Advanced Indexing Technique for Temporal Data Abstract. The need for efficient access and management of time dependent data in modern database applications is well recognised and researched. Existing access methods are mostly derived from the family of spatial R-tree indexing techniques. These techniques are particularly not suitable to handle data involving open ended intervals, which are common in temporal databases. This is due to overlapping between nodes and huge dead space found in the database. In this study, we describe a detailed investigation of a new approach called "Triangular Decomposition Tree" (TD-Tree). The underlying idea for the TD-Tree is to manage temporal intervals by virtual index structures relying on geometric interpretations of intervals, and a space partition method that results in an unbalanced binary tree. We demonstrate that the unbalanced binary tree can be efficiently manipulated using a virtual index. We also show that the single query algorithm can be applied uniformly to different query types without the need of dedicated query transformations. In addition to the advantages related to the usage of a single query algorithm for different query types and better space complexity, the empirical performance of the TDtree has been found to be superior to its best known competitors. While being ever changing, time is an important aspect of all real world phenomena. Each event bears a time attached to it, sometimes in more than one form. Time marks the starting and ending of an event and establishes the validity of data. Facts, i.e. data, valid today may have had no meaning in the past and may hold no identity in the future. Some data, on the other hand may hold historical significance or may continue to be valid up to a predefined point in time. This relationship with time adds a temporal identity to most data and, in this light, it would be hard to identify applications that do not require or would not benefit from database support for time-varying data. Most current database systems represent a single state of data and this is most commonly assumed to be its current state. Any modifications normally result in the overwriting of the data with the old data being discarded. Although commercial databases offer some capabilities to keep track of old and discarded data (e.g. the Oracle TimeSeries cartridge, Oracle "Flash-Back", and the Informix TimeSeries DataBlade), this is solely for the purpose of database recovery and not to retain the previous state of the data.. In the last two decades, research on temporal databases has advanced in various aspects and reported many important results, however, many challenges still remain [4] , [18] . In most of the previous studies, core concepts have been established, but it is yet to be shown how they can be applied for efficiently managing time dependent data. Because temporal databases are in general append-only and usually very large in size, an efficient access method is even more important than for conventional databases. Numerous access structures were proposed, however, they have usually lacked practical credibility. Moreover most of these structures cannot handle now-relative data adequately. This means that these structures assume that the starting and ending points of intervals are known explicitly when recorded into the database. Obviously, this is unrealistic and this particular constraint makes these structures unsuitable for practical temporal applications.. Many multidimensional access structures have been proposed and some of them have been recommended for handling temporal data [12] . The effectiveness of the majority of these index structures has been theoretically evaluated [17] . We classify existing access methods for temporal data into four groups. The first group contains methods which represents extensions of data partitioning spatial indexing structures such as the Segment R-tree [9] , 4R-tree [3] , or a number of partially persistent methods [12] . In the second group, we have identified modifications of regular B + -tree access structures, such as the Fully Persistent B + -tree [13] and the Snapshot index [23] . The third group includes techniques based on incremental structures, such as, the Time Index [5] , Time Index + [24] , and the Monotonic B + -tree [16] . Finally, in fourth group are methods which are employing the existing B + -tree access structure by mapping of one dimensional ranges to one dimensional points, such as, MAP21 [14] , mapping strategy that linearize the data like Interval Space Transformation method (IST) [7] or managing the intervals by two relational indexes the RI-tree [11] , [6] .. Data partitioning access methods, such as spatial indexes, use a spatial containment hierarchy that clusters data into bounding regions at the leaf level. The nearby internal nodes are then clustered into bounding regions of the parent node forming a hierarchical directory structure. These regions may not represent the entire data space and could overlap. Overlapping is a problem for data partitioning access methods because even for a simple point query it may need to examine multiple paths. When open ended now-relative intervals (where the ending point of the temporal interval follows the current time) are represented with widely used maximum timestamp approach a significant overlapping between nodes and dead space causes very poor performance of the index [19] , [21] .. We intend to propose an access method for temporal data that relies on the exploitation of the relational database systems built-in functionalities; to utilises the native Data Definition Language (DDL), Data Manipulation Lan-guage (DML); and to use PL/SQL procedure environment within the SQL standard.. A number of access methods for temporal data that utilise the relational database systems built-in functionalities have been proposed, including: MAP21 [14] , Time Index [5] , Interval B-tree [2] , those based on interval space transformation [7] and RI-tree [11] . We observe that the proposed access methods that rely on relational database systems built-in functionalities, such as Time Index, Interval B-tree and those based on interval space transformation IST, have either space complexity problem or are generally tailored to be efficient only for specific query types. In [11] , it has been shown that the RI-tree is superior to the Window-List [15] , Oracle Tile Index (T-Index) and IST-technique. In the work [10] , it was extended and an algorithm for general interval relationships has been presented, but there is still a need to tailor query transformation to the specific query types. It is our intention to propose an efficient access method for temporal data with logarithmic access time and guaranteed minimum space complexity that can answer a wide range of query types with the same query algorithm.. In this paper we present and investigate the "Triangular Decomposition Tree" (TD-tree) access method to index and query temporal data. In contrast to previously proposed access methods for temporal data, this method can efficiently answer a wide range of query types, including point queries, intersection queries, and all nontrivial interval relationships queries, using a single algorithm, without dedicated query transformations.. The TD-tree is a space partitioning access method. The basic idea is to manage the temporal intervals by a virtual index structure that relies on a two-dimensional representation of intervals [20] , and a triangular decomposition method. The resulting binary tree stores a bounded number of intervals at each leaf and, hence, may be unbalanced. As data is only stored in leaves, traversing the tree avoids disk accesses, and the tree depth does not affect the performance. Using the interval representation, any query type can be reduced to a spatial problem of finding those (triangular) leaves that intersect with the spatial query region. TD-trees can be implemented on top of a standard relational DBMS.. The efficiency of the TD-tree is due to the virtual internal structure, so there is no need for physical disk I/O's, query algorithms that ensures pruning, and efficient clustering of interval data. On top of the advantages related to the usage of a single query algorithm for different query types and better space complexity, the empirical performance of the TD-tree is demonstrated to be superior to its best known competitors.. The remainder of this paper is organised as follows: In the next Section, we briefly describe several temporal access methods of interest for this discussion and highlight their advantages and disadvantages. In Section 3, we define the mapping strategy and determine regions of interest. Section 4 describes the structure of TD-trees, and the key insertion and query algorithms. Section 5 contains the results and analysis of the empirical study conducted to demon-strate the practical relevance and efficiency of the TD-tree. Finally, in Section 6, we present our conclusions. We described a new approach that is demonstratively better than existing approaches for handling temporal, and more generally, interval data. More specifically, in this study, we:. -Presented a two-dimensional interval space representation of intervals and interval relationships to reduce all interval relationship problems to simpler spatial intersection problems; -Showed that a wide range of interval query types can be reduced to an intersection of data with a rectangular region, so one algorithm can be applied uniformly; -Proposed the "Triangular Decomposition Tree" (TD-tree) and associated algorithms that can efficiently answer a wide range of query types including point or timeslice queries; -Experimentally evaluated the TD-tree by comparing its performance with RI-tree, and demonstrated its overall superior performance.. The TD-tree is a unique access method as it uses tree structures, and at the same time has some characteristics of hashing approaches due to it only stores data in leaf nodes. In contrast to hashing methods that do not perform well on range queries, the TD-trees can efficiently answer a wide range of different query types. It is important to mention that the management of the virtual structures is done automatically by using database triggers, which fire on insert, calculates, updates the region of the record and also increments the region in the directory. If required, it also initiates and performs splits. Similarly, database triggers fire on updates/deletes and performs actions in line with Deletion and Insert Algorithms.. As a wide range of query regions of interest can be reduced to rectangles, it is possible to answer such queries using a single algorithm without requiring any query transformation. This itself, and the fact that the TD-tree can be incorporated within commercial RDBMS, makes the TD-trees superior to other methods proposed for temporal data. To compare the space requirements for RI-tree and TD-tree, we considered tables with different number of rows. We generated tables with 250,000 rows, 500,000 rows and 1,000,000 tuples. All tables are altered to suit the particular approach and all required primary and secondary indexes are created. In Fig. 9 we show the space requirement for the TD-tree and RI-tree. Results represent the sum of used space for table, primary/secondary indexes and for the TD-tree we also added required space for the directory table. (Table plus indexes) To measure the query performance we used a data set of one million tuples. Results shown in Fig. 10 are for the point query with uniformly distributed start and exponentially distributed length with 20% of now-relative data. Results represent disk I/O and average CPU usage for different points on timeline which contain different answer sizes. We performed tests with all data distributions mentioned in subsection 5.1, but testing resulted in similar qualitative results as those presented here.. The Theory of Indexability [8] identifies I/O complexity cost, measured by the number of disk accesses, as one of the most important factors for measuring query performance. Other measures of importance such as CPU usage and query response time are also used in conjunction with the number of disk accesses to assess the performance of the query processes. For the TD-tree the number of leaf regions accessed to answer the query is simply the number of regions returned in the Primary filter. Secondary filtering only does pruning so it does not require any additional disk access, it only adds CPU usage. When the answer is smaller, interval objects pruned with the secondary filter effect the performance of the TD-tree and number of answers per one physical disk I/O is relatively smaller. In Table 3 we can see that TDtree even for a small answer size has better factor of answers per physical disk reads. For the RI-tree the number of answers per physical disk read is not dependent on query load, however for the TD-tree, due to the secondary filter features, the number of answers per physical read is dependent on query load and reaches the best performance on larger query loads.. Beside the queries mentioned in subsection 5.2, we tested applicability and performance of the TD-tree on several other query types, such as during, contain, and even before and after. These results will be mentioned and analysed in the next subsection.. The TD-tree performs well on now-relative data using MAX approach to represent current time, because the area where these intervals are stored can be divided as often as required as shown in Figure 12 . If we represent interval objects that belong to the particular RI-tree nodes in two dimensional space, it can Fig. 11 . CPU usage as a factor of answer size Fig. 12 . Now-relative data in TD-tree and RI-tree be seen that all now-relative data will be located in the root node (biggest rectangle in Figure 12 ) or on the right edge of the RI-tree. Knowing the importance of now-relative data in temporal databases this is a significant constraint. In the literature, two time lines of interest have been mentioned, transaction time and valid time. The valid time line represents when a fact is valid in the modelled world and the transaction time line represents when a transaction was performed. A bitemporal database is a combination of valid and transaction time databases [4] . Because temporal databases are in general append only, they are usually very large in size, thus efficient access method is even more important in temporal databases than in conventional databases. A number of index structures for temporal data are described in the literature [17] . The existing temporal access structures, as highlighted in section 1, fit in one of four groups. We will focus on indexing structures from group four, which can be utilised by exploiting the structures and functionality of commercial RDBMSs and rely on the relational paradigm. We briefly discuss typical representatives from group three and four and highlight their advantages and disadvantages.. The Time Index [5] is an index structure for valid time intervals. It is a set of linearly ordered indexing points that is maintained by a B + −tree. To overcomes the deficiencies of the Time Index, related to the space requirement which is O(n 2 ) for storing n intervals, the Time Index + has been proposed [24] . Time Index + relies on efficient storage model for partitioning logical buckets and on employing a new method to handle object versions with long and very long time intervals. The Time Index + requires less storage than the Time Index but but still requires significantly more space, even more than the spatial index methods. The disadvantage of this approach is the space required for the index, as for each point in time a bucket of pointers refers to the associated set of valid intervals. Since an interval may be registered with several points in time, This is a problem, particularly for data with many long living tuples.. The Interval B-tree (IB-tree) [2] overcomes the problems related to the extensive space usage of the Time index. It represents an implementation of the Edelsbrunner's interval tree using an augmented B + -tree rather than a binary tree. The main memory model of the interval tree is transformed into an efficient secondary storage structure that preserves the optimal space and time complexity. The disadvantage of this approach is the complex three-fold model, which requires a dedicated structure for each level. This makes the IB-tree less attractive from the view point of time complexity.. The access method (ISP) [7] is based on interval space transformation. Since the data space may grow dynamically at the upper bound, this method is well suited for appending intervals. It indexes lists on different orders, start time, end time or duration. This access method is highly specialized with respect to the suggested mapping and can not efficiently answer more complex queries such as intersection query or point query.. The Hierarchical Triangular Mesh (HTM) is method [22] suited for indexing the sphere and especially for astronomy data. It subdivides the half surface of a sphere into four spherical triangles of similar, but not identical, shapes and sizes. Every triangle is further subdivided into four smaller triangles. Division forms a balanced tree, which is then indexed with the Quad-tree. The HTM is highly dedicated for the data that have an inherent location on the celestial sphere. The HTM has been mentioned as it has triangles as a region as our method and to highlight the differences.. The Relational Interval Tree (RI-tree) is an access method for general closed interval data, it can be created for any relational or object-relational table containing intervals [11] . Analytical and experimental evaluation of the RI-tree shows that the performance of this method is superior to the other approaches. This is achieved by introducing a virtual primary structure. Although the structure is space-oriented, the storage of intervals is object-driven so no storage space is wasted for empty regions in the data space. In [10] work was extended and an algorithm for general interval relationships has been presented but still there is a need for tailored query transformation to the specific query types. It is our intention to propose an efficient access method for temporal data that can answer wide range of query types with the same algorithm and that does not require tailored query transformation for different query types. The same data set is used both for RI-tree and TD-tree testing experiment. The initial relations with structure Employment(ID, Name, Position, Start, End) were replicated and altered accordingly to suit each particular method.. Relations for testing the performance of the RI-Tree, were altered with column node, which is calculated for every row of data by algorithm as explained in paper [10] . Two B + -tree composite indexes have been created LowerIndex (node, Start) and UpperIndex (node, End). A point query is performed by calling the dedicated procedure that collects leftnodes and rightnodes and then performs the transformed SQL statement as instructed in [11] .. Relations for testing the performance of the TD-tree were altered with column Region, which is calculated according the algorithm as explained in Subsection 4.1. The root node, which contains information for λ, blocking-factor, adjustment date and maximum depth of the tree we stored as one tuple relation. Because TD-tree has only leaf nodes it can be organised as a list and stored in directory tables. To ensure that the population of a region corresponds to one block, so it can be be efficiently retrieved, we introduced a blocking factor. We built relation Employment as index organised table using Region and ID as a primary key.

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


Cellular Automata to More Efficiently Compute the Collatz Map The Collatz, or 3x+1, Conjecture claims that for every positive integer n, there exists some k such that T^k(n)=1, where T is the Collatz map. We present three cellular automata (CA) that transform the global problem of mimicking the Collatz map in bases 2, 3, and 4 into a local one of transforming the digits of iterates. The CAs streamline computation first by bypassing calculation of certain parts of trajectories: the binary CA bypasses division by two altogether. In addition, they allow for multiple trajectories to be calculated simultaneously, representing both a significant improvement upon existing sequential methods of computing the Collatz map and a demonstration of the efficacy of using a massively parallel approach with cellular automata to tackle iterative problems like the Collatz Conjecture. Consider the Collatz map T : N → N defined by T (n) = 3n + 1, n ≡ 1 mod 2 n/2, n ≡ 0 mod 2.. email: sitanchen@college.harvard.edu. Given n, define the total stopping time to be the smallest k for which T k (n) = 1. The Collatz Conjecture claims that every n has a finite total stopping time; it has been verified for inputs as high as 20 · 2 58 by Oliveira e Silva [1] , and a generalization of the Conjecture by Kurtz and Simon was shown to be recursively undecidable [2] . If we define the stopping time to be the smallest k for which T k (n) < n, the claim that every n has a finite stopping time is equivalent to the Collatz Conjecture.. The trajectory for an input n is the sequence n, T (n), T 2 (n), T 3 (n), .... We can categorize the possible behaviors of the trajectory as follows [3] :. (i) Convergent trajectory: T k (n) = 1 for some positive integer k.. (ii) Non-trivial cyclic trajectory: T k (n) becomes periodic and T k (n) = 1. for any positive k.. (iii) Divergent trajectory: lim. The iterative nature of the problem and the complexity of behavior that arises from the simple premises of the Collatz Conjecture suggest the use of cellular automata to mimic computation.. Notable instances of using deterministic computational models to simulate the behavior of the Collatz map include De Mol's 2-tag system using a set of three production rules over an alphabet of three symbols to mimic the Collatz map [4] , Michel's two one-tape Turing machines [5] whose halting problems depend on generalizations of the Collatz problem, and Bruschi's two one-dimensional cellular automata that calculate trajectories using tagging operations to detect parity [6] . In this paper, we demonstrate one threedimensional and two two-dimensional cellular automata that also mimic the behavior of the Collatz map but whose evolution laws operate independent of parity, depending solely on local relationships between digits of the iterates. We find that our automata have the potential to compute trajectories more efficiently than do current methods both by bypassing computation of large parts of trajectories and by verifying an arbitrary number of inputs in parallel. Call the n-efficiency of any of the above CAs the number of iterates that have been computed by the CA upon reaching 1 given input n, divided by the total stopping time of that input. The average n-efficiency over all n such that 1 ≤ n ≤ 2 14 was determined to be roughly 69.4%, 63.7%, and 32.2% for CA1, CA2, and CA3, respectively. In addition, observe that it is not necessary to initialize any of these CAs with only one input. In fact, these CAs are able to compute the trajectories of an arbitrary number of inputs at a time. As an example, in the case of CA3, let the set of inputs be {n j } 1≤j≤M , where input n j has binary representation Nj i=0 2 i d j i such that the smallest i for which d i = 0 is some L j . The CA is initialized as follows: pick an arbitrary k 0 ∈ Z. For all j such that 1 < j ≤ M , let k j = k j−1 + N j−1 + j , where j is chosen so that the trajectories of Note however, that the difficulty in initializing a CA to compute multiple trajectories in parallel this way lies in the unpredictability of the behavior of j : it is not certain how large the space between two inputs must be for their trajectories not to collide.. As a workaround, if we place each iterate whose trajectory we want to compute on its own grid and, roughly speaking, stack those grids on top of FIGURE 10: Parallel computing for initial iterates n =183, 120767, 53132499 one another to form an arbitrarily high three-dimensional grid of cubical cells, then this CA can verify multiple inputs in parallel.. FIGURE 11: Parallel computing in three dimensions. In conclusion, we have found three CAs that mimic the behavior of the Collatz map in bases two, three, and four, and streamline the process of verification of the Collatz Conjecture by bypassing calculation of certain parts of the trajectory. Beyond speeding the progress towards potentially finding a counterexample, this work affords insights into the distribution of the (mod 2 k ) residues of iterates, which may justify the existing heuristic probabilistic argument that trajectories tend to decrease [7] . Topics for further study include applying the parallel computing model we propose to similar iterative computations, exploring whether it is possible to create evolution laws that depend entirely on digits from the previous iterate, and exploring other potentially viable radices for new CAs. With regards to the latter, it is known that the distribution of (3/2) k (mod 1) is closely related to the "sorting properties" of the Collatz map, that is, whether the function distributes odd iterates equally among the residues (mod 2 k ) [3] . If no reasonable CA exists in base 3/2, it could still be worth exploring possible CAs for computing (3/2) k . Implementations in Java of CA2 and CA3 can be found at www.sitanchen.com/collatz4.html and www.sitanchen. com/collatz.html, respectively.

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


Morphological Computation and Morphological Control: Steps Toward a Formal Theory and Applications A version of this paper with color figures is available online at http://dx.doi.org/10.1162/ artl_a_00079. Subscription required.Abstract Morphological computation can be loosely defined as the exploitation of the shape, material properties, and physical dynamics of a physical system to improve the efficiency of a computation. Morphological control is the application of morphological computing to a control task. In its theoretical part, this article sharpens and extends these definitions by suggesting new formalized definitions and identifying areas in which the definitions we propose are still inadequate. We go on to describe three ongoing studies, in which we are applying morphological control to problems in medicine and in chemistry. The first involves an inflatable support system for patients with impaired movement, and is based on macroscopic physics and concepts already tested in robotics. The two other case studies (selfassembly of chemical microreactors; models of induced cell repair in radio-oncology) describe processes and devices on the micrometer scale, in which the emergent dynamics of the underlying physical system (e.g., phase transitions) are dominated by stochastic processes such as diffusion. Some of the most important current applications of morphological computing are in robotics, a field in which it is widely accepted that the intrinsic dynamics of a physical system (the robot body) need not be regarded only as a potential source of perturbations, but can be exploited to facilitate the control of the system [28] . Control implies computation. The use of the dynamics of the robot body to facilitate control can thus be interpreted as an outsourcing of computational tasks to the body. In this interpretation, the body is performing morphological computation [25] .. In robotics, the concept of morphological computing has been around for some time, though the term itself is relatively recent (see [17] and, for a broader presentation, [27] ). Today, however, it is clear that the concept of morphological computing can be applied not just to systems such as robots, whose dynamics are governed by classical mechanics, but also to systems, such as self-assembling and/or chemical systems, that are better described in terms of statistical physics [29] .. In 2007, a workshop at the first International Conference on Morphological Computing in Venice, Italy, led by Norman Packard, informally defined morphological computing as "any process that (a) serves for a computational purpose, (b) has clearly assignable input and output states and (c) is programmable, where 'programmable' is understood in the broad sense that a programmer can vary the behavior of the system by varying a set of parameters." This definition implies that conventional digital computing systems are instances of morphological computing. However, many researchers require that at least part of the computation should rely in a significant way on the physical dynamics of the system implementing the computation, which should be entirely defined by the "program." By this definition, the execution of a conventional computer program that completely specifies the transformation of an input to an output cannot be classed as morphological computation. The formalization we propose in Section 2.2 casts new light on this issue.. The rest of the article will be structured as follows. We begin by discussing conceptual aspects of morphological computation and morphological control. We then examine how these concepts apply to robotics and to more general computational applications. On this basis, we suggest a more formalized definition. Our definition is a suggestion and reflects our point of view; in what follows "morphological computation" should be interpreted as "the view of morphological computation held by the authors." The article concludes with three case studies, two of which go beyond robotics and the underlying classical mechanics to consider systems whose dynamics are governed by statistical mechanics. One effect of aging is the gradual loss of control over complex movement patterns. This loss may have many causes, one of them being reduced sensory and neural performance. The notion of morphological computation suggests another possible explanation. Aging changes the mechanical properties of the body, altering its attractor landscape and thereby reducing the bodyʼs ability to contribute to control tasks. Viewed from this perspective, the difficulty many elderly people experience in controlling their movements is not due (at least not exclusively) to poor performance by their brains, but to changes in their body that make the morphological control problem harder. In what follows, we describe the use of a novel technology, tensairity [19] , to reshape the bodyʼs attractor landscape so as to restore morphological control. The system we have in mind is not some kind of machinery that physically moves the patient as though he or she were a passive object. Rather it modulates the patientʼs own actions.. The synthesis of complex branched molecules (e.g., oligosaccharides for glycol conjugates with medical applications) is still a demanding task. One of the important tasks is controlling potential side reactions [16] . Whereas the synthesis of a linear chain molecule can happen in a template-based manner and the reaction, at least in theory, leads to an unambiguously defined end product, no comparable technique is available for branched structures. Without a template, the only way to achieve unambiguously defined end products would be to use addresses specific to each connection. Unique addressing based on strands of DNA or related chain molecules has previously been used to construct large supramolecular structures [34, 41] and even for the construction of self-assembled compounds of vesicles [8] . However, large linkers are not always suitable for the connection of small molecules. Using small linker structures means that, instead of being able to exploit a combinatorial variety of addresses, one has only a small number of linkers at hand, and that it may be necessary to use the same linker more than once. With one-pot reactions, the multiplicity of reaction pathways lowers the yield [16] . The term tensairity brings together tensegrity with air; inflatable elements play a crucial role. Tensairity has made it possible to build inflatable bridges that can carry a car using pressures of only 300 mbar. More recently, it has been demonstrated that tensairity can also be used to implement actuated structures [18] . In therapeutic contexts, such structures offer a variety of benefits, including low weight and cost, high intrinsic safety, and high adaptability. However, their softness means they cannot be programmed in the same way as, say, an exoskeleton.. Work by one of the authors (K.J.H.) has shown that the tensairity actuator systems can be used to provide soft support to patients undergoing rehabilitation following stroke, spinal cord injuries, and other conditions leading to partial paralysis. The idea is to provide additional support during standing up, standing, walking, and sitting down. Similar techniques can also be useful for elderly people with weak lower-limb musculature.. Several systems to support walking are already in widespread use for clinical rehabilitation. One such system is the Lokomat (Hocoma AG, Volketswil, Switzerland), a device that combines a treadmill with powered, rigid walking orthoses and an overhead body-weight unloading system. The G-EO System (Reha Technology AG, Olten, Switzerland) offers an alternative approach based on endpoint control: The patientʼs feet are attached to an external powered actuator system that allows simulation of walking on the level, upstairs, and downstairs. Other powered exoskeleton devices to support walking are under development (e.g., eLEGS, Berkeley Bionics, California, USA; ReWalk, Argo Medical Technologies, Haifa, Israel).. Compared to these systems, tensairity actuators offer several potential advantages. The key differentiating feature is that the actuator provides lightweight soft support to patients suffering from partial paralysis or muscle weakness due to injury, disease, or aging. The idea is to supplement joint supports and orthoses with customized tensairity actuators, or to integrate the actuators into wearable garments. The actuators would not replace the action of the patient but would help the patient to regain control over his or her movements.. To evaluate the potential of tensairity actuators, two of the authors (K.J.H., A.D.) have constructed and tested a biomechanical prototype system that mechanically simulates the human thigh, calf (shank), and knee joint, allowing the integration of different tensairity support actuators (Figure 3) . The actuators themselves were custom designed and manufactured to fit the mechanical construction. They were then positioned on each side of the artificial knee joint, and the joint angle was measured using a digital encoder. This setup made it possible to implement a feedback control system so that the knee-joint angle could follow arbitrary, prespecified trajectories (Figure 4) . The feedback controller drives a three-way valve, which bidirectionally supplies air to the actuators. In a real-life implementation, the feedback system would take its target angle trajectory from values corresponding to physiological knee-joint motion during functional tasks such as standing up or walking.. Tests showed that the system can lift a 3-kg mass at the notional ankle joint (i.e., at the bottom of the shank) from the vertical to the horizontal, using a pressure of less than 1 bar. The torque generated in this way is 15 N m. This suggests that the system could provide useful joint support at low cost, low weight, and low pressure. The next phase of the study will investigate combinations of controlled tensairity actuators with existing or custom-built joint supports and orthoses. The resulting systems will be tested first with healthy people and then in people with lower-limb impairments.

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


Residual as Linear Sum of Matrix Determinants in Multiway Contingency Tables A Pearson residual is defined as a residual between an observed value and expected one of each cell in a contingency table, which measures the degree of statistical dependence of two attribute-value pairs corresponding to the cell. This paper shows that this residual is decomposed into a linear sum of determinants of 2 × 2 subtables, which means that the geometrical nature of the residuals can be viewed from grasmmanian algebra. Statistical independence between two attributes is a very important concept in data mining and statistics. The definition P(A, B) = P(A)P(B) show that the joint probability of A and B is the product of both probabilities. This gives several useful formula, such as P(A|B) = P(A), P(B|A) = P(B). In a data mining context, these formulae show that these two attributes may not be correlated with each other. Thus, when A or B is a classification target, the other attribute may not play an important role in its classification.. Although independence is a very important concept, it has not been fully and formally investigated as a relation between two attributes.. In this paper, a statistical independence in a contingency table is focused on from the viewpoint of granular computing and linear algebra, which is continuation of studies on contingency matrix theory 2,4,6,5 . Tsumoto 2, 5 discusses that a contingency table compares two attributes with respect to information granularity and shows that statistifcal independence in a contingency table is a special form of linear depedence of two attributes. Especially, when the table is viewed as a matrix, the above discussion shows that the rank of the matrix is equal to 1.0. Tsumoto 4 matrix algebra is a key point of analysis of this table. A contingency table can be viewed as a matrix and several operations and ideas of matrix theory are introduced into the analysis of the contingency table. On the other hand, in another paper 6 , Tsumoto shows that the Pearson residual of a contingency matrix is represented as a linear sum of 2 × 2 submatrices, whose number is equal to the degree of freedom.. In this paper, we extend residual analysis to multidimensional cases. The results show that multidimensional residuals are also represented as a linear sum of determinants of 2 × 2 submatrices, the number of which is equal to the degree of freedom in a given contingency table. Furthermore, the sum includes several kinds of units for statistical independence/dependence, such as total independence and partial independence. This also suggests that 2 × 2 submatrices in a multidimensional data cube can be viewed as information granules for measuring statistical dependence.. The paper is organized as follows: Section 2 discusses the characteristics of contingency tables. Section 3 shows the conditions on statistical independence for contingency tables. Section 4 gives the results of residual analysis of multiway contingency tables. Section 5 illustrates the nature of residuals of multiway tables by using several samples. Section 6 shows that the number of the determinants of 2 × 2 submatrices is exactly the same as the degree of freedom in a three-way contingency table. Finally, Section 7 concludes this paper. Table Definition 1 . Let R 1 , R 2 , · · · , R n denote n(∈ N) multinominal attributes in an attribute space A which have m 1 , m 2 , · · · , m n values Let |R j = A j i | denote the set of data whose jth-attribute is equal to A j i (ith-partition of j). A contingency table T (R 1 , R 2 , · · · , R n ) is a table, each of whose cells can be defined as: This paper focuses on statistical independence of three variables from the viewpoint of linear algebra and show that information granules of statistical independence of three or four variables are decomposed into linear sum of determinants of 2 × 2-submatrices. The analysis also shows that the residuals of a multiway contigency table can be defined in a recursive way. For example, the residuals of four-way tables are described as those of three-way and two-way tables. Then, we focus on this recursive nature in the case of three-way contingency tables. The geometric characteristics of selected dertimants in a residual x i jk show that the components of the sum give possible combinations of parallelograms which has one fixed edge with x i jk as a vertex. Furthermore, The total number of derminants of 2 × 2 submatrices in a three-way contingency table is equal to the degree of freedom of χ 2 test statistic in contingency table analysis.. Thus, the derminants of 2 × 2 matrices are principal information granules to measure the degree of statistical dependence in a given contingency table.

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


Evaluation and design of highly reliable and highly utilized cloud computing systems Cloud computing paradigm has ushered in the need to provide resources to users in a scalable, flexible, and transparent fashion much like any other utility. This has led to a need for developing evaluation techniques that can provide quantitative measures of reliability of a cloud computing system (CCS) for efficient planning and expansion. This paper presents a new, scalable algorithm based on non-sequential Monte Carlo Simulation (MCS) to evaluate large scale cloud computing system (CCS) reliability, and it develops appropriate performance measures. Also, a new iterative algorithm is proposed and developed that leverages the MCS method for the design of highly reliable and highly utilized CCSs. The combination of these two algorithms allows CCSs to be evaluated by providers and users alike, providing a new method for estimating the parameters of service level agreements (SLAs) and designing CCSs to match those contractual requirements posed in SLAs. Results demonstrate that the proposed methods are effective and applicable to systems at a large scale. Multiple insights are also provided into the nature of CCS reliability and CCS design. Cloud computing provides a cost-effective means of transparently providing scalable computing resources to match the needs of individual and corporate consumers. Despite the heavy reliance of society on this new technological paradigm, failure and inaccessibility are quickly becoming a major issue. Current reports state that up to $ 285 million yearly have been lost due to such failures with an average of 7.74 hours of unavailability per service per year (about 99.91 % availability) [1] [2] [3] . Despite these outages, rapid adoption of cloud computing has continued for the mission-critical aspects of the private and public sectors, particularly due to the fact that industrial partners are unaware of this issue [2, 3] . This is particularly disconcerting considering President Obama's $ 20 billion dollar Federal Cloud Computing Strategy and the rapid migration of government organizations like NASA, the Army, the Federal Treasury, Alcohol, Tobacco, and Firearms, the Government Service agency, the Department of Defense, and the Federal Risk and Authorization Management This need to provide a highly reliable, uninterrupted cloud service while effectively utilizing all available resources is highly desired by cloud providers/users and clearly demonstrates a gap in current CCS research, calling for the establishment of efficient methods which can quantitatively evaluate and design CCSs based on the competing needs of users (reliability) and providers (utilization). As such, the goal of this study is the design and evaluation of CCSs considering stochastic failures in the CCS as well as stochastic virtual machine (VM) requests.. In order to achieve this goal, this study makes multiple contributions including 1) Developing a computationally efficient method for evaluating the reliability of CCSs using non-sequential Monte Carlo simulation (MCS) considering stochastic hardware failures and VM requests, 2) Extending this new model in order to design highly reliable and utilized CCSs based on potential workloads, and 3) Discussing the practical implications of the proposed technique. As opposed to most previous work, the proposed method 1) Focuses on simulationbased analysis, 2) Is highly scalable due to the use of MCS, and 3) Uses a newly developed, intuitive system representation.. The remainder of this paper is organized as follows: Section "Related works" reviews background literature that is pertinent to the proposed methodology; Section "Proposed methodologies" presents the the newly proposed application of non-sequential MCS, its formulation for assessing the reliability of a CCS, and its use in a new, iterative algorithm for designing highly reliable and highly utilized CCSs; Section "Experimental results" details the experimental results achieved including CCS test systems designed and evaluated using the proposed methods; Section "Discussion" presents a discussion and comments on using non-sequential MCS as a tool for CCS reliability assessment and the role of this technology in SLAs. Insights gathered during CCS reliability assessments and CCS design are also given in Section "Practical implications"; and, finally, Section "Conclusion" concludes the paper with a summary as well as directions for future work. This study has presented and analyzed a novel approach to assessing the reliability of CCSs using non-sequential MCS. It was shown that non-sequential MCS provides an efficient and flexible way to determine the reliability of a CCS based on a set of discrete resources. A novel algorithm for CCS expansion planning was also introduced which facilitates the design of highly reliable and highly utilized CCSs. Finally, new test-bed CCS systems were developed that can be used for future CCS reliability and availability analyses. Based on the insights garnered during this study, future work may include the following:. • An extension of the CCS expansion planning algorithm developed in this study to incorporate economic factors to simultaneously maximize CCS reliability and the cloud providers return on investment (ROI); • As this study considered a CCS to have only CPU, memory, HDD, and bandwidth resources, a future extension may include graphics processing units (GPUs), databases, software packages, etc. This extension would provide for highly realistic simulations that take into account many more variables than were considered in this preliminary study.. • An extension of the proposed algorithm to consider partially failed or derated states. For instance, a multiple core CPU may still function at a reduced level if only a subset of the available cores fail; • Evaluating implications of server and storage hypervisors on the reliability of a CCS instead of using a simple resources requested vs. available scheme; and • This study has made an important approximationcalculating resource assignment and usage in an

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


Combined shared and distributed memory ab-initio computations of molecular-hydrogen systems in the correlated state: process pool solution and two-level parallelism An efficient computational scheme devised for investigations of ground state properties of the electronically correlated systems is presented. As an example, (H2)n chain is considered with the long-range electron-electron interactions taken into account. The implemented procedure covers: (i) single-particle Wannier wave-function basis construction in the correlated state, (ii) microscopic parameters calculation, and (iii) ground state energy optimization. The optimization loop is based on highly effective process-pool solution -specific root-workers approach. The hierarchical, two-level parallelism was applied: both shared (by use of Open Multi-Processing) and distributed (by use of Message Passing Interface) memory models were utilized. We discuss in detail the feature that such approach results in a substantial increase of the calculation speed reaching factor of 300 for the fully parallelized solution. Electronically correlated systems are important both from the point of view of their unique physical properties and from nontrivial computational methods developed to determine them. The latter cover methods based on the Density Functional Theory (DFT) with the energy functional enriched by the correlation terms -the on-site repulsion U in the Hubbard model [1] and the Hund's rule term in the case of orbital degeneracy. Often, they are incorporated into either DFT or the Dynamic Mean Field Theory (DMFT) approach supplemented with the LDA-type calculations (see e.g. [2] ). On the other hand, the Configuration-Interaction (CI) method does not suffer from the well-known double counting problem [1, 2] , inherent in the DFT+U or LDA+DMFT methods. Another approach, similar in its spirit to the CI method, formulated as a combination of the first-and second quantization (FQ, SQ respectively) formalisms was elaborated in our group in the last decade and termed the Exact Diagonalization Ab Intito (EDABI) approach [3, 4] . This method allows for a natural incorporation of the correlation effects consistently by the advantages of using the SQ language so that the double-counting problem does not arise at all. Also, by construction, it includes the Pauli principle for the fermionic systems. In contrast to CI the EDABI approach avoids any direct dealing with the many-body wave function expressed via a * andrzej.biborski@agh.edu.pl † kadzielawa@th.if.uj.edu.pl ‡ ufspalek@if.uj.edu.pl linear combination of the Slater determinants [5] . Instead, it is based on the many-particle quantum states constructed in the occupation number representation [5] -typical procedure for the SQ formulated problems.The application of EDABI was found promising in view of research devoted to the hydrogen molecular systems with inclusion of interelectronic correlations [6] , nano-clusters [7] , and to atomic hydrogen metallization [8] . As the many-particle state is explicitly written in the occupation-number representation (Fock space), the starting Hamiltonian is formulated in the SQ language. Electronic correlations are then automatically included in the modeled system. However, in the Hubbard-like starting Hamiltonians [9-12] the knowledge of microscopic parameters, such as the on-site and the intersite hopping and the Coulomb repulsion magnitudes are regarded as input information. These parameters are often estimated indirectly. With this limitation, specific phase-diagrams are constructed and the phase boundaries of interest are determined as a function of those microscopic parameters which are not directly measurable (cf. e.g. [13] [14] [15] ). In EDABI we take a different route: relatively simple and small systems are to be described consistently in the sense that the microscopic parameters are obtained explicitly as an output of an appropriate ab-initio variational procedure. Therefore, the EDABI approach should be regarded as an ab-initio method but with the single-particle wave functions being determined self-consistently in the correlated state. In this manner, the problem solution is reversed with respect to that in either LDA+U or LDA+DMFT. Namely, we first formulate the Hamiltonian and diagonalize it in SQ formalism and determine the single-particle wave function only as a second step. However realistic, such an approach to arXiv:1504.00500v1 [cond-mat.str-el] 2 Apr 2015 We have presented an effective computational approach related to the EDABI method -quantum- mechanical approach allowing to treat the electronic correlations in a consistent manner. This means that we combine the second-quantization aspect (evaluation of energies for different many-particle configurations) with an explicit evaluation of the renormalized wave functions (first-quantization aspect) in the resultant correlated many-particle state. The number of microscopic parameters that are necessary for description of the physical system can be meaningful in many cases. Hence, their computations become challenging as an effect of numerical complexity caused by the vast number of integrations to be performed (9) . We have proposed the scheme based on the process-pool concept enhanced by the twolevel parallelism, and test it utilizing self-made generic implementation [34] configured for the specific computational problem -(H 2 ) n chain. The proposed approach is intuitive and has allowed us to speed up the calculations significantly (of the order of 10 2 ) while preserving its generic character. Employing process-pool solution to other systems is then straightforward.. Since the considered physical example serves as an illustration of the elaborated scheme capability, one may consider engaging it to a wide class of computationally advanced physical problems tractable within the framework of EDABI or similar methods. Such problems cover:. • lattice vibration (phonon) spectrum via the so-called direct method (where all but few symmetries are lost, increasing the number of integrals dramatically -from 510 to over 10 000 for (H 2 ) n chain);. • calculation of the electron-lattice coupling parameters in direct space;. • electronic structure calculations of the realistic two-and three-dimensional atomic and molecular crystals (e.g. hydrogen, lithium hydride), where both the number of atomic orbitals and the background field increase essentially.. Neither form of the starting Hamiltonian nor the diagonalization scheme choice is essential for the applicability of the method, allowing us to incorporate other approaches such as the Gutzwiller approximation [8, 15, 21] or Gutzwiller Wave Function -Diagramatic Expansion [35] to study molecular and extended spatially systems. In this manner, one can address e.g. the fundamental question of metallization in correlated systems [36, 37] with the explicit evaluation of an model parameters.

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


High-Accuracy Sub-Pixel Registration for Noisy Images Based on Phase Correlation This paper proposes a high-accuracy sub-pixel registration framework based on phase correlation for noisy images. First we introduce a denoising module, where the edge-preserving filter is adopted. This strategy not only filters off the noise but also preserves most of the original image signal. A confidence-weighted optimization module is then proposed to fit the linear phase plane discriminately and to achieve subpixel shifts. Experiments demonstrate the effectiveness of the combination of our modules and improvements of the accuracy and robustness against noise compared to other sub-pixel phase correlation methods in the Fourier domain. Sub-pixel image registration plays a crucial role in computer vision and image processing, such as super resolution, denoising and medical reconstruction [1] , [2] . Phase correlation has proved to be an attractive solution [4] among a wide variety of registration techniques.. Shift-estimation based on phase correlation falls into two categories: methods in the spatial and the Fourier domains. The methods in the spatial domain obtain the peak of the phase correlation surface as the shifts [3] , [5] , [7] . Foroosh [5] calculated the shifts by linear-weighting the maximum and sub-maximum peaks. J Ren [7] took into consideration the difference between two side neighbors of the maximum peak to improve the robustness against noise.. Methods in the Fourier domain fit the linear phase plane to achieve sub-pixel estimations [4] , [8] , [9] . Patrick [8] picked data points in the low-frequency band only of the linear phase plane to alleviate the effects of the high-frequency outliers. Keller [9] utilized the energy concentration property of the phase correlation surface and used the low-pass filter to suppress the noise. However, these methods utilize all picked data points in the linear phase plane equally when outliers of this plane, sometimes existing in the low-frequency band, might corrupt the estimations.. In this paper, a high-accuracy sub-pixel registration framework is proposed based on phase correlation in the Fourier domain. First, a denoising module is introduced, where the edge-preserving filter is proposed and utilized before the traditional phase correlation module to retain a more original image signal. Second, we propose a confidenceweighted optimization module to fit the linear phase plane discriminately which leads to accurate and robust estimations. The rest of the paper is organized as follows. The formulation of phase correlation is introduced in Sect. 2. Our proposed scheme is presented in Sect. 3. Evaluation of our framework is given in Sect. 4, followed by a brief conclusion in Sect. 5. In summary, we propose a high-accuracy sub-pixel registration framework which is composed of the denoising and optimization modules. In the denoising module, we acquire a more original image signal by applying an edge-preserving filter. In the optimization module, we fit the confidenceweighted plane to achieve sub-pixel shifts. Experimental results on both synthetic and real data demonstrate that our framework is reasonable and achieves the most accurate and robust estimations among recent research works.

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


Hierarchical Cross-Entropy Optimization for Fast On-Chip Decap Budgeting Abstract-Decoupling capacitor (decap) has been widely used to effectively reduce dynamic power supply noise. Traditional decap budgeting algorithms usually explore the sensitivity-based nonlinear optimizations or conjugate gradient (CG) methods, which can be prohibitively expensive for large-scale decap budgeting problems and cannot be easily parallelized. In this paper, we propose a hierarchical cross-entropy based optimization technique which is more efficient and parallel-friendly. Cross-entropy (CE) is an advanced optimization framework which explores the power of rare event probability theory and importance sampling. To achieve the high efficiency, a sensitivity-guided cross-entropy (SCE) algorithm is introduced which integrates CE with a partitioning-based sampling strategy to effectively reduce the solution space in solving the large-scale decap budgeting problems. Compared to improved CG method and conventional CE method, SCE with Latin hypercube sampling method (SCE-LHS) can provide 2× speedups, while achieving up to 25% improvement on power supply noise. To further improve decap optimization solution quality, SCE with sequential importance sampling (SCE-SIS) method is also studied and implemented. Compared to SCE-LHS, in similar runtime, SCE-SIS can lead to 16.8% further reduction on the total power supply noise.Index Terms-Adjoint sensitivity analysis, cross-entropy optimization, decoupling capacitor budgeting, power grid design, power supply noise. In this paper, we presented a hierarchical CE-based optimization approach that is more efficient and parallel-friendly than prior decap optimization algorithms, by exploring the power of rare event probability theory and importance sampling. To gain higher efficiency, an SCE framework is introduced that integrates traditional CE method with a partitioning-based sampling strategy to effectively reduce the number of optimization variables in large-scale decap budgeting problems. Compared to previous iCG method and conventional CE method, SCE algorithm with Latin hypercube sampling method (SCE-LHS) can provide 2× speedups, while achieving up to 25% improvement on power supply noise. To further improve decap optimization efficiency and solution quality, SCE-SIS is also developed, which leads to up to 16.8% further reduction on the total power supply noise in similar runtime compared to the original SCE-LHS method. We also observed up to 1.8× speedups when running the SCE-LHS algorithm on a dual-CPU-dual-GPU machine.

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


Application of the RIMARC algorithm to a large data set of action potentials and clinical parameters for risk prediction of atrial fibrillation learned by the RIMARC algorithm can be used for accurately classifying the preoperative rhythm status. APs were included from 221 SR and 158 AF patients. During a learning phase, the RIMARC algorithm established a ranking order of 62 features by predictive value for SR or AF. The model was then challenged with an additional test set of features from 28 patients in whom rhythm status was blinded. The accuracy of the risk prediction for AF by the model was very good (0.93) when all features were used. Without the seven AP features, accuracy still reached 0.71. In conclusion, we have shown that training the machine-learning algorithm RIMARC with an experimental and clinical data set allows predicting a classification in a test data set with high accuracy. In a clinical setting, this approach may prove useful for finding hypothesis-generating associations between different parameters.Abstract Ex vivo recorded action potentials (APs) in human right atrial tissue from patients in sinus rhythm (SR) or atrial fibrillation (AF) display a characteristic spike-anddome or triangular shape, respectively, but variability is huge within each rhythm group. The aim of our study was to apply the machine-learning algorithm ranking instances by maximizing the area under the ROC curve (RIMARC) to a large data set of 480 APs combined with retrospectively collected general clinical parameters and to test whether the rules Ursula Ravens, Deniz Katircioglu-Öztürk, Ali Oto and H. Altay Güvenir have equally contributed. Action potential duration at 20 % of repolarization (ms) APD 50 Action potential duration at 50 % of repolarization (ms) APD 90 Action potential duration at 90 % of repolarization (ms) dV/dt max Maximum rate of depolarization (Vs −1 ) MAD Maximum area under ROC curve-based discretization PLT 20 "Plateau potential" defined as the mean potential (mV) in the time window between 20 % of APD 90 plus 5 ms RIMARC Ranking instances by maximizing the area under the ROC curve RMP Resting membrane potential (mV) ROC Receiver operating characteristics SR Sinus rhythmElectronic supplementary material During open-heart surgery, the outer rim of the right atrial appendage is removed in order to introduce the tubing for connecting the patient to the extracorporeal circulation. Most patients agree that these tissue samples are made available for basic research rather than being disposed. Therefore, right atrial tissue can be studied ex vivo for its basic electrophysiological properties.. Action potentials (APs) recorded in right atrial tissue from patients in sinus rhythm (SR) exhibit a characteristic spikeand-dome morphology that changes into a triangular form due to electrical remodeling in chronic atrial fibrillation (AF) [4, 19, 22] . Many studies have reported in silico modeling of atrial repolarization in order to understand the complex processes which underlie AF-induced changes [6, 7, 15] . Despite the clear association of AP shape with the patient's preoperative rhythm status, the variability in individual AP morphology is large and does not always allow a clear distinction between SR and AF. Besides preoperative rhythm status, other demographic and clinical factors could have an influence on AP shape. Therefore, most published experimental studies with human atrial tissue also include additional information on the patients' age, height, body weight, concomitant diseases, basal hemodynamic parameters, pre-surgical medication, etc. (e.g., [5, 23, 24] ). However, cohort sizes are usually quite small (<50 patients) so that weak influences of accompanying clinical conditions cannot be ruled out.. In the context of our electrophysiological interest in AF pathophysiology, we have accumulated a large data pool of human right atrial action potential recordings during the past 8 years. From all patients, we have also collected clinical parameters from the electronic (scanned) patient files. Instead of using conventional statistics to find associations between AF and electrophysiological and clinical features, we used a machine-learning approach for risk prediction. In this context, the term "risk prediction" is used in a mathematical sense of correct classification and is not related to the clinical prediction of risk of getting a disease based on empirically observed risk factors for that disease.. The general objective of all machine-learning approaches can be stated as non-trivial extraction of previously unknown, however, hypothesis-generating premises, rules and relations from large data sets. Aligned with this particular objective, our study incorporated a machinelearning algorithm ranking instances by maximizing the area under the ROC curve (RIMARC) [10] instead of a multivariate statistical approach.. The RIMARC algorithm was applied to a large data set of ex vivo recorded human right atrial APs combined with retrospectively collected general clinical parameters. Therefore, the aim of our study was to test whether the rules learned by this algorithm could be used for an accurate classification of a patient's rhythm status. The machine-learning algorithm RIMARC provides a very useful tool for classifying patients according to their preoperative rhythm status ("predicting" rhythm status) with high accuracy from an experimental and clinical set of data. In a clinical setting, this approach may prove useful for finding hypothesis-generating associations between different parameters. In the present study, we have used a large ex vivo electrophysiological data set from human atrial biopsies as well as clinical information for training a machine-learning algorithm to establish a ranking order of features by predictive value for preoperative AF. The major findings were (i) APD 90 , APD 20 , and left atrial diastolic diameter had the highest predictive values; (ii) pulmonary hypertension ranked on place seven for predictive weight, (iii) the clinical features "diabetes" and "treatment with β-blockers" had lowest predictive values, and (iv) challenging the model with a test data set yielded high accuracy in risk prediction. Data included in this study were collected in the period from January 2006 to February 2014. The study conforms to the Declaration of Helsinki and was approved by the ethics committee of Dresden University of Technology (No. EK790799). Each patient gave written informed consent. Right atrial appendages were obtained from 221 patients with SR and 158 patients with chronic AF at the time of open-heart surgery. The criteria for a patient to be considered in permanent AF were history of ECG-documented AF and symptoms of AF for ≥6 months. Patients with paroxysmal or intermittent AF were excluded. Demographic and clinical data of the patients are summarized in Table 1 and are comparable to the characteristics published previously [6, 7, 15] . The MannWhitney U test was applied for a complete statistical analysis of all features between the SR and AF group of patients, the results are provided in supplementary Either free-running trabeculae or trabeculae together with attached atrial wall were dissected and mounted on the bottom of a 5-ml organ bath perfused with 50 ml of recirculating, oxygenized Tyrode's solution at a flow rate of 7 ml/ min at 36 ± 1 °C (composition in mM: 126.7 NaCl, 0.42 NaH 2 PO 4 , 22 NaHCO 3 , 5.4 KCl, 1.8 CaCl 2 , 1.5 MgCl 2 , pH 7.4 when equilibrated with 5 % CO 2 in O 2 ). Preparations were electrically stimulated at a single constant rate of 1 Hz with isolated square-wave stimuli of 1 ms duration, two times threshold intensity. Transmembrane potentials were recorded with glass microelectrodes filled with 2.5 M KCl. Tip resistances of the electrodes were between 20 and 80 MΩ. Both timing of the driving stimuli and preprocessing of the transmembrane potential responses were carried out with a computer-aided AP recording system.. The trabeculae were used for various different experiments; however, each experiment was preceded by a 60-min equilibration period during which the preparations were allowed to stabilize and residual BDM was completely washed out. At the end of the equilibration period, 10 consecutive APs were averaged and analysed for the following parameters ( Fig. 1 ): resting membrane potential, RMP (mV), action potential amplitude, APA (mV), action potential duration at 20, 50, and 90 % of repolarization (APD 20 , APD 50 and APD 90 in ms), maximum rate of depolarization, dV/dt max (V/s), and the "plateau potential" (PLT 20 ) defined as the mean absolute membrane potential (mV) in a 5-ms window starting from 20 % of APD 90 .. The clinical parameters chosen for our data set are demographic characteristics such as age, weight, body mass index (BMI), etc., clinical conditions associated with heart disease, hemodynamic parameters, and medication. Routine methods and clinical laboratory tests were used for assessment of clinical parameters. For example, left atrial or left ventricular enddiastolic diameter, right ventricular systolic pressure, left ventricular end-diastolic pressure, left ventricular end-diastolic diameter, ejection fraction, cardiomyopathy, left ventricular posterior wall thickness, interventricular septum thickness, mitral or aortic valve insufficiency, aortic stenosis, and patent foramen ovale were determined with trans-thoracal or transesophageal echocardiography. Right heart catheterization was required for diagnosis of pulmonary hypertension and sometimes for measuring right ventricular systolic pressure. Right coronary artery stenosis and number of occluded vessels were diagnosed by coronary angiography. Chronic pulmonary obstructive disease (CPOD) was quantified with spiro-ergometric methods. The complete list of all electrophysiological and clinical parameters is given in Table 2 .

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