Odd-flavor Simulations by the Hybrid Monte Carlo

The standard hybrid Monte Carlo algorithm is known to simulate even flavors QCD only. Simulations of odd flavors QCD, however, can be also performed in the framework of the hybrid Monte Carlo algorithm where the inverse of the fermion matrix is approximated by a polynomial. In this exploratory study we perform three flavors QCD simulations. We make a comparison of the hybrid Monte Carlo algorithm and the R-algorithm which also simulates odd flavors systems but has step-size errors. We find that results from our hybrid Monte Carlo algorithm are in agreement with those from the R-algorithm obtained at very small step-size.Comment: 9 pages, 8 figures, Proceedings of the International Workshop on Nonperturbative Methods and Lattice QCD, Guangzhou, Chin

Key schedule algorithm based on coordinate geometry of a three-dimensional hybrid cube

Cryptographic algorithms play an important role in information security where it ensures the security of data across the network or storage. A key schedule algorithm is the mechanism that generates and schedules all session-keys for the encryption process. The 2-dimensional hybrid cube is generated based on permutation and combination of integer numbers that are utilized in the construction of encryption and decryption key in the non-binary block cipher. The generation of key space by using the 2-dimensional hybrid cubes are not sufficient to resist attacks and could easily be exploited. Therefore, the large key space is more desirable to resist any attack on the secret key. This research proposed a new Key Schedule Algorithm based on the coordinate geometry of a Hybrid Cube (KSAHC) for the non-binary block cipher. By using the three-dimensional hybrid cube in KSAHC transformation, encryption keys are represented as n × n × n matrix of integer numbers and used in the development of the permutation and substitution of order 4 square matrix. Triangular Coordinate Extraction (TCE) technique has also been introduced to extract the coordinates during the rotation of Hybrid Cube surface (HCs) and plays an important role in the development of KSAHC algorithm. The Hybrid Cube Encryption Algorithm (HiSea) has been implemented to validate the encryption keys that are generated from the proposed algorithm. The strength of the keys and ciphertext are compared with the Advanced Encryption Standard (AES), HiSea, and Dynamic Key Schedule Algorithm (DKSA). The proposed KSAHC algorithm has been validated using the randomness test proposed and recommended by NIST, the average result of avalanche test is 93%, entropy is 0.9968, correlation assessment test is -0.000601 and having large key space 2.70 × 1067 keys that makes the Brute Force attack difficult and time-consuming. Therefore, it can be concluded that the strength and validity of KSAHC algorithm have been enhanced as compared to other algorithms and can serve as the alternative algorithm in designing security systems

Simulation of n_f =3 QCD by Hybrid Monte Carlo

Simulations of odd flavors QCD can be performed in the framework of the hybrid Monte Carlo algorithm where the inverse of the fermion matrix is approximated by a polynomial. In this exploratory study we perform three flavors QCD simulations. We make a comparison of the hybrid Monte Carlo algorithm and the R-algorithm which also simulates odd flavors systems but has step-size errors. We find that results from our hybrid Monte Carlo algorithm are in agreement with those from the R-algorithm obtained at very small step-size.Comment: Lattice 2000 (Algorithms), 5 pages, 8 figures, LaTe

On the Hybrid Minimum Principle On Lie Groups and the Exponential Gradient HMP Algorithm

This paper provides a geometrical derivation of the Hybrid Minimum Principle (HMP) for autonomous hybrid systems whose state manifolds constitute Lie groups $(G,\star)$ which are left invariant under the controlled dynamics of the system, and whose switching manifolds are defined as smooth embedded time invariant submanifolds of $G$. The analysis is expressed in terms of extremal (i.e. optimal) trajectories on the cotangent bundle of the state manifold $G$. The Hybrid Maximum Principle (HMP) algorithm introduced in \cite{Shaikh} is extended to the so-called Exponential Gradient algorithm. The convergence analysis for the algorithm is based upon the LaSalle Invariance Principle and simulation results illustrate their efficacy

A hybrid clustering algorithm for data mining

Data clustering is a process of arranging similar data into groups. A clustering algorithm partitions a data set into several groups such that the similarity within a group is better than among groups. In this paper a hybrid clustering algorithm based on K-mean and K-harmonic mean (KHM) is described. The proposed algorithm is tested on five different datasets. The research is focused on fast and accurate clustering. Its performance is compared with the traditional K-means & KHM algorithm. The result obtained from proposed hybrid algorithm is much better than the traditional K-mean & KHM algorithm