Group representations that resist random sampling We show that there exists a family of groups G n and nontrivial irreducible representations ρ n such that, for any constant t, the average of ρ n over t uniformly random elements g 1 , . . . , g t ∈ G n has operator norm 1 with probability approaching 1 as n → ∞. More quantitatively, we show that there exist families of finite groups for which Ω(log log |G|) random elements are required to bound the norm of a typical representation below 1. This settles a conjecture of A. Wigderson. The Alon-Roichman theorem [1] asserts that O(log |G|/ε 2 ) elements, chosen independently and uniformly from a finite group G, yield with high probability a Cayley graph with second eigenvalue no more than ε. As there are groups for which O(log |G|) elements are necessary to even generate the group, this bound is tight up to a constant when ε = Ω (1) . The condition that a collection of group elements g 1 , . . . , g t yield a graph with second eigenvalue ε is equivalent to the condition that every nontrivial irreducible representation ρ of G is approximately annihilated in the sense that. (The appearance of the inverses g . holds for all finite groups G and all nontrivial irreducible representations ρ of G? As above, the g i are selected independently and uniformly from G.. To support this notion, we remark that there are known families of "highly nonabelian" finite groups, such as SL 2 ( p ) as p → ∞, which yield expanding Cayley graphs over a constant number of uniformly random group elements g 1 , . . . , g t [2] . It follows that (2) holds for every representation. Likewise, (2) holds for all nontrivial irreducible representations of abelian groups: for example, while no constant number of elements suffice to make n 2 into an expander, or even to generate the group, just t = 2 uniformly random elements suffice to bound the expected norm of any one irreducible representation to 1 − δ, with a universal constant δ > 0.. Distinct irreducible representations of a finite group possess various independence properties when viewed as random variables by selecting a uniformly random group element: for example, their entries are pairwise uncorrelated in any basis. Intuitively, Wigderson's question asks whether the dependence on log |G| in the Alon-Roichman theorem is an artifact of the requirement that every representation be annihilated-a collection of ostensibly independent events which one might imagine occur with constant probability with the selection of each new group element-or is a feature that can manifest even in a single irreducible representation. Indeed, a positive answer to the question would imply that O(log | G|) random elements suffice to turn any group G into an expanding Cayley graph, whereĜ denotes the set of irreducible representations of G.. We answer this question in the negative. Our strategy will be to work in a family of finite groups of the form G = K n , where K has constant size, is nonabelian, and has trivial center. Such groups simultaneously possess high-dimensional representations and the property that any collection of a bounded number of group elements generate a subgroup of bounded size. In this setting, for each constant t > 0, we establish two results:. • When K has a faithful irreducible representation ρ of dimension at least two, we show that the representation ρ n = ρ ⊗ · · · ⊗ ρ of G = K n has the property that. where the g i are elements of G chosen uniformly and independently at random. See Theorem 1 for a more precise statement.. This result holds, for instance, if K = S 3 , the group of permutations of three elements, and ρ is its two-dimensional representation. We also show. • When ρ is selected according to the Plancherel measure, which assigns each irreducible representation probability mass proportional to the square of its dimension, we show that with probability. where the g i are elements of G chosen uniformly and independently at random. See Theorem 2 for a more precise statement.. In fact, these estimates establish that there are infinite families of groups for which there is a representation ρ such that Ω(log log |G|) uniformly random elements are necessary to bound the norm of ρ as in (2), for any constant δ > 0. Recall that the Alon-Roichman theorem guarantees that O(log |G|) random elements suffice with high probability to bound the norm of every irrep ρ, and thus turn G into an expander. Closing this gap remains an interesting open question.. These negative results for independent and uniformly random group elements suggest the following question, which is existential rather than probabilistic: Are there constants t and δ > 0 such that, for any group G and any nontrivial irreducible representation ρ, there exist t elements g 1 , . . . , g t ∈ G such that 1. Our construction cannot rule out this possibility.

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


Counting inequivalent monotone Boolean functions Abstract. Monotone Boolean functions (MBFs) are Boolean functions f : {0, 1} n → {0, 1} satisfying the monotonicity condition x ≤ y ⇒ f (x) ≤ f (y) for any x, y ∈ {0, 1} n . The number of MBFs in n variables is known as the nth Dedekind number. It is a longstanding computational challenge to determine these numbers exactly -these values are only known for n at most 8. Two monotone Boolean functions are inequivalent if one can be obtained from the other by renaming the variables. The number of inequivalent MBFs in n variables was known only for up to n = 6. In this paper we propose a strategy to count inequivalent MBF's by breaking the calculation into parts based on the profiles of these functions. As a result we are able to compute the number of inequivalent MBFs in 7 variables. The number obtained is 490013148. A Boolean function on n variables (BF) is a function f : {0, 1} n → {0, 1}. A monotone Boolean function (MBF) additionally satisfies the condition x ≤ y ⇒ f (x) ≤ f (y), for any x, y ∈ {0, 1} n . We write x ≤ y if x i ≤ y i for all i = 1, 2, . . . , n, and x < y if x ≤ y and x i < y i for some i. A BF is monotone if and only if it can be written as a combination of conjunctions and disjunctions only.. Since each input state in {0, 1} n has two possible output states, there are a total of 2 2 n Boolean functions on n variables. On the other hand, no exact closed form is known for the number of monotone Boolean functions on n variables. This number is usually denoted by D(n), which is also called the nth Dedekind number. These numbers are named after Richard Dedekind who defined them in [Ded97] . The first few values are given in Table 1 , taken from [Slo11] . Currently, only values of D(n) up to n = 8 are known.. Kisielewicz gives in [Kis88] a logical summation formula for D(n), however performing the computation using his summation has the same complexity as brute force enumeration of D(n). (See [Kor03] , e.g.) There are some asymptotic results concerning the behavior of D(n), one of the earliest of which was a result of Kleitman in 1969 , that log 2 D(n) ∼ n n/2 [Kle69] . So far, the most accurate one is given by Korshunov in [Kor03] , given in Table 2 . 2 (−n−1)/2 − n 2 2 −n−4 , for odd n Table 2 . Korshunov's Asymptotics 1.1. Inequivalent MBFs. We define an MBF f to be equivalent to another MBF g if g can be obtained from f by a renaming of the variables. For example, the function f (x 1 , x 2 , x 3 ) = (x 1 ∧ x 2 ) ∨ (x 2 ∧ x 3 ) is equivalent to g(x 1 , x 2 , x 3 ) = (x 1 ∧ x 2 ) ∨ (x 1 ∧ x 3 ), since interchanging x 1 and x 2 sends f to g. We write this as f ∼ g. For brevity, from here on we write x i ∧ x j as x i x j . Let R(n) be the number of equivalence classes defined by "∼" among monotone Boolean functions on n variables. As with D(n), no closed form is known for R(n), and in fact only the values up to n = 6 have been computed. These appear to have been obtained by the straightforward method of listing all monotone Boolean functions on n variables and then sorting them into equivalence classes. The known values from [Slo11] are shown in Table 3 . Example 1.1. The five functions in R(2) are: f = 0, f = 1, f = x 1 , f = x 1 ∨x 2 , and f = x 1 x 2 . The functions in D(2) are exactly these functions plus f = x 2 , which is equivalent to f = x 1 . n R (n) 0 2 1 3 2 5 3 10 4 30 5 210 6 16 353 Table 3 . Known Values of R(n), A003182 1.2. Terminology and Elementary Facts. Define a minimal term of an MBF f to be an input x ∈ {0, 1} n such that f (x) = 1 and f (y) = 0 if y < x. The minimal terms of a monotone Boolean function represent the "smallest" sets where the function equals one -any input below x evaluates to zero, and everything above evaluates to one by virtue of monotonicity. For example, the function f (x 1 , x 2 , x 3 ) = x 1 ∨ x 2 x 3 evaluates to one at (1, 0, 0) and (0, 1, 1), as well as at all vectors above (1, 0, 0) and (0, 1, 1), and evaluates to 0 at all other vectors. Indeed, each MBF can be written as a disjunction of clauses, each representing one of its minimal terms.. MBFs can be classified according to the number of minimal terms they have. Call D k (n) the number of monotone Boolean functions on n variables with k minimal terms. Kilibarda and Jovovic [KJ03] derive closed form expressions for D k (n) for fixed k = 4, 5, . . . , 10, these sequences are sequences A051112 to A051118 of [Slo11] .. A truth table for a Boolean function is a row of zeros and ones which encodes the outputs of the function corresponding to every possible input state. To illustrate, the function on three variables f (x 1 , x 2 , x 3 ) = x 1 ∨ x 2 x 3 has minimal terms {{1}, {2, 3}}, and it has the following truth table:. variables set to 1 x 1 , x 2 , x 3 x 2 , x 3 x 1 , x 3 x 3 x 1 , x 2 x 2 x 1 none output states 1 1 1 0 1 0 1 0 . Note that the input states on the top row are arranged in a reverse colexicographic (or colex ) order on {0, 1} 3 , defined as x < y if x = y and x k < y k where k = max{i : x i = y i }. Fixing this order, we write f as 11101010. In general, any Boolean function on n variables can be written as a 0-1 string of length 2 n where each entry corresponds to an input state; we use this convention throughout this paper. The choice for the ordering has the nice property that the first 2 n−1 of its entries all involve setting the variable x n to 1, and the second half has inputs with x n = 0. [n] , that is, pairwise incomparable subsets of the power set of {1, 2, . . . , n}. Specifically, the set of minimal terms of an MBF in D(n) is an antichain in 2 [n] . Since by Sperner's Theorem, any antichain on the n-set can have at most n n/2 elements, we have that any n-variable MBF can have at most n n/2 minimal terms. The one-to-one correspondence between n-variable MBFs and Sperner hypergraphs is also well-known. In particular, each minimal term of an MBF maps to a hyperedge in the corresponding hypergraph, and because of pairwise incomparability, the hypergraph thus exhibits the Sperner property, that is, no hyperedge contains another.. Some other fields in which monotone Boolean functions appear include lattice theory [SSGC95] , nonlinear signal processing [SSGC95] , coding theory [IKN07] , computational learning theory [Shm] , game theory [RP11] , and computational biology ( [KG04] , [HKS08] ).. For a comprehensive discussion of Boolean functions, see the recentlypublished book by Crama and Hammer [CH11] .

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


In Vivo Characterization of the Mechanics of Human Uterine Cervices The uterine cervix has to provide mechanical resistance to ensure a normal development of the fetus. This is guaranteed by the composition of its extracellular matrix, which functions as a fiber-reinforced composite. At term a complex remodeling process allows the cervical canal to open for birth. This remodeling is achieved by changes in the quality and quantity of collagen fibers and ground substance and their interplay, which influences the biomechanical behavior of the cervix but also contributes to pathologic conditions such as cervical incompetence (CI). We start by reviewing the anatomy and histological composition of the human cervix, and discuss its physiologic function and pathologic condition in pregnancy including biomechanical aspects. Established diagnostic methods on the cervix (palpation, endovaginal ultrasound) used in clinics as well as methods for assessment of cervical consistency (lightinduced fluorescence, electrical current, and impedance) are discussed. We show the first clinical application of an aspiration device, which allows in vivo testing of the biomechanical properties of the cervix with the aim to establish the physiological biomechanical changes throughout gestation and to detect pregnant women at risk for CI. In a pilot study on nonpregnant cervices before and after hysterectomy we found no considerable difference in the biomechanical response between in vivo and The cervix is a biochemically active tissue that changes its biomechanical properties in a remodeling process during pregnancy to be prepared for parturition. Understanding the evolution of this process during gestation is essential for acquiring more insight into the pathogenesis of conditions associated with cervical malfunction. Cervical incompetence (CI) and preterm labor are both associated with preterm cervical ripening leading to preterm birth. Despite tremendous advances in neonatal intensive care preterm birth is the greatest risk factor for infant mortality and morbidity. Among the 27,970 infant deaths in 2002 in the United States, 65% were born preterm. 1 Once the biochemical cascade leading to cervical ripening has started, any therapeutic interventions are temporary. Hence, early detection or prediction of cervical malfunction is one of the keys to prevent preterm birth.. The methods used in clinical practice to diagnose cervical changes are digital palpation and endovaginal ultrasound. Both methods, unfortunately, detect only substantial changes of the cervix; the first method is subjective and gives information of cervical parameters summarized in the Bishop Score, whereas the second shows the length of the cervix and the shape of the internal os. Diagnostic tests that provide objective information of the biomechanical behavior of the tissue would be beneficial. Recently, instruments that indirectly measure the hydration and collagen content of the cervix were tested on human pregnant cervices in an experimental setting. Both methods, light-induced fluorescence 2 and electrical impedance measurements, 3 are easy to apply but have not yet found their way into clinical practice. It is, however, not clear whether these methods have negative effects on the fetus or not.. We present our data of the first in vivo application of an aspiration device on nonpregnant human cervices, which directly measures the biomechanical properties of the tissue. The aspiration test, which has the potential for application to pregnant cervices, provides information of the biomechanical properties, such as stiffness, softening, creep, and rising time. Information on the tissue structure and on these parameters will allow the design of reliable threedimensional constitutive and computational models to better investigate the biomechanical behavior of the cervix under physiological loading condition, during pregnancy, and parturition.

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


Metabolic network destruction: Relating topology to robustness Biological networks exhibit intriguing topological properties such as small-worldness. In this paper, we investigate whether the topology of a particular type of biological network, a metabolic network, is related to its robustness. We do so by perturbing a metabolic system in silico, one reaction at a time and studying the correlations between growth, as predicted by flux balance analysis, and a number of topological metrics, as computed from three network representations of the metabolic system.We find that a small number of metrics correlate with growth and that only one of the network representations stands out in terms of correlated metrics. The most correlated metrics point to the importance of hub nodes in this network, so-called ''currency metabolites''. Since they are responsible for interconnecting distant functional modules in the network, they are important points in the network for predicting if reaction removal affects growth. A second set of correlations in contrast is related to ''loner'' nodes that uniquely connect important pathways and thus correspond to essential steps in metabolism. In the last decade, advances in high-throughput biological measurement systems have made it possible to extract large-scale networks from biological systems. Jeong et al. [7] were among the first to study the topologies of metabolic networks, networks of interconversions of small compounds. The metabolic networks of the 43 organisms that they studied gave evidence of a scale-free structure. Characteristic properties of these so-called ''small-world'' networks are their power-law distributed node degrees and their small average shortest path lengths.. Subsequently, researchers studied the topologies of a number of other types of biological networks [2, 12, 3] .. Much of this work confirmed the results of Jeong et al.: scale-free behavior was everywhere. Even the Internet and some power grids are thought to display scalefree behavior [1] . These latter networks have expanded in a seemingly organic fashion through a process of preferential attachment -new nodes are more likely to attach to existing high-degree nodes than to lowdegree nodes. This expansion process forms the basis of Barabási and Albert's [1] random network model. They show that it leads to the characteristic power-law nodedegree distribution and small-world properties. Although Kim and Marcotte [8] and Lima-Mendez and Helden [11] argue that biological networks do not develop through simple processes of preferential attachment, the presence of similar topological elements, such as hub nodes, begs the question whether these topological properties confer some benefit or whether certain topologies are inherently suited for particular functionality.. In an effort to understand the relationship between the function of a network and its topological properties, Milo et al. [13] introduced the concept of motifs. A motif is a small sub-network (3-5 nodes) whose overrepresentation may be indicative of its role in maintaining function at a local level. They found that certain motifs occur more often in biological networks than expected by chance and that they may correspond to certain desired behavior such as response acceleration, signal delay and stability. Prill et al. [18] took this idea further and claimed that certain motifs were inherently more prone to display stable behavior than others. By abstracting away from the underlying functionality, they demonstrated that such relations held to some extent over a variety of biological networks. However, Ingram et al. [6] considered gene networks and compared the results of a differential equation model of gene expression to specific motif counts in the gene network but found no correlation. Lima-Mendez and Helden [11] argue that global topological properties cannot explain the function of networks. While they claim that the significance of motif frequencies may have been overestimated (since the frequencies only capture global properties), they do consider a localized approach to be more promising as the key to understanding biological networks lies in understanding local details.. In our work, we take a global approach and investigate to what extent network topology can be related to more systems-level network properties shared by the various network types studied by Barabási et al. An interesting property in this respect is that of robustness. Stelling et al. [21] and Kitano [9] define robustness as the ability of a system to maintain its function in the face of perturbations or uncertainty. Biological systems are known to be robust [10] to many forms of perturbation while being highly sensitive to other forms, so-called ''highly optimized tolerance'' [21] . The question is whether there is something in the topology of these networks that confers robustness to the overall system.. In this paper, we study the relationship between the robustness of a micro-organism (baker's yeast, Saccharomyces cerevisiae) and the topologies of network representations of its metabolic system. Microbial metabolic systems provide a good test bed, since an often assumed functional objective -growth -is easily expressed in terms of fluxes through these systems. Furthermore, good quality metabolic datasets are readily available and resulting flux models can be studied computationally with high efficacy.. To study the link between network topology and robustness, we propose an in silico metabolic system perturbation experiment. We define robustness as the ability of the yeast cell to maintain growth under reaction removals. First, we show how its metabolic system can be represented by three different networks. Then, through a number of trials, reactions are removed from the metabolic system until growth ceases. This provides a number of snapshots of partially ''destructed'' metabolic systems. For each snapshot, growth and a number of network-wide topological metrics can be computed. By calculating correlations between growth and these metrics, we find that most of the topological metrics are not related to function. The strongest correlations point to the importance of both ''hub'' nodes (so-called ''currency metabolites'') and ''loner'' nodes. The goal of this study was to determine whether topology and robustness of biological systems are related. To this end, we generated a number of reaction removal sequences or trials, each of which resulted in the cessation of growth of our metabolic system. Each step in a trial provided a snapshot of the metabolic system from which growth could be computed as well as topological metrics of the metabolite-reaction network G B , the metabolite network G M and the reaction network G R . This allowed us to calculate a measure of correlation between growth and each of the metrics. In this section, we will summarize some of our findings.. Unambiguously linking robustness to topology is difficult. The term ''robustness'' is meaningless without context. Since the context of an organism constitutes all its interactions by computing their minima, means and maxima respectively, as discussed in Section 2.2.1. As the legend shows, the light gray bars correspond to hub nodes, the dark gray bars correspond to loner nodes and the medium gray bars correspond to metrics that were either not interpreted or that do not fit the hub/loner distinction. with its environment, a precise definition may forever elude us. However, every organism engages in a (small) number of vital functions that dominate its struggle for survival. By studying only these functions and their degradation in the face of perturbations, we may discover some of the principles that help organisms to achieve their resilience. However, an unambiguous connection between such functions/perturbations and the topology of the underlying biochemical network is usually hard to define.. As we studied microbial metabolism, we focused on the one function at which the cell must be successful before all else: biomass production, or growth. While this is a simple representation of cellular activity, it has the advantage of being based on a well-studied theoretical model of metabolism, flux balance analysis, that can easily be modified to work with a perturbation model of reaction removal. Still, although we were able to directly link metabolic networks, functions and perturbations, finding correlations between robustness and topology proved not to be trivial.. There is no obvious way to reduce a metabolic system to a network. This is a consequence of the correspondence between metabolic systems and hyper-networks. Analyzing hyper-networks directly is the ideal approach but these general structures have resisted the theoretical analysis that has produced the useful tools of (classical) network theory. Therefore, conversion is an analytical necessity. We described three ways of converting a hyper-network to a network: the metabolite-reaction network G B , the metabolite network G M and the reaction network G R . The multiplicity of representations is a well-known problem that Holme and Huss [5] investigated by matching graph theoretical properties of the three network representations to biological data in order to discover the network representation that ''best'' captures biological knowledge. We found the correlations were strongest for the metabolite nodes in G B and for G M . These findings suggest that metabolite nodes are most important for studying the structure of a metabolic system. In line with this, Holme and Huss found G M to be the most favorable representation, although we favor G B since it maintains most of the original metabolic information.. Topology correlates weakly with growth. Many of the topological metrics we calculated did not correlate with growth. We classified those that did correlate into two groups: those caused by hub metabolite nodes and those caused by loner metabolite nodes. They point to the importance of (a) global connectivity (by hub nodes that tie the network together by connecting many reaction nodes); and (b) local connectivity (by metabolites that are produced and/or consumed by few reactions). The role of hub nodes was verified in an experiment where we removed currency metabolites, which led to a large shift in metrics correlated to growth. We used the genome-scale metabolic dataset which is available from the UCSD Systems Biology Research Group website [17] . The website provides a minimal aerobic growth environment which was used for our experiments. In this experiment,. • the rate of the ATP maintenance reaction (ATPM) is 1 µmol gDW −1 h whilst the acetyl-CoA hydrolase (ACOAH) and the glutamate synthase for NADH (GLUSx) reactions are disabled;. • the reaction rates of reactions that transport O 2 , NH

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


AN INFORMATION SYSTEM FOR THE SHORTEST ORIGEN-DESTINATION ROUTE IN A TRANSPORTATION NETWORK There exist several information systems to find and display the shortest origin-destination route in a transportation network. Usually these systems are created by organizations purchasing expensive software aiming to build them easily, quickly and correctly. This goal, however, still remains elusive. In this paper, an information system that finds and displays the shortest origin-destination route in a transportation network is presented. The system is mainly built using free software. In the literature, there were found at least three fast algorithms to obtain the shortest route in a given network. From these three, one was selected for being more efficient and less memory consuming according to the experimental analysis carried out. The functionality of the system is showed using Toluca's transportation network, one of the largest cities in Mexico. The widespread use of Information and Communication Technologies has increased the interest in new developments in computing. One of such developments are the Geographical Information Systems (GIS). GIS technology has been extensively used to deal with issues such as crime analysis (Chainey and Ratcliffe, 2005) , meteorology (Dyras et al., 2005) , transportation (Wu, 2007; Mitra, 2007) , urban planning (Easa and Chan, 2000) , among other applications.. Nowadays, a desirable and often necessary feature of a GIS is the presentation of geographical information in real time over the internet. There is a huge amount of software both commercially and freely available to design such applications. The wide variety of applications supported by commercial software has been one of the strong advantages over free software which is often limited to the level of technical support available and to what the free software group is interested in. However, commercial software for GIS applications has been characterized for its high licensing costs (Newham and Field, 2001) .. A common use of a GIS is the cartographical presentation of a required place. For example GoogleMaps (http://maps.google.com) is well known for presenting the cartography of a vast number of cities in the world. The design of a GIS for other applications such as calculating and displaying the shortest Origin-Destination (O-D) route over a transportation network has not been widely carried out over the world. One of the limitations to develop this kind of applications is the necessity of an accurate database with the required information. In different continents around the world there are well known applications. One of such applications is MapQuest (http://www.mapquest.co.uk) developed in the United Kingdom. Even though we can search in MapQuest for maps of almost every country around the world, the O-D route is limited to European and North American countries. GoogleMaps, Map24, among others are not the exception.. In this paper, an Information System (IS) is presented which integrates: Geographical information, database information and freely available software. The IS finds and displays the shortest route between two different places in a transportation network. One of the relevant characteristics of our IS is that it can be used freely in any city or country provided the required database information is available. Our IS is tested in the transportation network of Toluca, one of the main cities of Mexico.. The paper is organized as follows. In Section 2, the algorithm used to implement the shortest O-D route is described. In Section 3, the components used to build the GIS are presented. In Section 4 the functionality of the GIS is shown. In Section 5, the interface and the answers given by the GIS are presented. Finally, in Section 6 conclusions and future perspectives are given. In this paper we have described an Information System built using free software to compute and display the shortest origin-destination route in a transportation network. GIS technology and Internet communications are used to manipulate spatial data and to respond to user requests in real time.. In a large number of instances, the information delivered provides effective and attractive results, but they still remain expensive to integrate and to deploy. In this sense, free software offers a cost-effective alternative to counteract the economic burden of implementing large scale IS.. Nevertheless, implementing GIS technology using free software should not be taken as a universally proven proposition. While the economic benefits could be sufficient to opt for a free software ensemble, the recognized problems associated with noncommercial software should not be ignored. Therefore, the potential costs and benefits must be understood in the context of the particular environment in which the Information System is implemented.. Finally, before deciding which Information System should be used for a particular need, it is essential to realize and accept the numerous costs associated with the technology to be implemented. Hardware needs, permanent staff and maintenance costs must be taken into account. In addition, the often forgotten time cost must also be considered, for in many cases, a couple of years is required to start seeing significant and palpable results. Nevertheless, the costs of implementing GIS technology are lower than ever, and before looking for expensive solutions is always advisable to learn from previous experiences.

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 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


Incremental network design with shortest paths We introduce a class of incremental network design problems focused on investigating the optimal choice and timing of network expansions. We concentrate on an incremental network design problem with shortest paths. We investigate structural properties of optimal solutions, we show that the simplest variant is NP-hard, we analyze the worst-case performance of natural greedy heuristics, and we derive a 4-approximation algorithm.

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


Generalized fuzzy clustering for segmentation of multi-spectral magnetic resonance images An integrated approach for multi-spectral segmentation of MR images is presented. This method is based on the fuzzy c-means (FCM) and includes bias field correction and contextual constraints over spatial intensity distribution and accounts for the non-spherical cluster's shape in the feature space. The bias field is modeled as a linear combination of smooth polynomial basis functions for fast computation in the clustering iterations. Regularization terms for the neighborhood continuity of intensity are added into the FCM cost functions. To reduce the computational complexity, the contextual regularizations are separated from the clustering iterations. Since the feature space is not isotropic, distance measure adopted in Gustafson-Kessel (G-K) algorithm is used instead of the Euclidean distance, to account for the non-spherical shape of the clusters in the feature space. These algorithms are quantitatively evaluated on MR brain images using the similarity measures. The superb soft tissue contrast seen on magnetic resonance imaging (MRI) is ideally suited for tissue classification and volumetry. This has significant implications in understanding the neural basis for many neurological disorders [19] . For instance, in a number of neurological disorders, such as multiple sclerosis (MS) and Alzheimer's disease, the volume changes in total brain, gray matter (GM), and white matter (WM) provide important information about the neuronal and axonal loss [4, 25, 26] . In addition, MRI-derived tissue volumetry is increasingly employed as a secondary end point in many clinical trials [22] . Accurate and robust tissue classification or segmentation is critical for detecting changes in tissue volumes in healthy and diseased brain. Commonly used techniques for segmentation have been recently reviewed [24] .. A unique feature of MRI is its multi-model nature that allows acquisition of images with different tissue contrasts (T1-, T2-, density-weighting, etc.) It is possible to improve the quality of segmentation by combining information from images with multiple contrasts [3, 13, 16, 32] . Feature map-based classification techniques for MR image segmentation have attracted considerable attention because they are fast, simple to implement, and allow expert's input in tissue classification. However, in practice, this multi-spectral segmentation is prone to false tissue classifications and requires significant manual intervention and pre-processing since the distribution of intensities in the feature space is distorted by various factors that include image intensity inhomogeneity arising from the radio frequency receiver and transmitter coil profiles, partial volume averaging effects from the limited resolution, image noise, and spatial misalignment of images. While there are a few methods to overcome some of these problems, we focus on fuzzy c-means (FCM)-based methods [1, 8, 10, 23, 27, 28, 31, 33] because of their many desirable features in tissue classification.. Conventional FCM-based methods do not correct the intensity inhomogeneity and do not exploit contextual information. The adaptive FCM (AFCM) incorporates the intensity inhomogeneity correction, contextual constraints to overcome the noise problems and fuzzy membership to address the partial volume averaging effect, and automatic clustering [1, 20, 23, 27, 28, 30, 34] .. One essential problem with AFCM (and a number of other clustering algorithms) is that they are totally based on the objective cost function. Therefore, the performance of the algorithms is greatly dependent on the way the objective cost function is constructed. When using the Euclidean distance in the objective cost function, as in FCM, the algorithm has a tendency to generate equal cluster volumes with spherical occupancy in the feature space [7, 8, 9, 14, 21] . This could have a significant effect on the MRI segmentation results. To deal with this problem, a few methods have been proposed in MR image segmentation in which some pre-selected seeds are included [5, 6] . Methods aimed at automating the selection of seeds are proposed by Suckling et al. [30] . However, these methods are cumbersome to implement. In order to automatically produce reasonable clusters, more sophisticated distance measure is included in the Gustafson-Kessel (G-K) algorithm [15, 17] in which a positive definite, symmetric scatter matrix (or covariance matrix) is used instead of the Euclidean distance to define the Mahalanobis distance to form an ellipsoidal cluster in the feature space. In the G-K algorithm each cluster is characterized by a symmetric and positive definite matrix for automatic adaptation of each individual cluster volume.. The fundamentals of fuzzy clustering in medical image segmentation are well described in Sutton et al. [31] . The main formalism presented in this paper is based on the grouped coordinate descent method (also called alternating optimization (AO)) [31] . Important details, such as singularity, initialization, rules of thumb for the parameters, methods to determine the number of clusters are not described in this paper due to space limitation, but can be found elsewhere [17] . Throughout this paper, we assumed that the total number of clusters is known and that proper initialization is available.. In the current studies, we extended AFCM to multi-spectral segmentation that included efficient intensity non-uniformity (or bias field) correction and contextual constraints over neighborhood spatial intensity distribution. The non-spherical occupancy of the feature space was accounted by utilizing cluster scatter measures to define the Mahalanobis distance. This method was applied to segment GM, WM and CSF (cerebrospinal fluid) of MR images acquired with fast spin echo (FSE) pulse sequence which is commonly used in the routine clinical practice. The performance of the algorithm was quantitatively evaluated using similarity measures. A comprehensive GFCM technique for multi-spectral segmentation of MR images is described. This technique incorporates an efficient bias field correction along with contextual constraints. In addition, this method takes into account the non-spherical occupancy of the feature space by replacing the Euclidean distance with cluster scatter measures to define the Mahalanobis distance. Qualitative and quantitative evaluation on Brain Web and real brain images indicates that GFCM outperforms the AFCM method.

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


Large-scale analysis of the evolutionary histories of phosphorylation motifs in the human genome Background: Protein phosphorylation is a post-translational modification that is essential for a wide range of eukaryotic physiological processes, such as transcription, cytoskeletal regulation, cell metabolism, and signal transduction. Although more than 200,000 phosphorylation sites have been reported in the human genome, the physiological roles of most remain unknown. In this study, we provide some useful datasets for the assessment of functional phosphorylation signaling using a comparative genome analysis of phosphorylation motifs.We described the evolutionary patterns of conservation of these and comparative genomic data for 93,101 phosphosites and 1,003,756 potential phosphosites in human phosphomotifs, using 178 phosphomotifs identified in a previous study that occupied 69% of known phosphosites in public databases. Comparative genomic analyses were performed using genomes from nine species from yeast to humans. Here we provide an overview of the evolutionary patterns of phosphomotif acquisition and indicate the dependence on motif structures. Using the data from our previous study, we describe the interaction networks of phosphoproteins, identify the kinase substrates associated with phosphoproteins, and perform gene ontology enrichment analyses. In addition, we show how this dataset can help to elucidate the function of phosphomotifs. Conclusions: Our characterizations of motif structures and assessments of evolutionary conservation of phosphosites reveal physiological roles of unreported phosphosites. Thus, interactions between protein groups that share motifs are likely to be helpful for inferring kinase-substrate interaction networks. Our computational methods can be used to elucidate the relationships between phosphorylation signaling and cellular functions.

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Planar Object Detection under Scaled Orthographic Projection Abstract. In this work a new method to detect objects under scaled orthographic projections is shown. It also calculates the parameters of the transformations the object has suffered. The method is based on the use of the Generalized Hough Transform (GHT) that compares a template with a projected image. The computational requirements of the algorithm are reduced by restricting the transformation to the template edge points and using invariant information during the comparison process. This information is obtained from a precomputed table of the template that is directly transformed and compared with the image table. Moreover, a multiresolution design of the algorithm speeds-up the parameters calculation. Planar object recognition and three-dimensional (3D) pose estimation are the most important tasks in computer vision. Some applications related to these methods are object manipulation, autonomous vehicle driving, etc.. Perspective projection is one of the most suitable models for real camera image formation. However, it introduces non-linear relations. Simpler camera models can be used [1] under more relaxed situations which produce a negligible error. When the size of the object is relatively small (in comparison to its depth) and placed near the camera optical axis, the orthoperspective projection (or, in general, the subgroup of affine transformations [2] ) is a good approximation to the perspective projection [3] . Here, the scaled orthographic projection will be studied. This projection only incorporates the distance and the foreshortening effects, but it eliminates the non-linear dependencies.. There are several methods to find the transformations between a planar template and an image where this template is included and viewed from an arbitrary position [4] . Selection of the most suitable method will be based on considerations such as the kind of shapes we are dealing with and the ability to cope with practical problems such as occlusion, noise, etc.. A simple approach to object detection is to find, for every possible orientation and position, the template transformation that produces a better matching with the image shape. However, the search space can become overwhelmingly large. An efficient evaluate and subdivide search algorithm is carried out in [5] in order to find the affine transformation that brings the larger number of model features close to image features. A variant of the Hausdorff distance is used as a similarity measure between the two point sets.. Search space can be reduced if invariant features are used. Geometric invariants are shape descriptors that remain unchanged under geometric transformations such as changing the viewpoint. Algebraic invariants are obtained using the classical results derived from perspective geometry of algebraic curves. The fundamental invariant in projective geometry is the cross-ratio (CR). Guo Lei [6] uses the CR to recognize 3D views of different polygons. B.S. Song et al. present in [7] a target recognition method based in CR that selects stable points for complex scenes. More general algebraic invariants can be derived from configurations of conics [8] , points [9] and lines [10] . Besides the algebraic invariants, Rothwell et al. use a canonical frame, invariant to perspective transformations of the plane, to implement index functions that select models from a model database, as part of a recognition system [11] .. Differential invariants can also be applied. In [12] , affine invariants requiring one point correspondence and second order derivative, or requiring two points correspondences and first order derivative, are used to determine whether one curve may be a perspective projection of another one.. Other methods based on Fourier Descriptors [13] are aimed to exploit viewpoint invariants, but they are not fully invariant in perspective transformations. Furthermore, they are not robust when occlusion appears.. Several methods have been proposed to detect the 3D pose of a planar object based on the Hough transform (hashing methods). Using the HT we can take advantage of its useful properties, like relative insensivity to noise, and robustness to occlusions. However, it needs high computational and storage requirements.. In this paper we undertake a new approach to planar object detection based on the Generalized Hough Transform (GHT) that compares template and image information in order to calculate the transformations between the template and the corresponding image shape. Computational and storage requirements are greatly reduced by using invariant template and image information derived from the gradients and positions associated with the edge points. Invariant information is stored in template and image tables which are compared during the detection process. Template (or model) table information will be directly modified during algorithm application without needing further computationally expensive shape processing.. The rest of the paper is organized as follows. Next section introduces the mathematical expressions involved in an orthoperspective transformation. Section 3 presents the new method for planar shape detection and the expressions that allows us to speed-up the generation and comparison of the tables. In section 4, several real experiments have been carried out in order to test the algorithm's behaviour. Finally, in section 5 several related works are analyzed more deeply. A new method to detect planar shapes under orthoperspective projection has been presented. The method copes with a situation in which the shape of the projected image presents a different displacement, orientation and scaling in relation to a template. The method is based on the GHT and generates invariant information, by using gradient information, that allows us to uncouple the parameter calculation and, in this way, reduce computational complexity. A new table generation is accomplished by only using the edge points of the template shape. Generally, the number of edge points in the template is lower than in the image, making the computational complexity of our method to be lower than algorithms using the image shape. Important improvements have been introduced to save gradient angle calculation of the projected points. Several examples, that show the accuracy of the algorithm with real images, have also been presented. In this section, a brief review of another works that use the HT to estimate the 3D orientation and position of a planar patch is presented. Others papers, using the HT for detecting 2D transformations are not covered here [17, 18] .. The method described in [19] claims to be the first one in using the HT for planar object 3D pose estimation. It consists in mapping the classical 2D Hough space into another Hough space of the same dimensions using only geometrical considerations. The new space is related to the former through a 3D transformation that takes into account the orientation and location of an object. In this way, data and model are transformed in a common representation space, where a direct matching can be carried out by determining the pose of the actual object with respect to the known pose of the model. The method is based on the classical HT to detect straight lines, and hence it deals with rigid planar Fig. 3 . Practical situation objects bounded by straight segments. Planar shapes bounded by curvilinear edges, polyhedra and scenes containing several objects can also be tackled, in an indirect and more complex fashion, but they are not addressed in the work presented. The main limitation of this approach, as pointed by the authors, lies in the computational complexity of the matching process, which involves exploring a 6-dimensional space for pose estimation.. A new version of the GHT, called PTIGHT [20] , is proposed for detecting a perspectively transformed planar shape in a perspective image that is taken from an unknown viewpoint. In order to build a perspective reference table from a given template, all possible perspective shape images are derived by applying forward perspective transformation on the template for all viewing directions and positions. The overlapping of this information imposes two restrictions. First, the positions in the HT with votes greater than a threshold are considered potential candidates. This hypothesis must be verified by back-projecting the image shape over the template in order to find the best solution. The resolutions than can be achieved are poor, 5. • for the tilt and pan angles in the reported results. Although the images tested there are not complex, the computational time is high. Also, a camera calibration is required in order to know the focal distance.. The algorithm presented in [15] detects planar objects that are rotated a tilt and pan angle, and distorted by a perspective projection before applying a chain of 2D transformations. Our method reduce the computational complexity of this approach by using a less complex perspective model and restricting the transformation to be applied to the template table which, usually, has a lower number of entries than the image table.. Finally, a technique dealing with parallel projected planar objects with rotational symmetry is presented by Yip [21] . The main contribution of the paper is that it provides a method to reduce the dimensionality of the HT space by breaking it down into several lower order ones. The problem is the shape form and projection model restrictions it imposes.

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


Semantic model for flood management Risk assessment involves the study of vulnerability and hazards. When focused on flood events, such an analysis should evidently include the theoretical and practical study of floods and their behavior.Nevertheless, risk assessment is not useful if the results are not subsequently used for more effective management and planning by local authorities and qualified personnel. The risk evaluation process is composed of a set of actions, each of which requires different inputs. In fact, the results of one action are used as the input for another. This paper describes a semantic model for the study and management of floods with a view to elaborating a conceptual framework and designing a knowledge base. The model is based on the environmental assessment ontology and demonstrates how a brief ontology can be generated.Floods have undesirable consequences, and risk assessment seeks to prevent them by studying hazard risk and potential vulnerability to such events. Furthermore, the results of risk assessment are used in management procedures and decision-making. The main goal is always to 918 The hydrologic cycle describes the continuous movement of water and its many processes. Water evaporates from the oceans and the land surface to become part of the atmosphere by the action of the sun. Water vapor is transported and lifted in the atmosphere by the rising air currents until cooler temperatures cause it to condense into clouds.. Then, it precipitates on the land or the oceans as rain, snow or hail (most water falls back as rain). Precipitated water may be intercepted by vegetation, become overland flow over the ground surface, accumulate as ice caps and glaciers, infiltrate into the ground, flow through the soil as subsurface flow, and discharge into streams as surface runoff. Despite the water that is intercepted or flows as superficial water, much of it returns to the atmosphere through evaporation. The infiltrated water may percolate to recharge groundwater, later emerging in springs or seeping into streams to form surface runoff, and finally flowing out to the sea or evaporating into the atmosphere as the hydrologic cycle continues (Chow et al. ) .. Although the hydrologic cycle seems simple, the phenomenon is enormously complex because of the many interrelated processes. In general, the processes associated with the water cycle are precipitation, canopy interception, snowmelt, runoff, infiltration, groundwater flow, evaporation, sublimation, advection, condensation, and transpiration. However, for flow wave characteristics (and potential flood assessment), such phenomena have to be analyzed on a catchment scale and with relatively short durations (ranging from a few hours to a few days) (Chow et al. ) .. The hydrologic cycle is affected by the weather patterns and physical factors, but also by human progress and activities that alter the equilibrium of the hydrologic cycle, and that start new processes and events. The water cycle affects human development in many ways. It is an essential resource but it also may endanger infrastructures or human activities. Climate change is related to a change in rainfall patterns, and rainfall (as well as other factors) is generally the cause of streamflow. If water flow exceeds normal parameters or if there is some other kind of anomalous event, a flood may occur (Mascarenhas ) .. interact with other natural events as well as with human activities.. This paper proposes the inclusion of a semantic model for flood management in the Environmental Impact Assessment (EIA) ontology and the final generation of a brief ontology in order to simplify and optimize the use of the ontology for flood information. It describes the semantic modeling of floods and flood-related concepts.. The organization of the paper is as follows. The first section briefly outlines the environmental assessment ontology in which the flood model was included. The next section discusses the flood model and its concepts. It then outlines the procedure used to build a separate brief ontology for floods, and discusses its potential application. The final sections include a glossary, the conclusions of this study, and the references cited.

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


Min/max on-chip inductance models and delay metrics This paper proposes an analytical inductance extraction model for characterizing min/max values of typical on-chip global interconnect structures, and a corresponding delay metric that can be used to provide RLC delay prediction from physical geometries. The model extraction and analysis is efficient enough to be used within optimization and physical design exploration loops. The analytical min/max inductance approximations also provide insight into the effects caused by inductances. As integrated circuit and system technologies continue to evolve, the delays associated with global interconnects have an increasingly dominant impact on the overall performance. With higher clocking frequencies and longer global interconnects to span the larger chip dimensions [1] [4] , interconnects are sometimes designed and optimized such that inductance effects become evident [2] . The inclusion of inductance in the timing analyses, however, can be a substantial problem for the overall design flows and methodologies. This difficulty is mainly because of the complexity associated with modeling inductance on an IC, which unlike capacitance that is solved via pattern matching, requires characterization via a field solver such as Fasthenry [3] . While significant progress has been made in speeding up field solvers such as Fasthenry, these solutions are impractical for use in an optimization loop or as part of a routing metric for early phase design planning. Since the global interconnects can have a dominant impact on the overall performance, it is imperative that metrics and models are available to assess the global RLC interconnect paths as early in the design flow as the architecture exploration process.. During the early phases of design, there is generally not even enough physical information to build a precise inductance model. Exact locations of the ground returns and densities and lengths of neighboring wires may not be available when assessment of the global interconnects is required. For this reason we would like to have a simple inductance extraction model, which when provided with the physical information that is available, could predict the minimum and maximum inductance that might result once the physical design is completed. Along with this min/max model we would like to have a delay metric that could be used to guide the optimization of the routing, insertion of repeaters, or changes in the overall foreplay.. In this paper, we propose an analytical inductance extraction model for characterizing min/max values of typical on-chip global interconnect structures. We further describe a delay metric that can be used in cooperation with these models to provide RLC delay prediction from physical geometries with efficiency that is sufficient for inclusion within optimization and physical design exploration loops. We have shown new analytical models for estimating the minimum and maximum loop inductance for on-chip RLC interconnect signal paths. By avoiding the need for a field solver, and providing an equally efficient delay measure in terms of central moments of the RLC model, this work can be used for performance estimation and design optimization during the early phases of design. We first compare the loop inductance values obtained analytically with the results obtained from Fasthenry. The circuit shown in Fig. 5 is used for this comparison. For analytical approximations, eqns. (4), (5) , and (7) are used. The thickness and width numbers are taken from TSMC quarter micron technology [29] . As seen from Table 2 , the results match very well.. Importantly, our analytical model can be used to quickly estimate the loop inductance or changes in loop inductance as a function of wire sizes and spacings. As a demonstration, in Fig. 7 , we show the loop inductance dependency on the width of the return wires for different layers of the TSMC 0.25um technology. The results in Fig. 7 correspond to the minimum loop inductance calculation described in Section 4. In Fig. 8 , we display the loop inductance behavior as a function of the spacing between the signal and ground wires. Once again, these results are for the minimum loop inductance configuration described in Section4.. To demonstrate a complete analysis which includes extracting the parameters and estimating the delay via our proposed metric, we consider a 1 mm long interconnect which is divided into 10 RLC segments. The width and thickness of the wire are 0.5 and 0.58 microns, respectively. The resistance per square is 0.065 ohms and the capacitance per unit length is 0.00024 picofarads per microns. The line is excited with a step input voltage source with a 10 ohms source resistance and is terminated with a 25 femtofarad capacitive load. The minimum loop inductance model was calculated as 0.26 nanohenries for this 1 mm long wire. The maximum loop inductance estimate was 0.98 nanohenries assuming a 10 microns separation between the rails. The absolute maximum inductance value is the partial self inductance of the wire, which for this example had a value of 1.61nH. The second and third order central moments were calculated for this range of inductance values, and the results are summarized in Table 3 . The step response delays for these cases were also analyzed with a second order AWE approximation, and are also included in the table. The Elmore delay value is 0.0215 nanoseconds, and since it is invariant to inductance it is the same for all the cases. The corresponding output waveforms are plotted in Fig. 9 .. Comparing the central moments from the table with the waveforms in Fig. 9 , it is apparent that the second and third central moments are very good indicators of the inductance. When the minimum inductance model is used, the delay is changed very little compared to the RC case. The central moments accurately predict that the inductance effect is not significant in this case. Small changes in the central moments compared to RC case imply that the Elmore delay can still be used as the delay metric. As seen from the waveforms, the change in the slope is also small for the minimum inductance case.. In contrast, when only the partial self inductance value (last column) is used, both the second and third central moments become negative. Although the delay in this case is closer to the Elmore delay, use of the Elmore delay metric is no longer reliable since the waveshape is non-monotonic, and the slope is not easily measured.. The negative values for the second and third central moments clearly indicate the underdamped response shown in Fig. 9 .

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


Vaidurya: A multiple-ontology, concept-based, context-sensitive clinical-guideline search engine We designed and implemented a generic search engine (Vaidurya) Effective search and retrieval of relevant documents has become crucial with the recent growth in digital literature, in general, and the medical literature, in particular [1] . The requirement for effective retrieval is especially crucial when searching for a clinical guideline to manage a particular patient or a group of patients at the point of care, or when assessing retrospectively the quality of care that should have been administered according to one or more established state-of-the-art guidelines. The need has become further emphasized by the recent trend towards provision of automated support to guideline-based clinical care, and search engines must consider the special requirements introduced by the process of structuring guidelines for such a purpose. As we demonstrate in our study, exploitation of that structuring is both quite feasible and beneficial.. Typically, documents are retrieved using traditional full-text search, as originally described by Salton et al [2] , however this approach is not accurate enough and doesn't exploit the potential existence of rich domain-specific knowledge, which is common in the medical domain, and especially when searching for clinical guidelines appropriate for application to a specific patient.. For example, the medical domain offers controlled vocabularies and various tools for using them, such as the Unified Medical Language System (UMLS) [3] . Current search methods, such as the one used in Medline, index documents according to the MeSH conceptual hierarchy [4] , either manually or by automatic means, such as the MetaMap tool [5] . Thus, a textual query is also converted into a set of representative concepts, which are matched to the indexed documents, leading to a concept-based search. Such approaches, however, do not fully exploit the hierarchical relations among the concepts, such as the semantics of parent and Page 4 of 38 pages child links, and thus do not necessarily lead to an improvement over traditional full-text search [6] .. Furthermore, medical documents often have an explicit and meaningful internal structure.. For example, medical documents usually include sections such as "Introduction" and "Discussion," while clinical-guideline documents often contain even more semantically meaningful segments, such as "Description of the eligible population" or "Objectives". Such a structure can support a context-sensitive search, in which terms are searched only within certain meaningful segments of the documents, potentially enhancing the precision of the retrieval process.. Both of these avenues for enhancement of the search precision have been explored in our study and were found to indeed be fruitful. In this paper, we describe in detail Vaidurya -a search engine that uses concept-based and context-sensitive search in addition to the traditional full text search. For example, Vaidurya explicitly capitalizes on the existence of external conceptual hierarchies, exploits the semantics of their inner structure, and enables the user to specify certain logical relations among them.. Vaidurya [7] is a search engine originally developed for retrieval of clinical guidelines within our digital guideline library, DeGeL [8] , a set of Web-based tools for structuring, search, retrieval, and application of clinical guidelines. As we describe below, retrieval of suitable guidelines for care of particular chronic patients is an important and highly motivating objective. However, the Vaidurya search engine was designed to be quite generic, and is appropriate for search and retrieval within any collection of structured and indexed documents for which certain ontological assumptions hold, a situation that is most common in medical domains. Other examples include collections of articles in biomedical domains, as we had recently demonstrated in the case of the Trec Genomics collection [9] . Throughout this paper, Page 5 of 38 pages we will exemplify our new approach to concept-based and context-sensitive search using the example of searching within a clinical-guideline library, a sub-domain in which we had rigorously and quantitatively evaluated our framework. For the purposes of that evaluation, reported elsewhere [10, 11] , we used the National Guideline Clearinghouse (NGC 1 ) clinicalguideline collection, and its internal hierarchical structure, which we briefly describe in the Evaluation section.. In this paper, we present in detail the Vaidurya system's computational infrastructure and present briefly an integrated view of the results of its evaluation. We start by introducing the domain of supporting clinical-guideline retrieval and application; then we proceed with introducing concept-based and context-sensitive search; we continue by describing Vaidurya's computational architecture and by summarizing the results of its evaluation in the guideline domain. Although we had evaluated the methodology within a particular guideline ontology and set of conceptual indices, the results are independent of the particular guideline ontology and conceptual hierarchy used. We conclude by presenting our overall insights regarding the limitations and advantages of the Vaidurya framework, and the specific measures that we had already taken to overcome some of its limitations. We have demonstrated the feasibility of designing and implementing a functional full-text, concept-based, and context-sensitive search engine for clinical, semi structured documents Page 28 of 38 pages that are classified into several levels of several conceptual hierarchies. In the case of the concept-based search, the queries use concepts from multiple hierarchies; the documents classified to these concepts and to their ontological descendents are retrieved based on internal and external logical operators defined by the query among the concepts. Furthermore, we have demonstrated the potential value of concept-based and context-sensitive search in addition to full-text search, at least within a relatively significant-size electronic clinical-guideline repository, and especially when base-line precision is low.. Although the described search-and-retrieval framework is a general one, we evaluated the approach on a collection of textual CPGs, whose effective search and retrieval is one of our main objectives, as explained in the introduction.. Indexing the documents along multiple hierarchical semantic axes, such as is done by the NGC Disorders and Therapies axes, or by the seven indexing hierarchies currently implemented in the DeGeL framework, supports a concept-based search, in which the user explicitly indicates in the query multiple concepts from one or more semantic axes.. The markup process that a CPG goes through, for example within the DeGeL architecture, using the URUZ hybrid (multiple-format) mark-up and specification tool for the grad- Combining several types of search based on weighting schemas, such as in text retrieval, and Boolean chemas in the case of conceptual retrieval were used also in Text Categorization [41] , knowledge based text retrieval [42, 43] , question-answering [44] . Our use in this study of concept-based search is somewhat different from previous work, which has not often demonstrated an improvement; this difference in method might explain the enhancement in results achieved here. Concept-based indexing in the medical domain often uses concepts that are extracted automatically from the text contents, usually referring to the MeSH conceptual hierarchy. Similarly, the user's query (also a document) is converted automatically into a concept query, and matched against all the indexed documents, as in the case of the PubMed tool. In contrast, the concept-based queries in Vaidurya are specified explicitly by the user. In addition, the libraries we have applied it to (DeGeL and NGC) use mostly manual indexing. Our experimental results show that the concept-based search improved the retrieval performance when used in addition to full-text and context sensitive queries [10, 11] .. One of the limitations of the current study is that we had performed before the main experiments a preliminary experimentation with multiple different settings, using an automated test and a small set of judgments; changing the relative weights of the three search types did not seem to change the performance, so the weights were left as uniform. However, future experiments with multiple additional queries might be needed to better validate these preliminary default settings.. During the performance of our study, there were two potential obstacles to the use of concept-based and context-sensitive search that were mentioned by the DeGeL and Vaidurya users; we have since then attempted to address both. The first obstacle mentioned in our preliminary experiments was that the CBQ and CSQ search interface, although powerful, was highly overloaded from the point of view of a casual clinical user. It displays both the semanPage 30 of 38 pages tic axes used by the concept-based search and the target ontology's semantic roles, which are used by the context-sensitive search. To overcome this potential problem, we developed and presented elsewhere new interfaces that are simpler and that we expect to be significantly more user-friendly. These interfaces offer several versions of the search screen, each at a different sophistication level, all customizable by the user [45] . In addition to these customizable interfaces, which mainly select contexts from the selected document's contextual model, we have also developed a query interface in which clinicians assisted by a medical informatics expert can create query templates for end users, who are not familiar with the underlying context model, and possibly not even with the specific medical domain in which they wish to search [46] . A second potential obstacle to the use of concept-based search, mentioned by IndexiGuide users within the DeGeL library, was the need for the manual classification of each new document added to the digital library (unless originally classified by the author using the same semantic axes; even in that case, additional indices are often useful for the Vaiduyra engine purposes), potentially a time-consuming task even for an expert mark-up tool editor.. Non-satisfactory indexing may conceivably harm the precision of the concept-based retrieval method. Thus, we have developed an automatic classifier that classifies new guidelines along multiple semantic hierarchical axes, based on a given set of guidelines previously classified using the same axes. The guideline classifier thus proposes to the human editor, given a new guideline, a set of paths (i.e., both intermediate and leaf nodes) in the concept hierarchy, by which the new guideline might be indexed, thus significantly facilitating the task of multiplehierarchical indexing of the new guideline. We have rigorously evaluated the new automatedclassification approach within the NGC framework, with encouraging results [47] .. Our conclusions are thus that the Vaidurya engine's concept-based and contextsensitive search and retrieval methods are both usable and useful, and that the potential obsta- We start by introducing the need for effective search and retrieval of electronically represented clinical practice guidelines. We then introduce in more detail the ideas of conceptbased search and context-sensitive search, before focusing on our specific methods.

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


Optimal Cuts and Partitions in Tree Metrics in Polynomial Time We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one dimensional geometric metric settings. Our method of solution could be also of independent interest in other applications. We discuss also an extension of our method to the class of metrics induced by the bounded treewidth graphs. The optimal partition problems for unweighted and weighted graphs are classical NP-hard combinatorial optimization problems.. The typical partition problems, like MAX-CUT and MAX-BISECTION are well known to be APX-hard [9] . Also the existence of a PTAS for MIN-BISECTION has been likely ruled out in [13] . The metric counterparts of these problems are to find the corresponding optimal partitions of the complete graph on the input point set, where edges are weighted by metric distances between their endpoints. The metric MAX-CUT, MAX-BISECTION, MIN-BISECTION and other partitioning problems were all proved to have polynomial time approximation schemes (PTAS) [1, 8, 11, 5, 7, 6, 10] . These problems are known to be NP-hard in general metric setting (e.g., for 1 − 2 metrics [8] ). Their exact computational status for geometric (i.e., L p ) metrics and this even for dimension one was widely open.. In this paper, in particular, we resolve the complexity status of these problems for just dimension one by giving a polynomial time algorithm. Our solution, somewhat surprisingly, involves certain new ideas for applying dynamic programming which could be also of independent interest (see [12] for a preliminary version). In fact, our dynamic programming method works for the more general case of tree metric spaces, where the underlying trees have nonnegative real edge weights (see also the embeddability properties of arbitrary metrics in tree metrics [4] ). Observe that the one dimensional case can be modeled by line graphs with nonnegative real edge weights. We also give an evidence that our polynomial time method can be extended to include analogous partition problems in metric spaces induced by shortest paths in graphs of constant treewidth.

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