Involutive Bases Algorithm Incorporating F5 Criterion

Faugere's F5 algorithm is the fastest known algorithm to compute Groebner bases. It has a signature-based and an incremental structure that allow to apply the F5 criterion for deletion of unnecessary reductions. In this paper, we present an involutive completion algorithm which outputs a minimal involutive basis. Our completion algorithm has a nonincremental structure and in addition to the involutive form of Buchberger's criteria it applies the F5 criterion whenever this criterion is applicable in the course of completion to involution. In doing so, we use the G2V form of the F5 criterion developed by Gao, Guan and Volny IV. To compare the proposed algorithm, via a set of benchmarks, with the Gerdt-Blinkov involutive algorithm (which does not apply the F5 criterion) we use implementations of both algorithms done on the same platform in Maple.Comment: 24 pages, 2 figure

Fastpass: A Centralized “Zero-Queue” Datacenter Network

An ideal datacenter network should provide several properties, including low median and tail latency, high utilization (throughput), fair allocation of network resources between users or applications, deadline-aware scheduling, and congestion (loss) avoidance. Current datacenter networks inherit the principles that went into the design of the Internet, where packet transmission and path selection decisions are distributed among the endpoints and routers. Instead, we propose that each sender should delegate control—to a centralized arbiter—of when each packet should be transmitted and what path it should follow. This paper describes Fastpass, a datacenter network architecture built using this principle. Fastpass incorporates two fast algorithms: the first determines the time at which each packet should be transmitted, while the second determines the path to use for that packet. In addition, Fastpass uses an efficient protocol between the endpoints and the arbiter and an arbiter replication strategy for fault-tolerant failover. We deployed and evaluated Fastpass in a portion of Facebook’s datacenter network. Our results show that Fastpass achieves high throughput comparable to current networks at a 240 reduction is queue lengths (4.35 Mbytes reducing to 18 Kbytes), achieves much fairer and consistent flow throughputs than the baseline TCP (5200 reduction in the standard deviation of per-flow throughput with five concurrent connections), scalability from 1 to 8 cores in the arbiter implementation with the ability to schedule 2.21 Terabits/s of traffic in software on eight cores, and a 2.5 reduction in the number of TCP retransmissions in a latency-sensitive service at Facebook.National Science Foundation (U.S.) (grant IIS-1065219)Irwin Mark Jacobs and Joan Klein Jacobs Presidential FellowshipHertz Foundation (Fellowship

Studies of Microbiota Dynamics Reveals Association of “Candidatus Liberibacter Asiaticus” Infection with Citrus (Citrus sinensis) Decline in South of Iran

Citrus Decline Disease was recently reported to affect several citrus species in Iran when grafted on a local rootstock variety, Bakraee. Preliminary studies found \u201cCandidatus Phytoplasma aurantifoliae\u201d and \u201cCandidatus Liberibacter asiaticus\u201d as putative etiological agents, but were not ultimately able to determine which one, or if an association of both, were causing the disease. The current study has the aim of characterizing the microbiota of citrus plants that are either asymptomatic, showing early symptoms, or showing late symptoms through amplification of the V1\u2013V3 region of 16S rRNA gene using an Illumina sequencer in order to (i) clarify the etiology of the disease, and (ii) describe the microbiota associated to different symptom stages. Our results suggest that liberibacter may be the main pathogen causing Citrus Decline Disease, but cannot rule out the possibility of phytoplasma being involved as well. The characterization of microbiota shows that the leaves show only two kinds of communities, either symptomatic or asymptomatic, while roots show clear distinction between early and late symptoms. These results could lead to the identification of bacteria that are related to successful plant defense response and, therefore, to immunity to the Citrus Decline Disease

Optimal quantum detectors for unambiguous detection of mixed states

We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient conditions for an optimal measurement that maximizes the probability of correct detection. We show that the previous optimal measurements that were derived for certain special cases satisfy these optimality conditions. We then consider state sets with strong symmetry properties, and show that the optimal measurement operators for distinguishing between these states share the same symmetries, and can be computed very efficiently by solving a reduced size semidefinite program.Comment: Submitted to Phys. Rev.

NUMFabric: Fast and Flexible Bandwidth Allocation in Datacenters

We present xFabric, a novel datacenter transport design that provides flexible and fast bandwidth allocation control. xFabric is flexible: it enables operators to specify how bandwidth is allocated amongst contending flows to optimize for different service-level objectives such as minimizing flow completion times, weighted allocations, different notions of fairness, etc. xFabric is also very fast, it converges to the specified allocation one-to-two order of magnitudes faster than prior schemes. Underlying xFabric, is a novel distributed algorithm that uses in-network packet scheduling to rapidly solve general network utility maximization problems for bandwidth allocation. We evaluate xFabric using realistic datacenter topologies and highly dynamic workloads and show that it is able to provide flexibility and fast convergence in such stressful environments.Google Faculty Research Awar