Logarithmic Growth Rate Research Articles

Laminar burning velocity, cellular instability, and the superadiabatic flame temperature phenomenon for NH3/syngas/air premixed flames

The laminar burning velocity (LBV) and cellular instability of ammonia/syngas/air were investigated using the spherically expanding flame method at an initial pressure of 3 atm and temperatures of 298–448 K. The impacts of equivalence ratio, temperature, and hydrogen ratio on LBV were scrutinized. The results demonstrate that the LBV varies non-monotonically with the equivalence ratio and increases with increasing temperature and hydrogen ratio. Flame instability was analyzed using flame uplift rate, Lewis number, thermal expansion ratio, flame thickness, critical radius, critical Peclet number and logarithmic growth rate of perturbation in combination with the schlieren images. Of these, the flame uplift rate is used to quantify buoyancy instability, a flame instability that has received little attention. At high pressures, lower LBV makes the flame susceptible to buoyancy instability. The flame uplift rate increases with increasing flame radius, suggesting that the buoyancy instability becomes increasingly significant as the spherical flame expands. The diffusional-thermal instability is weaker at the fuel-rich side and enhanced at the leaner side. As the hydrogen ratio increases, the flame instability increases. Hydrodynamic instability is not susceptible to temperature, which is only slightly weakened with increasing temperature. Additionally, the phenomenon of superadiabatic flame temperature (SAFT) in ammonia/syngas/air flames was first found and analyzed its temperature dependence. Increasing the initial temperature suppresses SAFT occurrence.

Decay rate of discrete-time homogeneous delayed systems with cone invariance

This paper is dedicated to analysing the decay rate of discrete-time homogeneous delayed systems that exhibit order preservation within a proper cone. First, a sufficient criterion ensuring the cone invariance of the system is introduced. By exploring the monotonicity of system trajectories, a condition that is both sufficient and necessary for guaranteeing the asymptotic stability of the system is presented. Importantly, under a weak assumption for the growth rate of time-varying delays, a universal framework is provided for characterising the decay rate of the system. Furthermore, typical examples of decay rate analysis are presented when delays are bounded or experience linear, sublinear, or logarithmic growth rates. Eventually, the rationality of the results is illustrated through a numerical simulation.

A comprehensive data-driven odyssey to explore the equation of state of dark energy

For the first time, we reconstruct the dark energy equation of the state parameter w from the combination of background and perturbation observations, specifically combining the Hubble parameter data from cosmic chronometer observations and the logarithmic growth rate data from the growth rate observations. We do this analysis using posterior Gaussian process regression without considering any specific cosmological model or parametrization. However there are three main assumptions: (I) a flat Friedmann–Lemaître–Robertson–Walker (FLRW) metric is considered for the cosmological background, (II) there is no interaction between dark energy and matter sectors, and (III) for the growth of inhomogeneity, sub-Hubble approximation and linear perturbations are considered. This study is unique in the sense that the reconstruction of w is independent of any derived parameters such as the present values of the matter-energy density parameter and Hubble parameter. From the reconstruction, we look at how the dark energy equation of state evolves between redshifts 0 and 1.5, finding a slight hint of dynamical behavior in dark energy. However, the evidence is not significant. We also find a leaning towards non-phantom behavior over phantom behavior. We observe that the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model (w=-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(w=-1)$$\\end{document} nearly touches the lower boundary of the 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} confidence region in the redshift range 0.6≲z≲0.85.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.6 \\lesssim z \\lesssim 0.85.$$\\end{document} However, it comfortably resides within the 2σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} confidence region in the whole redshift range under investigation, 0≤z≤1.5.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0\\le z \\le 1.5.$$\\end{document} Consequently, the non-parametric, model-independent reconstruction of dark energy provides no compelling evidence to deviate from the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model when considering cosmic chronometer and growth rate observations.

Laminar burning velocity, radiative heat loss and cellular instability for NH3/biogas/H2/air premixed flame

This study presents, for the first time, a comprehensive investigation into the laminar flame propagation of ammonia/biogas/hydrogen/air mixtures. The laminar burning velocities (LBVs) were determined using the outwardly propagating spherical flame method under atmospheric temperature and elevated pressures across various equivalence ratios. The Okafor and CEU–NH3–Mech-1.1 mechanisms showed the best agreement with flame speed measurements. The influence of equivalence ratio, hydrogen ratio, and initial pressure on LBV was examined. Results indicate that LBV varies non-monotonically with the equivalence ratio, decreases with increasing pressure, and increases with higher hydrogen ratios. The enhancement of LBV due to hydrogen addition is mainly attributed to chemical effects, with thermal effects also playing a role. Given the significant CO2 content in biogas, which is a key radiative species, the study also analyzed the radiative heat loss of ammonia/biogas/hydrogen mixtures. It was found that as the equivalence ratio nears the flammability limit, LBV is more affected by radiative heat loss, with a lower hydrogen ratio increasing this effect. Additionally, higher CO2 mole fractions in biogas increase radiative heat loss. Detailed analysis of cellular instability, considering factors such as thermal expansion ratio, flame thickness, effective Lewis number, the logarithmic growth rate of perturbations and in conjunction with schlieren images, revealed that flame instability is enhanced with higher initial pressure and hydrogen ratios, while higher equivalence ratios inhibit instability.

Cellular instabilities of expanding hydrogen-propane-nitrous oxide spherical flames: Experiment and theory

The cellular instabilities of expanding hydrogen-propane-nitrous oxide spherical flames were experimentally and theoretically investigated at various equivalence ratios (ϕ=0.4–1.6), hydrogen fractions (XH=0–0.8), and initial pressures (Pu=1.1–1.5 bar). The experiments were conducted in a constant volume combustion chamber (CVCC) using high-speed schlieren technology to record the flame morphology, while the theoretical analysis was based on linear stability theory. The controlling parameters, critical conditions for the onset of instability, flame front oscillation intensity, logarithmic growth rate of perturbation, etc. were studied. The results indicate that the instability of premixed hydrogen-propane-nitrous oxide flames is dominated by hydrodynamic instability at XH≤0.6, while the competitive mechanism between thermal-diffusion and hydrodynamic instabilities is considered at XH=0.8. The oscillation intensity in the horizontal direction of the flame profile is more prominent than those in other directions, and with the increasing hydrogen fraction, the equivalence ratio at which the highest oscillation strength occurs shifts from ϕ=1.0 to ϕ=0.6. The trends of the experimental critical radius and Peclet number with each initial condition are completely identical to that of the theoretical value, but the experimental value is somewhat underpredicted. The three main reasons are proposed in the paper.Novelty and Significance Statement: This work is the first study on the cellular instabilities of hydrogen-propane-nitrous oxide flames by experiment and theory. It is under a small scale and reduced initial pressure condition that the cellular destabilization of hydrogen-propane flames is realized in the nitrous oxide atmosphere, while in the air atmosphere, the initial condition at which flame cellular destabilization occurs is harsher. Flame front oscillation strength, growth rate of disturbance, etc. were used to characterize quantitatively the degree of wrinkles and instabilities. Some novel findings were presented in the study. The present work is of great significance for the combustion community to understand deeply the cellular instabilities characteristic of expanding spherical flames supported by nitrous oxide, as well as for the engineering community to optimize the engine, propulsion, and energy supply systems, etc.

A Comparative Analysis of COVID-19 Response Measures and Their Impact on Mortality Rate

(1) Background: The coronavirus disease 2019 (COVID-19) pandemic significantly affected the population worldwide, with varying responses implemented to control its spread. This study aimed to compare the epidemic data compiled by the World Health Organization (WHO) to understand the impact of the measures adopted by each country on the mortality rate. (2) Methods: The increase or decrease in the number of confirmed cases was understood in logarithmic terms, for which logarithmic growth rates “K” were used. The mortality rate was calculated as the percentage of deaths from the confirmed cases, which was also used for logarithmic comparison. (3) Results: Countries that effectively detected and isolated patients had a mortality rate 10 times lower than those who did not. Although strict lockdowns were once effective, they could not be implemented on an ongoing basis. After their cancellation, large outbreaks occurred because of medical breakdowns. The virus variants mutated with increased infectivity, which impeded the measures that were once effective, including vaccinations. Although the designs of mRNA vaccines were renewed, they could not keep up with the virus mutation rate. The only effective defence lies in steadily identifying and isolating patients. (4) Conclusions: these findings have crucial implications for the complete containment of the pandemic and future pandemic preparedness.

E-values for k-Sample Tests with Exponential Families

AbstractWe develop and compare e-variables for testing whether k samples of data are drawn from the same distribution, the alternative being that they come from different elements of an exponential family. We consider the GRO (growth-rate optimal) e-variables for (1) a ‘small’ null inside the same exponential family, and (2) a ‘large’ nonparametric null, as well as (3) an e-variable arrived at by conditioning on the sum of the sufficient statistics. (2) and (3) are efficiently computable, and extend ideas from Turner et al. (2021) and Wald (1947) respectively from Bernoulli to general exponential families. We provide theoretical and simulation-based comparisons of these e-variables in terms of their logarithmic growth rate, and find that for small effects all four e-variables behave surprisingly similarly; for the Gaussian location and Poisson families, e-variables (1) and (3) coincide; for Bernoulli, (1) and (2) coincide; but in general, whether (2) or (3) grows faster under the alternative is family-dependent. We furthermore discuss algorithms for numerically approximating (1).

Hydrogen addition effect on cellularization and intrinsic instability of ethyl acetate spherical expanding flame

The cellularization and intrinsic instability of ethyl acetate (EA) spherical expanding flame with different proportions of hydrogen (4%, 8%, 12%) were studied through experiments and theoretical analysis. The high-speed schlieren imaging technique combined with the image processing method was used in the constant volume combustion chamber to quantify the development of flame surface cracks and saturation time, crack length, number of cellular units, and average cellular area. The results show that the evolution of flame cracks can be mainly classified into two periods. In the first period, several initial cracks are generated on the flame surface. In the second period, cracks rapidly expand while forming a large number of small cellular units, and the surface areas also increase rapidly. The increase in the proportion of hydrogen led to an increase in minor cellular cracks and a more moderate structural evolution of flame cells during the second period. Afterwards, the involved thermodynamic parameters, including the thermal expansion ratio, flame thickness, effective Lewis number, critical Peclet number, and perturbation logarithmic growth rate of unstable flames, were quantitatively analyzed. The results show that an increase in initial pressure significantly reduces the flame thickness, leading to more unstable flame. In contrast, the proportion of hydrogen has less impact on the involved thermodynamic parameters, while the equivalence ratio is the primary factor influencing instability parameters. Additionally, the study examined the flame's self-acceleration characteristics and found that increasing the proportion of hydrogen reduces the tendency for ethyl acetate self-acceleration.

On asymptotic log-optimal portfolio optimization

In this paper, we consider a frequency-dependent portfolio optimization problem with multiple assets using a control-theoretic approach. The expected logarithmic growth (ELG) rate of wealth is used as the objective performance metric. It is known that if the portfolio contains a special asset, the so-called dominant asset, then the optimal ELG level is achieved by investing all available funds in that asset. However, this “all-in” strategy is arguably too risky to implement. As a result, we study the case where the portfolio weights are chosen in a rather ad-hoc manner, and a linear buy-and-hold strategy is subsequently used. We show that if the underlying portfolio contains a dominant asset, buy and hold on that specific asset is asymptotically log-optimal with a logarithmic convergence rate. This result also extends to the scenario when a trader does not have a probabilistic model for returns or does not trust a model based on historical data. Specifically, we prove a version of the one fund theorem, which states that if a market contains a dominant asset, buying and holding a market portfolio with nonzero weights for each asset is asymptotically log-optimal. Additionally, we extend an existing result regarding the property called high-frequency maximality of an ELG-based portfolio from a single asset to a multi-asset portfolio case. This means that, in the absence of transaction costs, high-frequency rebalancing is unbeatable in terms of ELG. This result enables us to further improve the log-optimality obtained previously. Finally, we provide a result on the issue of how often a portfolio should be rebalanced, if needed. Examples using simulations with high-frequency historical trading data are included throughout to illustrate the theory.

Boosting Nitrogen Activation via Ag Nanoneedle Arrays for Efficient Ammonia Synthesis

Electrocatalytic N2 reduction reaction (eNRR) provides a promising carbon-neutral and sustainable ammonia-synthesizing alternative to the Haber-Bosch process. However, the nonpolar N2 has significant thermodynamic stability and requires ultrahigh energy to break down the N≡N bond. Here, we report the construction of local enhanced electric fields (LEEFs) by Ag nanoneedle arrays to promote N≡N fracture thus assisting the eNRR. The LEEFs could induce charge polarization on nitrogen atoms and reduce the energy barrier in the N2 first-protonation step. The detected N─N and N─H intermediates prove the cleavage of the N≡N bond and the hydrogenation of N2 by LEEFs. The increased LEEFs lead to logarithmic growth rates for the targeted eNRR and exponential growth rates for the unavoidable competitive hydrogen evolution reaction. Thus, regulation and tuning of LEEFs to ∼4 × 104 kV m-1 endows the raise of eNRR to the summit, achieving high ammonia selectivity with a Faradaic efficiency of 72.3 ± 4.0%.

Fast computation of non-linear power spectrum in cosmologies with massive neutrinos

We compute 1-loop corrections to the redshift space galaxy power spectrum in cosmologies containing additional scales, and hence kernels different from Einstein-de Sitter (EdS). Specifically, our method is tailored for cosmologies in the presence of massive neutrinos and some modified gravity models; in this article we concentrate on the former case. The perturbative kernels have contributions that we notice appear either from the logarithmic growth rate f(k,t), which is scale-dependent because of the neutrino free-streaming, or from the failure of the commonly used approximation f 2 = Ω m . The latter contributions make the computation of loop corrections quite slow, precluding full-shape analyses for parameter estimation. However, we identify that the dominant pieces of the kernels come from the growth factor, allowing us to simplify the kernels but retaining the characteristic free-streaming scale introduced by the neutrinos' mass. Moreover, with this simplification one can exploit FFTLog methods to speed up the computations even more. We validate our analytical modeling and numerical method with halo catalogs extracted from the Quijote simulations finding good agreement with the, a priori, known cosmological parameters. We make public our Python code FOLPSν to compute the redshift space power spectrum in a fraction of second. Code available at https://github.com/henoriega/FOLPS-nu.

COVID-19 Epidemics Monitored Through the Logarithmic Growth Rate and SIR Model

The SIR model is often used to analyse and forecast an epidemic. In this model, the number of patients exponentially increases and decreases in the early and late phases; hence the logarithmic growth rate K is constant at the phases. However, in the case of COVID-19 epidemics, K never remains constant but increases and decreases linearly. Simulation showed that a situation in which smaller epidemics were repeated with short time intervals makes the changes in K; it also showed relationship between K to the mean infectious time τ and the basic reproduction number R0. Using this relationship, we analysed epidemic data from 279 countries and regions. The changes in K represented the state of the epidemics and were several weeks to a month ahead of the changes in the number of confirmed cases. If the negative peaks of K could not be reduced to 0.1, the number of patients remained high. To control the epidemic, it was important to observe K daily, not to allow K to remain positive continuously and to terminate a peak with a series of K-negative days. To accomplish this, it was necessary to shorten τ by finding and isolating a patient earlier.

Continuality of classes of functions in multivalued logic with minimal logarithmic growth rate

Abstract We show that in multivalued logic there exist a continual family of pairwise incomparable closed sets with minimal logarithmic growth rate and a continual chain of nested closed sets with minimal logarithmic growth rate. As a corollary we prove that any subset-preserving class in multivalued logic contains a continual chain of nested closed sets and a continual family of pairwise incomparable closed sets such that none of the sets is a subset of any other precomplete class.

Investigation on hydrogen/ethanol intrinsic flame instability

The instability of laminar premixed hydrogen–ethanol flame was studied under different initial pressure, hydrogen ratio, and equivalence ratio conditions by using a constant volume combustion bomb. The unstable laminar premixed flame was measured using its thermal expansion ratio, flame thickness, effective Lewis number, and logarithmic growth rate of perturbation. The results demonstrated that the thermal expansion ratio and effective Lewis number were insensitive to initial pressure variation, but hydrogen ratio variation was significantly affected. The linear stability analysis indicated that when the hydrogen ratio increased, the premixed flame became hydrodynamically unstable; thermal diffusion effects later stabilized the flame as the hydrogen ratio increased. The critical radius and Peclet number decreased with the increased equivalence ratio of a 20% hydrogen mixture, but both parameters increased with an increased equivalence ratio under an 80% hydrogen ratio. Finally, the growth rate of perturbation decreased when the equivalence ratio increased.

Effect of control measures on the pattern of COVID-19 Epidemics in Japan.

BackgroundCOVID-19 has spread worldwide since its emergence in 2019. In contrast to many other countries with epidemics, Japan differed in that it avoided lockdowns and instead asked people for self-control. A travel campaign was conducted with a sizable budget, but the number of PCR tests was severely limited. These choices may have influenced the course of the epidemic.MethodsThe increase or decrease in the classes of SARS-CoV-2 variants was estimated by analyzing the published sequences with an objective multivariate analysis. This approach observes the samples in multiple directions, digesting complex differences into simpler forms. The results were compared over time with the number of confirmed cases, PCR tests, and overseas visitors. The kinetics of infection were analyzed using the logarithmic growth rate.ResultsThe declared states of emergency failed to alter the movement of the growth rate. Three epidemic peaks were caused by domestically mutated variants. In other countries, there are few cases in which multiple variants have peaked. However, due to the relaxation of immigration restrictions, several infective variants have been imported from abroad and are currently competing for expansion, creating the fourth peak. By April 2021, these foreign variants exceeded 80%. The chaotic situation in Japan will continue for some time, in part because no effort has been made to identify asymptomatic carriers, and details of the vaccination program are undecided.

Evolution of heterogeneity under constant and variable environments.

Various definitions of fitness are essentially based on the number of descendants of an allele or a phenotype after a sufficiently long time. However, these different definitions do not explicate the continuous evolution of life histories. Herein, we focus on the eigenfunction of an age-structured population model as fitness. The function generates an equation, called the Hamilton-Jacobi-Bellman equation, that achieves adaptive control of life history in terms of both the presence and absence of the density effect. Further, we introduce a perturbation method that applies the solution of this equation to the long-term logarithmic growth rate of a stochastic structured population model. We adopt this method to realize the adaptive control of heterogeneity for an optimal foraging problem in a variable environment as the analyzable example. The result indicates that the eigenfunction is involved in adaptive strategies under all the environments listed herein. Thus, we aim to systematize adaptive life histories in the presence of density effects and variable environments using the proposed objective function as a universal fitness candidate.

Improving phase stability, hardness, and oxidation resistance of reactively magnetron sputtered (Al,Cr,Nb,Ta,Ti)N thin films by Si-alloying

Reactively magnetron sputtered high-entropy metal-sublattice (Al,Cr,Nb,Ta,Ti)N coatings have been alloyed with Si concentrations between x Si = 6.4 and 15.0 at.%. All coatings are single-phase fcc structured and their hardness initially increases from ~32 to 35 GPa with Si-alloying up to x Si = 9.8 at.%, and then decreases to ~24 GPa for higher Si contents. Contrary, the indentation modulus E continuously decreases from ~470 to 350 GPa by Si-alloying. Also, the decomposition of the fcc structure during vacuum annealing is shifted from 1000 to 1200 °C with the addition of Si. The hardness initially increases during vacuum annealing and reaches a maximum of 37 GPa with T a = 1000 °C at x Si = 12.0 at.%. During oxidation experiments in ambient air at 850 °C for up to 100 h, a 2700 nm single-phase rutile-structured oxide scale forms at the Si-free (Al,Cr,Nb,Ta,Ti)N with a parabolic growth rate. The rate changes to a logarithmic-like behavior with the addition of Si, resulting in only ~280 nm oxide scale after 100 h. Also, for the Si-containing coatings, the oxide scale shows only one crystalline rutile structure. The pore size in the oxide scale of the Si-free coating is considerably reduced by Si-addition. The oxides growing at the Si-containing coatings show an opposing Si- and Cr-gradient - with much smaller pores in the Si-rich inner region - which shows a gradual transition to the remaining nitride. Ab initio based calculations confirm that the formation of a single-phase rutile-structured solid solution oxide, (Al,Cr,Nb,Ta,Ti)O 2 , is energetically preferred over separate phases above 509 K, due to the higher configurational entropy. Below this temperature the decomposition towards (Al,Ta,Ti)O 2 + (Cr,Nb)O 2 would be favored (when considering just chemical contributions), but kinetically restricted. • Reactively sputtered fcc-(Al,Cr,Nb,Ta,Ti)N alloyed with Si • Improved phase stability in vacuum, hardness, and lower E -modulus • Logarithmic oxide growth rate in ambient air at 850 °C • Single phase rutile structured oxide forms during oxidation. • Ab-initio calculations confirm thermodynamically stable (Al,Cr,Nb,Ta,Ti)O 2 phase.

Galaxy skew-spectra in redshift-space

Modern galaxy surveys focus on the galaxy power spectrum or 2-point correlation function to test and constrain cosmological models.Additional information comes from higher-order N-point functions, but their analysis is challenging. A simple solution is to compute the cross-power spectrum between the squared galaxy density and the galaxy density. Being simple to measure and to plot, this skew-spectrum shares many of the familiar useful properties of the standard galaxy power spectrum. We show that by computing multiple quadratic fields and correlating them with the density, all contributions to the tree-level redshift-space galaxy bispectrum can be captured with skew-spectra. Using synthetic datasets, we show that our measurement pipeline matches analytical predictions, and that their dependence on galaxy bias parameters and the logarithmic growth rate is as expected theoretically.

Boundary Values in Ultradistribution Spaces Related to Extended Gevrey Regularity

Following the well-known theory of Beurling and Roumieu ultradistributions, we investigate new spaces of ultradistributions as dual spaces of test functions which correspond to associated functions of logarithmic-type growth at infinity. In the given framework we prove that boundary values of analytic functions with the corresponding logarithmic growth rate towards the real domain are ultradistributions. The essential condition for that purpose, known as stability under ultradifferential operators in the classical ultradistribution theory, is replaced by a weaker condition, in which the growth properties are controlled by an additional parameter. For that reason, new techniques were used in the proofs. As an application, we discuss the corresponding wave front sets.

Aggregating exponential gradient expert advice for online portfolio selection

In recent years, online portfolio selection, one of the fundamental problems in computational finance, has attracted increasing interest from online learning. Although existing online portfolio strategies have been shown to achieve good performance, appropriate values of their parameters need to be set in advance. However, the optimal values can only be known in hindsight. To overcome this limitation, this paper proposes a new online portfolio strategy by aggregating exponential gradient (EG) expert advice using the weak aggregating algorithm (WAA). First, we consider a pool of EG strategies with different learning rates as experts, and compute the portfolio on the next period by aggregating all the expert advice using the WAA according to their previous performance. Second, we theoretically prove that the proposed strategy is universal, i.e. its average logarithmic growth rate is asymptotically the same as that of the best constant rebalanced portfolio (BCRP) in hindsight. Finally, we conduct extensive experiments to examine the performance of the proposed strategy on actual stock market. Numerical results show that the proposed strategy overcomes the drawbacks of existing online strategies and achieves significant performance.