The lack of rapid antibiotic susceptibility tests adversely affects the treatment of bacterial infections and contributes to increased prevalence of multidrug resistant bacteria. Here, we describe an all-electrical approach that allows for ultra-sensitive measurement of growth signals from only tens of bacteria in a microfluidic device. Our device is essentially a set of microfluidic channels, each with a nano-constriction at one end and cross-sectional dimensions close to that of a single bacterium. Flowing a liquid bacteria sample (e.g., urine) through the microchannels rapidly traps the bacteria in the device, allowing for subsequent incubation in drugs. We measure the electrical resistance of the microchannels, which increases (or decreases) in proportion to the number of bacteria in the microchannels. The method and device allow for rapid antibiotic susceptibility tests in about two hours. Further, the short-time fluctuations in the electrical resistance during an antibiotic susceptibility test are correlated with the morphological changes of bacteria caused by the antibiotic. In contrast to other electrical approaches, the underlying geometric blockage effect provides a robust and sensitive signal, which is straightforward to interpret without electrical models. The approach also obviates the need for a high-resolution microscope and other complex equipment, making it potentially usable in resource-limited settings.

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Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type subseeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for (rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also, we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras.Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case. Contents1. Introduction and preliminaries 1 2. Seed homomorphisms and some elementary properties 5 3. Rooted cluster morphisms and the relationship with seed homomorphisms 10 4. Sub-rooted cluster algebras and rooted cluster subalgebras 16 4.1. Sub-rooted cluster algebras and two special cases 16 4.2. Rooted cluster subalgebras as sub-class of sub-rooted cluster algebras 18 5. On enumeration and monoidal categorification 21 5.1. The number of rooted cluster subalgebras of the form A(Σ I0,I1 ) 21 5.2. Monoidal sub-categorification of a rooted cluster algebra 22 6. Rooted cluster quotient algebras 25 6.1. Rooted cluster quotient algebras via pure sub-cluster algebras 25 6.2. Rooted cluster quotient algebras via gluing method 29 References 40 Introduction and preliminariesCluster algebras are commutative algebras that were introduced by Fomin and Zelevinsky [9] in order to give a combinatorial characterization of total positivity and canonical bases in algebraic groups. The theory of cluster algebras is related to numerous other fields. Since its introduction, the study on cluster algebras mainly involves intersection with Lie theory, representation theory of algebras, its combinatorial method (e.g. the periodicity issue) and categorification and the sub-class constructed from Riemannian surfaces and its topological setting, including the Teichmüller theory.The algebraic structure and properties of cluster algebras were originally studied in a series of articles [9,10,2,11] involving bases and the positivity conjecture. The positive conjecture has been Mathematics Subject Classification(2010): 13F60, 05E15, 20M10. 1 2 MIN HUANG FANG LI YICHAO YANG 1 , that is, Σ ∅,I1 and Σ ∅,I ′ 1 are non-trivial. Since Σ is connected, we have Σ = Σ ∅,I1 ∐ Σ ∅,I ′ 1 , which contradicts to the indecomposability of Σ. "If": Clearly, Σ is connected. If Q is decomposable, then we have Σ = Σ 1 ∐ Σ 2 with non-trivial Σ 1 = (X 1 , (X 1 ) f r , B 1 ) and Σ 2 = (X 2 , (X 2 ) f r , B 2 ). Then we can find x ∈ X 1 , y ∈ X 2 such that there exists a sequence of exchangeable cluster variables (x 1 , · · · , x s ) in X = X 1 ∪ X 2 satisfying that b x1x = 0, b xixi+1 = 0 and b xsy = 0 for i = 1, · · · , s, which is impossible according to (4), the form of B.Lemma 2.9. If a non-trivial seed Σ = (X, X f r , B) is indecomposable, then any seed homomorphism f : Σ → Σ ′ is either positive or negative.Proof. Assume th...

Cloud computing emerges as new computing paradigms in which virtualized resources provide reliable and guarantee service for users demand. Actually, cloud is a serviceoriented platform because all kind of virtual resources are treated as service to users. Nowadays, most of data-intensive applications have been developed on cloud system. These applications reaches geographically separated storage or data resource with even cross-continental-networks. Then, the performance degradation of networks will surely affect the cloud application performance and user request. In order to ensure guarantee service of bulk data transfer in cloud computing, the reservation and combined resources utilization become critical issues which include data and network resources. This issue involves reserve and assign combined resources to meet user's QoS requirement. According to this problem, a cloud infrastructure service framework (CISF) is proposed to achieve guarantee service for data-intensive applications in this paper. And a service-oriented resource broker (SRB) based on this framework which is proposed to discovery, select, reserve and assign best combined resources. Finally, under user's QoS constraint dynamic resource selection algorithm has been implemented for optimization of combined resources allocation.

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Cloud computing technology facilitates computing-intensive applications by providing virtualized resources which can be dynamically provisioned. However, user’s requests are varied according to different applications’ computation ability needs. These applications can be presented as meta-job of user’s demand. The total processing time of these jobs may need data transmission time over the Internet as well as the completed time of jobs to execute on the virtual machine must be taken into account. In this paper, we presented V-heuristics scheduling algorithm for allocation of virtualized network and computing resources under user’s constraint which applied into a service-oriented resource broker for jobs scheduling. This scheduling algorithm takes into account both data transmission time and computation time that related to virtualized network and virtual machine. The simulation results are compared with three different types of heuristic algorithms under conventional network or virtual network conditions such as MCT, Min-Min and Max-Min. e evaluate these algorithms within a simulated cloud environment via an abilenenetwork topology which is real physical core network topology. These experimental results show that V-heuristic scheduling algorithm achieved significant performance gain for a variety of applications in terms of load balance, Makespan, average resource utilization and total processing time.

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