In this paper, the methodology of the so-called Linear Irreversible Thermodynamics (LIT) is applied to analyze the properties of an energetic-converting biological process using simple model for an enzymatic reaction that couples one exothermic and one endothermic reaction in the same fashion as Diaz-Hernandez et al. (Physica A, 2010, 389, 3476–3483). We extend the former analysis to consider three different operating regimes; namely, Maximum Power Output (MPO), Maximum Ecological Function (MEF) and Maximum Efficient Power Function (MEPF), respectively. Based on the later, it is possible to generalize the obtained results. Additionally, results show analogies in the optimal performance between the different optimization criteria where all thermodynamic features are determined by three parameters (the chemical potential gap $\Delta =\frac{{\mu }_1-{\mu }_4}{RT}$ , the degree of coupling q and the efficiency $\eta$ ). This depends on the election that leads to more or less efficient energy exchange.

The infusion times and drug quantities are two primary variables to optimize when designing a therapeutic schedule. In this work, we test and analyze several extensions to the gradient descent equations in an optimal control algorithm conceived for therapy scheduling optimization. The goal is to provide insights into the best strategies to follow in terms of convergence speed when implementing our method in models for dendritic cell immunotherapy. The method gives a pulsed-like control that models a series of bolus injections and aims to minimize a cost a function, which minimizes tumor size and to keep the tumor under a threshold. Additionally, we introduce a stochastic iteration step in the algorithm, which serves to reduce the number of gradient computations, similar to a stochastic gradient descent scheme in machine learning. Finally, we employ the algorithm to two therapy schedule optimization problems in dendritic cell immunotherapy and contrast our method’s stochastic and non-stochastic optimizations.

Many technologies have been developed to improve the quality of broadcasting, but persist with the problem that avoids the continuity of communications when the physical conditions of the media change. However, loss of signal propagation cannot be avoided because the refractive index of propagation media changes at the same time as magnetization, electromagnetic potential and other local parameters. That is, there is neither a device nor theories that take into account the effect of the sign of the refractive index under the broadcasting process. Simultaneously with the change of refractive index, conventional waves may find travel conditions inaccessible to the desired destination. In this chapter, we proposed that a sudden change in conditions is due to a resonant behavior of the media naturally described by a homogeneous integral equation of Fredholm. In addition, we propose a method to avoid the loss of the signal due to drastic changes in the broadcasting regime.

With the aim to increase the knowledge of the broadcasting properties under circumstances like time reversal, change on refractive index, presence of random obstacles, and so on, we developed new type of hybrid equations named Maxwell-Fredholm equations. These new equations fuse the Maxwell equations’ description of the electromagnetic fields with the Fourier transform of the Fredholm integral equations appropriate for a broadcasting process. Now we have a new tool, which resembles the Maxwell equations but including contributions from the Fredholm formulation like the resonant behaviour of the left-hand material conditions. To illustrate the usefulness of this new class of equations, we include an academic example that shows the deflection of an electromagnetic beam traveling among a highly anisotropic and left-handed behaviour media.

We devote the current chapter to describe a class of integral operators with properties equivalent to a killer operator of the quantum mechanics theory acting over a determined state, literally killing the state but now operating over some kind of Fourier integral transforms that satisfies a certain Fredholm integral equation, we call this operators Zap Integral Operators (ZIO). The result of this action is to eliminate the inhomogeneous term and recover a homogeneous integral equation. We show that thanks to this class of operators we can explain the presence of two extremely different solutions of the same Generalized Inhomogeneous Fredholm equation. So we can regard the Generalized Inhomogeneous Fredholm Equation as a Super-Equation with two kinds of solutions, the resonant and the conventional but coexisting simultaneously. Also, we remember the generalized projection operators and we show they are the precursors of the ZIO. We present simultaneous academic examples for both kinds of solutions.