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In distributed optimization and iterative consensus literature, a standard problem is for N agents to minimize a function f over a subset of Euclidean space, where the cost function is expressed as a sum fi. In this paper, we study the private distributed optimization problem (PDOP) with the additional requirement that the cost function of the individual agents should remain differentially private. The adversary attempts to infer information about the private cost functions from the messages that the agents exchange. Achieving differential privacy requires that any change of an individual's cost function only results in unsubstantial changes in the statistics of the messages. We propose a class of iterative algorithms for solving PDOP, which achieves differential privacy and convergence to a common value. Our analysis reveals the dependence of the achieved accuracy and the privacy levels on the the parameters of the algorithm. We observe that to achieve -differential privacy the accuracy of the algorithm has the order of O( 1 2 ).

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The iterative consensus problem requires a set of processes or agents with different initial values, to interact and update their states to eventually converge to a common value. Protocols solving iterative consensus serve as building blocks in a variety of systems where distributed coordination is required for load balancing, data aggregation, sensor fusion, filtering, clock synchronization and platooning of autonomous vehicles. In this paper, we introduce the private iterative consensus problem where agents are required to converge while protecting the privacy of their initial values from honest but curious adversaries. Protecting the initial states, in many applications, suffice to protect all subsequent states of the individual participants.First, we adapt the notion of differential privacy in this setting of iterative computation. Next, we present a server-based and a completely distributed randomized mechanism for solving private iterative consensus with adversaries who can observe the messages as well as the internal states of the server and a subset of the clients. Finally, we establish the tradeoff between privacy and the accuracy of the proposed randomized mechanism.

Field-evolved resistance of goosegrass to glyphosate is due to double or single mutation in EPSPS , or amplification of EPSPS leads to increased transcription and protein levels. Glyphosate has been used widely in the south of China. The high selection pressure from glyphosate use has led to the evolution of resistance to glyphosate in weeds. We investigated the molecular mechanisms of three recently discovered glyphosate-resistant Eleusine indica populations (R1, R2 and R3). The results showed that R1 and R2 had double Thr102Ile and Pro106Ser mutation and a single mutation of Pro106Leu in the 5-enolpyruvylshikimate-3-phosphate synthase (EPSPS) gene, respectively. Escherichia coli containing the mutated EPSPS genes was tolerant to glyphosate. EPSPS activity in R1 and R2 plants was higher than in the sensitive plants. There was no amino acid substitution in EPSPS gene in R3. However, expression of EPSPS in R3 plants was higher than in glyphosate-susceptible (S) population (13.8-fold) after glyphosate treatment. EPSPS enzyme activity in both R3 and S plants was inhibited by glyphosate, while shikimate accumulation in R3 was significantly lower than for the S population. Further analysis revealed that the genome of R3 contained 28.3-fold more copies of the EPSPS gene than that of susceptible population. EPSPS expression was positively correlated with copy number of EPSPS. In conclusion, mutation of the EPSPS gene and increased EPSPS expression are part of the molecular mechanisms of resistance to glyphosate in Eleusine indica.

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Goosegrass (Eleusine indica) is one of the most serious annual grassy weeds worldwide, and its evolved herbicide-resistant populations are more difficult to control. Quantitative real-time PCR (qPCR) is a common technique for investigating the resistance mechanism; however, there is as yet no report on the systematic selection of stable reference genes for goosegrass. This study proposed to test the expression stability of 9 candidate reference genes in goosegrass in different tissues and developmental stages and under stress from three types of herbicide. The results show that for different developmental stages and organs (control), eukaryotic initiation factor 4 A (eIF-4) is the most stable reference gene. Chloroplast acetolactate synthase (ALS) is the most stable reference gene under glyphosate stress. Under glufosinate stress, eIF-4 is the best reference gene. Ubiquitin-conjugating enzyme (UCE) is the most stable reference gene under quizalofop-p-ethyl stress. The gene eIF-4 is the recommended reference gene for goosegrass under the stress of all three herbicides. Moreover, pairwise analysis showed that seven reference genes were sufficient to normalize the gene expression data under three herbicides treatment. This study provides a list of reliable reference genes for transcript normalization in goosegrass, which will facilitate resistance mechanism studies in this weed species.

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