Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)

Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie algebra $\mathfrak{g}_{\bar{0}}$. In an earlier paper the authors demonstrated that for any module $M$ in $\mathcal{F}$ the rate of growth of the minimal projective resolution (i.e., the complexity of $M$) is bounded by the dimension of $\mathfrak{g}_{\bar{1}}$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module.Comment: 32 page

Number theoretic example of scale-free topology inducing self-organized criticality

In this work we present a general mechanism by which simple dynamics running on networks become self-organized critical for scale free topologies. We illustrate this mechanism with a simple arithmetic model of division between integers, the division model. This is the simplest self-organized critical model advanced so far, and in this sense it may help to elucidate the mechanism of self-organization to criticality. Its simplicity allows analytical tractability, characterizing several scaling relations. Furthermore, its mathematical nature brings about interesting connections between statistical physics and number theoretical concepts. We show how this model can be understood as a self-organized stochastic process embedded on a network, where the onset of criticality is induced by the topology.Comment: 4 pages, 3 figures. Physical Review Letters, in pres

Local distinguishability of quantum states in infinite dimensional systems

We investigate local distinguishability of quantum states by use of the convex analysis about joint numerical range of operators on a Hilbert space. We show that any two orthogonal pure states are distinguishable by local operations and classical communications, even for infinite dimensional systems. An estimate of the local discrimination probability is also given for some family of more than two pure states

Capturing Nucleation at 4D Atomic Resolution

Nucleation plays a critical role in many physical and biological phenomena ranging from crystallization, melting and evaporation to the formation of clouds and the initiation of neurodegenerative diseases. However, nucleation is a challenging process to study in experiments especially in the early stage when several atoms/molecules start to form a new phase from its parent phase. Here, we advance atomic electron tomography to study early stage nucleation at 4D atomic resolution. Using FePt nanoparticles as a model system, we reveal that early stage nuclei are irregularly shaped, each has a core of one to few atoms with the maximum order parameter, and the order parameter gradient points from the core to the boundary of the nucleus. We capture the structure and dynamics of the same nuclei undergoing growth, fluctuation, dissolution, merging and/or division, which are regulated by the order parameter distribution and its gradient. These experimental observations differ from classical nucleation theory (CNT) and to explain them we propose the order parameter gradient (OPG) model. We show the OPG model generalizes CNT and energetically favours diffuse interfaces for small nuclei and sharp interfaces for large nuclei. We further corroborate this model using molecular dynamics simulations of heterogeneous and homogeneous nucleation in liquid-solid phase transitions of Pt. We anticipate that the OPG model is applicable to different nucleation processes and our experimental method opens the door to study the structure and dynamics of materials with 4D atomic resolution.Comment: 42 pages, 5 figures, 12 supplementary figures and one supplementary tabl

Pauli Diagonal Channels Constant on Axes

We define and study the properties of channels which are analogous to unital qubit channels in several ways. A full treatment can be given only when the dimension d is a prime power, in which case each of the (d+1) mutually unbiased bases (MUB) defines an axis. Along each axis the channel looks like a depolarizing channel, but the degree of depolarization depends on the axis. When d is not a prime power, some of our results still hold, particularly in the case of channels with one symmetry axis. We describe the convex structure of this class of channels and the subclass of entanglement breaking channels. We find new bound entangled states for d = 3. For these channels, we show that the multiplicativity conjecture for maximal output p-norm holds for p=2. We also find channels with behavior not exhibited by unital qubit channels, including two pairs of orthogonal bases with equal output entropy in the absence of symmetry. This provides new numerical evidence for the additivity of minimal output entropy

Apical localization of inositol 1,4,5-trisphosphate receptors is independent of extended synaptotagmins in hepatocytes.

Extended synaptotagmins (E-Syts) are a recently identified family of proteins that tether the endoplasmic reticulum (ER) to the plasma membrane (PM) in part by conferring regulation of cytosolic calcium (Ca2+) at these contact sites (Cell, 2013). However, the mechanism by which E-Syts link this tethering to Ca2+ signaling is unknown. Ca2+ waves in polarized epithelia are initiated by inositol 1,4,5-trisphosphate receptors (InsP3Rs), and these waves begin in the apical region because InsP3Rs are targeted to the ER adjacent to the apical membrane. In this study we investigated whether E-Syts are responsible for this targeting. Primary rat hepatocytes were used as a model system, because a single InsP3R isoform (InsP3R-II) is tethered to the peri-apical ER in these cells. Additionally, it has been established in hepatocytes that the apical localization of InsP3Rs is responsible for Ca2+ waves and secretion and is disrupted in disease states in which secretion is impaired. We found that rat hepatocytes express two of the three identified E-Syts (E-Syt1 and E-Syt2). Individual or simultaneous siRNA knockdown of these proteins did not alter InsP3R-II expression levels, apical localization or average InsP3R-II cluster size. Moreover, apical secretion of the organic anion 5-chloromethylfluorescein diacetate (CMFDA) was not changed in cells lacking E-Syts but was reduced in cells in which cytosolic Ca2+ was buffered. These data provide evidence that E-Syts do not participate in the targeting of InsP3Rs to the apical region. Identifying tethers that bring InsP3Rs to the apical region remains an important question, since mis-targeting of InsP3Rs leads to impaired secretory activity

From Emergence to Eradication: The Epidemiology of Poliomyelitis Deconstructed

Poliomyelitis has appeared in epidemic form, become endemic on a global scale, and been reduced to near-elimination, all within the span of documented medical history. Epidemics of the disease appeared in the late 19th century in many European countries and North America, following which polio became a global disease with annual epidemics. During the period of its epidemicity, 1900–1950, the age distribution of poliomyelitis cases increased gradually. Beginning in 1955, the creation of poliovirus vaccines led to a stepwise reduction in poliomyelitis, culminating in the unpredicted elimination of wild polioviruses in the United States by 1972. Global expansion of polio immunization resulted in a reduction of paralytic disease from an estimated annual prevaccine level of at least 600,000 cases to fewer than 1,000 cases in 2000. Indigenous wild type 2 poliovirus was eradicated in 1999, but unbroken localized circulation of poliovirus types 1 and 3 continues in 4 countries in Asia and Africa. Current challenges to the final eradication of paralytic poliomyelitis include the continued transmission of wild polioviruses in endemic reservoirs, reinfection of polio-free areas, outbreaks due to circulating vaccine-derived polioviruses, and persistent excretion of vaccine-derived poliovirus by a few vaccinees with B-cell immunodeficiencies. Beyond the current efforts to eradicate the last remaining wild polioviruses, global eradication efforts must safely navigate through an unprecedented series of endgame challenges to assure the permanent cessation of all human poliovirus infections

Retinoblastoma treatment: impact of the glycolytic inhibitor 2-deoxy-d-glucose on molecular genomics expression in LHBETATAG retinal tumors

Purpose: The purpose of this study was to evaluate the effect of 2-deoxy-D-glucose (2-DG) on the spatial distribution of the genetic expression of key elements involved in angiogenesis, hypoxia, cellular metabolism, and apoptosis in LHBETATAG retinal tumors. Methods: The right eye of each LHBETATAG transgenic mouse (n = 24) was treated with either two or six subconjunctival injections of 2-DG (500 mg/kg) or saline control at 16 weeks of age. A gene expression array analysis was performed on five different intratumoral regions (apex, center, base, anterior-lateral, and posterior-lateral) using Affymetrix GeneChip Mouse Gene 1.0 ST arrays. To test for treatment effects of each probe within each region, a two-way analysis of variance was used. Results: Significant differences between treatment groups (ie, 0, 2, and 6 injections) were found as well as differences among the five retinal tumor regions evaluated (P \u3c 0.01). More than 100 genes were observed to be dysregulated by ≥2-fold difference in expression between the three treatment groups, and their dysregulation varied across the five regions assayed. Several genes involved in pathways important for tumor cell growth (ie, angiogenesis, hypoxia, cellular metabolism, and apoptosis) were identified. Conclusions: 2-DG was found to significantly alter the gene expression in LHBETATAG retinal tumor cells according to their location within the tumor as well as the treatment schedule. 2-DG’s effects on genetic expression found here correlate with previous reported results on varied processes involved in its in vitro and in vivo activity in inhibiting tumor cell growth

Extending additivity from symmetric to asymmetric channels

We prove a lemma which allows one to extend results about the additivity of the minimal output entropy from highly symmetric channels to a much larger class. A similar result holds for the maximal output $p$-norm. Examples are given showing its use in a variety of situations. In particular, we prove the additivity and the multiplicativity for the shifted depolarising channel.Comment: 8 pages. This is the latest version of the first half of the original paper. The other half will appear in another pape