Resilience options for provisioning anycast cloud services with virtual optical networks

Optical networks are crucial to support increasingly demanding cloud services. Delivering the requested quality of services (in particular latency) is key to successfully provisioning end-to-end services in clouds. Therefore, as for traditional optical network services, it is of utter importance to guarantee that clouds are resilient to any failure of either network infrastructure (links and/or nodes) or data centers. A crucial concept in establishing cloud services is that of network virtualization: the physical infrastructure is logically partitioned in separate virtual networks. To guarantee end-to-end resilience for cloud services in such a set-up, we need to simultaneously route the services and map the virtual network, in such a way that an alternate routing in case of physical resource failures is always available. Note that combined control of the network and data center resources is exploited, and the anycast routing concept applies: we can choose the data center to provide server resources requested by the customer to optimize resource usage and/or resiliency. This paper investigates the design of scalable optimization models to perform the virtual network mapping resiliently. We compare various resilience options, and analyze their compromise between bandwidth requirements and resiliency quality

Gaps between zeros of the Riemann zeta-function

We prove that there exist infinitely many consecutive zeros of the Riemann zeta-function on the critical line whose gaps are greater than $3.18$ times the average spacing. Using a modification of our method, we also show that there are even larger gaps between the multiple zeros of the zeta function on the critical line (if such zeros exist)

Central values of derivatives of Dirichlet L-functions

Let C(q,+) be the set of even, primitive Dirichlet characters (mod q). Using the mollifier method we show that L^{(k)}(1/2,chi) is not equal to zero for almost all the characters chi in C(q,+) when k and q are large. Here, L^{(k)}(s,chi) is the k-th derivative of of the Dirichlet L-function L(s,chi).Comment: submitted for publicatio

A note on the gaps between consecutive zeros of the Riemann zeta-function

Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and infinitely often they differ by at least 2.69 times the average spacing.Comment: 7 pages. Submitted for publicatio

On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t) in the theory of the Riemann zeta-function.Comment: 11 page

A shared cis-regulatory module activates transcription in the suspensor of plant embryos.

The mechanisms controlling the transcription of gene sets in specific regions of a plant embryo shortly after fertilization remain unknown. Previously, we showed that G564 mRNA, encoding a protein of unknown function, accumulates to high levels in the giant suspensor of both Scarlet Runner Bean (SRB) and Common Bean embryos, and a cis-regulatory module containing three unique DNA sequences, designated as the 10-bp, Region 2, and Fifth motifs, is required for G564 suspensor-specific transcription [Henry KF, et al. (2015) Plant Mol Biol 88:207-217; Kawashima T, et al. (2009) Proc Natl Acad Sci USA 106:3627-3632]. We tested the hypothesis that these motifs are also required for transcription of the SRB GA 20-oxidase gene, which encodes a gibberellic acid hormone biosynthesis enzyme and is coexpressed with G564 at a high level in giant bean suspensors. We used deletion and gain-of-function experiments in transgenic tobacco embryos to show that two GA 20-oxidase DNA regions are required for suspensor-specific transcription, one in the 5' UTR (+119 to +205) and another in the 5' upstream region (-341 to -316). Mutagenesis of sequences in these two regions determined that the cis-regulatory motifs required for G564 suspensor transcription are also required for GA 20-oxidase transcription within the suspensor, although the motif arrangement differs. Our results demonstrate the flexibility of motif positioning within a cis-regulatory module that activates gene transcription within giant bean suspensors and suggest that G564 and GA 20-oxidase comprise part of a suspensor gene regulatory network

Model Counting for Formulas of Bounded Clique-Width

We show that #SAT is polynomial-time tractable for classes of CNF formulas whose incidence graphs have bounded symmetric clique-width (or bounded clique-width, or bounded rank-width). This result strictly generalizes polynomial-time tractability results for classes of formulas with signed incidence graphs of bounded clique-width and classes of formulas with incidence graphs of bounded modular treewidth, which were the most general results of this kind known so far.Comment: Extended version of a paper published at ISAAC 201