Fractional optimal control of a 2-dimensional distributed system using eigenfunctions

This paper presents an eigenfunctions expansion based scheme for Fractional Optimal Control (FOC) of a 2-dimensional distributed system. The fractional derivative is defined in the Riemann–Liouville sense. The performance index of a FOC problem is considered as a function of both state and control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE) containing two space parameters and one time parameter. Eigenfunctions are used to eliminate the terms containing space parameters and to define the problem in terms of a set of generalized state and control variables. For numerical computation Grünwald–Letnikov approximation is used. A direct numerical technique is proposed to obtain the state and the control variables. For a linear case, the numerical technique results into a set of algebraic equations which can be solved using a direct or an iterative scheme. The problem is solved for different number of eigenfunctions and time discretization. Numerical results show that only a few eigenfunctions are sufficient to obtain good results, and the solutions converge as the size of the time step is reduced.     

A strategy based on protein-protein interface motifs may help in identifying drug off-targets

Networks are increasingly used to study the impact of drugs at the systems level. From the algorithmic standpoint, a drug can "attack" nodes or edges of a protein-protein interaction network. In this work, we propose a new network strategy, "The Interface Attack", based on protein-protein interfaces. Similar interface architectures can occur between unrelated proteins. Consequently, in principle, a drug that binds to one has a certain probability of binding to others. The interface attack strategy simultaneously removes from the network all interactions that consist of similar interface motifs. This strategy is inspired by network pharmacology and allows inferring potential off-targets. We introduce a network model that we call "Protein Interface and Interaction Network (P2IN)", which is the integration of protein-protein interface structures and protein interaction networks. This interface-based network organization clarifies which protein pairs have structurally similar interfaces and which proteins may compete to bind the same surface region. We built the P2IN with the p53 signaling network and performed network robustness analysis. We show that (1) "hitting" frequent interfaces (a set of edges distributed around the network) might be as destructive as eleminating high degree proteins (hub nodes), (2) frequent interfaces are not always topologically critical elements in the network, and (3) interface attack may reveal functional changes in the system better than the attack of single proteins. In the off-target detection case study, we found that drugs blocking the interface between CDK6 and CDKN2D may also affect the interaction between CDK4 and CDKN2D.     

Convolution and Filtering in Fractional Fourier Domains

Fractional Fourier transforms, which are related to chirp and wavelet transforms, lead to the notion of fractional Fourier domains. The concept of filtering of signals in fractional domains is developed, revealing that under certain conditions one can improve upon the special cases of these operations in the conventional space and frequency domains. Because of the ease of performing the fractional Fourier transform optically, these operations are relevant for optical information processing.     

A heat transfer problem with exponential memory and the associated thermal stresses

In this study, a heat transfer problem defined by the Caputo–Fabrizio derivative, which is known to behave by the exponential decaying law, is addressed in an axially symmetric cylindrical region. Thus, the fundamental solutions of the heat diffusion process and the associated thermal stresses are aimed to find. For this purpose, Laplace and finite Hankel integral transforms are applied according to the geometry of the region. To obtain the thermal stresses, constitutive relations of the classical thermoelasticity theory are used. The effects of fractional orders on the diffusion process are illustrated graphically using MATLAB.