Revised Michaelis-Menten rate law with time-varying molecular concentrations

Despite over a century's use as a dominant paradigm in the description of biochemical rate processes, the Michaelis-Menten (MM) rate law stands on the restrictive assumption that the concentration of the complex of interacting molecules, at each moment, approaches an equilibrium much faster than the molecular concentration changes. The increasingly-appreciated, remedied form of the MM rate law is also based on this quasi-steady state assumption. Although this assumption may be valid for a range of biochemical systems, the exact extent of such systems is not clear. In this study, we relax the quasi-steady state requirement and propose the revised MM rate law for the interactions of molecules with active concentration changes over time. Our revised rate law, characterized by rigorously-derived time delay effects in molecular complex formation, improves the accuracy of models especially for protein-protein and protein-DNA interactions. Our simulation and empirical data analysis show that the improvement is not limited to the quantitatively better characterization of the dynamics, but also allows the prediction for qualitatively new patterns in the systems of interest. The latter include the oscillation condition and period patterns of the mammalian circadian clock and the spontaneous rhythmicity in the degradation rates of circadian proteins, both not properly captured by the previous approaches. Moreover, our revised rate law is capable of more accurate parameter estimation. This work offers an analytical framework for understanding rich dynamics of biomolecular systems, which goes beyond the quasi-steady state assumption.

Stabilization of Switched Time-Delay Linear Systems through a State-Dependent Switching Strategy

This paper considers the problem of stabilizing switched time-delay linear systems through a state-dependent switching strategy. In contrast to the existing works, we adopt a less restrictive assumption of the system, and show that this assumption is sufficient to guarantee asymptotic stability of the considered system under the min-projection switching strategy. Our results also imply that the min-projection switching strategy, originally designed for delay-free switched systems, is robust with respect to small state delays. An optimization problem is formulated to estimate the upper bound of the tolerable time delay. Numerical examples are presented to show that our method is applicable to a larger class of switched systems and leads to a greater delay bound.

ASYMPTOTIC PROPERTIES IN THE PROBIT-ZERO-INFLATED BINOMIAL REGRESSION MODEL

Zero-inflated regression models have had wide application recently and have provenuseful in modeling data with many zeros. Zero-inflated Binomial (ZIB) regression model is an extension of the ordinary binomial distribution that takes into account the excess of zeros. In comparing the probit model to the logistic model, many authors believe that there is little theoretical justification in choosing one formulation over the other in most circumstances involving binary responses. The logit model is considered to be computationally simpler but it is based on a more restrictive assumption of error independence, although many other generalizations have dealt with that assumption as well. By contrast, the probit model assumes that random errors have a multivariate normal distribution. This assumption makes the probit model attractive because the normal distribution provides a good approximation to many other distributions. In this paper, we develop a maximum likelihood estimation procedure for the parameters of a zero-inflated Binomial regression model with probit link function for both component of the model. We establish the existency, consistency and asymptotic normality of the proposed estimator.

On the Convergence of LHAM and its Application to Fractional Generalised Boussinesq Equations for Closed Form Solutions

By fractional generalised Boussinesq equations we mean equations of the form \begin{equation} \Delta\equiv D_{t}^{2\alpha}-[\mathcal{N}(u)]_{xx}-u_{xxxx}=0, \: 0<\alpha\le1,\label{main}\nonumber \end{equation} where $\mathcal{N}(u)$ is a differentiable function and $\mathcal{N}_{uu}\ne0$ (to ensure nonlinearity). In this paper we lay emphasis on the cubic Boussinesq and Boussinesq-like equations of fractional order and we apply the Laplace homotopy analysis method (LHAM) for their rational and solitary wave solutions respectively. It is true that nonlinear fractional differential equations are often difficult to solve for their {\em exact} solutions and this single reason has prompted researchers over the years to come up with different methods and approach for their {\em analytic approximate} solutions. Most of these methods require huge computations which are sometimes complicated and a very good knowledge of computer aided softwares (CAS) are usually needed. To bridge this gap, we propose a method that requires no linearization, perturbation or any particularly restrictive assumption that can be easily used to solve strongly nonlinear fractional differential equations by hand and simple computer computations with a very quick run time. For the closed form solution, we set $\alpha =1$ for each of the solutions and our results coincides with those of others in the literature.

Fuzzy-based adaptive asymptotic tracking control design for uncertain MIMO nonlinear systems with state constraints

This article concentrates on designing an adaptive fuzzy asymptotic tracking control strategy for uncertain multi-input and multi-output (MIMO) nonlinear systems with state constraints and unknown virtual control coefficients (UVCCs). Such design apply the fuzzy logic systems to approximate unknown dynamics, and an asymptotic controller is recursively constructed by employing a bound estimation method and some smooth functions. The predefined state constrains are guaranteed by virtue of barrier Lyapunov function. Different from the reporting achievements, the restrictive assumption about the prior knowledge of UVCCs is removed in our context. By fusing the lower bounds of UVCCs into iterative Lyapunov functions, the stability of the controlled system is guaranteed. Finally, simulation example is conducted to exhibit the validity of theoretical findings.

Crossing Empirical Trend Analysis (CETA) At Risk Levels In Hydro-Meteorological Time Series

Trend identification procedures are employed to determine the systematic monotonic trend lines in a given hydro-meteorological time series records for depiction of time dependent changes in the form of increase or decrease. Different methodologies are proposed for such identifications, but most of them require restrictive assumptions such as the normal (Gaussian) probability distribution, serial independence and long sample sizes. In order to relieve especially the serial independence requirement pre-whitening and over-whitening procedures are suggested, but they cannot render a serially dependent series into completely independent structure. In this paper, a new trend methodology is proposed on the basis of crossing features along any given straight-line within the given time series and the one with the maximum crossing number is the searched trend component. This approach does not require any restrictive assumption. Contrary to the previous trend algorithms, the suggested crossing empirical trend analysis (CETA) yields not a single trend, but a set of trends at different levels within the variation range of hydro-meteorological time series records. In this paper for the sake of brevity only three levels are considered at 10%, 50% and 90% risk levels. The comparison of the CETA approach is presented with the classical and frequently used method of Mann-Kendall (MK) trend identification procedure based on the Sen’s slope calculation. For small serial correlation coefficients and normal probability distribution (PDF) function cases CETA and classical technique yield almost the same trend line within +5% error band limits. The application of this methodology is presented for monthly and annual discharge records of Danube River and annual precipitation records from seven geographical regions of Turkey.

Higher integrability for variational integrals with non-standard growth

We consider autonomous integral functionals of the form $$\begin{aligned} {\mathcal {F}}[u]:=\int _\varOmega f(D u)\,dx \quad \text{ where } u:\varOmega \rightarrow {\mathbb {R}}^N, N\ge 1, \end{aligned}$$ F [ u ] : = ∫ Ω f ( D u ) d x where u : Ω → R N , N ≥ 1 , where the convex integrand f satisfies controlled (p, q)-growth conditions. We establish higher gradient integrability and partial regularity for minimizers of $${\mathcal {F}}$$ F assuming $$\frac{q}{p}<1+\frac{2}{n-1}$$ q p < 1 + 2 n - 1 , $$n\ge 3$$ n ≥ 3 . This improves earlier results valid under the more restrictive assumption $$\frac{q}{p}<1+\frac{2}{n}$$ q p < 1 + 2 n .

The rigid hybrid number for two phylogenetic trees

Recently there has been considerable interest in the problem of finding a phylogenetic network with a minimum number of reticulation vertices which displays a given set of phylogenetic trees, that is, a network with minimum hybrid number. Such networks are useful for representing the evolution of species whose genomes have undergone processes such as lateral gene transfer and recombination that cannot be represented appropriately by a phylogenetic tree. Even so, as was recently pointed out in the literature, insisting that a network displays the set of trees can be an overly restrictive assumption when modeling certain evolutionary phenomena such as incomplete lineage sorting. In this paper, we thus consider the less restrictive notion of rigidly displaying which we introduce and study here. More specifically, we characterize when two trees can be rigidly displayed by a certain type of phylogenetic network called a temporal tree-child network in terms of fork-picking sequences. These are sequences of special subconfigurations of the two trees related to the well-studied cherry-picking sequences. We also show that, in case it exists, the rigid hybrid number for two phylogenetic trees is given by a minimum weight fork-picking sequence for the trees. Finally, we consider the relationship between the rigid hybrid number and three closely related numbers; the weak, beaded, and temporal hybrid numbers. In particular, we show that these numbers can all be different even for a fixed pair of trees, and also present an infinite family of pairs of trees which demonstrates that the difference between the rigid hybrid number and the temporal-hybrid number for two phylogenetic trees on the same set of n leaves can grow at least linearly with n.

CROSS-SHORE MODEL APPLICATION TO HASAKI BEACH, JAPAN: EVALUATION OF PARAMETER SETTING

Japan's coasts is being suffered by significant erosion. There is already a high demand to protect coasts from the erosion but climate change threatens further erosion. Udo and Takeda (2017) projected future beach loss in Japan due to sea-level rise using Bruun rule. However, its restrictive assumption that they probably do not exist in nature makes difficult to assess uncertainties of the projection results. In this paper, Cross-shore (CS) model developed by Larson et al. (2016), which is more realistic model considering the cross-shore sediment exchange, is applied to calibrate the parameter settings at Hasaki beach in Japan, and model applicability was evaluated.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/sOFr9Jb5a_s

Robustness of phylogenetic inference to model misspecification caused by pairwise epistasis

Likelihood-based phylogenetic inference posits a probabilistic model of character state change along branches of a phylogenetic tree. These models typically assume statistical independence of sites in the sequence alignment. This is a restrictive assumption that facilitates computational tractability, but ignores how epistasis, the effect of genetic background on mutational effects, influences the evolution of functional sequences. We consider the effect of using a misspecified site-independent model on the accuracy of Bayesian phylogenetic inference in the setting of pairwise-site epistasis. Previous work has shown that as alignment length increases, tree reconstruction accuracy also increases. Here, we present a simulation study demonstrating that accuracy increases with alignment size even if the additional sites are epistatically coupled. We introduce an alignment-based test statistic that is a diagnostic for pair-wise epistasis and can be used in posterior predictive checks.