Quantum generalized Reed-Solomon codes: Unified framework for quantum MDS codes

We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them analytically. We find that existing quantum MDS codes can be unified under these codes in the sense that when a quantum MDS code exists, then a quantum code of this type with the same parameters also exists. Thus as far as is known at present, they are the most important family of quantum MDS codes.Comment: 9 pages, no figure

Controllability of nonlinear fractional delay dynamical systems with prescribed controls

In this paper, we consider controllability of nonlinear fractional delay dynamical systems with prescribed controls. We firstly give the solution representation of the fractional delay dynamical systems using Laplace transform and Mittag–Leffler functions. Then we give necessary and sufficient conditions for the controllability criteria of linear fractional delay dynamical systems with prescribed controls. Further, we use a fixed point theorem to establish the sufficient condition for the controllability of nonlinear fractional delay dynamical systems with prescribed controls. In particular, we determine several sufficient conditions on the nonlinear function term so that if the linear system is controllable, then the nonlinear system is controllable. Finally, we give two examples to demonstrate the applicability of our obtained results

The magnetic phase diagram of underdoped YBa2Cu3Oy inferred from torque magnetization and thermal conductivity

Strong evidence for charge-density correlation in the underdoped phase of the cuprate YBa2Cu3Oy was obtained by nuclear magnetic resonance (NMR) and resonant x-ray scatter- ing. The fluctuations were found to be enhanced in strong magnetic fields. Recently, 3D (three dimensional) charge-density wave (CDW) formation with long-range order (LRO) was observed by x-ray diffraction in H >15 T. To elucidate how the CDW transition impacts the pair condensate, we have used torque magnetization to 45 T and thermal conductivity $\kappa_{xx}$ to construct the magnetic phase diagram in untwinned crystals with hole density p = 0.11. We show that the 3D CDW transitions appear as sharp features in the susceptibility and $\kappa_{xx}$ at the fields HK and Hp, which define phase boundaries in agreement with spectroscopic techniques. From measurements of the melting field Hm(T) of the vortex solid, we obtain evidence for two vortex solid states below 8 K. At 0.5 K, the pair condensate appears to adjust to the 3D CDW by a sharp transition at 24 T between two vortex solids with very different shear moduli. At even higher H (42 T) the second vortex solid melts to a vortex liquid which survives to fields well above 45 T. de Haas-van Alphen oscillations appear at fields 24-28 T, below the lower bound for the upper critical field Hc2.Comment: 7 pages, 8 figures; New version of previous posting, reporting torque measurements to 45 Tesla and final magnetic phase diagra

Characterizing mixed mode oscillations shaped by noise and bifurcation structure

Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been proposed to generate this type of behavior. Stochastic versions of these models can produce similarly looking time series, often with noise-driven mechanisms different from those of the deterministic models. We present a suite of measures which, when applied to the time series, serves to distinguish models and classify routes to producing MMOs, such as noise-induced oscillations or delay bifurcation. By focusing on the subthreshold oscillations, we analyze the interspike interval density, trends in the amplitude and a coherence measure. We develop these measures on a biophysical model for stellate cells and a phenomenological FitzHugh-Nagumo-type model and apply them on related models. The analysis highlights the influence of model parameters and reset and return mechanisms in the context of a novel approach using noise level to distinguish model types and MMO mechanisms. Ultimately, we indicate how the suite of measures can be applied to experimental time series to reveal the underlying dynamical structure, while exploiting either the intrinsic noise of the system or tunable extrinsic noise.Comment: 22 page

Statistical Origin of Constituent-Quark Scaling in the QGP hadronization

Nonextensive statistics in a Blast-Wave model (TBW) is implemented to describe the identified hadron production in relativistic p+p and nucleus-nucleus collisions. Incorporating the core and corona components within the TBW formalism allows us to describe simultaneously some of the major observations in hadronic observables at the Relativistic Heavy-Ion Collider (RHIC): the Number of Constituent Quark Scaling (NCQ), the large radial and elliptic flow, the effect of gluon saturation and the suppression of hadron production at high transverse momentum (pT) due to jet quenching. In this formalism, the NCQ scaling at RHIC appears as a consequence of non-equilibrium process. Our study also provides concise reference distributions with a least chi2 fit of the available experimental data for future experiments and models.Comment: 4 pages, 3 figures; added two tables, explained a little bit more on TBW_p

Revealing nascent proteomics in signaling pathways and cell differentiation.

Regulation of gene expression at the level of protein synthesis is a crucial element in driving how the genetic landscape is expressed. However, we are still limited in technologies that can quantitatively capture the immediate proteomic changes that allow cells to respond to specific stimuli. Here, we present a method to capture and identify nascent proteomes in situ across different cell types without disturbing normal growth conditions, using O-propargyl-puromycin (OPP). Cell-permeable OPP rapidly labels nascent elongating polypeptides, which are subsequently conjugated to biotin-azide, using click chemistry, and captured with streptavidin beads, followed by digestion and analysis, using liquid chromatography-tandem mass spectrometry. Our technique of OPP-mediated identification (OPP-ID) allows detection of widespread proteomic changes within a short 2-hour pulse of OPP. We illustrate our technique by recapitulating alterations of proteomic networks induced by a potent mammalian target of rapamycin inhibitor, MLN128. In addition, by employing OPP-ID, we identify more than 2,100 proteins and uncover distinct protein networks underlying early erythroid progenitor and differentiation states not amenable to alternative approaches such as amino acid analog labeling. We present OPP-ID as a method to quantitatively identify nascent proteomes across an array of biological contexts while preserving the subtleties directing signaling in the native cellular environment