Fast Detection of Common Geometric Substructure in Proteins We consider the problem of identifying common three-dimensional substructures between proteins. Our method is based on comparing the shape of the α-carbon backbone structures of the proteins in order to find 3D rigid motions that bring portions of the geometric structures into correspondence. We propose a geometric representation of protein backbone chains that is compact yet allows for similarity measures that are robust against noise and outliers. We represent the structure of the backbone as a sequence of unit vectors, defined by each adjacent pair of α-carbons; we then define a measure of the similarity of two protein structures based on the RMS (root mean squared) distance between corresponding orientation vectors of the two proteins.Our measure has several advantages over measures that are commonly used for comparing protein shapes, such as the minimum RMS distance between the 3D positions of corresponding atoms in two proteins. This new measure behaves well for identifying common substructures, in contrast with position-based measures where the nonmatching portions of the structure dominate the measure. At the same time, it avoids the quadratic space and computational difficulties associated with methods based on distance matrices and contact maps. We show applications of our approach to detecting common contiguous substructures in pairs of proteins, as well as the more difficult problem of identifying common protein domains (i.e., larger substructures that are not necessarily contiguous along the protein chain). As an increasing number of protein structures become known, the need for algorithms to analyze three-dimensional conformational structure increases as well. The search for common substructure is of value in uncovering relationships among different proteins -for inferring similarities in function and discovering common evolutionary origins. There is now widespread agreement that similarities among distantly related proteins are often preserved at the level of three-dimensional structure, even after very little similarity remains at the sequence level [7] . We are interested in developing efficient comparison methods for threedimensional protein structures.. The goal of our work is to automatically identify common substructures shared by two proteins, based on similarity in their three-dimensional structure. A key element of our approach is the development of a geometric notion of similarity that is appropriate to the task of protein structure comparison. This is a problem that has received considerable attention in the biological research literature (cf. [22] ), and a variety of different methods have been proposed.. For protein chains that are very similar (e.g., candidate structures produced in crystallography experiments), a common measure of similarity is the RMS (root mean square) distance between the positions of corresponding atoms of the proteins, after the proteins have been superimposed by a three-dimensional rigid motion (e.g. [10, 19] ). While this approach is reasonable for comparing two structures that are highly similar, it does not work well for finding similar substructures in otherwise dissimilar proteins. The difficulty with dissimilar proteins is that the portions of the structure that do not match dominate the RMS value, making it difficult to identify matching substructures. This is an instance of the classical issue of outliers, or bad data, dominating the measure in fitting or estimation problems.. Other methods for structural matching address the limitations of techiques that use the RMS distance. One widespread set of approaches is based on comparing the distance matrices or contact maps of two proteins (see e.g. [3, 9, 13, 24, 25] ). The distance matrix records all pairwise distances between selected atoms within a given protein -often for all the α-carbons of the residues. For a protein with n residues, such a distance matrix therefore contains O(n 2 ) entries. The distance matrix representation is invariant with respect to the position and orientation of the protein; thus the distance matrices for two proteins can be compared directly, without the need to find a rigid motion superimposing them as RMS distance approaches require. The use of distance matrices has a number of drawbacks, however. First of all, a full distance matrix is quadratic in the size of the protein it represents. Moreover, algorithms for aligning distance matrices have typically been computationally expensive; identifying corresponding substructures between two proteins requires finding corresponding submatrices that are nearly the same, and this appears to be a difficult optimization problem (e.g. [7, 9] ).. Finally, a different set of approaches to structure comparison is based on using a purely local representation of a protein chain. Some common local representations are the set of (φ, ψ) torsion angles along the backbone [3, 22] ; the set of virtual-bond angles and virtualbond dihedral angles [11, 12, 21] between consecutive α-carbons; and variations on these (e.g. [17, 18] ). Such representations are compact and independent of the position and ori-entation of the protein; however, there are settings in which two proteins with similar local representations can be geometrically very different. Consider, for example, two protein structures that are the same except for a bend in the middle. Although the sets of threedimensional coordinates and pairwise distances of the proteins will be quite different, the data in a local representation of the two proteins will be the same except for those residues directly at the bend.. In this paper we present a new algorithm for efficiently detecting common substructures in proteins, based on a comparison methodology for protein chains that has both global and local aspects. For a given protein, we begin with the sequence of α-carbons that form its backbone chain. Rather than encoding the three-dimensional coordinates of these atoms, we record the unit vector v i in the direction from the i th α-carbon to the (i + 1) st α-carbon along the chain. The distance between successive α-carbons is essentially a fixed constant (approximately four angstroms), and thus this set of unit vectors captures the structure of the backbone. Indeed, these unit vectors correspond to the virtual-bond vectors of the protein [11, 12, 21] .. By chaining the unit vectors v i end to end, we obtain the standard model of a protein as a sequence of α-carbons in space. By placing all of the unit vectors at the origin of R 3 , we can view the protein as a sequence of points on the unit sphere. We will represent the protein in this latter way: by its collection {v i } of unit vectors with respect to a common origin. Thus we see that our representation has both a local and a global nature: although each individual vector v i records the position of the (i + 1) st α-carbon in a local reference frame centered at the i th α-carbon, our representation implicitly situates all the unit vectors {v i } in a common global reference frame. This is contrast to traditional approaches that have used virtual bonds among α-carbons to define purely local representations.. Our representation is therefore compact, having size O(n) for a protein with n residues, and it reflects global aspects of a protein's structure -introducing a single bend in the middle of structure affects all the vectors v i that come after the bend. Our unit-vector representation is not independent of the orientation of the protein, since the vectors {v i } are placed in a global frame of reference. However, we will see that unlike representations based on raw three-dimensional coordinates, the unit-vector representation allows for geometric similarity measures that are robust against outliers.. Our algorithm for comparing two protein chains, based on the unit-vector representation, consists of the following three steps.. 1. Determine a small set of shifts, or contiguous alignments, that are likely to include those alignments that bring matching substructures into 3D correspondence.. 2. For each shift chosen above, determine the contiguous substructures for which there is a 3D geometric alignment (i.e., substructures of the two proteins that can be superimposed using a 3D rigid motion).. The first step of our algorithm runs in O(n log n) time, where n is the number of α-carbons in the larger of the two proteins being compared. The second step takes O(n) time for each shift identified in step one; typically only the best 10 shifts provide any useful information, but our current implementation checks the best 20. The running time of the third step depends on s, the number of substructures found in the second step.. Our approach makes use of two very different kinds of alignment. The first of these, employed in Step 1, is the alignment of two sequences by a simple shift relative to one another. We refer to this as contiguous alignment, as it is simpler than the standard biological notion of sequence alignment (which further allows for insertions and deletions into a sequence). More formally, for integers k = 0, 1, . . . , n − 1, we match each residue i of the shorter protein with residue i + k of the longer protein. Here addition is taken modulo n, so that our shift includes a "wrap-around". The wrap-around ensures that each unit vector in protein A is compared against each unit vector in protein B.. The second kind of alignment that we employ is geometric alignment, which is the 3D positioning of two proteins such that corresponding atoms in the two structures are approximately superimposed.. Our method will be based on a variant of the RMS distance, measuring differences between the global orientation vectors v i at corresponding α-carbons of two proteins, rather than measuring differences between the positions of the α-carbons themselves. The key underlying observation is that the difference between two orientation vectors is bounded by a small constant, whereas the distance between two points can grow arbitrarily large. This makes the unit-vector RMS (URMS) that we propose naturally robust with respect to differences between nonmatching parts of the structure, whereas the conventional position-RMS is not.. The RMS distance. A basic method for determining geometric similarity between two sets of points is the root mean square (RMS) distance on point sets. This measure of distance requires a one-to-one correspondence between the point sets. The standard (position-based) RMS distance between point sets A = {a 1 , . . . , a n } and B = {b 1 , . . . , b n } is defined as the square root of the sum of the squared distances between the points of A and the corresponding points of B. Generally one seeks the best possible RMS distance; that is, the RMS distance between A ′ and B where A ′ is the set A after application of the 3D rigid motion that minimizes the RMS distance. We refer to this as the minimum RMS distance between A and B.. To compute the minimum RMS distance, first transform A to make it have the same center-of-mass as B. Then compute the correlation matrix for A and B. This is a 3 × 3 matrix in which the (p, q) entry is n i=1 a i,p b i,q . This matrix is factored using the singular value decomposition; the resulting factors can be used to construct in constant time both (1) the orthogonal matrix that brings A into the closest possible match with B and (2) the resulting RMS distance. For a concise description of the algorithm and an explanation of why it works see Golub and Van Loan [6] (where it is referred to as the orthogonal Procrustes problem) or Lesk [10] .. The minimum RMS distance between two sets of atoms in R 3 is useful primarily when aligning two structures that are extremely similar. Thus, it is widely used for aligning structures produced in the course of crystallographic or NMR analysis of molecules.. It is less appropriate for comparing structures that have only a distant similarity. This is due to its sensitivity to outliers. Indeed, a few outliers can have a significant effect on the resulting minimum RMS distance. For instance, consider sets A and B, each with n points, where the minimum RMS distance between A and B is 0. Now suppose we take the point b 1 and gradually move it along a straight line. As we move b 1 , the minimum RMS distance between A and B increases without bound, and the rigid motion corresponding to this minimum distance also changes so that the congruent point sets A − {a 1 } and B − {b 1 } become arbitrarily far apart. Thus a small number of gross outliers can hide a large shared substructure.. Another issue with the minimum RMS distance is that points far from the center of mass are, in effect, weighted more heavily than points near the center of mass. Consequently, a common "core" shared by two structures is difficult to detect using the minimum RMS distance. This is problematic in the case of proteins, where some crucial similarities occur near the center of mass.. Our Approach. Using an RMS distance on the unit-vector representation {v i } allows us to avoid the drawbacks discussed above while retaining the computational efficiency of the minimum RMS calculations. Recall our view of the representation {v i } as consisting of a sequence of points on the unit sphere in R 3 . To compare two proteins, with sets of unit vectors {v i } and {w i }, we compute the minimum RMS distance between the two sets {v i } and {w i }, viewed as subsets of the unit sphere. Since we wish the origins of the vectors to remain fixed in space, we minimize the RMS distance only over possible rotations of the vectors, not over translations. Henceforth we use the term position-RMS to refer to the standard, position-based, minimum RMS distance; we use the term unit-vector RMS (URMS) to refer to the minimum RMS distance for a pair of sets in our unit-vector representation.. Because the maximum squared distance between any two unit vectors is 4, no single outlier can have a large effect on the URMS. As a result, the URMS exhibits a natural resilience to the presence of outliers, such as those arising due to portions of two protein structures that do not match.. Other Related Work. Above, we have indicated a number of the approaches that have been proposed for protein structure comparison. Here, we discuss several of these in more detail; see [2, 8, 22] for recent surveys on the topic.. There has been work on discovering geometric alignments that are not required to respect the order of the sequence, using distance matrices on α-carbons and secondary structural elements of proteins (Vriend and Sander [24] , Holm and Sander [9] , Grindley et al. [5] ). In particular, Vreind and Sander [24] use the distance matrix to find pairs of matching fragments of two proteins and then combine them into larger units which are compatible in R 3 . The latter step is based on comparisons of the centers of mass of the fragments and of relative rotations between combined fragments. Yee and Dill [25] use distance matrices as part of an algorithm whose high-level structure is similar to ours. They also search over contiguous alignments of two protein sequences to discover similarities, but their notion of similarity is different from ours. It is based on shifting the alignments of the distance matrices of the two proteins and computing the "distance" between the matrices (by means of the Frobenius norm). The shifts that give the smallest norms are predicted to yield matching contiguous alignments. Though the running time is not discussed explicitly in their work, it is easy to see that it can be O(n 3 ). (It is possible that an application of the Fast Fourier Transform could improve this to O(n 2 log n).) There has also been work by a number of groups on extending classical sequence alignment algorithms to handle pairwise relationships among residue positions (Taylor and Orengo [23] , Orengo et al. [14] , Sali and Blundell [20] ).. Rackovsky and Scheraga [17, 18] develop a purely local representation of protein chains, by defining discrete analogues of curvature and torsion in terms of the virtual bond vectors. They propose a method of searching for structural similarities based on comparing these parameters for different proteins [16, 18] .. Fischer et al [4] apply geometric hashing to find matching pairs of atoms (alpha carbons) between two molecules. The common subsequences they find are not necessarily consecutive. To use geometric hashing, a base molecule is preprocessed to find all possible matching coordinate frames. This may involve up to O(n 3 ) pre-processing and storage, since a rigid motion in three dimensions is specified by its action on three points. (Distance constraints imposed by the protein can improve this bound somewhat.) Given a second target molecule, each triplet of points "votes" for a rigid motion with respect to the base molecule; a large number of common votes indicates a possible large match between the two molecules. Assuming that the rigid motions are indexed in a well-distributed hash table, the running time is O(n 3 ). Recent work on this technique has suggested that it may be possible to reduce the running time for protein matching applications to a roughly quadratic bound [15] .

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Runtime Resonance Noise Reduction with Current Prediction Enabled Frequency Actuator Abstract-Power delivery network (PDN) is a distributed resistance-inductance-capacitance (RLC) network with its dominant resonance frequency in the low-to-middle frequency range. Though high-performance chips' working frequencies are much higher than this resonance frequency in general, chip runtime loading frequency is not. When a chip executes a chunk of instructions repeatedly, the induced current load may have harmonic components close to this resonance frequency, causing excessive power integrity degradation. Existing PDN design solutions are, however, mainly targeted at reducing high-frequency noise and not effective to suppress such resonance noise. In this work, we propose a novel approach to proactively suppress this type of noise. A method based on the high dimension generalized Markov process is developed to predict current load variation. Based on such prediction, a clock frequency actuator design is proposed to proactively select an optimal clock frequency to suppress the resonance. To the best of our knowledge, this is the first in-depth study on proactively reducing instruction loop induced PDN resonance noise at the runtime. The continuous scaling trends of higher operating frequency, lower power supply voltage, and more functionality for integrated circuits have made it extremely challenging to design a reliable power delivery network (PDN). There are two dominant types of noise present in a PDN: peak noise and resonance noise [2] . Peak noise usually occurs when the instantaneous switching current load becomes maximum [8] for a short duration with its energy spectrum lying in the high-frequency range [2] . Abundant research has been done to minimize peak noise for PDN design (e.g., [3] , [7] , [10] , [13] ).. Resonance noise is a result of the distributed resistance-inductance-capacitance (RLC) characteristics of the PDN, which includes parasitic inductance of interconnect and decoupling capacitance. With details to be discussed in Section II, it compromises chip performance, hold-time margins, and gate oxide integrity [1] , [12] . Despite the importance of resonance noise for reliable PDN design, resonance noise suppression has not gained enough attention in the electronic design automation (EDA) community. The traditional solutions, such as adding more passive capacitors to diminish the supply's ac impedance, more supply pins, using C4 packages to lower inductance, are not effective to suppress the resonance noise, as both off-chip Y. Shi and even on-board capacitors are self-resonant at frequencies well below f res . Recently, Ang et al. [1] proposed to dynamically switch on-chip decoupling capacitors to suppress resonance noise for microprocessors' PDN designs, while the authors of [12] provided an on-die resonance-suppression circuit that uses band-limited active damping to reduce resonance noise. However, in addition to the large area overhead and leakage issues due to decaps, all these approaches are retroactive, i.e., they only remedy the noise problem when the noise problem has occurred already. However, this is often too late: Wrong values might be latched at the rising/falling edge of the clock right after the violation occurs, thus causing a full save and restore of the whole architecture state later. To avoid such performance lost, a better way would be proactively suppressing the resonance noise when such issues are predicted to happen soon. In this paper, we propose a proactive PDN design approach to suppress resonance noise by dynamically adjusting run-time clock frequency with the aid of a frequency actuator, which contains on-chip dynamic power supply current sensors to measure the dynamic current loads and programmable phase-locked loops (PLLs) to change clock frequencies. Compared with baseline design without frequency actuator, experimental results show that the frequency actuator without current prediction reduces maximum noise by 16% and average noise by 30%, while the frequency actuator with current prediction reduces maximum noise by 77% and average noise by 85%.. The remainder of this paper is organized as follows. We motivate the study of this work in Section II, and present the problem formulation and overall design methodology in Section III. We develop the stochastic current prediction and optimal frequency selection algorithm in Section IV. The experimental results are presented in Section V and concluding remarks are given in Section VI. Because of the distributed RLC characteristics of a PDN, resonance noise at the low-to-middle frequency range significantly affects the reliability of a PDN and chip performance. In contrast to existing retroactive solution that only remedies the noise problem when the noise problem has occurred already, we have proposed a novel design approach to proactively suppress resonance noise. To achieve this goal, we have developed an efficient stochastic current load prediction method based on a generalized Markov process modeling. We have presented a frequency actuator that utilizes both on-chip dynamic current sensors and a programmable PLL for frequency adjustment. Significant resonance noise reduction has been achieved on industrial testcases.

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IT and Firm Agility: An Electronic Integration Perspective Abstract Firms invest substantial sums of money in IT with the hope of increasing efficiency, effectiveness, productivity, and profits (Banker, Bardhan, Chang, & Lin, 2006; Davamanirajan, Kauffman, Kriebel, & Mukhopadhyay, 2006; Mukhopadhyay & Kekre, 2002; Oh & Pinsonneault, 2007) . With the recent surge in environmental turbulence, increased competition, volatile consumer demand, and rapid product obsolescence, firms are also increasingly concerned with their agility, that is, the ability to sense and respond to opportunities and threats with ease, speed, and dexterity (D'Aveni, 1994; Goldman, Nagel, & Preiss, 1995) .. Our understanding of the relationship between IT and firm agility is limited. Most literature on the IT business value to date has largely overlooked agility as a potential outcome, focusing instead on standard firm performance metrics (Oh & Pinsonneault, 2007) . The literature on agility has mainly focused on conceptual concerns and, more recently, on the benefits of agility (Galliers, 2007; Hitt, Keats, & DeMarie, 1998; Overby, Bharadwaj, & Sambamurthy, 2006; Rai, Patnayakuni, & Seth, 2006; Sambamurthy, Bharadwaj, & Grover, 2003; Weill, Subramani, & Broadbent, 2002) . The few papers that have looked at the link between IT and agility suggest a positive relationship (Sambamurthy et al., 2003; Tallon & Pinsonneault, 2011) . For example, IT was found to allow firms to sense their customers' needs and respond to their needs through close collaboration with suppliers (Rai et al., 2006) . Dell used IT to blur organizational boundaries with its suppliers and improve its ability to sense and respond to opportunities and threats in the market (Magretta, 1998) . This paper extends the literature by analyzing the link between IT and firm agility through an electronic integration perspective. We suggest that the relationship between IT and agility depends on the degree of electronic integration (i.e., the degree to which IT applications work as a functional whole with other internal and/or external IT applications) achieved in a firm. Electronic integration affects agility because it facilitates the efficient and effective communication and sharing of specialized knowledge among distinct organizational components (internal integration) and with suppliers and customers (external integration) 1 . Electronic integration also facilitates the coordination of process activities, both within a firm and with its business partners and customers (Barki & Pinsonneault, 2005) . Thus, we expect that two factors -how knowledge is used and how processes are coupled -play an important mediating role in the relation between IT and firm agility (Dyer & Singh, 1998; Saraf, Langdon, & Gosain, 2007) .. Our paper contributes to the literature in three ways. First, we develop an electronic integration perspective to explain the effects of IT on firm agility and, as such, we extend Sambamurthy et al.'s (2003) work on the topic. Second, the paper explains how IT affects the two capabilities of agility (i.e., sensing and responding) through the mediation of knowledge exploration, knowledge exploitation, and process coupling. This mediation process seems key to understanding the relationship between IT and firm agility. Finally, the paper contributes to the literature on the business value of IT by showing how IT affects an intermediate outcome variable (agility) , which, in turn, is likely to affect the typical organizational outcomes studied in the extant literature (e.g., efficiency, cost, profit, revenues) (Tallon & Pinsonneault, 2011) .. The rest of the paper is organized as follows. Section 2 presents our framework and the propositions that link integration to agility through the mediation of knowledge exploitation, knowledge exploration, and process coupling. Section 3 presents the discussion and section 4 the contributions of our paper. The paper concludes by elaborating some avenues for future research. IS research provides significant insights into how IT affects firm agility (Overby et al., 2006 , Sambamurthy et al., 2003 Tallon & Pinsonneault, 2011) . We now need to understand how specific IT characteristics (such as integration, flexibility, and so forth) affect the two key capabilities of agility: sensing and responding. It is also important to better understand the role of mediating variables, such as firm knowledge and process coupling. This paper extends the literature on the topic by analyzing how two key dimensions of IT, internal and external integration, affect the two capabilities of agility (sensing, responding). We also looked at how knowledge and process variables mediate the IT-agility relationship. By doing so, we were able to explain how each electronic type of electronic integration affects the sensing and responding capabilities of the firm. We argued that internal integration has a primary enabling effect on the responding component of firm agility through the mediating role of knowledge exploitation and process coupling. External integration has a primary enabling effect on the sensing element of firm agility through the mediating role of knowledge exploration.. Our framework helps firms understand in which agility quadrant they reside. In addition, the framework can also be helpful for understanding how a firm evolves from one situation to another. Essentially, there are three possible paths for a stagnant firm to become agile. First, a stagnant firm can move toward agility by achieving internal integration. This internal integration improves the firm's responsiveness and allows it to coordinate internal activities. This places the firm in the responding firm quadrant. Further improvements in external integration will enable the move toward the agile firm quadrant. This is the most likely path because it starts with improving the organization's infrastructure and then making improvements across organizational boundaries (Venkatraman, 1991) . In order to gain agility, it is important to first integrate internal units in a way that they become responsive to each other's needs and start behaving as a unified whole (Barki & Pinsonneault, 2005) . Once internal integration is achieved, external integration complements organizational responsiveness by enabling access to greater insights from outside partners.. DDM, a Canadian plastics manufacturing firm, became responsive to a highly competitive environment by following this path (Saeed, Malhotra, & Grover, 2005) . DDM already had an enterprise system in place that allowed coordination among internal units. What DDM lacked was connections with external suppliers. The company introduced an Internet-based system called SupplyWEB that allowed integration with external partners, which enabled it to lower its inventory and reduce uncertainty in its environment by gaining greater visibility across organizational boundaries.. Another potential path toward agility is one where a firm achieves external integration first. The external integration improves the sensing capability of the firm and places it in the sensing firm quadrant. This path, however, is much more uncertain and is more risky. Without first integrating internal resources, the organization might find itself unable to quickly respond to opportunities. Challenges associated with this path are rife in the EDI literature (Curtin, Kauffman, & Riggins, 2007; Riggins & Mukhopadhyay, 1994) . For instance, research shows that firms that chose to implement EDI with partners (external integration) without having internal integration of processes gained limited benefits and often did not see any performance improvements (Riggins & Mukhopadhyay, 1994) . More recent research on RFID-enabled supply chains has also confirmed that integration with external partners without the capability to seamlessly handle information among internal departments results in failure to see performance gains (Asif & Mandviwalla, 2005) .. Finally, another path toward the agile-firm quadrant is to attain both internal and external integration at the same time. This is a difficult strategy because it involves simultaneously handling several organizational variables (processes, units, technologies, cultures) and entails important implementation challenges and barriers (Barki & Pinsonneault, 2005) . However, if achieved, it can result in improved agility over competitors. Harris Tea, which has an impressive 160-year history of procuring and blending teas, is the largest blender and packer of private label teas in North America. As its business grew, Harris Tea struggled with maintaining visibility and coordination among internal units and with partners and customers, which were critical for inventory operations and customer support. To solve these problems, Harris Tea implemented an enterprise system that integrated internal operations as well as

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A New Watermarking Method for 3D Models Based on Integral Invariants Abstract-In this paper, we propose a new semifragile watermarking algorithm for the authentication of 3D models based on integral invariants. A watermark image is embedded by modifying the integral invariants of some of the vertices. In order to modify the integral invariants, the positions of a vertex and its neighbors are shifted. To extract the watermark, all the vertices are tested for the embedded information, and this information is combined to recover the watermark image. The number of parts of the watermark image that can be recovered will determine the authentication decision. Experimental tests show that this method is robust against normal use modifications introduced by rigid transformations, format conversions, rounding errors, etc., and can be used to test for malicious attacks such as mesh editing and cropping. An additional contribution of this paper is a new algorithm for computing two kinds of integral invariants.Index Terms-Semifragile watermark, 3D model watermarking, integral invariants. We have presented a semifragile watermarking method based on integral invariants. It is a spatial domain method robust against rigid transformations and noise attacks. Experimental tests show that this method is suitable to determine whether a model was attacked.. We could improve our algorithm by increasing its embedding capacity, currently limited to two integral invariants. One solution would be using multiresolution analysis methods to simplify the model and embed a watermark at the corresponding simplified model vertex. Another solution would be to find a method to simultaneously change four kinds of integral invariants. These solutions are the directions of our future work. Yu-Ping Wang is currently a PhD student in the Department of Computer Science and Technology, Tsinghua University, Beijing. He is also with the Tsinghua National Laboratory for Information Science and Technology. His research interests include digital watermarking, computer graphics, geometric modeling, and processing.. Shi-Min Hu received the PhD degree from Zhejiang University in 1996. He is currently a chair professor in the Department of Computer Science and Technology, Tsinghua University, Beijing. He is also with the Tsinghua National Laboratory for Information Science and Technology. His research interests include digital geometry processing, video processing, rendering, computer animation, and computer-aided geometric design. He is on the editorial board of Computer Aided Design. He is a member of the IEEE.. . For more information on this or any other computing topic, please visit our Digital Library at www.computer.org/publications/dlib.

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A Note on Low-Correlation Zone Signal Sets In this correspondence, we present a connection between designing low-correlation zone (LCZ) sequences and the results of correlation of sequences with subfield decompositions presented in a recent book by the first two authors. This results in LCZ signal sets with huge sizes over three different alphabetic sets: finite field of size, integer residue ring modulo , and the subset in the complex field which consists of powers of a primitive th root of unity. We show a connection between these sequence designs and ldquocompletely noncyclicrdquo Hadamard matrices and a construction for those sequences. We also provide some open problems along this direction. Recently, there have been some interesting developments involving quasi-synchronous (QS) code-division multiple-access (CDMA) communication systems and on the design of sequences with low-correlation zone (LCZ) that can be used in such systems [2] , [12] , [13] , [8] , [11] , [14] .. This correspondence will describe a general approach to the design of LCZ sequences using the results on sequences with subfield decompositions, presented in [3, Ch. 8] written by the first two authors. The above known cited results on LCZ sequences can be obtained easily from this general setting.. The connection between an optimal set of LCZ sequences (in terms of family size) with subfield factorization and Hadamard matrices have been observed now by many others, e.g., see [14] . We show, in particular, that the LCZ sequences in this correspondence are connected to Hadamard matrices of "completely noncyclic type."

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Minimum energy control of positive continuous-time linear systems with bounded inputs The minimum energy control problem for positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example. A dynamical system is called positive if its trajectory starting from any nonnegative initial state remains forever in the positive orthant for all nonnegative inputs. An overview of the state of the art in positive system theory is given by Farina and Rinaldi (2000) as well as Kaczorek (2001) . A variety of models having positive behavior can be found in engineering, economics, social sciences, biology and medicine, etc.. Positive fractional linear systems were investigated by Kaczorek (2008a; 2011b; 2011c; 2012) . The stability of fractional linear 1D discrete-time and continuous-time systems was investigated by Busłowicz (2008) , Dzieliński and Sierociuk (2008a) as well as Kaczorek (2012) , and that of 2D fractional positive linear systems by Kaczorek (2009) . The notion of the practical stability of positive fractional discrete-time linear systems was introduced by Kaczorek (2008b) . The minimum energy control problem for standard linear systems was formulated and solved by Klamka (1991; 1983; 1976; 2010; 1993; 1977) , while for 2D linear systems with variable coefficients by Kaczorek and Klamka (1986) . The controllability and minimum energy control problems of fractional discrete-time linear systems were investigated by Klamka (2010; 1993) . The minimum energy control of fractional positive continuous-time linear systems was addressed by Kaczorek (2013a) , and for descriptor positive discrete-time linear systems by the same author (Kaczorek, 2013b) .. In this paper the minimum energy control problem for positive continuous-time linear systems with bounded inputs will be formulated and solved. The paper is organized as follows. In Section 2 basic definitions and theorems of positive continuous-time linear systems are recalled and necessary and sufficient conditions for the reachability of positive systems are given. The minimum energy control problem of positive linear systems with bounded inputs is formulated and solved in Section 3. Sufficient conditions for the existence of a problem solution are established and a procedure for computation of the optimal inputs and the minimum value of the performance index are also presented. Concluding remarks are given in Section 4.. The following notation will be used: R is the set of real numbers, R n×m is the set of n × m real matrices, R n×m + is the set of n × m matrices with nonnegative entries and R n + = R n×1 + , M n is the set of n × n Metzler matrices (real matrices with nonnegative off-diagonal entries), I n is the n × n identity matrix.

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Fast equilibration of coarse-grained polymeric liquids The study of macromolecular systems may require large computer simulations that are too time consuming and resource intensive to execute in full atomic detail. The integral equation coarse-graining approach by Guenza and co-workers enables the exploration of longer time and spatial scales without sacrificing thermodynamic consistency, by approximating collections of atoms using analytically-derived soft-sphere potentials. Because coarse-grained (CG) characterizations evolve polymer systems far more efficiently than the corresponding united atom (UA) descriptions, we can feasibly equilibrate a CG system to a reasonable geometry, then transform back to the UA description for a more complete equilibration. Automating the transformation between the two different representations simultaneously exploits CG efficiency and UA accuracy. By iteratively mapping back and forth between CG and UA, we can quickly guide the simulation towards a configuration that would have taken many more time steps within the UA representation alone. Accomplishing this feat requires a diligent workflow for managing input/output coordinate data between the different steps, deriving the potential at runtime, and inspecting convergence. In this paper, we present a lightweight workflow environment that accomplishes such fast equilibration without user intervention. The workflow supports automated mapping between the CG and UA descriptions in an iterative, scalable, and customizable manner. We describe this technique, examine its feasibility, and analyze its correctness. Despite considerable advancements in hardware and software technologies for supporting large-scale molecular simulations, computational chemists are confined to simulating relatively small systems compared to most laboratory experiments and real world bulk measurements. This constraint quickly becomes apparent in the simulation of polymer melts, which is important for materials science applications. Polymers are macromolecules that consist of repeating units of monomers (such as CH 2 ) that form long molecular chains. When simulating polymeric systems, many interesting properties depend on the chain length [20] , such as the boiling/melting points, the viscosity, and the glass transition temperature. Even with a small number of molecules, however, it is computationally expensive to simulate chains with more than 10 5 monomers each, which is a reasonable chain length to study. Limited memory space also constrains simulations to 10 6 -10 10 total atoms, even on large allocations of modern supercomputers. Considering that a drop of butane contains approximately 10 20 atoms suggests that these capabilities do not come close to bulk experiments in the laboratory.. Defining a new representation of the polymer as a chain of soft colloidal particles greatly reduces the amount of information to be collected and controlled, which speeds up the simulation. It is well known that modeling fewer colloidal particles with an appropriate potential decreases the degrees of freedom and computational requirements by an amount proportional to the granularity [3] . The representation of a polymer as a chain of soft blobs also allows the chains to more easily cross each other, decreasing the required time for the simulation to find the equilibrium structure. However, the information on the molecular local scale needs to be restored at the end of the simulation to account for properties on the united atom (UA) scale. In a nutshell, it is important to alternate between the coarse-grained (CG) representation (which speeds up the simulation) and the UA representation (which conserves the local scale information). By quickly switching back and forth from UA to CG, we open doors to new studies of polymeric systems while maintaining simulation accuracy and efficiency. While optimizing the computational performance of CG codes is important, without a way to incorporate UA-level detail, CG efficiency has relatively less value. Therefore, this paper focuses on integrating an approach for conducting simulations that exploit both CG efficiency and UA accuracy (Fig. 1) .. Unfortunately, it is not trivial to automate the transformation between the CG and UA representations for general sets of input parameters. Accomplishing the overall task involves multiple processing steps, with different applications, programming languages, naming schemes, and data representations. This issue is common to many other scientific software environments and is collectively referred to as the scientific workflow problem [10] . In short, the collection of all the required steps to conduct an overall research study comprises a workflow that may consist of several large simulations, real-world experiments, human intervention and analysis, and more. In this paper, we present a lightweight and customizable approach for creating an effective scientific workflow in the context of our CG/UA simulation experiments. We discuss techniques that are general to other computational problems and explore new ideas that are not prevalent in other more heavyweight workflow toolkits.. The paper is organized as follows: Section 2 contains background information regarding the CG approach and integral equation theory, Section 3 discusses the design and implementation of the fast equilibration workflow, Section 4 presents our experiments in evaluating the workflow, Section 5 discusses related work, and Section 6 contains concluding remarks. Coarse-graining methods benefit from reduced computational requirements, which expands our capabilities towards simulating systems with a realistic number of atoms relative to laboratory bulk experiments. However, without integrating local scale UA information, configurations cannot equilibrate as completely. This paper focuses on a workflow based solution for exploiting CG efficiency and UA accuracy by iterating between UA and CG representations towards convergence. By utilizing a lightweight scheme for propagating parameters, controlling simulation input files via template processing, and generating multi-block potentials in the CG description, we have constructed an automated system for conducting large scale experiments of polymer liquid systems. We have verified the correctness of the approach of mapping between the atomic and coarse-grained descriptions by comparing the radial distribution function of a long-running atomic simulation with a series of iterations through the workflow.. The fast equilibration workflow system enables the running of experiments that were previously not possible, such as parameter sweeps across different densities, CG granularities, temperatures, and more. Our simple workflow system is based on Python, and incorporates support for parallel (MPI) simulations, data provenance, and template processing. Future work will examine and optimize the computational efficiency, introduce more powerful workflow features, and explore more thorough verifications of correctness. Related research supports the notion that the CG representation equilibrates more quickly than fully atomistic replicas, and that re-expressing a melt in the UA description can more completely equilibrate the system [3] . While our verification of h mm (r) is encouraging for verifying correctness, this function is known to be relatively insensitive to certain geometric flaws, particularly in bonding. For instance, it may be possible to have a well-matched h mm (r), but still have occasional bond lengths that are unphysical. Instead, Auhl [2] evaluates R 2 (n) /n and shows that this phenomenon may occur and can be fixed. Future work will examine R 2 (n) /n in Stage 7 of the workflow (which may be less expensive to compute than h mm (r)).. Research and development on scientific workflows is pervasive. Some of the more popular frameworks include Kepler (with recent notable applications in drug design [11] and support of distributed data-parallel patterns, such as MapReduce [22] ) Pegasus [9] , and Taverna [18] . Other related work focuses on the intricacies of data modeling and dataflow in scientific workflows [4] . Instead of committing to a full-blown workflow framework up-front, this paper has focused on the advantages of using a considerably lightweight system for managing input parameters while benefiting from simple data provenance and template processing. As far as we are aware, template processing capabilities within other scientific workflows is limited, and is not to be confused with reusable "workflow templates", which is a powerful plug-and-play concept found in any good workflow suite. Our future work may consider porting our implementation to a more powerful workflow system, but we are so far content with the portability, ease of customization, lack of a GUI, and template processing features within this work. This section briefly reviews the coarse-grained approach based on integral equation theory. We consider a homopolymer fluid (in which all monomers are the same type) with molecular number density, m , consisting of n polymer chains. Some number of monomer sites, N, makes up each polymer chain, where each site is usually taken to be either a CH, CH 2 or CH 3 group. This bead-spring description is the UA simulation model. Within the UA description, the Polymer Reference Inter Site Model (PRISM) site-averaged Ornstein-Zernike equation relates the relevant pair correlation functions in Fourier Space [21] :. where the "mm" superscript denotes monomer-monomer interactions and h mm (k) is the Fourier transform of the total correlation function, h mm (r). In fact, h mm (r) = g mm (r) − 1, where g(r) is the well known radial distribution function. Also from Eq. (1), c mm (k) is the direct correlation function, ω mm (k) is the intra-chain structure factor, and is the monomer site density, given as = N m . The CG representation can be fully represented as a function of the physical and molecular parameters that define the atomistic description. The key quantity to be solved in the CG representation is the potential, which must be included as an input to the molecular dynamics (MD) simulation of the polymer melt in the reduced CG representation. This potential has been derived analytically using an integral equation formalism. In the CG model, each chain contains an arbitrary number n b of chemically identical blocks, or "blobs". Each block contains a sufficiently large number of sites so that we can utilize Markovian properties of the internal chain's random walk. The integral equation coarse-graining approach (IECG) allows us to determine an analytical solution to the potential when N/n b = N b ≈ 30. At that scale the structure of the chain follows a random walk, and the distribution of the CG units along the chain is Markovian, so that the IECG formalism can be solved analytically [6] . In a macromolecular liquid, the random distribution of the CG units is a general property of any molecule when sampled at large enough lengthscales [8] .. The IECG model conserves thermodynamics while accurately reproducing the structure of polymer liquids across variable levels of resolution [6, 7, 16] . Insights from the IECG theory provide reasonable justifications for some of the advantages and shortcomings of coarse-graining methods in general [13, 14] .. The potential is solved analytically in the mean spherical approximation, which is valid for low compressible polymer liquids [12] . In the limit of large separations in real space, where r 1 (in units of the polymer size), the potential is approximated as [5, 7] . where Q = 5 1/4 3/2. . The key quantity of interest here is the universal parameter b = N b |c 0 |, which is defined once we decide the level of coarse-graining, N b , as well as the molecular and thermodynamic parameters of our system. This quantity also depends on the direct correlation function at k = 0, c 0 , which is in principle not known. However, this function relates to the potential between atomistic units and the isothermal compressibility of the liquid, so it can be determined numerically or from experiments.. When compared with full atomistic simulation (i.e., UA) the CG simulations that use the potential of Eq. (2) show quantitative consistency in the structure and thermodynamics. The CG potential is in this way fully transferable, and it can be conveniently applied in MD simulations of polymer melts, at the chosen thermodynamic and molecular parameters, with computational gain. The ability of CG models to maintain thermodynamic and structural properties while varying the coarse-graining resolution is important when one develops computational techniques with variable resolution. It allows the computational time of the MD simulations to be controlled by changing the resolution as needed. This notion motivates the development of a workflow that supports transformation between the UA and CG descriptions, which dynamically adjusts CG resolution at desired simulation times and spatial regions, while maintaining simulation accuracy and equilibrium through transitions to united-atom simulation.

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


INCREMENTAL COMPILATION OF BAYESIAN NETWORKS BASED ON MAXIMAL PRIME SUBGRAPHS When a Bayesian network (BN) is modified, for example adding or deleting a node, or changing the probability distributions, we usually will need a total recompilation of the model, despite feeling that a partial (re)compilation could have been enough. Especially when considering dynamic models, in which variables are added and removed very frequently, these recompilations are quite resource consuming. But even further, for the task of building a model, which is in many occasions an iterative process, there is a clear lack of flexibility. When we use the term Incremental Compilation or IC we refer to the possibility of modifying a network and avoiding a complete recompilation to obtain the new (and different) join tree (JT). The main point we intend to study in this work is JT-based inference in Bayesian networks. Apart from undertaking the triangulation problem itself, we have achieved a great improvement for the compilation in BNs. We do not develop a new architecture for BNs inference, but taking some already existing framework JT-based for probability propagation such as Hugin or Shenoy and Shafer, we have designed a method that can be successfully applied to get better performance, as the experimental evaluation will show. Methods for probabilistic inference have been known for centuries, but it is only within the last two decades that these methods have matured into practical applicable methods. The obstacle has been computational complexity. The joint probability distribution for a set of discrete random variables can be represented by a table, but the size of such a table is the product of the number of states for each additional variable. Thus it becomes impossible to represent the joint distribution of even moderately-sized domains in practice. In the 1980s Pearl suggested representing domains graphically and exploiting (in)dependence relations between variables in the inference process, 34 and his groundbreaking work led to a flourishing interest in the area, resulting in modern tools and techniques for construction and execution of Bayesian networks.. By inference in Bayesian networks we generally refer to the task of obtaining the posterior probabilities for a set of interest variables X I ⊂ V given the evidence e. That is to say, we wish:. There exist other inference tasks such as abductive inference, 15, 33 where the aim is to look for the most likely overall hypothesis or explanation accounting for the current observations.. In both cases, the basic idea in modern techniques is to modularize the domain in question and represent it by a set of tables, so that later procedures for their interaction could be used rather than using one big table. This is achieved by grouping variables according to their dependence relations and these groups of variables are often organized in a tree structure. Variations of this idea were fostered independently by Lauritzen and Spiegelhalter, 25 and Shafer and Shenoy, 35, 36 and form the foundation for the Hugin architecture. 19 More recent methods such as lazy propagation, 29 penniless propagation, 5 lazy-penniless propagation, 6 and methods for stochastic simulation, 7, 30 also take advantage of the modular representation. The grouping of variables and the organisation of these groups in a tree structure is typically performed offline through a process termed compilation. This process operates with a Bayesian network as input and the resulting structure is called a join tree. The efficiency of the resulting system is proportional to the size of the join tree and therefore considerable effort is devoted to this task. Compilation makes big demands on resources and its complexity increases considerably for large networks. Once the join tree has been constructed future modifications over the network may be necessary. In this case a whole re-compilation is needed. However, changes are normally located in the same area, and if the network is large, a set of changes will typically influence only a small part of the network. For this reason we started working on a compilation that could be carried out partially.. Hence, incremental compilation tries to give an answer to the following question: "When modifying a Bayesian network, is it absolutely necessary to recompile it from scratch? ". We could guess that if this modification does not affect the network globally, it might be possible to find a manner to save some time in obtaining the associated tree. In this paper we expose the compilation process itself to modularization. We analyze the procedures and split the problem into subproblems, thereby enabling online compilation or at least more efficient offline procedures. Fig. 1 tries to illustrate this simple idea: let us assume that we have an initial

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


A FPGA-BASED RECONFIGURABLE PARALLEL ARCHITECTURE FOR HIGH-PERFORMANCE NUMERICAL COMPUTATION Many real-world engineering problems require high computational power, especially regarding to the processing time. Current parallel processing techniques play an important role in reducing the processing time. Recently, reconfigurable computation has gained large attention thanks to its ability to combine hardware performance and software flexibility. Also, the availability of high-density FPGA (Field Programmable Gate Array) devices and corresponding development systems, allowed the popularization of reconfigurable computation, encouraging the development of very complex, compact and powerful systems for custom applications. This work presents an architecture for parallel reconfigurable computation based on the dataflow concept. This architecture allows reconfigurability of the system for many problems and, particularly, for numerical computation. Several experiments were done analyzing the scalability of the architecture, as well as comparing its performance with other approaches. Overall results are relevant and promising. The developed architecture has performance and scalability suited for engineering problems that demand intensive numerical computation. Parallel reconfigurable architectures are computer architectures in which several processing elements work in parallel, and their logic blocks can be reconfigured (logically or functionally) to adapt the system features to a particular problem.. Reconfigurable computation 1 can override the bottleneck of Von Neumann's machines implemented with ordinary processors, allowing multiple levels of par-allelism. It allies the performance of hardware-based solutions and the flexibility of software-based solutions. This approach can be an interesting solution for the computational resources growing required in many research areas (see, for instance, 2, 3, 4 ) .. Many complex problems are solved with sequential software-based solutions using conventional (mono-processed) hardware and cannot attain the required performance constraints, therefore justifying the research for more efficient architectures.. Reconfigurable computing systems present advantages over conventional approaches, such as: low power consumption, high processing speed, improved integration capability, flexibility and modular operation 5 . Differently from generalpurpose computers, the flexibility of a reconfigurable architecture allows a better customization of the hardware to the application, allowing, for example, the exploration of the parallelism events in a computational solution, particularly in those including scientific computations. Such parallelism, massive or not, can lead to a significant reduction in the processing time, dividing the computational demands among several processing elements.. More than a decade ago, Manners and Makimoto 6 described three waves of circuits technology. In the first wave, the dominant technology was standard transistors and simple logic gates, used for customized solutions in which both algorithm and physical resources were fixed. In the next wave, microprocessors become available, and a paradigm shift from hardware to software took place. In this new paradigm, resources remained fixed, but the algorithm was variable. More recently, hardware reconfiguration started the third wave in circuits projects, establishing a migration from procedural solutions to structural solutions. This new approach is characterized by the reconfigurability of both algorithm and resources. This work is developed in the context of this third wave. This paper presents a reconfigurable computer architecture using parallel computing concepts to obtain a scalable performance. The concept of adapting the architecture to the application is explored here. The proposed architecture can be adapted to several problems, such as numerical computation. For instance, this architecture can explore the inherent parallelism of the numerical operations required for computing differential equations such as Eq. (1), where many operations can be done simultaneously using a dataflow model.. Differential equations, such as the one above, have operations that can be done in parallel. The the specific processing elements available in the proposed architecture can explore efficiently such possible parallelism, not achievable by sequential processing.. Reconfigurable Parallel Architecture FPGA-Based 3 Three groups of experiments were done to evaluate the performance of the proposed reconfigurable architecture, as well as to compare it with other approaches.. Results of the experiments showed that using only 4 PEs the processing time was 60% above the estimated ideal time, while using 16 PEs, this value was above 180%. However, it should be stressed that this is a real-world application and, consequently, it presents many dependencies among operations, precluding the proposed architecture to reach its idealized peak performance. This result is justified due to the bottleneck imposed by the access to the template memory. Another important performance measure for analyzing parallel machines is the speedup 20 . Speedup is the ratio between the execution time with a single PE, and the execution time for several PEs in parallel. In the experiment with 16 PEs, a speedup of 5 was obtained, corresponding to 31% of the ideal value. This is due to the parallelization constraints implicit in the application code and that can be explicable by the Amdhal's Law 26 . The comparison of performance running the 5-tap FIR algorithm in our architecture (with a single PE) and in other architectures showed that it is faster than conventional microprocessors (including the DSP). As expected, the proposed architecture was slower than the architectures specifically designed for digital filtering. However, it should be taken into account that those results would be quite different in favor of the proposed architecture if using 16 PEs. Also, thanks to the dataflow approach, the number of instructions necessary to execute the algorithm was significantly smaller when compared with the other conventional architectures.. An important comparison was done with other parallel reconfigurable architectures (COLT and KressArray). The results showed that our approach is around 1.8 to 3.8 times faster, depending on the number of PEs used. Even with only 4 PEs, our architecture achieved better performance than the other architectures using much more parallel PEs.. The experiment with a real FIR filter benchmark showed that the proposed architecture needs less processing cycles than other specific digital signal processing architectures (TMS320C64X, ADSP-TS201S e MSC8103), while consuming the same power. This fact suggests that our proposed architecture could be used efficiently for such digital signal processing task. On the other hand, our architecture was run at 50 MHz, which is significantly smaller than the other architectures. Since this speed is due to the technological limitation of the device used in the current implementation, it is expected that future versions could run at higher frequencies, thus leading to even higher performance.. Besides the parallelism of execution at the PEs level, and the low-level Instruction-Level Parallelism (ILP) -see section 5, the use of a pipeline structure allowed an additional level of parallelism in the execution, taking advantage of the simultaneous operation the internal units (Dispatch, PEs and Storage). The joint effect of all these levels of parallelism contributed to efficiency of the architecture.. Although the use of buffers in PEs and parallel busses helped to minimize the bottleneck in accessing the internal units, there are still another bottlenecks in the architecture, as inferred from the plot of Figure 7 . This issue will be focused in future works.. Current results can be considered relevant. We emphasize the fact that the number of PEs can be increased up to the limit established by the FPGA resources. Besides, it is possible to increase the complexity of each PE by including operations that require a larger number of clock cycles to be done. It is obvious that a tradeoff between the complexity of PEs and their number must be established. We believe that, as more powerful FPGA devices become available, the more the proposed architecture becomes feasible and interesting for complex numerical problems.. Overall, the results of the experiments suggest the appropriateness of the architecture for solving intensive numerical problems such as in digital signal processing and other problems found scientific computation.. There are some issues that shall be addressed in future developments so as to improve the architecture, for instance: improvement of the dataflow machines to increase performance, and adaptation of the PEs to operate with floating point arithmetic.

O 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 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 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


Eigenspace Method for Spatiotemporal Hotspot Detection Hotspot detection aims at identifying subgroups in the observations that are unexpected, with respect to the some baseline information. For instance, in disease surveillance, the purpose is to detect sub-regions in spatiotemporal space, where the count of reported diseases (e.g. Cancer) is higher than expected, with respect to the population. The state-of-the-art method for this kind of problem is the Space-Time Scan Statistics (STScan), which exhaustively search the whole space through a sliding window looking for significant spatiotemporal clusters. STScan makes some restrictive assumptions about the distribution of data, the shape of the hotspots and the quality of data, which can be unrealistic for some nontraditional data sources. A novel methodology called EigenSpot is proposed where instead of an exhaustive search over the space, tracks the changes in a spacetime correlation structure. Not only does the new approach presents much more computational efficiency, but also makes no assumption about the data distribution, hotspot shape or the data quality. The principal idea is that with the joint combination of abnormal elements in the principal spatial and the temporal singular vectors, the location of hotspots in the spatiotemporal space can be approximated. A comprehensive experimental evaluation, both on simulated and real data sets reveals the effectiveness of the proposed method. Eigenspace techniques are very popular ones, which encompass many applications in data mining, signal processing, information retrieval and other domains. A famous instance of such an application relates to the current success of Google search engine. As described in an article entitled $25,000,000,000 Eigenvector [7] Google search engine is largely attributed to the eigenspace techniques. Another success story is related to the application of the Singular Value Decomposition (SVD) [13] in collaborative filtering. In the year 2008, the BellKor team won the $1,000,000 prize for the improvement of the system of the Netflix movie recommendation. The report later [5] stated that SVD was the key data analysis tools that they used. However, the application of the eigenspace techniques is not restricted to the above instances. There are several different examples in other areas and sciences. For instance, in face recognition [31] the specific set of the largest eigenvectors can be used to approximate the images of the human face. In structural engineering, both the eigenvalue and eigenvectors are used to estimate the vibration of structures. In control engineering, the eigenvalues of the linear system are used to assess the stability and response of the system [32] .. Nevertheless, despite the merits of the eigenspace techniques, they have not been applied yet to some potential problems, such as hotspot detection. Hotspot detection which may come with different terminologies, such as outbreak detection, cluster detection or event detection is somehow related to the clustering and anomaly detection, however it is distinct from these two. In clustering, the entire data set is partitioned into some groups, but in the anomaly detection, the anomalous points are searched for and sought after. Hotspot detection addresses the same problem, but with this difference that anomalous instances are recognized given some baseline information. In other words, looking into the dataset, everything might seem normal, however, when the cases along the baseline are considered, some points might be considered unexpected. A realistic scenario of the application of the hotspot detection is in disease surveillance. Suppose that we have the population of different postal codesŮduring a range of yearsŮas the baseline information and the count of the reported diseases in a range of postal codes, throughout different years as the cases dataset. The goal is to detect those spatiotemporal regions that contain unexpected counts. For instance, the output like zones S1,S2 and S3 during the years T1 to T5 might be considered a spatiotemporal hotspot. The detection of such hotspots enables the officials to better understand their target of interest for essential medical care and preventive measures.. The current methods for hotspot detection are twofold: clustering-based techniques and the scan statistics-based ones. Clustering-based techniques, such as [21] infer some thresholds from the population data and then apply the thresholds for clustering of data points in the cases set. Their prominent benefit, as opposed to the other methods, is that they provide the exact shape of the clusters. However, handling complex data, such as spatiotemporal data is not straightforward for these techniques. Besides, the clustering methods do not consider chance and randomness issues, which are very important in sensitive applications, such as security and public health. Moreover, there is not a standard clustering method for hotspot detection, which is widely accepted by the community. The methods are mostly outspread and diverse, in terms of the technical details. The clustering methods also require restrictive input parameters, which make their usage limited in automatic settings.. The second group of techniques which relies on scan statistics are widely used and accepted by the epidemiological community. These groups of techniques exhaustively scan the whole space to find interesting spatial and spatiotemporal clusters. A specific statistic is computed for each possible window and then potential clusters are sorted, based on the obtained statistics. Thereafter, the statistical significance of the top-k clusters is simulated via a Monte-Carlo simulation. Since these methods scan an entire space, they are extremely computationally expensive. Spatial scan statistics [14] requires computation time of O(N 3 ) and space-time scan statistics (STScan) [14, 15, 18, 19] requires O(N 4 ). Some recent efforts are made to reduce this complexity. For instance, [2] propose a method that requires O( 1 N 2 Log 2 N ) for spatial scan, which is more efficient than O(N 3 ). However, the minimum complexity for space-time scan statistics in the best condition has not reached less than O(N 3 ). This high computational cost practically has restricted their use in real-time applications or large-scale data sets. Besides, scan statistics-based techniques are highly associated with the strong parametric model assumptions (e.g. Poisson or Gaussian counts) [28] . These assumptions mitigate the performance when the models are incorrect for nontraditional data sources. Additionally, scan statistics-based methods are not efficient for detection of irregular shape clusters [9, 30] apart from the circles (spatial scan) and cylinders (space-time scan). They also assume that data is presented in a high quality format, hence is vulnerable against the noises and outliers [27] .. Our proposed method is a solution to some of the above mentioned issues, in scan statistics-based methods. An efficient method is proposed (linear with both space and time dimensions) for approximation of hotspots in the spatiotemporal space, without the need for exhaustive search. Instead of looking for deviations in the assumed parametric model, we track changes in the space-time correlation structure, using the eigenspace techniques. This approach enables us to detect irregular shape hotspots from even noisy data sets, without any prior knowledge about the data nature or hotspot characteristics. To the best of our knowledge this problem has not already been addressed by other researchers. Our approach also differs from those of ones that focus on the improvement of scan statistics-based methods efficiency (e.g. [2, 25, 26] ). We do not improve the efficiency of scan statistics-based methods; rather we propose and examine a new methodology, which follows a different aim. Hence, this is not an "apples to apples" comparison, as both groups of approaches have inherent differences and subsequently their own applications. STScan can be more helpful for retrospective and sensitive applications, when some prior knowledge exists about the nature of hotspot and data. On the other hand, our presented approach focuses more on real-time applications, where neither the nature of data nor the hotspot characteristics is known in advance. In such circumstances, a computationally feasible approximation method that rapidly identifies the alarming areas, without any prior knowledge might be very useful.. The rest of the paper is organized as follows: The section 2 describes the problem, the proposed solution and algorithm, as well as an illustrative example. The section 3 includes an experimental evaluation and results of the simulation study and the real case study. The last section concludes the exposition presenting the final remarks.

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