jobs to the batches, and then minimizing the lateness of the batches on a single machine. This formulation is enhanced by a new optimization constraint which is based on a relaxed problem and applies cost-based domain filtering techniques. Experimental results demonstrate the efficiency of cost-based domain filtering techniques. Comparisons to other exact approaches clearly show the benefits of the proposed approach: it can optimally solve problems that are one order of magnitude greater than those solved by a mathematical formulation or by a branch-and-price. This paper presents a constraint programming approach for a batch processing machine on which a finite number of jobs of non-identical sizes must be scheduled. A batch processing machine can process several jobs simultaneously. Such machines are encountered in chemical, pharmaceutical, aeronautical and semiconductor wafer industries where an oven, a drier or an autoclave is used during the process. These machines are often bottleneck because of their long processing times. Several papers have been proposed for identical job sizes and due date related performance measures. However, papers on problems with non-identical job sizes, concern mostly completion time related performance measures. For an extensive review on scheduling with batching, we refer the reader to Potts and Kovalyov [4] . Surprisingly, although they have been successfully used to solve various scheduling problems, only one constraint programming approach has been developed for this kind of problem (with sequence dependent setup times and job families). In this paper, we propose a new constraint programming approach for a problem derived from a real application in aeronautical industry. To our knowledge, only two papers [2, 3] concern the resolution of this problem: the minimization of the maximum lateness of a batch processing machine with non-identical job sizes. In these papers, the authors propose a mathematical formulation and a branch-andprice. More formally, the problem can be described as follows. A set J of n jobs and one single batching machine with capacity b are given. Each job j is characterized by an integer triplet (p j , d j , s j ), where p j is its processing time, d j is its due date, and s j is its size. The batch processing machine can process several jobs simultaneously as a batch as long as the sum of the sizes of the jobs that are in the batch does not exceed the capacity b of the machine. The processing time of a batch is equal to the longest processing time among the jobs in the batch. The completion time C j of a job j is the completion time of the batch to which it belongs. The machine and jobs are assumed to be continuously available from time zero onwards, or equivalently, they have equal releases dates. Once the processing of a batch has been initiated, no job can be removed from or added to the batch. The objective is to minimize the maximum lateness L max = max 1≤j≤n (C j − d j ). This problem, denoted by 1|p − batch, b < n, non − identical|L max , is unary NP-hard since Brucker et al. [1] proved that the same problem with identical job sizes is unary NP-hard. We have presented a constraint programming approach to schedule a batch processing machine on which a finite number of jobs of non-identical sizes must be scheduled. This approach exploits an optimization constraint based on a relaxed problem which applies cost based domain filtering rules and is enhanced with a dedicated branching heuristics. Computational results demonstrate the positive effect of each component and give better solution with computation times that are orders of magnitude lower than a mathematical formulation based on bin packing and sequencing models.. In further research, we will apply our approach to problems with completion time related measures (C max , C j , w j C j ). In addition, subsequent research topics include the study of parallel batching machines and additional constraints, for instance job release dates that remain incompatible with our approach.

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