Brain-like Computing Based on Distributed Representations and Neurodynamics A key to overcoming the limitations of classical artificial intelligence and to deal well with enormous amounts of information might be brain-like computing in which distributed representations of information are processed by dynamical systems without using symbols. We present a method for such computing. We constructed an inference system using a nonmonotone neural network, which is a kind of recurrent neural network with continuous-time dynamics. This system deduces a conclusion according to state transitions of the network in which knowledge is embedded as trajectory attractors. It has the powerful ability of analogical reasoning without special treatment for exceptional knowledge. We also propose a method of linking different neurodynamical systems and show that two mutually interacting systems can process complex spatiotemporal patterns. It has been noticed that classical artificial intelligence (AI) based on sym-bolic manipulation has the symbol grounding problem 1) and the frame problem. The inferential system described above has the following brain-like features that most existing systems do not have.. (a) Analogy based on similarity between cue patterns A production system model, 22) a typical inference engine of classical AI, basically cannot make an inference unless all the knowledge necessary for leading to the conclusion have been given as "if-then" rules. By contrast, the present system can reason analogically using other knowledge. For example, the system answers "Eagle can fly" to a novel question "Can Eagle fly?" because Eagle is represented using a code pattern similar to <Sparrow >. Therefore, the network state is attracted to the trajectory attractor <Sparrow → Bird → can fly>.. (b) Analogy based on similarity between context patterns The system can perform analogical reasoning when the context is different but similar to a familiar context. For example, if the system knows that X can fly, then it is generally inferred that X has wings, even though it learned nothing about wings. This is because contexts <Flying Ability> and <Wing> are represented by similar patterns and trajectory attractors formed in the former context produce flows parallel to them in the subspace corresponding to the latter context. This feature is unique compared with other neural network models such as mixture of local experts models, in which each local network or "expert" is specialized to a particular context and generalization across different contexts does not occur.. (c) Nonmonotonic reasoning In general, inference systems with high ability of analogical reasoning suffer from exceptional knowledge. In stark contrast, systems that deal excellently with exceptional knowledge require numerous detailed rules and have difficulty using analogy. Although various methods have been proposed [23] [24] [25] [26] to cope with this dilemma, it seems impossible to solve it using classical AI approaches only because this problem is deeply related to the frame problem. However, the present system is not troubled by exceptional knowledge that causes a logical inconsistency because logical inferences are not used in this system.. For example, although Bat is a Mammal and is therefore represented by a similar code pattern to <Horse>, <Dog>, etc., the system replies "Bat can fly" to the question "Can Bat fly?" because exceptional knowledge has been given. Nevertheless, it performs analogical reasoning to other questions about Bat similarly as it does to questions about Horse and Dog (e.g. "Bat bears young"). In other words, the trajectory attractor <Bat → can fly> in the context <Flying Ability> does not much affect the flow from <Bat> toward <Mammal > in other contexts because the influence of trajectory attractors toward <Mammal > in various contexts, such as <Horse → Mammal > in <Flying Ability> and <Dog → Mammal > in <Breed>, is stronger.. For the same reason, the influence of exceptional knowledge in the same context is limited and does not impair the ability of analogical reasoning as long as the knowledge is exceptional. For example, when a novel cue pattern with equal similarities to <Bat> and to <Dog> is given in the context <Flying Ability>, the network state moves to <cannot fly> through the neighborhood of <Mammal >. Such an inference can be regarded as common-sense reasoning of a kind.. (d) Analogical reasoning using a structure of similarities among code patterns A crucial advantage of distributed representations over symbolic representations is that the relation among objects, like that shown in Fig. 3 , can be expressed implicitly by similarities or distances between code patterns. The present system can make good use of this advantage for inference.. For example, although the system has learned nothing about Fish in the context <Mobility> and has not learned explicitly that they belong to Animal in any context, it drew the conclusion that "Tuna moves." The process of inference is shown in Fig. 4(a) , in which the time course of similarities between the network state x and individual code patterns is shown (the abscissa is scaled by the time constant τ ). As this graph shows, the network state moves initially from <Tuna> toward <Fish> and <Animal > as a result of the influence of various trajectory attractors to them. Then it is attracted to the trajectory attractor <Animal → move>, which was formed when the system learned "Eagle is an Animal; consequently, moves." Similarly, the system infers "Tuna will die," as depicted in Fig. 4(b) , where the network state is carried by a flow along <Tuna → Fish → Animal >. It is then attracted to a trajectory attractor formed when the system learned "Duck, Cow and Apple are living. Consequently, will die." (e) Addition of knowledge Conventional multilayer neural networks confront the serious problem that previously acquired knowledge is disrupted suddenly in the process of learning a new set of knowledge, which is called catastrophic interference.. 21) The present system is, however, robust to additional learning of new knowledge.. In the experiment described above, for example, addition of knowledge about Fish caused no error in inference as to acquired knowledge because <Fish> is distant from other code patterns. Similarly, additional learning in a novel context <Death> has little influence on acquired knowledge.. However, if completely conflicting knowledge such as "Horse can fly" is added, some previous knowledge ("Horse cannot fly") is lost. Furthermore, the addition of exceptional knowledge can interfere with related general knowledge. In particular, addition of much exceptional knowledge of the same kind can change some general knowledge. Some examples are that if very many flightless birds are newly learned, the system will infer "it cannot fly" for an unknown bird. Nevertheless, the interference is actually limited in most cases. For example, even after the system additionally learned "Helicopter has no wings," it can infer by analogy that "Eagle has wings" and "Car has no wings.". To examine the interference effects more specifically, we gradually increased the amount of additional knowledge in the experiment described above while maintaining the ratio of exceptional knowledge around 20%. Ratio of added knowledge to the original shows the result in which the percentage of correct inferences as to original knowledge is shown against the ratio of added knowledge to the original. That figure shows that the rate does not decrease rapidly; it remains higher than 80%, even when a double amount of knowledge is added. This result indicates that the system can accumulate knowledge merely through occasional relearning. §4 Interaction between Neurodynamical Systems. The objects and concepts involved in the inference system presented above are represented by static patterns and can be symbolized, but we believe that a critical advantage of brain-like computing will be revealed when we deal with objects that are difficult to represent as symbols such as motions of the body. However, the system described above is insufficient for dealing with such objects because they should often be represented by spatiotemporal patterns and because a single neurodynamical system cannot process complex spatiotemporal patterns. Considering that the actual brain comprises many areas with specific functions working together, we describe in this section a method of linking multiple neurodynamical systems to construct a modular system.

O O O O B I 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 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 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 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


Applying CEGAR to the petri net state equation Abstract. We propose a reachability verification technique that combines the Petri net state equation (a linear algebraic overapproximation of the set of reachable states) with the concept of counterexample guided abstraction refinement. In essence, we replace the search through the set of reachable states by a search through the space of solutions of the state equation. We demonstrate the excellent performance of the technique on several real-world examples. The technique is particularly useful in those cases where the reachability query yields a negative result: While state space based techniques need to fully expand the state space in this case, our technique often terminates promptly. In addition, we can derive some diagnostic information in case of unreachability while state space methods can only provide witness paths in the case of reachability. Reachability is the fundamental verification problem. For place/transition Petri nets (which may have infinitely many states), it is one of the hardest decision problems known among the naturally emerging yet decidable problems in computer science. General solutions have been found by Mayr [12] and Kosaraju [7] with later simplifications made by Lambert [9] , but there are complexity issues. All these approaches use coverability graphs which can have a non-primitive-recursive size with respect to the corresponding Petri net. A new approach by Leroux [10] not using such graphs gives some hope, but a concrete upper bound for the worst case complexity so far eludes us. In a sense even worse, Lipton [11] has shown that the problem is EXPSPACE-hard, so any try at programming a tool efficiently solving this problem to the full extent must surely fail.. Nevertheless, efficient tools exist that are applicable to a considerable number of problem instances. Model checkers, symbolic [2] or with partial order reduction [17] , have been used successfully to solve quite large reachability problems. On a positive answer, a model checker can typically generate a trace, i.e. a firing sequence leading to the final marking. In contrast, negative answers are usually not accompanied by any diagnostic information. Such information, i.e. a counterexample or reasoning why the problem has a negative solution would require a deep analysis of the structure of the Petri net. So far, no tools are known that analyze the structure of a net and allow for such reasoning.. This paper presents an approach to the reachability problem that combines two existing methods. First, we employ the state equation for Petri nets. This is a linear-algebraic overapproximation on the set of reachable states. Second, we use the concept of counterexample guided abstraction refinement (CEGAR) [3] for enhancing the expressiveness of the state equation. In essence, we iteratively analyse spurious solutions of the state equation and add constraints that exclude a solution found to be spurious but do not exclude any real solution. The approach has several advantages compared to (explicit or symbolic) purely state space based verification techniques:. -The search is quite focussed from the beginning as we traverse the solution space of the state equation rather than the set of reachable states; -The search is close to breadth-first traversal, so small witness traces are generated; -The method may perform well on unreachable problem instances (where state space techniques compute maximum size state spaces); -In several unreachable problem instances, some kind of diagnostic information can be provided; -A considerable workload can be shifted to very mature tools for solving linear programming problems.. In Sect. 2 we give the basic definitions. Section 3 shows how to use integer programming tools to find candidates for a solution. Section 4 deals with the analysis of the Petri net structure that is needed to push the integer programming onto the right path.. In Sect. 5 we use methods of partial order reduction to mold the results of the integer programming into firing sequences solving the reachability problem. Finally, section 6 compares the results of an implementation with another model checker, showing that structure analysis can compete with other approaches. . is the number of occurrences of t in σ. For any firing sequence σ, we call ℘(σ) realizable.. As usual, places are drawn as circles (with tokens as black dots inside them), transitions as rectangles, and arcs as arrows with F (x, y) > 0 yielding an arrow pointing from x to y. If an arc has a weight of more than one, i.e. F (x, y) > 1, the number F (x, y) is written next to the arc. In case F (x, y) = F (y, x) > 0, we may sometimes draw a line with arrowheads at both ends.. Note, that the Parikh image is not an injective function. Therefore, ℘(σ) can be realizable even if σ is not a firing sequence (provided there is another firing sequence σ with ℘(σ) = ℘(σ )). Fig. 1 . The word tt cannot fire, but we can borrow a token from the circle uu , so utt u can fire and leads to the same marking as tt . The incidence matrix of the net is shown on the right. It is well-known that a necessary condition for a positive answer to the reachability problem is the feasibility of the state equation. It is possible to have a sequence σ such that its Parikh image fulfills the state equation but it is not a firing sequence. The easiest example for this occurs in a net N = ({s}, {t}, F ) with F (s, t) = 1 = F (t, s). Let m and m be the empty marking, i.e. one with zero tokens overall, then m[t m is obviously wrong but m + C℘(σ) = m holds since C = (0). The effect can occur whenever the Petri net contains a cycle of transitions. Interestingly, certain cycles of transitions can also help to overcome this problem, see Fig. 1 . Here, we would like to fire a word tt from the marking m with m(s 1 ) = m(s 2 ) = 0 and m(s 3 ) = 1, but obviously, this is impossible. If we borrow a token from s 3 , we can fire tt , or more precisely utt u . As we return the borrowed token to s 3 in the end we reach the same marking tt would have reached (if enabledness were neglected). We proposed a promising technique for reachability verification. For reachable problem instances, it tends to yield short witness paths. For unreachable instances, it may terminate early, without an exhaustive search. Furthermore, it may provide some diagnostic information in that case. Our approach applies the concept of counterexample guided abstraction refinement in a novel context: the abstraction is not given as a transition system but as a linear-algebraic overapproximation of the reachable states. In essence, we replace the search in the set of states by the more focussed search through the solutions of the state equation. The state equation as such has been used earlier for verification purposes, see for instance [4] . In [14] , it is used as an initial way of narrowing the state space exploration but not refined according to the CEGAR.

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


Automated design of operational transconductance amplifiers using reversed geometric programming We present a method for designing operational amplifiers using reversed geometric programming, which is an extension of geometric programming that allows both convex and non-convex constraints. Adding a limited set of non-convex constraints can improve the accuracy of convex equationbased optimization, without compromising global optimality. These constraints allow increased accuracy for critical modeling equations, such as the relationship between gm and IDS . To demonstrate the design methodology, a foldedcascode amplifier is designed in a 0.18 µm technology for varying speed requirements and is compared with simulations and designs obtained from geometric programming. The evolution of the microelectronics industry is characterized by an ever increasing level of integration and complexity. This trend has resulted from the industry's ability to exponentially decrease over time the minimum feature sizes used to fabricate integrated circuits. The greatest threat to the continuation of this evolution is the cost of design.. The recent trend towards systems-on-a-chip forces the rapid adoption of "digital" semiconductor technologies for analog/RF circuits and a shortening of the analog design cycle to coincide with the digital design cycle [7] . Analog/RF circuits account for an increasing portion of the design cost in mixed-signal chips, even though they typically occupy only a small fraction of the total chip area. This motivates analog design automation.. An important component in automated analog design is circuit synthesis, which consists of topology selection and circuit sizing. The first attempts at the analog sizing problem tried to capture the analog design knowledge heuristically, which proved to be too inflexible. Sizing methods using general purpose optimization techniques, whereby a cost metric, such as power or area, is minimized under a set of performance constraints, have been the subject of active research since the late 1980s [7] and offer the advantage of being straightforward to evaluate, and hence suitable for large and complex designs, but have the limitation of possibly finding local minima.. However, by using convex optimization, a global minimum can be computed with great efficiency [12] . Geometric programming is one particular form of convex optimization, which traditionally has been used for engineering design [5, 1] , and more recently also for analog circuit sizing [9] .. But this great computational efficiency comes at a price: the objective and the constraints have to be convex functions of the design variables. In section 3, we will give several examples of constraints which occur in analog design and which are essentially non-convex. Non-convex constraints are hard to approximate accurately with convex constraints, and this approximation leads to poorly optimized circuits.. Instead of approximating non-convex constraints with convex constraints, we can trade some of the efficiency in computing the solution for modeling accuracy in the constraints. For example, reversed geometric programming [4] , which is introduced in section 2.3, allows non-convex reversed constraints in addition to the regular convex constraints. where g k (x) is of the form. The functions g k (x) are called posynomials and the functions h l (x) monomials; both posynomials and monomials can only have strictly positive coefficients ci, but real exponents ai,j. An optimization program of the form GP is called a geometric program.. Notice that the equality constraints can only have a single term, since they have to be monomials.. It is well-known that the optimization program GP can be cast in a convex form by transforming the variables according to yj = log xj [5] . Hence, efficient computational techniques for general convex optimization problems, such as interior-point algorithms, can be applied to the transformed problem [12] . Operational transconductance amplifiers can be designed with accurate models using reversed geometric programming, an extension of geometric programming. Reversed geometric programming allows both convex and non-convex constraints. Adding a limited set of non-convex constraints allows accurate modeling of critical design equations and yields more efficient solutions.

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


Grid Vertex-Unfolding Orthogonal Polyhedra An edge-unfolding of a polyhedron is produced by cutting along edges and flattening the faces to a net, a connected planar piece with no overlaps. A grid unfolding allows additional cuts along grid edges induced by coordinate planes passing through every vertex. A vertexunfolding permits faces in the net to be connected at single vertices, not necessarily along edges. We show that any orthogonal polyhedra of genus zero has a grid vertex-unfolding. (There are orthogonal polyhedra that cannot be vertex-unfolded, so some type of "gridding" of the faces is necessary.) For any orthogonal polyhedron P with n vertices, we describe an algorithm that vertex-unfolds P in O(n 2 ) time. Enroute to explaining this algorithm, we present a simpler vertex-unfolding algorithm that requires a 3 × 1 refinement of the vertex grid. Two unfolding problems have remained unsolved for many years [DO05a] : (1) Can every convex polyhedron be edge-unfolded? (2) Can every polyhedron be unfolded? An unfolding of a 3D object is an isometric mapping of its surface to a single, connected planar piece, the "net" for the object, that avoids overlap. An edge-unfolding achieves the unfolding by cutting edges of a polyhedron, whereas a general unfolding places no restriction on the cuts. A net representation of a polyhedron finds use in a variety of applications [O'R00] -from flattening monkey brains [SSW89] to manufacturing from sheet metal [Wan97] to low-distortion texture mapping [THCM04] .. It is known that some nonconvex polyhedra cannot be unfolded without overlap with cuts along edges. However, no example is known of a nonconvex polyhedron that cannot be unfolded with unrestricted cuts. Advances on these difficult problems have been made by specializing the class of polyhedra, or easing the stringency of the unfolding criteria. On one hand, it was established in [BDD + 98] that certain subclasses of orthogonal polyhedra -those whose faces meet at angles that are multiples of 90 • -have an unfolding. In particular, the class of orthostacks, stacks of extruded orthogonal polygons, was proven to have an unfolding (but not an edge-unfolding). On the other hand, loosening the criteria of what constitutes a net to permit connection through points/vertices, the so-called vertex-unfoldings, led to an algorithm to vertex-unfold any triangulated manifold [DEE + 03] (and indeed, any simplicial manifold in higher dimensions). A vertex unfolding maps the surface to a single, connected piece P in the plane, but P may have "cut vertices" whose removal disconnect P .. A second loosening of the criteria is the notion of grid unfoldings, which are especially natural for orthogonal polyhedra. A grid unfolding adds edges to the surface by intersecting the polyhedron with planes parallel to Cartesian coordinate planes through every vertex. The two approaches were recently married in [DIL04] , which established that any orthostack may be grid vertex-unfolded. For orthogonal polyhedra, a grid unfolding is a natural median between edge-unfoldings and unrestricted unfoldings.. Our main result is that any orthogonal polyhedron, without shape restriction except that its surface be homeomorphic to a sphere, has a grid vertex-unfolding. We present an algorithm that grid vertex-unfolds any orthogonal polyhedron with n vertices in O(n 2 ) time. We also present, along the way, a simpler algorithm for 3 × 1 refinement unfolding, a weakening of grid unfolding that we define below. We believe that the techniques in our algorithms may help show that all orthogonal polyhedra can be grid edge-unfolded. The two algorithms we present share a common central structure, with the second achieving a stronger result; both are vertex-unfoldings that use orthogonal cuts only. We note that it is the restriction to orthogonal cuts that makes the vertex-unfolding problem difficult: if arbitrary cuts are allowed, then a general vertex-unfolding can be obtained by simply triangulating each face and applying the algorithm from [DEE + 03].. The (3 × 1)-algorithm unfolds any genus-0 orthogonal polyhedron that has been refined in one direction 3-fold. The bands themselves are never split (unlike in [BDD + 98]). The algorithm is simple. The (1 × 1)-algorithm also unfolds any genus-0 orthogonal polyhedron, but this time achieving a grid vertex-unfolding, i.e., without refinement. This algorithm is more delicate, with several cases not present in the (3 × 1)-algorithm that need careful detailing. Clearly this latter algorithm is stronger, and we vary the detail of presentation to favor it. The overall structure of the two algorithms is the same:. 1. A band "unfolding tree" T U is constructed by shooting rays vertically from the top of bands.. The root of T U is a frontmost band (of smallest y-coordinate), with ties broken arbitrarily.. 2. A forward and return connecting path of vertical faces is identified, each of which connects a parent band to a child band in T U .. 3. Each band is unfolded horizontally as a unit, but interrupted when a connecting path to a child is encountered. The parent band unfolding is suspended at that point, and the child band is unfolded recursively.. 4. The vertical front and back faces of each slab are partitioned according to an illumination model, with variations for the more complex (1 × 1)-algorithm. These vertical faces are attached below and above appropriate horizontal sections of the band unfolding.. The final unfolding lays out all bands horizontally, with the vertical faces hanging below and above the bands. Non-overlap is guaranteed by this strict two-direction structure. Although our result is a broadening of that in [DIL04] from orthostacks to all orthogonal polyhedra, we found it necessary to employ techniques different from those used in that work. The main reason is that, in an orthostack, the adjacency structure of bands yields a path, which allows the unfolding to proceed from one band to the next along this path, never needing to return. In an orthogonal polyhedron, the adjacency structure of bands yields a tree (cf. Fig. 1b) . Thus unfolding band-by-band leads to a tree traversal, which requires traversing each arc of the tree in both directions. It is this aspect which we consider our main novelty, and which leads us to hope for an extension to edge-unfoldings as well.

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


Minimal Energy Asynchronous Dynamic Adders In battery-operated portable or implantable digital devices, where battery life needs to be maximized, it is necessary to minimize not only power consumption but also energy dissipation. Typical energy optimization measures include voltage reduction and operating at the slowest possible speed. We employ additional methods, including hybrid asynchronous dynamic design to enable operating over a wide range of battery voltage, aggregating large combinational logic blocks, and transistor sizing and reordering. We demonstrate the methods on simple adders, and discuss extension to other circuits. Three novel adders are proposed and analyzed: A two-bit PTL adder and two dynamic two-bit adders. Circuit simulations on a 0.18μm process at low voltage show that leakage energy is below 1% and that short-circuit energy depends on circuit topology and can be as high as 50% of total energy when operating at low voltage and low fanout. The proposed adders achieve up to 40% energy savings relative to previously published results, while also operating faster. Certain digital battery-operated portable or implanted systems require maximum battery life. To achieve that goal, the designer needs to minimize energy dissipation (rather than optimizing for low power). One useful means is to allow operating at the slowest possible computational speed, and this is possible in devices such as hearing aids in which the computational requirements are limited. Another obvious method is operating at the lowest possible supply voltage. In addition, many batteries provide a varying level of voltage over their lifetime, and the circuit be better designed to accommodate a wide range of supply voltages. Such voltage variation results in wide delay variation.. Common approaches to low power and low energy design include the following. Asynchronous, delayinsensitive circuits [1] - [13] enable operation over a wide voltage range. Some of them employ dual rail logic [1] - [4] , others use single-rail design [5] - [9] [26] , while still others combine single-and dual-rail for further energy minimization [10] - [13] . General purpose programmable instruction-execution based processors are avoided when possible, to eliminate the energy required for instruction fetch and decode [1] [2] [14] [15] . A variety of low power / low energy circuit techniques are proposed in [14] [16]- [20] .. Adders are representative of signal processing architectures, and the results can be extended to other data path circuits. Fast static, bundled-data asynchronous adders are described in [26] [27] . Both papers describe various speed-up techniques that may trade-off power efficiency for speed. These techniques are best avoided when the lowest energy per computation is sought. Thus, we focus on ripple-carry adders. References [26] [27] also indicate power and energy advantages of asynchronous adders, but are inconclusive regarding whether static or dynamic circuits would dissipate lower energy. In this paper we focus on dynamic adders.. We consider some previously published low energy dynamic adders [11] [21]- [23] and apply a number of transformations to them, resulting in three novel architectures. The transformations include various topology changes, the aggregation of full-adders into larger combinational circuits, the combination of dual-and single-rail asynchronous logic, proper transistor sizing, and transistor reordering to minimize the charge drawn from the supply. We operate the circuits at the lowest possible voltage, and consider their operation over a wide range of voltages.. We discuss four previously published low power adders in Section 2, and introduce three novel adders in Section 3. Circuit simulation analysis on a 0.18μm process is presented in Section 4, where we show that leakage energy is negligible, short-circuit energy can be significant depending on circuit topology, and in general our Minimum Energy Dual-Bit Dynamic adder achieves up to 40% energy savings while operating up to 60% faster than the other adders. In this work we describe some existing techniques for energy minimization and their application to asynchronous dynamic adders. These techniques include simpler ripple-carry adders without redundant logic (which consumes extra energy), using minimal size transistors for capacitance reduction, and selecting circuit topologies that minimize switching activity. Some existing adders are introduced in Section 2 and low energy characteristics of each one are emphasized. Based on these techniques and some additional methods described in Section 3, we have defined and proposed the following rules for energy minimization:. • Combine asynchronous dual-and single-rail circuits. • Employ large blocks of combinational logic. • Connect the last transitioning input signal as close as possible to the precharged output. The advantages and energy minimization contribution can be summarized as follows.. Energy dissipation simulation results ( Table 1) show that larger blocks of logic save 16-20% of energy thanks to reducing the number of wires and transistors, as well as the number of blocks. Buffers are eliminated and consequently the number of transitions is reduced (cf. the Chong and DBPTL columns relative to Nielsen and PTL, respectively, and consider also Figure 12 ). This observation provides a strong incentive to design larger blocks of logic in order to gain maximal energy reduction.. Correct transistor ordering provides additional energy savings, thanks to decreasing the number of charged/discharged nodes. Thus, the DDBR adder consumes 10% less energy than the Chong adder and the MEDB adder saves up to 20% energy, despite the fact that it was implemented using the same set of logic expressions [22] .. Decreasing supply voltage contributes about 20% energy savings per each 0.1V (see Figure 12 ).. We conclude that the proposed set of rules can lead of up to 40% energy reduction, as can be observed by comparing the Nielsen and MEDB adder columns in the table.. Regarding delay simulations ( Table 2) , for most levels of supply voltage (above 0.8V), the dual-bit basic adder cells in Chong and DBPTL reduce delay by 13% and 27% relative to their single-bit dynamic and PTL counterparts, respectively, thanks to using fewer blocks and buffers. Optimal transistor ordering improves performance almost twofold, thanks to the fact that the amount of charge in the output nodes is smaller than in the original Chong's adder and charging and discharging are faster.. The energy and delay results are combined in Figure 16 and Figure 15 : The MEDB adder exhibits more than 60% savings in ET and more than 80% in ET 2 , relative to the Nielsen and Chong adders.. Having considered adders, we take advantage of the fact that the carry signal arrives last. Other circuits do not necessarily have this characteristic. However, it might be worthwhile to delay one of the input signals relative to the others and use it to gate an NMOS transistor placed as close as possible to the output node, to save precharge and evaluation energy. Novel asynchronous low energy dynamic adder circuits have been introduced and analyzed: A dynamic dual-bit reodered (DDBR) adder, an asynchronous dual-bit PTL (DBPTL) adder, and a minimum energy asynchronous dual-bit dynamic (MEDB) adder. We first reviewed some existing circuits, which exploited large combinational blocks, dynamic logic, hybrid single-and dual-rail, and path-transistor logic. We employed similar techniques, and also added transistor reordering to assure that the last transitioning signal is connected as close as possible to the precharged output. We eliminated redundant logic, employed only minimum size transistors, and sought to minimize transitions whenever possible. As a result, we show that larger blocks of logic saved up to 20% energy, transistor reordering saved about 20% energy, and operating at the lowest supply voltage enabled even further energy savings. The circuits are shown superior not only in terms of energy but also in terms of ET and ET

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


Interactive training of advanced classifiers for mining remote sensing image archives Advances in satellite technology and availability of downloaded images constantly increase the sizes of remote sensing image archives. Automatic content extraction, classification and content-based retrieval have become highly desired goals for the development of intelligent remote sensing databases. The common approach for mining these databases uses rules created by analysts. However, incorporating GIS information and human expert knowledge with digital image processing improves remote sensing image analysis. We developed a system that uses decision tree classifiers for interactive learning of land cover models and mining of image archives. Decision trees provide a promising solution for this problem because they can operate on both numerical (continuous) and categorical (discrete) data sources, and they do not require any assumptions about neither the distributions nor the independence of attribute values. This is especially important for the fusion of measurements from different sources like spectral data, DEM data and other ancillary GIS data. Furthermore, using surrogate splits provides the capability of dealing with missing data during both training and classification, and enables handling instrument malfunctions or the cases where one or more measurements do not exist for some locations. Quantitative and qualitative performance evaluation showed that decision trees provide powerful tools for modeling both pixel and region contents of images and mining of remote sensing image archives. Remotely sensed imagery has become an invaluable tool for scientists, governments, military and the general public to understand the world and its surrounding environment. Military applications include using land cover classification to derive tactical decision aids like landing zone and troop movement plans, to manage ecosystems of military lands and waterways, and to study interactions between mission activities and ecological patterns. Similarly, land cover maps help civil users to perform land use monitoring and management, fire protection, site suitability, agricultural and public health studies.. The amount of data received from satellites is constantly increasing. For example, NASA's Terra satellite sends more than 850GB of data to Earth every day [15] . Automatic content extraction, classification and content-based retrieval have become highly desired goals to develop intelligent remote sensing image databases. State-of-the-art remote sensing image analysis systems aid users by providing classification tools that use spectral information or texture features as the input for statistical classifiers that are built using unsupervised or supervised algorithms. The most commonly used classifiers are the minimum distance classifier and the maximum likelihood classifier with a Gaussian density assumption. Spectral signatures and other features do not always map conceptually similar patterns to nearby locations in the feature space and limit the success of minimum distance classifiers. Furthermore, these features do not always have Gaussian distributions so maximum likelihood classifiers with this assumption fail to model the data adequately.. Like any data analysis problem, domain knowledge and prior information is very useful in land cover classification. Incorporating supplemental GIS information and human expert knowledge into digital image processing has long been acknowledged as a necessity for improving remote sensing image analysis [8] . Artificial intelligence research and developments in rule-based classification systems have enabled a computer to mimic the heuristics and knowledge that a human expert uses in interpreting an image. Consequently, rule-based classification systems [10] have been successfully used for fusion of spectral and ancillary data in applications such as land cover classification [8, 11] , land cover change monitoring [17] , sea ice classification [18] , and ridge line extraction from Digital Elevation Model (DEM) data [14] .. However, a common problem in all of these attempts has been the translation of expert knowledge to a computer-usable format. First, remotely sensed data are converted into formats supported by statistical analysis packages; then, these packages are used to create rules; finally, the rules are re-formatted so that they can be used in a rule-based image classifier [8, 11] . Today, commercial-of-the-shelf remote sensing image analysis systems have rule-based classification modules but they operate on individual scenes and require an expert to create the rules. This requirement for an enormous amount of manual processing even for small data sets makes knowledge discovery in large remote sensing archives practically impossible.. The VisiMine system [9] we have developed supports interactive classification and retrieval of remote sensing images by modeling them on pixel, region and scene levels. Pixel level characterization provides classification details for each pixel with regard to its spectral, textural and other ancillary attributes. Following a segmentation process, region level features describe properties shared by groups of pixels. Scene level features model the spatial relationships of the regions composing a scene using a visual grammar. This hierarchical scene modeling with a visual grammar aims to bridge the gap between features and semantic interpretation.. This paper describes our work on developing decision treebased tools to automate the process of acquiring knowledge for image analysis and mining in remote sensing archives. Decision tree classifiers are used to model image content in pixel and region levels. VisiMine provides an interactive environment for training customized semantic land cover labels from a fusion of visual attributes. Spectral values, ancillary GIS layers and other image attributes like textural features are used in decision tree learning. The learning process also includes algorithms for handling missing data and automatic conversion of models into rule bases.. The rest of the paper is organized as follows. The system architecture and data used in the experiments is introduced in Section 2. The classifiers used for land cover modeling are described in Section 3. User interaction tools for training and evaluating these models are presented in Section 4. Performance evaluation for the proposed system is discussed in Section 5. Conclusions are given in Section 6. We described decision tree and rule-based tools for building statistical land cover models using our VisiMine system for interactive classification and mining of remote sensing image archives. The decision tree classifiers and the corresponding rules proved to be very powerful in building land cover models by fusing data from different numerical and categorical data layers. They were also very robust to missing data and provided efficient land cover models with a small amount of training examples.. We compared the decision tree classifier with the rulebased classifier. Classification accuracy for generalized rules was very similar to (even slightly higher than) the one for the decision tree classifier. We also compared these two classifiers with the unsupervised k-means clustering algorithm and the supervised minimum distance classifier. The decision tree classifier appeared superior, not only in its capability to handle numerical as well as categorical data and to cope with missing data values, but also in regard to handling pure numerical feature data. The Gabor features that we used as an additional ancillary data layer were also quite useful especially in smoothing noisy Aerial data. Micro-texture analysis algorithms like Gabor features are useful for modeling neighborhoods of pixels and distinguishing areas that may have similar spectral responses but have different spatial structures.. Our current work includes modeling interactions between multiple regions using region spatial relationships and using these relationships for mining image archives to find characteristic features that can distinguish different scene classes, and learning of decision forests as ensembles that use multiple decision tree classifiers. We believe that incorporating spatial relationships information into the region level rules will help modeling of higher-level structures that cannot be modeled by individual pixels or regions and will provide remote sensing analysts with very valuable tools.

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


A Generalized Discrete Event System (G-DEVS) Flattened Simulation Structure: Application to High-Level Architecture (HLA) Compliant Simulation of Workflow The objective of the paper is to specify a new flattened Generalized Discrete Event System simulation engine structure and the Workflow modeling and simulation environment embedding it. We express first the new flattened simulation structure and give the corresponding transformation functions. We analyze performance tests conducted on this new simulation structure to measure its efficiency. Then, having selected the essential concepts in the elaboration of the Workflow, we present a language of description to define the Workflow processes. Finally, we define a distributed Workflow Reference Model that interfaces components of the Workflow with respect to the HighLevel Architecture standard. Today enterprises can take advantage of this platform in the context of networking where interoperability, flexibility, and efficiency are challenging concepts. The Discrete Event System (DEVS) [1] is a well-known formalism used to describe the behavior of complex systems. Its formal framework separates modeling from a simulation process. The DEVS is a powerful modeling and simulation (M&S) formalism, with a clear semantics and modular approach. It is based on event and state concepts (the simulation is event driven, which makes it faster). However, we based our works on the DEVS extension: the Generalized-DEVS (G-DEVS) [2] . In this formalism, event and state trajectories are polynomials (multi-values) instead of piecewise linear constants trajectories like the DEVS, and thus represent complex continuous phenomena more precisely. On the simulation side, the G-DEVS keeps the DEVS semantics specification. Nevertheless, the hierarchical simulation structure in the DEVS/G-DEVS results from the user-specified modeling structure (e.g. multi-hierarchical imbrications' reuse of previous models)1 we postulate that this feature is not required at simulation run time. From that postulation, we propose a new simulation structure that is simplified (flattened) to increase execution speed.. An applicative goal of such a M&S structure can be found in representing industrial processes (Workflow). Indeed, this field is recent (early 1990s [3] ) and not fully standardized. The Workflow Management Coalition (WfMC) works at standardizing this field1 it provides a consistent high-level framework to develop the business process. The Workflow specification involves different tasks, items, applications, and actors that are essential to its execution. This specification is quite intuitive (it can be automatically generated from a graphical specification) and the user does not need to develop programming code. The lack of Workflow M&S is, in addition to most vendor tools not conforming to the WfMC standard, the missing formal simulation semantics associated with Workflow engines. Clearly, the Workflow M&S is a semi-formal language to model user requirements and then, most of the Workflow simulations engines are ad hoc. Consequently, the Workflow does not guarantee formal and clear semantics. This fact may lead to incompatibility and errors that are difficult to detect (such as coding errors, codes that do not conform to the Workflow specification, etc.). A solution could exist in more formal modeling1 however, Workflow users are not familiar with formal specifications (e.g. DEVS). Thus we have proposed in [4] to automatically transform high-level graphical Workflow specifications to G-DEVS models feeding a new embedded efficient G-DEVS simulator. In addition, current complex industrial processes need to interoperate [5] , being combined, and to cooperate with heterogeneous distributed components. High-level Architecture (HLA) is a distributed simulation and execution standard originally defined for interoperability of US military simulation tools and now employed in the civilian domain1 it can address actual enterprise requirements. From the preceding enounced challenges and to address their requirements, we introduce in this paper a HLA-compliant Workflow Modeling Environment.. The paper is organized as follows. Section 2 gives an overview of the G-DEVS, HLA, and Workflow. Section 3 details the specification of the new flattened G-DEVS simulation structure proposed, gives the transformation functions, and reports on performance results of this new simulator. Section 4 presents the integration of the G-DEVS flattened simulator in a HLA context. Section 5 introduces the application field of our environment and gives the key points to transforming a Workflow graphical specification into a G-DEVS executable model. In addition, we describe the new HLA-compliant Workflow Modeling platform. Finally, we conclude by introducing our future works and conclusion. This paper presented a flattened G-DEVS model simulation structure. It detailed the flattening transformation algorithm involved in LSIS_DME. We have performed comprehensive tests on the LSIS_DME flattened simulator. The results reveal that the flattening of the simulation structure shortened the simulation duration. However, the efficiency of the flattening remains dependent on the number of events handled and the complexity of the model. As perspectives, we will propose to divide the event list into several lists, to distinguish events in near occurrence time and the far future. Such heuristics, which have shown their efficiency in scheduling problem solving, should considerably reduce the size of the event lists and improve sorting duration each time an occurred event should be handled in this list. In addition, in order to prove the efficiency of the flatten simulator with regard to the hierarchical one, we could compute the algorithmic complexity of each simulator. Once this is known, previously to conduct the simulation on a computer, we should formally estimate the heap memory and the execution time of each technique (flattened, hierarchical). This will be possible by giving a detailed study on the computational complexity of the algorithms used and data structure of the simulation (sort events, number of coordinators, number of event lists that depends on the number of coordinator, etc.).. We proposed to employ the new flattened structure for simulating complex Workflow models in the G-DEVS formalism. Consequently, G-DEVS Workflows models can be verified faster by simulation. Furthermore, we introduced a new HLA-compliant Workflow environment using the flattened G-DEVS structure that speeds the local execution and so orchestrates the distributed components faster. We have verified, on this occasion, that the use of the HLA specification facilitates connecting the G-DEVS components defined in the paper with other heterogeneous HLA-compliant components in the Workflow environment.. Finally, the application field of research on Workflow and, more generally, process modeling has been a fast growing research domain during recent years, and it is still a promising domain, in particular for service orchestration in the enterprise. The European International Virtual Laboratory for Enterprise Interoperability [32] has recently defined interoperability as a science for enterprise modeling1 this confirms the actual high interest of enterprises for distributed and interoperable information systems solutions (systems of systems, enterprise 2.0). We believe the crossing of research domains, Workflow M&S and HLA, will facilitate supporting the next-generation of information systems for interoperating networked enterprises.

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


Detecting Object Boundaries Using Low-, Mid-, and High-level Information Object boundary detection and segmentation is a central problem in computer vision. The importance of combining low-level, mid-level, and high-level Object boundary detection and segmentation is a key problem in computer vision. It has been well accepted that low-level cues such as classical edge detectors are insufficient to perform this task. For example, Fig. 1 shows the results of the Canny edge detector [3] when applied to horse images [2] . It is a nontrivial problem to detect the horse boundary from the edge map. Marr conceived an outline of a solution for this problem [13] by combining low-, mid-, and high-level cues. Despite promising work in this direction [4, 21, 5, 15] , no complete solution has been established so far. Recently, the problem of combining low-,mid-, and highlevel information for this task has become more tractable due to progress in machine learning and statistics. Borenstein et al. [2] combined top-down information (configuration on learned image patches) and bottom-up approaches (segmentation based on intensity) for figure-ground segmentation. In the image parsing framework [18] , datadriven techniques (bottom-up) were used to guide generative (top-down) inference. Fergus et al. [8] built a top-down model based on features extracted by interest point operators. Conditional Markov random fields models [10, 16] have been used to enforce local consistency between neighboring structures. Combining both top-down and bottomup learning in a loop is emphasized in [20] . OBJCUT [12] also combined different levels of information and performs segmentation by graph cuts.. These approaches have shown the promise of combining low-level and high-level information. However, when, where and how to combine different channels of information is yet unclear. For example, the image parsing algorithm [18] assumes that generative models are available for modelling the appearance of objects, but no existing generative models are able to capture the complex appearance patterns of the horses in Fig. 1 . The patches used in [2] cannot deal with large scale changes and they also have difficulties in capturing the complex variations in appearance. Some approaches like [8, 10, 16] rely on representing features and are unable to locate object boundaries. Other ap-proaches, while effective, lead to complex models which require solving time consuming inference problems [20, 12] .. In this paper, we use learning based methods to combine different levels of information both implicitly and explicitly. This results in simple models which require only simple inference and can be computed in about one minute. We rely on the probabilistic boosting tree (PBT) [17, 6] algorithm to learn models for low-level and mid-level cues while implicitly taking high-level context into account, then we use shape matching [19] to supply explicit high-level information and to parse the horses into head, back, legs, and other parts. Stacking [23] builds classifiers on top of other classifiers and, thus, is slightly related to our approach. However, stacking is a general term rather than a specific algorithm.. We compare our system with other approaches which have tackled this problem. The most directly comparable approach is the work of Ren et al. [14] which gives detailed performance evaluations for combining low-,mid-, and high-level information. Our results show significant improvements at all levels. It is less easy to make direct comparison with other works [2, 12, 20] because some of them were not evaluated on large testing datasets, and the details of performance evaluation were not given for others. Also some approaches [12, 20] used color images, which are less challenging than gray-scale images we are using. Our approach is a very simple and clear one, and it only needs about 1.5 minutes on an ordinary PC for a typical image, while speed is not reported in other works. Our system was trained on 100 randomly selected images from a dataset consisting 328 horse images [2] . The dataset also contains manually annotated ground truth boundaries. We use the remaining images for testing and we work on gray scale images. Section 5 gives an outline of our algorithm. First, we adopt the BEL edge detector [6] for detecting object boundaries. The training and testing procedures are briefly described in section 3.2. Similarly, we can train a classifier to classify pixels on the foreground regions, which are horse bodies in this paper. We use the same procedures as those for training/testing the boundaries, with different positive and negative examples.. Both the detectors share the same set of candidate features in training, e.g. different Haar filters with different sizes at various locations [22] , and histogram features on various Gabor functions. Not surprisingly, the boundary classifier mostly selects Haar filters and the body detector picks more histogram features, which are effective in capturing the complex appearances of the foreground. Fig. 8a shows some testing images and we can see that they have large variations in texture, pose, scale, and lighting patterns. Examples of the detected boundaries and the foreground regions are shown in Fig. 8b and Fig. 8c , respectively. The training stage needs about 10 hours on a computer with 2.4GHz CPU and 1.0GB memory and the testing stage only needs about 15 seconds for a typical 300 × 200 gray scale image.. After the first level information (boundaries and foreground regions) is obtained, we train another classifier to account for more middle level information. We can either use that for the "short-range" or the "long-range" context information. The procedure is stated in section 3.3. In practice, the classifier for short-range context information gives slightly better results (see Fig. 7 ). One possible reason is that the long-range context considers the affinity between two boundary points. Though they have some consistency in terms of normal direction, curvature, and texture, they observe more variations. This makes the classification task more difficult. We use short-range context classifier in this paper, which combines information from Canny edges at a small scale, and both the boundary and body maps. Once trained, the classifier gives refined boundaries on the testing images, see Fig. 8(d) . This step gives the biggest performance improvement in our system. Once refined object boundaries are obtained, we then use high level shape information to further improve the results. Rather than using an average template of all the training examples [14] , we represent our shape model by a mixture model based on all the training examples. We sample around 300 points from a refined boundary map. Each template in the 100 training examples is used to match against these points using the method described in [19] . The best match with the lowest energy is then used. The time spent on matching is about one minute although we have 100 templates. Moreover, since we can annotate each segment of template boundaries, e.g. head, back, legs, the matching result also provides identified parts. Therefore, not only can we detect the object boundaries, but also we are able to tell where the body parts are. This shape matching process obtains an approximation to minimizing the energy function in Eqn. 1. Based on the matched results, we can further remove some false alarms and infer some missing parts. Fig. 7 shows a precision-recall curve after this procedure and Fig. 8(e) demonstrates the final results for some testing images and the different parts of the horses are labelled according to the matching results. The last two rows in both the columns Fig. 8(e) show the "failure" examples by our algorithm, which are due to confusing and cluttered backgrounds.. The shape matching results can further be used to eliminate the false alarms from the body map and thus we can get a cleaner probability map. When thresholding the resulting probability body map at 0.1, we get 95% of the foreground and 76% of the background in the manually labelled map coincide with our classification result. This is better than the performance reported in [2, 20] .. We evaluated our system using precision-recall rates; see the curves in Fig. 7 . Compared to [14] , our system achieves better performance with even fewer training images and more testing images. There are other works [2, 20, 12] in the literature which tackled the same problem. However, [20] and [12] worked on color images while we only used gray scale images. Moreover, the details of the performance evaluation in [2, 20, 12] are not so clear. The speed of our algorithm is about 1.5 minutes per image, while speed is not reported in all the above works. Figure 7 . Precision-recall curves by our results on the testing images (three black curves). Results on the same dataset from [14] are also displayed for a comparison (three grey/green curves). The dotted curve shows the result of using long-range context information. The F value shown in the legend is the maximal harmonic mean of precision and recall and provides an overall ranking.

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


Developing for autism with user-centred design This paper describes the process undertaken to develop software that allows children with Autism Spectrum Disorders (ASD) to explore social situations, in particular the concept of sharing. The User-Centred Design (UCD) process is described, along with adaptations made to alleviate anxiety resulting from the reduced social skills seen in ASD. In the typically developing population, the ability to display appropriate social skills is developed through scaffolding by parents and caregivers from an early age [1] . In Autism Spectrum Disorders (ASD), the typical trajectory of development is compromised. Affecting more than 500,000 people in the UK [2] , there is a lack of appreciation of the thoughts, beliefs and feelings of others (Theory of Mind) [1] , with established difficulties in social interaction, social communication and social imagination. This lack of social competency can result in significant difficulties in daily living, academic achievement and poor adult outcomes related to employment and social relationship [3] . One particular area of difficulty is sharing, a complex behaviour that forms the basis of many friendships.. The use of technology is limited within the scope of developing social skills, despite those with Autism Spectrum Disorders having a natural affinity with computers [4] due to the predictable and repeatable nature of technology. Furthermore, little work has been conducted in the area of User-Centred Design with children with ASD. This research seeks to involve children with ASD as a valuable source of design inspiration throughout the design and development of the system. The system developed aims to allow children to increase their awareness of their sharing abilities through exploration of these skills in a safe and predictable environment. Through the implementation of User-Centred methodologies, the software developed aims to allow children with ASD to explore their social skills in relation to sharing. The system will be evaluated within a special school to assess the potential of the software to improve children's awareness of sharing.

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


NUMERICAL APPROXIMATION OF VECTOR-VALUED HIGHLY OSCILLATORY INTEGRALS Abstract We present a method for the efficient approximation of integrals with highly oscillatory vector-valued kernels, such as integrals involving Airy functions or Bessel functions. We construct a vector-valued version of the asymptotic expansion, which allows us to determine the asymptotic order of a Levin-type method. Levin-type methods are constructed using collocation, and choosing a basis based on the asymptotic expansion results in an approximation with significantly higher asymptotic order. We are concerned with numerically approximating integral. where f : R → R d is a smooth vector-valued function and y : R → R d is a smooth, highly oscillatory vectorvalued function. We assume that y depends on a parameter ω that determines the frequency of oscillations. We also assume that y satisfies the differential equation where Ai is an Airy function and J m is a Bessel function [8] .. For large values of ω, traditional quadrature techniques fail to approximate I[f ] efficiently. Unless the number of sample points is sufficiently greater than the frequency of oscillations, the relative error of GaussLegendre quadrature increases drastically as the frequency increases. In the one-dimensional case of y = e iωg with no stationary points, the integral I[f ] is O ω −1 for increasing ω [12] . This compares with an error of order O(1) of the traditional quadrature methods [3] . This implies that it is more accurate to approximate I[f ] by zero than to use Gauss-Legendre quadrature! The goal of this paper is to generalize a method developed by Levin in [7] to obtain higher asymptotic orders. This will be accomplished in a similar vein to the Levin-type method [9] , which generalized the original Levin collocation method [6] , where the kernel was y = e iωg . In [9] , the asymptotic expansion was used to determine the asymptotic behaviour of the error of a Levin-type method. Thus our first task is to derive a vector-valued kernel version of the asymptotic expansion. This is accomplished in Section 3, using the asymptotic tools developed in Section 2. With an asymptotic expansion in hand, we can successfully find the order of error for a Levin-type method in Section 4. In [9] , it was noted that choosing a particular basis for a Levin-type method causes the asymptotic order to increase without the need for nontrivial multiplicities. In Section 5, we construct a vector-valued version of such a basis, allowing us to obtain higher asymptotic orders with significantly smaller systems.. Remark : After the original submission of this article, the author became aware of contemporary research by Shuhang Xiang with similar results to Theorem 3.1 and Corollary 4.2. Xiang's work is unpublished as of April 2007. The matrix 1 p×q , where p and q are implied by context.. The row vector 1 1×q , where the dimension q is implied by context.

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