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Oscillations appear in all levels of biological organization. Oscillatory phenomena do not always possess a simple periodic nature. In this work, we analyze a gene transcriptional network in which we assume an almost periodic input that regulates gene. We use an almost periodic input k (t) since a periodic one is very restrictive. We show that the almost periodic model proposed has a unique almost periodic attractor. Numerical simulations show that the retroactivity is highly affected when an almost periodic input is used in an upstream system that is interconnected to a downstream system. By comparison of the solutions of the model, we can conclude that when the amount of protein bound to the promoter is modeled by either a periodic function or an almost periodic one, which is denoted by k (t) , the amount of protein concentration X can be underestimated or overestimated depending on if k (t) is modeling by a periodic or an almost periodic function. These estimation errors can lead to an error in the quantification of retroactivity which in turn can alter the coordination between an upstream system and a downstream one. [ABSTRACT FROM AUTHOR]

We incorporate almost periodic functions in a mosquito model to take into account a loss of synchronicity in the population dynamics of mosquitoes due to climate change. The model takes into account the skip oviposition strategy that is associated with the mosquitoes that are vectors of infectious diseases as dengue, malaria and leishmaniasis. We prove existence and uniqueness of a stable almost periodic solution for some conditions over the parameters of the model. Numerical simulations are performed using values estimated for the life cycle of Aedes albopictus gathered in literature. The results show that the vector population can be underestimated or overestimated if an almost periodic dynamics is approximated by a periodic dynamics. Therefore, using an almost seasonal model can be more adequate to design breeding habitat-targeted mosquito control strategies when seasonal drivers are modeled since climate-mediated shifts can induce a loss of periodicity in environmental drivers. [ABSTRACT FROM AUTHOR]

Modeling of multi-layered cell cultures (MCC) assume flat geometry in a 3D tumor growth model. Some results available in the time-dependent framework assume a periodic nutrient supply ф(t)/. Our aim is to generalize such considerations. Namely, we show that a stable oscillating tumor growth arises in the long term, whenever the mean value of the almost periodic nutrient supply ф surpasses certain threshold level, ф > σ. Meanwhile, a vanishing tumor is predicted in the complementary case, ф ≤σ. [ABSTRACT FROM AUTHOR]

In this work, we study models of enzyme-catalysed reactions which include an almost periodic substrate input. The main results are the existence, uniqueness and global stability of an almost periodic solution of the system under some restrictions on the parameters. [ABSTRACT FROM AUTHOR]

We consider the Dirichlet to Neumann operator for Abelian Yang-Mills boundary conditions. The aim is constructing a complex structure for the symplectic space of boundary conditions of Euler-Lagrange solutions modulo gauge for space-time manifolds with smooth boundary. Thus we prepare a suitable scenario for geometric quantization within the reduced symplectic space of boundary conditions of Abelian gauge fields. [ABSTRACT FROM AUTHOR]

We introduce a notion of measuring scales for quantum Abelian gauge systems. At each measuring scale a finite dimensional affine space stores information about the evaluation of the curvature on a discrete family of surfaces. Affine maps from the spaces assigned to finer scales to those assigned to coarser scales play the role of coarse graining maps. This structure induces a continuum limit space which contains information regarding curvature evaluation on all piecewise linear surfaces with boundary. The evaluation of holonomies along loops is also encoded in the spaces introduced here; thus, our framework is closely related to loop quantization and it allows us to discuss effective theories in a sensible way. We develop basic elements of measure theory on the introduced spaces which are essential for the applicability of the framework to the construction of quantum Abelian gauge theories. [ABSTRACT FROM AUTHOR]

We define a family of observables for abelian Yang-Mills fields associated to compact regions U ⊆ M with smooth boundary in Riemannian manifolds. Each observable is parametrized by a first variation of solutions and arises as the integration of gauge invariant conserved current along admissible hypersurfaces contained in the region. The Poisson bracket uses the integration of a canonical multisymplectic current. [ABSTRACT FROM AUTHOR]