Multisets and Structural Congruence of the pi-Calculus with Replication Abstract. In the -calculus with replication, two processes are multiset congruent if they have the same semantics in the multiset transition system M . It is proved that (extended) structural congruence is the same as multiset congruence, and that it is decidable. A particularly elegant version of the -calculus was presented in 7] . The main aspects in which it di ers from the usual -calculus of 8] are twofold.. First, it has replication as an operation on processes, rather than recursion.. The replication !P of a process P consists of the parallel composition of in nitely many copies of P. Replication can be used to simulate recursion, but is much easier to handle theoretically. Thus, it seems to be more basic than recursion. In a certain sense, from the point of view of formal language theory, replication is similar to the Kleene star operation in regular expressions, whereas recursion is similar to context-free grammars. Second, a natural relation of structural congruence between process terms is de ned, and used to present the axioms and rules of the transition system of the -calculus in a compact way. The idea is that process terms are descriptions of processes, and that these processes are characterized by their \spatial" structure. In other words, two process terms describe the same process if and only if they have the same structure, and such process terms are said to be structurally congruent. Compactness of the axioms and rules is obtained by the natural stipulation that structurally congruent process terms have the same behaviour (in fact, it is the behaviour of the process that they describe). As an example, process terms (P j Q) j R and Q j (R j P) are structurally congruent because they both describe a process consisting of three subprocesses P, Q, and R that are placed in parallel, i.e., the parallel composition of P, Q, and R. Structural congruence is de ned in 7] to be the smallest congruence that satis es eight such structural laws.. These two main aspects are closely related. Replication is a typically structural operation on processes, just like parallel composition. In fact, it is \just" ? The research of this author was supported by the Esprit Basic Working Group No.6067 CALIBAN an in nite version of parallel composition. On the other hand, recursion is usually viewed as a behavioural construction (although it is also possible to view it structurally, by unfolding the recursion). Thus, the use of replication ts well in the structural approach; in fact, replication can be completely described by structural laws, and no separate transition rules are needed.. Restriction, of the scope of a name to a (sub)process, is also usually viewed as a structural operation. Certain subprocesses of a process \know" the name and others do not, and this can be seen as \spatial" information. In fact, in 6], the operations of CCS are divided into static (or structural) operations and dynamic (or behavioural) operations. The static operations are parallel composition, restriction, and relabeling, and the dynamic operations are pre x (or guard), sum, and recursion. Since the -calculus of 7] has no relabeling or sum, and dynamic recursion is replaced by static replication, only the use of guards is dynamic in this version of the -calculus.. In 4, 5] the process terms of CCS are interpreted as \ owgraphs" that correspond intuitively to their structure, i.e., to the processes they describe (see also the informal use of owgraphs in 6, 8] ). Structural laws for the process terms of CCS (called \laws of ow") are given that are sound and complete with respect to the owgraph interpretation. To be more precise, two such process terms have the same owgraph if and only if they are in the smallest congruence (with respect to the static operations) that satis es the given structural laws. Also, process terms with the same owgraph have the same behaviour, where, in this case, \same" means \strongly bisimilar". The corresponding laws for strong bisimilarity are the \static laws" in Section 3.4 of 6].. In 2, 3] a \multiset semantics" (or Petri net semantics) of the -calculus of 7] is given that is closely related to the structural approach. A transition system M is de ned of which the states are \solutions", which are multisets of molecules, and a \molecule"' is a guarded solution (the chemical terminology is taken from the Chemical Abstract Machine of 1]). A multiset of molecules can be viewed as a \spatial" distribution of molecules, where several copies of the same molecule may be present in the solution. In accordance with the operation of replication, there may even be in nitely many such copies. Moreover, a semantic mapping is de ned that associates with each process term of the -calculus a state of M . It is proved in 2, 3] that the semantic mapping is a strong bisimulation between a process term and its corresponding multiset in M . Thus, from the interleaving point of view they have the same behaviour. The gain is that, intuitively, the behaviour of the multiset in M is the \true concurrency" behaviour of the process term.. Two process terms are said to be multiset congruent if they correspond to the same multiset in M . It is claimed in 3] that the multiset corresponding to a process term represents its \spatial" structure, i.e., the process it describes. In fact, the multisets can be viewed as a kind of nested owgraphs (\nested" because multiset congruence is a congruence for all operations of the -calculus rather than only the static ones). It turned out in 3] that, indeed, multiset congruence and structural congruence (as de ned in 7] ) are closely related, but unfortunately not as closely as one would wish. It was shown that structurally congruent process terms are multiset congruent, but not vice versa. However, the failure of the reverse direction seemed to be due to the omission of a few natural structural laws that from an intuitive point of view should be valid.. An example of such a law is the structural equivalence of !P j !P and !P . This is basically a cardinality law which expresses that adding in nitely many copies of P to in nitely many copies of P still leaves you with in nitely many copies of P. In this paper we show that, indeed, after the addition of a few such natural structural laws, structural congruence and multiset congruence are the same. This means that the laws of structural congruence are now sound and complete with respect to the multiset semantics (or rather, its structural part). It is the analogue of the results of 5] for the -calculus. As a second result, we show that multiset congruence, and hence (extended) structural congruence, is decidable. Clearly, any \good" notion of static, structural equivalence should be decidable; intuitively, you should only have to \look at" two processes in order to see whether or not they have the same structure. Thus, the two results of this paper support the thesis that the general notion of structure of processes, as introduced in 4, 5, 6] for CCS and in 7] for the -calculus, is a natural one.. The main technical concept in the proof of the two main results is that of a \connected" solution. Each molecule in a solution \knows" a number of names (i.e., communication links). Some of these names are public (or global), i.e., known to all molecules, whereas others are secret (or local), i.e., known to a restricted number of molecules only. The secret names are also called \new" names, because they are new, unique, names that are introduced by the semantical mapping as a result of the restrictions that occur in the process term. As an example, a replication of a restriction gives in nitely many copies of the restriction, each of which should have its own \new" name. Let us now say that two molecules are \related" if they \know" at least one common \new" name. This is a natural relationship, because two such molecules are into the same secret; thus, they naturally belong to each other. We will say that a solution is connected if the resulting graph of molecules with their relationships is connected, in the usual sense. This means that everybody is (transitively) related to everybody else. More in general, any solution can be divided into \connected components". This division gives an intuitive picture of clusters of relationships. The proof of the main results uses a normal form lemma: every process term is structurally congruent with one that only replicates subterms of which the corresponding solution is connected. Intuitively, if a connected component corresponds to a \module" that does a certain job, then it is natural to replicate such a module. The normal form lemma says that the use of replication can be restricted to such cases.. The structure of the paper is as follows. In Section 2 some de nitions from 7] and 2, 3] are recalled. The reader is assumed to be more or less familiar with the de ned concepts and their basic properties. Section 2 contains in particular the full de nition of structural congruence, with the addition of the new structural laws. In Section 3 we discuss a few basic properties of multisets in general that are needed in the formal proofs. Section 4 introduces the notion of a connected solution and investigates the relationship between connectedness and multiset union. Section 5 contains the above-mentioned normal form of process terms. In Section 6 the two main results are proved: structural congruence and multiset congruence are the same, and decidable.

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


Algorithms for Joint Optimization of Stability and Diversity in Planning Combinatorial Libraries of Chimeric Proteins Abstract. In engineering protein variants by constructing and screening combinatorial libraries of chimeric proteins, two complementary and competing goals are desired: the new proteins must be similar enough to the evolutionarily-selected wild-type proteins to be stably folded, and they must be different enough to display functional variation. We present here the first method, Staversity, to simultaneously optimize stability and diversity in selecting sets of breakpoint locations for site-directed recombination. Our goal is to uncover all "undominated" breakpoint sets, for which no other breakpoint set is better in both factors. Our first algorithm finds the undominated sets serving as the vertices of the lower envelope of the two-dimensional (stability and diversity) convex hull containing all possible breakpoint sets. Our second algorithm identifies additional breakpoint sets in the concavities that are either undominated or dominated only by undiscovered breakpoint sets within a distance bound computed by the algorithm. Both algorithms are efficient, requiring only time polynomial in the numbers of residues and breakpoints, while characterizing a space defined by an exponential number of possible breakpoint sets. We applied Staversity to identify 2-10 breakpoint sets for three different sets of parent proteins from the purE family of biosynthetic enzymes. The average normalized distance between our plans and the lower bound for optimal plans is around 1 percent. Our plans dominate most (60-90% on average for each parent set) of the plans found by other possible approaches, random sampling or explicit optimization for stability with implicit optimization for diversity. The identified breakpoint sets provide a compact representation of good plans, enabling a protein engineer to understand and account for the trade-offs between two key considerations in combinatorial chimeragenesis. Protein engineering by site-directed recombination ( Fig. 1(a) ) generates libraries of hybrid proteins (or "chimeras") by mimicking the mixing and inheritance that occur in natural reproduction. A set of homologous parent genes are recombined at defined breakpoint locations, yielding a combinatorial set of hybrids [1] [2] [3] [4] . In contrast to stochastic library construction methods (e.g., [5] [6] [7] ), site-directed approaches explicitly choose breakpoint locations to optimize expected library quality (e.g., predicted disruption [2, 8, 9] or library diversity [10] ). In contrast to mutagenesis, the mutations introduced by site-directed recombination are known to be compatible with each other in parent proteins with a similar structural context (due to homology), and are thus expected to be less disruptive. Without requiring precise modeling or prediction of the effects of mutation, sitedirected recombination can produce variant proteins with improved properties and activities [2, 3, 11, 12] .. There are two competing goals in recombination experiment planning. We want the resulting hybrids to be stably folded, which is easiest to achieve if they are just like wild-type proteins. At the same time, we want the hybrids to have different activity, which of course requires that they be different from wild-type. By construction, site-directed recombination preserves single-position conservation statistics, since each residue position in the hybrid library is simply taken from one of the parents, and all parents are equally represented within the combinatorial library. Thus evaluation of stability typically focuses on correlation statistics between interacting residues [1, [13] [14] [15] 9] . The key insight (middle of Fig. 1(a) ) is that recombination "perturbs" the distributions of amino acid types for interacting residues, thereby potentially disrupting the interactions underlying stable folding. Models of residue correlation have been shown to capture important information in a number of applications, including prediction of free energy changes caused by hydrophobic core mutations [16] , prediction and recognition of native-like protein structure [17] , and functional classification of members of protein families [18] . Pairwise [1] and higher-order [9] models have been used in algorithms to plan site-directed recombination experiments minimizing perturbation (and thereby maximizing expected stability), and have led to the creation of variant proteins with improved or novel activities [2, 3, 11, 12] .. In addition to stable hybrids, we also want a diverse hybrid library in order to obtain hybrids with improved or novel activities. Under various methodologies and on a number of systems, including cytochromes P450 [14] , β-lactamases [19] , and single chain Fv antibodies [20] , functional change from wild-type has been correlated with the number of mutations in protein variants. Earlier work on sitedirected recombination optimizes for stability while indirectly forcing diversity by constraining the minimum fragment length [14] . Our recent work developed the first approach to explicitly optimize for diversity, by finding breakpoint locations that sample protein sequence space relatively uniformly [10] (right of Fig. 1(a) ). However, since diversity competes with stability, it is desirable to explicitly consider both criteria simultaneously. This paper presents Staversity (a hybrid word with both "stability" and "diversity"), the first method to explicitly optimize both stability and diversity in planning site-directed recombination experiments. A set of breakpoints defines a hybrid library that can be evaluated by metrics we call "perturbation" and "diversity variance" (Fig. 1(a) ). We seek to minimize perturbation as a way to ensure stable hybrids, and we seek to minimize diversity variance as a way to evenly spread out hybrids in sequence space. Using diversity variance and perturbation values as two dimensions, we can consider possible breakpoint sets as points in a two-dimensional space ( Fig. 1(b) ). Since it is difficult for an experimenter to decide a priori upon the "best" combination of these two incommensurate factors, our methods provide insights into the trade-offs by finding undominated sets of breakpoints-those for which no other set of breakpoints is better for both factors ("Pareto optimal", in economics jargon). Our goal is to find the undominated sets efficiently, without explicitly enumerating the exponential number of possible plans. The problem of finding optimal trade-offs between competing desired criteria is a common one. For example, in considering how to segment records in a large shared database, Eisner and Severance studied the optimal trade-off between the cost of storage and the benefit of retrieval [21] . The goal was assumed to be either a linear or non-linear combination of cost and benefit, and parametric analysis was applied to find the optimal trade-off under all possible parameter values. In computational biology, such ideas are also at the heart of a parametric approach to sequence alignment, e.g., trading off match scores and gap penalties [22] . A comprehensive analysis of parameteric sequence alignment [23] showed that for both global and local alignment, the number of parametric regions to be considered is bounded, and that fast algorithms [24] can be employed to perform the alignment.. In the present case, there is no underlying notion of an optimal trade-off; instead, we want to provide the experimenter with an overview of all possibilities worth considering (because they are undominated). We prove that the results of convex optimization (breakpoint sets on the lower convex hull) are undominated, and develop the natural polynomial-time algorithm to find those breakpoint sets (similar to the parametric analysis in [21] [22] [23] ). We also develop a polynomialtime algorithm to uncover many of the breakpoint sets in the concavities which are either undominated or can be shown by the algorithm to be within a small distance of any undiscovered set that would dominate them.. We present planning results for cases with from 2 to 10 breakpoints and three different sets of parents from the purE family of biosynthetic enzymes that we are currently studying by site-directed recombination. Overall, our plans can be proved to be quite good-the average normalized distance between our plans and the lower bound on optimal plans is around 1 percent. Other possible methods (either sampling breakpoint sets randomly, or explicitly optimizing for stability while implicitly optimizing for diversity) don't do nearly as well-on average for each parent set, our plans dominate 60-90% of those. We present a method to optimize breakpoint selection for site-directed protein recombination considering stability and diversity simultaneously. Our method is generic in metrics for stability and diversity, and by finding undominated breakpoint sets, it allows the experimenter to assess the trade-offs between these factors. Unlike other methods, we can provide optimality guarantees on identified breakpoint sets. In practice, our method significantly outperforms existing alternatives, finding more and better breakpoint sets. Staversity should be a valuable tool enabling protein engineers to choose experiments that better explore sequence space, improving the "hit-rate" of finding proteins that are stably folded and have novel activity. Let P = {P 1 , P 2 , . . . , P n } represent a multiple sequence alignment of n parent proteins, with each sequence of length l including residues and gaps. A recombination experiment with λ breakpoints is defined by a set of breakpoint locations X = {x 1 , x 2 , . . . , x λ | 1 ≤ x 1 < x 2 < . . . < x λ < l}. The breakpoints partition each parent P a into λ + 1 fragments with sequences P a [1,. , where in general we use P a [r, r ] to denote the amino acid string from position r to r in sequence P a , and P a [r] to denote the single amino acid at position r. A hybrid protein H i is a concatenation of chosen parental fragments, assembled in the original order. Thus it is also of length l. Then a hybrid library H(P, X) = {H 1 , H 2 , . . . , H n λ+1 } includes all combinations.. Given a breakpoint set X, we can evaluate the perturbation and diversity variance of the resulting hybrid library with metrics v p (X) and v d (X) (see below). We assume, without loss of generality, that both v d and v p are to be minimized. For two breakpoint sets X and X , if. , and one of the two inequalities is strict, we say that X is dominated by X. Let X λ be the set of all possible λ-breakpoint sets. If for some breakpoint set X there is no X ∈ X λ that dominates it, we say that X is undominated. If X is not dominated by any X ∈ X λ for some subset X λ ⊂ X λ of possible breakpoint sets, we say that X is locally undominated. Our goal is then:. Goal: Given parent proteins P and number of breakpoints λ, find the set U λ of undominated λ-breakpoint sets.. Once undominated breakpoint sets have been computed, the experimenter can readily evaluate trade-offs between diversity variance and perturbation. For example, the minimal perturbation experiment X * for a given maximum diversity variance threshold θ d is readily found as X * = arg min. If desired, appropriate data structures can be established to efficiently support such queries.

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


Alternating decision tree algorithm for assessing protein interaction reliability Abstract This paper presents a machine learning approach for assessing the reliability of protein-protein interactions in a high-throughput dataset. We use an alternating decision tree algorithm to distinguish true interacting protein pairs from noisy high-throughput data using various biological attributes of interacting proteins. The alternating decision tree algorithm is used both for identifying discriminating biological features that could be used for assessing protein interaction reliability and for constructing a classifier to identify true positive interacting pairs. Experimental results show that the proposed approach has a good performance in distinguishing true interacting protein pairs from noisy proteinprotein interaction data. Moreover, our alternating decision tree classifier supplemented with domain knowledge may be helpful to understand the biological conditions in connection with interacting protein pairs. In this paper, we presented an assessment scheme for the reliability of candidate interacting proteins in a PPI dataset. This scheme is based on the alternating decision tree algorithm and utilizes the domain knowledge of PPIs. Since the quality of training data determines the reliability and robustness of classifiers, we carefully derived a negative dataset based on co-localization enrichment measure. As a result, we constructed an evaluation system for assessing protein interaction reliability using positive datasets obtained from known protein complex and negative datasets derived based on co-localization characteristics. The experimental results show that applying an alternating decision tree algorithm supplemented with various biological attributes provides excellent performance overall in distinguishing true interacting protein pairs from a noisy PPI dataset. Moreover, our alternating decision tree classifier is helpful to understand the biological conditions of interacting protein pairs with confidence score. The classifier may also be helpful in predicting new candidate interaction protein pairs.. Studies of biological networks should start with reliable interaction data. A number of reliable PPI datasets assessed by this system can be used as a valuable resource for proteomics research.. Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

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An Adaptive Correspondence Algorithm for Modeling Scenes with Strong Interreflections Abstract-Modeling real-world scenes, beyond diffuse objects, plays an important role in computer graphics, virtual reality, and other commercial applications. One active approach is projecting binary patterns in order to obtain correspondence and reconstruct a densely sampled 3D model. In such structured-light systems, determining whether a pixel is directly illuminated by the projector is essential to decoding the patterns. When a scene has abundant indirect light, this process is especially difficult. In this paper, we present a robust pixel classification algorithm for this purpose. Our method correctly establishes the lower and upper bounds of the possible intensity values of an illuminated pixel and of a nonilluminated pixel. Based on the two intervals, our method classifies a pixel by determining whether its intensity is within one interval but not in the other. Our method performs better than standard method due to the fact that it avoids gross errors during decoding process caused by strong interreflections. For the remaining uncertain pixels, we apply an iterative algorithm to reduce the interreflection within the scene. Thus, more points can be decoded and reconstructed after each iteration. Moreover, the iterative algorithm is carried out in an adaptive fashion for fast convergence. C REATING high-quality models for real-world scenes, such as shiny ornaments and artifacts, plays an important role in computer graphics, virtual reality, and other commercial applications. Active methods, e.g., structured-light systems, add light into the scene and, thus, are more robust than passive methods (e.g., stereo vision [26] ) that only receive energy from the scene. One popular option among structured-light systems is a camera-projector system. A naive system will turn on one or a cluster of projector pixels at a time and search for the single dot being projected onto the scene. To reduce the total number of projections, many different codification strategies have been proposed [22] . Pairs of camera and projector pixels that see the same codeword are corresponded and triangulated to obtain 3D scene samples allowing for point-based modeling and rendering [10] , and other graphics applications, such as surface reconstruction [8] . Among the many strategies, time-multiplexed codes, e.g., Gray codes [9] , yield robust and high-resolution 3D information with a relatively small number of patterns. To achieve greater precision, phase shifting patterns, such as sine waves [25] , can also be applied. We present an approach using a structured-light-based method with Gray code binary patterns which iteratively obtains an increased number of accurately reconstructed scene points as compared to the conventional approach (Fig. 1) . Our algorithm adapts the structured-light patterns according to the partially reconstructed scene geometry and reflectance property of the scene so as to reduce the amount of indirect illumination, while keeping the same amount of direct illumination for the remaining nondecoded pixels. Pixels are attempted to be corresponded using a robust decoding algorithm based on estimated tight intensity value bounds. A projector-space subdivision is used whenever the number of additionally decoded pixels for an iteration is too small. Parallelism is automatically exploited during subdivision in order to simultaneously decode as many nonconflicting pixel subsets as possible and, consequently, reduce acquisition time. Fig. 2 summarizes our entire algorithm pipeline. After separation of the scene under the illumination of a fully lit projector into its direct and indirect components (Fig. 2a) , we capture images and reconstruct 3D points (Fig. 2b) . Based on the reconstruction result, we reduce the interreflection within the scene (Fig. 2c ) and generate new projector patterns (Fig. 2d) . Then, we iterate the capturing and reconstruction again. If the gain for an iteration is too small, we adaptively subdivide the projector image in order to further reduce interreflection (Fig. 2e) . After each iteration, the reconstruction of the scene is more complete. The algorithm continues until no more points can be decoded and reconstructed. The end result is a significantly improved model of the scene including objects with strong interreflections at the cost of more photographs compared to a standard structured-light method. We have used our approach to capture several data sets of nondiffuse (e.g., glossy) 3D objects. Our method is consistently able to increase the number of correctly reconstructed points by almost 2Â and to decrease the number of incorrectly classified pixels by about 10Â .. Our major contributions can be summarized as. . a robust method to classify a pixel as directly illuminated or not, based on the intensity intervals of a pixel under the illumination of a binary pattern, . an adaptive structured-light algorithm which iteratively reduces the per-pixel indirect component and thus allows better reconstruction, and . an acquisition system which can acquire complex scenes with strong interreflections. The work introduced in this paper significantly extends our previous conference publication [33] by presenting an iterative and adaptive structured-light method enabling a complete reconstruction of complex scenes. We have presented an adaptive and iterative algorithm for modeling scenes with strong interreflections. Our algorithm is based on establishing accurate pixel intensity intervals of a We have applied our approach to the capture of five example scenes, ranging from a single concave object to complex scenes with several objects. Table 3 summarizes the statistics of our data sets. The first data set is a single bowl. The dinnerware data set consists of three mugs, one bowl, and two Vitrelle glass plates. The objects 1 data set has two plastic buckets and three porcelain ornaments. The objects 2 data set is formed of several shiny objects which generate a lot of interreflection. Finally, the lady data set is a case containing strong diffuse interreflection. We list the total number of photographs captured, the amount of time spent capturing images and reconstructing the models, the number of iterations and adaptive subdivisions to capture the final model, and the number of points reconstructed using standard classification (the method that compares pattern image and its inverse as in Fig. 3c ), our classification for only one iteration, and our classification for all iterations. The number of points reported is obtained by adjusting global culling thresholds until there are no visual outliers. Since our cameras have much higher resolution than the projector, the number of reconstructed points is much less than the number of camera pixels. For bowl and dinnerware, only areas containing the objects are reconstructed, additional points belonging to walls and tables are discarded. As shown in the table, a significant amount of time was spent capturing images and transferring them from our cameras to the computer using USB cables. In addition, our high-resolution 3CCD camera produces highquality imagery but increases processing time because of the greater number of pixels. Using a lower-resolution camera can reduce both acquisition and processing time but at the expense of lower image quality.. The first data set is a single concave and white porcelain bowl. Fig. 7 shows pictorially the classification results of the bowl. As one can see, the actual images (Fig. 7a) are difficult to classify due to strong interreflection. The standard method produces a lot of false positives (Fig. 7b) . In contrast, our method avoids misclassifications by declaring these difficult pixels as uncertain (Fig. 7c) . The unclassified pixels are resolved during later iterations of our algorithm (Fig. 7d) . In the presence of highlights and caustics, the smoothness constraint assumed by the separation method does not hold [20] . Therefore, the estimated direct and indirect components are inaccurate. In this case, our method does generate false labeling for the pixels belonging to such regions (circular structure in Fig. 7d ). However, we found that the postprocessing of the correspondence data will easily reject these outliers. Our final classification is very close to the ground truth (Fig. 7e) . The ground truth results are generated by manually classifying the pixels in each pattern image.. To understand the behavior better, we graph the number of correctly classified pixels and incorrectly classified pixels for both standard method and our method. A pixel is correctly classified if its on/off decision is the same as that of the ground truth. A pixel is incorrectly classified if its on/off decision is opposite to that of the ground truth. Fig. 8 shows the two graphs. When computing the number of correctly classified pixels for level l, we only count those that are correctly classified for all levels up to l. For incorrectly classified pixels, we count those that are incorrectly classified for any level up to l. As can be seen, although standard classification can produce 45 percent more correct classifications than one step of our method, it also generates 41 times more incorrectly classified pixels. During reconstruction, these false positives cause correctly classified pixels to be culled away. By applying our robust classification for all the iterations, we obtained 21 percent more correct classifications and 10 times less incorrect ones. Thus, the overall modeling quality is much higher. The numbers reported for all iterations includes those of the first iteration and all the later iterations. Fig. 9 shows the pictures of the results for the bowl. The quantitative improvement over standard method is 21 percent for the first iteration and 88 percent after eight iterations. The reconstructed point cloud using standard method is irregular (Fig. 9a) . In contrast, our method initially avoids dealing with ambiguous regions and reconstructs the nonambiguous areas fairly well (Fig. 9b) . The final reconstruction after several iterations of our method is close to a complete model (Fig. 9c) . The remaining small holes are due to difficult configurations such as caustics, pixel overflow due to specular highlights, and surface patches that are nearly parallel to the viewing or lighting directions.. Since we have manually labeled the pixel-code maps for this data set, we can apply the same reconstruction engine to produce a ground truth point cloud. Then, points reconstructed using ground truth classification, standard classification, and our classification can all be corresponded through their projector pixel coordinates; this allows us to easily compute the distance between the ground truth model and a reconstructed model without aligning models and/or finding the closest points between the models. To evaluate the accuracy and completeness of our approach, we use the same metric as in [28] . We first compute the perpoint distance between the ground truth model (G) and the model to be evaluated (R). To evaluate accuracy, we compute the distance d, for which, X percent of points of R are within distance d to ground truth G. A more accurate reconstruction tends to have a smaller d value. Fig. 10a shows the results for different X values (plotted along the horizontal axis) using standard method and our method. As can be seen, our method consistently produces more accurate reconstructions than standard method. To measure completeness, we compute the fraction of points of ground truth G that are within a certain distance d to the model R. Fig. 10b shows the results for different d values (plotted along the horizontal axis). Our method produces about 30 percent more points than standard method. The completeness score for our method is close to 100 percent when the distance d is sufficiently large. The base of the percentage is different in the two graphs; therefore, the d values are different for the same X value. We avoided very difficult regions during manual classification for creating the ground truth model. This leads to the fact that the ground truth model has fewer points than the model reconstructed by our method. Hence, the d value for the second graph may be smaller even when the percentage number is the same. Fig. 8 . Number of correctly and incorrectly classified pixels. The horizontal axis is the level of Gray code subdivision; higher values correspond to more stripes in the projected pattern. The vertical axis represents the number of correctly/incorrectly classified pixels. As compared to the standard method, our method produces both more correctly classified pixels and less incorrectly classified pixels. Fig. 9 . Modeling the bowl. Point cloud reconstructed using (a) standard method, (b) our robust classification for one iteration, and (c) our method for all iterations. (d) The final model is rendered from a novel viewpoint using texture mapping.. To evaluate the contributions from different components of our iterative algorithm (i.e., initial pixel classification, iterative reflection peeling, and adaptive subdivision), we compute the accuracy and completeness score of each step for the bowl data set. For computing accuracy score, we set the X percent value to be 90 percent. For completeness score, we set the distance d to be 1.0 mm. The results are listed in Table 4 . The accuracy of our method decreases when using more iterations because the later iterations are eventually dealing with more optically difficult regions of the scenes; thus are less robust. However, the overall error is still rather small. Our reflection peeling algorithm (step 2) completes the object from 60 percent to 90 percent. The gain of adaptive subdivision (steps 3 and 4) on this particular data set is relatively small; in general, it is very dependent on scene geometry and reflectance.. To show the effects of outlier rejection (image-and world-space culling discussed earlier in Section 5), we show synthetically shaded models without and with outlier rejection using standard method and our method in Fig. 11 . The original reconstruction using standard method (Fig. 11a) is noisier than that using our method (Fig. 11c) .. After outlier rejection, standard method only reconstructs an incomplete model (Fig. 11b) . In contrast, our method produces both improved correctness and improved completeness (Fig. 11d) .. For the more complicated dinnerware, objects 1, and objects 2 data sets, our method also performs better than standard method. The improvement of the first step ranges from 10 percent to 34 percent. After all iterations, the improvement is 17 percent-88 percent. Figs. 12, 13a, 13b , 13c, and 13d show the reconstruction results for dinnerware and objects 1. The results for objects 2 were shown in Fig. 1 . With 8-23 iterations and at most three levels of subdivision, our algorithm can reconstruct quite complete models for various types of scenes. It is interesting to note that for a subdivision level 3, the projector image is divided into 8 Â 8 small patches. However, there are only about a little more than 20 iterations in total. This is because parallelism is exploited by efficiently combining nonconflicting projector patches together.. The lady statue is white and diffuse; thus a perfect subject for standard structured light. However, when it is placed in a corner, diffuse interreflection prevails. Although for the entire scene, standard method produces slightly more points than our method with only one iteration (58,672 versus 57,833), our method generates more points on the lady statue (8,900 versus 9,066). After five iterations, our points reconstruct a nearly complete model of 60,677 points (9,413 points on the statue). Figs. 13e, 13f, 13g, and 13h show the results. As related work, we first review various other approaches to modeling optically challenging objects, and then focus on difficulties with using structured light to acquire such objects, provide an outline of adaptive structured-light systems, and finally a summary of methods for separating illumination components. Altogether, our research builds upon these works to create an adaptive structured-light system for objects with strong interreflections by using binary patterns and by using insight provided by direct and indirect component separation.

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


Decidability of Code Properties Abstract. We explore the borderline between decidability and undecidability of the following question: \Let C be a class of codes. Given a machine M of type X, is it decidable whether the language L(M) lies in C or not?" for codes in general, !-codes, codes of nite and bounded deciphering delay, pre x, su x and bi(pre) x codes, and for nite automata equipped with di erent versions of push-down stores and counters.

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 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


A Built-in Self-Test Circuitry Based on Reconfiguration for Analog and Mixed-Signal IC Abstract. Application of built-in self-test circuitries allows to improve the testing quality and reliability of complex analog and mixed-signal IC. BIST-circuitry is integrated to original circuit for the purpose of test signal generation, measurement of output responses and decision-making about correctness of circuit under test functioning. The most part of BIST-circuitries for analog and mixed-signal IC uses generators of sine wave or multifrequency wave for test signal generation, but it is not applicable for majority of practical implementations because of crucial increasing the chip area required for in-circuit realization of generator. The built-in self test circuitry for analog and mixed-signal IC based on reconfiguring original circuit in oscillator, which does not need the generator of input test signals, has been proposed. The principles of functioning and main components of the solution have been considered. The correct and incorrect behaviour of analog subcircuit is reflected in digital way by logical 0 or 1. The proposed circuitry provides possibility for joint testing analog and digital subcircuits of mixed-signal IC. The experimental results for benchmark second-order active filter demonstrating high efficiency of proposed BIST-circuitry have been represented. The fault coverage obtained by application of proposed BIST-circuitry is not inferior to results of other authors for the same filter, but measuring and estimation of output responses are performed in-circuit. There are several reasons of high complexity of analog circuits testing, the main of which are tolerance range of internal components parameters, and consequently tolerance of output characteristics, continuous character of signal transformation, nonlinear dependence between output and input signals, etc. The additional complication deals with restricted access to internal nodes of a device in the case of integrated realization.. Many problems in testing could be overcome by using of structural solution of built-in self-test (BIST) realized in the framework of design-for-testability approach (DFT) [1] . BIST-solutions are placed in a chip together with designed devices for the purpose of test signal generation, measurement of output responses and decision-making about quality of circuit under test functioning. The BIST-circuitries are realized on early stages of IC design process. It provides optimal conditions for the next reliable testing of completely realized device. Such an approach is effective for both analog and mixed-signal IC.. The most part of proposed BIST-solutions uses generators of sine wave or multifrequency wave represented by sum or sequence of sine waves for test signal generation [2, 3] . However, such a solution is not applicable for the majority of mixed-signal IC because of crucial increasing the chip area required for in-circuit realization of generator.. The common concept of approach to testing analog IC based on reconfiguration of original circuit in oscillator, which does not need the generator of input test signals, was proposed in [4] . This concept was called as Oscillation-BIST (OBIST). In papers of many authors who use this concept the main attention is paid to ways of transformation the original circuit to oscillator [5 -8] . The topics of measurement the oscillating frequency and decision-making about functional correspondence of tested circuit were not studied completely.. The built-in self-test circuitry based on OBIST concept and oriented at the usage for analog and mixed-signal IC when analog subcircuit can be tested jointly with digital part is proposed in the paper. The solution takes into account tolerances on parameters of analog subcircuits' internal components. The main attention is paid to architecture of the testing subcurcuit, realization of the measurement circuit and the estimating oscillated frequency of a circuit under test.

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


Drift-resistant SNR scalable video coding Abstract-We address the problem of enhancement layer drift estimation for fine granular scalable video. An optimal per-pixel drift estimation algorithm is introduced. The encoder assumes that there is some truncation of the enhancement layer, which does not allow the enhancement layer reference to be properly reconstructed, and the encoder recursively estimates the associated drift and chooses coding modes accordingly. The approach yields performance gains of about 1 dB across low to medium rates. In addition, we investigate dual frame prediction, for both base and enhancement layer, with pulsed-quality allocation in the base layer. The proposed drift estimation approach yielded performance gains of about 1 dB for most sequences across low to medium rates, with negligible loss at high rates. This was true, even though the encoder persisted with a simplistic assumption about the truncation rates, an assumption that did not hold true in the actual simulations, for which the enhancement reference truncation rates varied substantially. The reason is that, even for a crude channel description, it is better to assume some amount of drift and estimate its effect rather than disregarding it altogether. Pulsed-quality long-term frame prediction was shown to be advantageous for low-to-medium rates and video content with sufficient temporal redundancy.. Future work can include modeling drift in the evolving SVC standard [2] . FGS is used in an LPLR coding approach that encodes base layer motion-compensated residuals to achieve SNR scalability. Prediction from EL frames, similarly to HPLR and HPHR coding modes, can be used to improve the compression efficiency of the FGS layer, introducing potential drift.

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


Theoretical description of hydrogen bonding in oxalic acid dimer and trimer based on the combined extended-transition-state energy decomposition analysis and natural orbitals for chemical valence (ETS-NOCV) Abstract In the present study we have analyzed hydrogen bonding in dimer and trimer of oxalic acid, based on a recently proposed charge and energy decomposition scheme (ETS-NOCV). In the case of a dimer, two conformations, α and β, were considered. The deformation density contributions originating from NOCV's revealed that the formation of hydrogen bonding is associated with the electronic charge deformation in both the σ-(Δρ σ ) and π-networks (Δρ π ). It was demonstrated that σ-donation is realized by electron transfer from the lone pair of oxygen on one monomer into the empty r » HÀO orbital of the second oxalic acid fragment. In addition, a covalent contribution is observed by the density transfer from hydrogen of H-O group in one oxalic acid monomer to the oxygen atom of the second fragment. The resonance assisted component (Δρ π ), is based on the transfer of electron density from the π-orbital localized on the oxygen of OH on one oxalic acid monomer to the oxygen atom of the other fragment.ETS-NOCV allowed to conclude that the σ(O-HO) component is roughly eight times as important as π (RAHB) contribution in terms of energetic estimation. The electrostatic factor (ΔE elstat ) is equally as important as orbital interaction term (ΔE orb ). Finally, comparing β-dimer of oxalic acid with trimer we found practically no difference concerning each of the O--HO bonds, neither qualitative nor quantitative. Hydrogen bonding (HB) plays an important role in biochemistry [1, 2] . Accordingly, many attempts were made to describe HB-phenomenon in both experimental and theoretical laboratories [3] [4] [5] [6] [7] [8] [9] [10] [11] . For the purpose of understanding the nature of hydrogen bonding, theoretical approaches appeared to be of significant importance [12] [13] [14] [15] [16] [17] [18] [19] . Especially, electrostatic-covalent HB model, derived by Gilli [20, 21] from the systematic analysis of structural and spectroscopic data, allowed to make a comprehensive classification of H-bonds in a different chemical classes: e. g., charge assisted hydrogen bonds, low barrier hydrogen bonds, dihydrogen bonds, and resonance-assisted hydrogen bonds (RAHBs). It clearly shows that different factors can influence the nature of hydrogen connections.. For the purpose of HB description, various energy decomposition analysis (EDA) were also used [22] [23] [24] [25] 46] . In such decomposition schemes, the total interaction energy between interacting sub-systems is divided up into a few chemically meaningful contributions (electrostatic, exchange, charge-transfer, relaxation, etc.). Despite great usefulness of these methods, as they allow to extract stabilizing and destabilizing factors, none of them provide direct, qualitative and quantitative, separated information about σ-and π-contributions. Such specific knowledge on the hydrogen bonding phenomenon can be useful in understanding the structures of bio-molecules and further in a description of reactivity.. We have recently developed the ETS-NOCV scheme by combining the extended transition state (ETS) [26, 27] energy decomposition approach with the natural orbitals for chemical valence (NOCV) density analysis method [28] [29] [30] [31] [32] [33] [34] . It was shown that ETS-NOCV is able to extract and directly quantify the crucial components (σ,π,δ, etc.) that participate in various types of chemical bonds including predominantly donor-acceptor and covalent interactions [35, 36] . Furthermore, we have shown that ETS-NOCV can also be useful in a description of weak bonds [35, 36] , including intra-and inter-molecular hydrogen bonding. For example, we have found, based on the analysis of intermolecular bonding in Adenine-Thymine base pair, that ETS-NOCV provides separated, qualitative and quantitative information not only about both σ(O-HN) and σ(N-HN) interactions, but also about the resonance assisted hydrogen bonding contribution (π) [35] .. The main goal of this article is to extend our study on weak intermolecular interaction by characterization of hydrogen bonding in the dimeric and trimeric systems consisting of both σ(O-HO) and π-interactions between the monomers. We will consider in our analysis the oxalic acid dimers exhibiting two different conformations α and β (1 and 2), Fig. 1 . In addition, we will investigate oxalic acid trimers, 3 and 4, based on two different bond-partitioning, as indicated in Fig. 1 . The purpose of doing so is to obtain a compact description of each O--HO interaction in trimer of oxalic acid. To the best of our knowledge this is the first study reporting on the character of bonding in the oxalic acid systems based on charge and energy decomposition analysis. All structures discussed here were fully optimized after initial guesses taken from the Cambridge Structural Database [37, 38] . For the sake of clarity of presentation we will use throughout our study the "α-dimer" and "β-dimer" terms to describe the oxalic acid dimers that exhibit two different conformations α and β, respectively. In the present study we have characterized hydrogen bonding in the dimer and the trimer of α-and β-oxalic acid, based on the recently proposed ETS-NOCV procedure. The main attention was paid to characterization of HB from both qualitative (by providing deformation density contributions, Δρ k ) and a quantitative (by providing energetic estimations ΔE k for each Δρ k ) point of view. We found based on the NOCV-deformation density contours that the formation of hydrogen bonding is associated with the electronic charge redistribution in both the σ-(Δρ σ ) and π-networks (Δρ π ). It was shown that σ-donation is realized by electron transfer from the lone pair of oxygen on one monomer into the empty r » HÀO orbital of the second oxalic acid fragment. In addition, a covalent contribution is observed by the density transfer from hydrogen of H-O group in one oxalic acid monomer to the oxygen atom of the second fragment. The resonance assisted component (Δρ π ), RAHB, is based on the transfer of electron density from the π-orbital localized on the oxygen of OH on one oxalic acid monomer to the oxygen atom of the other fragment. The σ(O-HO) component is roughly eight times as important as π-contribution in β-oxalic acid dimer (2) and trimers (3, 4) . The electrostatic factor (ΔE elstat ) is quantitatively as important as orbital interaction term (ΔE orb ). Finally, comparing β-dimer (2) with trimer of oxalic acid (3) we found practically no difference in the characteristics of each of the O-HO bonds, neither qualitative nor quantitative.

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


Practical

statistical

methods

for

call

centres

with

a

case

study

addressing

urgent

medical

care

delivery

'Practical

statistical

methods

for

call

centres

with

a

case

study

addressing

urgent

medical

care

delivery.',

Annals

of

operations

research.,

pp.

Further

information

on

publisher's

copyright

statement:The

nal

publication

is

available

at

Springer

via

information:The

full-text

may

be

used

and/or

reproduced,

and

given

to

third

parties

in

any

format

or

medium,

without

prior

permission

or

charge,

for

personal

research

or

study,

educational,

or

not-for-prot

purposes

provided

that:•

a

full

bibliographic

reference

is

made

to

the

original

source

a

link

is

made

to

the

metadata

record

in

DRO

the

full-text

is

not

changed

in

any

way

The

full-text

must

not

be

sold

in

any

format

or

medium

without

the

formal

permission

of

the

copyright

holders.Please

consult

the

full

DRO

policy

for

further

details.

Abstract

Outside

normal

working

hours,

UK

citizens

requiring

advice

or

treatment

from

a

doctor

must

telephone

a

local

out-of-hours

call

centre.

Each

call

enters

a

queue

and

is

subsequently

assessed

by

a

call-handler

and

classed

as

urgent

or

routine.

Calls

then

enter

another

queue

to

await

a

response

from

a

qualified

doctor.

A

doctor

telephones

the

patient

to

offer

advice,

or

may

arrange

a

home

or

centre

visit.From

the

patient's

perspective,

it

is

necessary

to

provide

care

in

a

timely

fashion.

From

the

perspective

of

Government

funding

of

health

care,

resources

are

limited

and

certain

lengths

of

queue

are

deemed

acceptable.

Typically,

call

centres

must

meet

performance

targets

which

relate

principally

to

delays

suffered

by

patients,

as

well

as

to

quality

of

advice

and

treatment.

As

such,

staff-loads

must

be

carefully

planned.Planning

needs

accurate

forecasts

of

incoming

call

volumes.

These

vary

by

hour,

day,

and

season,

and

must

account

for

calendar

effects

such

as

Christmas.

We

demonstrate

the

construction

of

models

to

predict

interday

and

intraday

call

volumes.

We

show

that

simple

models

capture

all

the

important

features.

We

show

how

simulation

models

may

then

be

used

for

resource

allocation,

uncertainty

analysis,

and

staff

scheduling.

The

data

are

details

of

call

numbers

and

queue

lengths

from

all

parts

of

the

patientadvice

process

for

around

five

years,

for

a

call

centre

based

in

Newcastle-upon-Tyne.

There

are

around

complete

cases

in

total.

The

methods

are

easily

extended

to

other

kinds

of

call

centre.

We

describe

the

impact

Swine

flu

had

on

call

volumes

in

the

summer

of

and

our

reactions

to

amend

models

in

order

to

maintain

forecast

quality.

Our

interest

is

in

forecasting

for

call

centres,

and

in

particular

out-of-hours

call

centres

(OOHCC)

which

deal

with

patient

requests

for

medical

advice

outside

normal

working

hours.

For

such

applications

we

need

explicitly

to

take

into

account

that

demand

varies

strongly

by

day

-because

of

a

number

of

calendar

effects,

and

by

hour

-because

the

call

centre

only

operates

at

certain

times

and

because

demand

varies

with

peaks

typically

during

the

early

evening

for

weekdays

and

mornings

at

weekends.

We

refer

to

the

forecasting

of

volume

of

calls

expected

each

day

as

interday

forecasting,

and

the

pattern

of

calls

arriving

within

the

day

as

intraday

forecasting.

Other

kinds

of

call

centre

may

exhibit

different

interday

and

intraday

arrival

patterns;

however

the

methodology

we

suggest

should

cope

easily

with

other

scenarios,

without

detailed

modification..

The

nature

of

medical

emergency

call-centre

handling

is

that

staffing

appropriately

is

the

key

consideration.

First,

callers

are

patients

in

difficulty

and

there

is

an

obligation

to

treat

them

as

soon

as

possible,

within

reason.

Typically

there

are

specified

guidelines

on

the

timeliness

of

such

treatment

to

which

the

call-centre

needs

to

adhere.

Secondly,

patients

are

treated

by

qualified

physicians.

This

is

a

very

costly

resource.

The

call-centre

must

therefore

arrange

staffing

levels

that

are

sufficient

to

meet

demand

subject

to

specified

constraints,

but

must

avoid

prohibitively

expensive

idle

capacity..

Interday

and

intraday

forecasting

can

be

correlated

and

as

such,

are

generally

modelled

together

Huang

Weinberg

et

al.

Avramidis

et

al.

Avramidis

et

al.

investigate

the

property

that

there

is

correlation

between

arrival

counts

during

parts

of

the

day,

as

well

as

dependency

between

arrival

counts

on

successive

days.

For

our

purposes,

interday

and

intraday

forecasting

need

to

be

considered

in

some

way

separately.

Interday

forecasts

were

required

to

cover

a

volume

of

calls

from

midnight

to

midnight,

as

required

by

service

commissioners

to

illustrate

activity

levels.

Intraday

forecasts

run

over

staff

shifts

and

are

necessary

to

help

with

staffing

levels

at

particular

times.

Huang

apply

an

auto-regressive

model

incorporating

an

additional

day-of-week

effect

to

forecast

interday

rates.

This

lacks

any

seasonal

or

holiday

component;

for

example,

flu

has

a

higher

prevalence

in

winter

than

summer

and

demand

will

be

higher

then.

Patient

case-mix

over

holidays

will

also

have

an

effect,

for

example

patients

seeking

repeat

prescriptions

of

routine

medication

may

find

their

local

clinic

closed

for

a

holiday

period.

We

thus

need

a

framework

that

will

allow

particular

modelling

of

holidays

and

seasonal

effects..

Weinberg

et

al.

Weinberg

et

al.

build

a

multiplicative

Gaussian

model

for

forecasting

call

centre

arrival

rates.

They

consider

a

nonhomogenous

Poisson

model

modelling

intraday

and

interday

demand

separately

before

combining

them

in

a

multiplicative

model.

The

dataset

used

in

the

study

was

an

eightmonth

period

between

March

and

October

and

again,

seasonality

and

holiday

effects

were

not

included.

The

dataset

in

this

case

spanned

over

four

years,

and

seasonality

and

holiday

effects

could

be

visualized

quite

easily,

allowing

a

sensible

model

to

be

built

to

capture

them..

Alternative

approaches

to

modelling

interday

and

intraday

call

centre

demand

are

well

documented

in

Shen

and

Haung's

paper

Shen

and

Huang

which

compares

competing

models

by

applying

them

to

a

case

study.

These

include

a

linear

model

with

day

of

week-and-time-of-day

effects

(referred

to

as

the

historical

average

approach),

the

Bayesian

Gaussian

model

Weinberg

et

al.

as

well

as

multiplicative

and

additive

models.

Here

they

found

their

model

performed

well

against

the

other

methods,

however

it

is

still

not

adequate

for

application

here

without

some

seasonality

and

holiday

components..

The

U.S.

Census

Bureau's

software

package

for

seasonal

adjustment,

may

also

be

considered,

see

for

example

Ladiray

and

Quenneville

On

testing

this

software,

we

found

that

we

could

not

adapt

it

to

forecast

to

the

level

that

we

wanted

-daily,

and

with

calls

forecast

for

each

arrival

period..

In

studying

and

testing

potential

methods,

we

came

to

the

conclusion

that

serve

very

well.

Some

are

statistically

elegant,

but

are

so

narrowly

focused

to

specific

characteristics

of

an

application

scenario

that

it

becomes

difficult

or

impossible

to

adapt

them

to

other

scenarios.

Our

requirement

is

for

accurate

(because

lives

may

be

at

stake)

and

adaptable

(because

calendar

effects

have

strong

implications

for

arrivals)

methods.

For

our

OOHCC

scenario,

we

had

the

advantage

of

historical

information

for

a

small

number

of

years.

As

such,

fitting

simple

models

to

historical

data

is

a

natural

starting

point.

As

we

shall

see,

one

of

the

lessons

we

draw

from

this

work

is

that

simple

models,

thoughtfully

applied,

offer

excellent

performance.

This

is

in

line

with

Hand's

Hand

view

that

the

improvements

attributed

to

the

more

advanced

and

recent

developments

are

small,

and

that

aspects

of

real

practical

problems

often

render

such

small

differences

irrelevant,

or

even

unreal,

so

that

the

gains

reported

on

theoretical

grounds,

or

on

empirical

comparisons

from

simulated

or

even

real

data

sets,

do

not

translate

into

real

advantages

in

practice..

One

might

reasonably

expect

that

forecasting

technology

is

already

routinely

embedded

within

health

services

delivery.

Alas,

this

is

very

far

from

the

case.

Few

UK

OOHCCs

have

credible

statistically-based

forecasting

procedures.

One

reason

for

this

may

be

a

failure

of

academics

to

engage;

another

may

be

that

existing

methods

overfit

to

particular

details

of

a

problem

and

so

cannot

easily

be

adapted.

Academics

tend

to

concentrate

on

publication,

and

on

avant-garde

methodology,

rather

than

practical

solutions..

In

section

we

describe

the

scenario

for

which

we

developed

our

methods.

In

section

we

explain

how

we

forecast

call

volumes

arriving

on

specified

days.

In

section

we

explain

how

we

forecast

the

pattern

of

arrival

of

calls

during

a

specified

day.

In

section

we

discuss

some

features

of

operational

use

of

the

forecasts

for

planning

and

delivery

of

services.

Out-of-hours

medical

call

centre.

In

the

UK,

A

General

Practitioner

(GP)

OOHCC

provides

doctor

cover

between

and

on

weekdays,

and

all

day

on

weekends

and

bank

(i.e.

national)

holidays.

Companies

providing

this

service

are

commissioned

by

local

Primary

Care

Trusts.

A

patient

rings

the

OOH

number

and

reaches

a

non-clinical

call-handler

who

records

some

details.

Using

specified

urgency

criteria,

the

patient's

case

is

assessed

at

this

stage

as

being

urgent

or

routine.

The

call-handler

will

advise

the

patient

that

a

GP

will

return

their

call,

within

a

particular

time

frame.

This

process

is

termed

triage.

In

most

cases,

one

of

three

things

will

happen

when

the

GP

calls:.

the

patient's

symptoms

require

advice

over

the

telephone

from

a

GP;.

the

GP

decides

that

face-to-face

consultation

is

necessary

and

makes

an

appointment

for

the

patient

at

an

Urgent

Care

Centre

(UCC);

the

GP

arranges

for

a

GP

to

visit

the

patient

at

their

home..

This

patient

pathway

is

illustrated

in

Figure

There

are

key

performance

indicators

(KPIs)

for

each

stage

in

the

pathway.

We

focus

in

this

paper

on

the

first

stage,

the

triaging

of

calls,

for

which

the

targets

are

for

Urgent

(Routine)

calls

to

be

triaged

within

minutes.

An

OOHCC

must

score

at

least

in

all

KPIs

to

be

classed

as

'fully

compliant'

by

their

commissioners.

Nearly

all

cases

are

triaged

by

GPs

based

at

the

OOHCC.

For

centre

visit

consultations,

a

GP

is

based

at

an

Urgent

Care

Centre

with

minute

appointment

slots.

When

GPs

have

gaps

in

appointments,

they

can

telephone

in

and

help

remotely

with

the

triage

queue,

known

as

dipping

into

the

queue.

Therefore

there

is

periodically

extra

resource

available

for

triaging.

For

home

visit

consultations,

a

GP

based

at

the

OOHCC

will

be

driven

to

the

patient's

home.

These

tend

to

be

longer

visits

as

they

are

generally

more

complicated

cases.

Afterwards,

the

GP

will

either

travel

back

to

the

OOHCC,

or

to

another

home

visit

case.

Whilst

en

route,

GPs

are

encouraged

to

dip

into

the

triage

queue.

Planning

needs

taking

into

account

how

many

GPs

will

be

away

from

telephone

triaging

and

further

logistics

such

as

the

number

of

drivers

on

shift..

For

many

call-centres,

calls

arrive

directly

as

telephone

calls.

For

our

case

study,

as

for

some

other

medical

emergency

centres,

the

calls

arriving

are

pre-screened

by

trained

call

handlers.

There

are

clear

guidelines

about

which

cases

go

through

as

genuine

out-of-hours

cases

and

whether

they

should

be

labelled

as

routine

or

urgent.

Arrival

rates

are

likely

to

be

related

to

call

handler

behaviour;

call

handlers

going

on

breaks

at

the

same

time,

or

working

at

different

speeds.

We

could

not

observe

or

model

this

behaviour.

Consequently,

our

focus

is

on

pre-screened

call

arrival

volumes.

In

this

paper

we

have

described

statistical

approaches

to

a

number

of

complicated

and

interrelated

issues

involved

in

planning,

forecasting,

and

monitoring

for

an

out-of-hours

medical

call

centre.

We

have

provided

methods

to

forecast

daily

call

volumes

and

the

pattern

of

calls

arriving

during

the

day.

These

work

very

well

and

are

now

embedded

within

the

practice

of

our

collaborating

organization.

Figure

Estimates

of

arrival

rates

per

half-hour

for

typical

Saturdays

and

Sundays

each

December..

methods

capture

a

high

proportion

of

explainable

variation.

We

have

provided

methods

showing

how

we

may

begin

to

monitor

staff

activity

having

adjusted

for

relevant

factors.

We

show

how

simulation

methods

may

build

on

inputs

from

the

forecasts

to

allocate

staff

resource.

It

is

relatively

trivial

to

adapt

the

methods

to

other

kinds

of

call-centre.

We

have

not

yet

linked

interday

and

intraday

forecasting

statistically.

As

we

noted,

we

normalize

our

intraday

forecasts

to

the

volumes

suggested

by

the

interday

modelling,

and

this

ignores

discrepancies

that

may

arise

between

them,

and

fails

to

take

account

of

correlations

between

them.

From

the

operational

perspective,

this

is

a

reasonable

feasible

solution.

KPIs

tend

to

focus

on

daily

activity

such

as

call

volumes

and

queue

lengths

(interday),

whereas

for

planning

work

rotas

and

shifts

it

is

more

useful

to

forecast

arrival

rates

over

a

shift

(intraday)..

It

is

worth

describing

the

intellectual

resource

required

in

implementing

this

methodology.

One

requirement

is

the

availability

of

historical

data

allowing

sufficient

degrees

of

freedom

to

estimate

regression

model

parameters.

Longer

historical

time

periods

permit

finer

details

to

be

captured

by

the

modelling.

Cleaning

the

data

often

exposes

problems

in

its

original

collection,

requires

resolution

of

ambiguities,

and

so

forth.

These

are

themselves

valuable

from

the

institution's

perspective

and

tend

to

lead

to

improved

data

collection

processes.

The

basic

modelling

described

in

section

and

section

has

to

be

carried

out

by

a

competent

statistician,

who

will

also

be

responsible

for

addressing

resource

allocation

via

simulation.

Once

these

have

been

carried

out,

software

can

provide

routine

forecasts

and

diagnostics

and

these

can

be

managed

by

junior

staff

without

day-to-day

supervision

from

a

statistician.

For

our

work,

we

used

the

R

package

R

Development

Core

Team

for

the

background

modelling

and

for

provision

of

daily

forecasts,

and

a

Microsoft

Excel

front

end

Neuwirth

et

al.

to

present

all

outputs

in

a

format

acceptable

to

our

collaborating

institution,

and

which

could

be

readily

tied

in

with

their

KPI

systems.

It

is

necessary

to

maintain

contact

with

the

statistician

for

several

reasons.

The

two

most

important

are

to

monitor

performance

and

diagnose

discrepancies

in

model

behaviour,

and

to

handle

extra

modelling

when

there

are

external

shocks

to

the

system,

such

as

unforeseen

epidemics.

This

is

critical

because

otherwise

the

value

of

the

models

decays

and

institution

staff

begin

to

lose

trust

in

the

forecasts.

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Constructing Topical Hierarchies in Heterogeneous Information Networks Abstract Many digital documentary data collections (e.g., scientific publications, enterprise reports, news articles, and social media) can be modeled as a heterogeneous information network, linking text with multiple types of entities. Constructing high-quality hierarchies that can represent topics at multiple granularities benefits tasks such as search, information browsing, and pattern mining. In this work, we present an algorithm for recursively constructing multi-typed topical hierarchies. Contrary to traditional text-based topic modeling, our approach handles both textual phrases and multiple types of entities by a newly designed clustering and ranking algorithm for heterogeneous network data, as well as mining and ranking topical patterns of different types. Our experiments on datasets from two different domains demonstrate that our algorithm yields high-quality, multi-typed topical hierarchies. In this work, we address the problem of constructing a multi-typed topical hierarchy from heterogeneous information networks. We develop a novel clustering and ranking method which can be recursively applied to hierarchically discover multi-typed subtopics from heterogeneous network data. Our approach mines each discovered topic for topical patterns, yielding a comprehensive representation of each topic comprising lists of ranked patterns with different types (phrases, authors, etc.). Our experiments on the science and news domains demonstrate the significant advantage of our unified generative model for the task of hierarchical topic discovery, as compared to the state-of-the-art heterogeneous network analysis technique. We also show our constructed topical hierarchies have high quality based on human judgement.. We hope to further improve our multi-typed topical hierarchy construction method to be able to accommodate user preference for the particular hierarchical organization of a dataset. We are also interested in constructing evolving topical hierarchies that would be able to work with the constantly changing information found in data streams. Lack of gold standard is a known issue for unsupervised topic modeling methods. As such, people have proposed evaluation metrics without relying on labels. Our task of constructing multi-typed topic hierarchy is new and there is neither gold standard for it. We leverage the existing evaluation metrics, pointwise mutual information [15] and intrusion detection [2] that are proved to be effective in text-based topic modeling, and modify them to evaluate our multi-typed topic hierarchy. The metrics can be used to compare different methods in arbitrary datasets. We evaluate the performance of our proposed method on two datasets (see Table 3 for summary statistics of the constructed networks):. • DBLP Following [21] , we collected 33,313 recently published computer science papers from DBLP. 1 We constructed a heterogeneous network with three node types: term (from paper title), author and venue, and 5 link types: term-term, term-author, term-venue, author-author and author-venue. 2 • NEWS We crawled 43,168 news articles on 16 top stories from Google News, 3 extracted text content from html pages by heuristic rules, and ran an information extraction algo-rithm [12] to extract entities. We constructed a heterogeneous network with three node types: term (from article title), person and location, and 6 link types: term-term, termperson, term-location, person-person, person-location and location-location.. Our datasets will be online available at http://illimine.cs.illinois.edu. Our recursive framework relies on two key steps: subtopic discovery and topical pattern mining. The major contribution of this paper is the subtopic discovery step. Hence, our evaluation is twofold: (i) we evaluate the efficacy of subtopic discovery given a topic and its associated heterogeneous network; and (ii) we perform several 'intruder detection' tasks to evaluate the quality of the constructed hierarchy based on human judgment.

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