Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
- Publication Type
Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Decision Making Under Interval Uncertainty (And Beyond), Vladik Kreinovich
Decision Making Under Interval Uncertainty (And Beyond), Vladik Kreinovich
Departmental Technical Reports (CS)
To make a decision, we must find out the user's preference, and help the user select an alternative which is the best -- according to these preferences. Traditional utility-based decision theory is based on a simplifying assumption that for each two alternatives, a user can always meaningfully decide which of them is preferable. In reality, often, when the alternatives are close, the user is often unable to select one of these alternatives. In this chapter, we show how we can extend the utility-based decision theory to such realistic (interval) cases.
Should Voting Be Mandatory? Democratic Decision Making From The Economic Viewpoint, Olga Kosheleva, Vladik Kreinovich, Boakun Li
Should Voting Be Mandatory? Democratic Decision Making From The Economic Viewpoint, Olga Kosheleva, Vladik Kreinovich, Boakun Li
Departmental Technical Reports (CS)
Many decisions are made by voting. At first glance, the more people participate in the voting process, the more democratic -- and hence, better -- the decision. In this spirit, to encourage everyone's participation, several countries make voting mandatory. But does mandatory voting really make decisions better for the society? In this paper, we show that from the viewpoint of decision making theory, it is better to allow undecided voters not to participate in the voting process. We also show that the voting process would be even better -- for the society as a whole -- if we allow partial …
Ubiquity Of Data And Model Fusion: From Geophysics And Environmental Sciences To Estimating Individual Risk During An Epidemic, Omar Ochoa, Aline Jaimes, Christian Servin, Craig Tweedie, Aaron Velasco, Martine Ceberio, Vladik Kreinovich
Ubiquity Of Data And Model Fusion: From Geophysics And Environmental Sciences To Estimating Individual Risk During An Epidemic, Omar Ochoa, Aline Jaimes, Christian Servin, Craig Tweedie, Aaron Velasco, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we need to combine the results of measuring a local value of a certain quantity with results of measuring average values of this same quantity. For example, in geosciences, we need to combine the seismic models (which describe density at different locations and depths) with gravity models which describe density averaged over certain regions. Similarly, in estimating the risk of an epidemic to an individual, we need to combine probabilities describe the risk to people of the corresponding age group, to people of the corresponding geographical region, etc. In this paper, we provide general techniques for …
How To Define Relative Approximation Error Of An Interval Estimate: A Proposal, Vladik Kreinovich
How To Define Relative Approximation Error Of An Interval Estimate: A Proposal, Vladik Kreinovich
Departmental Technical Reports (CS)
The traditional definition of a relative approximation error of an estimate X as the ratio |X - x|/|x| does not work when the actual value x is 0. To avoid this problem, we propose a new definition |X - x|/|X|. We show how this definition can be naturally extended to the case when instead of a numerical estimate X, we have an interval estimate [x], i.e., an interval that is guaranteed to contain the actual (unknown) value x.
Constrained Optimal Control For A Multi-Group Discrete Time Influenza Model, Paula Andrea Gonzalez Parra
Constrained Optimal Control For A Multi-Group Discrete Time Influenza Model, Paula Andrea Gonzalez Parra
Open Access Theses & Dissertations
During the last decades, mathematical epidemiological models have been used to understand the dynamics of infectious diseases and guide public health policy. In particular, several continuous models have been considered to study single in uenza outbreaks and the impact of dierent control policies. In this dissertation, a discrete time model is introduced in order to study optimal control strategies for in uenza transmission; since epidemiological data is collected on discrete units of time, a discrete formulation is more ecient. From a mathematical point of view, continuous time model are easier to analyze, however, the numerical solution of discrete-time models is …
Granular Computing For Assessment Of Mild Traumatic Brain Injury, Melaku Ayenew Bogale
Granular Computing For Assessment Of Mild Traumatic Brain Injury, Melaku Ayenew Bogale
Open Access Theses & Dissertations
Mild traumatic brain injury (mTBI) is one of the most common neurological disorders. It is a serious public health problem in the United States. Although, penetrating (open) brain injuries that result in extended period of loss of consciousness (LOC) usually gets attention and well taken care of by the emergency departments, mild traumatic brain injury with no visible sign of damage, may be undetected or misdiagnosed. The clinical assessments and evaluations are mostly based on subjective cognitive and behavioral tests. Many people after suffering mTBI complain about decreased balance, coordination and stability even though the clinical evaluations show no sign …
Constrained Optimization Schemes For Geophysical Inversion Of Seismic Data, Uram Anibal Sosa Aguirre
Constrained Optimization Schemes For Geophysical Inversion Of Seismic Data, Uram Anibal Sosa Aguirre
Open Access Theses & Dissertations
Many experimental techniques in geophysics advance the understanding of Earth processes by estimating and interpreting Earth structure (e.g., velocity and/or density structure). These techniques use dierent types of geophysical data which can be collected and analyzed separately, sometimes resulting in inconsistent models of the Earth depending on data quality, methods and assumptions made. This dissertation presents two approaches for geophysical inversion of seismic data based on constrained optimization. In one approach we expand a one dimensional (1-D) joint inversion least-squares (LSQ) algorithm by introducing a constrained optimization methodology. Then we use the 1-D inversion results to produce 3-D Earth velocity …
Development Of New Mathematical Methods For Post-Pareto Optimality, Victor Manuel Carrillo
Development Of New Mathematical Methods For Post-Pareto Optimality, Victor Manuel Carrillo
Open Access Theses & Dissertations
Many real-world applications of multi-objective optimization involve a large number of objectives. A multi-objective optimization task involving multiple conflicting objectives ideally demands finding a multi-dimensional Pareto-optimal front. Although the classical methods have dealt with finding one preferred solution with the help of a decision-maker, evolutionary multi-objective optimization (EMO) methods have been attempted to find a representative set of solutions in the Pareto-optimal front. Multiple objective evolutionary algorithms (MOEAs), which are biologically-inspired optimization methods, have become popular approaches to solve problems with multiple objective functions. With the use of MOEAs, multiple objective optimization becomes a two-part problem. First, the multiple objective …
Analytical And Numerical Solution To The Partial Differential Equation Arising In Financial Modeling, Pavel Bezdek
Analytical And Numerical Solution To The Partial Differential Equation Arising In Financial Modeling, Pavel Bezdek
Open Access Theses & Dissertations
In this work we will present a self-contained introduction to the option pricing problem. We will introduce some basic ideas from the probability theory and stochastic differential equations. Later we will move to the partial differential equations since the option pricing problem arising in financial mathematics when asset is driven by a stochastic volatility process and assumed presence of transaction cost leads to solving non-linear partial dif- ferential equation. We will also present the complete process from deriving the desired partial differential equation to the proof of existence of a solution and also the numerical simulations. Using techniques form stochastic …