Statistical Computations on Biological Rhythms I: Dissecting Variable Cycles and Computing Signature Phases in Activity-Event Time Series

We propose a computational methodology to compute and extract circadian rhythmic patterns from an individual animal’s activity-event time series. This lengthy dataset, composed of a sequential event history, contains an unknown number of latent rhythmic cycles of varying duration and missing waveform information. Our computations aim at identifying the onset signature phase which individually indicates a sharp event intensity surge, where a subject-night ends and a brand new cycle’s subject-day begins, and collectively induces a linearity manifesting the individual circadian rhythmicity and information about the average period. Based on the induced linearity, the least squares criterion is employed to choose an optimal sequence of computed onset signature phases among a finite collection derived from the hierarchical factor segmentation (HFS) algorithm. The multiple levels of coding schemes in the HFS algorithm are designed to extract contrasting patterns of aggregation against sparsity of activity events along the entire temporal axis. This optimal sequence dissects the whole time series into a sequence of rhythmic cycles without model assumptions or ad hoc behavioral definitions regarding the missing waveform information. The performance of our methodology is favorably compared with two popular approaches based on the periodogram in a simulation study and in real data analyses. The computer code and data used in this article are available on the JCGS webpage.     

Some Invariant Manifolds for Functional Difference Equations with Infinite Delay

For nonlinear autonomous functional difference equations, the existence of the local stable manifolds, together with the local unstable manifolds and the local center-unstable manifolds, is shown. As an application, the principle of linearization which states that stabilities and instabilities for the zero solution of nonlinear equations can be derived from those of the zero solution of the linearized equations under some circumstances is established for functional difference equations.     

Design of an insensitive-polarization all-optical switch based on multimode interference structures

This paper presents a new design for an insensitive-polarization all-optical switch using 2 × 2 multimode interference (MMI) couplers. The switching structure can operate at central operating wavelength 1550 nm for both polarizations. A nonlinear directional coupler is used to realize the phase shifter and therefore switching mechanism is obtained. The transfer matrix method and beam propagation method are used to design and optimize the whole device structure.     

The dynamic compensation temperature in a kinetic spin-5/2 Ising model on a hexagonal lattice

We present a study of the dynamic behavior of a two-sublattice spin-5/2 Ising model with bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on alternating layers of a hexagonal lattice by using the Glauber-type stochastic dynamics.The lattice is formed by alternate layers of spins σ=5/2 and S=5/2.We employ the Glauber transition rates to construct the mean-field dynamic equations.First,we investigate the time variations of the average sublattice magnetizations to find the phases in the system and then the thermal behavior of the dynamic sublattice magnetizations to characterize the nature(first-or second-order) of the phase transitions and to obtain the dynamic phase transition(DPT) points.We also study the thermal behavior of the dynamic total magnetization to find the dynamic compensation temperature and to determine the type of the dynamic compensation behavior.We present the dynamic phase diagrams,including the dynamic compensation temperatures,in nine different planes.The phase diagrams contain seven different fundamental phases,thirteen different mixed phases,in which the binary and ternary combination of fundamental phases and the compensation temperature or the L-type behavior strongly depend on the interaction parameters.     

Stability of inclined planar flames as a local approximation of weakly curved flames

To evaluate the effect of vorticity usually generated by curved flames on the flame stability, laminar premixed planar flames inclined in the gravitational field is asymptotically examined. The flame structure is resolved by a large activation energy asymptotics and a long wave approximation. The coupling between hydrodynamics and diffusion processes is included and near-unity Lewis number is assumed. The results show that as the flame is more inclined from the horizontal plane it shows more unstable characteristics due to not only the decrease of the stabilizing effect of gravity but also the increase of the destabilizing effect of rotational flow. Unlike the planar flame propagating downward with the right angle to the upstream flow, the obtained dispersion relation involves the Prandtl number and shows the destabilizing effect of viscosity. The analysis predicts that the phase velocity of unstable wave depends on the Lewis number as well as the flame angle and, especially for unity Lewis number, it is the same with tangential velocity at the reaction zone. For relatively short wave disturbances, still much larger than flame thickness, the most unstable wavelength is nearly independent on the flame angle and the flame can be stabilized by gravity and diffusion mechanism.     

Phase transition in hexacelsian at about 580 K

Temperature-induced structure and microstructure changes in hexacelsians (BaAl₂Si₂O₈) that have been synthesised from the Ba-exchanged LTA and FAU zeolites (hexacelsian_LTA and hexacelsian_FAU) show that the phase transition near 580?K exists only in hexacelsian_LTA. The X-ray powder diffraction method has been used to follow the evolution of the structure during the phase transition, as described here. The excess thermodynamic quantities Gibbs free energy (G), entropy (S) and enthalpy (H) are obtained through the Landau theory of phase transition. The constants of proportionality between the G and ordering parameter (Q) are: h?=??170345?J?mol^?1, a?=??66.6?J?mol^?1?K^?1 and b?=??410534?J?mol^?1. The abrupt change in the trigonal distortion of the single six-member tetrahedral [SiO₄]^4? and [AlO₄]^5? ring near 580?K is responsible for the phase transition. The phase transition is non-convergent, ferroelastic, pure and proper.     

Weakly first-order or nearly second-order phase transitions in ammonium halides

This work is mainly concerned with the application to the ammonium chloride system of the model that was developed by Yurtseven (1993).

Using the model, which is an Ising model superimposed on an Einstein and/or Debye model, the specific heat C _v has been calculated in the vicinity of the λ-phase transition in NH₄Cl.

Our calculated C _v values give a reasonable fit to the observed more recent C _p data from the literature.

The model predictions applicable to the ammonium halides are discussed.     

Dielectric and ultrasonic investigation of phase transition in cuinp2s6 crystals

Investigation results of dielectric and ultrasonic properties of layered CuInP₂S₆ crystals are presented. At low frequencies, dielectric spectra are highly influenced by the high ionic conductivity with the activation energy of 7357.4?K (0.635?eV). The high-frequency part of the spectra is determined by relaxational soft mode. The critical slowing down and Debye-type dispersion show the order–disorder type of the phase transition. The temperature dependence of the relaxational soft mode and dielectric contribution show a quasi-one-dimensional behaviour. Ultrasonic velocity exhibits critical slowing down which is accompanied by attenuation peaks in the phase transition region. Layered CuInP₂S₆ crystals have extremely large elastic nonlinearity in the direction perpendicular to layers. The nonlinear elastic parameters substantially increases at the PT temperature.     

Phase diagrams and dielectric studies of binary mixtures exhibiting intermediate nematic and induced smectic phases

Investigations on the phase diagrams of two bi-component mixtures of liquid crystals are presented. Whereas in one of the bi-component systems, smectic A (SmA) phase is seen to be induced, in the other case the so-called nematic “island” has been observed. The dielectric properties of magnetically oriented sample forming nematic phase and induced smectic phase in one of the mixtures, and a nematic “island” and SmA phase in the other mixture, were measured in the frequency range from 1?Hz to 10?MHz at different temperatures. The transition temperatures obtained from the polarizing microscope and differential scanning calorimeter measurements agree well with the dielectric relaxation data.