Approximable minimization problems and optimal solutions on random inputs

An electroelastic actuator for nanomechatronics is used in nanotechnology, adaptive optics, microsurgery, microelectronics, and biomedicine to actuate or control mechanisms, systems based on the electroelastic effect, and to convert electrical signals into mechanical displacements and forces. In nanomechatronic systems, a piezoactuator is used in scanning microscopy, laser systems, in astronomy for precision alignment, for compensation of temperature, gravitational deformations and atmospheric turbulence, focusing, and stabilizing the image. In this study, a condition for absolute stability of an electroelastic actuator control system for nanomechatronics under deterministic and random inputs is obtained. A number of equilibrium positions in an electroelastic actuator mechatronic control system are found, the totality of which is represented by a straight line segment. The electroelastic actuator’s deformation control system dead band relative width is determined for the actuator’s symmetric and asymmetric hysteresis characteristics. Under deterministic inputs and with fulfilling the condition for the derivative of the nonlinear hysteresis actuator deformation characteristic, the set of equilibrium positions of the electroelastic actuator control system for nanomechatronics is absolutely stable. Under random inputs, the system absolute stability with respect to the mathematical expectations of the electroelastic actuator mechatronic control system equilibrium positions has been determined subject to fulfilling the condition on the derivative of the actuator hysteresis characteristic.

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Combinatorial Optimization of Clustering Decisions: An Application to Refine Psychiatric Diagnoses

10.31234/osf.io/jpnmf ◽

2018 ◽

Author(s):

Jordan Stevens ◽

Douglas Steinley ◽

Cassandra L. Boness ◽

Timothy J Trull ◽

[email protected] ◽

...

Keyword(s):

Combinatorial Optimization ◽

Alcohol Use Disorder ◽

Point Of View ◽

Psychiatric Diagnoses ◽

Optimal Solutions ◽

Specific Function ◽

Significant Information ◽

Diagnosis Group ◽

Clustering Problems ◽

Unique Application

Using complete enumeration (e.g., generating all possible subsets of item combinations) to evaluate clustering problems has the benefit of locating globally optimal solutions automatically without the concern of sampling variability. The proposed method is meant to combine clustering variables in such a way as to create groups that are maximally different on a theoretically sound derivation variable(s). After the population of all unique sets is permuted, optimization on some predefined, user-specific function can occur. We apply this technique to optimizing the diagnosis of Alcohol Use Disorder. This is a unique application, from a clustering point of view, in that the decision rule for clustering observations into the diagnosis group relies on both the set of items being considered and a predefined threshold on the number of items required to be endorsed for the diagnosis to occur. In optimizing diagnostic rules, criteria set sizes can be reduced without a loss of significant information when compared to current and proposed, alternative, diagnostic schemes.

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