Improving Distributed Gradient Descent Using Reed-Solomon Codes

Today's massively-sized datasets have made it necessary to often perform computations on them in a distributed manner. In principle, a computational task is divided into subtasks which are distributed over a cluster operated by a taskmaster. One issue faced in practice is the delay incurred due to the presence of slow machines, known as \emph{stragglers}. Several schemes, including those based on replication, have been proposed in the literature to mitigate the effects of stragglers and more recently, those inspired by coding theory have begun to gain traction. In this work, we consider a distributed gradient descent setting suitable for a wide class of machine learning problems. We adapt the framework of Tandon et al. (arXiv:1612.03301) and present a deterministic scheme that, for a prescribed per-machine computational effort, recovers the gradient from the least number of machines $f$ theoretically permissible, via an $O(f^2)$ decoding algorithm. We also provide a theoretical delay model which can be used to minimize the expected waiting time per computation by optimally choosing the parameters of the scheme. Finally, we supplement our theoretical findings with numerical results that demonstrate the efficacy of the method and its advantages over competing schemes

Extrapancreatic actions of incretin-based therapies on bone in diabetes mellitus

Diabetes mellitus is correlated with modifications in bone microarchitectural and mechanical strength, leading to increased bone fragility. The incretin hormones, with a classical effect to increase insulin secretion following food ingestion, are now postulated to have important direct effects on bone. As such, glucose-dependent insulinotropic polypeptide (GIP) has dual actions on bone cells; enhancing bone�forming activity of osteoblasts and suppressing bone resorption by osteoclasts. The sister incretin of GIP, glucagon-like peptide-1 (GLP-1), is also suspected to directly influence bone health in a beneficial manner, although mechanism are less clear at present. The physiological actions of incretins are attenuated by dipeptidyl peptidase (DPP-4) activity and it is speculated that introduction of DPP-4 inhibitor may also positively affect quality of the skeleton. As such, this thesis evaluates the potential beneficial effects of a DPP-4 resistant GIP analogue, namely [D-Ala2 ]GIP, on osteoblastic-derived, SaOS-2 cells, and also preliminary in vivo studies on the impact of genetic deficiencies of GIPRs and GLP-1Rs on bone mineral density and content. Further studies characterised the beneficial effects of incretin-based therapies on metabolic control, bone microstructure and bone mechanical integrity in animal models of pharmacologically-, genetically- and environmentally-induced diabetes. GIP and related stable analogue increased bone-forming biomarkers in SaOS-2 cells and importantly, [D-Ala2 ]GIP was shown to be more potent than native GIP. Knockout mouse studies revealed that both GIPR and GLP-1R signaling are important for optimum bone mass. All diabetic mouse models displayed reduced bone mass, altered bone micromorphology and impairment of bone mechanical strength, similar to the human situation, confirming their appropriateness. The incretin-based therapeutics, [D-Ala2 ]GIP and Liraglutide, in streptozotocin-diabetic significantly increased bone matrix properties, indicating recovery of bone strength at the tissue level. The beneficial effects of administration of [D-Ala2 ]GIP�oxyntomodulin on bone health in db/db mice were more prominent as the Oxm analogue did not only improve bone strength at tissue level, but also at whole-bone level. These modifications were independent of metabolic status. Twice-daily Exendin-4 therapy improved glycaemic control and increased work required to resist bone fracture in high-fat fed mice. It was also established that Sitagliptin had neutral effects on bone microstructure and mechanical strength in high-fat mice. In summary, these data demonstrate the negative impact of diabetes mellitus on normal skeleton development and bone quality. Moreover, this thesis highlights the growing potential of incretin-based therapies for ameliorating bone defects and improving the increased fragility fracture risk associated with diabete

Extrapancreatic actions of incretin-based therapies on bone in diabetes mellitus

Diabetes mellitus is correlated with modifications in bone microarchitectural and mechanical strength, leading to increased bone fragility. The incretin hormones, with a classical effect to increase insulin secretion following food ingestion, are now postulated to have important direct effects on bone. As such, glucose-dependent insulinotropic polypeptide (GIP) has dual actions on bone cells; enhancing bone�forming activity of osteoblasts and suppressing bone resorption by osteoclasts. The sister incretin of GIP, glucagon-like peptide-1 (GLP-1), is also suspected to directly influence bone health in a beneficial manner, although mechanism are less clear at present. The physiological actions of incretins are attenuated by dipeptidyl peptidase (DPP-4) activity and it is speculated that introduction of DPP-4 inhibitor may also positively affect quality of the skeleton. As such, this thesis evaluates the potential beneficial effects of a DPP-4 resistant GIP analogue, namely [D-Ala2 ]GIP, on osteoblastic-derived, SaOS-2 cells, and also preliminary in vivo studies on the impact of genetic deficiencies of GIPRs and GLP-1Rs on bone mineral density and content. Further studies characterised the beneficial effects of incretin-based therapies on metabolic control, bone microstructure and bone mechanical integrity in animal models of pharmacologically-, genetically- and environmentally-induced diabetes. GIP and related stable analogue increased bone-forming biomarkers in SaOS-2 cells and importantly, [D-Ala2 ]GIP was shown to be more potent than native GIP. Knockout mouse studies revealed that both GIPR and GLP-1R signaling are important for optimum bone mass. All diabetic mouse models displayed reduced bone mass, altered bone micromorphology and impairment of bone mechanical strength, similar to the human situation, confirming their appropriateness. The incretin-based therapeutics, [D-Ala2 ]GIP and Liraglutide, in streptozotocin-diabetic significantly increased bone matrix properties, indicating recovery of bone strength at the tissue level. The beneficial effects of administration of [D-Ala2 ]GIP�oxyntomodulin on bone health in db/db mice were more prominent as the Oxm analogue did not only improve bone strength at tissue level, but also at whole-bone level. These modifications were independent of metabolic status. Twice-daily Exendin-4 therapy improved glycaemic control and increased work required to resist bone fracture in high-fat fed mice. It was also established that Sitagliptin had neutral effects on bone microstructure and mechanical strength in high-fat mice. In summary, these data demonstrate the negative impact of diabetes mellitus on normal skeleton development and bone quality. Moreover, this thesis highlights the growing potential of incretin-based therapies for ameliorating bone defects and improving the increased fragility fracture risk associated with diabete

Carotenoid biosynthesis and overproduction in Corynebacterium glutamicum

Heider S, Peters-Wendisch P, Wendisch VF. Carotenoid biosynthesis and overproduction in Corynebacterium glutamicum. BMC Microbiology. 2012;12(1): 198.Background Corynebacterium glutamicum contains the glycosylated C50 carotenoid decaprenoxanthin as yellow pigment. Starting from isopentenyl pyrophosphate, which is generated in the non-mevalonate pathway, decaprenoxanthin is synthesized via the intermediates farnesyl pyrophosphate, geranylgeranyl pyrophosphate, lycopene and flavuxanthin. Results Here, we showed that the genes of the carotenoid gene cluster crtE-cg0722-crtBIYeYfEb are co-transcribed and characterized defined gene deletion mutants. Gene deletion analysis revealed that crtI, crtEb, and crtYeYf, respectively, code for the only phytoene desaturase, lycopene elongase, and carotenoid C45/C50 epsilon-cyclase, respectively. However, the genome of C. glutamicum also encodes a second carotenoid gene cluster comprising crtB2I2-1/2 shown to be co-transcribed, as well. Ectopic expression of crtB2 could compensate for the lack of phytoene synthase CrtB in C. glutamicum DeltacrtB, thus, C. glutamicum possesses two functional phytoene synthases, namely CrtB and CrtB2. Genetic evidence for a crtI2-1/2 encoded phytoene desaturase could not be obtained since plasmid-borne expression of crtI2-1/2 did not compensate for the lack of phytoene desaturase CrtI in C. glutamicum DeltacrtI. The potential of C. glutamicum to overproduce carotenoids was estimated with lycopene as example. Deletion of the gene crtEb prevented conversion of lycopene to decaprenoxanthin and entailed accumulation of lycopene to 0.03 +/- 0.01 mg/g cell dry weight (CDW). When the genes crtE, crtB and crtI for conversion of geranylgeranyl pyrophosphate to lycopene were overexpressed in C. glutamicum DeltacrtEb intensely red-pigmented cells and an 80 fold increased lycopene content of 2.4 +/- 0.3 mg/g CDW were obtained. Conclusion C. glutamicum possesses a certain degree of redundancy in the biosynthesis of the C50 carotenoid decaprenoxanthin as it possesses two functional phytoene synthase genes. Already metabolic engineering of only the terminal reactions leading to lycopene resulted in considerable lycopene production indicating that C. glutamicum may serve as a potential host for carotenoid production

Fast Algebraic Attacks and Decomposition of Symmetric Boolean Functions

Algebraic and fast algebraic attacks are power tools to analyze stream ciphers. A class of symmetric Boolean functions with maximum algebraic immunity were found vulnerable to fast algebraic attacks at EUROCRYPT'06. Recently, the notion of AAR (algebraic attack resistant) functions was introduced as a unified measure of protection against both classical algebraic and fast algebraic attacks. In this correspondence, we first give a decomposition of symmetric Boolean functions, then we show that almost all symmetric Boolean functions, including these functions with good algebraic immunity, behave badly against fast algebraic attacks, and we also prove that no symmetric Boolean functions are AAR functions. Besides, we improve the relations between algebraic degree and algebraic immunity of symmetric Boolean functions.Comment: 13 pages, submitted to IEEE Transactions on Information Theor

A real-space grid implementation of the Projector Augmented Wave method

A grid-based real-space implementation of the Projector Augmented Wave (PAW) method of P. E. Blochl [Phys. Rev. B 50, 17953 (1994)] for Density Functional Theory (DFT) calculations is presented. The use of uniform 3D real-space grids for representing wave functions, densities and potentials allows for flexible boundary conditions, efficient multigrid algorithms for solving Poisson and Kohn-Sham equations, and efficient parallelization using simple real-space domain-decomposition. We use the PAW method to perform all-electron calculations in the frozen core approximation, with smooth valence wave functions that can be represented on relatively coarse grids. We demonstrate the accuracy of the method by calculating the atomization energies of twenty small molecules, and the bulk modulus and lattice constants of bulk aluminum. We show that the approach in terms of computational efficiency is comparable to standard plane-wave methods, but the memory requirements are higher.Comment: 13 pages, 3 figures, accepted for publication in Physical Review