Hilbert transform‐based time‐series analysis of the circadian gene regulatory network

In this work, the authors propose the Hilbert transform (HT)‐based numerical method to analyse the time series of the circadian rhythms. They demonstrate the application of HT by taking both deterministic and stochastic time series that they get from the simulation of the fruit fly model Drosophila melanogaster and show how to extract the period, construct phase response curves, determine period sensitivity of the parameters to perturbations and build Arnold tongues to identify the regions of entrainment. They also derive a phase model that they numerically simulate to capture whether the circadian time series entrains to the forcing period completely (phase locking) or only partially (phase slips) or neither. They validate the phase model, and numerics with the experimental time series forced under different temperature cycles. Application of HT to the circadian time series appears to be a promising tool to extract the characteristic information about circadian rhythms.Inspec keywords: time series, genetics, Hilbert transforms, stochastic processes, circadian rhythms, signal processing, medical signal processingOther keywords: phase model, experimental time series, circadian time series, circadian rhythms, circadian gene regulatory network, deterministic time series, stochastic time series, fruit fly model, phase response curves, period sensitivity, phase locking, phase slips, Hilbert transform, time‐series analysis, signal processing     

Modelling the functional roles of synaptic and extra-synaptic γ-aminobutyric acid receptor dynamics in circadian timekeeping

In the suprachiasmatic nucleus (SCN), γ-aminobutyric acid (GABA) is a primary neurotransmitter. GABA can signal through two types of GABA_A receptor subunits, often referred to as synaptic GABA_A (gamma subunit) and extra-synaptic GABA_A (delta subunit). To test the functional roles of these distinct GABA_A in regulating circadian rhythms, we developed a multicellular SCN model where we could separately compare the effects of manipulating GABA neurotransmitter or receptor dynamics. Our model predicted that blocking GABA signalling modestly increased synchrony among circadian cells, consistent with published SCN pharmacology. Conversely, the model predicted that lowering GABA_A receptor density reduced firing rate, circadian cell fraction, amplitude and synchrony among individual neurons. When we tested these predictions, we found that the knockdown of delta GABA_A reduced the amplitude and synchrony of clock gene expression among cells in SCN explants. The model further predicted that increasing gamma GABA_A densities could enhance synchrony, as opposed to increasing delta GABA_A densities. Overall, our model reveals how blocking GABA_A receptors can modestly increase synchrony, while increasing the relative density of gamma over delta subunits can dramatically increase synchrony. We hypothesize that increased gamma GABA_A density in the winter could underlie the tighter phase relationships among SCN cells.     

Genetic redundancy strengthens the circadian clock leading to a narrow entrainment range

Circadian clocks are internal timekeepers present in almost all organisms. Driven by a genetic network of highly conserved structure, they generate self-sustained oscillations that entrain to periodic external signals such as the 24 h light–dark cycle. Vertebrates possess multiple, functionally overlapping homologues of the core clock genes. Furthermore, vertebrate clocks entrain to a range of periods three times as narrow as that of other organisms. We asked whether genetic redundancies play a role in governing entrainment properties and analysed locomotor activity rhythms of genetically modified mice lacking one set of clock homologues. Exposing them to non-24 h light–dark cycles, we found that the mutant mice have a wider entrainment range than the wild types. Spectral analysis furthermore revealed nonlinear phenomena of periodically forced self-sustained oscillators for which the entrainment range relates inversely to oscillator amplitude. Using the forced oscillator model to explain the observed differences in entrainment range between mutant and wild-type mice, we sought to quantify the overall oscillator amplitude of their clocks from the activity rhythms and found that mutant mice have weaker circadian clocks than wild types. Our results suggest that genetic redundancy strengthens the circadian clock leading to a narrow entrainment range in vertebrates.     

Experimental and Theoretical Study of Kinetics of Bulk Crystallization in Poly(Chlorotrifluoroethylene)

The rate of isothermal bulk crystallization of poly(chlorotrifluoroethylene), T_m=221° C, was measured from 170° to 200° C. The intrinsic bulk crystallization, which accurately followed an n = 2 law, was shown to be a result of the injection of primary nuclei sporadically in time, with one-dimensional growth of centers derived from these nuclei. The crystallites are exceedingly small. The one-dimensional growth process was isolated by nucleating specimens with seed crystals, and its temperature-dependence determined between 191° and 205° C. The seed crystal isotherms followed an n = 1 law. The temperature coefficients of the rate of nucleation and the rate of growth were both strongly negative.A theory of homogeneous nucleation that takes into account the segmental character of the polymer chains is developed in some detail. A cylindrical nucleus is assumed. In the temperature range near the melting point, region A, where the radius and length of the nucleus are unrestricted, the rate of nucleation is shown to be proportional to exp(−α/T³ΔT²). The nucleation rate is proportional to exp (−β/T²ΔT) in region B, which extends from somewhat below the melting point to considerably lower temperatures; the length of the nucleus has a constant value l₀ in this region, but the radius is unrestricted. (In the above expressions, α and β are constants). Finally, at sufficiently low temperatures, region C is entered. Under certain circumstances, the rate of nucleation in region C will be extremely rapid, and correspond to a “nucleative collapse” of the supercooled liquid state. A calculation of the one-dimensional growth rate shows that it is proportional to exp(−γ/T²ΔT) where β=γ.A careful analysis of the experimental data obtained between 170° and 200° C clearly showed that both the rate of nucleation and the rate of growth were proportional to exp(−β/T²ΔT), and not exp(−α/T³ΔT²). The primary nucleation event was thus of type B in this interval. A detailed analysis of the data is given, and surface free energies and the dimensions of the nuclei quoted. Quenching experiments, where the polymer was crystallized well below 170° C, gave a firm indication of the existence of region C.An experimental study was made of the extremely slow crystallization process that prevailed when the degree of crystallinity became high. The onset of this stage of the crystallization was interpreted as being the result of a massive degree of impingement. This interpretation is justified by the calculations of Lauritzen, who has given a theory of impingements that predicts a pseudoequilibrium degree of crystallinity.As indicated above, the growth process originating at homogeneous nuclei is not of a three-dimensional or spherulitic character in the region of study. Such stray spherulites as do appear in this region are shown to originate at heterogeneities. The possibility that the intrinsic growth process may become three-dimensional at crystallization temperatures sufficiently near T_m is discussed.     

Crystal growth nucleation and Fermi energy equalization of intrinsic spherical nuclei in glass-forming melts

The energy saving resulting from the equalization of Fermi energies of a crystal and its melt is added to the Gibbs free-energy change ΔG_2ls associated with a crystal formation in glass-forming melts. This negative contribution being a fraction ε _ls(T) of the fusion heat is created by the electrostatic potential energy −U₀ resulting from the electron transfer from the crystal to the melt and is maximum at the melting temperature T_m in agreement with a thermodynamics constraint. The homogeneous nucleation critical temperature T₂, the nucleation critical barrier ΔG_2ls∗/k_BT and the critical radius R∗_2ls are determined as functions of ε_ls(T). In bulk metallic glass forming melts, ε_ls(T) and T₂ only depend on the free-volume disappearance temperature T_0l, and ε_ls(T_m) is larger than 1 (T_0l>T_m/3); in conventional undercooled melts ε_ls(T_m) is smaller than 1 (T_0l>T_m/3). Unmelted intrinsic crystals act as growth nuclei reducing ΔG_2ls∗/k_BT and the nucleation time. The temperature-time transformation diagrams of Mg₆₅Y₁₀Cu₂₅, Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5, Pd₄₃Cu₂₇ Ni₁₀P₂₀, Fe₈₃B₁₇ and Ni melts are predicted using classic nucleation models including time lags in transient nucleation, by varying the intrinsic nucleus contribution to the reduction of ΔG_2ls∗/k_BT. The energy-saving coefficient ε _nm(T) of an unmelted crystal of radius R_nm is reduced when R_nm ≪R∗_2ls; ε_nm is quantified and corresponds to the first energy level of one s-electron moving in vacuum in the same spherical attractive potential −U₀ despite the fact that the charge screening is built by many-body effects.     

Phase Transformations in the High-Tc Superconducting Compounds,Ba2RCu3O7?δ (R = Nd,Sm, Gd,Y, Ho,and Er)

The phase transformation between the orthorhombic and tetragonal structures of six high-T_c superconductors, Ba₂RCu₃O_7−δ, where R = Nd, Sm, Gd, Y, Ho, and Er, and δ = 0 to 1, has been investigated using techniques of x-ray diffraction, differential thermal analysis/thermogravimetric analysis (DTA/TGA) and electron diffraction. The transformation from the oxygen-rich orthorhombic phase to the oxygen-deficient tetragonal phase involves two orthorhombic phases. A superlattice cell caused by oxygen ordering, with a′ = 2a, was observed for materials with smaller ionic radius (Y, Ho, and Er). For the larger lanthanide samples (Nd, Sm, and Gd), the a′ = 2a type superlattice cell was not observed.The structural phase transition temperatures, oxygen stoichiometry and characteristics of the T_c plateaus appear to correlate with the ionic radius, which varies based on the number of f electrons. Lanthanide elements with a smaller ionic radius stabilize the orthorhombic phase to higher temperatures and lower oxygen content. Also, the superconducting temperature is less sensitive to the oxygen content for materials with smaller ionic radius. The trend of dependence of the phase transformation temperature on ionic radius across the lanthanide series can be explained using a quasi-chemical approximation (QCA) whereby the strain effect plays an important role on the order-disorder transition due to the effect of oxygen content on the CuO chain sites.     

Experimental study and thermodynamic modeling of the Al–Co–Cr–Ni system

A thermodynamic database for the Al–Co–Cr–Ni system is built via the Calphad method by extrapolating re-assessed ternary subsystems. A minimum number of quaternary parameters are included, which are optimized using experimental phase equilibrium data obtained by electron probe micro-analysis and x-ray diffraction analysis of NiCoCrAlY alloys spanning a wide compositional range, after annealing at 900 °C, 1100 °C and 1200 °C, and water quenching. These temperatures are relevant to oxidation and corrosion resistant MCrAlY coatings, where M corresponds to some combination of nickel and cobalt. Comparisons of calculated and measured phase compositions show excellent agreement for the β–γ equilibrium, and good agreement for three-phase β–γ–σ and β–γ–α equilibria. An extensive comparison with existing Ni-base databases (TCNI6, TTNI8, NIST) is presented in terms of phase compositions.     

Unconventional pairing in doped band insulators on a honeycomb lattice: the role of the disconnected Fermi surface and a possible application to superconducting β-MNCl (M=Hf,Zr)

We investigate the possibility of realizing unconventional superconductivity in doped band insulators on the square and honeycomb lattices. The latter lattice is found to be a good candidate due to the disconnectivity of the Fermi surface. We propose applying the theory to the superconductivity in doped layered nitride β-MNCl (M= Hf, Zr). Finally, we compare two groups of superconductors with disconnected Fermi surface, β-MNCl and the iron pnictides, which have high critical temperature T_c, despite some faults against superconductivity are present.     

Phase tracking and restoration of circadian rhythms by model-based optimal control

Periodic cellular processes and especially circadian rhythms governed by the oscillating expression of a set of genes based on feedback regulation by their products have become an important issue in biology and medicine. The central circadian clock is an autonomous biochemical oscillator with a period close to 24 h. Research in chronobiology demonstrated that light stimuli can be used to delay or advance the phase of the oscillator, allowing it to influence the underlying physiological processes. Phase shifting and restoration of altered rhythms can generally be viewed as open-loop control problems that may be used for therapeutic purposes in diseases. A circadian oscillator model of the central clock mechanism is studied for the fruit fly Drosophila and show how model-based mixed-integer optimal control allows for the design of chronomodulated pulse-stimuli schemes achieving circadian rhythm restoration in mutants and optimal phase synchronisation between the clock and its environment.     

Variation of Glass Temperature With Pressure in Polypropylene

By measurement of the specific volume of polypropylene as a function of temperature at various pressures, the variation of glass temperature with pressure, dT_g/dP, was determined. Within experimental error the magnitude of this quantity is the same as the value of Tv¯Δα/ΔCp, where Δα and ΔC_p are the change in coefficient of expansion and specific heat respectively at the glass temperature. This is an indication that thermodynamics can be applied to the glass transition. The value of dT_g/dP is the same as Δβ/Δα, where Δβ is the change in compressibility at T_g calculated from the data, but it is shown that this equality must follow as a consequence of the manner in which the experiments were carried out, quite independently of the application of thermodynamics.     

Can a Pressure Standard be Based on Capacitance Measurements?

We consider the feasibility of basing a pressure standard on measurements of the dielectric constant ϵ and the thermodynamic temperature T of helium near 0 °C. The pressure p of the helium would be calculated from fundamental constants, quantum mechanics, and statistical mechanics. At present, the relative standard uncertainty of the pressure u_r(p) would exceed 20 × 10⁻⁶, the relative uncertainty of the value of the molar polarizability of helium A_ϵ calculated ab initio. If the relativistic corrections to A_ϵ were calculated as accurately as the classical value is now known, a capacitance-based pressure standard might attain u_r(p) < 6 × 10⁻⁶ for pressures near 1 MPa, a result of considerable interest for pressure metrology. One obtains p by eliminating the density from the virial expansions for p and ϵ − 1. If ϵ − 1 were measured with a very stable, 0.5 pF toroidal cross capacitor, the small capacitance and the small values of ϵ − 1 would require state-of-the-art capacitance measurements to achieve a useful pressure standard.     

Whirligig beetles as corralled active Brownian particles

We study the collective dynamics of groups of whirligig beetles Dineutus discolor (Coleoptera: Gyrinidae) swimming freely on the surface of water. We extract individual trajectories for each beetle, including positions and orientations, and use this to discover (i) a density-dependent speed scaling like v ∼ ρ^−ν with ν ≈ 0.4 over two orders of magnitude in density (ii) an inertial delay for velocity alignment of approximately 13 ms and (iii) coexisting high and low-density phases, consistent with motility-induced phase separation (MIPS). We modify a standard active Brownian particle (ABP) model to a corralled ABP (CABP) model that functions in open space by incorporating a density-dependent reorientation of the beetles, towards the cluster. We use our new model to test our hypothesis that an motility-induced phase separation (MIPS) (or a MIPS like effect) can explain the co-occurrence of high- and low-density phases we see in our data. The fitted model then successfully recovers a MIPS-like condensed phase for N = 200 and the absence of such a phase for smaller group sizes N = 50, 100.     

Alkyl-π engineering in state control toward versatile optoelectronic soft materials

Organic π-conjugated molecules with extremely rich and tailorable electronic and optical properties are frequently utilized for the fabrication of optoelectronic devices. To achieve high solubility for facile solution processing and desirable softness for flexible device fabrication, the rigid π units were in most cases attached by alkyl chains through chemical modification. Considerable numbers of alkylated-π molecular systems with versatile applications have been reported. However, a profound understanding of the molecular state control through proper alkyl chain substitution is still highly demanded because effective applications of these molecules are closely related to their physical states. To explore the underlying rule, we review a large number of alkylated-π molecules with emphasis on the interplay of van der Waals interactions (vdW) of the alkyl chains and π–π interactions of the π moieties. Based on our comprehensive investigations of the two interactions’ impacts on the physical states of the molecules, a clear guidance for state control by alkyl-π engineering is proposed. Specifically, either with proper alkyl chain substitution or favorable additives, the vdW and π–π interactions can be adjusted, resulting in modulation of the physical states and optoelectronic properties of the molecules. We believe the strategy summarized here will significantly benefit the alkyl-π chemistry toward wide-spread applications in optoelectronic devices.     

Superconducting properties of iron chalcogenide thin films

Iron chalcogenides, binary FeSe, FeTe and ternary FeTe_xSe_1−x, FeTe_xS_1−x and FeTe:O_x, are the simplest compounds amongst the recently discovered iron-based superconductors. Thin films of iron chalcogenides present many attractive features that are covered in this review, such as: (i) easy fabrication and epitaxial growth on common single-crystal substrates; (ii) strong enhancement of superconducting transition temperature with respect to the bulk parent compounds (in FeTe_0.5Se_0.5, zero-resistance transition temperature T_c0^bulk = 13.5 K, but T_c0^film = 19 K on LaAlO₃ substrate); (iii) high critical current density (J_c ∼ 0.5 ×10⁶ A cm² at 4.2 K and 0 T for FeTe_0.5Se_0.5 film deposited on CaF₂, and similar values on flexible metallic substrates (Hastelloy tapes buffered by ion-beam assisted deposition) with a weak dependence on magnetic field; (iv) high upper critical field (∼50 T for FeTe_0.5Se_0.5, B_c2(0), with a low anisotropy, γ ∼ 2). These highlights explain why thin films of iron chalcogenides have been widely studied in recent years and are considered as promising materials for applications requiring high magnetic fields (20–50 T) and low temperatures (2–10 K).     

High-pressure studies on Tc and crystal structure of iron chalcogenide superconductors

The superconducting transition temperature, T_c, in iron-based solids can be enhanced by applied pressure: T_c increases from 8 to 37 K for the 11-type FeSe when the pressure is raised from 0 to 4 GPa. High-pressure studies can elucidate the mechanism of superconductivity in such novel materials. In this paper, we present a high-pressure study of Fe(Se_1−xTe_x) and Fe(Se_1−xS_x). In the case of Fe(Se_1−xTe_x), the maximum T_c under high pressure did not exceed the T_c of FeSe, which can be attributed to the structural transition to the monoclinic phase. For Fe(Se_1−xS_x) (0 < x < 0.3), T_c exhibited a significant increase with pressure; however, the maximum T_c under high pressure did not exceed the T_c of FeSe. This may be due to the disorder induced by substituting S for Se, which is similar to the pressure effect on T_c for the 1111-type superconductor Ca(Fe_1−xCo_x)AsF. The T_c of Fe(Se_1−xS_x) showed a complex behavior below 1 GPa, first decreasing and then increasing with increasing pressure. From high-pressure x-ray diffraction measurements, the T_c (P) curve was correlated with the local structural parameter.     

New aspects of π–d interactions in magnetic molecular conductors

The 2 : 1 cation radical salts of bent donor molecules of ethylenedithio-tetrathiafulvalenoquinone-1,3-dithiolemethide (EDT-TTFVO), ethylenedithio-diselenadithiafulvalenoquinone-1,3-dithiolemethide (EDT-DSDTFVO), ethylenedithio-diselenadithiafulvalenothioquinone-1,3-diselenolemethide (EDT-DSDTFVSDS), ethylenedioxy-tetrathiafulvalenoquinone-1,3-dithiolemethide (EDO-TTFVO) and ethylenedioxy-tetrathiafulvalenoquinone-1,3-diselenolemethide (EDO-TTFVODS) with FeX₄⁻ (X = Cl, Br) ions are prepared by electrocrystallization. The crystal structures of these salts are composed of alternately stacked donor molecule and magnetic anion layers. The band structures of the donor molecule layers are calculated using the overlap integrals between neighboring donor molecules and are compared with the observed electronic transport properties. The magnetic ordering of the Fe(III) d spins of FeX₄⁻ ions is determined from magnetization and heat capacity measurements. The magnetic ordering temperatures are estimated by considering a combination of a direct d–d interaction between the d spins and an indirect π–d interaction between the conduction π electron and the d spins, whose magnitudes are separately calculated from the crystal structures with an extended Hückel molecular orbital method. The occurrence of a π–d interaction is proved by the negative magnetoresistance, and the magnitude of magnetoresistance reflects the strength of the π–d interaction. The effect of pressure on the magnetoresistance is studied, and the result indicates that the magnitude of magnetoresistance increases, namely, the π–d interaction is enhanced with increasing pressure. From these experimental results it is shown that (EDT-TTFVO)₂•FeBr₄ is a ferromagnetic semiconductor, (EDT-DSDTFVO)₂•FeX₄ (X = Cl, Br) and (EDT-DSDTFVSDS)₂•FeBr₄ are metals exhibiting antiferromagnetic ordering of the d spins, and (EDO-TTFVO)₂•FeCl₄ and (EDO-TTFVODS)₂•FeBr₄•(DCE)_0.5 (DCE =-dichloroethane) are genuine antiferromagnetic metals. Among them, the (EDT-TTFVO)₂•FeBr₄ salt is the first π–d molecular system where the d spins of FeBr₄⁻ ions are ferromagnetically ordered through antiferromagnetic interaction with the conduction π electrons. Corresponding to this ferromagnetic ordering, an anomalous dielectric slow-down phenomenon toward the ordering temperature is observed. The π–d interaction in (EDT-DSDTFVSDS)₂•FeBr₄ is very large and comparable to that in λ-(BETS)₂•FeCl₄, which has the highest reported value so far, while the d–d interaction is fairly small. Concerning the ratio between the magnitudes of π–d and d–d interactions (J_πd/J_dd), this salt is currently the best π–d molecular system.