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Title: 2012-2013 Program Review Mathematics.
Creator: Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: Florida Atlantic University Departmental Dashboard Indicators. Department program reviews for Charles E. Schmidt College of Science, Florida Atlantic University.
Date Issued: 2012-2013
PURL: http://purl.flvc.org/fau/fd/FA00007690
Format: Document (PDF)

Title: 2010-2011 Program Review Mathematics.
Creator: Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: Florida Atlantic University Departmental Dashboard Indicators. Department program reviews for Charles E. Schmidt College of Science, Florida Atlantic University.
Date Issued: 2010-2011
PURL: http://purl.flvc.org/fau/fd/FA00007683
Format: Document (PDF)

Title: 2013-2014 Program Review Mathematics.
Creator: Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: Florida Atlantic University Departmental Dashboard Indicators. Department program reviews for Charles E. Schmidt College of Science, Florida Atlantic University.
Date Issued: 2013-2014
PURL: http://purl.flvc.org/fau/fd/FA00007697
Format: Document (PDF)

Title: 2014-2015 Program Review Mathematics.
Creator: Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: Florida Atlantic University Departmental Dashboard Indicators. Department program reviews for Charles E. Schmidt College of Science, Florida Atlantic University.
Date Issued: 2014-2015
PURL: http://purl.flvc.org/fau/fd/FA00007704
Format: Document (PDF)

Title: 2009-2010 Program Review Mathematics.
Creator: Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: Florida Atlantic University Departmental Dashboard Indicators. Department program reviews for Charles E. Schmidt College of Science, Florida Atlantic University.
Date Issued: 2009-2010
PURL: http://purl.flvc.org/fau/fd/FA00007676
Format: Document (PDF)

Title: 2015-2016 Program Review Mathematics.
Creator: Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: Florida Atlantic University Departmental Dashboard Indicators. Department program reviews for Charles E. Schmidt College of Science, Florida Atlantic University.
Date Issued: 2015-2016
PURL: http://purl.flvc.org/fau/fd/FA00007711
Format: Document (PDF)

Title: 2016-2017 Program Review Mathematics.
Creator: Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: Florida Atlantic University Departmental Dashboard Indicators. Department program reviews for Charles E. Schmidt College of Science, Florida Atlantic University.
Date Issued: 2016-2017
PURL: http://purl.flvc.org/fau/fd/FA00007718
Format: Document (PDF)

Title: Auslander-Reiten theory for systems of submodule embeddings.
Creator: Moore, Audrey., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In this dissertation, we will investigate aspects of Auslander-Reiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute Auslander-Reiten quivers of such categories, which among other information, yields valuable information about the indecomposable objects in such a category. A main result of the dissertation is an adaptation to this situation of the Auslander and Ringel-Tachikawa Theorem which states that for an artinian ring R of finite...
Show moreIn this dissertation, we will investigate aspects of Auslander-Reiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute Auslander-Reiten quivers of such categories, which among other information, yields valuable information about the indecomposable objects in such a category. A main result of the dissertation is an adaptation to this situation of the Auslander and Ringel-Tachikawa Theorem which states that for an artinian ring R of finite representation type, each R-module is a direct sum of finite-length indecomposable R-modules. In cases where this applies, the indecomposable objects obtained in the Auslander-Reiten quiver give the building blocks for the objects in the category. We also briefly discuss in which cases systems of submodule embeddings form a Frobenius category, and for a few examples explore pointwise Calabi-Yau dimension of such a category.
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Date Issued: 2009
PURL: http://purl.flvc.org/fcla/dt/210496
Subject Headings: Artin algebras, Rings (Algebra), Representation of algebras, Embeddings (Mathematics), Linear algebraic groups
Format: Document (PDF)

Title: Computing topological dynamics from time series.
Creator: Wess, Mark., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: The topological entropy of a continuous map quantifies the amount of chaos observed in the map. In this dissertation we present computational methods which enable us to compute topological entropy for given time series data generated from a continuous map with a transitive attractor. A triangulation is constructed in order to approximate the attractor and to construct a multivalued map that approximates the dynamics of the linear interpolant on the triangulation. The methods utilize...
Show moreThe topological entropy of a continuous map quantifies the amount of chaos observed in the map. In this dissertation we present computational methods which enable us to compute topological entropy for given time series data generated from a continuous map with a transitive attractor. A triangulation is constructed in order to approximate the attractor and to construct a multivalued map that approximates the dynamics of the linear interpolant on the triangulation. The methods utilize simplicial homology and in particular the Lefschetz Fixed Point Theorem to establish the existence of periodic orbits for the linear interpolant. A semiconjugacy is formed with a subshift of nite type for which the entropy can be calculated and provides a lower bound for the entropy of the linear interpolant. The dissertation concludes with a discussion of possible applications of this analysis to experimental time series.
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Date Issued: 2008
PURL: http://purl.flvc.org/FAU/186294
Subject Headings: Algebraic topology, Graph theory, Fixed point theory, Singularities (Mathematics)
Format: Document (PDF)

Title: Derivation of planar diffeomorphisms from Hamiltonians with a kick.
Creator: Barney, Zalmond C., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In this thesis we will discuss connections between Hamiltonian systems with a periodic kick and planar diffeomorphisms. After a brief overview of Hamiltonian theory we will focus, as an example, on derivations of the Hâenon map that can be obtained by considering kicked Hamiltonian systems. We will conclude with examples of Hâenon maps of interest.
Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3329833
Subject Headings: Mathematical physics, Differential equations, Partial, Hamiltonian systems, Algebra, Linear, Chaotic behavior in systems
Format: Document (PDF)

Title: Empirical likelihood method for segmented linear regression.
Creator: Liu, Zhihua., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: For a segmented regression system with an unknown change-point over two domains of a predictor, a new empirical likelihood ratio test statistic is proposed to test the null hypothesis of no change. The proposed method is a non-parametric method which releases the assumption of the error distribution. Under the null hypothesis of no change, the proposed test statistic is shown empirically Gumbel distributed with robust location and scale parameters under various parameter settings and error...
Show moreFor a segmented regression system with an unknown change-point over two domains of a predictor, a new empirical likelihood ratio test statistic is proposed to test the null hypothesis of no change. The proposed method is a non-parametric method which releases the assumption of the error distribution. Under the null hypothesis of no change, the proposed test statistic is shown empirically Gumbel distributed with robust location and scale parameters under various parameter settings and error distributions. Under the alternative hypothesis with a change-point, the comparisons with two other methods (Chen's SIC method and Muggeo's SEG method) show that the proposed method performs better when the slope change is small. A power analysis is conducted to illustrate the performance of the test. The proposed method is also applied to analyze two real datasets: the plasma osmolality dataset and the gasoline price dataset.
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Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3332719
Subject Headings: Change-point problems, Regression analysis, Econometrics, Limit theory (Probability theory)
Format: Document (PDF)

Title: Construction of combinatorial designs with prescribed automorphism groups.
Creator: Kolotoglu, Emre., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In this dissertation, we study some open problems concerning the existence or non-existence of some combinatorial designs. We give the construction or proof of non-existence of some Steiner systems, large sets of designs, and graph designs, with prescribed automorphism groups.
Date Issued: 2013
PURL: http://purl.flvc.org/fcla/dt/3360795
Subject Headings: Combinatorial designs and configurations, Finite geometries, Curves, Algebraic, Automorphisms, Mathematical optimization, Steiner systems
Format: Document (PDF)

Title: Cryptography in the presence of key-dependent messages.
Creator: Gonzalez, Madeline., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: The aim of this work is to investigate a security model in which we allow an adversary to have access to functions of the secret key. In recent years, significant progress has been made in understanding the security of encryption schemes in the presence of key-dependent plaintexts or messages (known as KDM). Here, we motivate and explore the security of a setting, where an adversary against a message authentication code (MAC) or signature scheme can access signatures on key-dependent messages...
Show moreThe aim of this work is to investigate a security model in which we allow an adversary to have access to functions of the secret key. In recent years, significant progress has been made in understanding the security of encryption schemes in the presence of key-dependent plaintexts or messages (known as KDM). Here, we motivate and explore the security of a setting, where an adversary against a message authentication code (MAC) or signature scheme can access signatures on key-dependent messages. We propose a way to formalize the security of message authentication schemes in the presence of key-dependent MACs (KD-EUF) and of signature schemes in the presence of key-dependent signatures (KDS). An attack on a message recognition protocol involving a MAC is presented. It turns out that the situation is quite different from key-dependent encryption: To achieve KD-EUF-security or KDS-security under non-adaptive chosen message attacks, the use of a stateful signing algorithm is inevitable even in the random oracle model. After discussing the connection between key-dependent signing and forward security, we describe a compiler which lifts any EUF-CMA secure one-time signature scheme to a forward secure signature scheme offering KDS-CMA security. Then, we discuss how aggregate signatures can be used to combine the signatures in the certificate chain used in the compiler. A natural question arises about how to combine the security definitions of KDM and KDS to come up with a signcryption scheme that is secure. We also offer a connection with Leakage-Resilient Signatures, which take into account side-channel attacks. Lastly, we present some open problems for future research.
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Date Issued: 2009
PURL: http://purl.flvc.org/FAU/2182087
Subject Headings: Cryptography, Data processing, Digital signatures, Computer security, Data encryption (Computer science), Software protection
Format: Document (PDF)

Title: Coset intersection problem and application to 3-nets.
Creator: Pace, Nicola, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In a projective plane (PG(2, K) defined over an algebraically closed field K of characteristic p = 0, we give a complete classification of 3-nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family and list all...
Show moreIn a projective plane (PG(2, K) defined over an algebraically closed field K of characteristic p = 0, we give a complete classification of 3-nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family and list all possible sporadic examples. If p is larger than the order of the group, the same classification holds true apart from three possible exceptions: Alt4, Sym4 and Alt5.
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3355866
Subject Headings: Finite fields (Algebra), Mathematical physics, Field theory (Physics), Curves, Algebraic
Format: Document (PDF)

Title: Design and analysis of key establishment protocols.
Creator: Neupane, Kashi., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Consider a scenario where a server S shares a symmetric key kU with each user U. Building on a 2-party solution of Bohli et al., we describe an authenticated 3-party key establishment which remains secure if a computational Bilinear Diffie Hellman problem is hard or the server is uncorrupted. If the BDH assumption holds during a protocol execution, but is invalidated later, entity authentication and integrity of the protocol are still guaranteed. Key establishment protocols based on hardness...
Show moreConsider a scenario where a server S shares a symmetric key kU with each user U. Building on a 2-party solution of Bohli et al., we describe an authenticated 3-party key establishment which remains secure if a computational Bilinear Diffie Hellman problem is hard or the server is uncorrupted. If the BDH assumption holds during a protocol execution, but is invalidated later, entity authentication and integrity of the protocol are still guaranteed. Key establishment protocols based on hardness assumptions, such as discrete logarithm problem (DLP) and integer factorization problem (IFP) are vulnerable to quantum computer attacks, whereas the protocols based on other hardness assumptions, such as conjugacy search problem and decomposition search problem can resist such attacks. The existing protocols based on the hardness assumptions which can resist quantum computer attacks are only passively secure. Compilers are used to convert a passively secure protocol to an actively secure protoc ol. Compilers involve some tools such as, signature scheme and a collision-resistant hash function. If there are only passively secure protocols but not a signature scheme based on same assumption then the application of existing compilers requires the use of such tools based on different assumptions. But the introduction of new tools, based on different assumptions, makes the new actively secure protocol rely on more than one hardness assumptions. We offer an approach to derive an actively secure two-party protocol from a passively secure two-party protocol without introducing further hardness assumptions. This serves as a useful formal tool to transform any basic algebric method of public key cryptography to the real world applicaticable cryptographic scheme. In a recent preprint, Vivek et al. propose a compiler to transform a passively secure 3-party key establishment to a passively secure group key establishment. To achieve active security, they apply this compiler to Joux's, protoc ol and apply a construction by Katz and Yung, resulting in a 3-round group key establishment. In this reserach, we show how Joux's protocol can be extended to an actively secure group key establishment with two rounds. The resulting solution is in the standard model, builds on a bilinear Diffie-Hellman assumption and offers forward security as well as strong entity authentication. If strong entity authentication is not required, then one half of the participants does not have to send any message in the second round, which may be of interest for scenarios where communication efficiency is a main concern.
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3342239
Subject Headings: Computer networks, Security measures, Computer network protocols, Data encryption (Computer science), Public key infrastructure (Computer security)
Format: Document (PDF)

Title: AUC estimation under various survival models.
Creator: Chang, Fazhe., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In the medical science, the receiving operationg characteristic (ROC) curve is a graphical representation to evaluate the accuracy of a medical diagnostic test for any cut-off point. The area under the ROC curve (AUC) is an overall performance measure for a diagnostic test. There are two parts in this dissertation. In the first part, we study the properties of bi-Exponentiated Weibull models. FIrst, we derive a general moment formula for single Exponentiated Weibull models. Then we move on to...
Show moreIn the medical science, the receiving operationg characteristic (ROC) curve is a graphical representation to evaluate the accuracy of a medical diagnostic test for any cut-off point. The area under the ROC curve (AUC) is an overall performance measure for a diagnostic test. There are two parts in this dissertation. In the first part, we study the properties of bi-Exponentiated Weibull models. FIrst, we derive a general moment formula for single Exponentiated Weibull models. Then we move on to derive the precise formula of AUC and study the maximus likelihood estimation (MLE) of the AUC. Finally, we obtain the asymptotoc distribution of the estimated AUC. Simulation studies are used to check the performance of MLE of AUC under the moderate sample sizes. The second part fo the dissertation is to study the estimation of AUC under the crossing model, which extends the AUC formula in Gonen and Heller (2007).
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3359287
Subject Headings: Receiver operating characteristic curves, Medical screening, Statistical methods, Diagnosis, Statistical methods, Smoothing (Statistics)
Format: Document (PDF)

Title: Implementation and comparison of the Golay and first order Reed-Muller codes.
Creator: Shukina, Olga., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In this project we perform data transmission across noisy channels and recover the message first by using the Golay code, and then by using the first-order Reed- Muller code. The main objective of this thesis is to determine which code among the above two is more efficient for text message transmission by applying the two codes to exactly the same data with the same channel error bit probabilities. We use the comparison of the error-correcting capability and the practical speed of the Golay...
Show moreIn this project we perform data transmission across noisy channels and recover the message first by using the Golay code, and then by using the first-order Reed- Muller code. The main objective of this thesis is to determine which code among the above two is more efficient for text message transmission by applying the two codes to exactly the same data with the same channel error bit probabilities. We use the comparison of the error-correcting capability and the practical speed of the Golay code and the first-order Reed-Muller code to meet our goal.
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Date Issued: 2013
PURL: http://purl.flvc.org/fcla/dt/3362579
Subject Headings: Error-correcting codes (Information theory), Coding theory, Computer algorithms, Digital modulation
Format: Document (PDF)

Title: On projected planes.
Creator: Caliskan, Cafer., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: This work was motivated by the well-known question: "Does there exist a nondesarguesian projective plane of prime order?" For a prime p 1, determine all subplanes of order p up to collineations, and check whether one of these is non-desarguesian." In this manuscript we use a group-theoretic methodology to determine the subplane structures of some non-desarguesian planes. In particular, we determine orbit representatives of all proper Q-subplanes both of a Veblen-Wedderburn (VW) plane of...
Show moreThis work was motivated by the well-known question: "Does there exist a nondesarguesian projective plane of prime order?" For a prime p < 11, there is only the pappian plane of order p. Hence, such planes are indeed desarguesian. Thus, it is of interest to examine whether there are non-desarguesian planes of order 11. A suggestion by Ascher Wagner in 1985 was made to Spyros S. Magliveras: "Begin with a non-desarguesian plane of order pk, k > 1, determine all subplanes of order p up to collineations, and check whether one of these is non-desarguesian." In this manuscript we use a group-theoretic methodology to determine the subplane structures of some non-desarguesian planes. In particular, we determine orbit representatives of all proper Q-subplanes both of a Veblen-Wedderburn (VW) plane of order 121 and of the Hughes plane of order 121, under their full collineation groups. In PI, there are 13 orbits of Baer subplanes, all of which are desarguesian, and approximately 3000 orbits of Fano subplanes. In Sigma , there are 8 orbits of Baer subplanes, all of which are desarguesian, 2 orbits of subplanes of order 3, and at most 408; 075 distinct Fano subplanes. In addition to the above results, we also study the subplane structures of some non-desarguesian planes, such as the Hall plane of order 25, the Hughes planes of order 25 and 49, and the Figueora planes of order 27 and 125. A surprising discovery by L. Puccio and M. J. de Resmini was the existence of a plane of order 3 in the Hughes plane of order 25. We generalize this result, showing that there are subplanes of order 3 in the Hughes planes of order q2, where q is a prime power and q 5 (mod 6). Furthermore, we analyze the structure of the full collineation groups of certain Veblen- Wedderburn (VW) planes of orders 25, 49 and 121, and discuss how to recover the planes from their collineation groups.
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Date Issued: 2010
PURL: http://purl.flvc.org/FAU/1927609
Subject Headings: Projected planes, Combinatorial designs and configurations, Surfaces, Algebraic, Manifolds (Mathematics)
Format: Document (PDF)

Title: On the spectrum of positive operators.
Creator: Acharya, Cheban P., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Spectral theory, mathematical system theory, evolution equations, differential and difference equations [electronic resource] : 21st International Workshop on Operator Theory and Applications, Berlin, July 2010.It is known that lattice homomorphisms and G-solvable positive operators on Banach lattices have cyclic peripheral spectrum (See [17]). In my thesis I prove that positive contractions whose spectral radius is 1 on Banach lattices with increasing norm have cyclic peripheral point...
Show moreSpectral theory, mathematical system theory, evolution equations, differential and difference equations [electronic resource] : 21st International Workshop on Operator Theory and Applications, Berlin, July 2010.It is known that lattice homomorphisms and G-solvable positive operators on Banach lattices have cyclic peripheral spectrum (See [17]). In my thesis I prove that positive contractions whose spectral radius is 1 on Banach lattices with increasing norm have cyclic peripheral point spectrum. I also prove that if the Banach lattice is a K B space satisfying the growth conditon and º is an eigenvalue of a positive contraction T such that [º] = 1, then 1 is also an eigenvalue of T as well as an eigenvalue of T¨, the dual of T. I also investigate the conditions on contraction operators on Hilbert lattices and AL-spaces which guanantee that 1 is an eigenvalue. As we know from [17], if T : E-E is a positive ideal irreducible operator on E such the r (T) = 1 is a pole of the resolvent R(º, T), then r (T) is simple pole with dimN (T -r(T)I) and ºper(T) is cyclic. Also all points of ºper(T) are simple poles of the resolvent R(º,T). SInce band irreducibility and º-order continuity do not imply ideal irreducibility [2], we prove the analogous results for band irreducible, º-order continuous operators.
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3359288
Subject Headings: Operator theory, Evolution equations, Banach spaces, Linear topological spaces, Functional analysis
Format: Document (PDF)

Title: Permutation-based data compression.
Creator: Mihnea, Amalya, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: The use of permutations in data compression is an aspect that is worthy of further exploration. The work that has been done in video compression based on permutations was primarily oriented towards lossless algorithms. The study of previous algorithms has led to a new algorithm that could be either lossless or lossy, for which the amount of compression and the quality of the output can be controlled. The lossless version of our algorithm performs close to lossy versions of H.264 and it...
Show moreThe use of permutations in data compression is an aspect that is worthy of further exploration. The work that has been done in video compression based on permutations was primarily oriented towards lossless algorithms. The study of previous algorithms has led to a new algorithm that could be either lossless or lossy, for which the amount of compression and the quality of the output can be controlled. The lossless version of our algorithm performs close to lossy versions of H.264 and it improves on them for the majority of the videos that we analyzed. Our algorithm could be used in situations where there is a need for lossless compression and the video sequences are part of a single scene, e.g., medical videos, where loss of information could be risky or expensive. Some results on permutations, which may be of independent interest, arose in developing this algorithm. We report on these as well.
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Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3333054
Subject Headings: Data compression (Telecommunication), Combinatorics, Network architecture and design, Computer network architectures, Mathematical optimization
Format: Document (PDF)

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