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

Guidelines for the use and interpretation of assays for monitoring autophagy (3rd edition)

In 2008 we published the first set of guidelines for standardizing research in autophagy. Since then, research on this topic has continued to accelerate, and many new scientists have entered the field. Our knowledge base and relevant new technologies have also been expanding. Accordingly, it is important to update these guidelines for monitoring autophagy in different organisms. Various reviews have described the range of assays that have been used for this purpose. Nevertheless, there continues to be confusion regarding acceptable methods to measure autophagy, especially in multicellular eukaryotes. For example, a key point that needs to be emphasized is that there is a difference between measurements that monitor the numbers or volume of autophagic elements (e.g., autophagosomes or autolysosomes) at any stage of the autophagic process versus those that measure fl ux through the autophagy pathway (i.e., the complete process including the amount and rate of cargo sequestered and degraded). In particular, a block in macroautophagy that results in autophagosome accumulation must be differentiated from stimuli that increase autophagic activity, defi ned as increased autophagy induction coupled with increased delivery to, and degradation within, lysosomes (inmost higher eukaryotes and some protists such as Dictyostelium ) or the vacuole (in plants and fungi). In other words, it is especially important that investigators new to the fi eld understand that the appearance of more autophagosomes does not necessarily equate with more autophagy. In fact, in many cases, autophagosomes accumulate because of a block in trafficking to lysosomes without a concomitant change in autophagosome biogenesis, whereas an increase in autolysosomes may reflect a reduction in degradative activity. It is worth emphasizing here that lysosomal digestion is a stage of autophagy and evaluating its competence is a crucial part of the evaluation of autophagic flux, or complete autophagy. Here, we present a set of guidelines for the selection and interpretation of methods for use by investigators who aim to examine macroautophagy and related processes, as well as for reviewers who need to provide realistic and reasonable critiques of papers that are focused on these processes. These guidelines are not meant to be a formulaic set of rules, because the appropriate assays depend in part on the question being asked and the system being used. In addition, we emphasize that no individual assay is guaranteed to be the most appropriate one in every situation, and we strongly recommend the use of multiple assays to monitor autophagy. Along these lines, because of the potential for pleiotropic effects due to blocking autophagy through genetic manipulation it is imperative to delete or knock down more than one autophagy-related gene. In addition, some individual Atg proteins, or groups of proteins, are involved in other cellular pathways so not all Atg proteins can be used as a specific marker for an autophagic process. In these guidelines, we consider these various methods of assessing autophagy and what information can, or cannot, be obtained from them. Finally, by discussing the merits and limits of particular autophagy assays, we hope to encourage technical innovation in the field