Resilient Multi-Dimensional Consensus in Adversarial Environment

This paper considers the multi-dimensional consensus in networked systems, where some of the agents might be misbehaving (or faulty). Despite the influence of these misbehaviors, the healthy agents aim to reach an agreement within the convex hull of their initial states. Towards this end, this paper develops a resilient consensus algorithm, where each healthy agent sorts its received values on one dimension, computes two "middle points" based on the sorted values, and moves its state toward these middle points. We further show that the computation of middle points can be efficiently achieved by linear programming. Compared with the existing works, this approach has lower computational complexity. Assuming that the number of malicious agents is upper bounded, sufficient conditions on the network topology are then presented to guarantee the achievement of resilient consensus. Some numerical examples are finally provided to verify the theoretical results.Comment: arXiv admin note: substantial text overlap with arXiv:1911.1083

Linear Model Predictive Control under Continuous Path Constraints via Parallelized Primal-Dual Hybrid Gradient Algorithm

In this paper, we consider a Model Predictive Control(MPC) problem of a continuous time linear time-invariant system under continuous time path constraints on the states and the inputs. By leveraging the concept of differential flatness, we can replace the differential equations governing the system with linear mapping between the states, inputs and the flat outputs (and their derivatives). The flat output is then parameterized by piecewise polynomials and the model predictive control problem can be equivalently transformed into an Semi-Definite Programming (SDP) problem via Sum-of-Squares with guaranteed constraint satisfaction at every continuous time instant. We further observe that the SDP problem contains a large number of small-size semi-definite matrices as optimization variables, and thus a Primal-Dual Hybrid Gradient (PDHF) algorithm, which can be efficiently parallelized, is developed to accelerate the optimization procedure. Simulation on a quadruple-tank process illustrates that our formulation can guarantee strict constraint satisfaction, while the standard MPC controller based on discretized system may violate the constraint in between a sampling period. On the other hand, we should that the our parallelized PDHG algorithm can outperform commercial solvers for problems with long planning horizon

Characterize the assembly of dark matter halos with protohalo size histories: I. Redshift evolution, relation to descendant halos, and halo assembly bias

We propose a novel method to quantify the assembly histories of dark matter halos with the redshift evolution of the mass-weighted spatial variance of their progenitor halos, i.e. the protohalo size history. We find that the protohalo size history for each individual halo at z~0 can be described by a double power-law function. The amplitude of the fitting function strongly correlates to the central-to-total stellar mass ratios of descendant halos. The variation of the amplitude of the protohalo size history can induce a strong halo assembly bias effect for massive halos. This effect is detectable in observation using the central-to-total stellar mass ratio as a proxy of the protohalo size. The correlation to the descendant central-to-total stellar mass ratio and the halo assembly bias effect seen in the protohalo size are much stronger than that seen in the commonly adopted half-mass formation time derived from the mass accretion history. This indicates that the information loss caused by the compression of halo merger trees to mass accretion histories can be captured by the protohalo size history. Protohalo size thus provides a useful quantity to connect protoclusters across cosmic time and to link protoclusters with their descendant clusters in observations.Comment: 19 pages, 12 + 8 figures, comments are welcome

Comparative Analyses by Sequencing of Transcriptomes during Skeletal Muscle Development between Pig Breeds Differing in Muscle Growth Rate and Fatness

Understanding the dynamics of muscle transcriptome during development and between breeds differing in muscle growth is necessary to uncover the complex mechanism underlying muscle development. Herein, we present the first transcriptome-wide longissimus dorsi muscle development research concerning Lantang (LT, obese) and Landrace (LR, lean) pig breeds during 10 time-points from 35 days-post-coitus (dpc) to 180 days-post-natum (dpn) using Solexa/Illumina's Genome Analyzer. The data demonstrated that myogenesis was almost completed before 77 dpc, but the muscle phenotypes were still changed from 77 dpc to 28 dpn. Comparative analysis of the two breeds suggested that myogenesis started earlier but progressed more slowly in LT than in LR, the stages ranging from 49 dpc to 77 dpc are critical for formation of different muscle phenotypes. 595 differentially expressed myogenesis genes were identified, and their roles in myogenesis were discussed. Furthermore, GSK3B, IKBKB, ACVR1, ITGA and STMN1 might contribute to later myogenesis and more muscle fibers in LR than LT. Some myogenesis inhibitors (ID1, ID2, CABIN1, MSTN, SMAD4, CTNNA1, NOTCH2, GPC3 and HMOX1) were higher expressed in LT than in LR, which might contribute to more slow muscle differentiation in LT than in LR. We also identified several genes which might contribute to intramuscular adipose differentiation. Most important, we further proposed a novel model in which MyoD and MEF2A controls the balance between intramuscular adipogenesis and myogenesis by regulating CEBP family; Myf5 and MEF2C are essential during the whole myogenesis process while MEF2D affects muscle growth and maturation. The MRFs and MEF2 families are also critical for the phenotypic differences between the two pig breeds. Overall, this study contributes to elucidating the mechanism underlying muscle development, which could provide valuable information for pig meat quality improvement

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data