Imposing tree-based topologies onto self organizing maps Summary. The beauty of the Kohonen map is that it has the property of organizing the codebook vectors, which represent the data points, both with respect to the underlying distribution and topologically. This topology is traditionally linear, even though the underlying lattice could be a grid, and this has been used in a variety of applications [19, 25, 28] . The most prominent efforts to render the topology to be structured involves the Evolving Tree (ET) due to Pakkanen et al. [26] , and the Self-Organizing Tree Maps (SOTM) due to Guan et al. [15] , among others. In this paper we propose a strategy, the Tree-based Topology-Oriented SOM (TTO-SOM) by which we can impose an arbitrary, user-defined, tree-like topology onto the codebooks. Such an imposition enforces a neighborhood phenomenon which is based on the user-defined tree, and consequently renders the so-called bubble of activity to be drastically different from the ones defined in the prior literature. The map learnt as a consequence of training with the TTO-SOM is able to infer both the distribution of the data and its structured topology interpreted via the perspective of the user-defined tree. The TTO-SOM also reveals multi-resolution capabilities, which are helpful for representing the original data set with different numbers of points, and this can be obtained without the necessity of recomputing the whole tree. The ability to extract an skeleton, which is a "stick-like" representation of the image in a lower dimensional space, is discussed as well. These properties has been confirmed by our experimental results on a variety of data sets. In an increasing number of applications, researchers today encounter situations which require the classification of patterns in large data sets. Central to these methods are approaches which identify the most important clusters of the given data in an unsupervised manner. A problem that arises in such situations is to capture the essence of the similarity in the samples, which implies that any given cluster should include data of a "similar" sort, while elements that are dissimilar are assigned to different subsets.. A fundamental approach to solve the clustering problem involves the use of Artificial Neural Networks (ANNs) capable of unsupervised learning. Within this model of computation, a key component is the phenomenon referred as the "competition" between the neurons. From this perspective, it is possible to classify ANNs into two main sub-categories: In the first family only a single output neuron is activated, and this is referred to as Hard Competitive Learning. As opposed to this, in the second approach, both the winner and other associated neurons are involved in the process, and this is referred to as Soft Competitive Learning.. Another important classification criterion that can be found in such ANNs is the type of topological relationship between the neurons. Some approaches present topologies that are imposed from the start of the training process, and which remain constant until the convergence is attained. Other strategies include topologies that are able to change with time, thus yielding, at the end of the learning process, a topology that represents the underlying data distribution.. One of the most important families of ANNs used to tackle the abovementioned problems is the well known Self-Organizing Map (SOM) [?] . Typically, the SOM is trained using (un)supervised learning to produce a neural representation in a space whose dimension is usually smaller than that in which the training samples lie. Further, they seek to preserve the topological properties of the input space.. Although the SOM has demonstrated an ability to solve problems over a wide spectrum, it possesses some fundamental drawbacks. One of these drawbacks is that the user must specify the lattice a priori, which has the effect that the user must run the ANN a number of times to obtain a suitable configuration. Other handicaps involve the size of the maps, where a lesser number of neurons often represent the data inaccurately.. The state-of-the-art approaches attempt to render the topology more flexible, so as to represent complicated data distributions in a better way and/or to make the process faster by, for instance, speeding up the task of determining the best matching neuron.. Some approaches try to start with a small lattice [15, 26] , while others attempt to grow a SOM grid by adding new rows or columns if the input samples are too concentrated in some areas of the feature space [9] . Others follow a symmetric growing of the original lattice [12] . Alternatively, some strategies add relations (edges) between units as time proceeds, thus not necessarily preserving a grid of neurons. In particular, the literature reports methods that use a tree-shaped arrangement [15] . Also, some researches have attempted to devise methods which "forget" old connections as time goes by [13] . There are strategies that add nodes during training [26] , while others use a fixed grid [?] or arrange different SOMs in layers [9] , and combinations of these principles have also been employed. On the other hand, strategies that try to reduce the time required for finding the winner neuron have also been designed. The related approaches focus on the accuracy of the resulting neurons being the ones to be modified, and on the consequent topology. It is important to remark that no single one of these approaches has been demonstrated to be a clear winner when compared to the other strategies, thus leaving the window of opportunity open for novel ideas that can be used to solve the above-mentioned problems.. The desirable feature of the SOM, namely, to yield prototypes which converge in distribution was a landmark, and the formal results which prove that the stochastic distribution of the prototypes follows the distribution of the underlying data points is available. However, this formal result is true only if the prototypes are linearly arranged, implying that the concept of neighborhood and the bubble of activity are also linear. This statement, of course, needs clarification. For example, if the nodes are arranged on a lattice, the neighbors of any node i, j are the nodes { i − 1, j , i + 1, j , i, j − 1 , i, j + 1 }, which, on a more critical inspection, can be seen to be those "linearly" close to i, j . But this leads us to a host of other open issues. The first issue is the following: Is it possible for a user to require the prototypes to follow any arbitrary topology? If this is possible, the implication is significant. First of all, the question of finding the nearest neuron with such a topology (i.e., the winner in the competition) has to be answered. Secondly, the whole issue of how one describes the bubble of activity, and of migrating neighbors of the winner is far more significant. Indeed, the question of what we mean by a neighbor, how the list of neighbors is maintained and what the final convergence is, are unresolved issues. This, indeed, is the goal of this paper.. Our aim is to permit the user to specify any tree-like topology which can be entirely up to his imagination. The reason why we prefer a tree-like topology is to prevent cyclic neighborhood correspondences. Once this topology has been fixed, the concepts of the neighborhood and bubble of activity are specified from this perspective. The question is whether the prototypes can ultimately learn the stochastic distribution and simultaneously arrange themselves with the topology that mimics the one that the user hypothesized from the outset. We show that this is indeed possible, as demonstrated by a set of rigorous experiments in which our enhanced ANN, the Tree-based Topology Oriented SOM (TTO-SOM) is able to learn both the distribution and the desired structured topology of the data. Furthermore, a consequence of this is the fact that as the number of neurons is increased, the approximation of the space will be correspondingly superior -both from the perspective of the distribution and of the user-defined topology. In the paper we have proposed a schema called the Tree-based TopologyOriented SOM (TTO-SOM) by which the operator/user is able to impose an arbitrary, user-defined, tree-like topology onto the codebook vectors of a SOM. This constraint leads to a neighborhood phenomenon based on the userdefined tree, and, as a result, the so-called bubble of activity becomes radically different from the ones studied in the previous literature. The map learnt as a consequence of training with the TTO-SOM is able to determine both the distribution of the data and its structured topology, interpreted through the perspective of the user-defined tree. In addition, we have shown that the TTO-SOM revealed the ability to represent the original data set in multiple levels of granularity, and this was achieved without the necessity of computing the entire tree again. Lastly, we discussed the capability of the TTO-SOM to extract an skeleton, which is a "stick-like" representation of the image in a lower dimension of space. All these properties have been confirmed by numerous experiments on a diversity of data sets. TTO-SOM Calculate Neighborhood(B,. parent=v.getParent(); 11:. if parent = NULL and parent / ∈ B then 12:. B ← B + {parent} 13:. TTO-SOM Calculate Neighborhood(B,parent, r − 1) 14:. end if 15: end if End Algorithm training steps which terminates when the convergence is acceptable to the user. The Training step involves requesting an input sample from the dataset, locating the BMU, computing the nodes within the current bubble of activity, and migrating those neurons toward the input signal using a SOM-like philosophy.. How the input sample is chosen may vary. In the case of the TTO-SOM, an input sample is drawn at random from the sample set. Other mechanisms may involve the shuffling of the elements in the set, generating an order, and then at each step the samples are chosen as per the pre-established order. Finally, when the last element in the sequence has been drawn, an epoch is said to be completed, and optionally a new shuffling takes place.. The TTO-SOM uses the SOM update rule to update the prototypes, and requires the definition of a learning rate α which is a real number between 0 and 1, which, in turn, specifies the fraction by which the BMU will move towards the input presented to the network. The value of the learning rate is initialized to a high value, for example 0.9, and is gradually decreased so as to achieve convergence. At first the updated positions of the BMU and neighbor neurons will be highly influenced by the input sample, but as time goes by, these will tend to move less, and at the end of the process only small changes in the positions of the neurons will be registered.. Alg. 4 gives the details on how the training step is performed. Initially, the index of the BMU is obtained by invoking Alg. 2, and will be the first neuron to be included in the bubble of activity. The next process involves the calculation of all the neurons in the bubble, which is obtained by calling Alg. 3. Finally, for each neuron in the bubble, an update process take place, which is similar to the SOM update rule.

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


Worst Case Behavior of List Algorithms for Dynamic Scheduling of Non-unit Execution Time Tasks with Arbitrary Precedence Constrains SUMMARY Performance properties of list scheduling algorithms under various dynamic assumptions are analyzed. The focus is on bounds for scheduling directed acyclic graphs with arbitrary precedence constrains and arbitrary task processing times subject to minimizing the makespan. New performance bounds are derived and compared with known results. key words: list scheduling, worst case analysis, on-line scheduling. Although list scheduling algorithms have been under investigation for decades [1, 2, 8, 11, 12, 13, 15, 16] , many important properties are still unexplored. Performance of list scheduling algorithms was studied for the case of unit (UET) and non unit execution time (NUET) tasks. For the case of UET tasks an analysis under various dynamic assumptions and different levels of knowledge available for scheduling is presented in [18] . Obviously, if arbitrary task processing times are allowed, we cannot get better bounds. The objective of this paper is to show that the bounds obtained for UET tasks remain valid even for arbitrary processing times.. We consider the problem of on-line scheduling tasks with arbitrary integer execution times, and generally assume that, at each point of time, we have knowledge about which tasks are ready to be started and what their execution time is. The performance of algorithms under various dynamic assumptions is analyzed. It is shown that, depending on the available knowledge, Graham's well known bound [9] may be improved.. This work is motivated by the dynamic scheduling of processes that spawn other processes. As a typical situation consider a parallel program represented by a dynamic precedence task graph (dynamic spawn task graph) that is constructed at run time. In such a model the set of tasks is indeed unknown in advance. Each node can be considered as a process (an instruction or a group of instructions) that is able to spawn other processes. In this case the precedence relation between tasks is interpreted as the spawn precedence. T i pT j means that while task T i is processing, T j is created, and T j can be started only after T i is completed. A process can dynamically create child processes via, for instance, the fork() system call. This in turn can create further child processes and so on. To estimate and verify the quality of a schedule obtained during the dynamic execution of the task system an analysis of performance bounds under different assumptions is performed. Additional knowledge such as the sum of processing times of all tasks and the weighted length of the longest chain in the task system could help to verify the worst case behavior and to justify a particular choice of algorithm.. The paper is organized as follows. Section 2 introduces the notation of scheduling problems. In Section 3, we first review results for the deterministic case of scheduling with arbitrary precedence constrains on a set of identical processors subject to minimizing the makespan. Next, the performance bound as a function of the length of the longest task chain in the precedence graph and the total workload is derived. Section 4 summarizes our conclusion. This paper addressed the problem of dynamic nonpreemptive list scheduling of P | prec | C max . We have analyzed the worst case behavior of arbitrary list scheduling strategies and presented new performance guaranties under different assumptions. Additional knowledge of the total workload and the weighted length of the longest chain in the task system allow producing an accurate analysis of performance bounds. Next we mention some simple facts about properties of deterministic schedules (see [6, 10] It is easy to see that with list algorithms we cannot expect a better bound than that of Graham [9] . Consider a -1)(2m-1) , Therefore the competitive ratio equals Graham's bound and is known to be the worst possible for list algorithms.. Assumption 2: The total workload and the weighted length of the longest chain in the task system are available for analysis. Now, the performance bound as a function of the length of the longest task chain in the precedence graph and the total workload is derived for P | prec | C max . It generalizes the result of [18] for P | prec, p j =1 | C max . Theorem 1. Given a set T of tasks, the performance of the general list strategy can be estimated by r w = min{r w ', r w "}, where Since list is an arbitrary schedule, the upper bound for the performance ratio is determined by r w .. To prove tightness of the bounds, notice first that is better. This result allows predicting the performance of the dynamic schedule. Furthermore, if an application requires a certain performance guarantee then, for given p and l c , the number of processors that should be used to ensure the required performance can be found.

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 B I B I I 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 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 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 B I 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


Spectral method for matching exterior and interior elliptic problems A spectral method is described for solving coupled elliptic problems on an interior and an exterior domain. The method is formulated and tested on the two-dimensional interior Poisson and exterior Laplace problems, whose solutions and their normal derivatives are required to be continuous across the interface. A complete basis of homogeneous solutions for the interior and exterior regions, corresponding to all possible Dirichlet boundary values at the interface, are calculated in a preprocessing step. This basis is used to construct the influence matrix which serves to transform the coupled boundary conditions into conditions on the interior problem. Chebyshev approximations are used to represent both the interior solutions and the boundary values. A standard Chebyshev spectral method is used to calculate the interior solutions. The exterior harmonic solutions are calculated as the convolution of the free-space Green's function with a surface density; this surface density is itself the solution to an integral equation which has an analytic solution when the boundary values are given as a Chebyshev expansion. Properties of Chebyshev approximations insure that the basis of exterior harmonic functions represents the external near-boundary solutions uniformly. The method is tested by calculating the electrostatic potential resulting from charge distributions in a rectangle. The resulting influence matrix is well-conditioned and solutions converge exponentially as the resolution is increased. The generalization of this approach to three-dimensional problems is discussed, in particular the magnetohydrodynamic equations in a finite cylindrical domain surrounded by a vacuum. As a test case for the magnetohydrodynamic equations, we have developed a method for solving the two-dimensional Poisson equation in a bounded domain, where the solution satisfies matching conditions with a harmonic potential outside the domain. The method solves only the interior problem and determines the boundary conditions ensuring smooth matching with the exterior solution. The essential element of this approach is construction of a basis of harmonic functions which represent the near-boundary exterior solutions uniformly. This basis is used to construct the influence matrix which serves to impose the coupled boundary conditions between the interior and exterior solutions. The method is numerically reasonably well conditioned and can be used for quite high spatial resolutions. For a spectral solver, this method guarantees exponential convergence.. Instead of corresponding to point sources on the boundary, each exterior harmonic solution corresponds to a spectral basis function. The most costly process -the construction of a basis of exterior harmonic functions -depends only on geometry and spatial resolution. Once the basis is computed it can be stored and used for any computation using the same resolution and domain shape. When used as a preprocessing step for time-dependent simulations, the cost of constructing the exterior harmonic basis is negligible compared to that of thousands of time steps.. Since cylindrical coordinates have one periodic direction, it should be possible to apply this method separately to each of the Fourier modes, treated individually as two-dimensional problems. The extension of this method to the MHD equations in a finite cylindrical geometry is currently under investigation.

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


Enhancement of DFT-calculations at Petascale: Nuclear Magnetic Resonance, Hybrid Density Functional Theory and Car-Parrinello calculations One of the most promising techniques used for studying the electronic properties of materials is based on Density Functional Theory (DFT) approach and its extensions. DFT has been widely applied in traditional solid state physics problems where periodicity and symmetry play a crucial role in reducing the computational workload. With growing compute power capability and the development of improved DFT methods, the range of potential applications is now including other scientific areas such as Chemistry and Biology. However, cross disciplinary combinations of traditional Solid-State Physics, Chemistry and Biology drastically improve the system complexity while reducing the degree of periodicity and symmetry. Large simulation cells containing of hundreds or even thousands of atoms are needed to model these kind of physical systems. The treatment of those systems still remains a computational challenge even with modern supercomputers. In this paper we describe our work to improve the scalability of Quantum ESPRESSO [1] for treating very large cells and huge numbers of electrons. To this end we have introduced an extra level of parallelism, over electronic bands, in three kernels for solving computationally expensive problems: the Sternheimer equation solver (Nuclear Magnetic Resonance, package QE-GIPAW), the Fock operator builder (electronic ground-state, package PWscf) and most of the Car-Parrinello routines (Car-Parrinello dynamics, package CP). Final benchmarks show our success in computing the Nuclear Magnetic Response (NMR) chemical shift of a large biological assembly, the electronic structure of defected amorphous silica with hybrid exchange-correlation functionals and the equilibrium atomic structure of height Porphyrins anchored to a Carbon Nanotube, on many thousands of CPU cores. Understanding the details of atomic/molecular structures as well as dynamics of solid materials and biological systems, is one of the major challenges confronting physical and chemical science in the early 21st Century. Such knowledge has direct impact on important issues in our society like: the design, synthesis and processing of new either eco-friendly or highefficiency materials; development of new energy sources; control of materials degradation and recycling; design of drugs for specific pathology.. The complexity of these areas of research is growing rapidly along with the need for computational tools to deal with such complexity. Computer simulation is the only way to study these large physical systems. However, extremely expensive largescale computational resources do not come for free. In addi-tion to the scientific value of the computer simulation, scientific codes must show good scalability and efficiency for access to world-class supercomputing facilities.. In this respect, parameter-free first principles (aka ab-initio) atomistic calculations in the framework of Density Functional Theory (DFT) [2, 3] are quite popular models, as they combine reasonable chemical accuracy with affordable complexity and good scalability. The current available codes implementing those models [1, 4, 5, 6, 7, 8] have enabled computer simulations at the frontier of science.. Computer technology is rapidly changing. The trajectory of major computer manufactures of the last few years illustrate that vendors are rapidly increasing the number of cores to build supercomputing technology, reducing the clock frequency of each single compute element. The most powerful supercomputers in the world are today equipped with million of cores capable of scheduling billions of threads concurrently. Without substantial updating, many legacy codes will not be able to exploit this massive parallelism. Nevertheless, such horsepower gives the opportunity to address problems of unprecedented size and complexity. This paper presents a parallelization strategy, based on the distribution of electronic band loops, for efficiently scaling calculations of hybrid-functionals and Nuclear Magnetic Resonance (NMR). In addition we describe how the same parallelization strategy impacts in the scalability of the Car-Parrinello computational kernels.. The paper is organized as follows. In Sec. 2 we briefly review related work reported by other groups. In Sec. 3 we describe the equations implemented in the QE-GIPAW code to calculate NMR shielding tensors and in Sec. 4 the formulas needed to evaluate the Fock-exchange operator and energy. In Sec. 5 we outline the parallelization strategy based on bands and q-point distribution. In Sec. 6 we report and discuss benchmark results of our parallelization. Finally, in the last section we present our conclusions and perspectives on this parallelization strategy. The work presented in this paper shows the advantage of the band parallelization approach to simulate challenging systems when the number of bands become huge. This was implemented for two DFT applications. (In fact, in order to accurately reproduce experimental data it is often necessary to keep the system size big enough). The results presented here suggest that it is mandatory to use this strategy on petascale hardware and beyond. Recently the memory distribution in some critical parts of Quantum-Espresso has been introduced. So, those two strategies coupled together are the workhorse that allow efficient simulation of DFT calculation on world-class supercomputers. The idea of distributing computation over electronic bands was pioneered in the '90s by the CASTEP [14] code and was found to be effective on early vector machines (i.e. Cray Y-MP). In the subsequent years, the improvement of collective communication along with the availability of efficient FFT libraries, enabled a good scaling of plane wave codes up to few hundreds of CPUs with a simple two-level parallelization (k-points and plane waves). Only since very recently, top-level HPC machines have a huge number of CPU cores (10 4 -10 5 ) with limited amount of memory. As the number of atoms in the system increase, the number of k-points can be reduced, deteriorating the scaling and parallel efficiency of the codes. At this stage, in order to exploit the large number of CPU cores, an extra level of parallelism, electronic bands, must be introduced. The iterative diagonalization has been the first kernel to benefit of this strategy allowing a scalability up to few thousands of cores for electronic groundstate calculations within traditional exchangecorrelation functionals. ABINIT implemented a block preconditioned conjugate gradient algorithm [12] , while VASP avoids explicit orthogonalization of bands by the RM-DIIS algorithm. Moreover, the QBOX [8] code was designed purposely for BlueGene machines by a clever data distribution and fully distributed linear algebra (ScaLAPACK [13] ). Similar schemes have been implemented in CPMD, BigDFT, CASTEP [14] and are being implemented within different packages of the Quantum ESPRESSO distribution. Regarding the Exact Exchange (EXX) kernel, the NWCHEM code introduced an extra level of parallelism over occupied states and reported excellent scaling up to 2,048 CPUs [15] . In this work we report scaling results up to many thousands of CPU core, thanks to the band parallelization on replicated data of two of the most computationally intensive kernels (linear response and the Fock operator). In addition to this, we show that every step of the Car-Parrinello algorithm can be fully distributed (both data and computation), enabling petascale computation. This parallelization stragtegy allows to fully exploit the new EU Tier-0 petascale facilities such as CURIE [9] , JUGENE [10] and FERMI [11] .

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


Application of the partitioning method to specific Toeplitz matrices We propose an adaptation of the partitioning method for determination of the Moore-Penrose inverse of a matrix augmented by a block-column matrix. A simplified implementation of the partitioning method on specific Toeplitz matrices is obtained. The idea for observing this type of Toeplitz matrices lies in the fact that they appear in the linear motion blur models in which blurring matrices (representing the convolution kernels) are known in advance. The advantage of the introduced method is a significant reduction in the computational time required to calculate the Moore-Penrose inverse of specific Toeplitz matrices of an arbitrary size. The method is implemented in MATLAB, and illustrative examples are presented. The Moore-Penrose inverse is a useful tool for solving linear systems and matrix equations (Ben-Israel and Grevile, 2003; Penrose, 1956) . Also, the Moore-Penrose inverse is frequently applied in the study of numerical properties of singular matrix pencils (Röbenack and Reinschke, 2011) . Górecki and Łuczak (2013) used a generalization of the Moore-Penrose pseudoinverse to resolve the problem in the Linear Discriminant Analysis (LDA) technique. More precisely, the problem appears when a sample covariance matrix is singular, and thus cannot be inverted. A lot of direct methods have been proposed to compute the Moore-Penrose generalized inverse of a matrix (see, e.g., Ben-Israel and Grevile, 2003; Shinozaki et al., 1972) . According to Shinozaki et al. (1972) , they can be classified as methods based on matrix decomposition, methods applicable on bordered matrices and others methods (including Greville's recursive method, methods based on the formula A † = (A * A) (1, 3) A * and Pyle's gradient projection methods).. The method based on singular-value decomposition possesses a very high computation load (approximately O(n 3 ) operations). Courrieu (2005) proposed an algorithm for fast computation of the Moore-Penrose inverse which is based on the reverse order law property and the full-rank Cholesky factorization of possibly singular symmetric positive matrices. A fast method for computing the Moore-Penrose inverse of full rank m × n matrices and of square matrices with at least one zero row or column was introduced by Karanasios and Pappas (2006) , as well as Katsikis and Pappas (2008) . This method exploits a special type of the tensor product of two vectors, which is usually used in infinite dimensional Hilbert spaces. Greville (1960) proposed a recurrent rule for determining the Moore-Penrose inverse. Udwadia and Kalaba (1997) gave an alternative and a simple constructive proof of Greville's formula. Due to its ability to undertake sequential computing, Greville's partitioning method has been extensively applied in statistical inference, filtering theory, linear estimation theory, system identification, optimization as well as in analytical dynamics (Graybill, 1983; MathWorks, 2009; Kalaba and Udwadia, 1996; 1993; Rao, 1962) .. Recursive computation of the Moore-Penrose inverse of a matrix to which a block is added was presented by Bhimasankaram (1971) . However, the author proposes a proof which simply verifies that the output of his algorithm satisfies the four Penrose equations. Udwadia and Kalaba (1999) provided a constructive proof for recursive determination of the Moore-Penrose inverse of a matrix to which a block of columns is added. These results were also extended to other types of generalized inverses by Udwadia and Kalaba (1999) .. Our intention in the present article is an adaptation of the recursive block partitioning method of Udwadia and Kalaba (1999) as well as the partitioning method of Greville (1960) for efficient numerical computation of the Moore-Penrose inverse of specific Toeplitz matrices. An application of the proposed method in the process of removing non-uniform blurs in the image restoration is presented.. In the next section we restate some basic definitions, motivations as well as both the recursive block partitioning method and the usual partitioning method for computing the Moore-Penrose inverse.. We also give an outline of the process of forming a mathematical model that reflects the removal of non-uniform blurs in images. In Section 3 we describe the adaptation of the block partitioning method of Udwadia and Kalaba (1999) and the partitioning method of Greville (1960) on characteristic sparse Toeplitz matrices. The computational complexity of the modified partitioning method is investigated and compared with the complexities of other known methods. An application of the proposed method in the image restoration is given in Section 4. Several illustrative examples and comparisons are presented in the last section. The presented method is based on appropriate adaptations of well-known computational methods introduced by Udwadia and Kalaba (1999) , as well as Greville (1960) . It is suitable for application to specific (sparse) Toeplitz matrices. Using the specific structure of these matrices (denoted by H) as well as the fact that the inverse of its square part (H † m ) can be computed easily, we adjust the partitioning methods in order to obtain the most efficient adaptation.. We compare the obtained method with respect to two methods for fast computing the Moore-Penrose inverse introduced by Karanasios and Pappas (2006) , as well as Katsikis and Pappas (2008) , and used by Chountasis et al. (2009a; 2010; 2009b) along with the Courrieu method (Courrieu, 2005) . The advantage of the proposed method is a significant reduction of the CPU time required to obtain the Moore-Penrose inverse of the observed class of matrices.. This fact coincides with the given theoretical results concerning the analysis of computational complexities of different algorithms.. The idea of observing this type of matrices comes from the fact that they appear in image restoration theory. Also, the computation of the Moore-Penrose inverse is required in the image deblurring process in the case when the blurring kernel is known in advance.

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Font Recognition Based on Global Texture Analysis In this paper, we describe a novel texture analysis based approach towards font recognition.Existing methods are typically based on local typographical features that often require connected components analysis. In our method, we take the document as an image containing some specific textures, and regard font recognition as texture identification. The method is content-independent and involves no detailed local feature analysis. Experiments are carried out by made using 14,000 samples of 24 frequently used Chinese fonts (6 typefaces combined with 4 styles) as well as 32 frequently used English fonts (8 typefaces combined with 4 styles). An average recognition rate of 99.1% is achieved. Experimental results are also included on the robustness of the method against image degradation (e.g. Pepper & Salt noise) and on the comparison with existing methods. Font recognition is a fundamental issue in document analysis and recognition, and is often a difficult and time-consuming task. Numerous optical character recognition (OCR) techniques have been proposed and some have been commercialized, but few of them take font recognition into account. Font recognition has great influence over automatic document processing (ADP) in at least two aspects. Font is an important factor both to character recognition and to script identification. Font classification can reduce the number of alternative shapes for each class, leading to essentially single-font character recognition [1] .. Secondly, the ideal output of an ADP system includes not only the content of the document but also the font used to print this document in order to achieve automatic typesetting.. In spite of the clear importance of automatic font recognition, only a few researchers have addressed the issue. In the method used by Khoubybari and Hull [2] , clusters of word images are generated from an input document and matched to a database of function word derived from fonts and document images. The font or document that matches best provides the identification of the predominant font and function words. Cooperman [3] discusses the estimation of font attributes in an OCR system. He uses a set of local detectors for individual attributes such as serifness, boldness, ect. Shi and Pavlidis [4] use page properties such as histogram of word length and stroke slopes for font feature extraction. Zramdini and Ingold present a statistical approach for font recognition based on local typographical features [5] . A similar approach is taken by Schreyer et. al. [16] where local texton features are used (see Julesz [17] for the definition of textons). Most of these methods are based on typographical features extracted by means of local attribute analysis.. In this paper, we propose a new algorithm for font identification based on the global texture of document images (we assume pure text documents as page segmentation and layout analysis are outside the scope of this paper). No explicit local analysis is needed in the method. The key point is using texture analysis to extract global features. A block of text printed in each font can be seen as having a specific texture. The spatial frequency and orientation contents represent the features of each texture. It is these texture features that we use to identify different fonts.. In principle, any texture analysis technique can be applied here. Here, we use multi-channel Gabor filters to extract these features. Multi-channel Gabor filtering is a well-established method for texture analysis and has been demonstrated to have good performance in texture discrimination and segmentation [6] [7] [8] [9] [10] [11] [12] .. The overall font identification system is illustrated in Figure 1 . The original image is preprocessed to form a uniform block of text. The multi-channel Gabor filtering technique is used to extract features from the uniform text blocks (i.e. the texture images). A weighted Euclidean distance classifier is used to identify the fonts.. In Section 2, we discuss pre-processing in detail. Section 3 describes font feature extraction based on mult-channel Gabor filtering. Section 4 outlines the classifier.. Experiments and results are discussed in Section 5. Conclusions are then drawn in Section 6. We have presented a new algorithm for automatic font recognition. Unlike existing methods, the new algorithm is based on global features. It is content-independent so the contents of training and testing documents are not required to be the same. Extensive experiments have shown that the algorithm performs very well. The average recognition accuracy of 24 Chinese fonts and 32 English fonts over 14,000 samples is as high as 99.1%.. The algorithm has also been demonstrated to exhibit strong robustness against noise and resolution variations. It requires no detailed local feature analysis and may easily be adopted in practical applications.

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Software designers, are you biased? Methods of representing and capturing design rationale have been studied in past years. Many meta-models, methods and techniques have been proposed. Are these software engineering methods sufficient to help designers make logical and appropriate design decisions? Studies have shown that people make biased decisions, software designers may also be subjected to such cognitive biases. In this paper, I give an overview of how cognitive biases and reasoning failures may lead to unsound design decisions. I conjecture that in order to improve the overall quality of software design, we as a community need to improve our understanding and teaching of software design reasoning. Software design was said to be a wicked problem by Rittel and Webber back in the 70's [25] . They suggested that there is no well-defined set of potential solutions. A solution is very much the results of what the designers devise. As such, the skills of a designer are very important and design is a handicraft that depends on this skill. The software industry has put much emphasis on the use of processes, methodologies and techniques to assure the quality of software design. Despite the common adoption of these software engineering processes and methodologies, it is still common to see sub-optimal and nonfunctioning software design. Why? It is because individual designers can still make bad design decisions.. The software engineering community has recognized that decision making is a key element in designing quality software. We have seen two waves of research activities on this subject. The first wave was in a period between the 70's and 90's. The research focus can be typified as argumentation-based design rationale. Notable methods proposed in this period were IBIS [19] , QOC [22] and DRL [21] . However, Shipman III and McCall [13] concluded that neither the argumentation nor the communication perspective of argumentation-based design rationale has been generally successful in practice. The second wave of design rationale research began from around 2003. The focus in this period can be typified as practice and knowledge management oriented. Notable works focus on the practice of software architecture design [4, 6] and the capturing of design decision [35] . Meta-models such as CORE [8] and SOAD [37] , tools such as SEURAT [7] , ADDSS, Archium, AREL, Knowledge Architect and PAKME were proposed (summarized in [30] ). Doubtless these methods would provide an orientation for a designer to justify his design decisions, but design decision making remains an internal thought process, and it relies on the ability of a person to reason. If the reasoning process fails or the basic information (i.e. we call premises) used for reasoning is untrue, then the resulting design decision is likely to be wrong. Using the research results of other disciplines such as cognitive psychology, I suggest that there are three fundamental causes of design reasoning failures:. • Cognitive Bias -a distortion of judgment in particular situations due to psychological effects and insufficient regards of probability [17] . For example, software designers select inappropriate design solutions because they are more familiar with these design solutions, despite that the solution is illsuited to solve the problem. A phenomenon we call "I have a hammer, and everything is a nail".. • Illogical Reasoning -a logical reasoning requires that the basic premises of a decision, in our case design concerns and requirements, should be factual and true; and the arguments and inferences to reach a design conclusion should be sound [15] . Quite often software designers make design decisions without regards for whether the premises are true or the conclusions are reasonable. Sometimes the design problems are ill-defined. When asked to justify his decisions, it is not uncommon to see designers make retrospective justifications.. • Low Quality Premises -in large software projects in which multiple designers make decisions, failures to represent the premises truly, i. unclear, that could cause a designer to make a decision based on faulty inputs.. Reasoning failures can lead to wrong or sub-optimal design decisions. Therefore it is important that we understand the fundamental causes of reasoning failures in order to find ways to improve the situation.. This paper intends to serve a few purposes. Firstly, it provides an overview of possible causes of design reasoning failures (Section 2). Secondly, it proposes to use a logic framework to support argumentation in design reasoning (Section 3). Thirdly, related work in this area is discussed and techniques are suggested to improve design reasoning (Section 4). This area of research is in its infancy as far as software engineering is concerned. We as a community should consider the challenges and the potentials that it may bring (Section 5). Studies in cognitive psychology tell us that people have a tendency to make biased and illogical decisions. Some contributors to these biases are (a) intuitive reasoning (System 1) which demands a lower cognitive load; (b) limitation in shortterm memory; (c) tendency to ignore probability representativeness. Although there is no hard evidence to demonstrate that systematic biases occur in software design, nor do we have data to show whether this issue is indeed serious in the software industry, there are enough examples to demonstrate that biases do exist and they may be more common than we think.. Systematic use of logical argument in design reasoning could help to improve general design quality. There are two basic conditions. Firstly, designers need to know the logical argument process to make sound and cogent design decisions. Secondly, premises such as requirements and design context must fulfill the quality criteria, and the communication of the premises faithfully between designers must be adequate and accurate.. Our understanding of this subject is limited. Doubtless the research community will continue to propose models and techniques to fix this problem. More importantly, we need to conduct empirical studies and experiments to understand how to make better software design decisions. This knowledge will allow us to improve design education of students and practitioners.

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


Modeling T cell receptor recognition of CD1-lipid and MR1-metabolite complexes Background: T cell receptors (TCRs) can recognize diverse lipid and metabolite antigens presented by MHC-like molecules CD1 and MR1, and the molecular basis of many of these interactions has not been determined. Here we applied our protein docking algorithm TCRFlexDock, previously developed to perform docking of TCRs to peptide-MHC (pMHC) molecules, to predict the binding of αβ and γδ TCRs to CD1 and MR1, starting with the structures of the unbound molecules.Results: Evaluating against TCR-CD1d complexes with crystal structures, we achieved near-native structures in the top 20 models for two out of four cases, and an acceptable-rated prediction for a third case. We also predicted the structure of an interaction between a MAIT TCR and MR1-antigen that has not been structurally characterized, yielding a top-ranked model that agreed remarkably with a characterized TCR-MR1-antigen structure that has a nearly identical TCR α chain but a different β chain, highlighting the likely dominance of the conserved α chain in MR1-antigen recognition. Docking performance was improved by re-training our scoring function with a set of TCR-pMHC complexes, and for a case with an outlier binding mode, we found that alternative docking start positions improved predictive accuracy. We then performed unbound docking with two mycolyl-lipid specific TCRs that recognize lipid-bound CD1b, which represent a class of interactions that is not structurally characterized. Highly-ranked models of these complexes showed remarkable agreement between their binding topologies, as expected based on their shared germline sequences, while differences in residue-level interactions with their respective antigens point to possible mechanisms underlying their distinct specificities.Conclusions: Together these results indicate that flexible docking simulations can provide accurate models and atomic-level insights into TCR recognition of MHC-like molecules presenting lipid and other small molecule antigens. These updates to the TCRFlexDock algorithm, as well as the docking test cases we assembled, represent an advance in modeling TCR-ligand recognition, extending capabilities beyond TCR-pMHC modeling methods reported by ourselves [11] and others [30, 31] to modeling complexes with lipid and metabolite antigens presented by MHC-like molecules. Our models of MAIT TCR-MR1-Ag and GEM TCR-CD1b-Ag complexes, which have not been described crystallographically, provide likely mechanisms of ligand engagement by these TCRs, and highlight the ability of advanced protein docking algorithms to complement experimental techniques in probing the structural basis of molecular recognition. These methods can be applied to model other TCRs bound to MHC-like ligands, as more of these interactions and TCRs become characterized, such as a γδ TCR clone that was recently found to engage the endothelial protein C receptor [32] . We have demonstrated that our TCR docking algorithm, TCRFlexDock, is capable of producing accurate models of TCRs recognizing MHC-like molecules presenting a variety of non-peptide ligands. By retraining our scoring function, we were able to improve the re-ranking performance for test cases representing this class of complexes. Further improvements, for instance to improve the ranking of hits for the 4MNG or 3HUJ cases and performance using pooled results from alternate docking start sites, could potentially be achieved through inclusion of other terms (e.g. longrange partial charge rather than full charge electrostatics), and further optimization of the pair potential parameters and antigen atom typing. Additionally, though antigen bond torsion angles were minimized during Rosetta docking simulations, explicit inclusion of lipid head group rotamers (based on pre-generated conformers) could represent another route for improving docking performance.. We report models of CD1b-bound GEM TCRs from TCRFlexDock that account for a likely shared docking orientation as well fine differences in antigen recognition. The docking searches for these cases were focused on the CD1b site analogous to the pMHC interface engaged by most TCRs; while outlier TCR binding modes have been observed for some non-MHC ligands [26] and would reduce change of docking success (as seen for test case 3HUJ), mutagenesis evidence strongly suggests that TCRs engage CD1b-Ag with a footprint similar to TCR-pMHC interactions [27] . Two previously reported TCR-CD1b-Ag modeling attempts (using other TCR clones) were based on homology with TCR-pMHC complex structures [25, 28] , rather than a flexible docking search; notably, in one of these studies the TCR loops exhibited considerable clash with antigen in the modeled complexes [25] , a challenge that is explicitly addressed during the conformational search of TCRFlexDock. Within our set of TCR-CD1b-Ag models, the dominant cluster was similar to the Class I MHC-bound Yae62 TCR ( Figure 5 and Additional file 7: Figure S6 ). However, we did identify alternative models, including several that were similar to the TRBV6 MAIT TCR-MR1-Ag and ELS4 TCR-HLA-peptide complexes. As noted by others [24] , the MAIT, ELS4 and GEM TCRs share TRAV1-2 genes and the former two exhibit similar docking orientations over their respective ligands [8] , yet given the structural and residue-level differences between CD1b, MR1 and MHC, there is a significant possibility that TCR-CD1b-Ag interactions exhibit a distinct binding conformation, as we identified using TCRFlexDock. Experimental structural characterization of GEM TCR-CD1b-Ag complexes will allow determination of which models are most accurate.. While this manuscript was under review, the x-ray structure of a TRBV20-containing MAIT TCR (corresponding to the unbound TCR we used for test case 4L4T) in complex with MR1 and antigen was reported [29] . Though the antigens of our docking simulation and the solved structure are not identical (thus preventing an analysis of native contacts and hits), we evaluated interface backbone RMSD between our models and the solved structure (PDB id 4PJ8), and the top-ranked model by ZRT score indeed had a low interface RMSD with respect to the experimentally determined complex structure (1.68 Å; Additional file 9: Figure S8 ). T cell receptors (TCRs) display remarkable versatility in their ability to specifically recognize a wide array of structurally and chemically diverse antigens. This is highlighted by a number of studies showing that, in addition to well-characterized recognition of peptide-major histocompatibility complex (pMHC) [1] , many TCRs engage MHC-like molecules CD1, which present a variety of lipid antigens [2] , and MR1, which presents vitamin B metabolites [3] . At the sequence level, these TCRs can be restricted or diverse in their germ-line chain usage, depending in part on the T cell type, antigen, and antigen-presenting molecule [2] .. The understanding of the molecular basis of TCR interactions with CD1 and MR1 has been greatly advanced by a number of crystallographic studies that have elucidated the interface sites, key contacts, and binding modes of several of these complexes. This includes type I and type II natural killer T cell (NKT) TCR interactions with CD1d-lipid [4] [5] [6] , mucosal-associated invariant T cell (MAIT) TCR interfaces with unliganded [7] and ligand-bound MR1 [8] , and recent studies of two γδ TCRs bound to CD1d-lipid [9, 10] . While these have provided a clear view of the antigen recognition underlying several of the invariant and diverse T cell subsets, owing to their variety and the effort required in experimental structure determination, the crystal structures of a number of key complexes have not yet been solved.. Here we describe the adaptation of the TCR docking algorithm, TCRFlexDock, previously shown to produce highly accurate TCR-pMHC structural predictions [11] , to predict complexes of TCRs with CD1 and MR1 with antigen (Ag). We assessed unbound docking performance using four known structures of TCRs with CD1d, showing that for most cases accurate models were produced. We also predicted the complex between a MAIT TCR and MR1-Ag, an interaction that has not yet been structurally described, and assessing models against a related MAIT TCR bound to MR1-Ag, found strong agreement between predicted complex and the likely conserved binding mode. Applying TCRFlexDock to predict the structure of two germline-encoded, mycolyl lipid-reactive (GEM) TCRs bound to CD1b, we produced models that provide insight into both their shared sequence features and distinct antigen specificities.

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


Efficient Genome-Wide TagSNP Selection Across Populations via the Linkage Disequilibrium Criterion In this article, we studied the tag single-nucleotide polymorphism (tagSNP) selection problem on multiple populations using the pairwise r 2 linkage disequilibrium criterion. We proposed a novel combinatorial optimization model for the tagSNP selection problem, called the minimum common tagSNP selection (MCTS) problem, and presented efficient solutions for MCTS. Our approach consists of the following three main steps: (i) partitioning the SNP markers into small disjoint components, (ii) applying some data reduction rules to simplify the problem, and (iii) applying either a fast greedy algorithm or a Lagrangian relaxation algorithm to solve the remaining (general) MCTS. These algorithms also provide lower bounds on tagging (i.e., the minimum number of tagSNPs needed). The lower bounds allow us to evaluate how far our solution is from the optimum. To the best of our knowledge, it is the first time the tagging lower bounds are discussed in the literature. We assessed the performance of our algorithms on real HapMap data for genome-wide tagging. The experiments demonstrated that our algorithms run 3-4 orders of magnitude faster than the existing singlepopulation tagging programs such as FESTA, LD-Select, and the multiple-population tagging method MultiPop-TagSelect. Our method also greatly reduced the required tagSNPs compared with LD-Select on a single population and MultiPop-TagSelect on multiple populations. Moreover, the numbers of tagSNPs selected by our algorithms are almost optimal because they are very close to the corresponding lower bounds obtained by our method.

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


An elementary proof of Sylvester's double sums for subresultants In 1853 Sylvester stated and proved an elegant formula that expresses the polynomial subresultants in terms of the roots of the input polynomials. Sylvester's formula was also recently proved by Lascoux and Pragacz by using multi-Schur functions and divided differences. In this paper, we provide an elementary proof that uses only basic properties of matrix multiplication and Vandermonde determinants. Subresultants play a fundamental role in Computer Algebra and Computational Algebraic Geometry (for instance, see (5; 3; 6; 15; 10; 9; 14; 12; 1)). In (16) Sylvester stated and proved an elegant formula that expresses the polynomial subresultants of two polynomials in terms of their roots, the so-called double-sum formula. This identity was proved also by Lascoux and Pragacz in (13) , by using the theory of multi-Schur functions and divided differences.. In this paper we provide a new and elementary proof that uses only the basic properties of matrix multiplication and Vandermonde determinants. As apparent in our proof, Sylvester's double-sum formula is only one simple step further a particular case, the so-called single-sum formula. Such connection between the single and the double-sum formulae was originally thought to be unlikely, as remarked in page 691 of (13) . There have been various proofs for the single-sum formula (1; 2; 4; 11; 8).. The matrix multiplication technique, presented in this papers, has proven to be quite powerful in that it is easily generalizable to multivariate polynomials: similar techniques were successfully applied to obtain expressions for multivariate subresultants in roots in (7) , and the generalization of Sylvester's single and double-sum formulae to the multivariate case is the subject of ongoing research.

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


A unified framework for structure identification We propose a general framework for structure identification, as defined by Dechter and Pearl. It is based on the notion of prime implicate, and handles Horn, bijunctive and affine, as well as Horn-renamable formulas, for which, to our knowledge, no polynomial algorithm has been proposed before. This framework, although quite general, gives good complexity results, and in particular we get for Horn formulas the same running time and better output size than the algorithms previously known.

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 B I 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


Patient-specific

biomechanical

model

as

whole-body

CT

image

registration

tool

Whole-body

computed

tomography

(CT)

image

registration

is

important

for

cancer

diagnosis,

therapy

planning

and

treatment.

Such

registration

requires

accounting

for

large

differences

between

source

and

target

images

caused

by

deformations

of

soft

organs/tissues

and

articulated

motion

of

skeletal

structures.

The

registration

algorithms

relying

solely

on

image

processing

methods

exhibit

deficiencies

in

accounting

for

such

deformations

and

motion.

We

propose

to

predict

the

deformations

and

movements

of

body

organs/tissues

and

skeletal

structures

for

whole-body

CT

image

registration

using

patient-specific

non-linear

biomechanical

modelling.

Unlike

the

conventional

biomechanical

modelling,

our

approach

for

building

the

biomechanical

models

does

not

require

time-consuming

segmentation

of

CT

scans

to

divide

the

whole

body

into

non-overlapping

constituents

with

different

material

properties.

Instead,

a

Fuzzy

C-Means

(FCM)

algorithm

is

used

for

tissue

classification

to

assign

the

constitutive

properties

automatically

at

integration

points

of

the

computation

grid.

We

use

only

very

simple

segmentation

of

the

spine

when

determining

vertebrae

displacements

to

define

loading

for

biomechanical

models.

We

demonstrate

the

feasibility

and

accuracy

of

our

approach

on

CT

images

of

seven

patients

suffering

from

cancer

and

aortic

disease.

The

results

confirm

that

accurate

whole-body

CT

image

registration

can

be

achieved

using

a

patient-specific

non-linear

biomechanical

model

constructed

without

time-consuming

segmentation

of

the

whole-body

images.

Reliable

and

accurate

radiographic

image

registration

that

aligns

the

source

and

target

images

is

critical

for

application

of

medical

imaging

in

cancer

diagnosis,

therapy

planning

and

treatment

(Black

et

al.,

D'Amico

et

al.,

Jenkinson

and

Smith,

Spicer

et

al.,

Van

Sint

Jan

et

al.,

Warfield

et

al.,

Zaidi,

A

large

number

of

medical

image

registration

algorithms

solely

relying

on

image

processing

methods

have

been

successfully

developed

over

the

years

(Cao

and

Ruan,

Jenkinson

and

Smith,

Sotiras

et

al.,

Wells

et

al.,

Many

of

them

have

been

demonstrated

to

be

effective

for

selected

organs,

such

as

the

brain,

breast,

prostate

and

lungs

(Goerres

et

al.,

Mattes

et

al.,

Oguro

et

al.,

Rueckert

et

al.,

Warfield

et

al.,

However,

it

has

been

also

recognised

that

large

differences

between

the

source

and

target

images

caused

by

complex

rigid-body

motion

of

articulated

bones,

skeletal

segments

and

body

organs

and

large

deformations

of

soft

tissues

associated

with

whole-body

CT/MRI

registration

are

very

challenging

for

such

algorithms

(Baiker

et

al.,

Li

et

al.,

Martin-Fernandez

et

al.,

Wittek

et

al.,

Despite

some

successful

attempts

to

improve

robustness

of

registration

algorithms

(Toews

and

Wells,

and

registration

accuracy

for

selected

body

segments

for

limited

range

of

rigid

body

motion

and

soft

organs/tissues

deformation

(Mahfouz

et

al.,

Stromqvist

et

al.,

the

whole-body

CT

image

registration

still

remains

a

largely

unsolved

problem

(Li

et

al.,

Elsevier

B.V.

All

rights

reserved..

Therefore,

patient-specific

biomechanical

modelling

methods

that

account

for

the

mechanical

behaviour

of

organs/tissues

were

recommended

by

many

researchers

for

registration

problems

involving

large

differences

(deformations)

between

the

source

and

target

images

(Al-Mayah

et

al.,

Hopp

et

al.,

Warfield

et

al.,

Wittek

et

al.,

Unlike

image-based

matching,

registration

algorithms

using

biomechanical

models

do

not

require

selection

of

specific

type

of

source-to-target

image

transformation

and

optimisation

of

the

transformation

parameters

to

maximise

a

selected

similarity

measure

between

the

transformed

and

target

images.

Instead,

they

rely

on

principles

of

mechanics

to

compute

deformations

that

transform

source

image

to

target

image.

This

ensures

plausibility

and

robustness

of

the

predicted

deformations.

In

particular,

patient-specific

biomechanical

modelling

has

been

successfully

used

in

numerous

studies

on

computing

the

brain

deformations

for

neuroimage

registration

(Garlapati

et

Challenges

to

overcome

when

applying

biomechanical

modelling

for

medical

image

registration

include

quick

and

reliable

generation

of

patient-specific

computational

models,

automatic

segmentation

of

radiographic

images

and

efficient

solution

of

the

models

(Miller,

Miller

et

al.,

Mostayed

et

al.,

To

facilitate

rapid

generation

of

patient-specific

biomechanical

models

for

whole-body

CT

image

registration,

we

abandon

time-consuming

image

segmentation

that

divides

the

problem

domain

into

nonoverlapping

constituents

with

different

material

properties.

Instead,

we

apply

tissue

classification

based

on

the

Fuzzy

C-Means

(FCM)

algorithm

to

assign

the

constitutive

properties

automatically

at

integration

points

of

the

computation

grid

(Bezdek

et

al.,

Zhang

et

al.,

This,

allows

us

to

generate

the

patient-specific

biomechanical

model

automatically

and

rapidly..

In

principle,

any

verified

method

of

non-linear

computational

mechanics

accounting

for

both

geometric

and

material

nonlinearity

can

be

used

to

solve

biomechanical

models

for

computing

soft

organ/tissue

deformations

for

image

registration.

Non-linear

finite

element

analysis

with

either

implicit

(Allard

et

al.,

Taylor

et

al.,

or

explicit

(Hu

et

al.,

Joldes

et

al.,

Miller

et

al.,

Wittek

et

al.,

integration

in

time

domain

remains

the

most

commonly

used

approach.

In

our

previous

research,

we

have

developed

and

verified

a

suite

of

efficient

algorithms

for

computing

soft

tissue

deformations

in

the

context

of

neuroimage

registration

(Joldes

et

al.,

Miller

et

al.,

Miller

et

al.,

In

this

study,

we

adapt

and

apply

these

algorithms

in

registration

of

whole-body

CT

images..

To

demonstrate

feasibility

and

accuracy

of

whole-body

CT

image

registration

using

the

proposed

non-linear

biomechanical

model,

we

analysed

sets

of

whole-body/torso

CT

images

of

seven

patients.

Deformation

within

the

patient's

body

to

align

a

source

image

to

target

image

is

predicted

using

a

patient-specific

model

that

relies

on

Total

Lagrangian

Explicit

Dynamics

TLED

non-linear

finite

element

algorithm

(Joldes

et

al.,

Miller

et

al.,

Miller

et

al.,

Accuracy

of

the

registration

is

quantitatively

assessed

using

the

Hausdorff

distance

metric

to

measure

the

spatial

distance

between

the

corresponding

Canny

edges

in

the

registered

(i.e.

deformed

using

the

deformations

computed

by

means

of

biomechanical

model)

and

target

images

(Fedorov

et

al.,

Garlapati

et

al.,

Garlapati

et

al.,

Huttenlocher

et

al.,

This

paper

is

organised

as

follows:

the

proposed

patient-specific

non-linear

finite

element

model

and

the

TLED

algorithm

are

presented

in

Section

the

computational

results,

including

accuracy

evaluation,

are

given

in

Section

which

is

followed

by

the

discussion

and

conclusions

in

Section

In

this

study,

a

comprehensive

patient-specific

non-linear

finite

element

model

is

proposed

for

computing

the

deformations

within

the

patient's

body

for

registration

of

whole-body

CT

images.

The

proposed

approach

accounts

for

rigid

body

motion

of

bones/skeletal

segments,

large

deformations,

and

non-linear

constitutive

properties

of

soft

tissues.

The

most

commonly

used

approach

for

generating

patient-specific

finite

element

models

involves

image

segmentation

to

divide

the

human

body

into

non-overlapping

constituents

with

different

material

properties-a

very

tedious

and

time

consuming

process.

Therefore,

we

replaced

segmentation

with

the

Fuzzy

C-Means

algorithm

to

quickly

and

automatically

classify

the

tissues

and

assign

the

mechanical

properties

directly

at

the

integration

points

based

on

this

classification

(see

Section

Therefore,

we

eliminated

the

need

for

body

organ/tissue

segmentation

when

constructing

biomechanical

models

for

registration

of

whole-body

radiographic

images.

Selection

of

'fuzzy'

method

rather

than

traditionally

used

''exact''

(i.e.

relying

on

image

segmentation)

approach

to

assign

the

mechanical

properties

is

supported

by

the

fact

that

when

loading

is

prescribed

through

forced

motion

of

the

boundary

(vertebrae

motion

in

this

study),

the

computed

deformations

are

only

very

weakly

sensitive

to

the

mechanical

properties

of

the

modelled

continuum

providing

that

appropriate

algorithms

of

non-linear

computational

mechanics

are

used

(Miller,

Miller

and

Lu,

Wittek

et

al.,

The

feasibility

and

accuracy

of

the

proposed

approach

for

whole-body

CT

image

registration

were

verified

for

CT

datasets

of

seven

patients

suffering

from

cancer

and

aortic

disease

obtained

from

publicly

available

image

databases

Wiki/index.php/Projects:RegistrationLibrary:RegLib_C20b

and

and

two

hospitals

(the

University

Hospital

Limerick,

Ireland

and

the

Fremantle

Hospital,

Australia).

Hausdorff

Distance

HD

metric

between

the

corresponding

features

(Canny

edges)

in

the

registered

(i.e.

source

image

warped

using

the

deformations

predicted

by

means

of

a

biomechanical

model)

and

target

images

was

used

as

a

quantitative

measure

of

the

registration

accuracy.

The

results

indicate

that

for

all

analysed

cases,

of

edge

pairs

were

registered

with

an

error

within

two

times

the

voxel

size

which

is

a

criterion

of

successful

registration

used

in

the

literature

(Mostayed

et

al.,

However,

some

local

misalignments

are

clearly

visible

in

Figs.

and

One

possible

source

of

these

misalignments

can

be

that

we

used

very

sparse

information

(vertebrae

displacements

between

the

source

and

target

images)

to

define

the

model

loading.

Although

one

may

argue

that

providing

more

information

to

drive

computation

of

the

organ

and

tissue

deformations

may

improve

the

registration

accuracy,

the

overall

results

are

very

promising.

It

should

be

noted

that

to

define

forced

motion

of

the

boundary

we

relied

on

simple

segmentation

of

the

spine

to

determine

vertebrae

displacements

between

the

source

and

target

images..

The

present

study

can

be

regarded

as

a

pioneering

effort

to

solve

challenging

problem

of

whole-body

CT

image

registration

by

applying

a

biomechanical

model

using

non-linear

finite

element

procedures

to

compute

the

deformations

to

warp

a

source

image

to

the

patient's

target

geometry.

For

all

the

analysed

image

sets,

the

average

Hausdorff

distance

between

the

pairs

edges

in

registered

and

target

images

was

within

two

times

the

voxel

size,

which

compares

well

with

the

studies

on

non-rigid

registration

of

whole-body

CTs

relying

solely

on

image-processing

algorithms.

For

instance,

Suh

et

al.

reported

the

maximum-likelihood

HD

(M-HD)

of

an

order

of

image

voxels

in

their

study

for

rat

whole-body

CT

non-rigid

registration

using

a

weighted

demons

algorithm.

Similarly,

Toews

and

Wells

observed

errors

of

an

order

of

image

voxel

when

applying

their

feature-based

alignment

(FBA)

method

for

inter-subject

registration

of

human

whole-body

CT

images.

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


Reuse of Manufacturing Knowledge to Facilitate Platform-Based Product Realization Product platforming is a technique for exploiting commonality across a family of products. While utilizing a common platform can have many advantages when developing and manufacturing products, the approach places greater demands on collaboration, in particular, the sharing and reuse of knowledge and information. Repositories are intended to facilitate information sharing across organizational groups and geographically distributed collaborators. A particular challenge in utilizing repositories is culling a search for the most appropriate information for the problem at hand. The Reuse Existing Unit for Shape and Efficiency (R.E.U.S.E.) method facilitates the search of information in a repository through three stages that consider similarity, efficiency, and configuration. Automated search and filter techniques are implemented with interaction with the user to effectively obtain the desired results. The similarity study uses thresholds to clarify different opportunities for reuse. The user can then select alternatives for further examination based on efficiency of satisfaction of desired characteristics. The degree of modification of the similar alternatives is reported to assist in the configuration of the new design. This method contributes to the field by (a) accounting for the variety of the product family during the reuse of existing process design information; (b) integrating an efficiency assessment for retrieval by considering characteristics beyond cost; and (c) addressing the search with a multicriteria method. The implementation of the R.E.U.S.E method is supported with an example of assembly line design for an air conditioner module in automobile production. Collaborative work can occur through face-to-face interactions between participants on a project, or collaboration can occur indirectly between geographically and temporally dispersed individuals or teams. In this second case, collaboration is facilitated by the reuse of previous knowledge ͑i.e., experiences, designs, processes, etc.͒. As of yet, the full potential of reusing manufacturing knowledge has not been realized. For instance, the Renault Company ͑with more than 100 years of experience to their credit͒ produces millions of vehicles every year in more than 25 assembly plants without a method to systematically reuse this experiential knowledge when a new model is designed. At the individual level, process designers try to reuse manufacturing information, but their efforts generally only address the latest models. Now that the Renault Company is part of the Renault-Nissan Group, which owns internationally recognized brands Renault, Nissan, Dacia, and Samsung, a method for reusing existing design knowledge ͑single products and families of products͒ would help retrieve the best experiences across all companies.. Reusing process information offers industry opportunities to improve manufacturing traceability, standardization, quality, and control while enabling decreases in cost. A knowledge reuse approach facilitates collaborative product development because it capitalizes on experiences of previous designs and manufacturing to design the current product. In terms of project development, knowledge reuse enables designers to consider modifications, increase convergence, and decrease lead time, all with greater ease than previously possible. Since product development involves almost all of the services in a company, reuse approaches can also include capturing, storing, and retrieving information for all of these services.. It is also important to consider platform-based products that are now widely available in the market. The platform-based approach specifies a family of products based on a compromise between common components ͑i.e., a common platform͒ and distinct/ unique components that differentiate each product. Thus, this technique adds variety, and it becomes more challenging to retrieve relevant design information without assistance. Consequently, there is an opportunity to increase collaboration by reusing knowledge across a family of products. The method described here is intended to facilitate collaboration among geographically and temporally dispersed teams by supporting knowledge reuse.. Section 2 provides the necessary background and information to understand the context of this study. The related literature in this research field is presented in Sec. 3. The Reuse Existing Unit for Shape and Efficiency ͑R.E.U.S.E.͒ method for the design approach is specified in Sec. 4, where its three stages are explained. An example based on an air conditioner module for the automotive industry is presented in Sec. 5. Finally, Sec. 6 provides closing remarks and future work.

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