The Relationship between Dependency Classes

This paper describes a fibrational categorical semantics for the modal necessity-only fragment of constructive modal type theory, both with and without dependent types. Constructive type theory does not usually discuss logical modalities, and modalities tend to be mostly studied within classical logic, not within type theory. But modalities should be very useful in type theory, as they are very useful in modelling theoretical computing systems. Providing constructive versions of modal logics and their associated Curry-Howard modal type theories is also a very productive program, e.g. helpful when dealing with computational effects, staged computation, and functional reactive types, for example. There seems to be renewed interest in the notion of constructive modal type theory (and in notions of linear type theory), in part because of the interest in homotopy type theory. The modal type theory presented here uses dependent types, in the style of Ritter's categorical models of the Calculus of Constructions. To build up to these, we first discuss the kinds of constructive modal type theory in the literature. Then we provide a non-dependent modal type theory, introduced in previous work, that we generalize to dependent types in the following section. Dependent type theories are usually but not always given categorical semantics in terms of fibrations. We provide semantics in terms of fibrations for both the non-dependent and the dependent type systems discussed and prove them sound and complete, thereby providing evidence that the type theory is meaningful. These fibrational models should be also applicable to the homotopy type theory setting.

Theories of drug dependence abound, ranging from moralistic interpretations to the more humanistic psychosocial and medical models. Whether any one or some combination of these various theories of drug abuse possess verisimilitude is an open question. What is incontestable is that drug abuse is a broader and more severe problem today than ever, and none of these theories have born significant practical fruit in terms of prevention or treatment of drug dependent persons. Perhaps some of these various approaches possess nuggets of truth; unfortunately, most fail to appreciate the multiplicity of factors leading to the development of drug taking, and ultimately to the bringing of drug abuse under control. More importantly, most approaches to the drug abuse problem lack an overall conceptual framework within which to better understand the various factors regulating drug use and abuse.

In the previous chapter, we offered a comprehensive study on modeling and detecting jamming attacks against time-critical wireless networks with applications to the smart grid. However, only modeling and detection cannot provide defense against jamming attacks, and is only the first setup towards anti-jamming communication for wireless smart grid applications. Hence, spread spectrum systems, which provide jamming resilience via multiple frequency and code channels, must be adapted to the smart grid for secure wireless communications, while at the same time providing latency guarantee for control messages. An open question is how to minimize message delay for timely smart grid communication under any potential jamming attack.To address this issue, we provide a paradigm shift from the case-by-case methodology, which is widely used in existing works to investigate well-adopted attack models (also used in the previous chapter), to the worst-case methodology, which offers delay performance guarantee for smart grid applications under any attack. We first define a generic jamming process that characterizes a wide range of existing attack models. Then, we show that in all strategies under the generic process, the worst-case message delay is a U-shaped function of network traffic load. This indicates that, interestingly, increasing a fair amount of traffic can in fact improve the worst-case delay performance. As a result, we demonstrate a lightweight yet promising system, TACT (transmitting adaptive camouflage traffic), to combat jamming attacks. TACT minimizes the message delay by generating extra traffic called camouflage to balance the network load at the optimum. Experiments show that TACT can decrease the probability that a message is not delivered on time in order of magnitude for smart grid applications.

A thorough understanding of femtosecond magnetism will address the important questions of how fast the magnetization can be reoriented in a material and what physical processes present fundamental limits to this speed. Ultimately, light represents the fastest means to alter the state of a material since laser pulses can now be generated with extremely short temporal duration down to a few tens of attoseconds. One particularly interesting and novel scheme for the ultrafast manipulation of spins using light takes advantage of the optically-induced spin transfer (OISTR), which was recently introduced by Dewhurst et al. [1]. This microscopic mechanism is driven by a spin-selective direct optical excitation from one magnetic sublattice to another. Guided by time dependent density functional theory calculations, we are able to monitor the optically induced transient changes in the model systems FeNi in real time by time-resolved magneto-optical Kerr spectroscopy using high-harmonic generation (HHG TMOKE) [2]. Exploiting the spectral sensitivity of this measurement technique we are able to follow the ultrafast spin transfer from Fe to Ni during the optical excitation. OISTR, therefore, opens up a new avenue towards manipulating solids on timescales only limited by the duration of the exciting light pulse, which forecasts a control of the spin dynamics on the attosecond time scale. How far this spin manipulation via OISTR is a general phenomenon or restricted to a subset of materials with specific properties is an open experimental and theoretical question. In order to opens up a systematic path for coherent manipulation of spin dynamics by direct light-matter interaction we started to investigate OISTR in a variety of different compounds with higher complexity [3]. We reveal for example that the half-Heusler materials NiMnSb and CoMnSb exhibit strong signatures of OISTR, whereas this is less pronounced in the full-Heusler compounds Co2MnSi, Co2FeSi, and Co2FeAl in agreement with ab initio calculations [4].

In many applications the information stored in relational databases is incomplete. Database designers and users quite often face difficulties due to the inadequate consideration of incomplete information. In this paper we present a theory for the treatment of incomplete information in relational databases using L-relations and algebras of L-relations. We show that the main results of the theory of relational databases like the theory of functional and mulivalued dependencies remain valid for L-relations. Furthermore, it is shown that in order to solve the decomposition problem for L-relations we have to investigate systems of equations with coefficients in L which express specific properties of L-relations.KeywordsBinary RelationBoolean AlgebraDistributive LatticeFunctional DependencyRelational AlgebraThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

One of the most difficult questions in the informal international lawmaking (IN-LAW) project as reflected in the present book, concerns the legal nature of the norms. In fact, during debates on the nature of IN-LAW it was precisely its legal nature that was questioned. As described in the first Chapter of this book international lawmaking is believed to be informal when it dispenses with certain formalities traditionally linked to international law. These formalities may have to do with output, process, or the actors involved. In our view, it is the notion of output informality in particular that raises the question to which extent informal law can be regarded as law. The purpose of the present contribution is simple: it aims to find out how we can keep informal international lawmaking within the realm of law. We will do so on the basis of a legal theoretical exercise, using insights developed in the so-called institutional legal theory (ILT). Admittedly, we do not treat the issue as an open question and merely look for arguments which would allow IN-LAW to be seen as part of the legal world, a presumption that lies beneath the IN-LAW project. Thus, we leave aside the question whether or not it matters to bring something within the legal realm, a question that was addressed by Pauwelyn in the previous Chapter. Other contributions in this Project extensively referred to the existing body of literature on informal and soft law. We are aware of the existing debates, but chose to start from scratch by using a different method. In doing so we hope to add a new dimension to the discussion on the legal nature of IN-LAW, albeit that the direction we propose remains to be developed further. In the previous Chapter Pauwelyn pointed to the idea that not all law or legal norms impose or proscribe specific behaviour or legally binding rights and obligations. Normativity

In this chapter, we present a list of “things we know” and “things we do not know” about manganites and related compounds. The chapter is informally organized to keep the discussion fluid. When results are mentioned that have already been considered in previous chapters, the associated references and details are omitted to avoid repetition. The reader can form a better opinion about the statements in this chapter by reading the appropriate chapters in the present book. Some of the comments and ideas are somewhat sketchy, but this is natural when addressing issues that are still not understood. Also, some items reflect the personal opinion of the author and may be debatable. An important portion of the chapter discusses results for other families of compounds that exhibit similarities with manganites. It is conceivable that the knowledge accumulated in Mn oxides may be applicable to the famous high-T c cuprates, as well as other materials discussed here and in Chap. 20. Coexisting nanoclusters appear to be a common phenomenon of a variety of compounds, and “colossal” effects of one form or another could be expected. There is plenty of work ahead, and surprises waiting to be unveiled.

In the previous chapters, we introduced several dimensions that are useful to describe and measure information quality in its different aspects and meanings. Focusing on structured data, database management systems (DBMSs) represent data and relative operations on it in terms of a data model and a data definition and manipulation language, i.e., a set of structures and commands that can be represented, interpreted, and executed by a computer. We can follow the same process to represent, besides data, their quality dimensions. This means that in order to represent data quality, we have to extend data models.

This paper presents an algorithm that decides whether two conjunctive query expressions always describe disjoint sets of tuples. The decision procedure solves an open problem identified by Blakeley, Coburn, and Larson: how to check whether an explicitly stored view relation must be recomputed after an update, taking into account functional dependencies. For nonconjunctive queries, the disjointness problem is NP-hard. For conjunctive queries, the time complexity of the algorithm given cannot be improved unless the reachability problem for directed graphs can be solved in sublinear time. The algorithm is novel in that it combines separate decision procedures for the theory of functional dependencies and for the theory of dense orders. Also, it uses tableaux that are capable of representing all six comparison operators , and ≠.

Proof assistants based on dependent type theory are closely related to functional programming languages, and so it is tempting to use them to prove the correctness of functional programs. In this paper, we show how Agda, such a proof assistant, can be used to prove theorems about Haskell programs. Haskell programs are translated into an Agda model of their semantics, by translating via GHC's Core language into a monadic form specially adapted to represent Haskell's polymorphism in Agda's predicative type system. The translation can support reasoning about either total values only, or total and partial values, by instantiating the monad appropriately. We claim that, although these Agda models are generated by a relatively complex translation process, proofs about them are simple and natural, and we offer a number of examples to support this claim.

In this article we continue the work started in [Ernesto Copello, Álvaro Tasistro, Nora Szasz, Ana Bove, and Maribel Fernández. Alpha-structural induction and recursion for the λ-calculus in constructive type theory. Electronic Notes in Theoretical Computer Science, 323:109–124, 2016], deriving in Constructive Type Theory new induction principles for the λ-calculus, using (the historical) first order syntax with only one sort of names for both bound and free variables, and with α-conversion based upon name swapping. The principles provide a flexible framework for mimicking pen-and-paper proofs within the rigorous formal setting of a proof assistant. We here report on one successful application, namely a complete proof of the Church-Rosser Theorem. The whole development has been machine-checked using the system Agda [Ulf Norell. Towards a Practical Programming Language Based on Dependent Type Theory. PhD thesis, Department of Computer Science and Engineering, Chalmers University of Technology, September 2007].

Previous chapter Next chapter Full AccessProceedings Proceedings of the 2014 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Half-integrality, LP-branching and FPT AlgorithmsMagnus WahlströmMagnus WahlströmRoyal Holloway, University of London.Search for more papers by this authorpp.1762 - 1781Chapter DOI:https://doi.org/10.1137/1.9781611973402.128PDFBibTexSections ToolsAdd to favoritesDownload CitationsTrack CitationsEmail SectionsAboutAbstract A recent trend in parameterized algorithms is the application of polytope tools (specifically, LP-branching) to FPT algorithms (e.g., Cygan et al., 2011; Narayanaswamy et al., 2012). Though the list of work in this direction is short, the results are already interesting, yielding significant speedups for a range of important problems. However, the existing approaches require the underlying polytope to have very restrictive properties, including half-integrality and Nemhauser-Trotter-style persistence properties. To date, these properties are essentially known to hold only for two classes of polytopes, covering the cases of Vertex Cover (Nemhauser and Trotter, 1975) and Node Multiway Cut (Garg et al., 1994). Taking a slightly different approach, we view half-integrality as a discrete relaxation of a problem, e.g., a relaxation of the search space from {0,1}V to {0,½,1}V such that the new problem admits a polynomial-time exact solution. Using tools from CSP (in particular Thapper and Živný, 2012) to study the existence of such relaxations, we are able to provide a much broader class of half-integral polytopes with the required properties. Our results unify and significantly extend the previously known cases. In addition to the new insight into problems with half-integral relaxations, our results yield a range of new and improved FPT algorithms, including an O*(|Σ|2k)-time algorithm for node-deletion Unique Label Cover with label set Σ (improving the previous bound of due to Chitnis et al., 2012) and an O*(4k)-time algorithm for Group Feedback Vertex Set, including the setting where the group is only given by oracle access (improving on the previous bound of O*(2O(klogk)) due to Cygan et al., 2012). The latter bound is optimal under the Exponential Time Hypothesis. The latter result also implies the first single-exponential time FPT algorithm for Subset Feedback Vertex Set, answering an open question of Cygan et al. (2012). Interestingly, despite the half-integrality, our result do not imply any approximation results (as may be expected, given the Unique Games-hardness of the covered problems). Previous chapter Next chapter RelatedDetails Published:2014ISBN:978-1-61197-338-9eISBN:978-1-61197-340-2 https://doi.org/10.1137/1.9781611973402Book Series Name:ProceedingsBook Code:PRDA14Book Pages:viii + 1885

I would like to dedicate this little exposition to Prof. Phan Dinh Dieu, one of the giants and pioneers of Mathematics in Computer Science in Vietnam. In the past 15 years or so, new and exciting connections between fundamental problems in database theory and information theory have emerged. There are several angles one can take to describe this connection. This paper takes one such angle, influenced by the author's own bias and research results. In particular, we will describe how the cardinality estimation problem -- a corner-stone problem for query optimizers -- is deeply connected to information theoretic inequalities. Furthermore, we explain how inequalities can also be used to derive a couple of classic geometric inequalities such as the Loomis-Whitney inequality. A purpose of the article is to introduce the reader to these new connections, where theory and practice meet in a wonderful way. Another objective is to point the reader to a research area with many new open questions.

Hypertree Decompositions and Tractable Queries

Constructions via Hamiltonian Theorems