Optimization of Network Robustness to Waves of Targeted and Random Attack

We study the robustness of complex networks to multiple waves of simultaneous (i) targeted attacks in which the highest degree nodes are removed and (ii) random attacks (or failures) in which fractions $p_t$ and $p_r$ respectively of the nodes are removed until the network collapses. We find that the network design which optimizes network robustness has a bimodal degree distribution, with a fraction $r$ of the nodes having degree k_2= (\kav - 1 +r)/r and the remainder of the nodes having degree $k_1=1$, where \kav is the average degree of all the nodes. We find that the optimal value of $r$ is of the order of $p_t/p_r$ for $p_t/p_r\ll 1$

Optimization of Robustness of Complex Networks

Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random failure and intentional attack while keeping the cost of the network (which we take to be the average number of links per node) constant. We find optimal parameters for: (i) scale free networks having degree distributions with a single power-law regime, (ii) networks having degree distributions with two power-law regimes, and (iii) networks described by degree distributions containing two peaks. Of these various kinds of distributions we find that the optimal network design is one in which all but one of the nodes have the same degree, $k_1$ (close to the average number of links per node), and one node is of very large degree, $k_2 \sim N^{2/3}$, where $N$ is the number of nodes in the network.Comment: Accepted for publication in European Physical Journal

Elastic properties of the Non-Fermi liquid metal CeRu4Sb12Ce Ru_4 Sb_{12} and the Dense Kondo semiconductor CeOs4Sb12Ce Os_4 Sb_{12}

We have investigated the elastic properties of the Ce-based filled skutterudite antimonides CeRu$_{4}$Sb$_{12}$ and CeOs$_{4}$Sb$_{12}$ by means of ultrasonic measurements. CeRu$_{4}$Sb$_{12}$ shows a slight increase around 130 K in the temperature dependence of the elastic constants $C$$_{11}$, ($C$$_{11}$-$C$$_{12}$)/2 and $C$$_{44}$. No apparent softening toward low temperature due to a quadrupolar response of the 4$f$-electronic ground state of the Ce ion was observed at low temperatures. In contrast CeOs$_{4}$Sb$_{12}$ shows a pronounced elastic softening toward low temperature in the longitudinal $C$$_{11}$ as a function of temperature ($T$) below about 15 K, while a slight elastic softening was observed in the transverse $C$$_{44}$ below about 1.5 K. Furthermore, CeOs$_{4}$Sb$_{12}$ shows a steep decrease around a phase transition temperature of 0.9 K in both $C$$_{11}$ and$C$$_{44}$. The elastic softening observed in $C$$_{11}$ below about 15 K cannot be explained reasonably only by the crystalline electric field effect. It is most likely to be responsible for the coupling between the elastic strain and the quasiparticle band with a small energy gap in the vicinity of Fermi level. The elastic properties and the 4$f$ ground state of Ce ions in CeRu$_{4}$Sb$_{12}$ and CeOs$_{4}$Sb$_{12}$ are discussed from the viewpoint of the crystalline electric field effect and the band structure in the vicinity of Fermi level.Comment: 9 pages, 11 figures, regular pape

Transmission Properties of the oscillating delta-function potential

We derive an exact expression for the transmission amplitude of a particle moving through a harmonically driven delta-function potential by using the method of continued-fractions within the framework of Floquet theory. We prove that the transmission through this potential as a function of the incident energy presents at most two real zeros, that its poles occur at energies $n\hbar\omega+\varepsilon^*$ ($0<Re(\varepsilon^*)<\hbar\omega$), and that the poles and zeros in the transmission amplitude come in pairs with the distance between the zeros and the poles (and their residue) decreasing with increasing energy of the incident particle. We also show the existence of non-resonant "bands" in the transmission amplitude as a function of the strength of the potential and the driving frequency.Comment: 21 pages, 12 figures, 1 tabl

Scaling of the buckling transition of ridges in thin sheets

When a thin elastic sheet crumples, the elastic energy condenses into a network of folding lines and point vertices. These folds and vertices have elastic energy densities much greater than the surrounding areas, and most of the work required to crumple the sheet is consumed in breaking the folding lines or ``ridges''. To understand crumpling it is then necessary to understand the strength of ridges. In this work, we consider the buckling of a single ridge under the action of inward forcing applied at its ends. We demonstrate a simple scaling relation for the response of the ridge to the force prior to buckling. We also show that the buckling instability depends only on the ratio of strain along the ridge to curvature across it. Numerically, we find for a wide range of boundary conditions that ridges buckle when our forcing has increased their elastic energy by 20% over their resting state value. We also observe a correlation between neighbor interactions and the location of initial buckling. Analytic arguments and numerical simulations are employed to prove these results. Implications for the strength of ridges as structural elements are discussed.Comment: 42 pages, latex, doctoral dissertation, to be submitted to Phys Rev

Annotation of two large contiguous regions from the Haemonchus contortus genome using RNA-seq and comparative analysis with Caenorhabditis elegans

The genomes of numerous parasitic nematodes are currently being sequenced, but their complexity and size, together with high levels of intra-specific sequence variation and a lack of reference genomes, makes their assembly and annotation a challenging task. Haemonchus contortus is an economically significant parasite of livestock that is widely used for basic research as well as for vaccine development and drug discovery. It is one of many medically and economically important parasites within the strongylid nematode group. This group of parasites has the closest phylogenetic relationship with the model organism Caenorhabditis elegans, making comparative analysis a potentially powerful tool for genome annotation and functional studies. To investigate this hypothesis, we sequenced two contiguous fragments from the H. contortus genome and undertook detailed annotation and comparative analysis with C. elegans. The adult H. contortus transcriptome was sequenced using an Illumina platform and RNA-seq was used to annotate a 409 kb overlapping BAC tiling path relating to the X chromosome and a 181 kb BAC insert relating to chromosome I. In total, 40 genes and 12 putative transposable elements were identified. 97.5% of the annotated genes had detectable homologues in C. elegans of which 60% had putative orthologues, significantly higher than previous analyses based on EST analysis. Gene density appears to be less in H. contortus than in C. elegans, with annotated H. contortus genes being an average of two-to-three times larger than their putative C. elegans orthologues due to a greater intron number and size. Synteny appears high but gene order is generally poorly conserved, although areas of conserved microsynteny are apparent. C. elegans operons appear to be partially conserved in H. contortus. Our findings suggest that a combination of RNA-seq and comparative analysis with C. elegans is a powerful approach for the annotation and analysis of strongylid nematode genomes

Identification of the sex-determining factor in the liverwort Marchantia polymorpha reveals unique evolution of sex chromosomes in a haploid system

半数体生物の性染色体上の性決定遺伝子を解明 --コケがもつ現生生物最古の起源の性染色体--. 京都大学プレスリリース. 2021-11-08.Sex determination is a central process for sexual reproduction and is often regulated by a sex determinant encoded on a sex chromosome. Rules that govern the evolution of sex chromosomes via specialization and degeneration following the evolution of a sex determinant have been well studied in diploid organisms. However, distinct predictions apply to sex chromosomes in organisms where sex is determined in the haploid phase of the life cycle: both sex chromosomes, female U and male V, are expected to maintain their gene functions, even though both are non-recombining. This is in contrast to the X-Y (or Z-W) asymmetry and Y (W) chromosome degeneration in XY (ZW) systems of diploids. Here, we provide evidence that sex chromosomes diverged early during the evolution of haploid liverworts and identify the sex determinant on the Marchantia polymorpha U chromosome. This gene, Feminizer, encodes a member of the plant-specific BASIC PENTACYSTEINE transcription factor family. It triggers female differentiation via regulation of the autosomal sex-determining locus of FEMALE GAMETOPHYTE MYB and SUPPRESSOR OF FEMINIZATION. Phylogenetic analyses of Feminizer and other sex chromosome genes indicate dimorphic sex chromosomes had already been established 430 mya in the ancestral liverwort. Feminizer also plays a role in reproductive induction that is shared with its gametolog on the V chromosome, suggesting an ancestral function, distinct from sex determination, was retained by the gametologs. This implies ancestral functions can be preserved after the acquisition of a sex determination mechanism during the evolution of a dominant haploid sex chromosome system

HMGB2 orchestrates the chromatin landscape of senescence-associated secretory phenotype gene loci

Cellular senescence is a stable cell growth arrest that is characterized by the silencing of proliferation-promoting genes through compaction of chromosomes into senescence-associated heterochromatin foci (SAHF). Paradoxically, senescence is also accompanied by increased transcription of certain genes encoding for secreted factors such as cytokines and chemokines, known as the senescence-associated secretory phenotype (SASP). How SASP genes are excluded from SAHF-mediated global gene silencing remains unclear. In this study, we report that high mobility group box 2 (HMGB2) orchestrates the chromatin landscape of SASP gene loci. HMGB2 preferentially localizes to SASP gene loci during senescence. Loss of HMGB2 during senescence blunts SASP gene expression by allowing for spreading of repressive heterochromatin into SASP gene loci. This correlates with incorporation of SASP gene loci into SAHF. Our results establish HMGB2 as a novel master regulator that orchestrates SASP through prevention of heterochromatin spreading to allow for exclusion of SASP gene loci from a global heterochromatin environment during senescence