33,927 research outputs found
Indefinite LQ Optimal Control with Terminal State Constraint for Discrete-Time Uncertain Systems
Uncertainty theory is a branch of mathematics for modeling human uncertainty based on the normality, duality, subadditivity, and product axioms. This paper studies a discrete-time LQ optimal control with terminal state constraint, whereas the weighting matrices in the cost function are indefinite and the system states are disturbed by uncertain noises. We first transform the uncertain LQ problem into an equivalent deterministic LQ problem. Then, the main result given in this paper is the necessary condition for the constrained indefinite LQ optimal control problem by means of the Lagrangian multiplier method. Moreover, in order to guarantee the well-posedness of the indefinite LQ problem and the existence of an optimal control, a sufficient condition is presented in the paper. Finally, a numerical example is presented at the end of the paper
Uncertainty in phylogenetic tree estimates
Estimating phylogenetic trees is an important problem in evolutionary
biology, environmental policy and medicine. Although trees are estimated, their
uncertainties are discarded by mathematicians working in tree space. Here we
explicitly model the multivariate uncertainty of tree estimates. We consider
both the cases where uncertainty information arises extrinsically (through
covariate information) and intrinsically (through the tree estimates
themselves). The importance of accounting for tree uncertainty in tree space is
demonstrated in two case studies. In the first instance, differences between
gene trees are small relative to their uncertainties, while in the second, the
differences are relatively large. Our main goal is visualization of tree
uncertainty, and we demonstrate advantages of our method with respect to
reproducibility, speed and preservation of topological differences compared to
visualization based on multidimensional scaling. The proposal highlights that
phylogenetic trees are estimated in an extremely high-dimensional space,
resulting in uncertainty information that cannot be discarded. Most
importantly, it is a method that allows biologists to diagnose whether
differences between gene trees are biologically meaningful, or due to
uncertainty in estimation.Comment: Final version accepted to Journal of Computational and Graphical
Statistic
Classical Logical versus Quantum Conceptual Thought: Examples in Economics, Decision theory and Concept Theory
Inspired by a quantum mechanical formalism to model concepts and their
disjunctions and conjunctions, we put forward in this paper a specific
hypothesis. Namely that within human thought two superposed layers can be
distinguished: (i) a layer given form by an underlying classical deterministic
process, incorporating essentially logical thought and its indeterministic
version modeled by classical probability theory; (ii) a layer given form under
influence of the totality of the surrounding conceptual landscape, where the
different concepts figure as individual entities rather than (logical)
combinations of others, with measurable quantities such as 'typicality',
'membership', 'representativeness', 'similarity', 'applicability', 'preference'
or 'utility' carrying the influences. We call the process in this second layer
'quantum conceptual thought', which is indeterministic in essence, and contains
holistic aspects, but is equally well, although very differently, organized
than logical thought. A substantial part of the 'quantum conceptual thought
process' can be modeled by quantum mechanical probabilistic and mathematical
structures. We consider examples of three specific domains of research where
the effects of the presence of quantum conceptual thought and its deviations
from classical logical thought have been noticed and studied, i.e. economics,
decision theory, and concept theories and which provide experimental evidence
for our hypothesis.Comment: 14 page
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