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Articles 1 - 12 of 12
Full-Text Articles in Theory and Algorithms
Hyperspectral Unmixing: A Theoretical Aspect And Applications To Crism Data Processing, Yuki Itoh
Hyperspectral Unmixing: A Theoretical Aspect And Applications To Crism Data Processing, Yuki Itoh
Doctoral Dissertations
Hyperspectral imaging has been deployed in earth and planetary remote sensing, and has contributed the development of new methods for monitoring the earth environment and new discoveries in planetary science. It has given scientists and engineers a new way to observe the surface of earth and planetary bodies by measuring the spectroscopic spectrum at a pixel scale. Hyperspectal images require complex processing before practical use. One of the important goals of hyperspectral imaging is to obtain the images of reflectance spectrum. A raw image obtained by hyperspectral remote sensing usually undergoes conversion to a physical quantity representing the intensity of …
Analysis Of A Quantum Attack On The Blum-Micali Pseudorandom Number Generator, Tingfei Feng
Analysis Of A Quantum Attack On The Blum-Micali Pseudorandom Number Generator, Tingfei Feng
Mathematical Sciences Technical Reports (MSTR)
In 2012, Guedes, Assis, and Lula proposed a quantum attack on a pseudorandom number generator named the Blum-Micali Pseudorandom number generator. They claimed that the quantum attack can outperform classical attacks super-polynomially. However, this paper shows that the quantum attack cannot get the correct seed and provides another corrected algorithm that is in exponential time but still faster than the classical attack. Since the original classical attacks are in exponential time, the Blum-Micali pseudorandom number generator would be still quantum resistant.
A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker
A Novel Method For Sensitivity Analysis Of Time-Averaged Chaotic System Solutions, Christian A. Spencer-Coker
Theses and Dissertations
The direct and adjoint methods are to linearize the time-averaged solution of bounded dynamical systems about one or more design parameters. Hence, such methods are one way to obtain the gradient necessary in locally optimizing a dynamical system’s time-averaged behavior over those design parameters. However, when analyzing nonlinear systems whose solutions exhibit chaos, standard direct and adjoint sensitivity methods yield meaningless results due to time-local instability of the system. The present work proposes a new method of solving the direct and adjoint linear systems in time, then tests that method’s ability to solve instances of the Lorenz system that exhibit …
The Primitive Root Problem: A Problem In Bqp, Shixin Wu
The Primitive Root Problem: A Problem In Bqp, Shixin Wu
Mathematical Sciences Technical Reports (MSTR)
Shor’s algorithm proves that the discrete logarithm problem is in BQP. Based on his algorithm, we prove that the primitive root problem, a problem that verifies if some integer g is a primitive root modulo p where p is the largest prime number smaller than 2n for a given n, which is assumed to be harder than the discrete logarithm problem, is in BQP by using an oracle quantum Turing machine.
Data And Algorithmic Modeling Approaches To Count Data, Andraya Hack
Data And Algorithmic Modeling Approaches To Count Data, Andraya Hack
Honors College Theses
Various techniques are used to create predictions based on count data. This type of data takes the form of a non-negative integers such as the number of claims an insurance policy holder may make. These predictions can allow people to prepare for likely outcomes. Thus, it is important to know how accurate the predictions are. Traditional statistical approaches for predicting count data include Poisson regression as well as negative binomial regression. Both methods also have a zero-inflated version that can be used when the data has an overabundance of zeros. Another procedure is to use computer algorithms, also known as …
A Novel Data Lineage Model For Critical Infrastructure And A Solution To A Special Case Of The Temporal Graph Reachability Problem, Ian Moncur
Graduate Theses and Dissertations
Rapid and accurate damage assessment is crucial to minimize downtime in critical infrastructure. Dependency on modern technology requires fast and consistent techniques to prevent damage from spreading while also minimizing the impact of damage on system users. One technique to assist in assessment is data lineage, which involves tracing a history of dependencies for data items. The goal of this thesis is to present one novel model and an algorithm that uses data lineage with the goal of being fast and accurate. In function this model operates as a directed graph, with the vertices being data items and edges representing …
Numerical Treatment For Special Type Of Mixed Linear Delay Volterra Integro-Differential Equations, Atheer J. Kadhim
Numerical Treatment For Special Type Of Mixed Linear Delay Volterra Integro-Differential Equations, Atheer J. Kadhim
Emirates Journal for Engineering Research
The idea of research is a representation of the nonlinear pseudo-random generators using state-space equations that is not based on the usual description as shift register synthesis but in terms of matrices. Different types of nonlinear pseudo-random generators with their algorithms have been applied in order to investigate the output pseudo-random sequences. Moreover, two examples are given for conciliated the results of this representation.
The Nature Of Numbers: Real Computing, Bradley J. Lucier
The Nature Of Numbers: Real Computing, Bradley J. Lucier
Journal of Humanistic Mathematics
While studying the computable real numbers as a professional mathematician, I came to see the computable reals, and not the real numbers as usually presented in undergraduate real analysis classes, as the natural culmination of my evolving understanding of numbers as a schoolchild. This paper attempts to trace and explain that evolution. The first part recounts the nature of numbers as they were presented to us grade-school children. In particular, the introduction of square roots induced a step change in my understanding of numbers. Another incident gave me insight into the brilliance of Alan Turing in his paper introducing both …
Robust Error Estimation Based On Factor-Graph Models For Non-Line-Of-Sight Localization, O. Arda Vanli, Clark N. Taylor
Robust Error Estimation Based On Factor-Graph Models For Non-Line-Of-Sight Localization, O. Arda Vanli, Clark N. Taylor
Faculty Publications
This paper presents a method to estimate the covariances of the inputs in a factor-graph formulation for localization under non-line-of-sight conditions. A general solution based on covariance estimation and M-estimators in linear regression problems, is presented that is shown to give unbiased estimators of multiple variances and are robust against outliers. An iteratively re-weighted least squares algorithm is proposed to jointly compute the proposed variance estimators and the state estimates for the nonlinear factor graph optimization. The efficacy of the method is illustrated in a simulation study using a robot localization problem under various process and measurement models and measurement …
A Simple Algorithm For Generating A New Two Sample Type-Ii Progressive Censoring With Applications, E. M. Shokr, Rashad Mohamed El-Sagheer, Mahmoud Mansour, H. M. Faied, B. S. El-Desouky
A Simple Algorithm For Generating A New Two Sample Type-Ii Progressive Censoring With Applications, E. M. Shokr, Rashad Mohamed El-Sagheer, Mahmoud Mansour, H. M. Faied, B. S. El-Desouky
Basic Science Engineering
In this article, we introduce a simple algorithm to generating a new type-II progressive censoring scheme for two samples. It is observed that the proposed algorithm can be applied for any continues probability distribution. Moreover, the description model and necessary assumptions are discussed. In addition, the steps of simple generation algorithm along with programming steps are also constructed on real example. The inference of two Weibull Frechet populations are discussed under the proposed algorithm. Both classical and Bayesian inferential approaches of the distribution parameters are discussed. Furthermore, approximate confidence intervals are constructed based on the asymptotic distribution of the maximum …
Interpretable Design Of Reservoir Computing Networks Using Realization Theory, Wei Miao, Vignesh Narayanan, Jr-Shin Li
Interpretable Design Of Reservoir Computing Networks Using Realization Theory, Wei Miao, Vignesh Narayanan, Jr-Shin Li
Publications
The reservoir computing networks (RCNs) have been successfully employed as a tool in learning and complex decision-making tasks. Despite their efficiency and low training cost, practical applications of RCNs rely heavily on empirical design. In this article, we develop an algorithm to design RCNs using the realization theory of linear dynamical systems. In particular, we introduce the notion of α-stable realization and provide an efficient approach to prune the size of a linear RCN without deteriorating the training accuracy. Furthermore, we derive a necessary and sufficient condition on the irreducibility of the number of hidden nodes in linear RCNs based …
Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa
Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa
Honors Theses
In this paper, we analyze the decoding of cyclic codes. First, we introduce linear and cyclic codes, standard decoding processes, and some standard theorems in coding theory. Then, we will introduce Gr¨obner Bases, and describe their connection to the decoding of cyclic codes. Finally, we go in-depth into how we decode cyclic codes using the key equation, and how a breakthrough by A. Brinton Cooper on decoding BCH codes using Gr¨obner Bases gave rise to the search for a polynomial-time algorithm that could someday decode any cyclic code. We discuss the different approaches taken toward developing such an algorithm and …