Minimal Homogeneous Latin Trades

A latin trade is a subset of a latin square which may be replaced with a disjoint mate to obtain a new latin square. A d-homogeneous latin trade is one which intersects each row, each column and each entry of the latin square either 0 or d times. In this paper we give a construction for minimal d-homogeneous latin trades of size dm, for every integer d >= 3, and m >= 1.75d(2) + 3. We also improve this bound for small values of d. Our proof relies on the construction of cyclic sequences whose adjacent sums are distinct. (c) 2006 Elsevier B.V. All rights reserved.

Clustering algorithm based on minimal path loss ratio for vehicular communication

Emerging vehicular comfort applications pose a host of completely new set of requirements such as maintaining end-to-end connectivity, packet routing, and reliable communication for internet access while on the move. One of the biggest challenges is to provide good quality of service (QoS) such as low packet delay while coping with the fast topological changes. In this paper, we propose a clustering algorithm based on minimal path loss ratio (MPLR) which should help in spectrum efficiency and reduce data congestion in the network. The vehicular nodes which experience minimal path loss are selected as the cluster heads. The performance of the MPLR clustering algorithm is calculated by rate of change of cluster heads, average number of clusters and average cluster size. Vehicular traffic models derived from the Traffic Wales data are fed as input to the motorway simulator. A mathematical analysis for the rate of change of cluster head is derived which validates the MPLR algorithm and is compared with the simulated results. The mathematical and simulated results are in good agreement indicating the stability of the algorithm and the accuracy of the simulator. The MPLR system is also compared with V2R system with MPLR system performing better. © 2013 IEEE.

Clustering algorithm based on minimal path loss ratio for vehicular communication

Emerging vehicular comfort applications pose a host of completely new set of requirements such as maintaining end-to-end connectivity, packet routing, and reliable communication for internet access while on the move. One of the biggest challenges is to provide good quality of service (QoS) such as low packet delay while coping with the fast topological changes. In this paper, we propose a clustering algorithm based on minimal path loss ratio (MPLR) which should help in spectrum efficiency and reduce data congestion in the network. The vehicular nodes which experience minimal path loss are selected as the cluster heads. The performance of the MPLR clustering algorithm is calculated by rate of change of cluster heads, average number of clusters and average cluster size. Vehicular traffic models derived from the Traffic Wales data are fed as input to the motorway simulator. A mathematical analysis for the rate of change of cluster head is derived which validates the MPLR algorithm and is compared with the simulated results. The mathematical and simulated results are in good agreement indicating the stability of the algorithm and the accuracy of the simulator. The MPLR system is also compared with V2R system with MPLR system performing better. © 2013 IEEE.

Groups with the Minimal Condition on Non-“Nilpotent-by-Finite” Subgroups

We characterize the groups which do not have non-trivial perfect sections and such that any strictly descending chain of non-“nilpotent-by-finite” subgroups is finite.

Greedy Approximation with Regard to Bases and General Minimal Systems

*This research was supported by the National Science Foundation Grant DMS 0200187 and by ONR Grant N00014-96-1-1003

Minimal Codewords in Linear Codes

2000 Mathematics Subject Classification: 94B05, 94B15.

Minimal Subspaces with Maximal Dimensioanal Diameters

Владимир Тодоров - Нека X е компактно метрично пространство с dim X = n. Тогава за n − 1 - мерния диаметър dn−1(X) на X е изпълнено неравенството dn−1(X) > 0, докато dn(X) = 0 (да отбележим, че това е една от характеристиките на размерността на Лебег). От тук се получава, че X съдържа минимално по включване затворено подмножество Y , за което dn−1(Y ) = dn−1(X). Известен резултат е, че от това следва, че Y е Канторово Многообразие. В тази бележка доказваме, че всяко такова (минимално) подпространство Y е даже континуум V^n. Получени са също така някои следствия.

On Optimal Quadratic Lagrange Interpolation: Extremal Node Systems with Minimal Lebesgue Constant via Symbolic Computation

ACM Computing Classification System (1998): G.1.1, G.1.2.

Algebraic theory of minimal nondeterministic finite automata with applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA’s behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

A Minimal History of the Cuban Revolution (Historia mínima de Ia Revolución Cubana), Book Presentation by Author Rafael Rojas

This flyer promotes the event "A Minimal History of the Cuban Revolution (Historia mínima de Ia Revolución Cubana), Book Presentation by Author Rafael Rojas", part at the SIPA at Books & Books series. This event held at Books & Books in Coral Gables.

Algebraic Theory of Minimal Nondeterministic Finite Automata with Applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA's behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

A minimal model of partial synchrony

Acknowledgement We wish to acknowledge A. Pikovsky and M. Zaks for useful discussions. This work has been financially supported by the EU project COSMOS (642563).

A minimal model of partial synchrony

We wish to acknowledge A Pikovsky and M Zaks for useful discussions. This work has been financially supported by the EU project COSMOS (642563).