Browsing by Subject "Partial information"

Now showing 1 - 4 of 4

Open Access
The effect of distribution of information on recovery of propagating signals
(2015-09) Karabulut, Özgecan
Interpolation is one of the fundamental concepts in signal processing. The analysis of the di fficulty of interpolation of propagating waves is the subject of this thesis. It is known that the information contained in a propagating wave fi eld can be fully described by its uniform samples taken on a planar surface transversal to the propagation direction, so the eld can be found anywhere in space by using the wave propagation equations. However in some cases, the sample locations may be irregular and/or nonuniform. We are concerned with interpolation from such samples. To be able to reduce the problem to a pure mathematical form, the fractional Fourier transform is used thanks to the direct analogy between wave propagation and fractional Fourier transformation. The linear relationship between each sample and the unknown field distribution is established this way. These relationships, which constitute a signal recovery problem based on multiple partial fractional Fourier transform information, are analyzed. Recoverability of the fi eld is examined by comparing the condition numbers of the constructed matrices corresponding to di fferent distributions of the available samples.
Open Access
Effect of spatial distribution of partial information on the accurate recovery of optical wave fields
(Optical Society of America, 2017) Oktem, F. S.; Özaktaş, Haldun M.
We consider the problem of recovering a signal from partial and redundant information distributed over two fractional Fourier domains. This corresponds to recovering a wave field from two planes perpendicular to the direction of propagation in a quadratic-phase multilens system. The distribution of the known information over the two planes has a significant effect on our ability to accurately recover the field. We observe that distributing the known samples more equally between the two planes, or increasing the distance between the planes in free space, generally makes the recovery more difficult. Spreading the known information uniformly over the planes, or acquiring additional samples to compensate for the redundant information, helps to improve the accuracy of the recovery. These results shed light onto redundancy and information relations among the given data for a broad class of systems of practical interest, and provide a deeper insight into the underlying mathematical problem.
Open Access
Predicting optimal facility location without customer locations
(ACM, 2017-08) Yilmaz, Emre; Elbaşı, Sanem; Ferhatosmanoğlu, Hakan
Deriving meaningful insights from location data helps businesses make better decisions. One critical decision made by a business is choosing a location for its new facility. Optimal location queries ask for a location to build a new facility that optimizes an objective function. Most of the existing works on optimal location queries propose solutions to return best location when the set of existing facilities and the set of customers are given. However, most businesses do not know the locations of their customers. In this paper, we introduce a new problem setting for optimal location queries by removing the assumption that the customer locations are known. We propose an optimal location predictor which accepts partial information about customer locations and returns a location for the new facility. The predictor generates synthetic customer locations by using given partial information and it runs optimal location queries with generated location data. Experiments with real data show that the predictor can find the optimal location when sufficient information is provided. © 2017 Copyright held by the owner/author(s).
Open Access
Structural results for average‐cost inventory models with Markov‐modulated demand and partial information
(Wiley-Blackwell, 2020) Avcı, Harun; Gökbayrak, Kağan; Nadar, Emre
We consider a discrete‐time infinite‐horizon inventory system with non‐stationary demand, full backlogging, and deterministic replenishment lead time. Demand arrives according to a probability distribution conditional on the state of the world that undergoes Markovian transitions over time. But the actual state of the world can only be imperfectly estimated based on past demand data. We model the inventory replenishment problem for this system as a Markov decision process (MDP) with an uncountable state space consisting of both the inventory position and the most recent belief, a conditional probability mass function, about the actual state of the world. Assuming that the state of the world evolves as an ergodic Markov chain, using the vanishing discount method along with a coupling argument, we prove the existence of an optimal average cost that is independent of the initial system state. For our linear cost structure, we also establish the average‐cost optimality of a belief‐dependent base‐stock policy. We then discretize the uncountable belief space into a regular grid and observe that the average cost under our discretization converges to the optimal average cost as the number of grid points grows large. Finally, we conduct numerical experiments to evaluate the use of a myopic belief‐dependent base‐stock policy as a heuristic for our MDP with the uncountable state space. On a test bed of 108 instances, the average cost obtained from the myopic policy deviates by no more than a few percent from the best lower bound on the optimal average cost obtained from our discretization.