Vertex operator algebras and operads

Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal to $0$, not just binary products. In this paper, a reformulation of the notion of vertex operator algebra in terms of operads is presented. This reformulation shows that the rich geometric structure revealed in the study of conformal field theory and the rich algebraic structure of the theory of vertex operator algebras share a precise common foundation in basic operations associated with a certain kind of (two-dimensional) ``complex'' geometric object, in the sense in which classical algebraic structures (groups, algebras, Lie algebras and the like) are always implicitly based on (one-dimensional) ``real'' geometric objects. In effect, the standard analogy between point-particle theory and string theory is being shown to manifest itself at a more fundamental mathematical level.Comment: 16 pages. Only the definitions of "partial operad" and of "rescaling group" have been improve

The role of stoichiometric vacancy periodicity in pressure-induced amorphization of the Ga2SeTe2 semiconductor alloy

We observe that pressure-induced amorphization of Ga2SeTe2 (a III-VI semiconductor) is directly influenced by the periodicity of its intrinsic defect structures. Specimens with periodic and semi-periodic two-dimensional vacancy structures become amorphous around 10-11 GPa in contrast to those with aperiodic structures, which amorphize around 7-8 GPa. The result is a notable instance of altering material phase-change properties via rearrangement of stoichiometric vacancies as opposed to adjusting their concentrations. Based on our experimental findings, we posit that periodic two-dimensional vacancy structures in Ga2SeTe2 provide an energetically preferred crystal lattice that is less prone to collapse under applied pressure. This is corroborated through first-principles electronic structure calculations, which demonstrate that the energy stability of III-VI structures under hydrostatic pressure is highly dependent on the configuration of intrinsic vacancies

Analysis of chain of events in major historic power outages

Contemporary power systems are facing increasing intricate conditions that have never been considered when initially designing the infrastructure, such as malicious threats, accommodating smart grids, etc. As a consequence, blackouts albeit seldom but stubbornly keep appearing from time to time the world around, and demonstrate their devastating capability to create vast damage on both power systems and the society at large. Patterns of the blackout starting from the first triggering events to the system final status have emerged. A framework of a coding system was proposed in this paper in order to capture the common feature in the system evolution during the development of cascades. Cascades in a blackout can be tracked by a chain of events with the help of the codes. It is facile to adopt the framework to build up a knowledge base of blackouts. By applying the proposed framework to 31 selected historic blackouts, most frequent events, effects and origins are identified; the findings can provide useful information for grid designers and security experts for ranking the most imminent issues in their study. © 2014 AECE

General entanglement

The paper contains a brief review of an approach to quantum entanglement based on analysis of dynamic symmetry of systems and quantum uncertainties, accompanying the measurement of mean value of certain basic observables. The latter are defined in terms of the orthogonal basis of Lie algebra, corresponding to the dynamic symmetry group. We discuss the relativity of entanglement with respect to the choice of basic observables and a way of stabilization of robust entanglement in physical systems.Comment: 7 pages, 1 figure,1 tabe, will be published in special issue of Journal of Physics (Conference Series) with Proceedings of CEWQO-200

Bounded Verification with On-the-Fly Discrepancy Computation

Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing reachtubes from simulations. In this paper, we eliminate this requirement by presenting an algorithm for computing piece-wise exponential discrepancy functions. The algorithm relies on computing local convergence or divergence rates of trajectories along a simulation using a coarse over-approximation of the reach set and bounding the maximal eigenvalue of the Jacobian over this over-approximation. The resulting discrepancy function preserves the soundness and the relative completeness of the verification algorithm. We also provide a coordinate transformation method to improve the local estimates for the convergence or divergence rates in practical examples. We extend the method to get the input-to-state discrepancy of nonlinear dynamical systems which can be used for compositional analysis. Our experiments show that the approach is effective in terms of running time for several benchmark problems, scales reasonably to larger dimensional systems, and compares favorably with respect to available tools for nonlinear models.Comment: 24 page

Palbociclib plus letrozole as first-line therapy in estrogen receptor-positive/human epidermal growth factor receptor 2-negative advanced breast cancer with extended follow-up.

PurposeIn the initial PALOMA-2 (NCT01740427) analysis with median follow-up of 23 months, palbociclib plus letrozole significantly prolonged progression-free survival (PFS) in women with estrogen receptor-positive (ER+)/human epidermal growth factor receptor 2-negative (HER2-) advanced breast cancer (ABC) [hazard ratio (HR) 0.58; P < 0.001]. Herein, we report results overall and by subgroups with extended follow-up.MethodsIn this double-blind, phase 3 study, post-menopausal women with ER+/HER2- ABC who had not received prior systemic therapy for their advanced disease were randomized 2:1 to palbociclib-letrozole or placebo-letrozole. Endpoints include investigator-assessed PFS (primary), safety, and patient-reported outcomes (PROs).ResultsAfter a median follow-up of approximately 38 months, median PFS was 27.6 months for palbociclib-letrozole (n = 444) and 14.5 months for placebo-letrozole (n = 222) (HR 0.563; 1-sided P < 0.0001). All subgroups benefited from palbociclib treatment. The improvement of PFS with palbociclib-letrozole was maintained in the next 2 subsequent lines of therapy and delayed the use of chemotherapy (40.4 vs. 29.9 months for palbociclib-letrozole vs. placebo-letrozole). Safety data were consistent with the known profile. Patients' quality of life was maintained.ConclusionsWith approximately 15 months of additional follow-up, palbociclib plus letrozole continued to demonstrate improved PFS compared with placebo plus letrozole in the overall population and across all patient subgroups, while the safety profile remained favorable and quality of life was maintained. These data confirm that palbociclib-letrozole should be considered the standard of care for first-line therapy in patients with ER+/HER2- ABC, including those with low disease burden or long disease-free interval. Sponsored by Pfizer; ClinicalTrials.gov: NCT01740427

The impact of the particle size of meat and bone meal (MBM) incineration ash on phosphate precipitation and phosphorus recovery

Meat and bone meal (MBM) ash was characterized and used for phosphate wastewater treatment and phosphorus recovery. The bottom ash (MBM-BA) with size >250 μm accounted for ~80% and distributed evenly in the >1000 μm, 500-1000 μm, and 250-500 μm fractions, while air pollution control residue (MBM-APCr) distributed evenly among the 250-500 μm, 125-250 μm, and 1000 μm and 8 was favorable to P removal. Based on the compositions of the solid phases, extracts before and after treatment, and Ca/P ratio 1.22-1.73, the phosphate removal mechanisms were dominated by HAP crystallization/precipitation. Using MBM-BA for wastewater treatment increased its P content to 16.30%. Depending on particle size, the acid consumption for P recovery of 84% from MBM-BA was 2.6-3.0 mM H+/mM P. Strategies for management and utilization of MBMA according to these findings were proposed

High-density information storage in an absolutely defined aperiodic sequence of monodisperse copolyester

Synthesis of a polymer composed of a large discrete number of chemically distinct monomers in an absolutely defined aperiodic sequence remains a challenge in polymer chemistry. The synthesis has largely been limited to oligomers having a limited number of repeating units due to the difficulties associated with the step-by-step addition of individual monomers to achieve high molecular weights. Here we report the copolymers of ??-hydroxy acids, poly(phenyllactic-co-lactic acid) (PcL) built via the cross-convergent method from four dyads of monomers as constituent units. Our proposed method allows scalable synthesis of sequence-defined PcL in a minimal number of coupling steps from reagents in stoichiometric amounts. Digital information can be stored in an aperiodic sequence of PcL, which can be fully retrieved as binary code by mass spectrometry sequencing. The information storage density (bit/Da) of PcL is 50% higher than DNA, and the storage capacity of PcL can also be increased by adjusting the molecular weight (~38???kDa)

Evaluation of mTOR-regulated mRNA translation.

mTOR, the mammalian target of rapamycin, regulates protein synthesis (mRNA translation) by affecting the phosphorylation or activity of several translation factors. Here, we describe methods for studying the impact of mTOR signalling on protein synthesis, using inhibitors of mTOR such as rapamycin (which impairs some of its functions) or mTOR kinase inhibitors (which probably block all functions).To assess effects of mTOR inhibition on general protein synthesis in cells, the incorporation of radiolabelled amino acids into protein is measured. This does not yield information on the effects of mTOR on the synthesis of specific proteins. To do this, two methods are described. In one, stable-isotope labelled amino acids are used, and their incorporation into new proteins is determined using mass spectrometric methods. The proportions of labelled vs. unlabeled versions of each peptide from a given protein provide quantitative information about the rate of that protein's synthesis under different conditions. Actively translated mRNAs are associated with ribosomes in polyribosomes (polysomes); thus, examining which mRNAs are found in polysomes under different conditions provides information on the translation of specific mRNAs under different conditions. A method for the separation of polysomes from non-polysomal mRNAs is describe