Stochastic Exploration of Ambiguities for Nonrigid Shape Recovery Abstract-Recovering the 3D shape of deformable surfaces from single images is known to be a highly ambiguous problem because many different shapes may have very similar projections. This is commonly addressed by restricting the set of possible shapes to linear combinations of deformation modes and by imposing additional geometric constraints. Unfortunately, because image measurements are noisy, such constraints do not always guarantee that the correct shape will be recovered. To overcome this limitation, we introduce a stochastic sampling approach to efficiently explore the set of solutions of an objective function based on point correspondences. This allows us to propose a small set of ambiguous candidate 3D shapes and then use additional image information to choose the best one. As a proof of concept, we use either motion or shading cues to this end and show that we can handle a complex objective function without having to solve a difficult nonlinear minimization problem. The advantages of our method are demonstrated on a variety of problems including both real and synthetic data. F OR the purpose of single view deformable 3D shape reconstruction, approaches that rely on purely geometric constraints can return incorrect answers because there are often many different shapes that obey, or nearly obey, these constraints while producing very similar projections.. For example, it has been shown that nonrigid 3D shape could be recovered from even single images provided that enough correspondences can be established between that image and one in which the surface's shape is already known [25] , [27] , [37] . Yet, while effective, these techniques return one single reconstruction without accounting for the fact that several plausible shapes could produce virtually the same projection and therefore be indistinguishable on the basis of correspondences and geometry alone. In practice, as shown in Fig. 1 , disambiguation is only possible using additional image information.. In this paper, we propose a generic approach to exploring the space of feasible solutions, which is grounded on the theory of uncertainty propagation and stochastic search. More specifically, we represent shape deformations as a weighted sum of deformation modes and relate uncertainties on the location of point correspondences to uncertainties on the modal weights. This lets us explore the space of modes using a stochastic sampling strategy and select a small number of ambiguous solutions which correspond to 3D nonrigid shapes such as those shown in Fig. 1 . As a proof of concept, we then propose two different approaches to disambiguation.. . Exploiting shading information. The best 3D shape is chosen among the candidates generated in this manner using shading information, both when the light sources are distant and when they are nearby. The latter is particularly significant because exploiting nearby light sources would involve solving a difficult nonlinear minimization problem if we did not have a reliable way to generate 3D shape hypotheses. In our examples, this is all the more true since the lighting parameters are initially unknown and must be estimated from the images. . Enforcing temporal consistency. Assuming that a video sequence is available, we will exploit threeframe sequences to pick the set of candidate 3D shapes that provides the most temporally consistent motion. Note that in contrast to traditional tracking and nonrigid shape from motion approaches [5] , [24] , [31] , [35] , we do not enforce temporal consistency across the whole sequence and therefore do not require points to be tracked across many images. We show that both these approaches outperform stateof-the-art nonrigid shape recovery methods [23] , [28] , and allow disambiguating 3D shapes without having to learn complex mappings or tracking a large number of frames.. In short, the contribution of this paper, which extends an earlier conference paper [22] , is an approach to avoiding being trapped in the local minima of a potentially complicated objective function by efficiently exploring the solution space of a simpler one. As a result, we only need to evaluate the full objective function for a few selected configurations, which implies we could use a very discriminating and expensive one if necessary. Geometry-based approaches to single view 3D reconstruction can easily return erroneous solutions that both satisfy the constraints and yield plausible reprojections. To overcome this problem, given that the input data is noisy, we use error propagation techniques to derive an analytical expression of the space of potential solutions and to propose a small but representative number of samples. The best among them can then be chosen using additional image cues, such as shading or motion, which significantly improves results at a limited computational cost.. We have demonstrated the effectiveness of this approach for 3D deformable shape reconstruction. However, our approach relies on representing deformation as weighted sums of deformation modes, which somewhat reduces its applicability. In future work, we will therefore seek to extend it using first order matrix perturbation theory [9] to reason directly in the space of vertex positions. While applying this relaxation of the problem would require having to consider much larger sampling densities, we believe it can be feasibly addressed in the context of specialized Monte Carlo techniques such as the Partitioned Sampling proposed in [19] . . For more information on this or any other computing topic, please visit our Digital Library at www.computer.org/publications/dlib. In this section, we will evaluate the performance of the proposed algorithm. Since one of the core elements of our approach is the exploration strategy described in Section 3, we will first perform an analysis that will bring to light its benefits compared to alternative strategies for exploring the solution space. We will then evaluate the whole methodology for recovering nonrigid shape and will compare to other state-of-the art approaches. Single-view 3D reconstruction of nonrigid surfaces has been extensively studied over the years. It is known to be a highly underconstrained problem that cannot be solved without a priori knowledge.. A typical approach to introducing such knowledge is to use deformation models, either physically inspired [7] , [20] , [21] , [32] or learned from training data [3] , [4] , [5] , [8] , [29] . Surface deformations are then expressed as weighted sums of modes and retrieving shape entails estimating the modal weights by minimizing an image-based objective function. However, since such functions usually have many local minima, a good initialization is required.. There have also been recent attempts at recovering the shape of inextensible surfaces without explicitly using a deformation model. Some approaches are specifically designed for applicable surfaces such as sheets of paper [12] , [17] . Others make use of local inextensibility constraints [11] , [25] , and are applicable to many materials that do not perceptibly shrink or stretch as they deform. However, while these are attractive approaches, using only inextensibility constraints is only effective for relatively small deformations.. Other methods use local rigidity constraints in conjunction with deformation models and achieve shape-recovery either in closed form [28] or by solving a convex optimization problem [27] , and thus eliminate the need for an initialization. To this end, they require 2D point correspondences between the image in which one wishes to compute the shape and one in which it is already known. However, as will be shown in the following sections, small inaccuracies in the correspondences can still result in erroneous reconstructions.. The method proposed in this paper builds on the formalism introduced in [28] to return not a single solution but a representative set of all possible solutions and then uses additional information to decide which one is best. In this paper, we use shading and motion, but any image cue could have been used instead.. Of course, some of the core elements of our approach have appeared before in the literature. For instance, a large number of recent methods, such as [1] , [10] , [33] , [34] , have been proposed to merge geometric and shading cues into a common framework. However, these techniques, unlike ours, involve multiple iterative processes that require reasonably good initial estimates. An exception is the algorithm of [23] that solves for shape in closed form but is only applicable to Lambertian surfaces lit by a distant point light source. In addition, shape ambiguities have also been discussed before, but mostly in the context of rigid surface estimation [6] , [26] , [30] . In the nonrigid case, [11] is the only paper we know of that discusses shape ambiguities. This discussion, however, is limited to ambiguities produced by the concave/convex reversal. By contrast, we propose here a stochastic sampling exploration method that is effective to handle continuous ambiguities.

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


Quantum Advantage without Entanglement We study the advantage of pure-state quantum computation without entanglement over classical computation. For the Deutsch-Jozsa algorithm we present the maximal subproblem that can be solved without entanglement, and show that the algorithm still has an advantage over the classical ones. We further show that this subproblem is of greater significance, by proving that it contains all the Boolean functions whose quantum phase-oracle is non-entangling. For Simon's and Grover's algorithms we provide simple proofs that no non-trivial subproblems can be solved by these algorithms without entanglement. The fusion of quantum theory and computer science has introduced new capabilities to the world of computation and communication. Utilizing these capabilities led to some spectacular results: Shor's factorization algorithm [1] , Grover's quantum search algorithm [2] , Bennett-Brassard's quantum key distribution [3] and quantum teleportation [4] , all extend beyond well-believed bounds.. The source of quantum computation power is still debated. Some argue that this power arises because unlike classical systems, the state of a multipartite quantum system cannot always be considered as a mere correlated combination of its subsystems. Such states are said to be entangled, as opposed to separable states. Entanglement appears in most of the great achievements of quantum information theory, from Shor's factorization algorithm [1] and other algorithms [2, 5, 6 ] to quantum teleportation [4] , superdense coding [7] , quantum error correction [8] , and some quantum key distribution schemes [9, 10, 11] . It is uncontested that entanglement is a key resource of quantum computation, or in the words of Micha l Horodecki [12] , entanglement is "the corner-stone of the quantum information theory". When no entanglement exists in a pure-state quantum algorithm, the computation can be simulated efficiently and exactly using classical means [13] . Furthermore, when entanglement exists but its amount is bounded, Jozsa and Linden showed [14] that the computation can still be efficiently simulated classically by a coin-tossing algorithm. However, their work does not rule out significant advantage of quantum computation without entanglement (QCWE) in an oracle-based setting (e.g. for the Deutsch-Jozsa algorithm). It also does not rule out exponential advantage of mixed-state QCWE over probabilistic classical computation.. Some cases have been found where even without entanglement, quantum computation outperforms classical computation. Collins, Kim and Holton [15] solve the Deutsch-

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Modifying the shape of NURBS surfaces with geometric constraints NURBS surfaces are among the most commonly used parametric surfaces in CAGD and Computer Graphics. This paper investigates shape modi®cation of NURBS surfaces with geometric constraints, such as point, normal vector, and curve constraints. Two new methods are presented by constrained optimization and energy minimization. The former is based on minimizing changes in control net of surfaces, whereas the latter is based on strain energy minimization. By these two methods, we change control points and weights of an original surface, such that the modi®ed surface satis®es the given constraints. Comparison results and practical examples are also given. q NURBS is one of the most popular and successful methods for designing complex surfaces in Computer Aided Geometric Design (CAGD) and Computer Graphics [6, 14] . After creating NURBS surfaces, we often need to modify them to satisfy the user's design requirements. By de®nition of NURBS surfaces, there are three ways to modify the shape:. ² by changing knot vector; ² by moving control points; ² by changing the weights.. Many efforts have been made towards developing more convenient methods for shape modi®cation of NURBS curves. Piegl [12] proposed two methods to vary the shape of NURBS curves and surfaces: control-point-based modi®cation and weight-based modi®cation. Fowler and Bartels [7] presented a method to let users interactively specify geometric properties that depend on a curve's values and derivatives at selected points. Au and Yuen [1] and Sa Ânchez-Reyes [15] introduced approaches that modify the shape of NURBS curves by altering the weights and location of the control points simultaneously. Ishida [9] proposed a method that enables arbitrary and direct modi®-cation of curves by constructing a displacement function. Zheng et al. [22] presented a new approach for directly manipulating the shape by modi®cation in control points and knot re®nements. Juha Âsz [10] provides a weight-based shape modi®cation method with point and tangent constraints for plane NURBS curves.. As for shape modi®cation of surfaces, besides Piegl's method [13] , Celniker and Wech [4] investigated a method for constrained deformation of B-spline surfaces by using linear constraints and global energy function minimizing. Welch and Watkin [20] also considered linear constraints for deformable B-splines, but different energy functions were used. Kimura et al. [11] considered the deformation of a given surface that smoothly connects to previously designed surfaces. Guillet and Le Âon [8] described an approach for deformation of multi-patch tensor based freeform surfaces, and the deformation generated is controlled by global geometric constrains. Singh and Fiume [16] presented an effective geometric deformation technique: wires for shape modi®cation of surfaces and objects.. Physically based modeling approaches such as the ®nite element method and physical-based NURBS are also powerful methods for shape modi®cation [3, 17] . Users interact with the model by exerting virtual forces to which the system responds. However, there is a point of concern: high computational cost is involved in those non-purely geometric methods. Therefore physically based modeling approaches have not found wide applications in current CAD systems.. For a given NURBS surface and a given target point, a problem is how to modify the control points or corresponding weights such that the modi®ed surface can pass through the target point. Piegl gave an ef®cient way to achieve this by moving one control point or changing one weight, and presented explicit formulae to compute the new control point or weight. Due to its ef®ciency, Piegl's method has been widely used in commercial CAD systems. The objective of this paper is to improve Piegl's purely geometric methods for modifying shape of NURBS more naturally.. The paper is organized as follows: the problem statement is given in Section 2. Section 3 presents the constrained optimization method by minimizing changes of control net or weights of NURBS surfaces in Least Square sense. Section 4 presents the constrained optimization method by minimizing changes of strain energy of surfaces. Comparison results and practical examples are given in Section 5. Remarks on shape modi®cation of NURBS curves are noted in Section 6.

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High-level synthesis under multi-cycle interconnect delay Abstract -As process technology goes into deep submicron range, interconnect delay becomes dominant among overall system delay, occupying most of the system clock cycle time. Interconnect delay is now a crucial factor that needs to be considered even during high-level synthesis. In this paper, we propose a concurrent scheduling and binding algorithm that takes interconnect delay into account. We first define our distributed target architecture, which minimizes the effect of interconnect delay on clock cycle time. We no longer assume that interconnect delay between functional units is a part of one clock cycle. Interconnect delay can span over multiple clock cycles. We incorporate the concept of multi-cycle interconnect delay into scheduling and binding process, to reduce the critical path length and therefore the system latency. We show that by introducing interconnect delay, we can obtain latency improvement of u p to 54 YO and of 37% on the average. A number of researchers have independently reported that interconnect delay dominates logic delay in current deep sub-micron (DSM) process technology [I, 21. In deeper submicron geometry in the future, which will be still with the continuous scaling of process technology and thereby generate longer interconnect delay due to RC delay, coupling noise, inductance, etc. [3, 41, the situation will be worse and worse. The interconnect delay is expected to occupy 80% or more of the overall critical path delay in the near future [5] .. In conventional target architecture based on centralized register files, functional units (FU's) read their operands from centralized register files (and write their results to centralized register files) through relatively long buses [6] . Fig. 1 shows a simple centralized architecture model. In such architecture, total clock cycle time is bounded by 662 represent FU delay, register setup time, clock-to-registeroutput delay, FU-to-register delay and register-to-FU delay, respectively. TCLoBAL represents the sum of interconnect delay between register tiles and functional units through relatively long global buses. In current DSM technology, TGLoBAL has become comparable to the rest of TcYCLE. Therefore, we usually insert latches at both inputs and output of a FU to reduce the cycle time, which results in complex two-phase clocking scheme. In this case the cycle time is computed as T,vCL, = micron technology, the case will be even worse because increased TcLOBAI, will dominate TCYTLE. In that case, TcLoBAL can be three or four times longer than TLoGlc and existing complex clocking scheme. including two-phase clocking, will be inefficient. In this paper, we first define our target architecture based on distributed memory architecture. The architecture minimizes the effect of interconnect delay on clock cycle time. In the target architecture, we do not regard the global data transfers among functional units to be completed within one clock cycle time. Instead, we allow global data transfers to be carried out over multiple clock cycles. We incorporate such concept of tntrlti-cycle inletromiec/ dela,, into scheduling and binding process, which is the extension of Continuous Time List Scheduling proposed in [8]. in order to reduce the critical path length and therefore the system latency during high-level synthesis.. We will focus on adaptation of tiiitlti-c:ix-le itiretrotirieci delqv to schcduling and binding process to improve overall system latency. Our target architecture and overall design flow are proposed in Section 11. In Section 111, we illustrate motivational example by considering the effect of multicycling on overall system latency and the effect of operation binding on critical path when interconnect delays, comparable to or longer than FU delays, are incorporated into scheduling and binding procedure. Performance driven scheduling algorithm with interconnect delay and its comparisons with those not considering interconnect delay are presented in Section IV and Section V. Finally conclusions and future work are given in Section VI. In this section, we explain the concept of multi-cycle inlerconnect delay in more detail using a simple example. It can be seen that overall system latency is improved by allowing multi-cycle global data transfer between FU's. For the multi-cycling of global data transfers, we treat a bus with multi-cycle delay like a FU with multicycle delay. Moreover, we explain the need for specific operation binding algorithm by showing the effect of operation binding on critical path length. Fig. 4 (a) represents a simple example that consists of two additions and one multiplication. Multiplierl accepts the result from the adderl to perform its multiplication operation. Assuming that interconnect delay from adderl to multiplier1 is 2011s. which is longer than the execution time of adderl, scheduling result of Fig. 4@ ) is obtained. If we apply pathbased scheduling [I51 to find the schedule with the minimum number of control-steps and assume the register-delay is 3ns, we get a clock cycle of 4611s (40+3+3) and then the system latency of 9211s (46*2). Note that in this case, interconnect delay is contained within a clock cycle. On the contrary, if we set a clock cycle time as 1611s (10+3+3) through our novel scheduling and binding algorithm considering interconnect delay, we achieve the latency of 6411s (16*4) as shown in Fig. 4 (c). Fig. 4(d) is the target architecture based on the scheduling result of Fig. 4 (c) , where the data transfer done is across two effective clock cycles. We call this delay multi-cycle interconnect delay and treat a bus with multi-cycle delay like a FU with multi-cycle delay. That is, we treat a global data transfer as an operation taking one or more clock cycles.. The multi-cycling of data transfers can reduce the system latency in two ways. First, it enables us to select smaller value of clock cycle time, which reduces the waste of clock slack induced by the difference between computation time and cycle time, thereby minimizing the system latency. Secondly, multicycling enables parallel execution of data transfers and functional units. While data is transferred on a global bus, we can initiate a new operation in a functional unit or we can initiate another global data transfer through a different bus, which is impossible if the concept of multicycle interconnect delay is not adopted. Recall that, in the conventional architecture, interconnect delay is merged with a FU delay into a clock cycle and therefore it is not allowed to initiate a new operation or data transfer. For minimizing latency, we should perform careful scheduling and binding because critical path length strongly depends on the binding state when interconnect delay is considered. Figure 5 illustrates the case where critical path varies according to operation binding. Without considering interconnect delay the path *I +*2 +*3 is the critical path with 60 ns delay. Let us introduce interconnect delay (IO ns between Multl and Adderl and 15 ns between Multl and Adder2) to the same example. In this case, the critical path in Fig. 5 (a) is no longer critical. In Fig. 5 (b) and (c), the *I -+ +I +*3 becomes a new critical path. However, the critical path length varies from 70 to 80 ns depending on operation binding. Therefore, we need to carefully perform scheduling and binding under the condition that interconnect delay dominates system latency. The PDSl algorithm first performs scheduling and binding in continuous time domain without fixed clock cycle time. Then we determine clock cycle time by using optimal clock selection algorithm proposed in [7] for minimizing total latency. Like conventional list scheduling, our algorithm selects operations among ready operations in descending order of path length. However, the path length strongly depends on operation binding when interconnect delay is introduced for the data transfer among functional units, as shown in Fig. 5 . To consider the effect of operation binding on critical path and to handle the interconnect delay that depends on operation binding, we use the concept of dynamic critical path scheduling algorithm [IO] . We define c& and as the critical path length from an operation node ni to the end node and the earliest schedulable time of ui, respectively when ni is bound to a functional ui1it.J;. The critical path length is computed as where succi and c, represents the set of successors of ni and the computation time ofJ, respectively. The critical path length is recursively computed from the end node to the start node in the graph. Table I and 2 show the interconnect delay and the computed critical path length for the example of Fig. 5, respectively. In the PDSl algorithm, we use min(cpli,,) as the priority function for the selection of an operation. Among ready operations, we select the one with highest priority. After selecting an operation, we select a functional unit4 to which the operation will be bound such that estimated latency is minimized. The estimated latency dcpl,,. is computed as Fig. 6 explains the procedure of our scheduling and binding algorithm.

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


Retracing the residual curve of a Lyapunov equation solver Abstract Let A ∈ R n×n and let B ∈ R n×p and consider the Lyapunov matrix equation AX + XA T + BB T = 0. If A + A T < 0, then the extended Krylov subspace method (EKSM) can be used to compute a sequence of low rank approximations of X. In this paper we show how to construct a symmetric negative definite matrix A and a column vector B, for which the EKSM generates a predetermined residual curve. We have shown that any positive residual curve is possible for the extended Krylov subspace method (EKSM) for the Lyapunov equation AX + XA T + BB T = 0, where A ∈ R n×n is symmetric negative definite and B ∈ R n satisfies K(A, B) = R n . The algorithm is well defined whenever A is negative definite, but this condition does not ensure that the residual curve decreases rapidly or monotonically to zero. Theorems guaranteeing such behavior must necessarily impose additional assumptions on A and B.

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


Planning in partially-observable switching-mode continuous domains Abstract Continuous-state POMDPs provide a natural representation for a variety of tasks, including many in robotics. However, most existing parametric continuousstate POMDP approaches are limited by their reliance on a single linear model to represent the world dynamics. We introduce a new switching-state dynamics model that can represent multi-modal state-dependent dynamics. We present the Switching Mode POMDP (SM-POMDP) planning algorithm for solving continuousstate POMDPs using this dynamics model. We also consider several procedures to approximate the value function as a mixture of a bounded number of Gaussians. Unlike the majority of prior work on approximate continuous-state POMDP planners, we provide a formal analysis of our SM-POMDP algorithm, providing bounds, where possible, on the quality of the resulting solution. We also analyze the computational complexity of SM-POMDP. Empirical results on an unmanned aerial vehicle collisions avoidance simulation, and a robot navigation simulation where the robot has faulty actuators, demonstrate the benefit of SM-POMDP over a prior parametric approach. Partially observable Markov decision processes (POMDPs) [9] provide a rich framework for describing a number of planning problems that arise in situations with hidden state and stochastic actions. In many applications, such as autonomous navigation across varying terrain or robotic grasping, the world is most naturally represented using continuous states. Planning in continuous environments is challenging because a continuous domain with even a single dimension offers an infinite number of different world states. For example, an autonomous car driving on a straight road could take on an infinite range of values, and the planner must determine an action for each value. If the world state is unknown, the decision-making algorithm must consider a distribution over an infinite number of possible states, known as the belief, and then compute the expected benefit of different actions given different beliefs, known as the value function. In this work we are interested in planning algorithms for operating in such partially-observable, continuous-valued domains with complex dynamics.. Outside of the famous linear quadratic Gaussian controller (see Burl [3] ), there has been relatively little work on continuous-state planning in partially observable environments. Brooks et al. [2] restrict the belief state to be a unimodal Gaussian, 1 and then plan by discretizing the Gaussian parameters and using Fitted Value Iteration over that representation. However, this approach will be limited in any domain that requires multi-modal beliefs to achieve good performance. In addition, the resulting plan quality depends on the resolution of the discretization of the parameter space, which is hard to know in advance and has a direct impact on computational cost. Thrun's Monte Carlo POMDP [21] approach can handle arbitrary dynamics models but requires often-expensive sampling to perform the belief updates and to compute the value function estimate. Recent work by Zhou et al. [24] generalizes the work of Brooks et al. to a more generic class of parametric families. While the authors present nice theoretical bounds on their approach, the cost scales as a function of the discretized parameter space, which may be expensive in domains that require a large number of parameters, or a fine discretization of the parameter space in order to achieve good empirical results.. This prior work demonstrates the interest in using parametric functions to encode the world models in continuous-domains; such functions provide a compact mechanism to represent distributions and values over infinite sets. Indeed, Porta et al. [15] have demonstrated that using linear Gaussian models allows the main operators of POMDP planning, value function backups and belief updating, to be done in closed form. By optimizing and adjusting both the parameters and the value function, Porta et al.'s planner can automatically adapt the value function representation at each backup, introducing new components to the representation as the structure of the value function changes. In this sense it can be considered a variable resolution approach to planning (see for example Munos and Moore [11] ), but one that dynamically determines the resolution as part of the standard value function computation. This can be a significant advantage over standard uniform resolution discrete-state POMDP planners, as Porta et al. demonstrated by showing their approach was faster than the discrete-state POMDP planner Perseus [20] in a simulation experiment.. However, if parametric functions are used to represent the world models and value function, it is also critical to ensure that the chosen functions are sufficiently expressive to adequately represent the problems of interest. The work by Brooks [2] , Porta [15] and their colleagues presented results on problems that used the simple linear Gaussian to describe the effects of an action. However, the dynamics of robotic grasping, autonomous navigation over varying terrain, and many other problems of interest are highly complex and nonlinear. For example, an autonomous car crossing varied terrain will exhibit different dynamics depending on whether the ground underneath is sand or rocks. Though such dynamics are easily represented in discrete-state environments using standard transition matrices, a single linear Gaussian continuous-state model will be insufficient to adequately model these multi-modal state-dependent dynamics.. In this paper we present the Switching Modes POMDP (SM-POMDP) algorithm which uses a switching state space representation of the world dynamics to perform approximate closed form planning in continuous-valued environments. SM-POMDP extends Porta et al.'s [15] prior work on continuous-state POMDPs by using a model that can both represent actions that result in multimodal stochastic distributions over the state space, and succinctly represent any shared dynamics among states. SM-POMDP is suitable for a much larger class of POMDP problems than past related approaches, but still maintains the strengths of parametric representations in continuous-state POMDP planning.. In contrast to most 2 prior approximate continuous-state POMDP work [2, 15, 21] , we also provide a theoretical analysis of several variants of our SM-POMDP planner, bounding where possible the error between the resulting SM-POMDP value function, and the optimal value function. We also analyze the computational complexity of planning using SM-POMDP. As is often the case, we show there is a tradeoff between computational tractability and guarantees on the resulting optimality of the produced plan. Our analysis could aid users in selecting the right variant of SM-POMDP appropriate for the tractability and optimality constraints of their own application.. Our paper proceeds as follows. In Section 2 we briefly provide an introduction to POMDPs, and then discuss switching state dynamics models in Section 3. We next present how to plan with these models in Section 4. To keep planning tractable, this section also presents several methods for ensuring that the value function representation uses a bounded number of parameters. In Section 5 we analyze SM-POMDP in terms of its computational complexity, and, where possible, provide bounds on the quality of its solutions. Experimental results are given in Section 6 that demonstrate the advantage of SM-POMDP over prior parametric approaches on an unmanned aerial vehicle collisions avoidance simulation, and a robot navigation simulation where the robot has faulty actuators. Section 7 concludes. In this paper we introduced SM-POMDP, an algorithm for planning in continuousstate domains characterized by switching-state, multi-modal dynamics. The parametric representation of the dynamics model allowed all POMDP planning operators (belief updating and value function backups) to be performed in closed form. SM-POMDP can handle more general dynamics models than the prior work it builds on by Porta et al. [15] and the benefit of this was demonstrated in three simulated experiments. We also provided a formal analysis of SM-POMDP, bounding the resulting SM-POMDP value function relative to the optimal value function where possible, and analyzing the computational complexity of the SM-POMDP algorithm variants. SM-POMDP indicates the potential promise of parametric approaches in planning in partially-observable, continuous-state environments with complex dynamics. We next provide bounds on a subset of the SM-POMDP variants' performance, and also analyze the computational complexity of all the prior SM-POMDP variants discussed.. In terms of performance quality, our objective lies in bounding the potential difference between the optimal value function, denoted by V * and the value function computed by the SM-POMDP algorithm, denoted by V SM . Let H represent an exact value function backup operation, H PB a point-based backup operation, and A the projection operator which maps the value function to a value function with a smaller number of components. Our goal is a bound on the error between the n-step optimal value function V * n and the SM-POMDP value function V SM n . The total error ||V * − V SM n || ∞ is bounded by the n-step error plus the error between the optimal n-step and infinite horizon value functions, ||V * − V * n || ∞ which is bounded by γ n ||V * − V * 0 || ∞ . We will show the n-step error can be decomposed into a term due to the error from point-based planning and a term due to the error from the projection to a fixed number of components. . Proof We proceed by first re-expressing the error in terms of the backup operators, and then add and subtract a new term in order to separate out the error due to performing backups on different value functions, versus the different backup operators themselves:. where the result follows by the use of the triangle inequality. We then add and subtract H PB V SM n−1 in order to separate the error introduced by performing a point-based backup, from the error introduced from the projection operator, and again use the triangle inequality:. This is a geometric series, therefore. In the following sections we will discuss bounds on proj , but the remainder of this section will focus on PB .. Pineau et al. [14] previously provided a proof for bounding the error induced by performing a point-based backup, PB for discrete-state POMDPs. We now provide a similar proof for continuous-state POMDPs. d KL ( p, q) will denote the KullbackLeibler divergence between two probability distributions p and q. B is the set of points in the belief set used to perform point-based backups and is the full belief space. The key advantage of SM-POMDP over prior techniques is its ability to handle a broader class of dynamics models. Therefore we examined its performance on three simulated examples that involve switching and/or multi-modal dynamics. The first example is a navigation domain where a robot must locate a hidden power supply. This problem exhibits switching dynamics because the robot's transitions depend on whether it is currently in the free space of the hallway, or near one of the walls. In the second example we consider a faulty robot trying to hop across treacherous terrain to reach a goal destination. This problem exhibits multi-modal dynamics since the robot's attempts to jump only sometimes succeed. In the final example we consider a two-dimensional unmanned aerial vehicle simulation where one agent must avoid another agent.. Except where otherwise noted, we focus on comparing SM-POMDP to a linearmodel parametric continuous-state planner, such as the planner developed by Porta et al. [15] . This is the most similar planner to SM-POMDP as only the dynamics models are changed, and is therefore an important benchmark.. In all examples SM-POMDP outperformed the comparison linear-model continuous-state planner. α-functions were projected down to at most 50 components using the empirical max norm projection method. Beliefs were restricted to have four components, and were projected down using the KL-divergence technique from Goldberger and Roweis [7] which is more appropriate for beliefs than value functions since beliefs represent a probability distribution over states. Porta et al. had previously demonstrated that their planner was faster than a standard discrete-state planner Perseus [20] on a simulation problem, demonstrating the benefits of parametric planners that automatically adjust the parameterization of the value function during planning. In the first experiment we confirm that this advantage holds for SM-POMDP which can handle domain dynamics that are poorly approximated by a single linear Gaussian model. In addition we show this advantage when comparing to a state-of-the-art discrete-state planner (HSVI2 [18] ) which is known to outperform Perseus [20] . We then focus our experimental efforts on demonstrating the additional flexibility and modeling power of SM-POMDP that allows it to find better plans than linear Gaussian POMDP planners.

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


Initialization by selection for wavelet network training We present an original initialization procedure for the parameters of feedforward wavelet networks, prior to training by gradient-based techniques. It takes advantage of wavelet frames stemming from the discrete wavelet transform, and uses a selection method to determine a set of best wavelets whose centers and dilation parameters are used as initial values for subsequent training. Results obtained for the modeling of two simulated processes are compared to those obtained with a heuristic initialization procedure, and demonstrate the effectiveness of the proposed method. Among the applications of wavelet functions, nonlinear regression by wavelet networks is attracting a growing interest. Wavelet networks have been used both for static [10, 12] modeling and for dynamic input-output modeling [9] . It was proved in [4] that families of wavelet functions -particularly wavelet frames -are universal approximators, which gives a theoretical basis to their use in the framework of function approximation and process modeling. For wavelet functions, this property can be expressed as follows: any function of L 2 (R) can be approximated to any prescribed accuracy with a finite sum of wavelets. Therefore, wavelet networks can be considered as an alternative to neural and radial basis function networks. In the present article, we present a network initialization procedure that takes advantage of the properties of discrete wavelet frames in order to improve the training efficiency of continuous wavelet frames. We focus on wavelet frames rather than on orthogonal wavelet bases, because the latter must comply with conditions that are seldom feasible. We first present the wavelet networks that we use, their architectures and the principle of their training. The difference between continuous and discrete wavelet frames will be emphasized, since both approaches will be used at different stages of wavelet network training. After outlining the problem of parameter initialization of a wavelet network, we first introduce a heuristic procedure, and subsequently describe the proposed method. Finally, two examples of static modeling are presented, and the efficiency of the procedure is shown, by comparing its results to those obtained with the heuristic initialization. Wavelet networks are an alternative to sigmoid neural networks for black-box modeling of processes having a small number of inputs, if both the weights of the connections and the parameters of the wavelets are adjusted from training data. However, due to the local character of the wavelets, the initialization of their translations and dilations requires more care than the initialization of the weights of a conventional neural net. We have proposed an initialization procedure for the centers and dilations, which is more principled than the usual heuristics, based on the properties of discrete wavelets,. We have shown that, when used together with efficient training algorithms, this initialization leads to results that are much more independent from the random initialization of the weights than the results obtained by a heuristic procedure.

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


Measuring the capacity of a streaming media server in a Utility Data Center environment Abstract In order to design a "utility-aware" streaming media service which automatically requests the necessary resources from Utility Data Center infrastructure, several classic performance questions should be answered: how to measure the basic capacity of a streaming media server? what is the set of basic benchmarks exposing the performance limits and main bottlenecks of a media server? In this paper, we propose a set of benchmarks for measuring the basic capacities of streaming media systems for different expected workloads, and demonstrate the results using an experimental testbed. The delivery of continuous media from a central server complex to a large number of (geographically distributed) clients is a challenging and resource intensive task. Delivering multimedia content over Internet faces many challenges: an immature broadband Internet infrastructure, the realtime nature of multimedia content and its sensitivity to congestion conditions in the Internet, high backbone transmission cost, a multiplicity of competing standards for media encoding and delivery.. The evidence from media workload analysis [1, 2, 3] indicates that client demands are highly variable: some days (hours) exhibit a magnitude higher load comparing to the typical daily (hourly) averages. Additionally, media applications are characterized by stringent real-time constraints, as each stream requires isochronous data playout. These features make the media applications a perfect candidate to benefit from flexible resource management and resource provisioning in Utility Data Center infrastructure.. Utility Data Center (UDC) [6, 7] is programmable data center that creates and runs virtual IT environments as a highly automated service. UDC provides a flexible, costeffective solution with advanced management software allowing resources to be automatically reassigned in response to changing business and IT requirements. UDC architecture is an ideal platform to support the efficient hosting services for Internet applications. Most Internet applications are difficult to manage due to their highly variable service demand. The most typical practice used by current service providers is to significantly over provision the amount of resources needed to support such applications by tailoring the resources to maximum expected load. The UDC infrastructure provides a set of new management capabilities for requesting/releasing the system resources to dynamically provision the application demands and their requirements.. In order to design and implement a "utility-aware" streaming media service which automatically requests from UDC infrastructure the resources, several classical performance questions should be answered:. • how to measure the basic capacity of a streaming media server? • what is the set of basic benchmarks exposing the performance limits and main bottlenecks of media server?. Commercial media server solutions are distinguished by the number of concurrent streams a server can support [4] without loosing a quality of stream, i.e. until real-time constraint of each stream can be met. A standard commercial stress test measures a maximum number of concurrent streams delivered by the server when all the clients are accessing the same file encoded at a certain bit rate, e.g. 500 Kb/s. However, a multimedia content is typically encoded at different bit rates depending on a type of content and a targeted population of clients and their connection bandwidth to the Internet. What are the scaling rules for server capacity when delivered media content encoded at different bit rates? For example, if a media server is capable of delivering N concurrent streams encoded at 500 Kb/s, will this server be capable of supporting 2 × N concurrent streams encoded at 250 Kb/s? The other issue with a standard commercial stress test is that all the clients are accessing the same file. Thus another question to answer is: how the media server performance is impacted when different clients retrieve different (unique) files of a media content?. We introduce a simple set of basic benchmarks to analyze the performance and main bottlenecks of media server:. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. • Single File Benchmark and • Unique Files Benchmark Using proposed set of basic benchmarks, the service providers could measure the capacities of their systems. These benchmarks provide the basic performance envelope for sizing streaming media systems under expected workload and lay down a performance foundation for "utility-aware" service design. Figure 1 shows our experimental testbed used for measuring the media system performance:

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Improved Maximum Entropy Analysis with an Extended Search Space I propose an improvement to the implementation of the well established Maximum Entropy Method by departing from Bryan's concept [1] of singular search space. Working with numerical data from Lattice QCD [2] I found that in cases where prior information is scarce and the number of data-points small, extension of the search space can dramatically improve the reconstructed spectra. The reason for the inadequacy of Bryan's method and a remedy are discussed based on the shape of the basis functions of the search space and results from a mock data analysis. In order to adequately approach problems where an exponentially damped Kernel is used, I provide an implementation using the C/C++ language that utilizes high precision arithmetic adjustable at run-time [3] . The LBFGS algorithm is included in the code in order to attack problems without the need to resort to a particular search space restriction. In this paper I would like to discuss an improvement to the implementation of the Maximum Entropy Method (MEM). This algorithm allows to address the generally ill-defined problem of determining the inverse Laplace Transform from a discrete and noisy set of datapoints using Bayesian inference. In the present case the bilateral Laplace transform is investigated, which connects the positive definite spectrum ρ(ω) ≥ 0 with the data D(τ) via an integral convolution. In the following I will restrict myself to the exponentially damped Kernel K(τ, ω) = exp[−τω]. In practice the data is obtained by an experimental apparatus or a numerical simulation and thus is known only at N τ discrete points D(τ i ) = D i and up to a given uncertainty given by an error matrix. where D k i denotes one of the N c individual measurements of the data-point at τ i .. In addition, to carry out the task of determining the spectrum from data, we discretize ρ(ω l ) = ρ l in the integral over the frequencies ω l using N ω points between an upper and lower cutoff ω max and ω min , i.e with a spacing of ∆ω = ωmax−ωmin Nω . This is the first time we use prior information about our system, since ω max and ω min need to be chosen such that all relevant frequencies of the spectrum encoded in the data can be accounted for. Such prior information can often be derived from sampling theorems in the case of an experimental apparatus or the finite size of the underlying numerical simulation that produces the datapoints.. Thus the fully discretized equation we are to supposed to invert reads. It can happen that one is faced with the situation that the number of data-points N τ is significantly smaller than the number of points one wishes to reconstruct in the spectrum. In such cases the inversion of Eq. (3) is an inherently ill-defined problem even if perfect data were available. Imagine performing a simple χ 2 fitting, i.e. finding a set of points ρ l that reproduces the data D i within the errors σ i = √ C ii . In such as case many degenerate solutions exist, none of which is superior to any other. The reason for this is that the finite number of data-points can only constrain parts of the spectrum, but at this stage we have no way to decide which of the reconstructed features in ρ these correspond to.. Let me note on another aspect, in that the problem at hand is not a linear problem as might be assumed from Eq.(3). The underlying physics required the values of ρ l to be positive definite, which corresponds to an additional constraint equation to be met. Therefore even in the case that N τ = N ω one cannot directly argue for the existence of a unique solution for the inversion of Eq.(3).. To address the challenges posed by both finite accuracy and finite resolution in the data, one can introduce a regularization for the χ 2 fitting procedure, which is motivated by arguments from Bayesian inference. This allows one to understand the above inversion problem as a test of hypotheses, in the sense of answering the arXiv:1110.6285v2 [physics.comp-ph] 4 Jun 2012 question: How probable is it that a chosen test-function ρ l is the correct spectral function, given the measured data D i and any other prior knowledge available about the system. I.e. one rephrases the problem in terms of probability distributions (Note that at this point ρ itself does not need to be a probability distribution).. The ingredients to our problem so far are measured data D i and prior knowledge I. The latter is encoded in the formalism through a function m(ω), which by definition corresponds to the correct spectral function in the absence of data. If such prior knowledge is interpreted as a sort of additional data available to us, one can construct from the joint probability function P(ρ, D, I(m)) the following expressions. from which the following relation can be obtained. In the case that our prior information is exactly known, the above term should simplify to the form usually used in the MEM. It is thus necessary to find the most probable spectral function, i.e a function ρ MEM , which maximizes Eq.(9) The Maximum Entropy method offers a solution to the question of how to bring meaning to the ill-defined problem (3) of inferring the values ρ l from a noisy and finite data-set D i . Instead of maximizing only the likelihood probability with a test spectral function ρ l , one regularizes the process by including the prior probability. The function ρ MEM l that represents the extremum of (10) is hence the most probable answer in the Bayesian sense.. Since the choice of the SVD basis functions does not depend on the choice of ω min and their number is fixed by the supplied number of data-points, I argued that Bryan's search space does not in general contain the correct global extremum of the functional Q(ρ, D, m). Numerical evidence was presented to support this conclusion. I thus propose to systematically expand the search space to N τ < N ext < N ω dimensions until the correct global extremum of the functional has been found.. Introducing a large number of basis functions inevitably leads to the appearance of "wiggly" structures in the reconstructed spectral function ρ MEM (ω). Since they are not constrained by the data, such artifacts can be identified through a variation of the prior function. In turn, those features of ρ MEM (ω) that are reliably encoded in the data do not suffer from such variations of m l .

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


Scalable PP-1 block cipher A totally involutional, highly scalable PP-1 cipher is proposed, evaluated and discussed. Having very low memory requirements and using only simple and fast arithmetic operations, the cipher is aimed at platforms with limited resources, e.g., smartcards. At the core of the cipher's processing is a carefully designed S-box. The paper discusses in detail all aspects of PP-1 cipher design including S-box construction, permutation and round key scheduling. The quality of the PP-1 cipher is also evaluated with respect to linear cryptanalysis and other attacks. PP-1's concurrent error detection is also discussed. Some processing speed test results are given and compared with those of other ciphers.Keywords: symmetric cipher, scalable cipher, S-box construction, resistance against cryptanalysis, error detection.Block ciphers constructed as a product of involutions are not new in cryptography. In fact, one of the most popular constructions, the Feistel permutation, is an involution. However, substitution and permutation encryption networks (SPNs) resulting from a product of involutions (e.g., both the nonlinear S-box layer and the affine bit permutation layer are involutions (Biryukov, 2003) ) have not been intensively studied.In this paper, we propose an n-bit (n = 64, 128, 192, . . .) scalable block cipher which is an involutional SPN. We use one S-box which is an involution and one bit permutation which is also an involution. As a result, we get a totally involutional cipher. This means that we use the same network, in particular, the same S-box S (S = S −1 ) and the same permutation P (P = P −1 ) in both encryption and decryption phases.Partial results were published in (Bucholc and Idzi kowska, 2007; Chmiel et al., 2008a; 2008b) . The paper is organized as follows: Section 2 describes basic assumptions which lay at the base of the PP-1 project. The algorithm is described in detail in Sections 3-5. Quality evaluation of the PP-1 cipher is presented in Section 6. In Section 7, resistance against various attacks (differential, linear and algebraic cryptanalysis) is discussed. Avalanche and statistical properties of PP-1 are presented in Section 8. Section 9 presents processing speed obtained in test implementations of PP-1. In Section 10, concurrent error detection in hardware implementations of the cipher is considered. Final remarks are presented in Section 11.The main objective of the PP-1 project was to develop a block cipher which can be implemented on a platform with limited resources. Two other important requirements were• scalability, which allows using different data block sizes and key sizes,• easy and efficient implementation in software and hardware.The ability to implement the algorithm on platforms with limited resources implies that operations should be simple and memory requirements as low as possible. One Sbox is preferred, and the same resources (e.g., round keys) should be used for encryption and decryption. Since some simple processors, especially those used in embedded systems, do not support multiplication and division, these operations are costly because, to perform them, a sequence of more elementary instructions must be executed.K. Bucholc et al.Therefore, multiplication and division should be avoided. Floating point operations are even more expensive when implemented in software and should also be avoided. Therefore, the preferred operation set contains sum modulo 2, addition and subtraction modulo 256, and shifts. Block ciphers constructed as a product of involutions are not new in cryptography. In fact, one of the most popular constructions, the Feistel permutation, is an involution. However, substitution and permutation encryption networks (SPNs) resulting from a product of involutions (e.g., both the nonlinear S-box layer and the affine bit permutation layer are involutions (Biryukov, 2003) ) have not been intensively studied.. In this paper, we propose an n-bit (n = 64, 128, 192, . . .) scalable block cipher which is an involutional SPN. We use one S-box which is an involution and one bit permutation which is also an involution. As a result, we get a totally involutional cipher. This means that we use the same network, in particular, the same S-box S (S = S −1 ) and the same permutation P (P = P −1 ) in both encryption and decryption phases.. Partial results were published in Chmiel et al., 2008a; 2008b) . The paper is organized as follows: Section 2 describes basic assumptions which lay at the base of the PP-1 project. The algorithm is described in detail in Sections 3-5. Quality evaluation of the PP-1 cipher is presented in Section 6. In Section 7, resistance against various attacks (differential, linear and algebraic cryptanalysis) is discussed. Avalanche and statistical properties of PP-1 are presented in Section 8. Section 9 presents processing speed obtained in test implementations of PP-1. In Section 10, concurrent error detection in hardware implementations of the cipher is considered. Final remarks are presented in Section 11.

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


Combining word problems through rewriting in categories with products We give an algorithm solving combined word problems (over non-necessarily disjoint signatures) based on rewriting of equivalence classes of terms. The canonical rewriting system we introduce consists of few transparent rules and is obtained by applying Knuth-Bendix completion procedure to presentations of pushouts among categories with products. It applies to pairs of theories which are both constructible over their common reduct (on which we do not make any special assumption). An essential problem in automated deduction consists in integrating theorem provers which are able to perform separated tasks. In the ÿeld of equational logic, this leads in particular to the following question: suppose that you are able to solve word problems for theories T 1 ; T 2 ; can you solve word problem for T 1 ∪ T 2 ? Moreover, can one design an algorithm taking as input two arbitrary algorithms for word problems for T 1 and T 2 and realizing a decision procedure for word problem for T 1 ∪ T 2 ?. In the case where T 1 ; T 2 have disjoint signatures the positive answer was known since long time [13] , although it was only more recently discovered within automated deduction community (see e.g. [12] ). In the general case, combining decidable word problems may lead to undecidability, even if we suppose that T 1 ; T 2 are both conservative over their common reduct T 0 . To this aim, consider the following example. Let T 0 be the theory of join-semilattices with zero (i.e. of commutative idempotent monoids) and let T 1 be the theory of Boolean algebras. As T 2 we take the theory of semilatticemonoids, which are algebras having both a monoid and a join-semilattice with zero structure and which satisfy the further equation:. T 2 clearly has decidable word problem (elements in a free algebra are ÿnite sets of lists of the generators), as well as T 1 . The union theory (which we indicate better with T 1 + T0 T 2 ) corresponds to the "distributive linear logic" of [9] and falls within the undecidability results of [1] .. Clearly something must be assumed in order to have positive solution to combined word problems; in the literature it is usually assumed that T 1 ; T 2 share a set of constructors (we prefer the terminology "they are both constructible over T 0 "). There are various deÿnitions of constructors and depending on such deÿnitions there are variable strength results. Main papers on the subject are [5] and [3] : the second has a weaker deÿnition and consequently, a stronger result. Quite recently, Baader and Tinelli, working independent of us, were able to strengthen their previous work in [3] by extending the related methods to the case in which T 0 may not be collapse-free. The general result they obtained was presented at FROCOS2000 and will appear in extended full version in the detailed paper [4] . The statement of their result coincides with the result we have in the present paper 2 (which is a very remarkable fact, given that we worked independently and given that-as it will appear from the remarks below-we used quite di erent methods, both in the formulation of the combination algorithm and in its mathematical justiÿcation).. In [3, 4] , the combined decision algorithm is obtained through a complex refutation technique manipulating equations according to certain non-deterministic rules. As such it has the advantage of being more exible, although it does not provide normal forms. On the contrary, in [5] (and in the similar method of [12] for the disjoint case) one can directly manipulate terms by abstracting and collapsing alien subterms and the suggested algorithm follows a rigidly preassigned procedure. Our method is more similar to that of [5] (in the sense that it manipulates terms), but has the same exibility advantages as the method of [3, 4] . The idea is simple: we build a canonical rewriting system which is able to normalize paths of mixed pure terms.. The realization of such a plan looks very hard at a ÿrst glance: terms from combined signatures are quite unreliable datatypes, basically because they can compose, decompose and even collapse in many uncontrolled and overlapping ways. However, we shall put such a complex combinatorics under the control framework provided by the categorical approach to equational logic: such an approach goes back to the classical pioneering paper of Lawvere [10] in functorial semantics. 3 Basically, equational theories are identiÿed with categories with products, so that in our situation we need to manipulate presentations of pushouts among such categories. We get a ÿrst general and simple presentation of these pushouts in Section 3 by means of two-sides rewrite rules. To this presentation we apply, in Section 5, Knuth-Bendix completion procedure and get the desired rewriting system, under some "constructors" hypothesis for our theories.. This constructors hypothesis is formulated within a categorical framework in Section 5 by means of (weak) factorization systems and translated in symbolic terms in Section 10: roughly speaking, T i is said to be constructible over T 0 i there is a class E i of terms (including variables and closed under renamings) in the signature i of T i so that any i -term t(x 1 ; : : : ; x n ) decomposes uniquely (up to provable identity) as u(v 1 ; : : : ; v k ), where the v i (x 1 ; : : : ; x n ) are (always up to provable identity) distinct terms from E i and u is a k-minimized term in the signature 0 of T 0 (a term u(x 1 ; : : : ; x k ) is said to be k-minimized i it is not provably identical to any term in which only variables coming from a proper subset of {x 1 ; : : : ; x k } occur). Thus, u is a kind of T 0 -head normal form of t. Examples are provided in Section 10 (a typical example is the case of commutative rings with unit which are constructible over abelian groups).. We brie y describe here the rewriting system R that we obtained. R consists of only four rules (for technical reasons concerning "colours" of terms, two of such rules are "duplicated"). The ÿrst rule (called composition rule) simply allows to compose equally coloured consecutive (equivalence classes of) terms. The second rule (called -extraction rule) minimizes terms by "moving left" projections (i.e. n-tuples of distinct variables). The fourth rule (called products rule) is suggested by the completion procedure and has the following meaning: any projection (i.e. any tuple of distinct variable terms) appearing in an internal position of a path of pure terms represents a "hole" and the normalization process is supposed to ÿll such a hole by "moving right" genuine terms (i.e. terms which are not projections). In addition, the normalization algorithm propagates to the right of the path the T 0 -chunks of terms coming from extraction of T 0 -head normal forms: this is done by the third rule (called -extraction rule). The complete table of rules of R is given in Section 5.. Although R is a quite simply described system, the con uence proof requires lot of work, because all critical pairs must be examined. This leads to a large amount of details, all consisting of elementary computations (in fact, once the technical tools are appropriately settled, single cases are treated in the most natural way).. The paper is organized as follows: in Section 2, we recall the necessary background and ÿx notations; in Section 3, we get a ÿrst presentation of pushouts among Lawvere categories. In Sections 4 and 5, we apply completion procedure and get the appropriate rewriting system R. In Section 6, we provide local con uence and termination for a simple subsystem R 0 of R. In Section 7, a third rewriting system, called R + is introduced (R + is equivalent to R, it normalizes slower but it is easier to manage); in addition, useful technical facts are collected. In Section 8, R + is proved to be locally con uent, whereas in Section 9 termination of both R and R + is established. Finally, equivalence between R and R + and canonicity of the former are obtained. Section 10 provides examples of constructible theories and of normalizations of paths of terms.. Sections 6 -9 can be skipped in a ÿrst reading by people mostly interested in our results (and less interested in their proofs).. For space reasons, some routine work is omitted in this paper; the reader may ÿnd all the details in the technical report [6] . We assume a certain familiarity with rewriting (for some unexplained notions readers may consult [2] ) and with the elementary formalism of categories with products.

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


A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method Minimization of functionals related to Euler's elastica energy has a wide range of applications in computer vision and image processing. A high order nonlinear partial differential equation (PDE) needs to be solved, and the gradient descent method usually takes high computational cost. In this paper, we propose a fast and efficient numerical algorithm to solve minimization problems related to Euler's elastica energy and show applications to variational image denoising, image inpainting, and image zooming. We reformulate the minimization problem as a constrained minimization problem, followed by an operator splitting method and relaxation. The proposed constrained minimization problem is solved by using an augmented Lagrangian approach. Numerical tests on real and synthetic cases are supplied to demonstrate the efficiency of our method.

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Generalizing preference elicitation in combinatorial auctions Combinatorial auctions where agents can bid on bundles of items are desirable because they allow the agents to express complementarity and substitutability between the items. However, expressing one's preferences can require bidding on all bundles. Selective incremental preference elicitation by the auctioneer was recently proposed to address this problem but the idea was not experimentally validated. This paper evaluates several approaches and finds that in many cases, automated elicitation is in fact beneficial: as the number of items for sale increases, the amount of information elicited is a small and diminishing fraction of the information collected in traditional "direct revelation mechanisms" where bidders reveal all their valuation information. In forward auctions, the benefit is slightly reduced by increasing the number of agents, while in reverse auctions the benefit increases with both agents and items. The exception is with rank-based elicitors, which limit themselves to eliciting the next-best bundle: these do not scale as the number of agents grows.A full-length version of this paper is on-line at Combinatorial auctions, where agents can submit bids on bundles of items, are attractive when the bidders' valuations on bundles exhibit complementarity (a bundle of items is worth more than the sum of its parts) and/or substitutability (a bundle is worth less than the sum of its parts). Determining the winners in such auctions is a complex optimization problem that has recently received * The material in this paper is based upon work supported by the National Science Foundation under CAREER Award IRI-9703122, Grant IIS-9800994, ITR IIS-0081246, and ITR IIS-0121678. Some of the results in this paper appeared in the AMEC 2002 workshop.. Copyright is held by the author/owner. AAMAS'03, July 14-18, 2003, Melbourne, Australia. ACM 1-58113-683-8/03/0007. considerable attention. However, bidding in such an auction is itself a difficult problem: there are exponentially many bundles, and each agent may need to bid on all of them to fully express its preferences [5] . Appropriate bidding languages can reduce the communication overhead in some cases. We investigate the orthogonal approach of having the auctioneer propose to the agents what bundles they should bid on [1, 2] . That is, the auctioneer incrementally elicits information from the bidders, stopping when enough information has been elicited to determine the winners of the auction.. We ran experiments to evaluate both previously proposed and novel elicitation algorithms. In addition, we study the complexity of determining the bidders' payments. Along with combinatorial auctions we study combinatorial reverse auctions (procurement auctions). Our experiments show that only a very small fraction of the bidders' preference information needs to be elicited in order to determine the provably optimal allocation and the VCG payments. The full-length version of the paper also proves some propositions useful in designing practical elicitors.

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