Exponential Gradient Research Articles

Efficient Generation of Dilution Gradients With Digital Microfluidic Biochips

Digital microfluidic biochips (DMFBs) are now being extensively used to automate several biochemical laboratory protocols such as clinical analysis, point-of-care diagnostics, or DNA sequencing. In many biological assays, e.g., bacterial susceptibility tests and cellular response analysis, samples, or reagents are required in multiple concentration (or dilution) factors, satisfying certain gradient patterns such as linear, exponential, or parabolic. Dilution gradients are traditionally prepared using continuous-flow microfluidic devices. Unfortunately, most of them suffer from inflexibility and nonprogrammability, and they require large volumes of costly stock-solutions. DMFBs, on the other hand, are shown to produce, more efficiently, samples with multiple dilution factors. However, none of the existing DMFB-based algorithms utilize the properties of the gradient-profile while optimizing reactant-cost and sample-preparation time. In this paper, we explore the underlying combinatorial attributes of different gradients and harnessed them for efficient production of the desired concentration profile. For linear gradients, we present theoretical results concerning the number of mix-split operations and waste production, and prove an upper bound on on-chip storage requirement. A cost-effective method for generating a wide class of exponential gradients is also proposed. Finally, in order to handle a complex-shaped gradient, we posit a digital-geometric technique to approximate it with a sequence of linear gradients. Experimental results on various gradient-profiles are presented in support of the proposed method.

Generalized Fractional Heat Conduction in a One-Dimensional Functionally Graded Material Layer

Functionally graded materials (FGMs) have been widely used. This work studies a heat conduction problem in an FGM layer with different exponential gradients. Based on a generalized fractional heat conduction theory with phase lag of heat flux, a mixed initial-boundary value problem is solved. Analytical expression for temperature change in the Laplace transform domain is derived. Numerical results of the transient temperature response in the time domain are evaluated by applying a numerical inversion of the Laplace transform. Two representative boundary conditions related to given temperature or heat convective transfer are discussed. For different Biot numbers, the effects of phase lag of heat flux, fractional order, and material properties on temperature field are illustrated graphically. A comparison of the temperature fields based on the non-Fourier model and classic Fourier model is made. The obtained results show that wave-like behaviors may occur for the generalized fractional heat transfer, which does not occur for the classical Fourier heat conduction. The material properties play an important role in the heat transfer process. The derived results are of benefit to the design of materials for thermoresistance and abstraction of heat.

Boosting Exponential Gradient Strategy for Online Portfolio Selection: An Aggregating Experts’ Advice Method

Online portfolio selection is one of the fundamental problems in the field of computational finance. Although existing online portfolio strategies have been shown to achieve good performance, we always have to set the values for different parameters of online portfolio strategies, where the optimal values can only be known in hindsight. To tackle the limits of existing strategies, we present a new online portfolio strategy based on the online learning character of Weak Aggregating Algorithm (WAA). Firstly, we consider a number of Exponential Gradient (EG$$(\eta )$$) strategies of different values of parameter $$\eta $$ as experts, and then determine the next portfolio by using the WAA to aggregate the experts’ advice. Furthermore, we theoretically prove that our strategy asymptotically achieves the same increasing rate as the best EG$$(\eta )$$ expert. We prove our strategy, as EG$$(\eta )$$ strategies, is universal. We present numerical analysis by using actual stock data from the American and Chinese markets, and the results show that it has good performance.

On propagation behavior of SH-wave and Rayleigh-type wave in an initially stressed exponentially graded fiber-reinforced viscoelastic layered structure

The present article undertakes the study of propagation of SH-wave and Rayleigh-type wave in a layered structure with a layer overlying a semi-infinite medium composed of distinct initially stressed exponentially graded fiber-reinforced viscoelastic materials in two separate cases. Adopting analytical treatment closed form of complex frequency equation is obtained for both the surface waves. The real part of complex frequency equation imparts dispersion equation whereas imaginary part accounts for the damped velocity equation. Dispersion and damped velocity equations for both the surface waves are in well-agreement with the classical results. Also as a special case of the problem, the deduced results are validated with the pre-established results. Numerical computation of the analytical finding has been accomplished and manifested through dispersion curves and damped velocity curves for both SH-wave and Rayleigh-type wave in order to analyze the influence of various affecting parameters, viz., initial stress, reinforcement, exponential gradient, volume and shear viscosity on their phase and damped velocities. Moreover, comparative study has also been carried out for various distinct cases associated with the considered layered structure for both the waves, which serves as a salient feature of the present study.

Love-type waves in a piezoelectric-viscoelastic bimaterial composite structure due to an impulsive point source

The analysis of wave propagation phenomenon piezoelectric-viscoelastic composites still remains an unexplored field of research. The usage of a passive polymer (Epoxy) with active piezoelectric ceramic causes viscoelasticity in the piezoelectric material which results into a piezoelectric-viscoelastic composite. The present study aims to analyze the propagation behavior of Love-type wave in an exponentially graded piezoelectric-viscoelastic material (EGPVM) stratum lying over a functionally graded piezoelectric-viscoelastic material (FGPVM) substrate due to an impulsive point source at its interfacial surface. The electro-visco-mechanical field equations are laid down for the piezoelectric-viscoelastic medium. The analytical solution procedure involves the use of suitable Green's function and admissible boundary conditions. The established frequency equation is in complex form; of which the real expression imparts the frequency curve and imaginary expression gives the attenuation curve of Love-type wave. To depict the results numerically, two distinct piezoelectric-viscoelastic materials (Epoxy-BNKLBT and Epoxy-KNLNTS ceramics) for EGPVM stratum and FGPVM substrate are taken into account. The phase velocity profile and attenuation coefficient profile of Love-type wave is portrayed graphically. Diagnostic results are simulated numerically which forefronts the effect of distinct parameters. The study manifests the impact of the material medium parameters, viz. piezoelectric constants, dielectric constants, piezoelectric loss moduli, dielectric loss moduli, exponential gradient parameter and magnifying gradient parameters on the phase velocity and attenuation coefficient of Love-type wave. For sake of validation, the obtained results are matched with the classical one, as a special case of the problem. The outcomes of the study may find its worth in better and optimum design of surface acoustic wave devices and Love wave sensors, keeping efficiency at its premium.

Modelling Creep Response of a Functionally Graded Rotating Disc with Exponential Reinforcement Gradient

Abstract Analysis is carried out to estimate creep response of a rotating Al-SiCp disc with exponential SiCp gradient. The results estimated for exponential FGM disc are compared with hyperbolic FGM and non-FGM discs, having the same amount of reinforcement. The imposition of reinforcement gradient increases the radial stress throughout and tangential stress near the inside radius and but decreases the tangential stress towards the outside radius, with maximum variation observed for exponential FGM disc. By imposing reinforcement gradient, the creep rates in the disc are observed to reduce largely, with minimum and more uniform distribution noticed for exponential gradient.

Influence of spatial heterogeneous environment on long-term dynamics of a reaction-diffusion SVIR epidemic model with relaps.

In this paper by adding the factors of disease relapse and vaccination in the space hetero-geneous environment, we establish and discuss a class of reaction-diffusion SVIR model with relapse and a varying external source in spatial heterogeneous environment. By applying a different method than the Lyapunov function, we study the long-term dynamic behavior of this model by means of global exponential attractor theory and gradient flow method. The global asymptotic stability and the persistence of epidemic are proved. To test the validity of our theoretical results, we choose some specific epidemic disease with some more practical and more definitive official data to simulate the global stability and exponential attraction of the model. The simulation results showed that the factors of disease relapse, vaccination and spatial heterogeneity had a great influence on the persists uniformly of the disease.

Self-focusing and defocusing of cosh Gaussian laser beam in the presence of nonlinearity of ponderomotive force and temperature gradient

In this paper, the propagation of Cosh Gaussian laser beam and its interaction with isothermal plasma without temperature gradient as well as the effect of the exponential electron temperature gradient are investigated. Here the ponderomotive nonlinearity force is effective mechanism. This force can modify the electron density distribution. All the investigations are carried out for different initial plasma temperatures. Using Maxwell’s equations we obtained the nonlinear second-order differential equation of the dimensionless beam-width parameter (f) on the distance of propagation for several initial electron temperatures and exponential temperature variations. These equations are solved numerically by taking WKB and paraxial approximation. Under the effect of initial electron temperature, self-focusing and defocusing of hyperbolic cosine (cosh) Gaussian laser beam is distinguished. Furthermore, the exponential temperature gradient cause to stationary propagation mode breaks, and self-focusing or defocusing properties is observable.

EGRank: An exponentiated gradient algorithm for sparse learning-to-rank

This paper focuses on the problem of sparse learning-to-rank, where the learned ranking models usually have very few non-zero coefficients. An exponential gradient algorithm is proposed to learn sparse models for learning-to-rank, which can be formulated as a convex optimization problem with the ℓ1 constraint. Our proposed algorithm has a competitive theoretical worst-case performance guarantee, that is, we can obtain an ϵ-accurate solution after O(1ϵ) iterations. An early stopping criterion based on Fenchel duality is proposed to make the algorithm be more efficient in practice. Extensive experiments are conducted on some benchmark datasets. The results demonstrate that a sparse ranking model can significantly improve the accuracy of ranking prediction compared to dense models, and the proposed algorithm shows stable and competitive performance compared to several state-of-the-art baseline algorithms.

Regional Boundary Gradient Detectability in Distributed Parameter Systems

The aim of this paper is study and explore the notion of the regional boundary gradient detectability in connection with the choice of strategic gradient sensors on sub-region of the considered system domain boundary. More precisely, the principal reason behind introducing this notion is that the possibility to design a dynamic system (may be called regional boundary gradient observer) which enable to estimate the unknown system state gradient. Then for linear infinite dimensional systems in a Hilbert space, we give various new results related with different measurements. In addition, we provided a description of the regional boundary exponential gradient strategic sensors for completion the regional boundary exponential gradient observability and regional boundary exponential gradient detectability. Finally, we present and illustrate the some applications of sensors structures which relate by regional boundary exponential gradient detectability in diffusion distributed parameter systems.

Determining the confined optical length of high index vertical Si nanoforest arrays for photonic applications

The structural and the optical properties of different Si nanostructures have been compared. Detailed optical properties of Si nanowires arrays of different optical lengths, fabricated by facile electroless etching technique, have been reported. The theoretical calculation of exponential sine profile at constant λ = 600 nm shows a better explanation in terms of gradient index with optical length for vertical nanowires. The observations signify the possibility of strong light trapping due to an exponential gradient towards the high index along the nanowires and the existence of dense subwavelength features. The optical admittance (Ƶ) shows a strong impact on optical distance (Z) for Z < H, owing to the electromagnetic wave interaction with the nanowires that perceive a different Ƶ at the oblique angle of incidence (AOI). In addition, the experimental reflectance data and the theoretical model for transverse electric and transverse magnetic modes predict that an optical length of 5 μm can exhibit a very low reflectance value. This indicates that the Si nanowires are polarization insensitive over a wide range of AOI (0°–80°). Moreover, Raman spectra showed a very strong light confinement effect in the first order transverse optical band with increasing etching depths. The morphological dependent resonance theory predicts a strong localized light field confinement in the lower wavelength regime for SiNWs. The effect on the strong resonant absorption modes was further correlated with the simulation results obtained by using COMSOL. The obtained results are likely to enhance the maximum absorption of SiNWs for various photonic applications.

Ion trajectory simulations of a conical octopole ion guide and its comparison with a parallel one in chemical ionization mass spectrometric applications.

Focusing and transmission are important characteristics of ion transportation in mass spectrometric applications. An ion guide device is an essential component in a mass spectrometer, especially when chemical ionization is employed. We present a conical octopole ion guide and its comparison with a parallel counterpart for simulating the ion trajectories through the ion guide and the quadrupole mass analyzer. Ion trajectory simulations using SIMION 8.0 were performed to evaluate the performance of both conical and parallel octopole ion guides and the overall ion transmission through combining the octopole ion guide and the quadrupole mass analyzer in the mass spectrometer. Through the simulations, parameters that control the ion guide were optimized for the focus and transport of weakly bonded cluster ions, including the DC bias voltage, the frequency and the amplitude of the sine wave applied to the guide. The results from ion trajectory simulations showed that the ion beam can be highly focused from initially 10mm down to 2mm in diameter for the conical octopole ion guide. The transmission efficiencies are dependent on the mass of the ion, the frequency and amplitude of the radiofrequency waveform applied to the octopoles. The simulated overall transmission efficiencies of the conical ion guide are consistent with the observed sensitivities from the previously reported calibration experiments in the low-mass region but are much higher than those in the high-mass region (i.e., masses greater than 400amu). The simulations showed that the conical octopole ion guide can efficiently transport ions with high focusing through differentially pumped vacuum chambers. However, the overall transmission efficiencies of the conical octopole ion guide are in general lower than the parallel one when combined with the quadrupole mass analyzer based on the assumed exponential pressure gradient along the axial of the octopole ion guide.

Exponential Discrete Gradient Schemes for Simulating Stochastic Hamiltonian Systems Preserving Hamiltonian Functions

The paper investigates the exponential discrete gradient methods simulating stochastic Hamiltonian systems with invariant Hamiltonians. We show that the methods are nearly symplectic, and nearly preserve the invariant Hamiltonians. Numerical experiments illustrate effectiveness and efficiency of the simulation methods.

Insights on the morphology of polymer donor:acceptor blends by optical metrology

One of the main challenges that need to be addressed to successfully implement polymer donor:acceptor blends as photoactive layers in Organic Electronic (OE) devices (e.g. Organic Photovoltaics - OPV) is the understanding of the effect of the processing and printing parameters on their morphology and the distribution of the donor and acceptor components in the photoactive layer. In this work, we present a comprehensive optical metrology methodology for the determination of the morphology of well-established polymer blends that include poly(3-hexylthiophene (P3HT) donors and phenyl-C61-butyric acid methyl ester (PC60BM) and phenyl-C71-butyric acid methyl ester (PC71BM) acceptors, which are used as photoactive layers for OPVs. Also, we determine the distribution of the donor and acceptor phases in the blend by analysis of the measured pseudodielectric function 〈ε(ω)〉 by the use of effective medium theory modelling in combination with an exponential gradient model that approximates the modification of the refractive index in the different parts of the blend. This methodology emphasizes the capabilities and potential of optical metrology to be used as a quality control tool in large scale manufacturing for OE devices.

Dominant features in three-dimensional turbulence structure: comparison of non-uniform accelerating and decelerating flows

The results are presented from an experimental study to investigate three-dimensional turbulence structure profiles, including turbulence intensity and Reynolds stress, of different non-uniform open channel flows over smooth bed in subcritical flow regime. In the analysis, the uniform flow profiles have been used to compare with those of the non-uniform flows to investigate their time-averaged spatial flow turbulence structure characteristics. The measured non-uniform velocity profiles are used to verify the von Karman constant κ and to estimate sets of log-law integration constant Br and wake parameter П, where their findings are also compared with values from previous studies. From κ, Br and П findings, it has been found that the log-wake law can sufficiently represent the non-uniform flow in its non-modified form, and all κ, Br and П follow universal rules for different bed roughness conditions. The non-uniform flow experiments also show that both the turbulence intensity and Reynolds stress are governed well by exponential pressure gradient parameter β equations. Their exponential constants are described by quadratic functions in the investigated β range. Through this experimental study, it has been observed that the decelerating flow shows higher empirical constants, in both the turbulence intensity and Reynolds stress compared to the accelerating flow. The decelerating flow also has stronger dominance to determine the flow non-uniformity, because it presents higher Reynolds stress profile than uniform flow, whereas the accelerating flow does not.

Drift and Behavior of E. coli Cells

Chemotaxis of the bacterium Escherichia coli is well understood in shallow chemical gradients, but its swimming behavior remains difficult to interpret in steep gradients. By focusing on single-cell trajectories from simulations, we investigated the dependence of the chemotactic drift velocity on attractant concentration in an exponential gradient. Whereas maxima of the average drift velocity can be interpreted within analytical linear-response theory of chemotaxis in shallow gradients, limits in drift due to steep gradients and finite number of receptor-methylation sites for adaptation go beyond perturbation theory. For instance, we found a surprising pinning of the cells to the concentration in the gradient at which cells run out of methylation sites. To validate the positions of maximal drift, we recorded single-cell trajectories in carefully designed chemical gradients using microfluidics.

Predicting Escherichia coli's chemotactic drift under exponential gradient.

Bacterial species are known to show chemotaxis, i.e., the directed motions in the presence of certain chemicals, whereas the motion is random in the absence of those chemicals. The bacteria modulate their run time to induce chemotactic drift towards the attractant chemicals and away from the repellent chemicals. However, the existing theoretical knowledge does not exhibit a proper match with experimental validation, and hence there is a need for developing alternate models and validating experimentally. In this paper a more robust theoretical model is proposed to investigate chemotactic drift of peritrichous Escherichia coli under an exponential nutrient gradient. An exponential gradient is used to understand the steady state behavior of drift because of the logarithmic functionality of the chemosensory receptors. Our theoretical estimations are validated through the experimentation and simulation results. Thus, the developed model successfully delineates the run time, run trajectory, and drift velocity as measured from the experiments.

Stiffness distribution in insect cuticle: a continuous or a discontinuous profile?

Insect cuticle is a biological composite with a high degree of complexity in terms of both architecture and material composition. Given the complex morphology of many insect body parts, finite-element (FE) models play an important role in the analysis and interpretation of biomechanical measurements, taken by either macroscopic or nanoscopic techniques. Many previous studies show that the interpretation of nanoindentation measurements of this layered composite material is very challenging. To develop accurate FE models, it is of particular interest to understand more about the variations in the stiffness through the thickness of the cuticle. Considering the difficulties of making direct measurements, in this study, we use the FE method to analyse previously published data and address this issue numerically. For this purpose, sets of continuous or discontinuous stiffness profiles through the thickness of the cuticle were mathematically described. The obtained profiles were assigned to models developed based on the cuticle of three insect species with different geometries and layer configurations. The models were then used to simulate the mechanical behaviour of insect cuticles subjected to nanoindentation experiments. Our results show that FE models with discontinuous exponential stiffness gradients along their thickness were able to predict the stress and deformation states in insect cuticle very well. Our results further suggest that, for more accurate measurements and interpretation of nanoindentation test data, the ratio of the indentation depth to cuticle thickness should be limited to 7% rather than the traditional '10% rule'. The results of this study thus might be useful to provide a deeper insight into the biomechanical consequences of the distinct material distribution in insect cuticle and also to form a basis for more realistic modelling of this complex natural composite.

Online Learning Algorithm Based on Adaptive Control Theory.

This paper proposes a new online learning algorithm which is based on adaptive control (AC) theory, thus, we call this proposed algorithm as AC algorithm. Comparing to the gradient descent (GD) and exponential gradient (EG) algorithm which have been applied to online prediction problems, we find a new form of AC theory for online prediction problems and investigate two key questions: how to get a new update law which has a tighter upper bound on the error than the square loss? How to compare the upper bound for accumulated losses for the three algorithms? We obtain a new update law which fully utilizes model reference AC theory. Moreover, we present upper bound on the worst-case expected loss for AC algorithm and compare it with previously known bounds for the GD and EG algorithm. The loss bound we get in this paper is a time-varying function, which provides increasingly accurate estimates for upper bound. The AC algorithm has a much smaller loss only if the number of the samples meets certain conditions which can be seen in this paper. We also performed experiments which show that our update law is reasonably feasible and our upper bound is quite tight on both simple artificial and real data sets. The main contributions of this paper are twofold. First of all, we develop a new online algorithm called AC algorithm, and second, we obtain improved bounds, see Theorems 2-4 in this paper.

Exponential leap-forward gradient scheme for determining the isothermal layer depth from profile data

Two distinct layers usually exist in the upper ocean. The first has a near-zero vertical gradient in temperature (or density) from the surface and is called the isothermal layer (or mixed layer). Beneath that is a layer with a strong vertical gradient in temperature (or density), called the thermocline (or pycnocline). The isothermal layer depth (ILD) or mixed layer depth (MLD) for the same profile varies depending on the method used to determine it. Also, whether they are subjective or objective, existing methods of determining the ILD do not estimate the thermocline (pycnocline) gradient. Here, we propose a new exponential leap-forward gradient (ELG) method of determining the ILD that retains the strengths of subjective (simplicity) and objective (gradient change) methods and avoids their weaknesses (subjective methods are threshold-sensitive and objective methods are computationally intensive). This new method involves two steps: (1) the estimation of the thermocline gradient G th for an individual temperature profile, and (2) the computation of the vertical gradient by averaging over gradients using exponential leap-forward steps. Such averaging can filter out noise in the profile data. Five existing methods of determining the ILD (difference, gradient, maximum curvature, maximum angle, and optimal linear fitting methods) as well as the proposed ELG method were verified using global expendable bathythermograph (XBT) temperature and conductivity–temperature–depth (CTD) datasets. Among all the methods considered, the ELG method yielded the highest skill score and the lowest Shannon information entropy (i.e., the lowest uncertainty).