Autophagy in Ocular Pathophysiology

Autophagy is an evolutionarily conserved intracellular recycling pathway that is indispensable for cellular quality control. Dysfunctional autophagy has been associated with several neurodegenerative, myodegenerative, infectious, and cancerous disorders. Autophagic processes are not only important for cellular maintenance in the retina but also intimately involved with phagocytosis and the very core of retinal visual process. Additionally, excessively upregulated autophagy may culminate into a cell death modality, which may be detrimental to the non-dividing cells of various eye segments. Major advances have been made in understanding the role and fate of autophagy in different ocular tissue layers. In this chapter, we summarize the current understanding of autophagy in the eye in the context of development, aging, and disease. We also speculate on the putative therapeutic strategies where autophagy may be incorporated to treat oculopathies

Algebraic methods for the study of some linear matrix equations

AbstractAn algebraic viewpoint permits the formulation of necessary and sufficient conditions for the existence of a unique solution to some linear matrix equations. The theory developed is then used to express the solution in a finite series form and to prove a stability theorem

Is the O(3) σO(3)~\sigma Model with the Hopf Term Exactly Equivalent to a Higher Spin Theory?

We write down a local $CP_1$ model involving two gauge fields, which is exactly equivalent to the O(3) $\sigma$ model with the Hopf term. We impose the $CP_1$ constraint by using the gaussian representation of the delta function. For the coefficient of the Hopf term, $\theta = {\pi \over 2s}$, 2s being an integer, we show that the resulting model is exactly equivalent to an interacting theory of spin-$s$ fields. Thus we conjecture that there should be a fixed point in the spin-$s$ theory near which it is exactly equal to the $\sigma$ model.Comment: 11 page

The Value of Information for Populations in Varying Environments

The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit where any information about future environmental variations is common to the members of the population, our model is equivalent to known models of financial investment. In this case, the population can be interpreted as a portfolio of financial assets and previous analyses have shown that a key quantity of Shannon's communication theory, the mutual information, sets a fundamental limit on the value of information. We show that this bound can be violated when accounting for features that are irrelevant in finance but inherent to biological systems, such as the stochasticity present at the individual level. This leads us to generalize the measures of uncertainty and information usually encountered in information theory

LQG control with minimum directed information: Semidefinite programming approach

We consider a discrete-time Linear-QuadraticGaussian (LQG) control problem in which Massey’s directed information from the observed output of the plant to the control input is minimized while required control performance is attainable. This problem arises in several different contexts, including joint encoder and controller design for data-rate minimization in networked control systems. We show that the optimal control law is a Linear-Gaussian randomized policy. We also identify the state space realization of the optimal policy, which can be synthesized by an efficient algorithm based on semidefinite programming. Our structural result indicates that the filter-controller separation principle from the LQG control theory, and the sensor-filter separation principle from the zero-delay rate-distortion theory for Gauss-Markov sources hold simultaneously in the considered problem. A connection to the data-rate theorem for mean-square stability by Nair & Evans is also established.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Team Tamas Keviczk