Searching For a Lost Plane

Malaysia plane MH370 disappeared en route from Kuala Lumpur to Beijing on 8, March 2014. Besides considering the factors such as air piracy, weather, electromagnetic wave, and kinds of bugs of the airplane, in order to find the wreckage efficiently the growing concern is to confirm a limited area where the airplane probably fell, and then to find an optimum way to find the plane. It’s essential to build such a model involving both of the two layers mentioned above that can cover all the searching area by using the most efficient way. The first layer is to confirm the limited area. We use the Poisson Probability Distribution, the Drag equation, and the Proper Orthogonal Decomposition Theorem to assume the direction of the airplane and the sea area where it probably fell. All assumptions are based on the actual situation. The second model will basically rely on the Bayesian principles. In this case, the model would be advantageous as it will rely on contingency as an important role in the search for lost objects in the sea or on land. As matter of fact, any information that is provided to the search team would be put into good use as it will be used in developing the probabilities. It is also good in that it\u27s flexible and would be good enough to sustain the ongoing search even with new information or facts obtained regarding the flight of the plane and/or the initial findings of the debris. This helps in rounding down to a lesser geographical search region and, by extension, increases the probability of getting the plane

Estimation for an additive growth curve model with orthogonal design matrices

An additive growth curve model with orthogonal design matrices is proposed in which observations may have different profile forms. The proposed model allows us to fit data and then estimate parameters in a more parsimonious way than the traditional growth curve model. Two-stage generalized least-squares estimators for the regression coefficients are derived where a quadratic estimator for the covariance of observations is taken as the first-stage estimator. Consistency, asymptotic normality and asymptotic independence of these estimators are investigated. Simulation studies and a numerical example are given to illustrate the efficiency and parsimony of the proposed model for model specifications in the sense of minimizing Akaike's information criterion (AIC).Comment: Published in at http://dx.doi.org/10.3150/10-BEJ315 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Expressive Completeness of Existential Rule Languages for Ontology-based Query Answering

Existential rules, also known as data dependencies in Databases, have been recently rediscovered as a promising family of languages for Ontology-based Query Answering. In this paper, we prove that disjunctive embedded dependencies exactly capture the class of recursively enumerable ontologies in Ontology-based Conjunctive Query Answering (OCQA). Our expressive completeness result does not rely on any built-in linear order on the database. To establish the expressive completeness, we introduce a novel semantic definition for OCQA ontologies. We also show that neither the class of disjunctive tuple-generating dependencies nor the class of embedded dependencies is expressively complete for recursively enumerable OCQA ontologies.Comment: 10 pages; the full version of a paper to appear in IJCAI 2016. Changes (regarding to v1): a new reference has been added, and some typos have been correcte

SLT-Resolution for the Well-Founded Semantics

Global SLS-resolution and SLG-resolution are two representative mechanisms for top-down evaluation of the well-founded semantics of general logic programs. Global SLS-resolution is linear for query evaluation but suffers from infinite loops and redundant computations. In contrast, SLG-resolution resolves infinite loops and redundant computations by means of tabling, but it is not linear. The principal disadvantage of a non-linear approach is that it cannot be implemented using a simple, efficient stack-based memory structure nor can it be easily extended to handle some strictly sequential operators such as cuts in Prolog. In this paper, we present a linear tabling method, called SLT-resolution, for top-down evaluation of the well-founded semantics. SLT-resolution is a substantial extension of SLDNF-resolution with tabling. Its main features include: (1) It resolves infinite loops and redundant computations while preserving the linearity. (2) It is terminating, and sound and complete w.r.t. the well-founded semantics for programs with the bounded-term-size property with non-floundering queries. Its time complexity is comparable with SLG-resolution and polynomial for function-free logic programs. (3) Because of its linearity for query evaluation, SLT-resolution bridges the gap between the well-founded semantics and standard Prolog implementation techniques. It can be implemented by an extension to any existing Prolog abstract machines such as WAM or ATOAM.Comment: Slight modificatio