A natural extension for the greedy β-transformation with three arbitrary digits

We construct a planar version of the natural extension of the piecewise linear transformation T generating greedy β-expansions with digits in an arbitrary set of real numbers A = {a ₀, a ₁, a ₂}. As a result, we derive in an easy way a closed formula for the density of the unique T-invariant measure µ absolutely continuous with respect to Lebesgue measure. Furthermore, we show that T is exact and weak Bernoulli with respect to µ.     

Equipartition of interval partitions and an application to number theory

We give wider application and simpler proofs of results describing the rate at which the digits of one number-theoretic expansion determine those of another. The proofs are based on general measure-theoretic covering arguments and not on the dynamics of specific maps.

     

Mechanisms for initiation of cardiac discordant alternans

Electrical alternans, defined as a beat-to-beat change in the duration of the excited phase of cardiac cells, is among the known precursors of sudden cardiac death. It may appear as concordant (all the tissue presenting the same phase of oscillation) or discordant (with out-of-phase regions distributed among tissue). Spatially discordant alternans can lead to unidirectional block that initiates reentry and ventricular fibrillation. The role played by tissue heterogeneities and heart rate changes in their initiation remains, however, unclear. We study the mechanisms for initiation of spatially discordant alternans by numerical simulations of an ionic model spatially distributed in a one-dimensional cable and in an anatomical model of the rabbit heart. The effects of CV-restitution, ectopic beats, and the role of spatial gradients of electrical restitution properties are investigated. In homogeneous tissue, the origin of discordant alternans may be dynamical, through CV-restitution, or due to a localized change in the pacing period. We also find that a sudden change of stimulation rate can initiate discordant alternans in the presence of a spatial gradient of APD-restitution without necessitating CV-restitution. The mechanism of, and the conditions for, initiation are determined based on an iterated map analysis of beat to beat changes of APD. This analysis leads to the definition of a vulnerable window for initiation of discordant alternans. Moreover, the pattern of spatially discordant alternans is found to change slowly over several beats following initiation, as reflected in ECG recordings.     

Ultrafast laser assisted fabrication of ZnO nanorod arrays for photon detection applications

Orderly aligned ZnO nanorod arrays were grown by the ultrafast laser assisted ablation deposition method. These nanorod arrays were further used to make efficient p-n heterojunction photodetector arrays, which have the potential to have nanoscale spatial resolution for imaging, unique incident polarization discrimination capability, and much improved quantum efficiency as well as detection sensitivity. Both front- and back-illumination photodetection schemes were demonstrated by growing those ZnO nanorod arrays on p-type silicon and p-type Zn_0.9Mg_0.1O-coated Al₂O₃ (0 0 0 1) substrates, respectively. Typical diode rectification behavior and photosensitivity were observed in both designs through I-V and photocurrent measurements.     

Crack path prediction in anisotropic brittle materials

A force balance condition to predict quasistatic crack paths in anisotropic brittle materials is derived from an analysis of diffuse interface continuum models that describe both short-scale failure and macroscopic linear elasticity. The path is uniquely determined by the directional anisotropy of the fracture energy, independent of details of the failure process. The derivation exploits the gradient dynamics and translation symmetry properties of this class of models to define a generalized energy-momentum tensor whose integral around an arbitrary closed path enclosing the crack tip yields all forces acting on this tip, including Eshelby's configurational forces, cohesive forces, and dissipative forces. Numerical simulations are in very good agreement with analytic predictions.     

Spatiotemporal control of cardiac alternans

Electrical alternans are believed to be linked to the onset of life-threatening ventricular arrhythmias and sudden cardiac death. Recent studies have shown that alternans can be suppressed temporally by dynamic feedback control of the pacing interval. Here we investigate theoretically whether control can suppress alternans both temporally and spatially in homogeneous tissue paced at a single site. We first carry out ionic model simulations in a one-dimensional cable geometry which show that control is only effective up to a maximum cable length that decreases sharply away from the alternans bifurcation point. We then explain this finding by a linear stability analysis of an amplitude equation that describes the spatiotemporal evolution of alternans. This analysis reveals that control failure above a critical cable length is caused by the formation of standing wave patterns of alternans that are eigenfunctions of a forced Helmholtz equation, and therefore remarkably analogous to sound harmonics in an open pipe. We discuss the implications of these results for using control to suppress alternans in the human ventricles as well as to probe fundamental aspects of alternans morphogenesis. (c) 2002 American Institute of Physics.     

Direct observation of photoinduced bent nitrosyl excited-state complexes

Ground-state structures with side-on nitrosyl (eta (2)-NO) and isonitrosyl (ON) ligands have been observed in a variety of transition-metal complexes. In contrast, excited-state structures with bent-NO ligands have been proposed for years but never directly observed. Here, we use picosecond time-resolved infrared spectroscopy and density functional theory (DFT) modeling to study the photochemistry of Co(CO) 3(NO), a model transition-metal-NO compound. Surprisingly, we have observed no evidence for ON and eta (2)-NO structural isomers, but we have observed two bent-NO complexes. DFT modeling of the ground- and excited-state potentials indicates that the bent-NO complexes correspond to triplet excited states. Photolysis of Co(CO) 3(NO) with a 400-nm pump pulse leads to population of a manifold of excited states which decay to form an excited-state triplet bent-NO complex within 1 ps. This structure relaxes to the ground triplet state in ca. 350 ps to form a second bent-NO structure.     

Protein phosphatase 2a (PP2A) binds within the oligomerization domain of striatin and regulates the phosphorylation and activation of the mammalian Ste20-Like kinase Mst3

Background

The repertoire of the antigen-binding receptors originates from the rearrangement of immunoglobulin and T-cell receptor genetic loci in a process known as V(D)J recombination. The initial site-specific DNA cleavage steps of this process are catalyzed by the lymphoid specific proteins RAG1 and RAG2. The majority of studies on RAG1 and RAG2 have focused on the minimal, core regions required for catalytic activity. Though not absolutely required, non-core regions of RAG1 and RAG2 have been shown to influence the efficiency and fidelity of the recombination reaction.

Results

Using a partial proteolysis approach in combination with bioinformatics analyses, we identified the domain boundaries of a structural domain that is present in the 380-residue N-terminal non-core region of RAG1. We term this domain the Central Non-core Domain (CND; residues 87-217).

Conclusions

We show how the CND alone, and in combination with other regions of non-core RAG1, functions in nuclear localization, zinc coordination, and interactions with nucleic acid. Together, these results demonstrate the multiple roles that the non-core region can play in the function of the full length protein.     

Control of electrical alternans in canine cardiac purkinje fibers

Alternation in the duration of consecutive cardiac action potentials (electrical alternans) may precipitate conduction block and the onset of arrhythmias. Consequently, suppression of alternans using properly timed premature stimuli may be antiarrhythmic. To determine the extent to which alternans control can be achieved in cardiac tissue, isolated canine Purkinje fibers were paced from one end using a feedback control method. Spatially uniform control of alternans was possible when alternans amplitude was small. However, control became attenuated spatially as alternans amplitude increased. The amplitude variation along the cable was well described by a theoretically expected standing wave profile that corresponds to the first quantized mode of the one-dimensional Helmholtz equation. These results confirm the wavelike nature of alternans and may have important implications for their control using electrical stimuli.