Hypothesis management in situation assessment

A situation assessment uses reports from sensors to produce hypotheses about a situation at a level of aggregation that is of direct interest to a military commander. A low level of aggregation could mean forming tracks from reports, which is well documented in the tracking literature as track initiation and data association. In this paper there is also discussion on higher level aggregation; assessing the membership of tracks to larger groups. Ideas used in joint tracking and identification are extended, using multi-entity Bayesian networks to model a number of static variables, of which the identity of a target is one. For higher level aggregation a scheme for hypothesis management is required. It is shown how an offline clustering of vehicles can be reduced to an assignment problem.

Keeping the dream of rigorous hypothesis testing alive

This article reviews recent work on hypothesis testing in the American Journal of AGricultural Economics and its predecessor journal, the Journal of Farm Economics

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

Why all counter-evidence to the critical period hypothesis in second language acquisition is not equal or problematic

That adult and child language acquisitions differ in route and outcome is observable. Notwithstanding, there is controversy as to what this observation means for the Critical Period Hypothesis’ (CPH) application to adult second language acquisition (SLA). As most versions of the CPH applied to SLA claim that differences result from maturational effects on in-born linguistic mechanisms, the CPH has many implications that are amendable to empirical investigation. To date, there is no shortage of literature claiming that the CPH applies or does not apply to normal adult SLA. Herein, I provide an epistemological discussion on the conceptual usefulness of the CPH in SLA (cf. Singleton 2005) coupled with a review of Long's (2005) evaluation of much available relevant research. Crucially, I review studies that Long did not consider and conclude differently that there is no critical/sensitive period for L2 syntactic and semantic acquisition.

Aspect selection in adult L2 Spanish and the competing systems hypothesis: when pedagogical and linguistic rules conflict.

Native-like use of preterit and imperfect morphology in all contexts by English learners of L2 Spanish is the exception rather than the rule, even for successful learners. Nevertheless, recent research has demonstrated that advanced English learners of L2 Spanish attain a native-like morphosyntactic competence for the preterit/imperfect contrast, as evidenced by their native-like knowledge of associated semantic entailments (Goodin-Mayeda and Rothman 2007, Montrul and Slabakova 2003, Slabakova and Montrul 2003, Rothman and Iverson 2007). In addition to an L2 disassociation of morphology and syntax (e.g., Bruhn de Garavito 2003, Lardiere 1998, 2000, 2005, Prévost and White 1999, 2000, Schwartz 2003), I hypothesize that a system of learned pedagogical rules contributes to target-deviant L2 performance in this domain through the most advanced stages of L2 acquisition via its competition with the generative system. I call this hypothesis the Competing Systems Hypothesis. To test its predictions, I compare and contrast the use of the preterit and imperfect in two production tasks by native, tutored (classroom), and naturalistic learners of L2 Spanish.

A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.