A Stochastic Model of Multivirus Dynamics Abstract-Understanding the spreading dynamics of computer viruses (worms, attacks) is an important research problem, and has received much attention from the communities of both computer security and statistical physics. However, previous studies have mainly focused on single-virus spreading dynamics. In this paper, we study multivirus spreading dynamics, where multiple viruses attempt to infect computers while possibly combating against each other because, for example, they are controlled by multiple botmasters. Specifically, we propose and analyze a general model (and its two special cases) of multivirus spreading dynamics in arbitrary networks (i.e., we do not make any restriction on network topologies), where the viruses may or may not coreside on computers. Our model offers analytical results for addressing questions such as: What are the sufficient conditions (also known as epidemic thresholds) under which the multiple viruses will die out? What if some viruses can "rob" others? What characteristics does the multivirus epidemic dynamics exhibit when the viruses are (approximately) equally powerful? The analytical results make a fundamental connection between two types of factors: defense capability and network connectivity. This allows us to draw various insights that can be used to guide security defense. T O solve the problem of computer viruses (malware, worms, or bots), we need a set of approaches, ranging from legislation to technology. One technological approach, we call the dynamical systems approach, aims to understand the attack(-defense) dynamics so as to offer insights and guidance for defense from a whole-system perspective (i.e., by addressing macroscopic questions). This approach is complementary to the well established approaches such as access control and cryptography. Despite the attention that has been paid by communities including computer security and statistical physics, existing studies mainly focused on single-virus spreading dynamics. In this paper, we study multivirus spreading dynamics, where multiple viruses may be controlled by multiple attackers and thus may combat against each other. We have witnessed incidents of this type. For example, the Welchia worm tried to "kill" the Blaster worm by deleting the Msblast.exe file created by W32.Blaster.Worm [26] . Although such incidents are not exactly as full-fledged and sophisticated as the virus combats investigated in the paper, they can be seen as a prelude to (some of) the investigated scenarios that may soon become reality. As such, we need to investigate and understand the consequences of fighting viruses so as to get prepared by enhancing our body of knowledge. We introduced a general model of multivirus spreading dynamics, where the viruses may combat against each other. We presented analytical results in the general model, including sufficient conditions under which the viruses die out when many or some nodes are initially infected, and deeper results for two special cases of the general model. The analytical results made a fundamental connection between the defense capability and the connectivity of the network (via the largest eigenvalue of its adjacency matrix), and allowed us to draw various insights that can be used to guide security defense.. This paper brings a range of new problems for future research. In addition to those mentioned in the body of the paper, we offer: When we state the degree of initial infection, we used the qualitative term "light initial infection," but can we quantify it? What are the necessary conditions under which the viruses will die out? What are the complete dynamics characteristics when (some or all of) the viruses do not die out? There are mainly two approaches to understanding security properties from a whole-system perspective: epidemic-like and attack-graph-like. This paper falls into the epidemiclike approach.. Epidemic-like approach. This approach aims to characterize, among other things, sufficient conditions (epidemic thresholds) under which the spreading will die out. The study of computer virus dynamics was started by Kephart and White [19] , [20] , who adopted/adapted some homogeneous biological epidemic models [22] , [21] , [3] , [2] , [15] . Recent studies investigated heterogeneous models (see, e.g., [35] , [4] , [25] , [30] , [31] , [29] , [10] ), which are interesting not only for their own sake but also because of their practical potential (because any topology is possible). These studies were mainly conducted by the statistical physics community with an emphasis on power law networks (see, e.g., [25] , [30] , [31] , [29] ). Very recently, computer scientists investigated spreading in arbitrary networks [34] , [13] , [10] (rather than just power law topologies). This paper moves a significant step beyond them by considering multiple viruses spreading in arbitrary networks, where the viruses may combat against each other as well.. Attack-graph-like approach. In an attack graph, a node is the state of a network and an arc depicts a step in an attack that exploits vulnerabilities uncovered by vulnerability scanners (cf. [33] , [18] , [1] and their follow-ons). This approach aims to identify, among other things, 1) attack paths between a starting node or a set of starting nodes and some target node, and 2) guidance for security hardening [27] , [24] . Recently, Bursztein and Goubault-Larrecq [8] , [7] , [6] , [9] introduced the novel concept of anticipation game, which aims to introduce game theory into attack graphs so as to prove that a safety property holds and further to answer questions about strategic objectives (e.g., what is the most effective patching strategy?).. On the relationship between the two approaches. At the current stage of our knowledge, the two approaches are incompatible. Here, we discuss some informal observations, while pointing out that it is an important future work to precisely characterize the relationship (e.g., how can we unify them into a more general framework?). First, the two approaches share some common goals. 1) Both approaches take a whole-system perspective, rather than a component perspective. For example, the vulnerabilities used in the attack-graph-like approach can be used as an input for constructing the system graph used in the epidemic-like approach. 2) Both approaches are useful for "what if" analysis as we show in this paper. Second, the two approaches can answer different kinds of questions under different premises. 1) Attack-graph-like approach often assumes known vulnerabilities that can be obtained using scanners, and thus cannot deal with zero-day exploits. Epidemic-like approach in principle can accommodate zeroday exploits, perhaps with the help of domain expert knowledge. 2) Attack-graph-like approach suffers from the state explosion problem [1] , [11] ; whereas, epidemic-like models can handle very large networks (e.g., hundreds of millions of nodes). 3) Epidemic-like approach can make a fundamental connection between the defense capability and the network connectivity. We do not know how to accommodate network connectivity into the attack-graphlike approach.. Outline. In Section 2, we present and explore a general model of multivirus dynamics. We investigate in Section 3 the special case that the viruses may fight against each other and do not coreside on computers, and in Section 4 the special case that the viruses may coreside on computers. In Section 5, we draw further insights from the analytical results. In Section 6, we report our simulation study. We conclude the paper in Section 7 with open problems.

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


Approximability and inapproximability of the minimum certificate dispersal problem Given an n-vertex directed graph G = (V, E) and a set R ⊆ V × V of requests, we consider to assign a set of edges to each vertex in G so that for every request (u, v) in R the union of the edge sets assigned to u and v contains a path from u to v. The Minimum Certificate Dispersal Problem (MCD) is defined as one to find an assignment that minimizes the sum of the cardinalities of the edge sets assigned to each vertex. This problem has been shown to be NP-hard in general, though it is polynomially solvable for some restricted classes of graphs and restricted request structures, such as bidirectional trees with requests of all pairs of vertices. In this paper, we give an advanced investigation about the difficulty of MCD by focusing on the relationship between its (in)approximability and request structures. We first show that MCD with general R has Θ(log n) lower and upper bounds on approximation ratio under the assumption P ̸ = N P . We then assume R forms a clique structure, called Subset-Full, which is a natural setting in the context of the application. Interestingly, under this natural setting, MCD becomes to be 2-approximable, though it has still no polynomial time approximation algorithm whose factor better than 677/676 unless P = N P . Finally, we show that this approximation ratio can be improved to 3/2 for undirected variant of MCD with Subset-Full. Background and Motivation. Let G = (V, E) be a directed graph and R ⊆ V ×V be a set of ordered pairs of vertices, which represents requests about reachability between two vertices. For given G and R, we consider an assignment of a set of edges to each vertex in G. The assignment satisfies a request (u, v) if the union of the edge sets assigned to u and v contains a path from u to v. The Minimum Certificate Dispersal Problem (MCD) is the one to find the assignment satisfying all requests in R that minimizes the sum of the cardinalities of the edge sets assigned to each vertex. This problem is motivated by a requirement in public-key based security systems, which are known as a major technique for supporting secure communication in a distributed system [1, 2, 3, 4, 5, 6, 7] . The main problem of the systems is to make each user's public key available to others in such a way that its authenticity is verifiable. One of well-known approaches to solve this problem is based on public-key certificates. A public-key certificate contains the public key of a user v encrypted by using the private key of a user u. If a user u knows the public key of another user v, user u can issue a certificate from u to v. Any user who knows the public key of u can use it to decrypt the certificate from u to v for obtaining the public key of v. All certificates issued by users in a network can be represented by a certificate graph: Each vertex corresponds to a user and each directed edge corresponds to a certificate. When a user w has communication request to send messages to a user v securely, w needs to know the public key of v to encrypt the messages with it. For satisfying a communication request from a vertex w to v, vertex w needs to get vertex v's public-key. To compute v's public-key, w uses a set of certificates stored in w and v in advance. Therefore, in a certificate graph, if a set of certificates stored in w and v contains a path from w to v, then the communication request from w to v is satisfied. In terms of cost to maintain certificates, the total number of certificates stored in all vertices must be minimized for satisfying all communication requests.. While, from the practical aspect, MCD should be handled in the context of distributed computing theory, its inherent difficulty as an optimization problem is not so clear even in centralized settings: Jung et al. discussed MCD with a restriction of available paths in [4] and proved that the problem is NP-hard. In their work, to assign edges to each vertex, only the restricted paths which are given for each request is allowed to be used. MCD, with no restriction of available paths, is first formulated in [7] . In [7] , MCD, with no restriction of available paths, is proved to be also NP-hard even if the input graph is strongly connected. Known results about the complexity of MCD are actually only these NP-hardness. This fact yields a theoretical interest of revealing the (in)approximability of MCD. As for the positive side, MCD is polynomially solvable for bidirectional trees, rings and Cartesian products of graphs [7] . This paper also investigates how the request structures affect the difficulty of MCD. As seen above, MCD is doubly structured in a sense: One structure is the graph G itself and the other is the request structure R. We would like to investigate how the tractability of MCD changes as the topology of R changes. In passing, a typical doubly structured problem in this sense is the H-coloring problem [8] . The H-coloring problem is coloring problem with restrictions of adjacent colors, which are given by a graph H. That is, when the graph H is a complete graph, the H-coloring problem is equivalent to the traditional coloring problem. About H-coloring, so-called dichotomy theorem is well known: Hcoloring is solvable in polynomial time if and only if H has a loop or is bipartite graph; otherwise the problem is NP-complete. On MCD, our interest here is to investigate whether the hardness (of approximation) of MCD depends on the restrictions about R. A similar structure is also found in the VPN design problem [14] . It is defined as a certain kind of connection-establishment problems, and allows the optimal solution computable within polynomial time when the request is all-to-all connections(i.e., in the context of MCD, R induces a complete subgraph) [15] .. Revealing the relationship between tractability and request structures is a natural problem not only from the theoretical viewpoint but also from the practical viewpoint, because, in public-key based security systems, a set of requests should have a certain type of structures. For example, it is reasonable to consider the situation in which a set of vertices belonging to a certain community should have requests between each other in the community. This situation is interpreted that R forms a clique structure. Thus the following question arises: If R forms a clique, can the approximability of MCD be improved?. Our Contribution. In this paper, we investigate the approximability of MCD from the perspective how the structure of R affects the complexity of MCD. We classify the set R of requests according to the elements of R: R is subset-full if for a subset V ′ of V , R consists of all reachable pairs of vertices in V ′ , and R is full if the subset V ′ is equal to V . Note that Subset-Full corresponds to the situation that R forms a clique. Table 1 summarizes the results in this paper.. Here we review our contribution. We first consider the general case: We show that if we have no restriction about R, a lower bound on approximation ratio for MCD is Ω(log n) and an upper bound is O(log n), where n is the number of vertices. Namely, the lower and upper bounds coincide as Θ(log n) in terms of order. Moreover, it is proved that we can still obtain the inapproximability Ω(1) of MCD even when the graph class is restricted to bidirectional graphs.. As the second half of the contribution, for subset-full requests, we show that the lower bound of approximation ratio for MCD is 677/676 and the upper bound is 2. The lower bound is obtained by a gap-preserving reduction from VERTEX-COVER. The upper bound is proved by a detailed analysis of the algorithm MinPivot , which is proposed in [7] . While Zheng et al. have shown that MinPivot achieves approximation ratio 2 with full requests, we can obtain the same approximation ratio by a different approach even when the set of requests is subset-full. In addition, by extending the approach, it is also shown that MinPivot guarantees 3/2 approximation ratio for MCD of the undirected variant with subset-full requests.. The remainder of the paper is organized as follows. In Section 2, we define the Minimum Certificate Dispersal Problem (MCD). Section 3 presents inapproximability of MCD with general R and one with Subset-Full. The upper bound of MCD with general R and one with Subset-Full are shown in Sections 4 and 5 respectively. Section 6 concludes the paper.

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


Children construct novel word meaning ad-hoc based on known words: Computational model of shape and material biases Taking the stance that two well-known word learning biases (shape and material bias) are formed through learning (learned bias account, LBA), we illustrated a concrete computational mechanism with "ad-hoc meaning substitution (AMS)" hypothesis, and verified it by two computer simulations. AMS represents that when given a novel word and a corresponding instance, children create novel word meaning by using the known word meaning and the instance as an ad-hoc template. The AMS function enables fast mapping and vocabulary spurt. To describe the AMS process computationally, we introduced "word distributional prototype (WDP)," which is the explicit representation of word meaning with an inductive learning function. Simulation 1 revealed that when a network with WDP and AMS was given a biased vocabulary reflecting young children, it demonstrated shape, material, and overgeneralized shape biases. This result suggested that a triad of word meaning induction, ad-hoc meaning substitution, and early biased vocabulary is essential for the emergence of biases. Simulation 2 introduced the notion of maturity that denoted a degree of learning convergence for each word meaning, and then the network showed neither shape nor material bias during an early small vocabulary. This result indicated that the period at which each bias emerges is decided by maturity. Though AMS consists of simpler and valider mechanisms than those proposed in previous studies, it could reproduce behavior of shape and material biases and explain their emergence process clearly. These results suggest that phenomena concerning shape and material biases are explicable with a simple ad-hoc learning instead of meta-learning among LBA or innate language-specific ones. When we encounter a novel word such as Gavagai and guess its meaning, too many logically possible meanings exist (Quine, 1960) . Nevertheless, children as well as adults can estimate the meaning of words relatively well. Although children have little knowledge of the world, their learning of words is so fast that they can achieve estimation even with a single experience (Carey & Bartlett, 1978) . Such fast mapping can't be explained by existing machine learning algorithms based on trial and error. However, children in the first stage of word acquisition don't show such intelligence. They need to hear a word repeatedly before producing it, and they still often use words incorrectly. And the pace with which they acquire * Corresponding author. meanings is slow. But after a children's productive noun vocabulary exceeds 50 words, which happens around eighteen months, their vocabulary begins to grow quite rapidly. This is called vocabulary spurt.. To explain these phenomena, developmental psychologists have suggested word learning biases, which made children focus on particular features when applying a novel name to an object instead of other possible features. They also greatly narrow the infinite number of possible correspondences between a word and objects and enable children to estimate a word's meaning more accurately (Markman, 1989; Markman & Hutchinson, 1984; Markman & Wachtel, 1988; Landau, Smith, & Jones, 1988; Clark, 1987; Soja, Carey, & Spelke, 1991) . The problem is that these biases are just phenomenological explanations that can't explain why they exist or how they are pro-cessed in the human brain. We have to describe a more detailed computational mechanism of these biases not only to explain them but also to apply these findings to studies of education and language related disorders. In this paper, we try to closely illustrate a computational mechanism of two well-known biases: shape bias (Landau, Smith, & Jones, 1988) and material bias (Dickinson, 1988; Soja et al., 1991) especially in their early stages.. Shape bias is the behavior that when people hear a novel solid object named with a novel noun, they tend to extend the noun to objects similar in shape to the named object (Landau, Smith, & Jones, 1988) . Material bias is the behavior that when people hear a novel nonsolid substance named with a novel noun, they tend to generalize the noun to the substance similar in material (Dickinson, 1988; Soja et al., 1991) . Some studies have argued against "learned bias account (LBA)," which proposes that these biases result from simple learning. But we discuss the counterargument in section 6.2. We support LBA for the following three reasons. First, shape bias doesn't appear in early stages of development. It only appears after children have acquired a certain number of words (Smith, 1995; Samuelson & Smith, 1999) . Material bias also appears in the same manner, but later than shape bias (Soja et al., 1991; Colunga & Smith, 2005) . This reason is necessary but not sufficient for supporting LBA; we can explain that specific modules for shape/material biases exist in human brains and that they begin to function along with development of the brain area concerned with word acquisition. The other reasons increase the persuasiveness of LBA. The second reason is existence of overgeneralization of shape bias to material bias. Samuelson (2002) reported that children extended novel nouns assigned to nonsolid substances to objects similar in shape to the named substance. The overgeneralization is not easy to explain if one assumes specific modules for those biases. Meanwhile, LBA may be able to explain it because such overgeneralization is just a behavior actually observed in machine learning. The third reason is that shape/material bias is behavior for solid/nonsolid objects and both arise in almost identical situations except for their target stimuli's solidity. This similarity indicates that they may possess the same internal mechanism. Based on these reasons, we assume in this paper that shape and material biases emerge from the same mechanism of simple learning; hence material bias is overgeneralized by shape bias and both appear after the learning of a certain amount of vocabulary.. Here, we propose a simpler computational hypothesis that can account for the behavior of biases and explain their emergence process from the LBA framework. Specifically, we hypothesize that shape and material biases arise from two internal general learning abilities that are available from infancy and one external factor -biased early vocabulary. The first internal general learning ability is the one to learn the meanings of words by induction. Though it is fundamental to word meaning learning, it isn't enough to explain fast mapping. Consequently, we hypothesize another internal general learning ability: the ability to instantly estimate novel word meaning based on already learned word meanings and given encounters with the word. This substitution of word meaning from a known noun to a novel noun enables us to show fast mapping. We call the second ability "ad-hoc meaning substitution (AMS)." When children with the two abilities are exposed to the early biased vocabulary, which contain among solid/nonsolid words a high percentage of nouns organized by shape/material similarity, they show shape and material bias because AMS accounts for the substitution of meaning among such biased vocabulary (solidshape, nonsolid-material) for meanings of novel solid/nonsolid nouns. In our model, this triad of the word meaning induction, the ad-hoc meaning substitution, and the learning of early biased vocabulary is a necessary and sufficient factor for the emergence of biases. But this triad can cause different behavior from children's no biases: stable biases from the beginning of word learning. So we introduce a notion of maturity to inhibit the early stable bias. Here maturity means a degree of learning convergence for each word meaning, and relates to the developmental level of the nervous system, the experience of each word's learn-ing, and other factors. We posit that immaturity prevents effects of inductive learning and AMS and causes no bias at the beginning of word learning.. The format of this paper is as follows. In section 2, we summarize findings about word learning biases and present behavior our simulation should reproduce. And we introduce previous LBA studies and clarify distinction between their hypotheses and ours. In section 3, we explain AMS and discuss the learning process with it, and in sections 4 and 5 we explain the design of simulations and discuss their results. In section 6, we give a general discussion and conclude this study in section 7. In this paper, we presented an integrated explanation of ad-hoc meaning substitution (AMS) for behaviors that had been described separately as shape and material biases and verified it by computer simulation. AMS is a hypothesis among learned bias account (LBA) and argues that children simply use the meaning of known words and given instances as ad-hoc templates of novel noun meanings. It is a simpler hypothesis than previous studies. However, it could replicate phenomena concerning shape and material biases and explain the process clearly. Besides, to describe AMS's processing, we introduced word distributional prototype (WDP) as the explicit represen-tation of word meaning with an inductive learning function. Few studies have explicitly represented word meaning. But we consider such representation is valid methodology for illustrating the computational mechanism of word learning bias, which itself is deeply committed to word meaning.. Simulation 1 revealed that when learners who possess WDP and AMS were exposed to early biased vocabulary, they showed shape and material biases as well as overgeneralized shape bias. This result suggested that the triad of word meaning induction, ad-hoc instantaneous estimation of meaning, and early biased vocabulary is essential for the emergence of biases. Simulation 2 revealed that when maturity was introduced, learners showed neither shape nor material bias during an early small vocabulary. This result indicated that the period of bias emergence is decided not by the triad but by maturity.. Though we have verified AMS from the perspective of reproductivity, illustrativity, and cognitive adequacy, there is no conclusive evidence that AMS causes shape and material biases. To prove AMS, we have to investigate prediction and its confirmation (2.3c). Additionally, it's also unlikely that only AMS realizes novel noun generalization throughout life because there are some functions which HOA and other models seem to be able to explain. We consider that AMS works as one mechanism of producing the biases and plays a central role, especially in their emerging stage. Future work includes investigations into how AMS cooperates with other cognitive functions (Fig. 12) and how AMS joins other word learning biases. Finally, computational modeling is one promising method for the illustration of a more concrete hypothesis of human internal processing such as word learning. We expect more advanced studies with this method and hope to integrate abundant findings from various fields including psychology, physiology, and others. The solid set results (Fig. 5 ) show that our model reproduced stable shape bias during a somewhat larger vocabulary (2.2.1b). We discuss the adequacy of the prediction in section 3.5 here and the appearance of shape bias during a small vocabulary in the next section.. The monotonic decrease of solidity distance along vocabulary development (Fig. 6, upper left) suggested that both the SOLID and NONSOLID fields were becoming dense and that the SOLID field was consistently the densest from the small vocabulary group to the largest one. Correspondingly, the solidity selection ratio of SOLID was consistently the highest (Fig. 7, upper left) because the WDPs in the SOLID field were more likely to be nearest to the target stimuli in solid set by NNH, and the SOLID field was dense enough to support selection in the field. The results of feature distance to solid set (Fig. 6 , upper right) can be explained by the above process and the structural ratio in Table 2 . Since the WDPs in the SOLID field were dominated by SHAPE-BASED ones (Table 2) , SHAPE-BASED WDPs were consistently nearest the solid set (Fig. 7, upper right) . To sum up, we found that all these mechanisms caused shape bias (2.2.1b) and supported the explanation in section 3.5.. Meanwhile, the results of the nonsolid set (Fig. 5 ) showed that our model could reproduce the overgeneralized shape bias during a small vocabulary (2.2.2b) and material bias during a large vocabulary (2.2.2a). We discuss the adequacy of our prediction in section 3.5 here and the consistent emergence of overgeneralized shape bias during a small vocabulary in the next section.. All solidity distances for nonsolid sets monotonically decreased (Fig. 6 lower left) , identical to the solid set, which indirectly suggests the sparseness disappearance in all SOLIDITY fields. The NONSOLID field was drastically becoming dense compared to its initial sparseness, and thus the order of the solidity distance of SOLID and NONSOLID changed with vocabulary development. In turn, although one advantage was that NONSOLID WDPs were more likely to be the nearest ones for the inputs of the nonsolid set, learners couldn't exploit the advantage during a small vocabulary: They managed to choose the nearest WDPs from the SOLID field (Fig. 7 , lower left, group 1-3). But increases of vocabulary and density in the NONSOLID field allowed them to take advantage: They came to choose the nearest WDPs from the NONSOLID field (Fig. 7 , lower left, groups 4-6).. The results of feature distance (Fig. 6 , lower right) were explained by the above reasons and the structural ratio in Table 2 . During a small vocabulary, since SOLID WDPs were chosen as the nearest ones by NNH and most SOLID WDPs were simultaneously SHAPE-BASED (Table 2) , SHAPE-BASED WDP was likely to became the nearest for the input of the nonsolid set (Fig. 7 , lower right). They resulted in the overgeneralized shape bias (2.2.2b). But just the opposite situation occurred after a somewhat large vocabulary. The WDPs in the NONSOLID field were chosen by NNH, and most were MATERIAL-BASED (Table 2) . Then the MATERIAL-BASED WDPs became the nearest (Fig. 7, lower right) and caused material bias (2.2.2c). To sum up, the results of the nonsolid set supported the explanation in section 3.5.. Finally, we conclude the results of simulation 1 as follows. Depending on just statistical bias in early vocabulary, AMS could explain not only the shape bias from the early period (2.2.1b) and the material bias after becoming a somewhat larger vocabulary (2.2.2c), but also the overgeneralized shape bias during small vocabulary (2.2.2b), which has not been reproduced in-tegratedly by previous model studies. However, unexplained phenomena remain: no shape bias (2.2.1a), and no material bias during a small vocabulary (2.2.2a). The inevitable overgeneralized shape bias during a small vocabulary was also contrary to the previous findings, which haven't show such a robust overgeneralized shape bias (2.2.2b). To explain these points, we introduce the notion of maturity in the next section.. First, we discuss the results of the solid set. The transition of shape choice (Fig. 9) showed no shape bias to the solid set during a small vocabulary in group 2 (2.2.1a) and stable shape bias to the solid set in subsequent groups (2.2.1b). The appearance of material bias in group 1 was inconsistent with the prediction in section 3.5, but it can be explained. In the very early group, the learning of WDPs was insufficient because of the small number of instances for each word, so it remained almost a hyperspherical WDP with wide variances. Then, calculating the likelihood of WDPs for novel noun input by Eq. (1), we didn't get large differences between the outputs of individual WDPs. This mechanism caused the problem of significant bias in group 1 (Fig. 9) . Since shape choices by such learners became almost random, p L (g, i) for all learners became around 0.5 and their deviation became very small. It resulted in statistically significant shape/material bias even though just slightly larger/smaller than chance. In other words, it was caused by setting maturity the same among learners within each group and making the extent of learning convergence identically. But in the actual development of infants, it isn't likely that all children in the same vocabulary group simultaneously show the same developmental levels. So the problem can be resolved by modifying the current simplification of uniform maturity. These results fulfilled the prediction for solid stimuli (2.2.1). Now, we discuss the consistency of the results with the computational process predicted in section 3.6. For the solidity and feature distances (Fig. 10) , those distances in very early groups were smaller than later groups because the WDPs in the very early groups were closer to hyperspheres, and novel WDPs formed in the generalizing phase copied the variance matrixes of hyperspherical WDPs. Such WDPs specificially output comparatively high likelihood values to every input. However, the performance is the consequence of their incomprehension of each word meaning and subsequent low ability to distinguish different words. This situation corresponds to children's overextension of words ("This is doggie, that is doggie too, ..."). Meanwhile, welllearned WDP output high likelihood for inputs likely to co-occur with the word corresponding to the WDP and low likelihood for inputs that aren't likely to do so. The target stimuli presented in the novel noun generalization task were unknown to learners. They output comparatively higher likelihood if they had a lot of unlearned WDPs and very low likelihood contrary if they had a lot of well-learned WDPs. Hence, though later groups superficially seemed to show worse performances than early groups with regard to solidity/feature distance (Fig. 10) , it was the consequence of their sophisticated knowledge clearly differentiating doggie from cat and so on.. As with simulation 1, the SOLID and NON-SOLID fields became dense with vocabulary development. The order among solidity and feature distances respectively decided the solidity and feature selection ratios, which subsequently affected the tendency of novel noun generalization. Hence the most important feature here was not the absolute value of those distances but the relative order among the solidity/feature distance in each group. In solid and feature distances, SOLID and SHAPE were nearest to the inputs except in the first two groups (Fig. 10, upper row) . Therefore, we found that all solidity and feature distances were equally small in the early groups because of their insufficiently learned hyperspherical WDPs; all distances became larger in the later groups because of their more learned and specialized WDPs for corresponding words, as predicted in section 3.6. Besides, the consistent orders in which SOLID and SHAPE were respectively the nearest were identical to simulation 1.. These discussions also affected the solidity and feature selection ratios (Fig. 11, upper row) . As presented in Fig. 10 , all the solidity and feature distances in the first two groups were almost the same to each other due to the influence of maturity. Hence, for the solidity and feature selection ratios, the rate with which each type of WDP was chosen as the nearest was almost random. In such cases, both solidity and feature selection ratios were determined depending on the structural ratio in the early vocabulary shown in the upper row of Table 2 . Along with increasing vocabulary and converging learning for each word, the WDP with the same SOLIDITY as the target stimulus output higher likelihood values. Thus WDPs in the SOLID field were chosen more often as the nearest ones for novel SOLID target stimulus (Fig. 11, upper left) . Following the choice, the feature selection ratio was automatically decided depending on the rate of the SOLID case in Table 2 (Fig. 11, upper right) . These results illustrated the following process. WDPs in the SOLID field tend to be chosen as the nearest ones; they are likely to be SHAPE-BASED, resulting in shape bias; such a tendency increases with the development of vocabulary and maturity. Therefore, we confirmed that our model behaved as predicted in section 3.6 and explained the emergence mechanism of word learning biases for the solid set.. Next, we discuss the nonsolid set results. In groups 1 and 2, the existence of material bias was suggested from the results of shape choice probability (Fig. 9 ). They were inconsistent with the prediction in section 3.6, but they could be explained by the same reason as the material bias of group 1 in the solid set: Almost the same likelihood output by insufficiently learned WDPs. Though our model couldn't so clearly show no material bias to the nonsolid set during a small vocabulary (2.2.1a), at least it inhibited the inevitable emergence of overgeneralized shape bias during a small vocabulary in simulation 1. And though the experimental evidence in subsequent groups was mixed (2.2.2a) (2.2.2c), there is no doubt that material bias finally settles in older children (Soja et al., 1991; Bloom, 2000) , as was also demonstrated in our model. The results of our model for the nonsolid set were almost consistent with previous evidence. Now we discuss whether our results arose from the same process as in section 3.6. As with the solid set, something important for NNH-based choice is the order among solidity and feature distances. We must consider the order in each group to explain the change of material bias with vocabulary development. In the early stage of groups 1 and 2, all solid and feature distances were almost equal (Fig. 10, lower row) . Contrary, in the last groups 5 and 6, the solidity distance of NON-SOLID became the nearest, but the NONSOLID field remained sparser compared to the SOLID field (Fig. 10, left) . Hence the feature distance of MATERIAL in the nonsolid set wasn't nearer than others compared with SHAPE in the solid set (Fig. 10, right) . To make material bias in the nonsolid set emerge as dominant as shape bias in the solid set, NONSOLID field must become much denser, that is, much larger NONSOLID vocabulary. In middle groups 3 and 4, the orders of SOLID and NONSOLID among solidity distance changed. But middle stage results should be unstable because they were composed of a subtle power relationship between maturity whose insufficiency led to no bias, the attracting force from WDPs in the SOLID field that produced shape bias, and from WDPs in the NONSOLID field that produced material bias. We confirmed by additional experiments that the results were unstable and changeable depending on such conditions as network parameters. Such changeable behavior might explain the mixed evidence of no material bias (2.2.2a) and stable material bias (2.2.2c) in previous behavioral studies.. This process also dealt with the solidity and feature selection ratios (Fig. 11, lower row) . In the first three groups, both selections were done depending on the structural ratio in the early vocabulary in the upper row in Table 2 , as with the solid set. Then with vocabulary development, the WDPs in the NONSOLID field output higher likelihood and were chosen more as the nearest ones for the novel NONSOLID target stimulus (Fig. 11, lower left) . But the solidity selection ratio of NONSOLID for the nonsolid set was much less than SOLID for the solid set, even in group 6, because the NONSOLID field resolved sparseness later than the SOLID field and thus temporarily remained affected by WDPs in the SOLID field.. In that case, feature selection was done depending on the NONSOLID rate in Table 2 ( Fig. 11 , lower right), but was affected by SOLID. These results demonstrated the following trajectory. Affected by the WDPs in the SOLID field, WDPs in the NONSOLID field are becoming more likely to be chosen as the nearest ones; they are likely to be MATERIAL-BASED ones, which cause material bias; such a tendency increases with the development of vocabulary and maturity. Therefore, we also confirmed that our model could explain the emergence mechanism of word learning biases for the nonsolid set.

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Visual analytics in cheminformatics: user-supervised descriptor selection for QSAR methods AbstractThe design of QSAR/QSPR models is a challenging problem, where the selection of the most relevant descriptors constitutes a key step of the process. Several feature selection methods that address this step are concentrated on statistical associations among descriptors and target properties, whereas the chemical knowledge is left out of the analysis. For this reason, the interpretability and generality of the QSAR/QSPR models obtained by these feature selection methods are drastically affected. Therefore, an approach for integrating domain expert's knowledge in the selection process is needed for increase the confidence in the final set of descriptors.In this paper a software tool, which we named Visual and Interactive DEscriptor ANalysis (VIDEAN), that combines statistical methods with interactive visualizations for choosing a set of descriptors for predicting a target property is proposed. Domain expertise can be added to the feature selection process by means of an interactive visual exploration of data, and aided by statistical tools and metrics based on information theory. Coordinated visual representations are presented for capturing different relationships and interactions among descriptors, target properties and candidate subsets of descriptors. The competencies of the proposed software were assessed through different scenarios. These scenarios reveal how an expert can use this tool to choose one subset of descriptors from a group of candidate subsets or how to modify existing descriptor subsets and even incorporate new descriptors according to his or her own knowledge of the target property.The reported experiences showed the suitability of our software for selecting sets of descriptors with low cardinality, high interpretability, low redundancy and high statistical performance in a visual exploratory way. Therefore, it is possible to conclude that the resulting tool allows the integration of a chemist's expertise in the descriptor selection process with a low cognitive effort in contrast with the alternative of using an ad-hoc manual analysis of the selected descriptors. The selection of a subset of molecular descriptors during the design of a QSAR/QSPR model is a hard task, where several simultaneous goals must be satisfied [1, 35] . Many feature selection methods used for dealing with this problem are focused on statistical relationships among the descriptors and target properties, leaving aspects associated with the chemical knowledge out of the picture. Therefore, the interpretability and generality of the models obtained by these methods are drastically affected. For this reason, a strategy that incorporated expert knowledge in the selection process is required in order to improve the user confidence in the final set of descriptors.. In this paper we address this challenge by proposing a software tool that conjoins statistical methods with interactive visualizations. The main idea is to exploit the expertise of chemists by an interactive visual exploration of different pieces of data generated from statistical and information theory based metrics. Several coordinated visual representations were designed with the aim of capturing different aspects and relationships among descriptors and target properties. Some key insights that can be gained aided by the interactive visualizations are: redundant descriptors, descriptors that provide discriminative information, relevant descriptors by consensus among alternative models, and descriptors whose knowledge helps reduce the uncertainty about the value of the target property.. The capabilities of the proposed tool were assessed through two different scenarios. The first case study corresponds to the prediction of log P liver . In this experiment the tool was used to choose one subset of descriptors from a group of alternative subsets generated automatically by one or more descriptor selection methods. The second study corresponds to the prediction of a relevant mechanical property useful in the design of polymers. In this case, we illustrate the case where the analyst wants to make an intervention in the automatic selection of descriptors in order to incorporate an experimental descriptor to the model. Thus, we showed how the expert can use our tool to analyze information coming from existing descriptor subsets and even incorporate new descriptors according to her own knowledge of the target property.. The results in both cases showed the suitability and convenience of this methodology for selecting sets of descriptors with desirable characteristics (low cardinality, high interpretability, low redundancy and high statistical performance) in an exploratory and versatile way, and with a lower "cognitive effort" in comparison with the alternative of using an ad-hoc manual analysis of the selected descriptors.. Besides the aforementioned advantages of incorporating the analyst in the loop, it is also important to establish the limitations and scope of this software. Here we focus on the descriptor selection stage. In order to address the more general problem of activity/property prediction, we would need to include aspects such as studying the compounds individually or in families, as well as the incorporation of visualizations related to the applicability domain of the QSAR models or the analysis of its outliers.. Finally, this analysis can be repeated by using different prediction methods, which could lead to different results. Yet the focus of this use case is not in the prediction or validation of the results themselves but on a rationale set of steps to find good candidate descriptors. These descriptors should then be evaluated in an unbiased manner and preferably using an external dataset [10] . The second column shows the predictive accuracy of the "best" model after applying 4-fold cross validation on three different methods (linear regression, decision trees, and neural networks). In this case, the best predictive accuracy for the three models was obtained by using a decision tree (M5P) and evaluating using 4-fold cross validation. The parameter setup and predictive accuracy for all methods is available in the Additional file 1: Table S3 . Quantitative structure-activity/structure-property relationship (QSAR/QSPR) models are regression or classification models widely used in cheminformatics, where a biological activity or a chemical property of chemical compounds are modeled in terms of their molecular descriptors. The design of QSAR/QSPR models requires dealing with several problems. One of them is the selection of the most relevant set of molecular descriptors for the property or activity that is intended to be modeled. Chemical structures are usually encoded by a variety of descriptor families such as functional groups, topological, constitutional, thermodynamic, quantum mechanical, etc. Several of them may contribute similar information or may be irrelevant for the biological activity under study, and thus, affecting the discovery of Open Access *Correspondence: ip@cs.uns.edu.arthe descriptor-activity relationship. For this reason, the selection of the most relevant descriptors is regarded as one of the most difficult and crucial tasks for QSAR/ QSPR modeling [1, 2] .. There are several families of methods for addressing the descriptor selection problem, but most of them can be classified into two main categories: classic methods, such as those using multiple linear regression [3] or VSMP [4] , and those using artificial intelligence-based techniques, such as the ones inspired on genetic algorithms, artificial neural networks or fuzzy logic methods [5] [6] [7] . In particular, the artificial intelligence-based methods are better suited to discover strong nonlinearities between the set of descriptors and a given biological activity (or property) and can overcome some limitations of classic descriptor selection methods [8] .. Despite the numerous statistical approaches for feature or descriptor selection, real users that want to extract the most informative descriptors to understand or predict a property/activity still face an important challenge. The main reason is because none of these methods can be claimed as the best approach for any possible combination of dataset and prediction method. Therefore, in a real setting, especially when unseen data is likely to be presented in a future, users do not have a certain way of knowing what descriptor selection method would work best.. Another common criticism that descriptor selection methods receive is that most of these approaches are deemed as "black-boxes" by chemists. This is due to the fact that in order to fine-tune the results or introduce domain knowledge in the selection criteria it is necessary to know the inner workings of the method [9] or, in the best case, to encode this knowledge in the form of some prior probabilities. While some works have overcome this limitation by ad-hoc analyses [10, 11] , we claim that there is a need for better support in the descriptor selection task, so that these methods can be embraced by the cheminformatics community.. There are two research questions that we aim at answering in this paper. The first one is whether we can leverage outcomes from different descriptor selection approaches to arrive at a more thorough decision on the subset of descriptors to be selected. While there exist several methods based on ensembles and voting schemes [12, 13] these approaches leave the chemical knowledge out of the selection process. The second research question is how we can involve the domain expert (e.g. a chemist), so that he or she can incorporate his or her knowledge and expertise during the feature selection process in a semi-automated manner.. In this paper we propose to deal with these two challenges by means of the proposal of a tool that combines statistical methods with interactive visualizations. This type of approaches falls under the emerging area of visual analytics [14] . The main idea behind visual analytics approaches is to merge the computational capacity of statistical and machine learning methods with the human natural ability of identifying patterns in visualizations. By allowing some form of interaction in the visualizations, domain experts can explore the data and provide feedback to the tool, and/or use the tool to arrive at more informative decisions. Visual analytics have been applied to different bioinformatics problems [15] [16] [17] , while its application on cheminformatics has not been considered until recently. In the area of cheminformatics some approaches have been presented, such as CheS-Mapper [18] , ChemMine [19] or MQN-Mapplet [20] , which aim at interactively exploring chemical datasets by means of clustering and dimensionality reduction methods. QSARINS [21] is a comprehensive tool for multiple linear regression QSAR models that aggregates different statistical methods with a special focus on the model validation. INFUSE [22] is a recent visual analytics tool designed to help the analyst understand the predictive power of features in predictive modeling. One limitation of this approach is that the visual analysis is done on a per-feature basis. In contrast to the previous methods, in this tool we propose an approach that focuses on the challenging task of analyzing and selecting subsets of descriptors for QSAR/QSPR. This is done by means of explorative and visual analytics techniques, where the tool facilitates the comparison of multiple descriptors and descriptor subsets coming from the output of different descriptor selection methods. As it was mentioned previously, when a physical chemistry expert develops a QSAR/QSPR predictive model, the choice of the most appropriate descriptors for this model constitutes the first complex challenge. Once the molecular descriptors have been computed for the dataset, different combinations of them should be analyzed in order to obtain a good quality model. In this context, the QSAR/QSPR model must satisfy two quality standards: high prediction accuracy, preferably evaluated with an external dataset, and good interpretability, evaluated from a physicochemical point of view. Considering the high number of molecular descriptors that are usually computed for a dataset, which could be in the range of thousands, a common practice consists of exploring different feature selection methods in order to obtain different smaller subsets of relevant descriptors [1, 5] .. In a next step, these subsets should be systematically compared to find the best combination of descriptors. This process encompasses several aspects, such as analyzing descriptor co-occurrence in the different candidate models, avoiding redundant descriptor sets, and analyzing descriptor-target relationships. This analysis has been traditionally carried out by the expert combining her expertise with the design of plots and tables in an ad-hoc manner [10, 11] .. This task can be tedious and time inefficient, because the relationships among the different pieces of information does not emerge in a straightforward way. At this point, it becomes valuable the contribution that visual analytics techniques can incorporate to this process. The main idea behind these strategies is to summarize and integrate data in a graphical and interactive way, facilitating the finding of key information for supporting domain expert decision making [14] .. At this stage an interactive visual analytics tool, which we will refer to as Visual and Interactive DEscriptor ANalysis (VIDEAN), is proposed for comparing alternative descriptor subsets. These descriptor subsets are obtained from different descriptor selection methods as candidates for the QSAR/QSPR model. The main idea is to use this tool as a decision support system. Undoubtedly, the analyst's task is complex since multiple aspects are involved in the modeling decisions. Therefore, different data exploration strategies are required in order to integrate these multiple pieces of information.. In this tool, we propose to visualize different aspects related to the information required for modeling, uncovering hidden connections among the descriptors and their relationships with the target property. In this way, the specific objectives that guided the design of these visualizations can be defined as follows:. 1. The avoidance of redundant descriptors in QSAR/ QSPR models. This means that if two or more descriptors are conveying similar information, the tool should help choose the most meaningful or suitable descriptors for the model, and thus keeping the descriptor subset small. 2. The complementarities among the selected descriptors and the target property. This means that each descriptor of the model should be relevant for prediction. In other words, if one descriptor were removed, the prediction accuracy of the model should worsen.

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


Embedding a pair of graphs in a surface, and the width of 4-dimensional prismatoids A prismatoid is a polytope with all its vertices contained in two parallel facets, called its bases. Its width is the number of steps needed to go from one base to the other in the dual graph. The first author recently showed that the existence of counter-examples to the Hirsch conjecture is equivalent to that of d-prismatoids of width larger than d, and constructed such prismatoids in dimension five. Here we show that the same is impossible in dimension four. This is proved by looking at the pair of graph embeddings on a 2-sphere that arise from the normal fans of the two bases of Q.The first author recently constructed counter-examples to the Hirsch conjecture [2] via the combination of the following two results:• If a d-dimensional prismatoid Q has width larger than d then it is possible to construct from it a polytope P that violates the Hirsch conjecture.• There exist 5-prismatoids of width larger than 5.Here, a prismatoid is a polytope that has all its vertices lying in two parallel facets Q + and Q − (called its bases), and its width is the dual graph distance between those two facets. That is, the width of Q is the minimum number of steps needed to go from Q + to Q − , where a step consists in moving from a facet of Q to an adjacent facet.The dimension of the non-Hirsch polytope P in the construction is much higher than that of Q (it equals | vertices(Q)| − | dim(Q)|) but still the question arose whether the dimension d = 5 for Q is the smallest possible. An easy argument shows d = 3 cannot work, and d = 4 was left open in [2] . In this paper we answer this question in the negative: *

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Creating scalable location-based games: lessons from Geocaching Abstract Location-based games seek to move computer gaming out from behind the PC and into the ''real world'' of cities, streets, parks, and other locations. This real-world physicality makes the experience fun for game players, yet it brings the unique challenge of creating and orchestrating such a game. That is, location-based games are often difficult to create, grow, and maintain over long periods of time. Our research investigates how location-based games can be designed to overcome this challenge of scalability. We studied the well-established location-based game of Geocaching through active participation and an online survey to better understand how it has succeeded in maintaining user involvement and growth over the last decade. Findings show that Geocaching benefits by having players directly create game content, including both lightweight and elaborate creations. Geocaching has also made it simple for players to perform game orchestration by monitoring game content, other players, and even nonplayers. We then characterize location-based games according to various attributes and suggest how the lessons learned from Geocaching could be applied more generally to the design of other location-based games and in which cases they should not be applied. Location-based games are played in everyday places, where game information is tied to these locations [20] . Over the last decade, researchers, artists, and companies have created and studied a variety of location-based games to investigate cultural, societal, technological, and community issues. For example, in the game Uncle Roy All Around You (Uncle Roy), players are directed through the streets of an urban center based on ambiguous clues given to them on a PDA by a stranger [7] . The goal is to find the mysterious character known as Uncle Roy. In this case, the game explores the culture of trust, as players must decide whether or not to trust directions given by people who are completely unknown to them.. One challenge that exists with many location-based games is the creation and orchestration of game content and activities [9] . By creation, we mean the construction and placement of game content. By orchestration, we are referring to the monitoring of players' activities in the game, and the quality and continued availability of game content, to ensure that play proceeds smoothly for players. For example, in Uncle Roy All Around You [7] , creation includes planning the scripts and routes that game administrators will use to lead players. Orchestration involves actively monitoring players to ensure they stay out of harm's way and continue to participate in the game. Here, the orchestration needs are highly dynamic [9] . In contrast to a typical board game, orchestration is far more complex: the physical constraints of the game appear unbounded to the player, as do the rules (i.e., who to interact with).. In general, game creation and orchestration in locationbased games are crucial to a game's success. If it is done poorly, players may not enjoy the game or may be at risk; perhaps, even worse, non-players who do not realize they are part of a game as bystanders may be at risk [9] . For example, in Uncle Roy, if orchestration was done poorly, players could accidentally trespass into incorrect buildings, which may cause unnecessary and potentially dangerous altercations with non-players. Similarly, Geocaching has gained notoriety among police officials as poorly placed geocaches have resulted in bomb scares (search online for ''geocache bomb scare''). In this case, the risk is more of a perception than a real one, but, nonetheless, the construction and placement of content can have dramatic effects. Pragmatically, challenges with creation and orchestration also mean that location-based games are often ''one offs'' and only available in a single location or conducted over a short period of time, never to be run again. As a result, participation is limited or game players cannot continue to play like they might computer or online games.. Our interest is in understanding how location-based games can be designed to be scalable. By scalable, we are referring to a game's ability to be: (1) played and orchestrated over long periods of time in a variety of locations and (2) played by a large number of players (e.g., hundreds or thousands of people). In some cases, location-based games are meant to be performance art and, as such, this type of scalability may not necessarily be desired. Instead, the game may have other goals such as providing different cultural perspectives. However, in other situations, it may be advantageous to be able to have a game that can be played in various locations over a long period of time. To understand this, we turn to what is arguably the most successful location-based game to date based on its longevity, user participation, and global presence: Geocaching. The game of Geocaching has been in existence since the year 2000 and currently has over four million players worldwide [12] . In simplest terms, Geocaching is a GPSenabled treasure hunt. Players known as geocachers, or cachers for short, hide physical containers with a paper logbook and record the GPS coordinates of the container's location on the Geocaching Web site. Other geocachers then use this information to find the containers.. We first studied Geocaching with a combination of in-depth participation over a 1-year period and an online survey of 185 geocachers [22] . Our findings highlighted the ways that geocachers actively create location-based experiences for other geocachers. We also showed how maintenance of the activity is also mostly left in the hands of the players. Our results from this are presented in [22] . Yet 2 years later, we recognized that our earlier work was limited in that it was more descriptive in nature than prescriptive. This made it difficult to understand in what context the lessons from Geocaching should or could be applied. The work was also tied more directly to locationbased experiences in general, as opposed to location-based games, our current focus of research. This made it difficult to understand its direct applicability to location-based game design. As such, we have extended our study of Geocaching to include an additional year of active participation, which comes with a needed reflection on the results of our earlier work. The current article explores the findings from our earlier Geocaching studies by situating them within the context of location-based games. Here, we present a series of seven lessons that describe how players of Geocaching create both lightweight and elaborate content for others to find; evolve the customs of the game over time to create new gaming experiences; and report on and monitor game elements, other players, and even nonplayers as a part of game orchestration. Then, through critical reflection, we suggest how game designers and researchers might apply these lessons from Geocaching to other types of location-based games.. Our article first describes related work on designing scalable location-based games. Second, we outline our study methodology including 2 years of active participation and observations of Geocaching along with an online survey. Third, we describe our findings on game creation and orchestration. Fourth, in our discussion section, we categorize existing location-based games and, through this, suggest how lessons from Geocaching could be applied more broadly to location-based game design. Our studies of Geocaching have revealed the ways in which game players (geocachers) actively create game content, monitor and maintain the game elements created by other players, and monitor the players and non-players themselves. We have presented this as a series of lessons that should be thought about when designing or researching location-based games. We recognize that not all games are of the same genre, scope, and structure as Geocaching. Some are much more complex in nature and could even be considered performance art pieces with complex narrative interwoven among game play (e.g., Uncle Roy All Around You [7] ). Yet there are also location-based games that are similar to Geocaching in terms of their ability to be played at any point in time, their varied locations, and the ease at which content can be created by players themselves (e.g., [4, 5] ). In these situations and more, it can be valuable to reflect on the lessons found in Geocaching to understand how a location-based game can be designed to be scalable. Our analysis provides a first step in this direction. The goal of our discussion section is to provide researchers and designers of location-based games with a better sense of how they might utilize the lessons from Geocaching, if at all, in their own game designs. Certainly, it is the case that not all types of location-based games lend themselves to be created and orchestrated in a manner similar to Geocaching. However, some can, and our discussion unravels this. We also recognize that our findings are qualitative and there are no clear causal relations between our lessons and the actual scalability of Geocaching. That is, there could certainly be other reasons beyond the lessons we provide that are the reason why Geocaching can be (1) played and orchestrated over long periods of time in a variety of locations and (2) played by a large number of players (e.g., hundreds or thousands of people). The lessons, when applied to other location-based games, could also yield little to no effects. Regardless of these issues, the lessons from Geocaching point to practices that are at the core of the game and one can speculate with reasonable certainly that they are one large piece behind Geocaching's growth over the last decade. There exists a plethora of books that describe how to design computer games (e.g., [1, 28, 29] ). Typical topics include structuring games for target audiences, structuring play, storytelling, narrative, and game genres [1, 28, 29] . One could certainly pull such concepts together to understand how to design a game such that it is both scalable to large volumes of players. Yet none of these topics are explored in the context of games that move away from the traditional desktop computer, and they certainly do not broach the genre of location-based games. Thus, applying the concepts to location-based game design is questionable. McGonigal explores the design of ''augmented-reality games,'' of which she includes location-based games, and argues that they should scale to large volumes of players [21] . However, rather than illustrate mechanisms to do so, her focus is instead on illustrating why large-scale games are important and how they might be able to solve realworld social problems (e.g., famine, war) [21] .. Recently, we have seen the popularity of casual games rise dramatically among smartphone (e.g., Apple iPhone, Android, Windows phone) and social media users (e.g., Facebook enthusiasts). Casual games are those that can be easily understood and played in short time increments throughout the day (e.g., Facebook games). Some are even location-based. For example, in Foursquare, players ''check-in'' into locations, score points, and can compete with their friends [18] . Such casual games have shown they can successfully scale to large numbers of players. However, the richness of the experiences they offer appears to be less than other non-casual location-based games (e.g., Uncle Roy All Around You, Geocaching). For example, studies of Foursquare have shown that while some players are motivated to use Foursquare because of its game-like properties, game play is not entirely compelling and some simply play in order to have ''something to do'' when bored [18] . Game elements (e.g., badges) also become less of a motivation for playing over time [18] .. There are also academic papers that have specifically looked at the problem of designing scalable location-based games. First, Barkhuus et al. [2] designed a game called Treasure so that it could be played multiple times in order to understand the effects of repeated game play on players' strategies and tactics. Here, their strategy was to use both GPS and Wifi within the game in order to determine a players' location. They suggest that to scale such games to even larger number of players, game designers should incorporate the use of mobile ad-hoc networks in addition to GPS and Wifi positioning systems. Second, after analyzing several location-based games [6] [7] [8] , Capra et al. [9] suggest games can scale to large numbers of users through ''campaign strategies'' where players upload multimedia from their own personal devices in conjunction with events organized by local organizations. Here, we see the beginning of the idea that players may directly contribute to game content. Third, Stanley et al. [31] suggest a similar player-focused strategy of game content creation. In their game, PiNiZoRo, parents can create walking routes for the game that their children must follow when playing [31] .. We also see other suggestions for creating scalable location-based games that emerge from studies of Geocaching. These are more directly related to our own research. First, forestry studies have described the environmental effects of Geocaching on forests and parks where players need to be concerned that they are not causing environmental destruction when they play [10] . This suggests that scalable location-based games should be designed cautiously to understand what effects a large volume of players might have on play areas. Second, studies have described the key motivations that people have for participating in Geocaching [11, 23] . These include giving purpose to walks and/or exercise, personal achievement, and exploring new and unfamiliar places, thereby reconnecting one to their own community or providing them with opportunities to understand new communities [11, 23] . This diversity suggests that scalable location-based games should allow players to choose their own personal goals as part of gameplay; this is similar to findings about users' motivations for using Foursquare [18] . Third, we also know that trust becomes an issue when games scale and must be taken into account. Kelley's [15] extensive autobiographical accounts of Geocaching describe how players must trust that an item is in fact placed at a certain location, albeit by a stranger, and travel to unknown locations to search. Kelley [15] labels this as thin trust; that is, trust between anonymous people rather than close friends or family [25] .. Despite the variety of suggestions offered by the related work, we see little in terms of understanding how player participation in game creation and orchestration can play a role in creating a scalable location-based game. O'Hara [23] and Salovaara et al. [30] highlight this as an important aspect of Geocaching, but do not elaborate on the mechanisms that enable player creation to occur. In the next sections, we build on this related research to explore Geocaching in order to articulate the variety of ways it encourages scalability through content creation and orchestration by players themselves.

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


Filtering in a Unit Quaternion Space for Model-Based Object Tracking The main idea in object tracking is to support the processing of incoming images by predicting future object's poses and features using the knowledge about the object's previous motion. In this paper we present a new method for the prediction and adjustment of motion parameters to the current measurements using the quaternion representation for the orientation and the Gauss-Newton iteration on the unit sphere S 3 . Unlike other trackers, our tracker searches for estimates directly in the space of rigid body motions (represented by R 3 × S 3 ) and takes into account the differential and geometric properties of this space. We present some results showing the successful tracking in synthetic and real image sequences. Object tracking in long image sequences is an important issue in many robotic applications and has been studied extensively in the past. Most of the proposed approaches consist of the initialisation and the tracking phase. In the initialisation phase, the object of interest must be found and its initial motion parameters must be determined. In this paper we deal only with the tracking phase, in which the information about the object's previous motion is used to calculate the next set of motion parameters. This is usually divided into four steps: prediction, projection, measurement and adjustment. Tracking systems usually use a variant of Kalman filtering to govern this process [3, 6, 10, 11, 13] .. The kinematics of any point P belonging to a rigid body is completely characterised by v(t), the velocity of the point of the body coinciding with the origin O of the body-fixed coordinate system, and ω(t), the angular velocity of the point P around the origin of the reference coordinate system v P (t) = v(t) + ω(t) × −−→ OP .. A closed form solution for this general motion is not known. A common approach in tracking is to assume that the acceleration of the origin of the body coordinate system and the angular acceleration are both random with expected value zero and with constant power spectra a and α, respectively, E(v) = 0, E(vv T ) = aI, E(ω) = 0, E(ωω. where I denotes the identity matrix. In this paper we show how to implement the prediction and the adjustment phase based on the above motion model.. The velocity of the origin of the body coordinate system v should not be mixed up with the spatial velocity of a rigid body v s , which is often used in kinematics and describes the velocity of a (possibly imaginary) point of the body coinciding with the origin of the reference coordinate system. They are related by v s = −ω × − → O + v. We prefer to use the velocity of the origin of the body coordinate system to parameterise the rigid body motion because the mapping describing the position of a rigid body undergoing motion with constant spatial velocity is nonlinear -it is given by screw actions of a constant twist multiplied by the time parameter [8, 13] .

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