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In this work, we introduce Bloch waves to study the homogenization process in a class of simple laminates which are obtained as a particular Hashin-Shtrikman microstructure involving translations and dilations in only one direction. This makes this class of microstructures non necessarily periodic in the direction of lamination. We derive explicit formulae for the Bloch wave spectral representation of the homogenized coefficients.

In this paper, we use spectral methods to introduce Bloch waves for studying the homogenization process in the non-periodic class of generalized Hashin–Shtrikman micro-structures (see Ref. 35), which incorporates both translation and dilation with a family of scales, including one subclass of laminates. We establish the classical homogenization result by providing the spectral representation of the homogenized coefficients. It offers a new lead towards extending the Bloch spectral analysis to general micro-structures, including the class of non-periodic media or the homogenization of Heisenberg operators (see Refs. 8 and 9). [ABSTRACT FROM AUTHOR]

For a diffusion problem modeled by the p-Laplacian operator, we are interested in obtaining numerically the two-phase material which maximizes the internal energy. We assume that the amount of the best material is limited. In the framework of a relaxed formulation, we present two algorithms, a feasible directions method and an alternating minimization method. We show the convergence for both of them, and we provide an estimate for the error. Since for p>2 both methods are only well-defined for a finite-dimensional approximation, we also study the difference between solving the finite-dimensional and the infinite-dimensional problems. Although the error bounds for both methods are similar, numerical experiments show that the alternating minimization method works better than the feasible directions one. [ABSTRACT FROM AUTHOR]

We consider the optimal arrangement of two diffusion materials in a bounded open set Ω ... RN in order to maximize the energy. The diffusion problem is modeled by the p-Laplacian operator. It is well known that this type of problem has no solution in general and then that it is necessary to work with a relaxed formulation. In the present paper, we obtain such relaxed formulation using the homogenization theory; i.e., we replace both materials by microscopic mixtures of them. Then we get some uniqueness results and a system of optimality conditions. As a consequence, we prove some regularity properties for the optimal solutions of the relaxed problem. Namely, we show that the flux is in the Sobolev space H¹(Ω)N and that the optimal proportion of the materials is derivable in the orthogonal direction to the flux. This will imply that the unrelaxed problem has no solution in general. Our results extend those obtained by the first author for the Laplace operator. [ABSTRACT FROM AUTHOR]

We present a new basis of representation for the graphene honeycomb structure that facilitates the solution of the eigenvalue problem by reducing it to one dimension. We define spaces in these geometrical basis that allow us to solve the Hamiltonian in the edges of the lattice. We conclude that it is enough to analyze a one-dimensional problem in a set of coupled ordinary second-order differential equations to obtain the behavior of the solutions in the whole graphene structure. [ABSTRACT FROM AUTHOR]

Wolbachia are alpha-proteobacteria known to infect arthropods, which are of interest for disease control since they have been associated with improved resistance to viral infection. Although several genomes for different strains have been sequenced, there is little knowledge regarding the relationship between this bacterium and their hosts, particularly on their dependency for survival. Motivated by the potential applications on disease control, we developed genome-scale models of four Wolbachia strains known to infect arthropods: wAlbB (Aedes albopictus), wVitA (Nasonia vitripennis), wMel and wMelPop (Drosophila melanogaster). The obtained metabolic reconstructions exhibit a metabolism relying mainly on amino acids for energy production and biomass synthesis. A gap analysis was performed to detect metabolic candidates which could explain the endosymbiotic nature of this bacterium, finding that amino acids, requirements for ubiquinone precursors and provisioning of metabolites such as riboflavin could play a crucial role in this relationship. This work provides a systems biology perspective for studying the relationship of Wolbachia with its host and the development of new approaches for control of the spread of arboviral diseases. This approach, where metabolic gaps are key objects of study instead of just additions to complete a model, could be applied to other endosymbiotic bacteria of interest. [ABSTRACT FROM AUTHOR]

The method of asymptotic partial decomposition of a domain proposed and justified earlier for thin domains (rod structures, tube structures consisting of a set of thin cylinders) generates some special interface conditions between the three-dimensional and one-dimensional parts. In the case of fluid mechanics these conditions prescribe a precomputed Poiseuille-type shape of a solution at the interface, which, however, are not generalizable to the case with a boundary layer in time. In this work we present a new more general version of the method which considered and justified the transient Navier-Stokes equations. Although theoretical justification (well posedness, asymptotic analysis) can be shown only for moderate Reynolds numbers, the provided numerical tests show good accuracies for higher values. [ABSTRACT FROM AUTHOR]

In this work we develop a general mathematical model and devise a practical identifiability approach for gastrointestinal stromal tumor (GIST) metastasis to the liver, with the aim of quantitatively describing therapy failure due to drug resistance. To this end, we have modeled metastatic growth and therapy failure produced by resistance to two standard treatments based on tyrosine kinase inhibitors (Imatinib and Sunitinib) that have been observed clinically in patients with GIST metastasis to the liver. The parameter identification problem is difficult to solve, since there are no general results on this issue for models based on ordinary differential equations (ODE) like the ones studied here. We propose a general modeling framework based on ODE for GIST metastatic growth and therapy failure due to drug resistance and analyzed five different model variants, using medical image observations (CT scans) from patients that exhibit drug resistance. The associated parameter estimation problem was solved using the Nelder-Mead simplex algorithm, by adding a regularization term to the objective function to address model instability, and assessing the agreement of either an absolute or proportional error in the objective function. We compared the goodness of fit to data for the proposed model variants, as well as evaluated both error forms in order to improve parameter estimation results. From the model variants analyzed, we identified the one that provides the best fit to all the available patient data sets, as well as the best assumption in computing the objective function (absolute or proportional error). This is the first work that reports mathematical models capable of capturing and quantitatively describing therapy failure due to drug resistance based on clinical images in a patient-specific manner. [ABSTRACT FROM AUTHOR]

We consider the stationary Boussinesq system with non-homogeneous Dirichlet boundary conditions in a bounded domain of class with a possibly disconnected boundary. We prove the existence of weak solutions in , strong solutions in and very weak solutions in of the stationary Boussinesq system by assuming that the fluxes of the velocity are sufficiently small. Finally, as it is expected, we obtain the uniqueness of the solution by considering small data. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a macroscopic quantity, namely the dispersion tensor or the Burnett coefficients in the class of generalized Hashin-Shtrikman micro-structures (Tartar in The general theory of homogenization, volume 7 of Lecture notes of the Unione Matematica Italiana, Springer, Berlin, p 281, 2009). In the case of two-phase materials associated with the periodic Hashin-Shtrikman structures, we settle the issue that the dispersion tensor has a unique minimizer, which is the so called Apollonian-Hashin-Shtrikman micro-structure. [ABSTRACT FROM AUTHOR]

The authors study an integral inverse problem arising in the biology of the olfactory system. The transduction of an odor into an electrical signal is accomplished by a depolarising influx of ions through cyclic-nucleotide-gated (CNG for short) channels on the cilium membrane. The inverse problem studied in this paper consists in finding the spatial distribution of the CNG channels from the measured transduce electrical signals. The Mellin transform allows us to write an explicit formula for its solution. Proving observability and continuity inequalities is then a question of estimating the Mellin transform of the kernel of this integral equation on vertical lines. New estimates using arguments in the spirit of the stationary phase method are proven and a numerical scheme is proposed to reconstruct the density of CNG channels from modeled current representing experimental data, for an approximated model. For the original model an identifiability and a non observability (in some weighted L2 spaces) results are proven. [ABSTRACT FROM AUTHOR]

In this article, we study the approximate controllability and homegenization results of a semi-linear elliptic problem with Robin boundary condition in a periodically perforated domain. We prove the existence of minimal norm control using Lions constructive approach, which is based on Fenchel-Rockafeller duality theory, and by means of Zuazua's fixed point arguments. Then, as the homogenization parameter goes to zero, we link the limit of the optimal controls (the limit of fixed point of the controllability problems) with the optimal control of the corresponding homogenized problem. [ABSTRACT FROM AUTHOR]

We consider the problem of distributing two conducting materials with a prescribed volume ratio in a given domain so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions. The gap between the two conductivities is assumed to be small (low contrast regime). For any geometrical configuration of the mixture, we provide a complete asymptotic expansion of the first eigenvalue. We then consider a relaxation approach to minimize the second-order approximation with respect to the mixture. We present numerical simulations in dimensions two and three to illustrate optimal distributions and the advantage of using a second-order method. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

One of the main challenges in cancer modelling is to improve the knowledge of tumor progression in areas related to tumor growth, tumor-induced angiogenesis and targeted therapies efficacy. For this purpose, incorporate the expertise from applied mathematicians, biologists and physicians is highly desirable. Despite the existence of a very wide range of models, involving many stages in cancer progression, few models have been proposed to take into account all relevant processes in tumor progression, in particular the effect of systemic treatments and angiogenesis. Composite biological experiments, both in vitro and in vivo, in addition with mathematical modelling can provide a better understanding of theses aspects. In this work we proposed that a rational experimental design associated with mathematical modelling could provide new insights into cancer progression. To accomplish this task, we reviewed mathematical models and cancer biology literature, describing in detail the basic principles of mathematical modelling. We also analyze how experimental data regarding tumor cells proliferation and angiogenesis in vitro may fit with mathematical modelling in order to reconstruct in vivo tumor evolution. Additionally, we explained the mathematical methodology in a comprehensible way in order to facilitate its future use by the scientific community. [ABSTRACT FROM AUTHOR]

In this paper we study a linear inverse problem with a biological interpretation, which is modeled by a Fredholm integral equation of the first kind. When the kernel in the Fredholm equation is represented by step functions, we obtain identifiability, stability and reconstruction results. Furthermore, we provide a numerical reconstruction algorithm for the kernel, whose main feature is that a non-regular mesh has to be used to ensure the invertibility of the matrix representing the numerical discretization of the system. Finally, a second identifiability result for a polynomial approximation of degree less than nine of the kernel is also established. [ABSTRACT FROM AUTHOR]

For the parabolic–elliptic Keller–Segel system in 2 it has been proved that if the initial mass is less than 8π/χ, a global solution exists, and in case the initial mass is larger than 8π/χ, blow-up happens. The case of several chemotactic species introduces an additional question: What is the analog for the critical mass obtained for the single species system? We find a threshold curve in the two species case that allows us to determine if the system is a blow-up or a global in time solution. No radial symmetry is assumed. [ABSTRACT FROM AUTHOR]

The object of discussion of this article is the fourth-order tensor d introduced as a set of macro coefficients associated with fine periodic structures. Focus of attention is its variation on laminated microstructures. Complete bounds are obtained on its quartic form along with the corresponding optimal structures. Differences with corresponding results for the homogenized matrix are pointed out. Using Blossoming Principle, it is shown that d is not negative in the sense of Legendre–Hadamard, even though its quartic form is negative. [ABSTRACT FROM PUBLISHER]

For the Keller–Segel model, it was conjectured by Childress and Percus (1984, Chemotactic collapse in two dimensions. In Lecture Notes in Biomath. Vol. 55, Springer, Berlin-Heidelberg-New York, 1984, pp. 61–66) that in a two-dimensional domain there exists a critical number C such that if the initial mass is strictly less than C, then the solution exists globally in time and if it is strictly larger than C blowup happens. For different versions of the Keller–Segel model, the conjecture has essentially been proved. The case of several chemotactic species introduces an additional question: What is the analogue for the critical mass obtained for the single species system? In this paper, we investigate for a two-species model for chemotaxis in 2 the conditions on the initial data, which determine blowup or global existence in time. Specifically, we find a curve in the plane of masses such that outside of it there is blowup and inside of it global existence in time is proved when the initial masses satisfy a threshold condition. Optimality of this condition is discussed through an analysis in the radial case. Finally, we show in the case of blowup for general data how it is possible to obtain a balance between entropies and prove what species should aggregates first. [ABSTRACT FROM AUTHOR]

Background: Iron is essential for the maintenance of basic cellular processes. In the regulation of its cellular levels, ferritin acts as the main intracellular iron storage protein. In this work we present a mathematical model for the dynamics of iron storage in ferritin during the process of intestinal iron absorption. A set of differential equations were established considering kinetic expressions for the main reactions and mass balances for ferritin, iron and a discrete population of ferritin species defined by their respective iron content. Results: Simulation results showing the evolution of ferritin iron content following a pulse of iron were compared with experimental data for ferritin iron distribution obtained with purified ferritin incubated in vitro with different iron levels. Distinctive features observed experimentally were successfully captured by the model, namely the distribution pattern of iron into ferritin protein nanocages with different iron content and the role of ferritin as a controller of the cytosolic labile iron pool (cLIP). Ferritin stabilizes the cLIP for a wide range of total intracellular iron concentrations, but the model predicts an exponential increment of the cLIP at an iron content > 2,500 Fe/ferritin protein cage, when the storage capacity of ferritin is exceeded. Conclusions: The results presented support the role of ferritin as an iron buffer in a cellular system. Moreover, the model predicts desirable characteristics for a buffer protein such as effective removal of excess iron, which keeps intracellular cLIP levels approximately constant even when large perturbations are introduced, and a freely available source of iron under iron starvation. In addition, the simulated dynamics of the iron removal process are extremely fast, with ferritin acting as a first defense against dangerous iron fluctuations and providing the time required by the cell to activate slower transcriptional regulation mechanisms and adapt to iron stress conditions. In summary, the model captures the complexity of the iron-ferritin equilibrium, and can be used for further theoretical exploration of the role of ferritin in the regulation of intracellular labile iron levels and, in particular, as a relevant regulator of transepithelial iron transport during the process of intestinal iron absorption. [ABSTRACT FROM AUTHOR]

In this paper, we consider the macroscopic quantity, namely the dispersion tensor associated with a periodic structure in one dimension (see Refs. 5 and 7). We describe the set in which this quantity lies, as the microstructure varies preserving the volume fraction. [ABSTRACT FROM AUTHOR]