Applied Mathematics Letters

We improve the lower bound on the extremal version of the Maximum Agreement Subtree problem. Namely we prove that two binary trees on the same n leaves have subtrees with the same ≥ c log log n leaves which are homeomorphic, such that homeomorphism is identity on the leaves.

We developed a series of models for the label decay in cell proliferation assays when the intracellular dye carboxyfluorescein succinimidyl ester (CFSE) is used as a staining agent. Data collected from two healthy patients were used to validate the models and to compare the models with the Akiake Information Criteria. The distinguishing features of multiple decay rates in the data are readily characterized and explained via time dependent decay models such as the logistic and Gompertz models.

We formulated a structured population model with distributed parameters to identify mechanisms that contribute to gene expression noise in time-dependent flow cytometry data. The model was validated using cell population-level gene expression data from two experiments with synthetically engineered eukaryotic cells. Our model captures the qualitative noise features of both experiments and accurately fit the data from the first experiment. Our results suggest that cellular switching between high and low expression states and transcriptional re-initiation are important factors needed to accurately describe gene expression noise with a structured population model.

We formulate an optimal design problem for the selection of best states to observe and optimal sampling times and locations for parameter estimation or inverse problems involving complex nonlinear nonlinear partial differential systems. An iterative algorithm for implementation of the resulting methodology is proposed.

There are two simple solutions to reaction-diffusion systems with limit-cycle reaction kinetics, producing oscillatory behaviour. The reaction parameter mu gives rise to a 'space-invariant' solution, and mu versus the ratio of the diffusion coefficients gives rise to a 'time-invariant' solution. We consider the case where both solution types may be possible. This leads to a refinement of the Turing model of pattern formation. We add convection to the system and investigate its effect. More complex solutions arise that appear to combine the two simple solutions. The convective system sheds light on the underlying behaviour of the diffusive system.

We formalize an algorithm for solving the L(1)-norm best-fit hyperplane problem derived using first principles and geometric insights about L(1) projection and L(1) regression. The procedure follows from a new proof of global optimality and relies on the solution of a small number of linear programs. The procedure is implemented for validation and testing. This analysis of the L(1)-norm best-fit hyperplane problem makes the procedure accessible to applications in areas such as location theory, computer vision, and multivariate statistics.

We present a general class of cell population models that can be used to track the proliferation of cells which have been labeled with a fluorescent dye. The mathematical models employ fluorescence intensity as a structure variable to describe the evolution in time of the population density of proliferating cells. While cell division is a major component of changes in cellular fluorescence intensity, models developed here also address overall label degradation.

The authors consider a partially replicated distributed database located on a tree network each of whose links may fail with a probability p . For small p they derive necessary conditions for optimal placement of copies in order to maximize the probabilities of successful read-only and write-only transactions. These results suggest several heuristics for general networks. Numerical results are presented

Queueing networks of the product-form type are widely used as models in the analysis and design of computer and telecommunication systems. But for many systems (closed networks or others with population constraints), the product form solution involves a normalization constant, whose calculation is not trivial. Harrison (1985) obtained some closed form expression for normalization constants. The method was elaborated by Gordon (1990). We propose an alternative method to obtain the closed form formula for normalization constants. Our approach is based on the fact that calculation of these normalization constants involves convolution procedures. The approach is a straightforward application of Z-transform

A (105, 10, 47) binary quasi-cyclic code is presented which improves the known lower bound on the maximum possible minimum distance. The generator matrix is characterized in terms of m × m circulant matrices, where m = 5. This code is extended with an even parity check bit to a (106, 10, 48) code which also improves the known bound. The weight distributions of these codes are presented.

Given non-negative integers j and k, an L(j,k)- of a graph G is a function f from the vertex set V(G) to the set of all non-negative integers such that |f(x)−f(y)|≥j if d(x,y)=1 and |f(x)−f(y)|≥k if d(x,y)=2. The L(j,k)-labeling number λj,k is the smallest number m such that there is an L(j,k)-labeling with the largest value m and the smallest label 0. This paper presents upper bounds on λ2,1 and λ2,1 of a graph G in terms of the maximum degree of G for several classes of planar graphs. These bounds are the same as or better than previous results for the maximum degree less than or equal to 4.

Explicit expressions for two-dimensional (2D) Green's functions in piezoelectric crystals of general anisotropy are derived. The Green's functions are used to produce the general solution for 2D problems in piezoelectric media. Evaluation for degenerate materials is also discussed.

I will prove a recurrence theorem which says that any H-s (s > 2) solution to the 2D inviscid channel flow returns repeatedly to an arbitrarily small H-0 neighborhood. The periodic boundary condition is imposed along the stream-wise direction. The result is an extension of an early result of Li [Y. Li, A recurrence theorem on the solutions to the 2D Euler equation, Asian J. Math. 13 (1) (2009) 1-6] on the 2D Euler equation under periodic boundary conditions along both directions. (c) 2012 Elsevier Ltd. All rights reserved.

We present a very simple proof of the global existence of a $C^\infty$ Lagrangian flow map for the 2D Euler and second-grade fluid equations (on a compact Riemannian manifold with boundary) which has $C^\infty$ dependence on initial data $u_0$ in the class of $H^s$ divergence-free vector fields for $s>2$.

We study the existence of positive solutions of the differential equation (−1)my(2m) (t) = f(t, y(t), y″(t),…, y(2(m−1)) (t)) with the boundary condition y(2i)(0) = 0 = y(2i)(1), 0 ≤ i ≤ m − 1, and y(2i)(0) = 0 = y(2i+1)(1), 0 ≤ i ≤ m − 1. We show the existence of at least one positive solution if f is either superlinear or sublinear by an application of a fixed-point theorem in a cone.

In the immersed interface method, a boundary immersed in a fluid is represented as a singular force in the Navier–Stokes equations. An explicit approach was proposed recently for determining the singular force for the boundary of a rigid object with prescribed motion in 2D [Sheng Xu, The immersed interface method for simulating prescribed motion of rigid objects in an incompressible viscous flow, J. Comput. Phys. 227 (2008) 5045–5071]. Necessary formulas for extending the approach to 3D are derived in this work. With the implementation of these formulas, the immersed interface method can accurately, stably, and efficiently simulate the prescribed motion of rigid objects in 3D.

We prove existence on infinite time intervals of regular solutions to the 3D rotating Navier-Stokes equations in the limit of strong rotation (large Coriolis parameter Ω). This uniform existence is proven for periodic or stress-free boundary conditions for all domain aspect ratios, including the case of three wave resonances which yield nonlinear “” limit equations; smoothness assumptions are the same as for local existence theorems. The global existence is proven using techniques of the Littlewood-Paley dyadic decomposition. Infinite time regularity for solutions of the 3D rotating Navier-Stokes equations is obtained by bootstrapping from global regularity of the limit equations and convergence theorems.

This paper presents a 3D mesh-aligning algorithm for convection-dominated convection-diffusion problems. The main difference between this algorithm and the 2D edge-swapping algorithms is that instead of swapping faces it splits the adjacent tetrahedra to obtain a more flow-aligned mesh, and thereby, increase solution accuracy without increasing the number of meshpoints.

A dynamics for frequency dependent selection is proposed and applied to several biological examples. The relation with game dynamics and evolutionary stability is analyzed.

We provide a mathematical technique leading to the construction of exact analytic solutions of the classes of Abel’s nonlinear ordinary differential equations (ODEs) of the second kind, as well as of the restricted form of the Abel nonlinear ODE of the first kind.

A mathematical model for endothelial cell migration during tumour-induced angiogenesis is presented. A possible explanation, in terms of desensitisation of cell-surface receptors, is given for the experimentally observed fact that without cell proliferation tumour vascularisation is never achieved.

An analysis of a parabolic partial differential equation modelling capillary network formation is presented. The model includes terms representing cell random motility, chemotaxis, and haptotaxis due to the presence of chemical stimuli: tumour angiogenic factors and fibronectin. The analysis provides an underlying insight into mechanisms of cell migration which are crucial for tumour angiogenesis. Specific 1 and 2D examples are discussed in detail.

A large number of studies have been made on the predator-prey system with Holling's functional response, namely, ø(χ) = χn/(a + χn) (n = 1, 2). This paper presents a sufficient condition under which the predator-prey system has no limit cycles for n = 3. The argument used here is based on a result of Liénard dynamics. The relation between previous results (n = 1, 2) and our result (n = 3) is cleared. Some phase portraits of trajectories of the predator-prey system are also given as an example of our result.

We consider a simplified Newton's cradle, which would be unobservable if the non-smooth impacts between the spheres were ignored. Nevertheless, under the assumption that there is an infinite sequence of nonsmooth impacts, it is possible to design an observer that is able to asymptotically estimate all the nonmeasurable state variables, including those that would be unobservable in absence of impacts.

In this paper, a general theorem of |A|k summability factors is presented. This generalization is accomplished by replacing the weighted mean matrix in Mazhar’s theorem in [S.M. Mazhar, A remark on a recent result on absolute summability factors, Indian J. Math. 40 (2) (1998) 123–131] with a triangular matrix.