An Extension Theorem with an Application to Formal Tree Series

A grove theory is a Lawvere algebraic theory T for which each hom-set T(n,p) is a commutative monoid; composition on the right distributes over all finite sums: (\sum f_i) . h = \sum f_i . h. A matrix theory is a grove theory in which composition on the left and right distributes over finite sums. A matrix theory M is isomorphic to a theory of all matrices over the semiring S = M(1,1). Examples of grove theories are theories of (bisimulation equivalence classes of) synchronization trees, and theories of formal tree series over a semiring S . Our main theorem states that if T is a grove theory which has a matrix subtheory M which is an iteration theory, then, under certain conditions, the fixed point operation on M can be extended in exactly one way to a fixed point operation on T such that T is an iteration theory. A second theorem is a Kleene-type result. Assume that T is an iteration grove theory and M is a sub iteration grove theory of T which is a matrix theory. For a given collection Sigma of scalar morphisms in T we describe the smallest sub iteration grove theory of T containing all the morphisms in M union Sigma

Towards Design Principles for Data-Driven Decision Making: An Action Design Research Project in the Maritime Industry

Data-driven decision making (DDD) refers to organizational decision-making practices that emphasize the use of data and statistical analysis instead of relying on human judgment only. Various empirical studies provide evidence for the value of DDD, both on individual decision maker level and the organizational level. Yet, the path from data to value is not always an easy one and various organizational and psychological factors mediate and moderate the translation of data-driven insights into better decisions and, subsequently, effective business actions. The current body of academic literature on DDD lacks prescriptive knowledge on how to successfully employ DDD in complex organizational settings. Against this background, this paper reports on an action design research study aimed at designing and implementing IT artifacts for DDD at one of the largest ship engine manufacturers in the world. Our main contribution is a set of design principles highlighting, besides decision quality, the importance of model comprehensibility, domain knowledge, and actionability of results

Analytic perturbative theories in highly inhomogeneous gravitational fields

Orbital motion about irregular bodies is highly nonlinear due to inhomogeneities in the gravitational field. Classical theories of motion close to spheroidal bodies cannot be applied as for inhomogeneous bodies the Keplerian forces do not provide a good approximation of the system dynamics. In this paper a closed form, analytical method for developing the motion of a spacecraft around small bodies is presented, for the so called fast rotating case, which generalize previous results to second order, arbitrary degree, gravitational fields. Through the application of two different Lie transformations, suitable changes of coordinates are found, which reduce the initial non integrable Hamiltonian of the system into an integrable one plus a negligible, perturbative remainder of higher degree. In addition, an explicit analytical formulation for the relegated, first and second order, arbitrary degree Hamiltonian for relatively high altitude motion in any inhomogeneous gravitational field is derived in closed-form. Applications of this algorithm include a method for determining initial conditions for frozen orbits around any irregular body by simply prescribing the desired inclination and eccentricity of the orbit. This method essentially reduces the problem of computing frozen orbits to a problem of solving a 2-D algebraic equation. Results are shown for the asteroid 433-Eros

A Stochastic Interpretation of Stochastic Mirror Descent: Risk-Sensitive Optimality

Stochastic mirror descent (SMD) is a fairly new family of algorithms that has recently found a wide range of applications in optimization, machine learning, and control. It can be considered a generalization of the classical stochastic gradient algorithm (SGD), where instead of updating the weight vector along the negative direction of the stochastic gradient, the update is performed in a "mirror domain" defined by the gradient of a (strictly convex) potential function. This potential function, and the mirror domain it yields, provides considerable flexibility in the algorithm compared to SGD. While many properties of SMD have already been obtained in the literature, in this paper we exhibit a new interpretation of SMD, namely that it is a risk-sensitive optimal estimator when the unknown weight vector and additive noise are non-Gaussian and belong to the exponential family of distributions. The analysis also suggests a modified version of SMD, which we refer to as symmetric SMD (SSMD). The proofs rely on some simple properties of Bregman divergence, which allow us to extend results from quadratics and Gaussians to certain convex functions and exponential families in a rather seamless way

A taxonomy for interactive educational multimedia

Learning is more than knowledge acquisition; it often involves the active participation of the learner in a variety of knowledge- and skills-based learning and training activities. Interactive multimedia technology can support the variety of interaction channels and languages required to facilitate interactive learning and teaching. We will present a taxonomy for interactive educational multimedia that supports the classification, description and development of such systems. Such a taxonomy needs to embed multimedia technology into a coherent educational context. A conceptual framework based on an integrated interaction model is needed to capture learning and training activities in an online setting from an educational perspective, describe them in the human-computer context, and integrate them with mechanisms and principles of multimedia interaction

Computational interferometric description of nested flow fields

Computer graphics and theoretical descriptions of density are used to obtain computer generated flow visualizations called computational interferograms. Computational interferograms are pictorially analogous to optical interferograms, and examples showing the fringe pattern for the flow about a sharp tip cone in a supersonic air stream are presented. To ascertain the effect of unsteady behavior, local density disturbances are added to the steady state flow field. This introduces irregularities to the computational interferogram like those seen in the optical interferograms. These theoretical disturbances can be varied in geometry, density description, translated with time, and strengthened or dissipated. The accuracy of computational interferometry relies on the accuracy of the theoretical density descriptions and therefore, it provides a way of verifying existing models of flow fields, especially those containing unsteady or turbulent behavior. In addition to being a unique method of flow visualization, computational interferometry can be used to develop and modify theories or numerical solutions to both simple and complex flow fields. The presented research is a general description of this process

MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure