Average Step Size Research Articles

General exponential basis set parametrization: Application to time-dependent bivariational wave functions.

We present equations of motion (EOMs) for general time-dependent wave functions with exponentially parameterized biorthogonal basis sets. The equations are fully bivariational in the sense of the time-dependent bivariational principle and offer an alternative, constraint-free formulation of adaptive basis sets for bivariational wave functions. We simplify the highly non-linear basis set equations using Lie algebraic techniques and show that the computationally intensive parts of the theory are, in fact, identical to those that arise with linearly parameterized basis sets. Thus, our approach offers easy implementation on top of existing code in the context of both nuclear dynamics and time-dependent electronic structure. Computationally tractable working equations are provided for single and double exponential parametrizations of the basis set evolution. The EOMs are generally applicable for any value of the basis set parameters, unlike the approach of transforming the parameters to zero at each evaluation of the EOMs. We show that the basis set equations contain a well-defined set of singularities, which are identified and removed by a simple scheme. The exponential basis set equations are implemented in conjunction with the time-dependent modals vibrational coupled cluster (TDMVCC) method, and we investigate the propagation properties in terms of the average integrator step size. For the systems we test, the exponentially parameterized basis sets yield slightly larger step sizes compared to the linearly parameterized basis set.

Growth and characterization of sodium potassium niobate single crystals near morphotropic phase boundaries

By using a high-temperature solution approach, lead-free single crystals of sodium potassium niobate Kx Na(1-x)NbO3 have been grown at three different phase boundary compositions (x = 0.17, 0.35, and 0.50). The monoclinic and orthorhombic crystal structures are present in the compositions × = 0.17 and × = 0.50 related crystal structures. Ferroelectricity is induced at lower temperatures and requires a smaller critical electric field when KNbO3 content is included into NaNbO3 crystals. Studies using the scanning electron microscope (SEM) and atomic force microscope (AFM) have shown how the sodium potassium niobate (KNN) crystals grow morphologically. With an increase in potassium concentration in the KNN system, the average step size falls. KNN crystals were subjected to impedance analyzer-based dielectric investigations. With an increase in concentration, a decrease in dielectric loss was found. The compositions with potassium concentrations of x = 0.50, 0.35, and 0.17 were found to have piezoelectric coefficients (d33) of 72 pC/N, 63 pC/N, and 52 pC/N, respectively.

Stable and Widely Tunable Optoelectronic Oscillator Using a Cascade Microwave Photonic Filter

A widely tunable optoelectronic oscillator (OEO) with stable output based on a cascade microwave photonic filter (MPF) is proposed and demonstrated. The cascade MPF is implemented by a combination of a finite impulse response (FIR) filter based on shifted dispersion-induced power fading and an infinite impulse response (IIR) filter based on a double-parallel recirculating delay lines (DP-RDLs). Through adjusting the time delay difference between the upper and lower connecting arms of the dual-input Mach-Zehnder modulator within FIR filter, the center frequency of cascade MPF is changed and the oscillation frequency of the OEO can be tuned. The theoretical analysis and verified experiment of the proposed OEO is performed. Tunable oscillation signals from 6.1 to 11.98 GHz with an average step size of 490 MHz are generated. Due to the introduce of the IIR filter, the stable performance of the OEO is obtained, where the maximum frequency drift at 7.48 GHz is observed to be 1.817 kHz over 1 hour. The phase noise of the structure is also investigated

Detection of individual conducting graphene nanoplatelet by electro-catalytic depression

We report a strategy to electrochemically detect individual conducting particles colliding with an ultra-microelectrode (UME). This method, called “electro-catalytic depression” (ECD), enables the detection of particles that are electrically conducting but catalytically inert, such as carbonaceous particles. The ECD method takes advantage of the intrinsic difference in heterogeneous kinetics of electron transfer for a given inner-sphere reaction to block the current at the surface of a particle made of a material having poor catalytic properties compared to the material of the electrode. We showcase this method with the detection of individual graphene nanoplatelets (GNPs) of few µm long and 15 nm thick. GNPs block the oxidation of hydrazine on a 5 µm radius Pt UME. We studied the influence of the potential on the current transient produced by individual GNP stochastically colliding on the UME. We evidence that, under 0.1 V vs AgAgCl 3.4 M KCl, electrically conducting GNPs produce discrete stair-shaped drops of current (negative steps) similar to the signal obtained with insulating particles like polystyrene beads. We show how the analysis of a “blocking-type” signal originally developed for insulating beads can be extended to the detection of conducting particles. However, at high potentials (> 0.1 V), where hydrazine oxidation occurs on the GNP, the kinetic difference between GNP and Pt decreases, leading to the decrease of both average and median current step size and the appearance of positive steps. The frequency of collision versus the concentration of GNP and the bias potential are discussed.

Dynamic Mass Isolation for Improving the Moving Efficiency of an Impact Drive Mechanism

When an impact drive mechanism (IDM) is subjected to a heavy load, the large inertia of that load will seriously decrease the moving efficiency of the IDM. To solve this problem, a method of dynamic mass isolation is introduced in this article. The influence of load inertia is decreased to a minute value by adopting a light slider and using a spring between the load and the IDM. Thus, the moving efficiency can be increased. Kinematic models have been established and calculated by MATLAB/Simulink. Two prototypes have been fabricated and used to conduct a series of experiments. With a load of 1.8 g, the prototype with dynamic mass isolation presents a moving efficiency of 50.6%, whereas the other prototype without isolation presents a moving efficiency of only 11.9%. As a result, the average step size of the former is approximately four times larger than that of the latter. Moreover, the prototype with dynamic mass isolation can hold almost the same average step size with a wide range of load mass. The proposed method is low cost and may have practical significance for application in any known IDM-based actuating system to improve the performance.

KCC2 Manipulation Alters Features of Migrating Interneurons in Ferret Neocortex.

KCC2 is a brain specific chloride-potassium cotransporter affecting neuronal development including migration and cellular maturation. It modulates chloride homeostasis influencing the switch of GABA from depolarizing to hyperpolarizing, which contributes to the cues that influence the termination of neuronal migration. The expression of KCC2 during migration of interneurons, therefore, correlates with the ability of these cells to respond to GABA as a stop signal. Manipulation of KCC2 in development can affect various aspects of migrating neurons, including the speed. We describe the effect of KCC2 downregulation and inhibition on features of migrating interneurons of normal ferret kits and those treated with methylazoxymethanol acetate, which increases KCC2. Treatment of organotypic cultures with Bisphenol A, an environmental toxin that alters gene expression, also downregulates KCC2 protein. In organotypic slices treated with the KCC2 antagonist VU0240551, chloride imaging shows inhibition of KCC2 via blockade of chloride flux. Time-lapse video imaging of organotypic cultures treated with either drug, shows a significant increase in the average speed, step size, and number of turns made by migrating neurons leaving the ganglionic eminence. Our findings demonstrate the harmful effect of environmental toxins on brain development and potential consequences in the pathogenesis of neurodevelopmental disorders.

New design for inertial piezoelectric motors

We have designed, implemented, and tested a novel inertial piezoelectric motor (IPM) that is the first IPM to have controllable total friction force, which means that it sticks with large total friction forces and slips with severely reduced total friction forces. This allows the IPM to work with greater robustness and produce a larger output force at a lower threshold voltage while also providing higher rigidity. This is a new IPM design that means that the total friction force can be dramatically reduced or even canceled where necessary by pushing the clamping points at the ends of a piezoelectric tube that contains the sliding shaft inside it in the opposite directions during piezoelectric deformation. Therefore, when the shaft is propelled forward by another exterior piezoelectric tube, the inner piezoelectric tube can deform to reduce the total friction force acting on the shaft instantly and cause more effective stepping movement of the shaft. While our new IPM requires the addition of another piezoelectric tube, which leads to an increase in volume of 120% when compared with traditional IPMs, the average step size has increased by more than 400% and the threshold voltage has decreased by more than 50 V. The improvement in performance is far more significant than the increase in volume. This enhanced performance will allow the proposed IPM to work under large load conditions where a simple and powerful piezoelectric motor is needed.

Quantumlike statistics of deterministic wave-particle interactions in a circular cavity.

A deterministic low-dimensional iterated map is proposed here to describe the interaction between a bouncing droplet and Faraday waves confined to a circular cavity. Its solutions are investigated theoretically and numerically. The horizontal trajectory of the droplet can be chaotic: it then corresponds to a random walk of average step size equal to half the Faraday wavelength. An analogy is made between the diffusion coefficient of this random walk and the action per unit mass ℏ/m of a quantum particle. The statistics of droplet position and speed are shaped by the cavity eigenmodes, in remarkable agreement with the solution of Schrödinger equation for a quantum particle in a similar potential well.

Constraints on Fluctuations in Sparsely Characterized Biological Systems.

Biochemical processes are inherently stochastic, creating molecular fluctuations in otherwise identical cells. Such "noise" is widespread but has proven difficult to analyze because most systems are sparsely characterized at the single cell level and because nonlinear stochastic models are analytically intractable. Here, we exactly relate average abundances, lifetimes, step sizes, and covariances for any pair of components in complex stochastic reaction systems even when the dynamics of other components are left unspecified. Using basic mathematical inequalities, we then establish bounds for whole classes of systems. These bounds highlight fundamental trade-offs that show how efficient assembly processes must invariably exhibit large fluctuations in subunit levels and how eliminating fluctuations in one cellular component requires creating heterogeneity in another.

Asteroseismic inversions for radial differential rotation of Sun-like stars: ensemble fits

Radial differential rotation is an important parameter for stellar dynamo theory and for understanding angular momentum transport. We investigate the potential of using a large number of similar stars simultaneously to constrain their average radial differential rotation gradient: we call this 'ensemble fitting'. We use a range of stellar models along the main sequence, each with a synthetic rotation profile. The rotation profiles are step functions with a step of -350 nHz, which is located at the base of the convection zone. These models are used to compute the rotational splittings of the p modes and to model their uncertainties. We then fit an ensemble of stars to infer the average step size. All the uncertainties on the inferred step size for individual stars are of the order 1 micro Hz. Using 15 stellar models in an ensemble fit, we show that the uncertainty on the average step size is reduced to less than the input step size, which allows us to constrain the sign of the radial differential rotation. We show that a solar-like step size (approximately 30 nHz) can be constrained by an ensemble fit of thousands of main-sequence stars. Observing the number of stars required to successfully exploit the ensemble fitting method will be possible with future asteroseismology missions, such as PLATO. We demonstrate the potential of ensemble fitting by showing that any systematic differences in the average step size between F, G, and K-type stars larger than 100 nHz can be detected.

Autoregulatory mechanism for dynactin control of processive and diffusive dynein transport.

Dynactin is the longest known cytoplasmic dynein regulator, with roles in dynein recruitment to subcellular cargo and in stimulating processive dynein movement. The latter function was thought to involve the N-terminal microtubule binding region of the major dynactin polypeptide p150Glued, though recent results disputed this. To understand how dynactin regulates dynein we generated recombinant fragments of the N-terminal half of p150Glued. We find that the dynein-binding coiled-coil α-helical domain CC1B is sufficient to stimulate dynein processivity, which it accomplishes by increasing average dynein step size and forward step frequency, while decreasing lateral stepping and microtubule detachment. In contrast, the immediate upstream coiled-coil domain, CC1A, activates a novel diffusive dynein state. CC1A interacts physically with CC1B and interferes with its effect on dynein processivity. We also identify a role for the N-terminal portion of p150Glued in coordinating these activities. Our results reveal an unexpected form of long-range allosteric control of dynein motor function by internal p150Glued sequences, and evidence for p150Glued auto regulation.

On the Behaviour of the (1, λ)-ES for Conically Constrained Linear Problems

We study the behaviour of a [Formula: see text]-ES that handles constraints by resampling infeasible candidate solutions for linear optimization problems with a conically constrained feasible region. The analysis generalizes prior work in that no particular orientation of the cone relative to the gradient of the objective function is assumed. Expressions that describe the strategy's single-step behaviour are derived. Assuming that the mutation strength is adapted in a scale-invariant manner, a simple zeroth-order model is used to determine the speed of convergence of the strategy. We then derive expressions that approximately characterize the average step size and convergence rate attained when using cumulative step size adaptation and compare the values with optimal ones.

Ventricular myosin modifies in vitro step-size when phosphorylated

Cardiac and skeletal muscle myosins have the central role in contraction transducing ATP free energy into the mechanical work of moving actin. Myosin has a motor domain containing ATP and actin binding sites and a lever-arm that undergoes rotation impelling bound actin. The lever-arm converts torque generated in the motor into the linear displacement known as step-size. The myosin lever-arm is stabilized by bound essential and regulatory light chains (ELC and RLC). RLC phosphorylation at S15 is linked to modified lever-arm mechanical characteristics contributing to myosin filament based contraction regulation and to the response of the muscle to disease. Myosin step-size was measured using a novel quantum dot (Qdot) assay that previously confirmed a 5nm step-size for fast skeletal myosin and multiple unitary steps, most frequently 5 and 8nm, and a rare 3nm displacement for β cardiac myosin (βMys). S15 phosphorylation in βMys is now shown to change step-size distribution by advancing the 8nm step frequency. After phosphorylation, the 8nm step is the dominant myosin step-size resulting in significant gain in the average step-size. An increase in myosin step-size will increase the amount of work produced per ATPase cycle. The results indicate that RLC phosphorylation modulates work production per ATPase cycle suggesting the mechanism for contraction regulation by the myosin filament.

Ventricular Myosin Modifies in Vitro Step-Size When Phosphorylated

Cardiac and skeletal muscle myosins have the central role in contraction transducing ATP free energy into the mechanical work of moving actin in transduction/mechanical coupling. Inheritable cardiomyopathies are more frequently linked to myosin mutations than other sarcomeric proteins. Hereditary skeletal myopathies linked to myosin are less common. They lead to muscle weakness or affect myosin isoforms expressed during development leading to arthrogryposis syndromes. Myosin has a motor domain containing ATP and actin binding sites and light chains stabilized lever-arm that undergoes rotation impelling bound actin. The lever-arm converts torque generated in the motor into linear displacement (step-size). Relative myosin and actin filament sliding is modeled in vitro with a motility assay quantitating actin filament translation over a myosin coated surface. A novel quantum dot super-resolution in vitro motility assay confirmed a 5 nm step-size for fast skeletal myosin while β cardiac myosin (βMys) had multiple unitary steps, most frequently 5 and 8 nm, and a rare 3 nm displacement. The myosin lever-arm is stabilized by bound essential and regulatory light chains (ELC and RLC). RLC phosphorylation at S15 is linked to modified lever-arm mechanical characteristics contributing to disease and to myosin filament based contraction regulation. We have studied the effect of RLC phosphorylation on the step-size of porcine βMys. Phosphorylated βMys has ∼85% of the myosin phosphorylated. We find RLC phosphorylation causing the distribution of longest step increasing from 37% to 71%. This dramatic re-distribution of step-sizes provides significant gain in average step-size. The results indicate a mechanism for contraction regulation by step-size adaptation using post-translational modification of the myosin filament via RLC phosphorylation. Research supported by R01AR049277, R01HL095572 and the Mayo Foundation.

An optically tunable wideband optoelectronic oscillator based on a bandpass microwave photonic filter

An optoelectronic oscillator (OEO) with wideband frequency tunability and stable output based on a bandpass microwave photonic filter (MPF) has been proposed and experimentally demonstrated. Realized by cascading a finite impulse response (FIR) filter and an infinite impulse response (IIR) filter together, the tunable bandpass MPF successfully replaces the narrowband electrical bandpass filter in a conventional single-loop OEO and serves as the oscillating frequency selector. The FIR filter is based on a tunable multi-wavelength laser and dispersion compensation fiber (DCF) while the IIR filter is simply based on an optical loop. Utilizing a long length of DCF as the dispersion medium for the FIR filter also provides a long delay line for the OEO feedback cavity and as a result, optical tuning over a wide frequency range can be achieved without sacrificing the quality of the generated signal. By tuning the wavelength spacing of the multi-wavelength laser, the oscillation frequency can be tuned from 6.88 GHz to 12.79 GHz with an average step-size of 0.128 GHz. The maximum frequency drift of the generated 10 GHz signal is observed to be 1.923 kHz over 1 hour and its phase noise reaches the -112 dBc/Hz limit of our measuring equipment at 10 kHz offset frequency.

Temperature-Compensated dB-linear Digitally Controlled Variable Gain Amplifier With DC Offset Cancellation

This paper presents a compact digitally controlled variable gain amplifier (DVGA) with capabilities of both temperature compensated linear-in-decibel (dB-linear) gain control and dc offset cancellation (DCOC) without making use of either the feedback or the feed-forward loop. The proposed DVGA design is a three-stage inductorless cascaded amplifier that is integrated with a temperature-compensated dB-linear gain control, a DCOC, an output common mode feedback, a 6-bit digital gain control (with a 64-step resolution), a power shutdown mode, and a linearizer for improving the 1-dB gain compression point. The design is fabricated using a commercial 0.18-μm SiGe BiCMOS technology. The DVGA has a measured gain range of 18.4 dB with an average step size of 0.3 dB, a 3-dB bandwidth from 2 MHz to 1.9 GHz with a ±0.75-dB gain flatness from 2.75 MHz to 1.2 GHz, an input 1-dB gain compression point better than -12.5 dBm, an input return loss better than 12 dB, an output return loss better than 16 dB, and a dc power consumption of 12.2 mW from a 1.8-V supply. The core DVGA, by excluding the I/O measurement pads, occupies a die area of 160 μm × 300 μm.

Force generation and step-size fluctuations in a dynein motor

Molecular motors such as dynein are known to move by taking steps of different sizes, depending on the load. Here, we develop a simple, discrete, minimal ratchet model for a motor that can take steps of sizes δ∘ and 2δ∘ in order to provide a bare-bones description of dynein. We obtain the force–velocity curves and diffusivity for this motor for different concentrations of ATP. We also study the mechano-chemical energy transduction and thermodynamic efficiency of the motor. Further, by investigating the statistics of step sizes for the motor, we show that the average step size and fluctuation in step sizes have a non-monotonic force dependence. We develop closed-form analytical expressions for all our results, which despite the simplicity of the model give a reasonable match with the known experiments and simulations on dynein.

Processive Steps in the Reverse Direction Require Uncoupling of the Lead Head Lever Arm of Myosin VI

Myosin VI is the only known reverse-direction myosin motor. It has an unprecedented means of amplifying movements within the motor involving rearrangements of the converter subdomain at the C terminus of the motor and an unusual lever arm projecting from the converter. While the average step size of a myosin VI dimer is 30-36nm, the step size is highly variable, presenting a challenge to the lever arm mechanism by which all myosins are thought to move. Herein, we present structures of myosin VI that reveal regions of compliance that allow an uncoupling of the lead head when movement is modeled on actin. The location of the compliance restricts the possible actin binding sites and predicts the observed stepping behavior. The model reveals that myosin VI, unlike plus-end directed myosins, does not use a pure lever arm mechanism, but instead steps with a mechanism analogous to the kinesin neck-linker uncoupling model.

A Differential Digitally Controlled Crystal Oscillator With a 14-Bit Tuning Resolution and Sine Wave Outputs for Cellular Applications

This paper describes the design topologies and considerations of a differential sinusoidal-output digitally controlled crystal oscillator (DCXO) intended for use in cellular applications. The oscillator has a fine-tuning range of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\pm}$</tex></formula> 44 ppm, approximately 14 bits of resolution, and an average step size of 0.005 ppm. All signals connecting externally to I/O pins are sine waves for reducing noise, interference, and spurs couplings. The 26 MHz DCXO fabricated in 65 nm CMOS achieves a phase noise of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${-}$</tex></formula> 149.1 dBc/Hz at 10 kHz offset measured at the sine wave buffer output. The DCXO is capable of meeting the stringent phase noise requirements for IEEE 802.11n 5 GHz WLAN devices. A typical frequency pulling of 0.01 ppm due to turning on/off the sine wave buffer is measured. The DCXO dissipates 1.2 mA of current, whereas each sine wave output buffer draws 1.4 mA. The DXCO occupies a total silicon area of 0.15 mm <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$^{2}$</tex> </formula> .

Single Molecule Stepping and Structural Dynamics of Myosin X

Myosin X is an unconventional myosin motor protein with puzzling motility properties that are under debate. We studied the motility, angular motions and stepping of myosin X in vitro using single molecule fluorescence of rhodamine bound to the lever arm calmodulins (CaMs) and quantum dots on the CaMs and at the C-terminus of the heavy chain. Myosin X walks processively both on single actin filaments and actin bundles. The average step size, measured by FIONA, is 34 nm, supporting the postulate that an α-helical domain extends the lever arm beyond the binding region of myosin X for its three CaMs per head.