Representing design tradeoffs in safety-critical systems Different fault-tolerance strategies have been shown to be effective at achieving fail-safe behavior in a number of safetycritical application domains with different dependability, service, and cost requirements. A technique for comparing the domain profiles and their fault-tolerance strategies could assist architects of new safety-critical systems in choosing an appropriate fault-tolerance strategy. We suggest an approach using Kiviat graphs to visually represent the dependability, service, and cost profile of a system, and show how such a graph can be used to analyze automotive x-by-wire applications. Safety-critical systems increasingly rely upon computerized controls to provide advanced services and safety features that are impracticable to realize in hardware alone. Meeting the safety and service requirements of these softwareintensive systems is challenging, not only because they are often more complex than their electromechanical predecessors, but also because their dependability and safety requirements are often greater [4] .. Safe software-based system design has been successful in some application domains where safety engineering for electromechanical systems has previously been well established.. Both the rail and commercial aviation industries use standard fault-tolerance techniques to minimize critical system failure rates to meet industry-determined standards. The techniques they choose, however, may vary according to the safety, service, and cost requirements of the particular system being designed. In railroads, signaling and switching systems that regulate traffic often use dual two-of-two redundancy because they have very high service availability demands over a long mission time. In commercial aircraft flight control systems, reliability and availability are also very high, but with a much shorter mission time. Therefore, the fault-tolerance level necessary to meet the safety and service requirements of a flight control system can often be achieved through triple-modular redundancy.. As other safety-critical application domains transition to greater reliance on software, a natural reaction of system designers might be to simply apply the same safety-critical strategies used in these well-established systems. If faulttolerance strategy X works for application A, why not use it in application B? The problem with this approach is that it often only takes into account the reliability and availability requirements of the new and existing systems, without considering differences in other system requirements. For example, strategy X may be too expensive to implement or excessive in application B. Also, safety requirements depend on the application domain.. A visual representation of high-level system requirements might be a useful tool for system designers trying to see the "big picture" of the application domain. There are a number of ways to model the detailed behavior of specific implementations, but relatively few tools for comparing application domain properties prior to system design. In this paper we propose a new technique that uses Kiviat graphs to profile system dependability, service, and cost requirements. We then demonstrate how these graphs can be used to consider safety design strategies for automotive X-by-wire applications. This work is not a proof of concept or implementation, but rather is a suggestion for a way to think about domain-specific requirements in safe system design. This paper has presented a possible technique for comparing application domain properties and demonstrated its use in the comparison of three general safety-critical application domains. The main purpose of such a tool would be to provide system architects with a structured way of comparing attributes of different application domains prior to system design. Future work in this field would require a more thorough definition of the parameters to be analyzed, more detailed analysis of specific systems, and verification of the results of analysis.

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


Algorithms for clique-independent sets on subclasses of circular-arc graphs A circular-arc graph is the intersection graph of arcs on a circle. A Helly circular-arc graph is a circular-arc graph admitting a model whose arcs satisfy the Helly property. A clique-independent set of a graph is a set of pairwise disjoint cliques of the graph. It is NP-hard to compute the maximum cardinality of a clique-independent set for a general graph. In the present paper, we propose polynomial time algorithms for finding the maximum cardinality and weight of a clique-independent set of a 3K 2 -free CA graph. Also, we apply the algorithms to the special case of an HCA graph. The complexity of the proposed algorithm for the cardinality problem in HCA graphs is O(n). This represents an improvement over the existing algorithm by Guruswami and Pandu Rangan, whose complexity is O(n 2 ). These algorithms suppose that an HCA model of the graph is given. The aim of this work is to describe algorithms for finding the clique-independence number for certain classes of graphs. We consider both the cardinality and weighted versions of the problem. The classes of graphs here considered are subclasses of circular-arc graphs: Helly circular-arc graphs and 3K 2 -free circular-arc graphs.. Helly circular-arc graphs form an important class of circular-arc graphs. Some properties of interval graphs are captured more closely by Helly circular-arc graphs than by other classes of circular-arc graphs. On the other hand, the class of 3K 2 -free circular-arc graphs contains that of Helly circular-arc graphs. Furthermore, the cliques of the 3K 2 -free circular-arc graphs preserve some of the properties of those of the Helly circular-arc graphs.. The first NP-hardness result for clique-independent sets appears in [?] . The following are some classes of graphs admitting polynomial time algorithms for the problems of determining a maximum clique-independent set: strongly chordal graphs [?] Let G be an undirected connected graph, V (G) and E(G) its vertex and edge sets, respectively, |V (G)| = n and |E(G)| = m. A clique is a maximal complete set. An independent set is a set of pairwise non adjacent vertices. A clique-independent set is a set of pairwise disjoint cliques.. The clique graph K(G) of G is the intersection graph of the cliques of G. Let M 1 , . . . , M k and v 1 , . . . , v n be the cliques and vertices of a graph G, respectively. We define A G , a clique matrix of G, as a 0-1 matrix whose entry (i, j) is 1 if v j ∈ M i , and 0 otherwise.. A circular-arc (CA) model for G is a pair (C, A), where C is a circle and A is a collection of arcs of C, such that each arc A i ∈ A corresponds to a vertex v i ∈ V (G), and A i , A j intersect precisely when v i , v j are adjacent, i = j. A circular-arc (CA) graph is one admitting a CA model. When traversing the circle C, we will always choose the clockwise direction. If s, t are points of C, write (s, t) to mean the arc of C defined by traversing the circle from s to t. Call s, t the extremes of (s, t), while s is the start and t the end of the arc. For A i ∈ A, write A i = (s i , t i ). Without loss of generality, all arcs of C are considered as open arcs, no two extremes of distinct arcs of A coincide and no single arc entirely covers C. We employ the following notation. Let G be a graph:. • α c (G), maximum cardinality of a clique-independent set of G, the clique-independence number •α c (G), maximum weight of a clique-independent set of G • α(G), maximum cardinality of an independent set of G, the independence number •α(G), maximum weight of an independent set of G In the present paper, we propose algorithms for solving the following problems. For Helly circular-arc graphs G, we describe algorithms for determining α c (G) andα c (G). The algorithm for the cardinality version of this problem requires O(n) time, while for the weighted version it requires O(n 2 ). For 3K 2 -free circular-arc graphs, the proposed algorithm determines α c (G) in O(m) time andα c (G) in O(m log log n + n 2 ). Besides clique-independent sets, the method also leads to the description of an algorithm for constructing the clique graph of a Helly circular-arc graph. The proposed algorithm runs in O(n 2 ) time. Clique graphs of Helly circular-arc graphs were considered in [?,? ].. An algorithm for solving the cardinality problem on Helly circular-arc graphs has been previously described by Guruswami and Pandu Rangan [?] . The complexity of this algorithm is O(n 2 ). Algorithms for the remaining above problems have not been reported so far, to our knowledge.. As usual for many algorithms on circular-arc graphs, we assume that the graph is given by its circular-arc model, with the extremes of the arcs circularly sorted. If they are not sorted we would need to add an extra O(n log n) time for the sorting. The Helly circular-arc graphs are assumed to be represented by a Helly model. All weights here considered are non negative real values.. Let G be a graph admitting a CA model (C, A). For A ∈ A, denote by V (A) the vertex of G corresponding to A. Similarly, for A ⊆ A, V (A ) = {V (A)|A ∈ A }. If V (A) is a universal vertex then A is a universal arc. If an arc A ∈ A contains some point p ∈ C then say that A is an arc of p. Denote by A(p) the collection of arcs of p. Clearly, V (A(p)) is a complete set of G. For p, p ∈ C say that p (properly) dominates p when A(p) (properly) contains A(p ). When A(p) = A(p ) then p, p are equivalent. Say that p ∈ C is a complete point when no point of C properly dominates p. In addition when V (A(p)) is a clique of G then p is a clique point of C. Such a clique is called a Helly clique. Clearly, G might contain cliques that are not Helly. However, if (C, A) is a Helly model then all its cliques are Helly. In this case, there is a one-to-one correspondence between cliques of G and non equivalent clique points of C. On the other hand, any non Helly clique contains at least three vertices. Furthermore, among the arcs of A corresponding to the vertices of a non Helly clique there exist always three of them which together cover the entire circle.. The plan of the paper is as follows. In Section 2, we describe methods for determining sets of complete and clique points, which are employed in the proposed algorithms. Algorithms for clique-independence problems are considered in Section 3. Further remarks form the last section. Preliminary results of this work appear published in [?]. The In all cases, the algorithms determine the cardinality or the weight of the corresponding maximum clique-independent set. There is no difficulty to modify them so as to compute the actual maximum sets.. It remains open to determine whether the clique-independence number of a general CA graph can be found in polynomial time.

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


Necessary Conditions for the Global Rigidity of Direction-Length Frameworks It is an intriguing open problem to give a combinatorial characterisation or polynomial algorithm for determining when a graph is globally rigid in R d . This means that any generic realisation is uniquely determined up to congruence when each edge represents a fixed length constraint. Hendrickson gave two natural necessary conditions, one involving connectivity and the other redundant rigidity. In general these are not sufficient, but they do suffice in two dimensions, as shown by Jackson and Jordán. Our main result is an analogue of the redundant rigidity condition for frameworks that have both direction and length constraints. For any generic globally rigid direction-length framework in R d with at least 2 length edges, we show that deleting any length edge results in a rigid framework. It seems harder to obtain a corresponding result when a direction edge is deleted: we can do this in two dimensions, under an additional hypothesis that we believe to be unnecessary. Our proofs use a lemma of independent interest, stating that a certain space parameterising equivalent frameworks is a smooth manifold. We prove this lemma using arguments from differential topology and the Tarski-Seidenberg theorem on semi-algebraic sets. A finite configuration of points in Euclidean space with local constraints may be informally described as globally rigid if the constraints determine the point set up to congruence. This concept has applications in chemistry and for sensor networks, where one wants to deduce the global structure of a configuration from local measurements. A d-dimensional length framework (G, p) consists of a graph G = (V, E) and a map p : V → R d . We say that (G, q) and (G, p) are length-equivalent if q(u)−q(v) = p(u)−p(v) for all uv ∈ E and length-congruent if q(u)−q(v) = p(u)−p(v) for all u, v ∈ V . Then we say that (G, p) is globally length-rigid if any framework (G, q) lengthequivalent to (G, p) is length-congruent to (G, p). To exclude pathologies arising from algebraic relationships between the co-ordinates of vertices it is natural to consider generic maps p. A graph G is globally length-rigid in R d if (G, p) is globally length-rigid for every generic p :. A combination of results of Connelly [1] and Gortler, Healy and Thurston [2] gives an algebraic characterisation of global length-rigidity for generic frameworks and implies that it depends only on the structure of the underlying graph G. On the other hand, there is no known combinatorial characterisation or polynomial algorithm for determining when a graph G is globally length-rigid in R d . It is easy to see that every complete graph is globally rigid in R d . Hendrickson [3] gave two necessary conditions for graphs G which are not complete:. (i) G must be d-connected, and. (ii) G must be redundantly length-rigid in R d , i.e. G \ e is length-rigid for any edge e of G.. (Informally, a framework is length-rigid if it does not admit continuous motions other than to congruent frameworks, and a graph G is length-rigid in R d if (G, p) is length-rigid for every generic p : V → R d .) For general d these conditions are not sufficient for global length-rigidity, as shown by Connelly [1] . They do suffice for d = 2, as shown by Jackson and Jordán [5] , who proved that a 2-dimensional generic length framework (G, p) is globally length-rigid if and only if either G is a complete graph on at most 3 vertices, or G is 3-connected and redundantly rigid.. In this paper we consider frameworks in which the local constraints can involve both lengths and directions. We consider mixed graphs G = (V ; D, L), where D and L are edge sets representing direction and length constraints. Given maps p, q from V to R d we say that the direction-length frameworks (G, p) and (G, q) are equivalent if q(u) − q(v) is a scalar multiple of p(u) − p(v) for all uv ∈ D with p(u) = p(v), and q(u) − q(v) = p(u) − p(v) for all uv ∈ L. They are congruent if (G, q) can be obtained from (G, p) by a translation and a dilation by ±1. Similarly to before, we say that (G, p) is globally rigid if any framework (G, q) equivalent to (G, p) is congruent to (G, p), and is rigid if every continuous motion of (G, p) results in a congruent framework. These concepts are illustrated in Figure 1 . We will investigate when G is globally rigid, i.e. (G, p) is globally rigid for any generic map p.. Suppose (G, p) is a d-dimensional generic direction-length framework. It is certainly necessary for G to be connected if (G, p) is to be rigid, let alone globally rigid. Also, 2-connectivity is necessary for global rigidity, as if x is a cutvertex of G then we can obtain a realisation (G, p ′ ) that is equivalent but not congruent to (G, p) by inverting one component of G \ x about the point p(x), without changing the rest of the realisation. On the other hand, if G = (V ; D, L) is 2-connected and D = L then (G, p) is globally rigid if and only if G is 2-connected, see [4, Theorem 7 .2], so 3-connectivity is no longer necessary for global rigidity in R d . However, an analogue of Hendrickson's connectivity condition may be obtained by considering more restricted cuts: if (G, p) is globally rigid then there can be no cutset X ⊆ V of size at most d such that there is a component C of G \ X that contains only length edges, as then we could obtain a realisation (G, p ′ ) which is equivalent but not congruent to (G, p) by reflecting C in a hyperplane containing the points p(x), x ∈ X. The main result of [4] is that this connectivity condition is both necessary and sufficient for the global rigidity of redundantly rigid 2-dimensional generic direction-length frameworks when |D ∪ L| = 2|V | − 1, i.e. D ∪ L is a circuit in the corresponding rigidity matroid. Now we turn to an analogue of Hendrickson's redundant rigidity condition. Our main theorem achieves this when a length edge is deleted. Theorem 1.1 (Length-redundant rigidity) Suppose that (G, p) is a generic globally rigid direction-length framework in R d with at least 2 length edges. Then G \ e is rigid in R d for any length edge e of G.. The proof uses the following lemma of independent interest, established using arguments from differential topology and the Tarski-Seidenberg theorem on semi-algebraic sets. (The framework space parameterises frameworks equivalent to (G, p) and will be formally defined in the next section, as will the rank of (G, p).). is a generic direction-length framework in R d with rank d|V | − d − t, for some t ≥ 1, and v 0 ∈ V . Then the framework space S G,p,v 0 is a smooth manifold of dimension t.. It is also natural to consider the result of deleting a direction edge, rather than a length edge, from a d-dimensional generic globally rigid direction-length framework. This can reduce the rank of the rigidity matrix by up to d − 1, so we expect a more complicated behaviour for d ≥ 3. However, in the special case d = 2, we can obtain the following weakening of Hendrickson's redundant rigidity condition. Theorem 1.3 Suppose (G, p) is a 2-dimensional generic globally rigid direction-length framework, e is a direction edge of G and G \ e has a rigid subgraph with more than one vertex. Then G \ e is either rigid or unbounded in R 2 .

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


Adaptive dissemination of data in time-critical asymmetric communication environments Abstract There is a growing need for information servers with capabilities to handle large amounts of information accessed by a potentially unlimited number of users in asymmetric communication environments (e.g., traffic information, stock quotes, weather, news). In some cases, the users require the information by a certain time, and therefore information should be provided with deadline constraints associated with the requests of the data. We will refer to these as time-critical asymmetric communication environments. For example, let us consider a traffic information server and the driver of a vehicle who, at some point ahead in the road, needs to take one of two possible routes in order to get to her destination. Obviously, it is necessary for the server to provide the driver with the desired traffic information (for example, one of the routes is congested because there has been an accident) before the decision point is reached, otherwise the information has no value for the driver.. One way to try to meet the needs of such applications is to use the classic client/server model. Unfortunately, it suffers from a lack of scalability. Beyond a certain workload, the server becomes overwhelmed, that is, it is not able to serve more than a certain number of requests per time unit, due to resource and bandwidth limitations. On the other side of the spectrum some bandwidth-efficient data broadcast models have been proposed [1] . They provide high scalability by broadcasting the information simultaneously to a large population of users, using a single, high-capacity downlink channel (i.e., a channel from the server to users). The weaknesses found in pure broadcast models result from the absence of direct interaction of the users with the server, which implies the impossibility of adaptation to changing access patterns.. Recently, some bidirectional broadcast models have been studied [2, 13] , trying to exploit on the one hand the benefits derived from the high bandwidth efficiency and scalability of data broadcasting, and on the other hand the direct interaction of users with the server. Bidirectional schemes are based on the incorporation of a low-capacity uplink channel (i.e., a channel from users to server), devoted to the transmission of requests made explicitly by those users not satisfied by the broadcast program. Most bidirectional broadcast models are hybrid, that is, there exist two different information transmission modes: the periodic broadcast mode, in which information is broadcast periodically, and the on-demand broadcast mode, devoted to broadcasting information explicitly requested by users via the uplink channel. Unfortunately, the only hybrid model in which deadline constraints are taken into account [13] is not adaptive, that is, the information that is broadcast periodically and the fraction of the bandwidth allocated to each mode do not vary.. Consequently, none of the existing models is adequate for environments in which the user access distribution is not static and there are timing constraints present. This paper addresses this lacuna. It introduces an adaptive hybrid broadcast model, that extends the functionality and performance of current hybrid schemes, by means of an online scheduling algorithm that takes into account the access frequency distribution of data, bandwidth limitations in both uplink and downlink channels, and deadline constraints associated with data requests. The information server dynamically adapts (a) the specific data items that have to be broadcast periodically, and (b) the amount of bandwidth assigned to each transmission mode. The remainder of this paper is organized as follows: Section 2 states the main issues and considerations when designing an information server for a time-critical asymmetric communication environment. Section 3 discusses related work. The description of our adaptive hybrid data broadcast model is presented in section 4, in which the adaptive scheduling approach is also detailed. Section 5 presents and analyzes the results of the experimental study. Finally, section 6 summarizes and concludes the paper. In TC-AHB, both (a) the specific data items being broadcast periodically, and (b) the amount of bandwidth assigned to each transmission mode change dynamically to adapt to the needs of the clients. The server performs this adaptation on a per-cycle basis. At the end of each broadcast cycle, the server classifies the data items, deciding which ones to broadcast periodically in the next broadcast cycle. This decision depends on the access distributions observed in the previous broadcast cycle and the amount of bandwidth needed to broadcast each item periodically. As we will see shortly, this amount is related to the deadline constraints associated with each item.. Then, the server computes the periodic broadcast program for the next cycle. An item is included in the periodic broadcast program if the server expects to save some bandwidth as compared to broadcasting the item upon request. In order to prevent the items not included in the periodic broadcast program from starving, we always leave a minimum fraction of bandwidth for on-demand broadcast mode. The broadcast frequency of a periodically broadcast item should be the minimum needed to satisfy all the deadlines associated with potential requests for that item.. After computing the periodic broadcast program using the classification of the items and their broadcast frequencies, the server assigns the remaining bandwidth to on-demand broadcast, where an on-line scheduling algorithm is used to prioritize requests according to their relative deadlines. Note that the periodic broadcast program is computed at the end of each cycle, whereas the ondemand broadcast is scheduled dynamically, as requests are received from the users.. Scalability of the server is compromised by the number of requests that have to be processed and the capacity of the uplink channel. Assuming that some indexing technique is used to help users know what is being broadcast and when, every user is supposed to first listen to the broadcast, check the index, and only issue a request if the desired item is not being broadcast periodically. This will lower the number of requests sent to the server via the uplink channel. In our model the index is interleaved with data and it is broadcast many times in each broadcast cycle, in order to decrease the time needed for a client to receive the index. There are several bandwidth efficient indexing techniques (e.g., [9] ) that keep the index bandwidth requirements very low.. We should observe that the more accurate the periodic broadcast program, the less information the server has about the user access distribution. The problem is that the server does not receive any information about the number of users that are being satisfied by the periodic broadcast program, and therefore is unable to know if any of the items should be removed from the program because its access frequency has decreased. As we will see in section 4.4, this problem is overcome using a sampling technique, that basically stops broadcasting some of the items included in the periodic broadcast during short time intervals. This results in the receipt of requests for those items. The server can then estimate the actual access frequencies for these requests, information needed to dynamically adjust the periodic broadcast program to the needs of the actual users. In this paper we have presented and evaluated a new model for effective data dissemination in dynamic, timecritical asymmetric communication environments. Our technique uses adaptive hybrid broadcast transmission, allowing the users to request specific items with deadline requirements. In order to minimize the total number of deadlines missed by making the most effective use of the available bandwidth, our scheduling approach combines factors such as access frequency, deadline distribution and bandwidth requirements. The results obtained from simulation show that, by broadcasting periodically only those items predicted to have high access frequencies and low bandwidth needs, our scheduling algorithm clearly outperforms non-adaptive broadcast servers in terms of deadlines missed and number of requests scheduled, when dynamic client profiles occur and in overload conditions.. The dynamic adaptation of the contents of the periodic broadcast program to the real client access profile is essential for any broadcast server to work in environments where the data access distribution changes over time, as in most real situations (specially if the clients have mobility).. The effect of the bandwidth limitations of the uplink channel is an important factor to be considered. Our adaptive broadcast model assigns more bandwidth to the periodic transmission mode when the workload is high, avoiding an excessive request traffic coming to the server and accommodating higher workloads before the uplink channel becomes congested.. Future work includes extending the functionality of the server by incorporating loss probability, different broadcast channels, and scheduling algorithms to allow multimedia information broadcasting and QoS guarantees. In the traditional Broadcast Disks (BD) model [1] , the server periodically repeats an off-line computed broadcast program, based on previously known user access patterns. A broadcast cycle is defined as one transmission of the periodic broadcast program. The broadcast program is static and only one downlink channel is used. The main disadvantages of this approach are the lack of adaptation to the current population demands (as there is no feedback from clients to the server), the impossibility of guaranteeing the meeting of deadline constraints for current clients, and the potential waste of bandwidth derived from the off-line decision about the items to broadcast and their corresponding broadcast frequency. The BD model has been extended in [2] , providing push and pull for data dissemination, by integrating an uplink channel.. Nevertheless, in this hybrid model the bandwidth is assigned to the two broadcast modes statically, and there is no adaptation to the current workload, as the contents of the periodic broadcast are constant. In addition, data requests are not associated with deadlines.. In [11, 12] , a model for adapting the allocation of the bandwidth to the periodic and on-demand modes is proposed. This work tries to provide adaptation in order to minimize average data access latency, so they minimize the number of requests arriving at the server by broadcasting periodically the most demanded items, providing the rest of the items only on demand. Clients listen to the broadcast first, and make a request only if the data item needed is not in the periodic broadcast program. All requests are served sooner or later, but again, information requests are not associated with deadline constraints.. Deadline constraints have been integrated into the BD model in [5, 6, 8] . The server tries to compute a periodic schedule that provides worst-case guarantees, even in the event of failures and data updates. However, this model is not bidirectional, that is, there is no uplink channel and consequently the server periodically broadcasts items based on a static estimation of the potential user population, not on the actual workload.. Closer to our work is the hybrid Broadcast On-Demand (BoD) model, presented in [13] , as an extension of the traditional BD model. BoD is a hybrid bidirectional server that considers data temporal constraints. Time division multiplexing is used, reserving a fixed fraction of the available bandwidth for periodic broadcast, and the remaining bandwidth for on-demand processing. Note that now a broadcast cycle includes the transmission of a periodic broadcast program and the time intervals when data chosen for on-demand broadcast is transmitted. BoD is not adaptive to dynamic workloads, as it is assumed that the access distribution will remain constant. In BD and BoD, a large amount of bandwidth is likely to be wasted, not only because the periodic broadcast program is static and the offline computed access patterns can differ from actual ones, but also because the broadcast frequency is not related to the deadline distribution of the items.

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


A Structural Approach to Reversible Computation Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on simulations of low-level machine models. By contrast, we develop a more structural approach. We show how high-level functional programs can be mapped compositionally (i.e. in a syntax-directed fashion) into a simple kind of automata which are immediately seen to be reversible. The size of the automaton is linear in the size of the functional term. In mathematical terms, we are building a concrete model of functional computation. This construction stems directly from ideas arising in Geometry of Interaction and Linear Logic-but can be understood without any knowledge of these topics. In fact, it serves as an excellent introduction to them. At the same time, an interesting logical delineation between reversible and irreversible forms of computation emerges from our analysis. The importance of reversibility in computation, for both foundational and, in the medium term, for practical reasons, is by now well established. We quote from the excellent summary in the introduction to the recent paper by Buhrman, Tromp and Vitányi [19] :. Reversible Computation: R. Landauer [41] has demonstrated that it is only the "logically irreversible" operations in a physical computer that necessarily dissipate energy by generating a corresponding amount of entropy for every bit of information that gets irreversibly erased; the logically reversible operations can in principle be performed dissipation-free. Currently, computations are commonly irreversible, even though the physical devices that execute them are fundamentally reversible. At the basic level, however, matter is governed by classical mechanics and quantum mechanics, which are reversible. This contrast is only possible at the cost of efficiency loss by generating thermal entropy into the environment. With computational device technology rapidly approaching the elementary particle level it has been argued many times that this effect gains in significance to the extent that efficient operation (or operation at all) of future computers requires them to be reversible . . . The mismatch of computing organization and reality will express itself in friction: computers will dissipate a lot of heat unless their mode of operation becomes reversible, possibly quantum mechanical.. The previous approaches of which we are aware (e.g. [43, 17, 18] ) proceed by showing that some standard, low-level, irreversible computational model such as Turing machines can be simulated by a reversible version of the same model. Our approach is more "structural". We firstly define a simple model of computation which is directly reversible in a very strong senseevery automaton A in our model has a "dual" automaton A op , defined quite trivially from A, whose computations are exactly the time-reversals of the computations of A. We then establish a connection to models of functional computation. We will show that our model gives rise to a combinatory algebra [33] , and derive universality as an easy consequence. This method of establishing universality has potential significance for the important issue of how to program reversible computations. To quote from [19] again:. Currently, almost no algorithms and other programs are designed according to reversible principles . . . To write reversible programs by hand is unnatural and difficult. The natural way is to compile irreversible programs to reversible ones.. Our approach can be seen as providing a simple, compositional (i.e. "syntaxdirected") compilation from high-level functional programs into a reversible model of computation. This offers a novel perspective on reversible computing.. Our approach also has conceptual interest in that our constructions, while quite concrete, are based directly on ideas stemming from Linear Logic and Geometry of Interaction [25, 26, 27, 28, 29, 45, 21, 22, 16] , and developed in previous work by the present author and a number of colleagues [2, 3, 5, 6, 7, 9, 10] . Our work here can be seen as a concrete manifestation of these more abstract and foundational developments. However, no knowledge of Linear Logic or Geometry of Interaction is required to read the present paper. In fact, it might serve as an introduction to these topics, from a very concrete point of view. At the same time, an interesting logical delineation between reversible and irreversible forms of computation emerges from our analysis. Geometry of Interaction (GoI) was initiated by Girard in a sequence of papers [26, 27, 28] , and extensively developed by Danos, Regnier, Malacaria, Baillot, Padicini and others, see e.g. [45, 21, 22, 16] . In particular, Danos and Regnier developed a computational view of GoI. In [22] they gave a compositional translation of the λ-calculus into a form of reversible abstract machine. We also note the thesis work of Mackie [44] , done under the present author's supervision, which develops a GoI-based implementation paradigm for functional programming languages.. The present paper further develops the connections between GoI as a mathematical model of computation, and computational schemes with an emphasis on reversibility. As we see it, the main contributions are as follows:. • Firstly, the approach in the present paper seems particularly simple and direct. As already mentioned, we believe it will be accessible even without any prior knowledge of GoI or Linear Logic. The basic computational formalism is related very directly to standard ideas in term-rewriting, automata and combinatory logic. By contrast, much of the literature on GoI can seem forbiddingly technical and esoteric to outsiders to the field. Thus we hope that this paper may help to open up some of the ideas in this field to a wider community.. • There are also some interesting new perspectives on the standard ideas, e.g. the idea of biorthogonal term-rewriting system, and of linear combinatory logic (which was introduced by the present author in [10] ).. • From the point of view of GoI itself, there are also some novelties.. In particular, we develop the reversible computational structure in a syntax-free fashion. We consider a general 'space' of reversible automata, and define a linear combinatory algebra structure on this universe, rather than pinning all constructions to an induction on a preconceived syntax. This allows the resulting structure to be revealed more clearly, and the definitions and results to be stated more generally.. We also believe that our descriptions of the linear combinators as automata, and of application and replication as constructions on automata, give a particularly clear and enlightening perspective on this approach to reversible functional computation.. • The discussion in section 7 of the boundary between reversible and irreversible computation, and its relationship to pure vs. applied functional calculi, and the multiplicative-exponential vs. additive levels of Linear Logic, seems of conceptual interest, and is surely worth further exploration.. • The results in section 8 on universality, and the consequent (and somewhat surprising) non-closure under linear application of finitely describable partial involutions, give rise to an interesting, and apparently challenging, open problem on the characterization of the realizable partial involutions.

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 O O O O O O O O O O O O O O O O O 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 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 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 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 B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B 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 B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 self-watching model of analogy-making and perception This paper describes Metacat, an extension of the Copycat model of analogy-making. The development of Copycat focused on modelling context-sensitive concepts and the ways in which they interact with perception within an abstract microworld of analogy problems. This approach differs from most other models of analogy in its insistence that concepts acquire their semantics from within the system itself, through perception, rather than being imposed from the outside. The present work extends these ideas by incorporating self-perception, episodic memory, and reminding into the model. These mechanisms enable Metacat to explain the similarities and differences that it perceives between analogies, and to monitor and respond to patterns that occur in its own behaviour as it works on analogy problems. This introspective capacity overcomes several limitations inherent in the earlier model, and affords the program a powerful degree of self-control. Metacat's architecture includes aspects of both symbolic and connectionist systems. The paper outlines the principal components of the architecture, analyses several sample runs and examples of program-generated commentary about analogies, and discusses Metacat's relation to some other well-known models of analogy. This paper describes a computational model of analogy-making and perception called Metacat, which is based on the earlier Copycat model developed by Mitchell (Hofstadter 1984, Mitchell 1993) . Like Copycat, Metacat models the complex interplay of bottom-up and top-down processes involved in perception, using an emergent architecture that incorporates aspects of both *Email: jmarshall@slc.edu symbolic and connectionist systems. Metacat, however, builds on the earlier model by focusing on self-perception and its relation to other cognitive processes. The long-term goal of this line of research is to understand how high-level cognitive phenomena such as concepts, analogical thinking, creativity, and self-awareness can emerge from a subcognitive substrate composed of a large number of fine-grained, nondeterministic actions, each of which is far too small by itself to support such phenomena.. Few people would claim that the individual neurons making up a human brain are ''conscious'' in anything like the normal sense in which humans experience consciousness. We are forced to accept the fact that self-awareness arises, somehow, out of nothing but billions of low-level chemical reactions and neuronal firings. How can individually meaningless physical events in a brain -even a huge number of them -ultimately give rise to meaningful awareness and understanding? Hofstadter has argued that two ideas are of paramount importance:. What seems to make brains conscious is the special way they are organized -in particular, the higher-level structures and mechanisms that come into being. I see two dimensions as being critical: (1) the fact that brains possess concepts, allowing complex representational structures to be built that automatically come with associative links to all sorts of prior experiences, and (2) the fact that brains can self-monitor, allowing a complex internal self-model to arise, allowing the system an enormous degree of self-control and open-endedness. (Hofstadter and FARG 1995) The development of Copycat was intended to explore the first idea, by creating a computer model of analogy-making in which the representation of concepts is deeply intertwined with the program's mechanisms for high-level perceptual processing. Concepts in Copycat are not modelled as static representational structures; rather, they are dynamic entities that respond to perceptual processing in a highly contextsensitive way, bending and adapting to the situation at hand in a flexible manner. Furthermore, they actively influence perceptual processing itself. This tight coupling of concepts and perception in the model gives rise to an ability to perceive similarities between different situations by describing them in terms of a common set of underlying concepts applicable to both situations. The ability of Copycat to make analogies is a direct consequence of the nature of the program's representation of concepts.. The Metacat model explores the second idea, by endowing Copycat with a capacity for self-watching, defined here as the ability of a system to perceive -and to create explicit representations of -its own perceptual processes. Our objective has been to develop mechanisms that allow the program to monitor its own activity and to explicitly characterize the conceptual associations that implicitly arise as it solves analogy problems (Marshall and Hofstadter 1997, Marshall 1999) . This can be thought of as adding a higher ''cognitive'' layer on top of Copycat's ''subcognitive'' layer, enabling the program to watch and remember what happens at its subcognitive level as perceptual structures are built, reconfigured, and destroyed. This type of self-reflective awareness is common in humans, who are quite capable of paying attention to, and explicitly articulating, patterns in their own thinking (Chi et al. 1989 (Chi et al. , 1994 .. Copycat and Metacat are concerned with high-level perception, by which we mean that level of perceptual processing in which concepts play a critical role (Chalmers et al. 1992) . In contrast, low-level perception refers to the processing of raw, modality-specific sensory data obtained directly from the environment, such as the detection of edges in retinal images, or the processing of audio frequencies from the inner ear, without regard to the meaning of this information. Low-level perceptual processing is the first step along the path leading to high-level perception, with many intermediate processing stages lying in-between involving ever greater degrees of abstraction. The end result of this process is the conscious recognition or understanding of the input stimulus as an instance of a particular mental concept or set of concepts.. Consider, for example, the everyday experience of recognizing your mother. A pattern of light falls on the hundred million or so photoreceptor cells in your retina, and a fraction of a second later, the idea of your mother comes to mind. A particular mental concept has become highly activated, while most others remain dormant. This process of recognition, for the most part, takes place below the level of conscious awareness. One does not have to do much deliberate thinking in order to recognize one's mother (at least in the absence of degraded environmental conditions such as poor lighting). High-level perception depends largely on subcognitive processing mechanisms (Hofstadter 1985b) .. The activation of the concept of mother elicited by a facial image is a relatively simple example of high-level perception in action. This same phenomenon, however, often occurs in more abstract contexts, such as when a person hears an unfamiliar piece of music for the first time and recognizes it as coming from a particular musical period or composer, or when a painting is recognized to be, say, an Impressionist work, or as belonging to Picasso's ''Blue period''. Moving to an even higher level of abstraction, a complicated social situation involving tangled webs of people, objects, relationships, and conflicting choices may collectively be perceived as a ''Catch-22'' situation. Even the concept of mother is, in reality, a subtle matter. Depending on context, a wide variety of things can be viewed as abstract instances of this concept. The Earth, for example, is sometimes described as the mother of all living things, an idea commonly expressed by the phrase ''Mother Earth''. Strictly speaking, of course, considering a planet to be a mother makes no sense, but given the right context we can effortlessly see how the idea applies, thanks to the natural flexibility of human concepts.. In general, concepts in the mind are not sharply defined entities with clear-cut boundaries, always applying to certain things but never to others. Rather, the boundaries of concepts are inherently ill-defined and blurry, and are strongly influenced by the context in which perception occurs. We refer to this type of inherent flexibility as conceptual fluidity, in order to stress the idea of concepts as nonrigid, adaptable, and highly context-sensitive. Much work has been done in cognitive psychology investigating the nature of the distances between concepts and categories (see, for example, Tversky 1977 , Smith and Medin 1981 , Goldstone et al. 1991 . In particular, the strength of associations between concepts can change dynamically, according to context. Under the right pressures, concepts that are normally far apart may be brought close together, so that they are both seen as applying to a particular situation (such as when the Earth is regarded simultaneously as an instance of planet and mother). This phenomenon, which we refer to as conceptual slippage, is what enables apparently dissimilar situations to be perceived as being ''the same'' at a deeper, more abstract level.. Copycat and Metacat differ in important ways from many other models of analogy proposed by researchers in AI and cognitive science. See French (2002) for a recent overview. Probably the most important difference is the emphasis our models place on the representation of concepts, and the role played by concepts in making analogies. Other well-known models have focused on the mechanisms and psychological constraints involved in mapping a source situation to a target situation (Gentner 1983 , Falkenhainer et al. 1990 , Forbus et al. 1994 ; on the satisfaction of multiple competing constraints when constructing this mapping (Holyoak and Thagard 1989) ; on the mechanisms that allow stored analogs to be retrieved from memory (Thagard et al. 1990 , Kolodner 1993 , Forbus et al. 1995 ; on the integration and mutual interaction of processes responsible for retrieval, mapping, and transfer (Eskridge 1994, Kokinov and Petrov 2001) ; and on distributed representations of structure , Hummel and Holyoak 1996 , 1997 , Holyoak and Hummel 2001 , Wilson et al. 2001 . All of these issues are important, and any full and satisfying theory of analogy should certainly include an account of them. In our view, however, a complete theory must also integrate concepts, perception, and meaning into the picture.. When humans make analogies, we not only construct mental mappings according to constraints, we also understand the meaning of the concepts connected by these mapping-structures. For example, a person making an analogy between a situation involving water and another involving heat presumably maps mental structures representing water to structures representing heat, at some level of abstraction. But people also understand what the underlying concepts of water and heat mean, from long experience with these concepts in the world. Of course, the act of making the analogy deepens this understanding by facilitating a transfer of knowledge from one situation to the other. But the important point is that the constituent concepts underlying the analogy are themselves meaningful to the person. Likewise, a computer model of analogy should offer some account of how the underlying symbols and structures that represent concepts in an analogy acquire meaning themselves, in addition to an account of the structure-mapping processes involved. That is, the structures that the program uses to represent analogies should be meaningful to the program itself. This is essentially the familiar symbol-grounding problem (Harnad 1990) , recast in analogical guise.. Some connectionist models of analogy have attempted to address this problem by moving away from the use of symbolic representations of source and target situations. Much recent work has focused on the use of distributed encoding techniques such as Plate's holographic reduced representations (Plate 1994 (Plate , 1998 ), Kanerva's binary spatter code (Kanerva 1996 (Kanerva , 1998 , or Smolensky's tensor products (Smolensky 1990) . Examples of such models include Drama (Eliasmith and Thagard 2001) and the STAR models of and Wilson et al. (2001) . All of these approaches encode explicitly structured representations of source and target situations as distributed activation patterns, which are suitable for processing by connectionist networks. These representations can be manipulated in a holistic fashion, without having to be decomposed into their constituent components (Chalmers 1990 , Chrisman 1991 , Blank et al. 1992 . However, currently the representations used by these models do not acquire their meaning internally through the system's own perceptions or through learning. Instead, meaning is imposed from outside the system through an essentially arbitrary assignment of semantics to the patterns of activation that serve as the constituent building blocks of representations. The hope is that eventually these systems will be able to use learned patterns based directly on sensory stimuli -instead of arbitrary patterns -as representational building blocks, which will make the representations meaningful to the system itself. Blank's (1997) Analogator model attempts to integrate learning and analogymaking into a single connectionist framework using distributed representations based on tensor products. Analogator learns to make analogies between very simple visual scenes composed of geometric shapes, on the basis of spatial relationships such as above or below. Unlike the models mentioned previously, however, Analogator does not start with explicitly structured representations. Instead, the system itself learns the meaning of spatial relationships by creating its own internal representations of analogies, through direct experience with visual scenes. In other words, the meaning of the underlying components of Analogator's analogies is acquired through the system's own perceptions. See Gasser (1993) for a more general discussion of perceptual grounding within the context of simple visual scenes.. In both Analogator and Metacat, perception is tightly interwoven with analogymaking. Analogator, however, focuses more on the learning of analogical behaviour than on the explicit modelling of concepts. In contrast, Metacat emphasizes concepts and the ways in which they interact with perception, but does not attempt to model learning. Another difference is that Metacat's representations have a more symbolic flavour than the purely distributed representations created by Analogator. Nevertheless, the representations created by both models are much more closely tied to perception than the traditional predicate-calculus-based representations used by many of the models cited earlier. A prime objective of this research is to explore how adaptable, context-sensitive concepts can give rise to understanding by enabling analogies between apparently dissimilar situations to be perceived. The present work extends and deepens the ideas developed in Copycat by incorporating mechanisms for self-watching, episodic memory, and reminding into the model. These mechanisms make it possible for Metacat to compare and contrast analogies in an insightful way. The ability of the program to perceive subtle parallels and distinctions between analogies represents a significant step beyond the perceptual abilities of Copycat, although much work still remains to be done.. The examples presented in section 7 illustrate Metacat's ability to observe and describe its own behaviour, to recall previously encountered answers, and to explain the similarities and differences it perceives between analogies. This ability relies on storing abstract descriptions of answers and processing events, characterized by patterns of themes, in memory. It is important to emphasize that answer descriptions are just organized collections of Slipnet concepts, since they are composed of themes and rules, which are in turn composed of concepts. These concepts, as the fundamental building-blocks of answer descriptions, form the substrate on which the program's understanding of analogies is based, and acquire their semantics through the ways in which they respond to situations in Metacat's letter-string world. Consequently, the English-language commentary generated by the program about analogies, although just a surface-level veneer in many ways, ultimately rests on a deeper foundation of conceptual representation tied to perception. A number of researchers have developed cognitive models that incorporate architectural principles similar to those of Metacat, including emergent processing arising from many nondeterministic agents acting concurrently, and the spreading of activation among nodes of a semantic network in response to context-sensitive pressures. Kokinov's DUAL cognitive architecture, which forms the basis of the AMBR1 and AMBR2 models of analogical reasoning and memory retrieval developed by Kokinov and Petrov, is a case in point (Kokinov 1994a , 1994b , Kokinov and Petrov 2001 . The development of these models has been guided by the belief that subprocesses underlying analogy-making should be integrated into a larger cognitive system comprising perception, memory, learning, and reasoning. As in Metacat, dynamic context-sensitive emergent processing plays a central role in DUAL and AMBR, allowing for the close interaction of representation-building, mapping, transfer, and reminding.. Despite their architectural similarities, however, Metacat and AMBR differ in terms of the relative emphasis each model places on different aspects of cognition. The more recent AMBR2 model (Kokinov and Petrov 2001) is particularly strong in its approach to modelling the storage and retrieval of memory episodes. In AMBR2, episode representations are highly emergent, decentralized, and context-sensitive, and interact with the mapping process in a psychologically plausible manner. In contrast, Metacat currently lacks sophisticated mechanisms for episodic memory indexing and retrieval. In the current version of the program, when a new answer is discovered, the newly created answer description is individually compared to all others stored in memory, in order to determine the new activation levels of the stored descriptions -and hence which answers will be recalled as a result of finding the new answer. This simplistic approach does not scale well if many answers exist in memory, and is thus unsatisfactory in principle. Furthermore, as Kokinov and Petrov have pointed out, these memory structures are essentially localized and static (although their activation levels may change, as mentioned above). Unlike themes and Slipnet concepts, answer descriptions do not interact with each other through spreading activation, and do not actively influence perceptual processing, as they undoubtedly should in order to model priming effects and other influences of previous problem-solving experiences on perception. Developing better mechanisms for episodic memory organization and retrieval in Metacat is thus a high priority for future research.. On the other hand, Metacat is strongly committed to modelling concepts as active, dynamic entities that acquire their meanings from within the system itself, through their interactions with perception, as discussed earlier in section 1. AMBR also models concepts, but their meanings are not tied to the system's own perceptions in the same way as in Metacat. For example, AMBR may solve analogy problems involving the concepts of water and teapot, but the structures representing these concepts in memory presumably do not become activated by the system's perception of real water or real teapots. In contrast, the concepts behind Metacat's analogies, such as letter or successor-group, acquire their meanings precisely as a consequence of how they respond to the perception of ''real'' letters and groups in Metacat's microworld.. Another important difference is Metacat's focus on modelling self-perception, an aspect of cognition that is not addressed by most other models of analogy-making. As we saw earlier, the information gleaned from self-watching plays a crucial role in the high-level characterization of answers, enabling the program to perceive abstract similarities and differences between analogies as a whole. We believe that a psychologically realistic and complete model of analogy-making should offer some account of higher perceptual levels, including those that reflect aspects of the system's own behaviour. In our model, the mechanisms responsible for internal self-perception are not fundamentally different from those responsible for external perception. Both involve the building and manipulation of structures by codelets, whether in the Temporal Trace (for internal perception) or in the Workspace (for external perception). Furthermore, these processes are tightly interwoven, and are highly dependent on the context-sensitive activations of concepts.. Metacat also shares similarities with case-based reasoning (CBR) approaches to analogy (Kolodner 1993 , Leake 1996 . For instance, Metacat's stored answer descriptions can be likened to cases in CBR, since they form a corpus of experience on which the program can draw when faced with new situations. The discovery of a new answer may trigger the retrieval of similar answers that the program has seen in the past, in a way reminiscent of the retrieval of stored cases in CBR according to their degree of similarity to the target situation. In Metacat, retrieved answers are compared to the current answer by analysing the similarities and differences between the answers' associated themes. This is roughly akin to comparing cases in CBR in order to determine which aspects of a retrieved case can be applied directly to the target situation without modification, and which aspects must be adapted to fit it. Finally, Metacat's snag descriptions can be viewed as cases that store failure information about analogies.. However, there are important differences between CBR and Metacat. First of all, even though Metacat solves analogy problems, it was not conceived as a model of problem-solving per se. Rather, its focus is on modelling the way in which contextsensitive concepts allow analogies to be perceived and understood. It is more concerned with analogical perception (and self-perception), than with analogical reasoning employed specifically as a tool for solving problems. Moreover, the goal of much CBR work has been to create systems that learn from experience to solve problems in an increasingly effective or efficient manner, whereas in Metacat the notion of improving the program's performance on analogy problems is not relevant. However, some recent CBR-based approaches to modelling creativity (Bento and Cardoso 2001, Cardoso and Wiggins 2002) seem to be more in harmony with Metacat's goals than previous CBR systems have been.

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Parametric Model Discrimination for Heavily Censored Survival Data Abstract-Simultaneous discrimination among various parametric lifetime models is an important step in the parametric analysis of survival data. We consider a plot of the skewness versus the coefficient of variation for the purpose of discriminating among parametric survival models. We extend the method of Cox & Oakes from complete to censored data by developing an algorithm based on a competing risks model and kernel function estimation. A by-product of this algorithm is a nonparametric survival function estimate. This section details the steps involved in extracting a survival distribution estimate from the observed failure & censoring times. We will use the following eight-point data set in our examples.. where an asterisk indicates a right-censored observation. The data could also be described as where , is the failure time, is the censoring time, and is 1 when , and 0 when . The random variables for failure times and censoring times are assumed to be mutually independent.. To verify the correctness of our method and the algorithm, we will work through two small examples.. The Gaussian distribution was an obvious choice for a kernel function. There are, however, several issues that preclude its use. The first issue is the range of support. Establishing a Gaussian kernel around any data value will include negative support values, which is an impossibility in lifetime data analysis because negative lifetimes never occur. The second issue is the intractability of the cumulative density function (CDF). While APPL was able to plot a (rather complicated) CDF, it was unable to calculate the coefficient of variation or the skewness.. We will instead use the PDF of the uniform, and triangular distributions as kernel functions. These distributions allow for simple, tractable CDF, and allow us to exploit APPL's piecewise function processing capability. We have avoided the problem of negative lifetimes with these distributions by carefully choosing our example data values and so as to avoid negative support for the kernel function.

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Learning payoff functions in infinite games We consider a class of games with real-valued strategies and payoff information available only in the form of data from a given sample of strategy profiles. Solving such games with respect to the underlying strategy space requires generalizing from the data to a complete payoff-function representation. We address payoff-function learning as a standard regression problem, with provision for capturing known structure (e.g., symmetry) in the multiagent environment. To measure learning performance, we consider the relative utility of prescribed strategies, rather than the accuracy of payoff functions per se. We demonstrate our approach and evaluate its effectiveness on two examples: a two-player version of the first-price sealed-bid auction (with known analytical form), and a five-player market-based scheduling game (with no known solution). Additionally, we explore the efficacy of using relative utility of strategies as a target of supervised learning and as a learning model selector. Our experiments demonstrate its effectiveness in the former case, though not in the latter. Whereas there has been much work in game theory attempting to solve particular games defined by given payoff functions, relatively little attention has been devoted to inducing such functions from data. This work addresses the question of payoff function induction by introducing regression learning techniques and applying them to representative games of interest. We evaluate the quality of a learned game model in terms of the potential gain, , to deviating from an equilibrium solution of this approximate model, measured in terms of the true underlying game. Our results in both the FPSB and market-based scheduling games suggest that when data is sparse, regression methods can provide better approximations of the underlying game than direct estimation of a discrete model from the given data set. We observed this in cases where data points corresponded to actual or supposed actual payoff values, as well as cases where the given data comprises noisy samples of such payoffs. In the FPSB setting, we were able to artificially control for the amount of noise present in the data set, observing the dynamics of the payoff function approximation methods as the noise in the system decreased. A particularly interesting result in this case was that low-degree polynomial models exhibited an increasing advantage over discrete approximation as the variance of noise decreased.. In the market-based scheduling setting, we obtained two sets of training data with varying number of samples per profile. As a result, we were able to test our methods both in a noiseless setting, by using the data with the same number of samples per profile for both training and testing, and in a noisy setting, by using data with fewer samples per profile as the training set. We found that local regression and SVM learning methods generally outperformed discrete approximation in our experiments, both on noiseless and noisy training data. While locally weighted average shined when training data contained no noise, SVM model yielded better performance when noise was present.. We also introduced strategy aggregation as a way to control regression model complexity. The comparison between the various degrees of strategy aggregation provided mixed conclusions. In several settings, with and without noise, aggregating the strategies of other players appeared to provide no advantage in function approximation. In one setting, however, we did observe improved quality of equilibrium approximation when a particular form of strategy aggregation was used, as compared to no aggregation at all.. Having used the quality of the approximate equilibrium, , as a metric for the success of functional fit, we felt it natural to consider it explicitly as a model selection criterion. We evaluated it in comparison to model selection based on mean squared error of the payoffs on a test data set. Our results in the FPSB setting, however, were not favorable, as model selection based on the more direct measure of function accuracy provided better average performance.. Finally, we considered the possibility of learning (s) directly, rather than deriving it from a learned payoff-function model. In a series of experiments using FPSB as the game of choice, we observed mixed results. Whereas the noisy environment favored payoff function approximation, (s) performed relatively well when the data contained little or no noise.. In summary, we performed a series of experiments comparing several methods of payoff function regression, an alternative approach of learning (s), and exploring the possibility of using as a model selection criterion. Regression or other generalization methods offer the potential to extend game-theoretic analysis to strategy spaces (even infinite sets) beyond directly available experience. By selecting target functions that support tractable equilibrium calculations, we render such analysis analytically convenient. By adopting functional forms that capture known structure of the payoff function (e.g., symmetry or strategy aggregation), we facilitate learnability. By using (s) as a target of function approximation, we may in some cases be able to exploit structure that may not be as apparent in the more direct payoff function. This study provides some evidence of the efficacy of the different methods that we considered and the tradeoffs between them that emerge in different environments.

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