Signals comprised of a stream of short pulses appear in many applications including bioimaging and radar. The recent finite rate of innovation framework, has paved the way to low rate sampling of such pulses by noticing that only a small number of parameters per unit time are needed to fully describe these signals. Unfortunately, for high rates of innovation, existing sampling schemes are numerically unstable. In this paper we propose a general sampling approach which leads to stable recovery even in the presence of many pulses. We begin by deriving a condition on the sampling kernel which allows perfect reconstruction of periodic streams from the minimal number of samples. We then design a compactly supported class of filters, satisfying this condition. The periodic solution is extended to finite and infinite streams and is shown to be numerically stable even for a large number of pulses. High noise robustness is also demonstrated when the delays are sufficiently separated. Finally, we process ultrasound imaging data using our techniques and show that substantial rate reduction with respect to traditional ultrasound sampling schemes can be achieved.
In this section we explore the relationship between our approach and previously developed solutions @cite_20 @cite_4 @cite_19 @cite_5 .
@cite_19 @cite_5 @cite_4 @cite_20
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Ginsberg and Smith [6, 7] propose a new method for reasoning about action, which they term a possible worlds approach (PWA). The PWA is an elegant, simple, and potentially very powerful domain-independent technique that has proven fruitful in other areas of AI [13, 5]. In the domain of reasoning about action, Ginsberg and Smith offer the PWA as a solution to the frame problem (What facts about the world remain true when an action is performed?) and its dual, the ramification problem [3] (What facts about the world must change when an action is performed?). In addition, Ginsberg and Smith offer the PWA as a solution to the qualification problem (When is it reasonable to assume that an action will succeed?), and claim for the PWA computational advantages over other approaches such as situation calculus. Here and in [16] I show that the PWA fails to solve the frame, ramification, and qualification problems, even with additional simplifying restrictions not imposed by Ginsberg and Smith. The cause of the failure seems to be a lack of distinction in the PWA between the state of the world and the description of the state of the world. I introduce a new approach to reasoning about action, called the possible models approach, and show that the possible models approach works as well as the PWA on the examples of [6, 7] but does not suffer from its deficiencies. We present a computational theory of the paragraph. Within it we formally define coherence, give semantics to the adversative conjunction "but" and to the Gricean maxim of quantity, and present some new methods for anaphora resolution.The theory precisely characterizes the relationship between the content of the paragraph and background knowledge needed for its understanding. This is achieved by introducing a new type of logical theory consisting of an object level, corresponding to the content of the paragraph, a referential level, which is a new logical level encoding background knowledge, and a met alevel containing constraints on models of discourse (e.g. a formal version of Gricean maxims). We propose also specific mechanisms of interaction between these levels, resembling both classical provability and abduction. Paragraphs are then represented by a class of structures called p-models. In this paper we present a new approach to the problem of planning with incomplete information and sensing. Our approach is based on a higher level, "knowledge-based", representation of the planner's knowledge and of the domain actions. In particular, in our approach we use a set of formulas from a first-order modal logic of knowledge to represent the planner's incomplete knowledge state. Actions are then represented as updates to this collection of formulas. Hence, actions are being modelled in terms of how they modify the knowledge state of the planner rather than in terms of how they modify the physical world. We have constructed a planner to utilize this representation and we use it to show that on many common problems this more abstract representation is perfectly adequate for solving the planning problem, and that in fact it scales better and supports features that make it applicable to much richer domains and problems. Several recent works on relation extraction have been applying the distant supervision paradigm: instead of relying on annotated text to learn how to predict relations, they employ existing knowledge bases (KBs) as source of supervision. Crucially, these approaches are trained based on the assumption that each sentence which mentions the two related entities is an expression of the given relation. Here we argue that this leads to noisy patterns that hurt precision, in particular if the knowledge base is not directly related to the text we are working with. We present a novel approach to distant supervision that can alleviate this problem based on the following two ideas: First, we use a factor graph to explicitly model the decision whether two entities are related, and the decision whether this relation is mentioned in a given sentence; second, we apply constraint-driven semi-supervision to train this model without any knowledge about which sentences express the relations in our training KB. We apply our approach to extract relations from the New York Times corpus and use Freebase as knowledge base. When compared to a state-of-the-art approach for relation extraction under distant supervision, we achieve 31 error reduction. Case-Based Reasoning systems retrieve and reuse solutions for previously solved problems that have been encountered and remembered as cases. In some domains, particularly where the problem solving is a classification task, the retrieved solution can be reused directly. But for design tasks it is common for the retrieved solution to be regarded as an initial solution that should be refined to reflect the differences between the new and retrieved problems. The acquisition of adaptation knowledge to achieve this refinement can be demanding, despite the fact that the knowledge source of stored cases captures a substantial part of the problem-solving expertise. This paper describes an introspective learning approach where the case knowledge itself provides a source from which training data for the adaptation task can be assembled. Different learning algorithms are explored and the effect of the learned adaptations is demonstrated for a demanding component-based pharmaceutical design task, tablet formulation. The evaluation highlights the incremental nature of adaptation as a further reasoning step after nearest-neighbour retrieval. A new property-based classification to adapt symbolic values is proposed, and an ensemble of these property-based adaptation classifiers has been particularly successful for the most difficult of the symbolic adaptation tasks in tablet formulation. This paper attempts to provide an adequate basis for formal definitions of the meanings of programs in appropriately defined programming languages, in such a way that a rigorous standard is established for proofs about computer programs, including proofs of correctness, equivalence, and termination. The basis of our approach is the notion of an interpretation of a program: that is, an association of a proposition with each connection in the flow of control through a program, where the proposition is asserted to hold whenever that connection is taken. To prevent an interpretation from being chosen arbitrarily, a condition is imposed on each command of the program. This condition guarantees that whenever a command is reached by way of a connection whose associated proposition is then true, it will be left (if at all) by a connection whose associated proposition will be true at that time. Then by induction on the number of commands executed, one sees that if a program is entered by a connection whose associated proposition is then true, it will be left (if at all) by a connection whose associated proposition will be true at that time. By this means, we may prove certain properties of programs, particularly properties of the form: ‘If the initial values of the program variables satisfy the relation R l, the final values on completion will satisfy the relation R 2’. In this paper, theidentification problem, thetolerance problem, and thecontrol problem are treated for the interval linear equation Ax=b. These problems require computing an inner approximation of theunited solution set Σ∃∃(A, b)= x ∈ ℝ n | (∃A ∈ A)(Ax ∈ b) , of thetolerable solution set Σ∀∃(A, b)= x ∈ ℝ n | (∀A ∈ A)(Ax ∈ b) , and of thecontrollable solution set Σ∃∀(A, b)= x ∈ ℝ n | (∀b ∈ b)(Ax ∈b) respectively. Analgebraic approach to their solution is developed in which the initial problem is replaced by that of finding analgebraic solution of some auxiliary interval linear system in Kaucher extended interval arithmetic. The algebraic approach is proved almost always to give inclusion-maximal inner interval estimates of the solutionsets considered. We investigate basic properties of the algebraic solutions to the interval linear systems and propose a number of numerical methods to compute them. In particular, we present the simple and fastsubdifferential Newton method, prove its convergence and discuss numerical experiments. In the context of reverse-engineering project we designed a use-case specification recovery technique for legacy information systems. With our technique, we can recover the alternative flows of each use-case of the system. It is based on a dynamic (i.e. runtime) analysis of the working of the system using execution traces. But "traditional" execution trace format do not contain enough information for this approach to work. Then we designed a new execution trace format together with the associated tool to get the program's dynamic decision tree corresponding to each of the use-case scenario. These trees are then processed to find the possible variants from the main scenario of each use-case. In this paper we first present our approach to the use-case specification recovery technique and the new trace format we designed. Then the decision tree compression technique is showed with a feasibility study. The contribution of the paper is our approach to the recovery of legacy systems' use-case, the new trace format and the decision tree processing technique. The paper presents an adaptive approach to perform impact analysis from a given change request to source code. Given a textual change request (e.g., a bug report), a single snapshot (release) of source code, indexed using Latent Semantic Indexing, is used to estimate the impact set. Should additional contextual information be available, the approach configures the best-fit combination to produce an improved impact set. Contextual information includes the execution trace and an initial source code entity verified for change. Combinations of information retrieval, dynamic analysis, and data mining of past source code commits are considered. The research hypothesis is that these combinations help counter the precision or recall deficit of individual techniques and improve the overall accuracy. The tandem operation of the three techniques sets it apart from other related solutions. Automation along with the effective utilization of two key sources of developer knowledge, which are often overlooked in impact analysis at the change request level, is achieved. To validate our approach, we conducted an empirical evaluation on four open source software systems. A benchmark consisting of a number of maintenance issues, such as feature requests and bug fixes, and their associated source code changes was established by manual examination of these systems and their change history. Our results indicate that there are combinations formed from the augmented developer contextual information that show statistically significant improvement over stand-alone approaches. We approach the problem of academic literature search by considering an unpublished manuscript as a query to a search system. We use the text of previous literature as well as the citation graph that connects it to find relevant related material. We evaluate our technique with manual and automatic evaluation methods, and find an order of magnitude improvement in mean average precision as compared to a text similarity baseline. In this paper we describe an application of language technology to policy formulation, where it can support policy makers assess the acceptance of a yet-unpublished policy before the policy enters public consultation. One of the key concepts is that instead of relying on thematic similarity, we extract arguments expressed in support or opposition of positions that are general statements that are, themselves, consistent with the policy or not. The focus of this paper in this overall pipeline, is identifying arguments in text: we present and empirically evaluate the hypothesis that verbal tense and mood are good indicators of arguments that have not been explored in the relevant literature. In this paper, we present the results of long-term research conducted in order to study the contribution made by software models based on the Unified Modeling Language (UML) to the comprehensibility of Java source-code deprived of comments. We have conducted 12 controlled experiments in different experimental contexts and on different sites with participants with different levels of expertise (i.e., Bachelor’s, Master’s, and PhD students and software practitioners from Italy and Spain). A total of 333 observations were obtained from these experiments. The UML models in our experiments were those produced in the analysis and design phases. The models produced in the analysis phase were created with the objective of abstracting the environment in which the software will work (i.e., the problem domain), while those produced in the design phase were created with the goal of abstracting implementation aspects of the software (i.e., the solution application domain). Source-code comprehensibility was assessed with regard to correctness of understanding, time taken to accomplish the comprehension tasks, and efficiency as regards accomplishing those tasks. In order to study the global effect of UML models on source-code comprehensibility, we aggregated results from the individual experiments using a meta-analysis. We made every effort to account for the heterogeneity of our experiments when aggregating the results obtained from them. The overall results suggest that the use of UML models affects the comprehensibility of source-code, when it is deprived of comments. Indeed, models produced in the analysis phase might reduce source-code comprehensibility, while increasing the time taken to complete comprehension tasks. That is, browsing source code and this kind of models together negatively impacts on the time taken to complete comprehension tasks without having a positive effect on the comprehensibility of source code. One plausible justification for this is that the UML models produced in the analysis phase focus on the problem domain. That is, models produced in the analysis phase say nothing about source code and there should be no expectation that they would, in any way, be beneficial to comprehensibility. On the other hand, UML models produced in the design phase improve source-code comprehensibility. One possible justification for this result is that models produced in the design phase are more focused on implementation details. Therefore, although the participants had more material to read and browse, this additional effort was paid back in the form of an improved comprehension of source code. This paper presents a novel approach to document-based discourse analysis by performing a global A* search over the space of possible structures while optimizing a global criterion over the set of potential coherence relations. Existing approaches to discourse analysis have so far relied on greedy search strategies or restricted themselves to sentence-level discourse parsing. Another advantage of our approach, over other global alternatives (like Maximum Spanning Tree decoding algorithms), is its flexibility in being able to integrate constraints (including linguistically motivated ones like the Right Frontier Constraint). Finally, our paper provides the first discourse parsing system for French; our evaluation is carried out on the Annodis corpus. While using a lot less training data than earlier approaches than previous work on English, our system manages to achieve state-of-the-art results, with F1-scores of 66.2 and 46.8 when compared to unlabeled and labeled reference structures. In the past several years studies have started to appear comparing the accuracies of various science mapping approaches. These studies primarily compare the cluster solutions resulting from different similarity approaches, and give varying results. In this study we compare the accuracies of cluster solutions of a large corpus of 2,153,769 recent articles from the biomedical literature (2004–2008) using four similarity approaches: co-citation analysis, bibliographic coupling, direct citation, and a bibliographic coupling-based citation-text hybrid approach. Each of the four approaches can be considered a way to represent the research front in biomedicine, and each is able to successfully cluster over 92p of the corpus. Accuracies are compared using two metrics—within-cluster textual coherence as defined by the Jensen-Shannon divergence, and a concentration measure based on the grant-to-article linkages indexed in MEDLINE. Of the three pure citation-based approaches, bibliographic coupling slightly outperforms co-citation analysis using both accuracy measures; direct citation is the least accurate mapping approach by far. The hybrid approach improves upon the bibliographic coupling results in all respects. We consider the results of this study to be robust given the very large size of the corpus, and the specificity of the accuracy measures used. © 2010 Wiley Periodicals, Inc. We present a novel approach to relation extraction, based on the observation that the information required to assert a relationship between two named entities in the same sentence is typically captured by the shortest path between the two entities in the dependency graph. Experiments on extracting top-level relations from the ACE (Automated Content Extraction) newspaper corpus show that the new shortest path dependency kernel outperforms a recent approach based on dependency tree kernels. The Situation Calculus is a logic of time and change in which there is a distinguished initial situation and all other situations arise from the different sequences of actions that might be performed starting in the initial one. Within this framework, it is difficult to incorporate the notion of an occurrence, since all situations after the initial one are hypothetical. These occurrences are important, for instance, when one wants to represent narratives. There have been proposals to incorporate the notion of an action occurrence in the language of the Situation Calculus, namely Miller and Shanahan’s work on narratives [22] and Pinto and Reiter’s work on actual lines of situations [27, 29]. Both approaches have in common the idea of incorporating a linear sequence of situations into the tree described by theories written in the Situation Calculus language. Unfortunately, several advantages of the Situation Calculus are lost when reasoning with a narrative line or with an actual line of occurrences. In this paper we propose a different approach to dealing with action occurrences and narratives, which can be seen as a generalization of narrative lines to narrative trees. In this approach we exploit the fact that, in the discrete Situation Calculus [13], each situation has a unique history. Then, occurrences are interpreted as constraints on valid histories. We argue that this new approach subsumes the linear approaches of Miller and Shanahan’s, and Pinto and Reiter’s. In this framework, we are able to represent various kinds of occurrences; namely, conditional, preventable and non-preventable occurrences. Other types of occurrences, not discussed in this article, can also be accommodated. These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental in the quantification of uncertainty within applications in volving the blending of mathematical models with data. The finite dimensional situation is described first, along with some motivational examples. Then the development of probability measures on separable Banach space is undertaken, using a random series over an infinite set of functions to construct draws; these probability measures are used as priors in the Bayesian approach to inverse problems. Regularity of draws from the priors is studied in the natural Sobolev or Besov spaces implied by the choice of functions in the random series construction, and the Kolmogorov continuity theorem is used to extend regularity considerations to the space of Holder continuous functions. Bayes’ theorem is de rived in this prior setting, and here interpreted as finding conditions under which the posterior is absolutely continuous with respect to the prior, and determining a formula for the Radon-Nikodym derivative in terms of the likelihood of the data. Having established the form of the posterior, we then describe various properties common to it in the infinite dimensional setting. These properties include well-posedness, approximation theory, and the existence of maximum a posteriori estimators. We then describe measure-preserving dynamics, again on the infinite dimensional space, including Markov chain-Monte C arlo and sequential Monte Carlo methods, and measure-preserving reversible stochastic differential equations. By formulating the theory and algorithms on the underlying infinite dimensional space, we obtain a framework suitable for rigorous analysis of the accuracy of reconstructions, of computational complexity, as well as naturally constructing algorithms which perform well under mesh refinement, since they are inherently well-defined in infinite dimensions. List of Figures. List of Tables. Preface. 1. Preliminaries. 2. Software Environments. 3. On Preconditioning. 4. Verified Solution of Nonlinear Systems. 5. Optimization. 6. Non-Differentiable Problems. 7. Use of Intermediate Quantities in the Expression Values. References. Index. A traditional counterexample to a linear-time safety property shows the values of all signals at all times prior to the error. However, some signals may not be critical to causing the failure. A succinct explanation may help human understanding as well as speed up algorithms that have to analyze many such traces. In Bounded Model Checking (BMC), a counterexample is constructed from a satisfying assignment to a Boolean formula, typically in CNF. Modern SAT solvers usually assign values to all variables when the input formula is satisfiable. Deriving minimal satisfying assignments from such complete assignments does not lead to concise explanations of counterexamples because of how CNF formulae are derived from the models. Hence, we formulate the extraction of a succinct counterexample as the problem of finding a minimal assignment that, together with the Boolean formula describing the model, implies an objective. We present a two-stage algorithm for this problem, such that the result of each stage contributes to identify the “interesting” events that cause the failure. We demonstrate the effectiveness of our approach with an example and with experimental results. Traditional fact checking by experts and analysts cannot keep pace with the volume of newly created information. It is important and necessary, therefore, to enhance our ability to computationally determine whether some statement of fact is true or false. We view this problem as a link-prediction task in a knowledge graph, and present a discriminative path-based method for fact checking in knowledge graphs that incorporates connectivity, type information, and predicate interactions. Given a statement S of the form (subject, predicate, object), for example, (Chicago, capitalOf, Illinois), our approach mines discriminative paths that alternatively define the generalized statement (U.S. city, predicate, U.S. state) and uses the mined rules to evaluate the veracity of statement S . We evaluate our approach by examining thousands of claims related to history, geography, biology, and politics using a public, million node knowledge graph extracted from Wikipedia and PubMedDB. Not only does our approach significantly outperform related models, we also find that the discriminative predicate path model is easily interpretable and provides sensible reasons for the final determination.