Regional gradient controllability of ultra-slow diffusions involving the Hadamard-Caputo time fractional derivative

This paper investigates the regional gradient controllability for ultra-slow diffusion processes governed by the time fractional diffusion systems with a Hadamard-Caputo time fractional derivative. Some necessary and sufficient conditions on regional gradient exact and approximate controllability are first given and proved in detail. Secondly, we propose an approach on how to calculate the minimum number of $\omega-$strategic actuators. Moreover, the existence, uniqueness and the concrete form of the optimal controller for the system under consideration are presented by employing the Hilbert Uniqueness Method (HUM) among all the admissible ones. Finally, we illustrate our results by an interesting example.Comment: 16 page

Existence Results for a Coupled System of Nonlinear Fractional Boundary Value Problems at Resonance

Some new Banach spaces are established. Based on those new Banach spaces and by using the coincidence degree theory, we present the existence results for a coupled system of nonlinear fractional differential equations with multipoint boundary value conditions at resonance case

A common framework of partition-based clustering for large scale dataset using sampling and its MapReduce implementation

Grupiranje (clustering) je jedan od važnih zadataka u rudarenu podataka (data mining), a algoritmi grupiranja utemeljenog na raspodjeli kao što su k-način jedno su od popularnih rješenja. Ipak, sve većim razvojem računarstva u oblaku i ogromne količine podataka, prijenos velikog broja podataka postao je veliki izazov za grupiranje. Na primjer, izvođenje algoritma grupiranja oduzima previše vremena, optimizacija parametara je teška, a kvaliteta grupa (klastera) nije dobra. U tu smo svrhu u ovom radu predložili uobičajeni okvir za algoritme grupiranja utemeljenog na raspodjeli kao što su k-način i dizajnirali njegovu MapReduce implementaciju. Posebice smo, u svrhu predstavljanja prijenosa velikog broja podataka, predložili primjenu tehnike uzorkovanja. Zatim, koristeći k-način algoritam, predlažemo uobičajeni postupak grupiranja i opisujemo primjenu na temelju k-način algoritma. Nadalje, implementiramo predloženi okvir primjenom MapReduce modela programiranja. Eksperimenti pokazuju da je naša metoda učinkovita za prijenos velikog broja podataka.Clustering is one of the significant tasks in data mining, and partition-based clustering algorithms such as k-means are one of the popular solutions. However, with the increasing development of cloud computing and big data, large scale dataset has been a big challenge for clustering. For example, the execution of clustering algorithm is too time-consuming, the optimization of parameters is difficult, and the quality of clusters is not good. To this end, in this paper, we proposed a common framework of partition-based clustering algorithms such as k-means, and designed its MapReduce implementation. Specifically, in order to deal with the representation of large scale dataset, we propose to employ sampling technique. Then, inspired by k-means algorithm, we propose a common procedure of clustering, and provide a k-means based implementation. Furthermore, we implement proposed framework using MapReduce programming model. Experiments show that our method is efficient for large scale dataset

Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique

This paper deals with the robust stabilization of continuous-time hybrid stochastic systems with timevarying delay by feedback controls based on discrete-time state observations. By employing the Razumikhin technique, delay-independent criteria to determine controllers and time lags are established just under a weaker condition that the time-varying delay should be a bounded function. Meanwhile, for the nondelay system, we obtain a better bound on the duration τ between two consecutive state observations. The new theory developed in this paper improves the existing results. Numerical examples are provided to demonstrate the effectiveness of our results

Information theory-based algorithm for in silico prediction of PCR products with whole genomic sequences as templates

BACKGROUND: A new algorithm for assessing similarity between primer and template has been developed based on the hypothesis that annealing of primer to template is an information transfer process. RESULTS: Primer sequence is converted to a vector of the full potential hydrogen numbers (3 for G or C, 2 for A or T), while template sequence is converted to a vector of the actual hydrogen bond numbers formed after primer annealing. The former is considered as source information and the latter destination information. An information coefficient is calculated as a measure for fidelity of this information transfer process and thus a measure of similarity between primer and potential annealing site on template. CONCLUSION: Successful prediction of PCR products from whole genomic sequences with a computer program based on the algorithm demonstrated the potential of this new algorithm in areas like in silico PCR and gene finding

Existence Results for Second-Order Impulsive Neutral Functional Differential Equations with Nonlocal Conditions

The existence of mild solutions for second-order impulsive semilinear neutral functional differential equations with nonlocal conditions in Banach spaces is investigated. The results are obtained by using fractional power of operators and Sadovskii's fixed point theorem