Connectomic constraints on computation in feedforward networks of spiking neurons Several efforts are currently underway to decipher the connectome or parts thereof in a variety of organisms. Ascertaining the detailed physiological properties of all the neurons in these connectomes, however, is out of the scope of such projects. It is therefore unclear to what extent knowledge of the connectome alone will advance a mechanistic understanding of computation occurring in these neural circuits, especially when the high-level function of the said circuit is unknown. We consider, here, the question of how the wiring diagram of neurons imposes constraints on what neural circuits can compute, when we cannot assume detailed information on the physiological response properties of the neurons. We call such constraints-that arise Action Editor: Stefano Fusi Electronic supplementary material The online version of this article (by virtue of the connectome-connectomic constraints on computation. For feedforward networks equipped with neurons that obey a deterministic spiking neuron model which satisfies a small number of properties, we ask if just by knowing the architecture of a network, we can rule out computations that it could be doing, no matter what response properties each of its neurons may have. We show results of this form, for certain classes of network architectures. On the other hand, we also prove that with the limited set of properties assumed for our model neurons, there are fundamental limits to the constraints imposed by network structure. Thus, our theory suggests that while connectomic constraints might restrict the computational ability of certain classes of network architectures, we may require more elaborate information on the properties of neurons in the network, before we can discern such results for other classes of networks. Recent remarkable experimental advances (Denk and Horstmann 2004; Hayworth et al. 2006; Knott et al. 2008; Mishchenko et al. 2010; Turaga et al. 2010; Helmstaedter et al. 2011; Mikula et al. 2012) have brought the prospect of ascertaining the connectome or parts thereof closer to reality Kleinfeld et al. 2011; Seung 2011; Denk et al. 2012; Reid 2012; Helmstaedter et al. 2013 ). This data is currently not expected to include information on the detailed physiological properties of all the neurons in the connectome. Even so, already, there have been two pioneering studies Bock et al. 2011) that fruitfully use electron-microscopy reconstructions in conjunction with two-photon calcium imaging on the same tissue. In Briggman et al. (2011) , the authors used this approach to rule out certain models of direction selectivity in the retina. The other study examined the orientation-selectivity circuitry in the cortex and found that inhibitory interneurons received convergent anatomical input from nearby excitatory neurons that had a broad range of preferred orientations. Recent work (Takemura et al. 2013 ) has also used connectomic reconstructions of the motion detection circuit in the fruit fly visual system, in order to identify cellular targets for future functional investigations; this is towards the goal of a comprehensive mechanistic understanding of this circuit. While this broad approach of combining functional imaging with structural reconstructions creates new opportunities to unravel structure-function relationships (Seung 2011) , to fruitfully use functional imaging seems to require that (a) we have an a priori credible hypothesis about at least one high-level computation that the neural circuit in question is performing and (b) we have a way of experimentally eliciting performance of the said computation, usually via an appropriate stimulus. Unfortunately, neither of these conditions appear to be satisfied for a majority of neuronal circuits in the brain, especially as one moves away from the sensory/motor periphery. Suppose, in addition to its wiring diagram, we knew the detailed physiological response properties of all the neurons in such a neural circuit to the extent that we could predict circuit behavior (via simulations, for example). This might provide a way forward towards advancing hypotheses about what high-level computation(s) the circuit is actually involved in. Regrettably, ascertaining the detailed physiological response properties of all the neurons in such a network appears to be out of reach of current experimental technology. The prospects of obtaining the wiring diagram, however, seem to hold more promise. The question therefore becomes: (1) What can we learn from the wiring diagram alone, even when the specific high-level function of the neural circuit may be unknown?. (2) Are there fundamental limits to what can be learned from the wiring diagram alone, in the absence of more detailed physiological information?. To investigate these questions, we have studied a network model equipped with neurons that obey a deterministic spiking neuron model. We ask what computations networks of specific architectures cannot perform, no matter what response properties each of their neurons may have. The implication, then, is that, owing to its structure, the network is unable to effect the computation in question. That is, connectomic constraints forbid the network from performing the said computation. In addition, to rule out the possibility that this computation is so "hard" that no network (of any architecture) can accomplish it, we stipulate the need to demonstrate that there exists a network (of a different architecture) comprising simple neurons that can indeed effect this computation. The goal of this paper is to establish results of this form for various network architectures, after setting up a mathematical framework within which these questions can be precisely posed. As a first simplifying step, in this paper, we limit our study to feedforward networks of neurons. Having started with this goal, however, we also find that with the small number of basic properties assumed for our model neurons, there are fundamental limits to the computational constraints imposed by network structure, in certain cases. In particular, we prove that, constrained only by the properties in the current neuron model, every feedforward network, of arbitrary size and depth, has an equivalent feedforward network of depth equal to two that effects exactly the same computation. The implication of this result is that we need more elaborate information about the properties of the neurons before connectomic constraints on the computational ability of such networks can be discerned.. Before we can examine these questions, we are confronted with the problem of having to define what computation exactly means, in this context. Physically, neurons and their networks are simply devices that receive spike-trains as input, and in turn generate spike-trains as output. It is this translation from spike-trains to spike-trains that characterizes information processing and indeed even cognition in the brain. It is tempting to view a feedforward network as a transformation, which is to say a function, that associates a unique output spike train with each combination of afferent input spike trains, since such networks do not have recurrent loops. This is the intuition we will seek to make precise.. Since the functional role of single neurons and small networks in the brain is not yet well understood, we do not make assumptions about particular high-level tasks that the network is trying to perform; we are just interested in physical spike-train to spike-train transformations. Likewise, since the kinds of neural code employed are unclear, we make no overarching assumptions about the neural code either. We study precise spike times since there is widespread evidence (Strehler and Lestienne 1986; Rieke et al. 1997, & references therein) that precise spike times play a role in information processing in the brain, in many cases. Indeed, Spike-Timing Dependent Plasticity, a class of Hebbian learning rules that are sensitive to the relative timing of pre and postsynaptic spikes have been discovered (Markram et al. 1997; Bi and Poo 1998) that support the role of precise spike-timing in computation in the brain. Studying spike times also subsumes cases where spiking rate may be the relevant parameter and therefore there is no loss of generality in making this assumption. There has been some debate about how useful data from the connectome projects might be in advancing a mechanistic understanding of computation occurring in the circuits of the brain. One of the main type of arguments that has been made against their utility is that, since these projects only 17 seek to ascertain the wiring diagram, without giving us detailed physiological information, it is not clear what we might learn from this data alone, especially for networks whose high-level function is not known. While it is acknowledged that network architecture places constraints on what a network can compute (Kleinfeld et al. 2011; Denk et al. 2012) , the nature and scope of these constraints have remained poorly understood. Our goal with this work was in asking, on one hand, if we can deduce non-trivial examples of computations that a network could not be doing, given just the knowledge of its architecture and assuming that the neurons obey some elementary properties. On the other hand, we asked if there are fundamental limits to what can be said, given just this information. We examined this question for the case of feedforward networks equipped with neurons that obeyed a deterministic spiking neuron model. We first set the stage by creating a mathematical framework in which this question could be precisely posed. Crucially, we needed to make precise what computation exactly meant in this context. This took a fair bit of work and led us to the view of feedforward networks as spike-train to spiketrain transformations under biologically-relevant spiking regimes. After setting up necessary definitions, we then showed some examples of transformations that networks of specific architectures cannot effect, that other networks can.. First of all, we showed 18 that there exist spike-train to spiketrain transformations that no feedforward network could effect. Next, we showed a transformation that no single neuron could effect but a network consisting of two neurons could. After this, we proved a result which shows that a class of architectures that share a certain structural property also share their inability to effect a particular class of transformations. Notably, while this class of architectures has networks with arbitrarily many neurons, we showed a class of networks with just two neurons which could effect this class of transformations. This suggests that network structure alone may impose crucial constraints on computational ability. Finally, we demonstrated that the small number of properties assumed for our model neurons can only take us so far. We proved that without making further assumptions about our model neurons, we couldn't discern such examples for the set of all feedforward networks of depth two.. While there is more to neuronal networks than just their wiring diagram, what our theory suggests is that the wiring diagram could impose crucial constraints on the computational ability of networks, in some cases. On the other hand, there seem to be classes of networks for which a more elaborate knowledge of single neuron properties may be necessary, before we can determine restrictions on their computational ability. While technical issues in electron microscopy ) have so far stood in the way of mapping, for example, distributions of ion-channels and neurotransmitter and neuromodulator receptors in neurons, it is conceivable that such hurdles may be overcome in future. If successful, these or other advances in conjunction with the wiring diagram could provide useful information to help us tease out pertinent constraints on the computational capabilities of these networks.. In this work, as a first step, we have aimed to demonstrate specific examples of computations that a network cannot accomplish, given its architecture. The more ambitious goal would be the ability to have an exact characterization of the set of all computations that a given neural circuit cannot perform, given knowledge of its architecture, to the extent that a given incomplete knowledge of the physiological properties of its neurons will allow. This is not necessarily a goal that is out of reach. Even in the present work, we have obtained such an exact characterization 19 of the set of all computations that the set of feedforward networks cannot accomplish, given the set of properties that our model neurons are presently assumed to obey. Therefore, in principle, there seems to be no reason why we may not be able to do likewise for specific network architectures.

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


Discrete sets with minimal moment of inertia We analyze the moment of inertia I(S), relative to the center of gravity, of finite plane lattice sets S. We classify these sets according to their roundness: a set S is rounder than a set T if I(S) < I(T ). We show that roundest sets of a given size are strongly convex in the discrete sense. Moreover, we introduce the notion of quasi-discs and show that roundest sets are quasi-discs. We use weakly unimodal partitions and an inequality for the radius to make a table of roundest discrete sets up to size 40. Surprisingly, it turns out that the radius of the smallest disc containing a roundest discrete set S is not necessarily the radius of S as a quasi-disc. In this paper we consider plane sets up to translations. By a discrete set we mean a finite set of lattice points or a finite union of lattice closed unit squares (pixels) (Figure 1 (a) ). In particular, the word polyomino means a finite union of pixels in the plane whose boundary consists of a disjoint union of simple closed polygonal paths using 4-connectedness (Figure 1(b) ). These sets are well-known combinatorial objects in discrete geometry. The dual of a polyomino, usually called animal, consisting of the set of centers of its pixels, is also considered (Figure 1(c) ). Using a ( Moreover, a polyomino is called v-convex (resp. h-convex) if all its columns (resp. rows) are connected (see Figure 2 (a),(b)). We say that a polyomino is hvconvex (see Figure 2 (c)) if all its columns and rows are connected and stronglyconvex (see Figure 2 (d)) if given any two points u and v in its corresponding animal, the lattice points w in the segment [u, v] are all in the animal. The goal of this paper is to study the roundest discrete sets S of N pixels (or N points) in the sense of having minimal moment of inertia I(S), relative to the center of gravity. This problem was raised in a previous paper [2,?] in the context of the study of incremental algorithms based on discrete Green theorem. The present notion of roundness is distinct from the one given in [1] where they consider minimizing the site perimeter of lattice sets, that is the number of points with Manhattan distance 1 from the sets. For a given N, minimizing I(S) is equivalent to minimizing I(A), where A is the associated set of centers of the pixels of S (equation (2)). To simplify notations and computations, in this paper the plane is identified with the complex plane C and Z × Z is identified with Z + iZ.. In Section 2, we recall some basic notions about moment of inertia of discrete sets. Section 3 is devoted to properties of roundest discrete sets. More precisely, we establish a useful lemma concerning the moment of inertia of a union of discrete sets. We also introduce the notions of strong convexity and discrete quasi-disc and apply the above lemma to prove that roundest discrete sets are strongly convex and quasi-discs. Then a method is developed for computing the roundest discrete sets according to size (≤ 40) and some parameters associated to them. Finally, we show in Section 4, how to extend our results to other kinds of lattices and to higher dimensions. The above results can be extended to other families of lattices. For instance, in the context of regular triangular lattices, a discrete set S is a union of N distinct closed equilateral triangles and the set A of the centers of these triangles satisfies the following formula, analoguous to (2),

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


Spatially-resolved metabolic cooperativity within dense bacterial colonies Background: The exchange of metabolites and the reprogramming of metabolism in response to shifting microenvironmental conditions can drive subpopulations of cells within colonies toward divergent behaviors. Understanding the interactions of these subpopulations-their potential for competition as well as cooperation-requires both a metabolic model capable of accounting for a wide range of environmental conditions, and a detailed dynamic description of the cells' shared extracellular space. Results: Here we show that a cell's position within an in silico Escherichia coli colony grown on glucose minimal agar can drastically affect its metabolism: "pioneer" cells at the outer edge engage in rapid growth that expands the colony, while dormant cells in the interior separate two spatially distinct subpopulations linked by a cooperative form of acetate crossfeeding that has so far gone unnoticed. Our hybrid simulation technique integrates 3D reaction-diffusion modeling with genome-scale flux balance analysis (FBA) to describe the position-dependent metabolism and growth of cells within a colony. Our results are supported by imaging experiments involving strains of fluorescently-labeled E. coli. The spatial patterns of fluorescence within these experimental colonies identify cells with upregulated genes associated with acetate crossfeeding and are in excellent agreement with the predictions. Furthermore, the height-to-width ratios of both the experimental and simulated colonies are in good agreement over a growth period of 48 hours. Conclusions: Our modeling paradigm can accurately reproduce a number of known features of E. coli colony growth, as well as predict a novel one that had until now gone unrecognized. The acetate crossfeeding we see has a direct analogue in a form of lactate crossfeeding observed in certain forms of cancer, and we anticipate future application of our methodology to models of tissues and tumors. The application of the 3DdFBA method described here focused on the growth and collective metabolism of E. coli colonies. Its integration of 3D reaction-diffusion simulations with a flux balance model of metabolism that involves thousands of reactions and metabolites enabled us to generate new hypotheses that we then tested directly in the laboratory.. The most striking result of this work was the prediction that subpopulations within E. coli colonies naturally engage in cooperative acetate crossfeeding. This was not due to the evolution of distinct crossfeeding genotypes, as is known to occur in long-term continuous culture experiments, but rather it emerged from the cells' own regulatory responses to their local microenvironments within the colony. Depending on location, some cells experienced a glucose-rich anoxic environment that drove them toward acetate-producing fermentative metabolism, while others experienced a glucose-poor aerobic environment that favored acetate-consumption. This behavior remained robust over a range of common agar glucose concentrations, meaning that it may be occurringcompletely unnoticed-in laboratory incubators the world over.. The simulated colonies exhibited realistic growth dynamics. The same glucose and oxygen gradients that gave rise to acetate crossfeeding also gave rise to a ring of fast-growing pioneer cells at the colony's edge, and significantly hindered the growth of much of the colony interior. The pioneer ring had a profound impact on the macroscopic shape and growth of the simulated colony, leading to both its broad and flat appearance and its linear radial expansion (both of which agree well with experimental values).. Several features of our modeling technique proved essential to our study. The first, and most critical, was its ability to perform 3D simulations with fine spatial resolution. The concentration profiles of oxygen and glucose within the colony changed dramatically over short distances in both the radial and vertical directions. The penetration depth of oxygen, for example, was only around 50 μm from the edge of the colony, while the penetration depth of glucose at the colony center was only around 60 μm upward from the agar. Accurately accounting for these steep gradients required the use of a 3D lattice with a spacing of on the order of 10 μm. Although a similar method was recently reported [21] , it was restricted to two spatial dimensions and its reliance on costly onthe-fly FBA calculations severely limit its practicality for performing the millions of metabolism evaluations pertimestep necessary to resolve these profiles. In contrast, our use of precomputed FBA lookup tables enabled us to preform our simulations at nearly real-time speeds. Our code, running on the Keeneland supercomputer (with Nvidia M2090 GPUs) and on a Linux desktop machine (with a single Nvidia GTX780 GPU) performed the simulations presented here at speeds of approximately 50.0 and 40.1 simulated minutes per wall-clock hour, respectively.. The second feature that proved critical was our method's ability to account for the regulation of resource use by the modeled cells. Naively using FBA alone led to some cells simultaneously taking up glucose and acetate in a manner at odds with experimental data. By requiring the colony to obey a phenomenological model of the acetate switch, this pathological behavior was ameliorated, and the potential for acetate crossfeeding to emerge within wild-type E. coli colonies was more realistically modeled.. It is worth noting that our use of precomputed FBA tables, while offering vast speedup over on-the-fly evaluation, does carry some drawbacks. The most pressing of these is that the modeler must have some notion of the substrates that are likely to play a role in the colony's collective metabolism before a simulation can be launched. Our choice to model only glucose, oxygen, and acetate was informed by earlier work simulating significantly smaller clusters of cells [10] and some preliminary FBA calculations. Nevertheless, this choice can in some ways limit the scope of the simulations. For example we knowingly ignore the potential for succinate crossfeeding (which was deemed unimportant due to the low predicted succinate production rate of anaerobically-growing cells) as well as possible toxic effects due to the production of ethanol within the colony (although, because the ethanol and acetate production rates are comparable, the concentration of ethanol should not rise significantly above the maximal acetate concentration, ∼ 5.8 × 10 −3 M, which is approximately 2 orders of magnitude below the concentration at which cellular growth is significantly inhibited [46] ). Incorporating larger numbers of substrates into a lookup table is straightforward, but can be time consuming as it increases the dimensionality of the table, and in turn, the number of FBA calculations required to produce it. Ultimately, the choice of using table lookups or on-the-fly FBA solving comes down to a choice between computational speed/resolution and model flexibility/universality. With enough prior knowledge of the phenomenon to be simulated, a table-based method vastly out-performs on-the-fly solving, but for purely exploratory simulations in which large numbers of metabolites are simulated simultaneously, an on-thefly method may potentially yield novel behaviors that the modeler did not anticipate.. Although our methodology represents an important step in using FBA in both a spatially-and temporallyresolved manner, neither it, nor any other current implementation, can fully account for all biologically significant phenomena. One important example stems from the inherent determinism of the method which yields only average behaviors. Stochastic gene expression has been shown to give rise to significant metabolic variability, even among cells in otherwise identical environments [6] . The method we present does not account for this type of cell-to-cell variability; the cells in a given lattice site are assumed to behave identically, engaging in the optimal metabolism possible given their local substrate availability. Additional uncertainties arise in the number of cells that actually seed a given colony; our simulations assume a single cell, but it is difficult to experimentally verify the exact number of cells left in a given location when an agar plate is streaked. These effects are evident even at the macroscopic level-while the heights and widths of experimental colonies show considerable variability (see Figure 6 ), our simulated colonies show none. A natural way forward in this regard is to shift toward an agentbased modeling approach where individual cells may be represented within a continuous field of diffusing substrates. This could allow for stochastic gene expression to be explicitly accounted for within each cell; the gene expression state of a cell might be sampled from experimental distributions and used to apply constraints within the cell's metabolic network in a manner similar to that of [6] . Additionally, by resolving individual cells and their intercellular forces, an agent-based approach may better account for the early development of the colony as it transitions from 2D to 3D growth [44] -a behavior that is poorly accounted for in our current implementation.. Our modeling technique can be applied to the study of communities involving many different microbial species. Several different cell types-each employing their own metabolic model-can be simultaneously simulated, and because the different cell types can transform into each other, regulation systems much more complex than the acetate switch described here can be studied. Beyond obvious future studies of biofilms, perhaps the most exciting applications of this technique may come in the form of tissue and tumor modeling. Like the colony models presented here, steep oxygen gradients are known to form within cancerous tumors that profoundly affect their metabolism [47] . Within certain cancers these oxygen gradients have even been reported to give rise to lactate crossfeeding in a manner strikingly similar to the acetate crossfeeding seen in our simulations [48, 49] . There are already several flux balance models of different human cancers available in the literature [50, 51] . These can be leveraged to build new 3D models capable of studying everything from environmental fluctuations and metabolic reprogramming within a cancer to the interactions between cancers and their surrounding tissues.

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


A Double-Layered Mixture Model for the Joint Analysis of DNA Copy Number and Gene Expression Data Copy number aberration is a common form of genomic instability in cancer. Gene expression is closely tied to cytogenetic events by the central dogma of molecular biology, and serves as a mediator of copy number changes in disease phenotypes. Accordingly, it is of interest to develop proper statistical methods for jointly analyzing copy number and gene expression data. This work describes a novel Bayesian inferential approach for a double-layered mixture model (DLMM) which directly models the stochastic nature of copy number data and identifies abnormally expressed genes due to aberrant copy number. Simulation studies were conducted to illustrate the robustness of DLMM under various settings of copy number aberration frequency, confounding effects, and signal-to-noise ratio in gene expression data. Analysis of a real breast cancer data shows that DLMM is able to identify expression changes specifically attributable to copy number aberration in tumors and that a sample-specific index built based on the selected genes is correlated with relevant clinical information. Genomic alterations including copy number variants (CNV), inversions, and tandem repeats have been implicated in phenotypic variation in recent studies (Freeman et al., 2006; Redon, 2006) . Copy number aberration refers to cytogenetic events in which the DNA replication process is disturbed and abnormal number of DNAs are copied in newly generated cells, leading to local chromosomal variation. These events are larger than genetic variants such as single nucleotide polymorphisms but smaller than chromosome-wide events such as aneuploidy, rearrangements, and fragile sites (Feuk et al., 2006) . Copy number aberration is localized on each chromosome and manifested in varying lengths, and thus the definition applies to a wide variety of cytogenetic events. Since gene expression has long been used as a proxy for phenotypic variation in human populations and copy number changes are directly related to transcription, it is therefore of great interest to study the association between the two levels of data (Stranger et al., 2007) .. Although copy number aberration has been characterized as genetic variants in large-scale studies (Redon, 2006) , it is challenging to identify copy number-associated gene expression in these studies because copy number aberration is a low frequency event in large populations. Delineating the association between the two data may be more promising in cancer studies because copy number aberration is more prevalent in cancer populations due to genomic instability in tumor cells, and thus the role of copy number in altering gene expression is supposed to be more pronounced in cancer studies. Paired data are already available for a variety of common cancer types under casecontrol design, often generated using array-based comparative hybridization (Pinkel et al., 1998), or array CGH, and gene expression microarrays. Pollack et al. (2002) was one of the earliest to investigate the direct association between the two data in breast cancer cell lines and tissue samples. Hyman et al. (2002) found that nearly half the amplification events in breast cancer cell lines were associated with elevated gene expression and replicated similar results in tumor tissue samples.. The association between the two types of data has also been reported in other types of cancer, such as in Tonon et al. (2005) . These genome-wide surveys of tumor samples generally suggest that changes in expression levels can be ascribed to copy number aberration in some genes, but also demonstrate that the association might not be so strong as to explain the variability in gene expression solely based on copy number changes.. Statistical analysis of these two data sets is challenging mainly because copy number data show dynamic stochastic behavior due to genomic alterations of varying lengths, often manifested in segmental patterns. Thus the measurement of each gene cannot be considered statistically independent as in the analysis of gene expression data, and accordingly, a de-noising procedure accounting for local homogeneity should be incorporated into the joint analysis simultaneously. Copy number segmentation has been a subject of various statistical methods. Popular algorithms include circular binary segmentation (Olshen et al., 2004) , hidden Markov Models (Fridlyand et al., 2004; Marioni et al., 2006; Stjernqvist et al., 2007; Rueda and Diaz-Uriarter, 2007) , hierarchical clustering-based algorithms (Wang et al., 2005) , information criteria-based change point model (Zhang and Siegmund, 2007) , and a mixture model-based dynamic programming algorithm (Picard et al., 2007) .. Comparison of some of these algorithms has been provided in recent reviews by Willenbrock and Fridlyand (2005) , Lai et al. (2005) , and Chari et al. (2006) . Segmentation algorithms are not only useful for identifying sites of common chromosomal aberration in cancer but are also helpful for joint analysis. This is because copy number-associated expression changes can be searched within the segments of aberrant copy number only, saving the effort to interrogate the entire genome. Tonon et al. (2005) and Kim et al. (2007) , for example, performed linear correlation analysis and differ-ential expression hypothesis testing respectively, after identifying candidate regions by applying segmentation algorithms.. To date, few systematic approaches are available for the joint analysis of copy number and gene expression data. Lipson et al. (2004) developed a regional analysis called genomic continuous submatrix (GCSM), which scans the genome with a moving window of linear correlation coefficients to screen for locally consistent correlations between the two data. GCSM uses the raw copy number data for linear correlation analysis and hence segmental patterns are captured by appropriate widths of scanning windows. However, the association between the two data is likely nonlinear in the sense that copy number aberration is a sample specific event and thus raw measurements are not comparable across different samples as in gene expression data. van Wieringen and van de Viel (2008) proposed a nonparametric hypothesis testing framework (vWvV test hereafter) for finding changes in the gene expression distribution that incorporates the probability of copy number gain or loss. Even though vWvV tests utilize the probability of copy number aberration in the testing procedure, the hypothesis testing framework may not be an optimal way to identify copy numberassociated expression because aberrant copy numbers are low frequency events even in cancer tissue samples and widely varies by genes, and many hypotheses may be untestable due to lack of data for genes with aberrant copy number.. The concept of copy number-associated expression is gene-centric but specific to individual samples at the same time. Hence it is important to be able to quantify the evidence for impact of copy number aberration on gene expression for every gene in every sample. In this work, a novel Bayesian inference and sampling algorithms for a double-layered mixture model (DLMM) is proposed. DLMM directly models segmental patterns in the copy number data to produce copy number aberration profile in probability scale, and simultaneously scores the association between paired copy number and gene expression data using related latent variables in the two data sets. The method assigns high scores to elevated or reduced expression measurements only if the expression changes are observed consistently across samples with copy number aberration. Since DLMM simultaneously computes the probability of copy number amplification and deletion and the probability of copy number-associated expression conditional on the former, DLMM ensures high specificity of copy number influence on gene expression and also removes the burden of separate analysis for the two data.. The organization of this article is as follows. In Section 2, the statistical model DLMM is described in three parts: model for copy number data, model for gene expression data, and scoring and selection criteria. Section 3 explains Bayesian inference using Markov chain Monte Carlo sampling. Section 4 describes simulation studies for characterizing the behavior of DLMM under various settings. Section 5 presents the application of the proposed methodology to a breast cancer data set by Pollack et al. (2002) , with comparison to two competing methods by Lipson et al. (2004) and van Wieringen and van de Viel (2008) . Section 6 concludes the article.. Figure 1: Graphical representation of the double-layered mixture model. X and Y denote the observed copy number and expression data respectively. Z and W are the calls of aberrant copy number and differential gene expression associated with aberrant copy number. X (1) and X (n) denote minimum and maximum copy numbers in the sample respectively. Note that the mixture model in the copy number data is sample-specific, while that in the gene expression data is genespecific. Given these parameters, the two data sets are independent. In this work, a model-based method DLMM has been proposed for identifying coherent signals in the paired profiles of copy number and gene expression. DLMM consists of copy number probability estimation and copy number-associated differential expression analysis. The method achieves the goal by computing the joint probability of aberrant copy number and concordant differential gene expression between samples with and without copy number changes, and thus accounts for uncertainty in both data simultaneously. The analysis of breast cancer data from Pollack et al. (2002) has shown that the copy number probabilities estimated by DLMM are largely congruent with a large-scale repository of breast cancer cases, and the selected signature of genes showing evidence of copy number associated expression are located in the vicinity of known oncogenes while many oncogenes were not directly under the influence themselves. The sample-specific index constructed from the selected genes was also correlated with the clinico-pathological information, highlighting the potential of this gene signature as a diagnostic or prognostic measure in cancer.. Joint inference of these two data sets is challenging particularly because copy number data should be analyzed within each sample while gene expression data analysis is a comparison across samples. The reason the copy number data analysis is specific to individual samples is that, unlike properly normalized gene expression data, experimental copy number of a gene is not directly comparable across samples for two main reasons. First, every tumor biopsy results in a mixture of tumor and normal cells and the ratio of this mixture varies by sample. Thus with a common reference sample used in competitive hybridization, the copy number levels in each sample are affected by the proportion of tumor cells in the specimen, especially for genes with aberrant copy number. Hence approaches that take the raw copy number data as measurements comparable across the samples, e.g. Lipson et al. (2004) , may be subject to unexpected errors and this was shown in the analysis of Pollack data. Secondly, relative copy number levels can be inferred more accurately if one considers the segmental patterns present in the copy number data, particularly because the signal-to-noise ratio is not often very high and thus local data may help identify signals that are weak but consistent in the neighborhood of each gene. For example, the median sample standard deviation in local windows of 100 clones was around 0.12, while the copy number ratio in the regions most frequently reported as amplified (1q, 8q) was as small as 0.35 in relevant samples. Therefore, those methods using sample-specific copy number probability calls such as DLMM and vWvV tests seem to be more relevant than linear correlation analysis.. Despite the differences in inferential techniques between DLMM and vWvV tests, the two methods share a common principle of distinguishing gene expression distributions between samples with and without aberrant copy numbers. vWvV tests adopt a nonparametric hypothesis testing framework for the hypothesis that the expression distributions are equal in the two groups of samples by incorporating uncertainty of copy number calls in each sample with a tuning algorithm for unbalanced grouping. However, it was shown that, through the examples of the oncogenes in the Pollack data, the method selects genes whose copy number calls are high in few samples only even after applying the tuning algorithm proposed in their work. DLMM takes a different approach, where the scores of copy number associated expression levels are computed for individual genes in each sample and the frequency that the score is above a chosen threshold across the samples is used for final selection of relevant events. This approach seems more relevant than both vWvV and GCSM in the joint analysis because copy number associated gene expression changes is a relatively rare event compared to our direct gene regulation activities.. DLMM can easily be extended to tumor-normal comparisons or comparisons between different types of tumors by changing the way the final joint probability is calculated from the latent variables Z and W . In tumor-normal case, one can perform a semi-supervised estimation by making the normal samples contribute to the estimation of parameters in the mixture component for samples without aberrant copy number levels, i.e. (δ g , η 2 g ) with 100% chance by fixing W = 0 since normal cells are supposed to have little copy number aberration. In tumor-tumor comparisons, one should keep track of copy number changes in the two groups separately, and select genes whose copy number-associated expression changes are unique in either group. DLMM can also be used for the data where more than a single copy number probe or clone can be mapped to a gene in the expression data. The segmentation applies to high-resolution arrays exactly the same way the Pollack data was analyzed in this work, and one can still score the coherent signal in the two data by defining multiple W variables for each pair of copy number probe and gene expression probe.

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


Multiscale morphological segmentation of gray-scale images Abstract-In this paper, the authors have proposed a method of segmenting gray level images using multiscale morphology. The approach resembles watershed algorithm in the sense that the dark (respectively bright) features which are basically canyons (respectively mountains) on the surface topography of the gray level image are gradually filled (respectively clipped) using multiscale morphological closing (respectively opening) by reconstruction with isotropic structuring element. The algorithm detects valid segments at each scale using three criteria namely growing, merging and saturation. Segments extracted at various scales are integrated in the final result. The algorithm is composed of two passes preceded by a preprocessing step for simplifying small scale details of the image that might cause over-segmentation. In the first pass feature images at various scales are extracted and kept in respective level of morphological towers. In the second pass, potential features contributing to the formation of segments at various scales are detected. Finally the algorithm traces the contours of all such contributing features at various scales. The scheme after its implementation is executed on a set of test images (synthetic as well as real) and the results are compared with those of few other standard methods. A quantitative measure of performance is also formulated for comparing the methods. In this paper, we have proposed a scheme for segmenting gray-level images of cluttered objects of different shape and size. The proposed multiscale morphological method is expected to work satisfactorily on gray-level images containing bright and dark features of various scales. The scheme starts with simplifying the image in the preprocessing step. In the first pass the algorithm extracts potential regions at various scales by multiscale top-and bottom-hat transformation and store them in different towers. In the second pass the algorithm compares pair of feature images corresponding to two successive scales and identifies the potential regions that contribute to final segmentation based on three criteria, namely growing, merging, and saturation. Finally the contours of all such potential regions are integrated. The results of the proposed scheme have been compared with those of two other well known methods, namely watershed algorithm and Canny's edge-based algorithm. It is evident that the results produced by Canny's method are far behind than those of the proposed scheme and watershed algorithm for the class of images we consider. The watershed algorithm produce over-segmentation in some cases. The proposed method, by and large, produce overall better results compared to two other methods. The positive features of the proposed scheme is that it is shape-and edge-preserving, scale-calibrated, and satisfy a set of goodness criteria. However, the CPU time and memory space requirement of the scheme are relatively higher. The proposed scheme being inherently parallel might improve this shortcoming after suitable parallel implementation.

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


The evaluation of a social adaptive website for cultural events In this paper, we present an evaluation of a social adaptive website in the domain of cultural events, iCITY DSA, which provides information about cultural resources and events that promote the cultural heritage in the city of Turin. Using this evaluation, our objective was to investigate the actual usage of a social adaptive website, in an effort to discover the real behavior of users, the unforeseen correlations among user actions and the consequent interactive behavior, the accuracy of both system and social recommendations and their impact on the users themselves, and the role of tagging in the user modeling process. The major contributions of the paper are manifold: insights into user interactions with social adaptive systems; guidelines for future designs; evaluation of the tagging activity and tag meanings in relation to the application domain and thus their impact on the representation of the user model; and a demonstration of how a combination and interplay of evaluation methodologies (e.g., quantitative and qualitative) can enhance our comprehension of evaluation data. This paper describes the real-world evaluation of a social adaptive website. A social adaptive website is a social web system that provides adaptive recommendations to users. An adaptive system personalizes its appearance and behavior in accordance with the characteristics of the user and the context. A social system offers so-called "social" functionality: on the one hand, it allow users to generate and share contents; on the other, it offers them social networking facilities. Thus, a social adaptive system has the unique capability to exploit both the information derived from user-generated content and social networking activities for the personalization of the user's experience and its adaptive capabilities for supporting users in their social activities.. As a test-bed for our evaluation, we chose iCITY DSA (Digital Semantic Assistant), 1 a website that deals with cultural events (exhibitions, concerts, etc.) taking place in the city of Turin, since it is a representative example of a social adaptive web-based system. In fact, it is social, in that it allows its users to post their own content (e.g., insert new events and add information about them, and post comments and tags), to connect with their friends, and to create their own social networks. It is also adaptive in that it provides recommendations of events, based on a user's implicit and explicit interests. As a social adaptive system, iCITY exploits social actions, and in particular the action of tagging, in order to infer user interests and update user models (see Carmagnola et al. 2008 for details).. The real-world evaluation of iCITY started in July 2008 and ended at the end of October (with a summer holidays break during August), and was promoted on the official website of the municipality of Turin. 2 In total, 313 users voluntarily registered on the website and joined in the social activity of the system. A large amount of data about user activities and opinions was then available. User actions, such as clicking on an event, a recommended event, or a tag, or adding a comment or a tag, or updating a profile or sending a message, were recorded and collected by means of log files, providing us with a valuable source of information, which we wanted to analyze in detail. Among all the user activities on the system, particular attention has been devoted to the analyses of tags, which could be either inserted by users in free text or chosen from among the system's suggestions. In particular, we analyzed both the meaning of tags and their usage. Finally, we collected information about the users' interests, users' demographics and their familiarity with technology, users' perception of the system, etc., by means of post-usage questionnaires.. This information allowed us to investigate the functioning of a social adaptive system. Since the beginning, in fact, iCITY was conceived as an adaptive system enriched by social components that favor user collaboration. Thus, the general goal of this realworld evaluation, as well as of previous system evaluations described in Sect. 4, was to discover how the social components enhance the adaptation features of the system. Our analysis concentrated mainly on: (i) users' behavior in general, and (ii) users' 1 http://torino.mydsa.it/dsa/. Notice that this is the URL we used for the evaluation described in this paper. The website is now available at http://www.icity.di.unito.it/dsa-dev/. An English version is also available at http://www.icity.di.unito.it/dsa-en/. 2 http://www.comune.torino.it/.. tagging activity in particular.User behavior data were collected by means of log files; following Gena and Weibelzahl (2007) , we exploited a log files' analysis as a kind of indirect observational method. In particular, in our analysis of log files we were inspired by "systematic observation methodology", a particular approach to quantifying behavior that is typically concerned with naturally occurring behavior observed in a real context (Bakeman and Gottman 1997) . Using correlational analysis, we evaluated the co-occurrences and the sequences of user actions; we also applied cluster analysis. In our comparison of these elaborated data and the qualitative measures obtained from the analysis of questionnaires, we aggregated actions in order to discover the more general behavioral schemes of the users of social adaptive systems, of which iCITY is an example.. Users' tagging activity is a peculiarity of social systems. Tags characterize social systems as a bottom-up activity that offers to the user a specific view of the presented content. In a social system that is also adaptive, tags have two purposes: they can be used to model user interests and preferences, and they can be recommended to the users. The analysis of tags has concentrated on the tagging activity of users and on other tag features, such as their meaning and their relation to the domain ontology, as well as their classification in more general categories.. Our results provided useful information, allowing us to understand better how adaptive and social features can benefit from each other when they co-exist in the same system, and to generalize our findings in a series of design guidelines for social adaptive systems. At a meta-level, they also confirmed the effectiveness of using a combination of evaluation methodologies. Thus, the main contributions of this paper are:. -Insights into user behavior and user interactions with social adaptive systems, and guidelines for future designs of such systems, in particular, tag-based user model systems (Sect. 6); -A definition of user profiles and behavior that characterize social adaptive systems and that can be taken into account when designing this kind of system (Sect. 6); -An evaluation of tagging activity and tag meanings and their role in the representation of the user model (Sect. 5.3). The central role of tags in iCITY is also demonstrated by the evolution of its user model toward an open user model that exports tags for interoperability purposes (Sect. 7); -An analysis of user tagging behavior that can be taken into account for tagging recommendation purposes (Sect. 5.3); -A demonstration of how a combination and interplay of evaluation methodologies (e.g., quantitative, qualitative) can enhance our comprehension of evaluation data. For more details see Table 8 and the related discussion.. The paper is structured as follows. Section 2 presents the state of the art of the evaluation of social adaptive systems. In Sect. 3, we present iCITY, the system under evaluation, focusing on its distinctive features and on the functionalities that aid our comprehension of its real-world evaluation. In Sect. 4, we summarize the first evaluations of iCITY, in order to obtain a background against which a better understanding of the evaluation presented in this paper is attained. The remaining sections describe the different steps of our real-world evaluation of iCITY. In Sect. 5, we present the analysis of log files containing the real usage data. We report the results of correlations, cluster analysis, precision, recall, Mean Absolute Error (MAE), and RMSE. Moreover, we discuss the evaluation of the meaning of tags and their impact on the user modeling process. At the end of the section, we describe the analysis of post-test questionnaires that were designed to assess user satisfaction. Sect. 6 provides a discussion of all the evaluations presented in Sect. 5. Sect. 7 concludes the paper and presents suggested future work, and a follow-up experiment on open user models, which we performed as a consequence of the results of this evaluation. In this paper, we have presented the evaluations we carried out of iCITY, a social, adaptive system that recommends cultural events. In this Sect., we summarize our main findings regarding user interactions with a social adaptive recommender system, and, at a meta-level, methodological issues for the evaluation of such systems. We also present a follow-up evaluation that we carried out in order to investigate further some of our findings.

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


On the Applicability of Post's Lattice For decision problems Π(B) defined over Boolean circuits using gates from a restricted set B only, we have Π(B) ≤ Let Π denote some decision problem defined over Boolean circuits such that membership in Π is invariant under the substitution of equivalent circuits. Denote by Π(B) its restriction to circuits using gates from a finite set B only. It is easily observed that then Π(B) ≤ [7, 20] ). If we consider formulae instead, this reduction does not necessarily hold; the size of the smallest formula over the Boolean connectives from B ′ computing some function from B might be of exponential size.. Building on works of [8, 9, 22] , we show that a weaker form of this property holds for decision problems defined over formulae, namely that Π(B) ≤ . , as in the circuit setting. These results provide a (partial) account for the polytomous complexity classifications of problems parametrized by the set of available Boolean connectives: the complexity of the satisfiability problem was, for instance, shown to be NP-complete if x y can be composed from the available Boolean connectives, and solvable in logspace in all other cases [13] . Further results include a variety of problems in propositional logic [5, 19] , modal logics [1] , temporal logics [2] [3] [4] 16] , their hybrid variants [14, 15] , and nonmonotonic logics [6, 11, 23] .. We point out that the results obtained herein are completely general in that they do not rely on properties of the considered ✩ Work supported by DFG grant VO 630/6-2 and performed while employed at the Gottfried Wilhelm Leibniz Universität Hannover.. Email address: michael.thomas@twt-gmbh.de (or thomas@thi.uni-hanover. de) problems except invariance of membership under substitution of logically equivalent formulae (i.e., if (ϕ, x) is an instance of Π with ϕ being a Boolean formula and if ϕ ′ is a Boolean formula logically equivalent to ϕ, then (ϕ, x) ∈ Π iff (ϕ ′ , x) ∈ Π). This generality comes at the price of a fairly powerful reduction. However, in practice, most problems exhibit additional structure that allow to further restrict the notion of reductions considered. The results presented in this note provide insight into why complexity classifications of problems in Post's lattice yield only a finite number of complexity degrees.. These results are completely general in the sense that we did not place any restrictions on the considered decision problems Π (unless, of course, that membership in Π is invariant under substitution of equivalent formulae). However, typically instances of natural decision problems exhibit additional structure; by exploiting this structure one may further reduce the computational power of the reduction ≤ . This holds for the propositional implication problem [5] , among others.. It is worth noting that, on the other hand, there exist natural problems that do not satisfy the conditions imposed on Π above. Amongst those is the problem BFMIN, which asks to determine, given a Boolean formula and an integer k, whether there exists an equivalent formula of size ≤ k. This problem has recently been shown to be Σ p 2 -complete for the Boolean standard base B = {∧, ∨, ¬} using Turing reductions [10] . However, considering its restriction to B-formulae, we obtain BFMIN(B) ≤ C m BFMIN(B ′ ): Let ϕ L(B) be some Boolean formula of arity n. Then (ϕ, c(n)) ∈ BFMIN(B ∪ {ϕ}) for some constant c (depending on n only), while (ϕ, k) BFMIN(B) for all k ∈ N.

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 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


Text Clustering with Seeds Affinity Propagation Abstract-Based on an effective clustering algorithm-Affinity Propagation (AP)-we present in this paper a novel semisupervised text clustering algorithm, called Seeds Affinity Propagation (SAP). There are two main contributions in our approach: 1) a new similarity metric that captures the structural information of texts, and 2) a novel seed construction method to improve the semisupervised clustering process. To study the performance of the new algorithm, we applied it to the benchmark data set Reuters-21578 and compared it to two state-of-the-art clustering algorithms, namely, k-means algorithm and the original AP algorithm. Furthermore, we have analyzed the individual impact of the two proposed contributions. Results show that the proposed similarity metric is more effective in text clustering (F-measures ca. 21 percent higher than in the AP algorithm) and the proposed semisupervised strategy achieves both better clustering results and faster convergence (using only 76 percent iterations of the original AP). The complete SAP algorithm obtains higher F-measure (ca. 40 percent improvement over k-means and AP) and lower entropy (ca. 28 percent decrease over k-means and AP), improves significantly clustering execution time (20 times faster) in respect that k-means, and provides enhanced robustness compared with all other methods. C LUSTERING digital objects (e.g., text documents) by identifying a subset of representative examples plays an important role in recent text mining and information retrieval research. In fact, organizing a large amount of objects into meaningful clusters (clustering) is often used to browse a collection of objects and organize the results returned by a search engine [1] , [2] . After the clustering process, the obtained clusters are represented with examples, which can include all or part of the features that appear in the cluster members. During cluster-based query processing, only those clusters that contain examples similar to the query are considered for further comparisons with cluster members, e.g., documents. This strategy, sometimes called Cluster-Based Retrieval, is intended to improve both efficiency and effectiveness of the document retrieval systems [3] , [4] , [5] , [6] . Our work focuses on the proposal and detailed analysis of a new effective and fast clustering algorithm that can be used in cluster-based retrieval tasks.. Traditional approaches for clustering data are based on metric similarities, i.e., nonnegative, symmetric, and satisfying the triangle inequality measures. More recent approaches, like Affinity Propagation (AP) algorithm [7] , can take as input also general nonmetric similarities. For instance, in the domain of image clustering, AP can use as input metric selected segments of images' pairs [8] . Accordingly, AP has been used to solve a wide range of clustering problems, such as image processing tasks [7] , [8] , gene detection tasks [9] , and individual preferences predictions [10] . Affinity Propagation is derived as an application of the max-sum algorithm in a factor graph, i.e., it searches for the minima of an energy function on the basis of message passing between data points [7] . The clustering performance depends on the similarity measure and message updating frequency. For its simplicity, general applicability, and good performance, AP has already been used in text clustering. By using AP to preprocess texts, Ma et al. developed an incremental method [11] for text clustering. Wang et al. combined AP with a parallel strategy for e-learning resources clustering [12] . However, they used AP only as an unsupervised algorithm and did not consider any structural information derived from the specific documents.. For text mining tasks, the majority of state-of-the-art frameworks employ the vector space model (VSM), which treats a document as a bag of words and uses plain language words as features [13] , [14] . This model can represent the text mining problems easily and directly. However, with the increase of data set size, the vector space becomes highdimensional, sparse, and the computational complexity grows exponentially. Moreover, in many practical applications, completely unsupervised learning is lacking relevant information. On the other hand, supervised learning needs an initial large number of class label information, which requires expensive human labor and time [15] , [16] . Therefore, in recent years, semisupervised learning has captured a great deal of attentions [17] , [18] , [19] , [20] , [21] . Semisupervised learning is a machine learning paradigm in which the model is constructed using both labeled and unlabeled data for training-typically a small amount of labeled data and a large amount of unlabeled data [16] , [22] .. In this paper, we present a new clustering algorithm by extending Affinity Propagation with 1) a novel asymmetric similarity measurement that captures the structural information of texts, and 2) a semisupervised learning approach, where we exploit the knowledge from a few labeled objects versus a large number of unlabeled ones.. In information retrieval, there are several commonly used measurements of similarities. The simplest of all similarity measures, namely, simple matching coefficient, is counting the number of shared terms in two sets (e.g., documents). where jZj gives the size of a set Z. This coefficient does not take into account the sizes of X and Y . A more powerful coefficient called Cosine coefficient takes this information into account [23] :. Both metrics are symmetric. However, such symmetric property is not always present in realistic cases. For instance, to measure the similarity among sentences, Frey and Dueck [7] proposed to compute the similarity between sentence i and sentence k based on the cost of encoding the words in sentence i using the words in sentence k. This ad hoc similarity measurement performed very well. In their study, it is found that about 97 percent of such similarities were not symmetric.. Similarly, in this paper, we propose an asymmetric similarity measurement for two different documents, which is different from the conventional symmetric measurements [23] , [24] . Specifically, in text clustering, text documents typically contain a large number of structural information which is completely ignored in conventional Cosine coefficient measures. For instance, in structured documents such as news articles and/or scientific papers, relevant words, or phrases emerge in specific sections of the document, i.e., title, author, abstract, keywords, and references (in scientific literatures) which may be considered as terms carrying structural information. Embracing some ideas of positive and negative association rules proposed in [25] , we define three feature sets containing structural information. An asymmetric similarity measurement-called Tri-Set method-is thus proposed based on these three feature sets.. Finally, we present and analyze the definition of specific initial values for the clustering algorithm, that we named Seeds, to bootstrap the initial phases of the new clustering algorithm. We thus propose a novel semisupervised clustering algorithm: Seeds Affinity Propagation (SAP). This model aims to address the complexity problem in text clustering which results from the high dimension and sparse matrix computations.. To examine the effectiveness of the proposed method, we have applied it to the benchmark data set Reuters-21578 . In order to analyze the behavior of the new algorithm (and also the impact of the two individual proposed contributions), we have performed a detail comparison with four clustering methods on the same data set, namely, 1. k-means approach; 2. the original Affinity Propagation algorithm with conventional similarity measurement (AP(CC)); 3. a modified Affinity Propagation method, which combines AP with the new similarity measurement (AP(Tri-Set)); and 4. a modified Affinity Propagation method which combines AP with the new seed construction semisupervised method (SAP(CC)). In our experiments, k-means (proposed by MacQueen [24] in 1967) is selected as the baseline state-of-the-art clustering algorithm. It is an important and successful method in data mining and knowledge discovering. Many algorithms are derived from k-means or compete with it (see, for instance, [26] , [27] , [28] ). In particular, Wu et al. discussed several limitations about k-means in detail, such as its sensitivity to initialization, to the presence of outliers [29] . Our experimental results show that SAP offers better speed (i.e., about 20 times faster than k-means) and overall precision than the other four clustering algorithms (i.e., Fmeasures increase up to 44 percent compared with k-means).. The rest of the article is organized as follows: we start in Section 2 with a brief review of the Affinity Propagation clustering approach and related work. In Section 3, the definitions of structural information sets are introduced, and then, the SAP algorithm is described in detail. Section 4 presents the experimental methodology and results on a benchmark data set as well as the comparison with the selected baseline algorithms. Section 5 discusses conclusions and future work. In this paper, we first proposed a similarity measurement which is extended from Cosine coefficient using structural information on the basis of Cofeature Set, Unilateral Feature Set, and Significant Cofeature Set. These three sets represent different features at different positions of texts. Their structural information improves the clustering results. The new similarity measurement can be used to calculate the asymmetric similarity directly, which is not limited to the symmetric space. Moreover, a new clustering algorithm which combines Affinity Propagation with semisupervised learning, namely, Seeds Affinity Propagation algorithm is proposed. SAP is applied to full text clustering which extends the application of Affinity Propagation. In the comparison with the classical clustering algorithm k-means, SAP not only reduces the computing complexity of text clustering and improves the accuracy, but also effectively avoids being random initialization and trapped in local minimum. SAP is also more robust and less sensitive to data distribution than k-means, conventional AP, AP (Tri-Set), and SAP (CC). In other words, it makes an important improvement in text clustering tasks. In addition, we believed that since SAP is based on a detailed similarity measurement and on a generic seeds construction strategy, it can be widely applied to other clustering problem domains. This is what we want to explore in our future work. AP was proposed as a new and powerful technique for exemplar learning. In brief, the user has to provide as initial input to the algorithm a complete matrix of similarities (for the selected metric(s)) among the input data points. At first, all data points are viewed as potential exemplars. Then, after a large number of real-valued information messages (i.e., named responsibility and availability messages, see below) are transmitted along the edges of the network (each data point is viewed as a node), a relevant set of exemplars and corresponding clusters is identified [7] .. In the following, we detail in brief the mathematical model of the AP approach. At start-up, AP takes in input a collection of real-valued similarities between data points. Given an N data point's data set, x i and x j are two objects in it. The similarity s(i, j) indicates how well x j is suited to be the exemplar for x i . For instance, it can be initialized to sði; jÞ ¼ Àkx i À x j k 2 ; i 6 ¼ j. Hereinto, if there is no heuristic knowledge, self-similarities are called as preference in [7] and often set as a constant. For instance, they could be set as sðl; lÞ ¼ P N i;j¼1;i6 ¼j sði; jÞ. Then, the AP approach computes two kinds of messages exchanged between data points. The first one is called "responsibility" r(i, j): it is sent from data point i to candidate exemplar point j and it reflects the accumulated evidence for how well-suited point j is to serve as the exemplar for point i.. The second message is called "availability" a(i, j): it is sent from candidate exemplar point j to point i and it reflects the accumulated evidence for how appropriate it would be for point i to choose point j as its exemplar. At the beginning, the availabilities are initialized to zero: aði; jÞ¼ 0. The update equations for r (i, j) and a(i, j) are written as rði; jÞ ¼ sði; jÞ À max. aði; jÞ ¼ min 0; rðj; jÞ þ X i 0 6 ¼i;j max 0; rði 0 ; jÞ f g ( ). In addition, during each messages' exchange between data points, a damping factor 2 ½0; 1 is added to avoid numerical oscillations that may arise in some circumstances:. where R ¼ ðrði; jÞÞ and A ¼ ðaði; jÞÞ represent the responsibility matrix and availability matrix, respectively, and t indicates the iteration times. The above two messages are updated iteratively, until they reach some specified values or the local decisions stay constant for a number of iterations. At this stage, availabilities and responsibilities can then be combined to identify exemplars: . Many detailed analyses of the AP approach have been carried out (see, for instance, [30] and [31] ) for various data sets with different scales. These studies show that for small data sets, there are only minor differences between traditional strategies (such as p-median model and vertex substitution heuristic) and Affinity Propagation clustering for both precision and CPU execution time. Nevertheless, for large data sets, AP offers obvious advantages over existing methods [7] , [31] . In particular, in their work, Frey and Dueck showed that an improvement in execution time of roughly 100 times is achieved on data sets of more than 10,000 objects and ca. 500 clusters. Moreover, in [7] , [8] , [9] , [10] , [11] , [12] , [30] , [31] , [32] , [33] , it has been identified that the similarity measurement has a great influence on AP clustering. The publicly available Reuters-21578 (Reuters) data set is preclassified manually [36] . This classification information is eliminated before the clustering processes, and is used to evaluate the clustering accuracy of each clustering algorithm at the end of the execution. The original Reuters data consist of 22 files (for a total of 21,578 documents) and contain special tags such as "<TOPICS>" and "<DATE>" among others. The preprocessing phase on the data set cuts the files into single texts and strips the document from the special tags. Then, those documents which belong to at least one topic are selected. At last, after stop words removal, word stemming, and word frequency computation for each document, the data set turns into the form of. For text clustering problem, Cofeature Set can be viewed as a two-tuples set. Each term in the set consists of one word that exists both in d i and d j , and the word's frequency in d j . The terms in the Unilateral Feature Set, on the other hand, consist of the words that only exist in d i and their frequencies in d i . Moreover, there are some words that exist in the title, abstract, or in the first sentence of each paragraph in d j and they can also be found in d i . These words and their frequencies at important positions of d j can be viewed as the two-tuples of the Significant Cofeature Set (we used the words (except stop words) in the title). For the construction of seeds, in order to quickly find out the representative features, the proposed Mean Features Selection strategy is applied.

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