A Traveler’s Guide to the Multiverse: Promises, Pitfalls, and a Framework for the Evaluation of Analytic Decisions

Decisions made by researchers while analyzing data (e.g., how to measure variables, how to handle outliers) are sometimes arbitrary, without an objective justification for choosing one alternative over another. Multiverse-style methods (e.g., specification curve, vibration of effects) estimate an effect across an entire set of possible specifications to expose the impact of hidden degrees of freedom and/or obtain robust, less biased estimates of the effect of interest. However, if specifications are not truly arbitrary, multiverse-style analyses can produce misleading results, potentially hiding meaningful effects within a mass of poorly justified alternatives. So far, a key question has received scant attention: How does one decide whether alternatives are arbitrary? We offer a framework and conceptual tools for doing so. We discuss three kinds of a priori nonequivalence among alternatives—measurement nonequivalence, effect nonequivalence, and power/precision nonequivalence. The criteria we review lead to three decision scenarios: Type E decisions (principled equivalence), Type N decisions (principled nonequivalence), and Type U decisions (uncertainty). In uncertain scenarios, multiverse-style analysis should be conducted in a deliberately exploratory fashion. The framework is discussed with reference to published examples and illustrated with the help of a simulated data set. Our framework will help researchers reap the benefits of multiverse-style methods while avoiding their pitfalls.

Clifford theory of Weil representations of unitary groups

Let {\mathcal{O}} be an involutive discrete valuation ring with residue field of characteristic not 2. Let A be a quotient of {\mathcal{O}} by a nonzero power of its maximal ideal, and let {*} be the involution that A inherits from {\mathcal{O}} . We consider various unitary groups {\mathcal{U}_{m}(A)} of rank m over A, depending on the nature of {*} and the equivalence type of the underlying hermitian or skew hermitian form. Each group {\mathcal{U}_{m}(A)} gives rise to a Weil representation. In this paper, we give a Clifford theory description of all irreducible components of the Weil representation of {\mathcal{U}_{m}(A)} with respect to all of its abelian congruence subgroups and a third of its nonabelian congruence subgroups.

THE TRANSLATION OF CIVIL AVIATION SAFETY REGULATION PART 170 AIR TRAFFIC RULES INTO INDONESIAN

The background of this research was based on the continued development of international aviation in the world which was a challenge for the translator to find an equivalent sentence. The purpose of this thesis was to find the equivalence type used in translating the source language to the target language and find the dominant equivalence type used. For solving this problem, the writer used Nida and Taber theory that divided equivalence types into two types, namely formal equivalence or formal correspondence and dynamic equivalence. The method used was descriptive qualitative method. The data was obtained through systematic sampling method. Based on the analysis, the equivalence types of 53 of 66 samples (80%) were translated by using formal correspondence; 12 of 66 samples were translated using dynamic equivalence (18%) and only one sample (2%) did not neither involve in formal correspondence nor dynamic equivalence because SL text did not have translation in TL (reserved). The most dominant equivalence type used in the translation was formal correspondence.

Beyond Alternating Permutations: Pattern Avoidance in Young Diagrams and Tableaux

We investigate pattern avoidance in alternating permutations and generalizations thereof. First, we study pattern avoidance in an alternating analogue of Young diagrams. In particular, we extend Babson-West's notion of shape-Wilf equivalence to apply to alternating permutations and so generalize results of Backelin-West-Xin and Ouchterlony to alternating permutations. Second, we study pattern avoidance in the more general context of permutations with restricted ascents and descents. We consider a question of Lewis regarding permutations that are the reading words of thickened staircase Young tableaux, that is, permutations that have $k-1$ ascents followed by a descent, followed by $k-1$ ascents, et cetera. We determine the relative sizes of the sets of pattern-avoiding $(k-1)$-ascent permutations in terms of the forbidden pattern. Furthermore, inequalities in the sizes of sets of pattern-avoiding permutations in this context arise from further extensions of shape-equivalence type enumerations. This paper is the first of a two-paper series presenting the work of Beyond alternating permutations: Pattern avoidance in Young diagrams and tableaux (arXiv:1301.6796v1). The second in the series is Ascent-descent Young diagrams and pattern avoidance in alternating permutations (by the second author, submitted).

Knowledge-Based Networking

Knowledge-Based Networking, which is built on-top of Content-based Networking (CBN), involves the forwarding of events across a network of brokers based on subscription filters applied to some semantics of the data and associated metadata of the events contents. Knowledge-based Networks (KBN) therefore support the efficient filtered dissemination of semantically enriched knowledge over a large, loosely coupled network of distributed heterogeneous agents. This is achieved by incorporating ontological semantics into event messages, allowing subscribers to define semantic filters, and providing a subscription brokering and routing mechanism. The KBN used for this work provides ontological concepts as an additional message attribute type, onto which subsumption relationships, equivalence, type queries and arbitrary ontological relationships can be applied. It also provides a bag type to be used that supports bags equivalence, sub-bag and super-bag relationships to be used in subscription filters, composed with traditional CBN subscription operators or the ontological operators. When combined with the benefits of Content–based Networking, this allows subscribers to easily express meaningful subscription interests and receive results in a more expressive and flexible distributed event system than heretofore. Within this chapter the detailed analysis of ontological operators and their application to a publish/subscribe (pub/sub) domain will be fully explored and evaluated.

Types and automata

A hierarchical type system for imperative programming languages gives rise to various computational problems, such as type equivalence, type ordering, etc. We present a particular class of finite automata which are shown to be isomorphic to type equations. All the relevant type concepts turn out to have well-known automata analogues, such as language equality, language inclusion, etc. This provides optimal or best known algorithms for the type system, by a process of translating type equations to automata, solving the analogous problem, and translating the result back to type equations. Apart from suggesting an implementation, this connection lends a certain naturality to our type system. We also introduce a very general form of extended (recursive) type equations which are explained in terms of (monotone) alternating automata. Since types are simply equationally defined trees, these results may have wider applications.

The inclusion-exclusion principle for finitely many isolated sets

A nonnegative integer is called a number, a collection of numbers a set and a collection of sets a class. We write ε for the set of all numbers, o for the empty set, N(α) for the cardinality of α, ⊂ for inclusion and ⊂+ for proper inclusion. Let α, β1,…, βk be subsets of some set υ. Then α′ stands for υ−α and β1 … βk for β1 ∩ … ∩ βk. For subsets α1, …, αr of υ we write:Note that α0 = υ, hence s0 = N(υ). If the set υ is finite, the classical inclusion-exclusion principle (abbreviated IEP) statesIn this paper we generalize (a) and(b) to the case where α1, …, αr are subsets of some countable but isolated set υ. Then the role of the cardinality N(α) of the set α is played by the RET (recursive equivalence type) Req α of α. These generalizations of (a) and (b) are proved in §3. Since they involve recursive distinctness, this notion is discussed in §2. In §4 we consider a natural extension of “the sum of the elements of a finite set σ” to the case where σ is countable. §5 deals with valuations, i.e., certain mappings μ from classes of isolated sets into the collection Λ of all isols which permit us to further generalize IEP by substituting μ(α) for Req α.