Visual Conceptualizations and Models of Science This Journal of Informetrics special issue aims to improve our understanding of the structure and dynamics of science by reviewing and advancing existing conceptualizations and models of scholarly activity.Several of these conceptualizations and models have visual manifestations supporting the combination and comparison of theories and approaches developed in different disciplines of science.The term -model‖ and -conceptualization‖ has diverse definitions in different disciplines and use contexts.In this issue, ‗conceptualization' refers to an unifying mental framework that identifies the boundaries of the system or object under study, its basic building blocks, interactions among building blocks, basic mechanisms of growth and change, and existing laws (static and dynamic). The term ‗model' refers to a precise description of a system or object under study in a formal language, e.g., using mathematical equations or computational algorithms. An older more comprehensive definition of ‗science' using a description by Cohen -… in its oldest and widest sense the term science (like the German word Wissenschaft) denotes all ordered and reliable knowledge-so that a philologist or a critical historian can truly be called scientific …‖ (Cohen, 1933) . Consequently, ‗science of science' refers to the scientific study of all scholarly activities in the natural sciences, the social sciences, and the arts and humanities. Given the number of scientific disciplines involved in the study of all sciences, the phrase ‗sciences of sciences' might be more appropriate yet the singular versions are commonly used.Subsequently, we discuss challenges towards a theoretically grounded and practically useful science of science and provide a brief chronological review of relevant work. Then, we exemplarily present three conceptualizations of science that attempt to provide frameworks for the comparison and combination of existing approaches, theories, laws, and measurements.Finally, we discuss the contributions of and interlinkages among the eight papers included in this issue.Each paper makes a unique contribution towards conceptualizations and models of science and roots this contribution in a review and comparison with existing work.To strengthen the historical embedding of current and anticipated future work, this special issue starts with an invited contribution by Eugene Garfield on the history of ‗science of science' studies. Eugene Garfield's paper combines personal autobiographic memories as an eye-witness from the very beginning of scientometrics with data driven historiographic citation analysis. This way, the paper makes a convincing The conceptualizations and models of science presented in this issue differ considerably in the Scope of the modeled system or object (from very specific fields of science to all of science but also from very specific static or dynamic effects to major interlinked effects), Basic building blocks of science (from papers, authors to scientific fields, institutions, regions),. Interactions of building blocks (via papers references and co-author linkages to spatial and topical distributions), Basic mechanisms of growth and change captured (indicators, network evolution, trajectories in geographic and topic spaces), Existing laws encapsulated (static and/or dynamic).. Eight papers and an editorial cannot possibly capture the breath of relevant work and the number of puzzle pieces needed for a theoretically grounded and practically useful science of science. Instead, they should be seen as ‗stepping stones' towards the envisioned shared conceptualization of science. In this process visual conceptualizations of the structure and dynamics of science have an important role to play as they help diffuse and combine existing and new knowledge and expertise across disciplinary, cultural and geospatial boundaries.

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


Automated Bidding for Media Services at the Edge of a Content Delivery Network Abstract-We investigate the problem of providing media services to multiple autonomous wireless users at the edge of a content delivery network (CDN) in a setting where wireless resources are priced based on real-time market demands. Our focus is on the multimedia service resource negotiation process, which is performed prior to the actual media transmission. We adopt the progressive second price (PSP) auction mechanism, which is used to determine the network resource allocation to the users and a corresponding tax for the consumed resources. Our interest in this negotiation mechanism lies in understanding a single user's (or agent's) ability to learn to improve its bids over time in order to increase its own utility in the face of time-varying resource valuations and contention for resources with other users. We pay particular attention to the implementation complexity and the information requirements of the agent's deployed learning rule, and we quantify the impact of these factors on the rule's ultimate performance (i.e., the cumulative utility achieved over time) and efficiency (i.e., the utility gained per unit of computation). These factors are especially important in the mobile video streaming context, where limited resources must be efficiently utilized, and where communication and computation overheads can significantly impact the quality of service experienced by the user.Index Terms-Content delivery networks, multiagent learning, multimedia service middleware, resource negotiation, session negotiation. A T THE EDGE of content delivery networks, independent media-service providers [1] deliver network-content to multiple autonomous mobile users through their wireless radios. The number of users that access a single media-service provider may vary depending on the available infrastructure (e.g., an 802.11-enabled access point versus a cellular network base-station). Regardless of the type of infrastructure-to-mobile wireless link, there are always limited network resources (i.e., bandwidth). Unfortunately, such bandwidth constraints conflict with the resource requirements of real-time, bandwidth intense, video streaming applications, which we will focus on in this paper. That being the case, resource allocation becomes of paramount importance in ensuring that multiple autonomous users fairly and optimally share the scarce wireless resources. We frame the resource allocation problem as an auction in which wireless resources are priced based on real-time market demands [2] - [8] . In contrast to charging a flat-rate (as is currently done for most services provided over cellular networks and the internet), this auction based framework allows mediaservice providers and other owners of communication bandwidth to manage the network resources by charging users based on their bandwidth usage and the real-time market price of those resources at the time of their usage. This obviates the need for service providers to implement controversial bandwidth "throttling" algorithms, which slow traffic from big consumers of bandwidth (such as those participating in peer-to-peer video streaming and other multimedia services), because, during times of high congestion, users would have to pay a premium for the bandwidth required by these services.. By framing the network resource management problem as an auction, the media-service provider is no longer the sole decider of how resources are allocated among users. Individual users now have incentive to actively participate in the resource negotiating process because they can influence their resource allocations through their bids. We assume that a user's mobile device automates the bidding process by acting as the user's agent; that is, it submits bids to the media-service provider on the user's behalf. Importantly, an agent's bid impacts its resource allocation as well as the resource allocations of the other competing agents, which we will regard as opponents in the auction. This auction game is played repeatedly over time such that agents can request more or less resources based on the congestion that they experience and their time-varying resource valuations.. In order to improve their bids over time (i.e., increase their payoffs), we assume that agents receive (limited) feedback from the media-server about their opponents' bids. Using this information, agents can learn to bid so that their utility is improved over time. For example, the agent can analyze its opponents' previously submitted bid quantities and then submit a bid commensurate with the anticipated future congestion level and its current valuation of the resources.. In this paper, we adopt the progressive second price (PSP) auction 1 mechanism [2] as the foundation of the decentralized media-service resource negotiation. In the early work on the PSP auction [2] , the authors assume that 1) an agent may learn to bid based on complete knowledge of its opponents' bid profile in the previous time slot; 2) bids are always submitted asynchronously, with only one agent submitting a new bid in each time slot; and 3) all agents deploy the same learning rule (i.e., "self-play" assumptions [4] ). These assumptions are designed to study the equilibrium and convergence properties of the PSP auction, but they are not appropriate for the considered multimedia resource allocation scenario for two reasons. Firstly, each agent (i.e.,mobile device) has limited (but different) computational capabilities, so it may be infeasible for it to process all of its opponents' bids in order to determine the bid that will maximize its payoffs within a tolerable delay. Secondly, due to the decentralized nature of the wireless resource allocation problem, and the possibility that there are many agents requesting resources, possibly significant communication overheads are incurred as the media-server repeatedly updates agents with information about all of their opponents' bids. Hence, unlike in conventional game-theoretic solutions, we shift our attention away from equilibrium concepts in favor of modeling, analyzing, and improving the dynamic behavior of interacting users in dynamic settings, out of equilibrium, while also explicitly considering the information requirements and implementation constraints occurring when deploying multimedia applications.. Considering the range of communication and processing capabilities in existing mobile devices (e.g., smart phones, PDAs, laptops), it is clear that there cannot be a one-size-fits-all learning algorithm. In other words, learning algorithms with various informational and computational requirements are necessary so that a wide range of mobile devices can all participate in the auction game. Despite this need for complexityand information-adaptive learning rules in real-life multiagent systems, most literature on multiagent learning in games only considers two categories of learning rules. These learning rules land on the extremes of both informational and computational requirements and have not been designed with any realistic application in mind (i.e., they are general and not application specific). For example, payoff-based learning rules (e.g., reinforcement learning [3] ) are simple to implement, but they assume that no a priori information about the system is available. Meanwhile, probabilistic learning rules (e.g., fictitious play [4] ) are informationally and computationally prohibitive, which precludes their applicability in the distributed mobile context. Our contributions in this paper are as follows.. • We cast the media-service resource negotiation problem at the edge of the content delivery network (CDN) as an auction game among multiple agents. In this auction scenario, the agents' resource valuations are defined based on operational rate-distortion models for the encoded video sequences. Hence, their valuations depend on such factors as the video source's characteristics (e.g.,high-motion, detailed textures) and multimedia format (e.g., MPEG-2, H.264/AVC). Importantly, the agent's utility, which is a quasi-linear function of the resource valuation and cost, is aligned with the user's desire to achieve a high-quality video at a low cost.. • We investigate different levels of centralized coordination in the auction game. Under the proposed coordination policies, the media-server can poll a variable number of agents to submit a new bid in each time slot, thereby impacting the learning dynamics.. • We introduce learning rules that require an agent to acquire different levels of information from the media-service provider about its opponents, and we consider the computational requirements (in floating point operations) of the different learning rules. We also consider heterogeneous opponents, which all deploy different learning rules.. • Finally, we propose two evaluation metrics with which we can quantify 1) the value of the information required by an agent to deploy a particular learning rule (i.e., the cumulative impact of more or less information about its opponents' bids on its utility), 2) the efficiency of the learning rule in terms of achieved utility per unit of computational complexity, 3) the cumulative impact of different levels of centralized coordination on an agent's utility, and 4) the utility impact when agents deviate from "self-play" assumptions, and employ heterogeneous learning rules with varying informational and computational requirements. The remainder of this paper is organized as follows. In Section II, we describe the system setup and the PSP auction mechanism. We then formalize the agents' goals and the repeated media-service resource negotiation framework. In Section III, we describe several coordination policies that can be employed in this framework. In Section IV, we introduce learning rules that vary in computational and informational complexity, and we propose two metrics for evaluating and comparing these learning rules. In Section V, we present our experimental results and in Section VI we conclude the paper. In this paper, we propose a solution for negotiating the network resources necessary for mobile multimedia streaming services over wireless networks. The focus of this paper is on understanding a single agent's (i.e., mobile multimedia device) ability to learn to improve its bids over time given its limited computational capabilities and (possibly) limited feedback about its environment (i.e., the bids of its opponents). Our experimental results show that, in a static environment, an agent can learn to make near optimal bids with limited information, and with very little computational overhead.. However, in a more dynamic environment, with many agents simultaneously submitting bids, any single agent's ability to bid well depends heavily on the degree of imposed centralized coordination. In very dynamic scenarios, our results show that a greedy bidding approach performs better over time than more complex approaches that consider other agent's bids. We note that, although we deployed the PSP auction, other auction mechanisms could be used in this framework.

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


Under-approximating loops in C programs for fast counterexample detection Many software model checkers only detect counterexamples with deep loops after exploring numerous spurious and increasingly longer counterexamples. We propose a technique that aims at eliminating this weakness by constructing auxiliary paths that represent the effect of a range of loop iterations. Unlike acceleration, which captures the exact effect of arbitrarily many loop iterations, these auxiliary paths may under-approximate the behaviour of the loops. In return, the approximation is sound with respect to the bit-vector semantics of programs. Our approach supports arbitrary conditions and assignments to arrays in the loop body, but may as a result introduce quantified conditionals. To reduce the resulting performance penalty, we present two quantifier elimination techniques specially geared towards our application. Loop under-approximation can be combined with a broad range of verification techniques. We paired our techniques with lazy abstraction and bounded model checking, and evaluated the resulting tool on a number of buffer overflow benchmarks, demonstrating its ability to efficiently detect deep counterexamples in C programs that manipulate arrays. The generation of diagnostic counterexamples is a key feature of model checking. Counterexamples serve as witness for the refutation of a property, and are an invaluable aid to the engineer for understanding and repairing the fault.. Counterexamples are particularly important in software model checking, as bugs in software frequently require thousands of transitions to be executed, and are thus difficult to reproduce without the help of an explicit error trace. Existing software model checkers, how-ever, fail to scale when analysing programs with bugs that involve many iterations of a loop. The primary reason for the inability of many existing tools to discover such "deep" bugs is that exploration is performed in a breadth-first fashion: the detection of an unsafe execution traversing a loop involves the repeated refutation of increasingly longer spurious counterexamples. The analyser first considers a potential error trace with one loop iteration, only to discover that this trace is infeasible. As consequence, the analyser will increase the search depth, usually by considering one further loop iteration. In practice, the computational effort required to discover an assertion violation thus grows exponentially with the depth of the bug.. Notably, the problem is not limited to procedures based on abstraction, such as predicate abstraction or abstraction with interpolants. Bounded model checking (BMC) is optimised for discovering bugs up to a given depth k, but the computational cost grows exponentially in k.. The contribution of this paper is a new technique that enables scalable detection of deep bugs. We transform the program by adding a new, auxiliary path to loops that summarises the effect of a parametric number of iterations of the loop. Similar to acceleration, which captures the exact effect of arbitrarily many iterations of an integer relation by computing its reflexive transitive closure in one step [4, 8, 11] , we construct a summary of the behaviour of the loop. By symbolically bounding the number of iterations, we obtain an under-approximation which is sound with respect to the bit-vector semantics of programs. Thus, we avoid false alarms that might be triggered by modeling variables as integers.. In contrast to related work, our technique supports assignments to arrays and arbitrary conditional branching by computing quantified conditionals. As the computational cost of analysing programs with quantifiers is high, we introduce two novel techniques for summarising certain conditionals without quantifiers. The key insight is that many conditionals in programs (e.g., loop exit conditions such as i ≤ 100 or even i = 100) exhibit a certain monotonicity property that allows us to drop quantifiers.. Our approximation can be combined soundly with a broad range of verification engines, including predicate abstraction, lazy abstraction with interpolation [19] , and bounded software model checking [5] . To demonstrate this versatility, we combined our technique with lazy abstraction and the Cbmc [5] model checker. We evaluated the resulting tool on a large suite of benchmarks known to contain deep paths, demonstrating our ability to efficiently detect deep counterexamples in C programs that manipulate arrays. We present a sound under-approximation technique for loops in C programs with bit-vector semantics. The approach is very effective for finding deep counterexamples in programs that manipulate arrays, and compatible with a variety of existing verification techniques. A short-coming of our under-approximation technique is its lack of support for dynamic data structures, which we see as a challenging future direction. The under-approximation technique presented in this paper is based on our previous work on loop detection [16, 17] . The algorithm in [16] , however, does not yield a strict under-approximation, and thus necessitates an additional step to validate the unwound counterexample. Our new technique avoids this problem.. The techniques in Sect. 3.1 constitute a simple form of acceleration [4, 8] . The subsequent restrictions in Sects. 3.3 and 3.4 on π , however, impose a symbolic bound on the number of iterations, yielding an under-approximation. In contrast to acceleration of integer relations, our approximation is sound for bit-vector arithmetic. Sinha uses term rewriting to compute symbolic states parametrised by the loop counter, stating that his technique can be extended to support bit-vectors [22] .. The quantifier elimination technique of Sect. 4.1 bears similarities with splitter predicates [21] , a program transformation facilitating the generation of disjunctive invariants. Similarly, trace partitioning [9] splits program paths to increase the precision of static analyses. Neither technique aims at eliminating quantifiers.. Loop summarisation [15] and path invariants [3] avoid loop unrolling by selecting an appropriate over-approximation of the loop from a catalogue of invariant templates. Overapproximations are also used in the context of loop bound inference [24] and reasoning about termination [6] . However, over-approximations do not enable the efficient detection of counterexamples.. Hojjat et al. [11] uses interpolation to derive inductive invariants from accelerated paths. While this work combines under-and over-approximation, it is not aimed at counterexample detection. Motivated by the results of [11] , we believe that under-approximation can, if combined with interpolation, improve the performance of verification tools on safe programs. We plan to support interpolation in a future version of our implementation.. Techniques to solve recurrences are frequently used in compiler construction [23] . For example, van Engelen et al. [7] present an algorithm to compute closed forms for systems of recurrence equations, which also supports induction variables that are updated conditionally by introducing a dynamic range for each variable. While it would be straight forward to incorporate these ideas into our work, the technique discussed in Sect. 3 is sufficient for all practical purposes if the bounded range of program variables is taken into account (see our remark at the end of Sect. 3.1.2).. We refer the reader to [17] for a description of additional related work.

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


Topology optimization using a mixed formulation: An alternative way to solve pressure load problems Abstract A shortcoming of the traditional density based approach to topology optimization is the handling of design dependent loads that relate to boundary data, such as for example pressure loads. Previous works have introduced spline and iso-density curves or alternative parametrization schemes to determine the load surfaces. In this work we suggest a new way to solve pressure load problems in topology optimization. Using a mixed displacement–pressure formulation for the underlying finite element problem, we define the void phase to be an incompressible hydrostatic fluid. In this way we can transfer pressure loads through the fluid without any needs for special load surface parametrizations. The method is easily implemented in the standard density approach and is demonstrated to work efficiently for both 2D and 3D problems. By extending the method to a three phase (solid/fluid/void) design method we also demonstrate design of water containing dams. Since its introduction almost two decades ago [1] , the topology optimization method for continuum structures [2] has increased tremendously in popularity and is now being used as an everyday mechanical design tool in larger industries and academia all over the world. Also a number of commercial topology optimization tools have been developed, either based on special Finite Element (FE) solvers or as add-ons to standard commercial FE packages.. While in academia, the applications of topology optimization methods has expanded to a multitude of problems in material design , MicroElectroMechanical Systems (MEMS), fluids , wave-propagation and nano-optics (see [2] for an overview), the most common design problems that are solved by commercial codes are still compliance minimization problems and maximization of lowest eigenfrequency problems with constraints on material resource. Although the solution procedures for these kinds of problems have matured to a satisfactory level, there are still a number of open or less-than-satisfactorily resolved issues with the fundamental topology optimization method. One group of problems concerns inclusion of manufacturing constraints such as minimum and maximum length-scale, draw directions and extrusion constraints; another group concerns inclusion of design dependent loads like pressure load problems.. In pressure load problems, the position of the loads depend on the shape and topology. Such problems are encountered in hydrostatics and dynamics of wind, water and snow loaded mechanical and civil structures such as ships, submerged structures, airplanes, pumps, etc.. A number of papers have addressed the pressure load problems in topology optimization. The Aalborg group [3] [4] [5] has suggested a formulation where the unknown load application curve is determined from an iso-density curve. The sensitivities of the distributed loads with respect to design changes are obtained from an efficient finite difference formulation and a scheme that prevents ill-defined load curves is suggested. In [6] it is suggested to implement the pressure loads by a manipulation of thermal prestrains and a special scheme for identification of "fluid" and void elements is applied. In [7] it is suggested to parametrize a load curve by a spline function and updating element densities and spline parameters in an integrated approach. A phase-field method involving a triple-well function that allows for distribution of three material phases (solid/fluid/void) is introduced in [8] . The scheme includes an explicit penalization of intermediate densities as well as perimeter. In all the above papers, it is stated that the pressure load problem is much more difficult to solve than standard (fixed) load problems. Different more or less elaborate schemes have to be applied in order to update the loading surface. Lately, several applications of the level set method to topology optimization have appeared. Since there exist implicitly given curves describing the boundaries for this method, it is fairly straight forward to implement pressure loads in the level set method [9, 10] .. In this paper we introduce a new way to solve the pressure load problem based on a mixed displacement-pressure (incompressible) formulation but using the standard density approach to topology optimization. Thus, the scheme can be implemented in existing softwares based on the density approach. In fact, the only necessary changes to the code lies in the interpolation scheme, the boundary conditions and possibly the linear system solver.. The idea of the method is the following. Instead of defining the equilibrium equations in the typical FE displacement formulation, we define it in mixed form by including the pressure as a separate variable. This makes it possible to define the void phase in the topology optimization formulation as a hydrostatic incompressible fluid, thus allowing for transfer of pressure from the external boundary conditions to the structure -independent of its shape or topology. A potentially weak point of this idea is that internal "void" regions in the structures also become incompressible (fluid-filled) -a possibility the optimization algorithm may take advantage of by using the void regions as "incompressible cavities". This possibility, that may or may not be physically relevant for a particular problem, can be avoided by introducing an extra (compressible) void phase in the design problem and limiting the volume fraction of the fluid phase. The method thus becomes a 3-phase (solid/fluid/void) topology optimization scheme (see e.g. refs. [11] [12] [13] for previous work on 3-phase topology optimization). This computational scheme immediately applies to the 2 as well as 3 dimensional cases without further modifications. Also, the idea may be applied to design of water loaded structures like dams or water towers by introducing mass density and gravity loads on the fluid and structural phases.. The paper is organized as follows. In section 2 we formulate the physical model and compare the standard and mixed formulations for the solving of elastoand hydrostatic problems. In section 3 we formulate the topology optimization problem for 2 and 3 phase problems. In section 4 we demonstrate the method by considering various test problems, some of which are known from the literature. In section 5 we draw the conclusions and discuss strong and weak points of the method. 3 2 Physical model In this paper we have proposed a new method for handling pressure load problems in the density approach to topology optimization. The basic idea of the method is to define the void phase to be incompressible, i.e. as a hydrostatic fluid, and thereby we can transfer the pressure load through the fluid regions. In order to solve problems involving incompressibility we have to define the finite element problem in a mixed displacement/pressure form. This mixed form is a standard method in many FE-codes and should thus not complicate the implementation of the method. Otherwise, our method works exactly as the usual density based approaches -one only has to add a fixed fluid region to the design domain in order to impose the pressure loading through the fluid region. Introducing a second design variable into the formulation we can solve three phase (solid/fluid/void) problems as encountered in the design of dams and we can prevent internal cavities in becoming fluid filled by constraining 26 the amount of fluid.. For the case of pure pressure load problems the convergence is very stable as long as we consider distribution of an incompressible elastic material. Here we typically obtain convergence (maximum change of design variables between two iterations less than 0.001) to nice black and white solutions in less than 100 iterations. For the case of distribution of compressible elastic material, the convergence is best if the fluid bulk modulus is at most 10-20 times larger than the bulk modulus of the elastic material. As demonstrated by several examples, however, the optimized topologies do not seem to change when the fluid bulk modulus is increased towards infinity thus the above limitation on the fluid bulk modulus does not constitute a problem.. For the design of dams, good convergence was difficult to obtain. However, it is well-known that self-weight problems are difficult to make converge (c.f. the discussion in [22] ) and we thus attribute the problems to the self-weight issue and not to the proposed interpolation scheme. In order to improve the convergence of these problems one may have to use improved MMA approximations or globally convergent methods [22] .. As demonstrated by the pressurized lid and dam examples the proposed scheme immediately applies to 3D problems. Here we only considered academic problems but it will be interesting to test the scheme on real life problems such as pressure vessels, pumps or other pressure loaded structures.. Finally, we note that the proposed mixed formulation can be extended to dynamic (acoustic-structure interaction) problems as discussed in refs. [27, 28] .

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Uniqueness of Meromorphic Functions and Differential Polynomials In this paper,we study the uniqueness of meromorphic functions concerning differential polynomials , prove two main theorems which generalize and improve some results earlier given by M.L. Fang and W.Hong, I.Lahiri and N.Mandal.

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Bandits With Heavy Tail The stochastic multiarmed bandit problem is well understood when the reward distributions are sub-Gaussian. In this paper, we examine the bandit problem under the weaker assumption that the distributions have moments of order , for some. Surprisingly, moments of order 2 (i.e., finite variance) are sufficient to obtain regret bounds of the same order as under sub-Gaussian reward distributions. In order to achieve such regret, we define sampling strategies based on refined estimators of the mean such as the truncated empirical mean, Catoni's -estimator, and the median-of-means estimator. We also derive matching lower bounds that also show that the best achievable regret deteriorates when .Index Terms-Heavy-tailed distributions, regret bounds, robust estimators, stochastic multi-armed bandit. I N this paper, we investigate the classical stochastic multiarmed bandit problem introduced by [1] and described as follows: an agent facing actions (or bandit arms) selects one arm at every time step. With each arm there is an associated probability distribution with finite mean . These distributions are unknown to the agent. At each round , the agent chooses an arm , and observes a reward drawn from independently from the past given . The goal of the agent is to minimize the regret We refer the reader to [2] for a survey of the extensive literature of this problem and its variations. The vast majority of authors assume that the unknown distributions are sub-Gaussian, that is, the moment generating function of each is such that if is a random variable drawn according to the distribution , then for all ,. where , the so-called "variance factor" is a parameter that is usually assumed to be known. In particular, if rewards take values in , then by Hoeffding's lemma, one may take . Similarly to the asymptotic bound of [3, Th. 4.10] , this moment assumption was generalized in [2, Ch. 2] by assuming that there exists a convex function such that, for all , Then, one can show that the so-called -UCB strategy (a variant of the basic UCB strategy of [4] ) satisfies the following regret guarantee. Let , and the Legendre-Fenchel transform of , defined by Then, -UCB 1 satisfies. In particular, when the reward distributions are sub-Gaussian, the regret bound is of the order , which is known to be optimal even for bounded reward distributions, see [4] .. While this result shows that assumptions weaker than sub-Gaussian distributions may suffice for a logarithmic regret, it still requires the distributions to have finite moment generating function. Another disadvantage of the bound above is that the dependence on the gaps deteriorates as the tail of the distributions become heavier. In fact, as we show it in this paper, the bound is suboptimal when the tails are heavier than sub-Gaussian.. Such heavy-tailed reward distributions naturally arise in various contexts where bandit algorithms have been used in the past. A prominent example is the distribution of delays in end-to-end network routing [5] , a typical application domain for bandits-see, e.g., [2] . Another interesting example is the distribution of running times of heuristics for solving hard combinatorial problems [6] , where bandit algorithms have been used to select the heuristics [7] .. In this paper, we investigate the behavior of the regret when the distributions are heavy tailed, and might not have a finite moment generating function. We show that under significantly weaker assumptions, regret bounds of the same form as in the sub-Gaussian case may be achieved. In fact, the only condition we need is that the reward distributions have a finite variance. Moreover, even if the variance is infinite but the distributions have finite moments of order for some , one may still achieve a regret logarithmic in the number of rounds through the dependency on the s worsens as gets smaller. For instance, for distributions with moment of order bounded by 1 we derive a strategy that satisfies. The key to this result is to replace the empirical mean by more refined robust estimators of the mean and construct "upper confidence bound" strategies. Note that algorithms based on the empirical mean estimator have been previously applied to heavy-1 More precisely, -UCB with .. 0018-9448 © 2013 IEEE tailed stochastic bandits in [8] but they obtained polynomial regret bounds while we show logarithmic regret bounds. We also prove matching lower bounds that show that the proposed strategies are optimal up to constant factors. In particular, the dependency in is unavoidable. In the following, we start by defining a general class of sampling strategies that are based on the availability of estimators of the mean with certain performance guarantees. Then, we examine various estimators for the mean. For each estimator, we describe their performance (in terms of concentration to the mean) and deduce the corresponding regret bound.

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


Enhanced wireless roaming security using three-party authentication and tunnels Many organizations and many home users have deployed WiFi networks permitting external users to connect to the Internet through their networks. Such WiFi sharing poses many security risks for the visited network as well as for the visiting user.In this paper, we focus on the recently introduced concept for tunneled WiFi roaming in which the infrastructure of the visited network is considered as part of the security architecture. A secure layer-2 tunneling between the user's device and his home network is performed by the visited network only after the successful authentication of all three parties. The authentication protocol provides the mobile device and its home network with a secret key that protects their end-to-end communication. Additionally, it provides another tunnel key, shared with the visited network, that protects the actual traffic exchanged between the visited and home networks and prevents diverse resource consumption attacks against the latter. This concept encourages users to provide roaming service in a more secure and privacyfriendly way. We show how to implement this concept using the IEEE802.11i/EAP framework, based on existing infrastructures and standard tunneling protocols. Almost all laptops, netbooks and many smartphones sold today are equipped with WiFi interfaces. The different WiFi variants have enabled new types of Internet access. Ten years ago, mobile employees had to use dial-up modems to contact their enterprise's VPN or access the Internet. During the last years, usage of WiFi has increased quickly in enterprise networks, but also in private houses, restaurants or hotels. In enterprise networks, the security of the WiFi network is today a strong concern for system administrators and most enterprise networks have implemented strong authentication schemes to authenticate their wireless users. At home, users often use a WEP or WPA shared key to connect to their router or set-top box. However, more and more WiFi users expect to be able to access the Internet from any location: at their favorite restaurant, at friends' house, in their hotel room, while shopping, during any conference, etc.. Several solutions have been implemented and deployed to serve these mobile users. Some users consider that Internet access should be free and so open their Internet access via WiFi. Others, grouped in communities such as FON [1] or wifi.com, share their connections with other members of their communities only. Some businesses, such as restaurants, consider the WiFi-based Internet access as an added value and propose a free access or install commercial hotspots to allow their visitors access the Internet. Finally, system administrators who manage enterprise and university networks are often pushed by their users to deploy an open WiFi-based Internet access for their visitors.. However, these ways of sharing an Internet access raise many security issues for the visited network as well as for the mobile guest. When visiting another company or institution for a very short stay, users often obtain temporary credentials to access the Internet. For the visited institution, dealing with the security risks brought on is not an easy task. Other users do not support the secure authentication mechanism (e.g., EAP-TTLS [2] ) used by the company and must be placed in a less secure subnet isolated from the rest of the institution network. Despite these precautions, a visitor will use IP addresses belonging to the visited network (directly or indirectly through a NAT) to access the Internet. This means that any network on the Internet will consider this visitor as an actual employee of that institution. Thus, if the visitor misbehaves, the reputation of the institution may be tarnished. Consider for example an insecure laptop that is part of a botnet, infected by a worm or sending spam. A remote network which is attacked by such a laptop may decide to blacklist the IP address or the entire prefix of the visited network. Such blacklistings are difficult to revert.. On the visitor side, there are also security risks. First of all, since the visited network forwards all the user traffic to and from the Internet, it is able to easily sniff the whole traffic and perform all kind of man-in-the-middle attacks. Rogue access points have already been used in many places and security specialists often avoid using public WiFi networks due to the associated risks. Unfortunately, most users do not have security skills and are often unable to determine whether the access point on which it is connecting does really belong to the visited institution.. In this paper, following the ideas from Manulis et al. [3] , we describe an infrastructure and a suitable authentication and key establishment protocol that permits users to use an authenticated and possibly encrypted tunnel through their home network to access the Internet. The visited network has control over the secure tunnel between the mobile guest and his home network which is established upon successful authentication of all the parties. In contrast to existing tunneling solutions, e.g., VPNs based on IKEv2 and IPsec [4] , authentication is now performed between the three parties in order to fit their trust models and security goals. The targeted type of roaming encompasses visits of short or medium duration in which it is undesirable for the visited network to issue any form of credentials to the mobile guests, i.e., enroll any registration procedure. Additionally, our scenarios do not assume high mobility of guests across different networks. Therefore, we are not concerned with the handover issues between different foreign networks. We remark that [3] provides theoretical evaluation and security analysis of the protocol. However, practical aspects such as deployment and implementation challenges based on known standards have not been investigated so far. The goal of this paper is to close this gap between theory and practice. This paper is organized as follows. Section 2 describes our proposed infrastructure and protocols. Then, we present the architecture of our prototype implementation on the Linux platform in Section 3. Section 4 compares our solution with related work and we conclude in Section 5. More and more users expect to be able to use their WiFi device to access the Internet everywhere. Besides commercial hotspots, many universities, enterprises and home WiFi networks have implemented techniques to share their WiFi networks with visitors. However, sharing a WiFi network induces security risks if the visitor misbehaves.. To counter these risks, we have proposed a safer WiFi roaming technique that combines three-party authentication with tunnels. We have described the encapsulation mechanisms, the RAKE protocol and its implementation on top of EAP. Our prototype, running on the Linux platform, shows that it is possible to achieve three-party authentication without causing higher computation delays than existing EAP schemes. Our further work is to deploy RAKE on a wider scale to gain operational experience with it. In an enterprise, a typical way to permit short-term visitors to connect to its network is to give them temporary credentials. In addition to the administrative cost of managing the creation of these accounts, the identity of the visitors should be checked and they should be informed about the acceptable usage practices. However, a user coming from another company has already credentials in his home network, so why do not use these? The Eduroam project [9] follows this idea and allows any user, from a partner educational institution, to connect in any other institution by using its "home" credentials. Eduroam uses IEEE802.1X with methods such as EAP-TTLS and a hierarchy of RADIUS servers to authenticate the user in his home institution. Other propositions suggested to provide authentication in roaming situations have already been discussed in [3] . A common issue of these solutions is that they are mainly authentication schemes and so do not allow key derivation for a tunnel-based approach. All these do not suggest solutions that would prevent the misuse of the IP address belonging to the visited institution by the mobile user.. For a user wishing to share its WiFi connection at home, some other solutions such as wifi.com or FON [1] exist. wifi.com acts more as a social network in which people share their home WEP/WPA personal secret key with their friends using the provided application. FON allows users from their community to connect with their own FON account credentials to a specific hardware placed by another user. With the latter, you can have people you absolutely do not know using your network to access the Internet. For both wifi.com and FON, if the visitor misbehaves, the owner of the access point will first be considered responsible. Moreover, unlike in enterprise networks, home routers use NAT to connect several users that will use the same public IP address. As a consequence, if several people are connected at the same time, it will be difficult, depending on whether the NAT maintains precise logs or not, to determine a posteriori who made a reprehensible action.. Anyway, connecting to a foreign WiFi network, whether owned by an enterprise or by a private user, is often a risky operation from the security point of view. Technically, the visited network is able to sniff and alter all unencrypted data sent or received by the user. Additionally, in most of the previously described solutions, the user is even not able to authenticate the access point. A classical solution used by enterprises is to force the employees to use a Virtual Private Network (VPN) to connect to the Internet outside the enterprise. VPN is an encrypted and eventually authenticated tunnel from the user's laptop to his home institution VPN server. Most VPNs use protocols such PPTP [10] and L2TP [7] over IPSec. They rely on specific authentication schemes. These authentications are only performed between the mobile user and his institution, disregarding the visited network. In other words, if used alone, VPN does not provide information to the visited network about who is connecting to the network. Another existing technology, worth to be mentioned, is Mobile IP [11] . Using encapsulation it allows a user to use an IP address from his home network while outside. However, Mobile IP provides neither authentication with the visited network nor tunnel encryption. It also forces the visited network to offer a public IP address to each visitor.. All the aforementioned solutions only address one concern at a time but do not enable to build a global solution tackling all different security threats. The only currently available tunnel-based solution in which the visited institution is aware that the mobile user is doing roaming to its home network has been proposed by Sastry et al. [12] . In their scheme the visited network accepts every device without any authentication and grants it access to its home network over the Internet. The mobile device can thus initiate a VPN connection (using NAT traversal techniques if necessary) to its home network. However, this solution has several weaknesses. First, the Internet access granted by the visited network, even a restricted one, may bear intrusion risks to its infrastructure. Second, the mobile device must comply with the network layer infrastructure of the foreign network, e.g., IPv4/IPv6, IP assignment via DHCP, etc. Third, VPN tunnels do not provide any proof to the visited network that the mobile device is connecting to its genuine home network as a VPN connection can be established to any server on the Internet. Fourth, visited and home networks do not authenticate each other and, as a consequence, neither accounting mechanisms nor quality-of-service contracts can be securely implemented. We fairly remark that Sastry et al. were focusing on the actual architecture for a city-wide WiFi roaming rather than dealing with the related authentication and key establishment goals. We have implemented the proposed WiFi roaming solution by extending the EAP supplicant and authenticator that are part of the hostap distribution 2 . Due to space limitations, we only describe our implementation of the RAKE protocol. For L2TP and IPSec, we reuse respectively the xl2tpd and Openswan implementation, both maintained by Xelerance Corporation.. One of the main advantages of EAP is that it is easily extendable. In practice, this means that new authentication scheme, denoted in general as an EAP method, can be added easily as a new module to an existing EAP implementation. Some EAP methods performing only simple authentication (e.g., EAP-MD5) or channel protection (e.g., EAP-TTLS) can be combined to securely authenticate a mobile node at an access point (or a delegate AAA server) and to eventually derive the WPA master key used for encrypting the wireless channel. EAP-RAKE is a standalone EAP method, it performs both authentication and key generation. It also provides other features that cannot be performed by other existing EAP methods, namely authentication and key exchange with a third party. The RAKE packets exchanged between F and H are sent using EAP over RADIUS.. In practice, in hostap, the EAP process interacts with the upper method through a simple API. It calls the EAP method hooks upon creation of the state at method startup, each time an EAP message is received or has to be sent, to know whether the method has succeeded and if so, to obtain the WPA master session key. The implementation of this new EAP method required, in addition to the support for the new configuration options, specific modules containing about 2700 lines of C. It runs on both Linux desktops and OpenWRT, a Linux distribution embedded in several WiFi access points. Cryptographic functions proposed for the RAKE protocol in [3] are also supported in our implementation. The source code has been written in a modular way so that new cryptographic algorithms can be added easily.. To evaluate the performance of our RAKE implementation, we have built a small testbed composed of one Pentium 4 2.6Ghz with 1 GBytes RAM running Linux acting as the mobile device, an ASUS 500 GP access point running OpenWRT 8.09.1 (Broadcom CPU BCM47XX 266 Mhz, 32 MBytes RAM) and a Linux server with a dual CPU E2180 2.00GHz and 2 GBytes of RAM.. Within this testbed we have measured the processing time required for the different messages of the RAKE protocol: 2 Hostap is composed of hostapd (the authenticator, i.e, the access point), WPA supplicant (i.e., M) and some utilities. The main contributor is Jouni Malinen. Project website: http://hostap.epitest.fi/ the low-end access point took 18 msec to perform the initialization and to generate I1. The mobile device replied directly with I2. The processing of the I2 message and the generation of the I3 by the access point took slightly less than 6 msec and the home network took 8 msec to initiate and reply with the HA1 message. The longest processing times were the processing of the HA1 message (46 msec) and the processing of the MA1 message (57 msec) by the access point.. In comparison when using PEAP+MSCHAPv2, the processing on the supplicant requires 14 msec while the access point takes more than 176 msec to process the authentication messages.

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


Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty The reliability of computer predictions of physical events depends on several factors: the mathematical model of the event, the numerical approximation of the model, and the random nature of data characterizing the model. This paper addresses the mathematical theories, algorithms, and results aimed at estimating and controlling modeling error, numerical approximation error, and error due to randomness in material coefficients and loads. A posteriori error estimates are derived and applications to problems in solid mechanics are presented. The reliability of computer simulations has become one of the most critical subjects in computational science. The expectations of users of computer predictions to make decisions about many events and processes that affect broad areas of technology has risen due to advances in computing and computational methods. The mere calculation of qualitative information on global trends of physical systems is no longer viewed as the primary goal of simulations. TodayÕs analysts expect to obtain quantitative information on system performance and outputs, and this expectation has put stringent demands on the sophistication and accuracy of computer simulations and on the use of effective methods of estimation and control of errors in computed results. In this paper, we review recent developments in the estimation and control of errors encountered in computer predictions in computational mechanics. Three error sources are considered: modeling error, due to use of simplified models of physical events, discretization error, due to use of discrete approximations of mathematical models of the events, and error due to uncertainty, due to scatter in data, particularly data involving material coefficients in the various models. The estimation of modeling error follows the theory developed in [1, 3, 6] and discretization error, the theory in [2, 4, 5, [7] [8] [9] and elsewhere. To estimate errors due to uncertainty, we employ first-order perturbation methods for stochastic partial differential equations. In this analysis, the ''worst-case-scenario'' is used to obtain upper and lower bounds on errors in quantities of interest in situations in which the material coefficients are random variables. Some applications to threedimensional elasticity models are presented.

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


New constructions of fuzzy identity-based encryption In this paper we construct two new fuzzy identity-based encryption (IBE) schemes in the random oracle model. Not only do our schemes provide public parameters whose size is independent of the number of attributes in each identity (used as public key) but they also have useful structures which result in more efficient key extraction and/or encryption than the random oracle version of Sahai and Water's fuzzy IBE scheme, considered recently by Pirretti et al. We prove that the confidentiality of the proposed schemes is relative to the Bilinear Decisional Bilinear Diffie-Hellman problem. Motivation. The concept of fuzzy identity-based encryption (IBE) recently introduced by Sahai and Waters [8] is to provide an error-tolerance property for IBE. Namely, in fuzzy IBE, a user with the secret key for the identity ω can decrypt a ciphertext encrypted with the public key ω if ω and ω are within a certain distance of each other.. As noted in [8] , fuzzy IBE can directly be applied to the situation where a user is traveling and another party wants to encrypt at an ad-hoc meeting between them. Another application of fuzzy IBE is "attribute-based encryption [8, 6, 7] " where a party can encrypt data to all users that have a certain set of attributes, e.g. {company, division, department}.. 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, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Related Work. Since Sahai and Water's work, fuzzy IBE has been discussed in the context of the attribute-based encryption (ABE). Very recently, Goyal et al. [6] proposed an ABE scheme that provides fine-grained sharing of encrypted data. Piretti et al. [7] used Sahai and Waters' "large universe" construction of fuzzy IBE, which we simply call "Sahai-Waters construction", to realize their secure information management architecture. They also observed that if the random oracle [2] is employed, computational overhead of the Sahai-Waters construction can greatly be reduced. We remark that the random oracle not only reduces computational overhead but also provides a very short public parameters whose size is independent of the number of attributes associated with an identity or the number of attributes in the defined universe, which is crucial in the storage constrained applications.. Our Contribution. In this paper, we go one step beyond Pirreti et al.'s results by presenting fuzzy IBE schemes in the random oracle model, which are structurally different from the Sahai-Waters construction. We show that the structural difference results in more efficient schemes than even the random oracle version of the Sahai-Waters construction considered by Pirretti et al. [7] . We prove that our schemes meet the security requirements as defined in [8] assuming that the Decisional Bilinear Diffie-Hellman (DBDH) problem is hard. In this paper we proposed two efficient fuzzy IBE schemes, which are proven to be secure in the random oracle model.. We expect that our new fuzzy IBE schemes will serve as efficient building blocks for biometric authentication systems or attribute-based encryption systems. Construction of fuzzy IBE schemes that have the exactly the same structures as ours (that is, non-random oracle version of our schemes using the technique of [8] ) is an interesting open problem.

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 O O O O O O O O O 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


Estimation of surface area and surface area measure of three-dimensional sets from digitizations Abstract. A local method for estimating surface area and surface area measure of three-dimensional objects from discrete binary images is presented. A weight is assigned to each 2 × 2 × 2 configuration of voxels and the total surface area of an object is given by summation of the local area contributions. The method is based on an exact asymptotic result that holds for increasing resolution of the digitization. It states that the number of occurrences of a 2 × 2 × 2 configuration is asymptotically proportional to an integral of its "h-function" with respect to the surface area measure of the object. We find explicit representations for these h-functions. Analyzing them in detail, we determine weights that lead to an asymptotic worst case error for surface area estimation of less than 4%. We show that this worst case error is the best possible. Exploiting the local nature of the asymptotic result, we also establish two parametric estimators for the surface area measure. The latter allow to quantify anisotropy of the object under consideration. Simulation studies illustrate the validity of the estimation procedure also for finite, but sufficiently high resolution. Already Gauss used the fact that the area of a planar object is approximately proportional to the number of lattice points contained in it. This observation, extended to three dimensions, is the basis of modern volume approximations based on voxel counts in digital black-and-white images of real-world structures. To approximate the surface area, counts of individual voxels are no longer sufficient. Instead, one determines the number of occurrences of certain patterns -so-called boundary configurations -of black and white voxels in 2 × 2 × 2 cubes. Then, a weight is assigned to each configuration of voxels and the total surface area is obtained by a summation of the local area contributions. As the choice of these weights is not unique, there is a number of competing choices, all motivated by geometric arguments. In [11] the weights are chosen as the areas of isosurfaces originating from a marching cubes representation. The weights in [13] are determined by discretizing an integral geometric relation (the Crofton formula) and using a digital version of the Euler-Poincaré characteristic in lattice-line sections. Under the assumption that the object is randomly translated and rotated before digitization, the weights derived in [10] are optimal, in the sense that the obtained estimator is an MVUE (minimal variance unbiased estimator). In the present paper we will also work with randomized positions of the object relative to the main axis of the digitization, but only allow for random "uniform" translations. Under this assumption there appears to be no unbiased estimator based on weighted configuration counts.. The purpose of this work is to present another estimator of surface area (giving a new set of weights), which has a better worst case behavior than the known ones when the resolution is high. Furthermore, we can also estimate a local version of the surface area, the surface area measure. Its normalization (also called the rose of normal directions) is the distribution of the outer unit normal of the object in a typical boundary point. If, for instance, the object is a ball, then this measure is proportional to the uniform distribution on the set of unit vectors. The deviation of the surface area measure from uniformity can therefore be used to quantify anisotropy of an object. Both estimators are based on a very general asymptotic result in [6] that was only recently shown. Asymptotics is understood here with respect to increasing resolution, or, equivalently, with lattice distance t > 0 of the digitization converging to zero. Let N t be the number of occurrences of the boundary configuration (B, W ) of black B and white W voxels in the digitized picture of an object Z. The asymptotic result states that N t behaves in mean like ct −2 as t → 0. Interestingly, the constant c can be given explicitly as an integral. over the unit sphere S 2 of R 3 . Here, h (B,W ) is the so-called h-function depending only on the configuration (B, W ) under consideration. The measure S 2 (Z, ·) is the surface area measure of Z and is independent of the configuration. The total mass S(Z) = S 2 1 S 2 (Z, dn) is the surface area of Z. Hence, any weighted sum of hfunctions, approximating the constant function one, can be used to estimate surface area from configuration counts. This is the key idea to construct a set of weight vectors such that the maximal relative error of the derived surface area estimator is asymptotically minimal. The best possible bound is 3.98%. Simulations suggest that this worst case bound even holds for finite (but reasonably high) resolution 1/t. We can show that the estimators of surface area proposed in [10] and [13] both have an asymptotic worst case error of 7.3%. The weights proposed in [11] have an asymptotic worst case error of 12.8%. Their weight vectors are substantially different from ours and from each other. The analysis of linear dependence between h-functions in Proposition 3.4 enables us to explain these differences to a large extend. Essentially there are only five types of configurations that contribute to the asymptotic worst case error. The coefficients for two of these types are approximately equal in all approaches, while for the other three they differ substantially. The linear dependence of certain h-functions implies that some weight can be shifted between the latter three types without changing the asymptotic worst case error.. As configuration counts allow to approximate certain integrals with respect to the surface area measure, it is natural to use these counts also for surface area measure estimation. As there are only finitely many 2 × 2 × 2 configurations, yielding finitely many integrals of the form (1) with different integrands, we will have to choose a model with finitely many parameters. This leads to the question to find the number of degrees of freedom that can possibly be determined by the integrals over all h-functions of 2 × 2 × 2 configurations. In other words, we ask for the dimension of the subspace H 2×2×2 , spanned by all h-functions, in the Banach space C(S 2 ) of all continuous functions on the unit sphere S 2 . Proposition 3.3 shows that dim(H 2×2×2 ) = 50. We then suggest two simple models for the surface area measure with 50 degrees of freedom. The first model allows for discrete measures with a prescribed support, the second model has a piecewise constant density. The first model has the advantage of statistical simplicity: we can derive explicit formulae for the model parameters depending on the configuration counts, and show that the derived estimator is asymptotically unbiased, i.e. the mean estimator converges (weakly) to the true surface area measure, as the resolution increases. The second model is interesting because it includes the isotropic case, hence it can more easily be used to detect and quantify deviations from isotropy. The two models are a natural extension of the two-dimensional models suggested in [4] and refine an existing approach of [2] allowing for 26 degrees of freedom. Note that estimation of the surface area measure from counts of point pairs (in the 26-neighborhood) instead of counts of 2 × 2 × 2 configurations only determines 13 degrees of freedom. The new methods clearly yield refined estimators, but build on the same lateral resolution. * * * We described the new approaches for subsets of three-dimensional space R 3 , but as many of the concepts also hold in d-dimensional space, we will present them in this general setting, where appropriate. Similarly, we develop parts of the theory for n × n × n configurations, which are natural extensions of the 2 × 2 × 2 case in R 3 . It should also be mentioned that asymptotic results always depend on certain regularity conditions of the underlying structure Z. Conditions in the literature are either not made explicit or rather strong, like polygonality or morphological openness and closeness with respect to suitable line segments. As we are working with asymptotic results, the conditions on the set Z in the present paper are very weak, we assume that Z is gentle; see Section 2 for a definition. Of course, the validity of the above worst case errors depends on the discretization model chosen. We formulate all results with respect to the common Gauss digitization model. As the underlying asymptotic identity from [6] also holds for the volume-threshold digitization, an extension to this setting is immediate.. Note that the surface area estimators in the present paper are all based on configuration counts and do not require a time consuming reconstruction of the actual object surface. This is the reason why the implementation is straightforward and the algorithms have an excellent time performance. Alternatives are a number of multigrid convergent estimators; see [7] for an overview. These estimators converge to the true surface area as lattice resolution increases. They are, however, computationally more intensive, as they require an explicit approximation of the boundary of the object, which apparently cannot be achieved by local methods. Examples in this spirit are [8] , based on global polyhedrization techniques, and [1] , where a discrete approximation of the normal vector field is integrated. * * * The paper is organized as follows. The main results are presented in Sections 4 and 5. Section 2 introduces notation, the most important definitions and some basic results about convex polytopes, which will be needed in the sequel. In Section 3 we start with a general analysis of the h-function of an n × n × n configuration (B, W ). Instead of representing it as the difference of two support functions of fairly complicated polytopes, we suggest a compact form as a minimum over the scalar products with only few, so-called visible points of the set B +W . This is a generalization of [4, Corollary 1] . The set of all informative n × n × n configurations can be determined by applying an algorithm suggested in [2] . For each of these configurations, Algorithm 1 in Section 3.1 determines all visible points and thus allows to express its h-function in a compact form, which gives insight into the structure of the h-function. Based on this, we identify linear dependencies between h-functions (Proposition 3.4), and subsequently determine the dimension of H 2×2×2 (Proposition 3.3). Estimation of surface area is treated in Section 4. Section 5 presents the two mentioned estimators for surface area measure.

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


Nominal rewriting systems We present a generalisation of first-order rewriting which allows us to deal with terms involving binding operations in an elegant and practical way. We use a nominal approach to binding, in which bound entities are explicitly named (rather than using a nameless syntax such as de Bruijn indices), yet we get a rewriting formalism which respects α-conversion and can be directly implemented. This is achieved by adapting to the rewriting framework the powerful techniques developed by Pitts et al. in the FreshML project.Nominal rewriting can be seen as higher-order rewriting with a first-order syntax and built-in α-conversion. We show that standard (first-order) rewriting is a particular case of nominal rewriting, and that very expressive higher-order systems such as Klop's Combinatory Reduction Systems can be easily defined as nominal rewriting systems. Finally we study confluence properties of nominal rewriting. Term rewriting systems (TRS) provide a general framework for specifying and reasoning about computation. They are defined as transformation rules working over trees labelled by variable and function symbols. This simple idea is very powerful: TRSs can be regarded as a universal programming language which can be used to express different programming paradigms (functional, logical, parallel, etc.), as an abstract model of computation, or as transformations that can be used for program optimisation and automated theorem proving.. Standard TRSs are first-order, but a lot of effort has been devoted in the past to develop systems manipulating higherorder terms. Higher-order terms are built with higher-order functions and variables which can be free or bound. Several examples of higher-order systems can be found in the literature: Combinatory Reduction Systems (CRS) [22] , Higherorder Rewrite Systems (HRS) [25] , Expression Reduction Systems (ERS) [21, 20] , and the rewriting calculus [10, 11] , combine first-order rewriting with a notion of bound variable. The λ-calculus can be seen as a higher-order rewrite system with one binder: λ-abstraction.. Systems that manipulate binders must also deal with α-conversion: first-order substitutions (i.e. replacements) may capture variables, so substitutions in a higher-order system use renamings. In all the higher-order formalisms that we mentioned above α-conversion is an implicit operation (in other words, terms are defined modulo renamings of bound variables), and substitution is also a meta-operation. Several notions of explicit substitutions and explicit α-conversion have been defined for the λ-calculus (e.g. [1, 24, 12] ) and more generally for higher-order rewrite systems (e.g. [28, 6] ) with the aim of specifying the higher-order notion of substitution as a set of first-order rewrite rules. In most of these systems variable names are replaced by de Bruijn indices to make easier the explicitation of α-conversion, at the expense of readability. The explicit substitution systems that use names for variables either restrict the rewriting mechanism to avoid cases in which α-conversion would arise, or do not address the problem of α-conversion.. In this paper we present a new formalism for rewriting with bound variables. In our systems variables are named (thus the title "nominal rewriting systems", abbreviated as NRS in the sequel), substitution is first-order, and we deal with α-conversion by using an auxiliary freshness relation between bound variables and terms, written as a#t (read "a is fresh for the term t"). We can see nominal terms as firstorder terms with built-in α-conversion. In this sense, NRSs can be seen as an explicit substitution version of higherorder rewriting where α-conversion is already formalised (it does not need to be specified explicitly).. The use of the notion of freshness in a rewriting framework is the main novelty of this work. It is based on the work reported in [29, 15] . A similar freshness relation is used to define a metalanguage for functional programming in [30] and to study unification problems in [33] .. Following [29, 15] , we call atoms the names that can be bound and reserve the word variable for the identifiers that cannot be bound (known as variables and metavariables respectively in CRSs), and leave implicit the dependencies between variables and names as it is common practice in informal presentations of higher-order reductions. More precisely, variables in NRSs have arity zero, as in ERSs. For example, the β-reduction rule and the η-expansion rule of the λ-calculus are written as: The technical foundations and style of this work are most directly derived from work on nominal logic [29] and nominal unification [33] . We use a nominal matching algorithm, which is easy to derive from the unification algorithm and inherits its good properties (such as most general unifiers), in our definition of rewriting.. Our theory stays close to the first-order case, while still allowing binding. We achieve this by working with concrete syntax, but up to a notion of equality ≈α which is not just structural identity. It is not α-equivalence either: ≈α is actually logical, in the sense that ∆ s ≈α s is something that we deduce using assumptions in ∆.. We pay the price that terms, rewrites, and equalities, happen in a context ∆, but ∆ is fixed and does not seem to behave perniciously.. This system is also powerful, in that it encodes first-order systems and CRSs. It can be seen as an explicit substitution version of higher-order rewriting, but with built-in α-conversion. We could easily implement a higher-order rewrite system using a nominal rewrite system: we only need to make the substitution explicit. We can spare the effort of 'implementing' α-conversion using de Bruijn indices and all the associated machinery. In this section we recall two formalisms that are closely related to nominal rewriting: first-order rewriting and CRSs. We refer the reader to [2, 13, 22] for details and examples.

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