Good Random Matrices over Finite Fields

The random matrix uniformly distributed over the set of all m-by-n matrices over a finite field plays an important role in many branches of information theory. In this paper a generalization of this random matrix, called k-good random matrices, is studied. It is shown that a k-good random m-by-n matrix with a distribution of minimum support size is uniformly distributed over a maximum-rank-distance (MRD) code of minimum rank distance min{m,n}-k+1, and vice versa. Further examples of k-good random matrices are derived from homogeneous weights on matrix modules. Several applications of k-good random matrices are given, establishing links with some well-known combinatorial problems. Finally, the related combinatorial concept of a k-dense set of m-by-n matrices is studied, identifying such sets as blocking sets with respect to (m-k)-dimensional flats in a certain m-by-n matrix geometry and determining their minimum size in special cases.Comment: 25 pages, publishe

Replenishing Age-Related Decline of IRAK-M Expression in Retinal Pigment Epithelium Attenuates Outer Retinal Degeneration

Unchecked, chronic inflammation is a constitutive component of age-related diseases, including age-related macular degeneration (AMD). Here we identified interleukin-1 receptor-associated kinase (IRAK)-M as a key immunoregulator in retinal pigment epithelium (RPE) that declines with age. Rare genetic variants of IRAK-M increased the likelihood of AMD. IRAK-M expression in RPE declined with age or oxidative stress and was further reduced in AMD. IRAK-M-deficient mice exhibited increased incidence of outer retinal degeneration at earlier ages, which was further exacerbated by oxidative stressors. The absence of IRAK-M disrupted RPE cell homeostasis, including compromised mitochondrial function, cellular senescence, and aberrant cytokine production. IRAK-M overexpression protected RPE cells against oxidative or immune stressors. Subretinal delivery of AAV-expressing IRAK-M rescued light-induced outer retinal degeneration in wild-type mice and attenuated age-related spontaneous retinal degeneration in IRAK-M-deficient mice. Our data support that replenishment of IRAK-M expression may redress dysregulated pro-inflammatory processes in AMD, thereby treating degeneration

Replenishing IRAK-M expression in retinal pigment epithelium attenuates outer retinal degeneration

Chronic inflammation is a constitutive component of many age-related diseases, including age-related macular degeneration (AMD). Here, we identified interleukin-1 receptor-associated kinase M (IRAK-M) as a key immunoregulator in retinal pigment epithelium (RPE) that declines during the aging process. Rare genetic variants of IRAK3, which encodes IRAK-M, were associated with an increased likelihood of developing AMD. In human samples and mouse models, IRAK-M abundance in the RPE declined with advancing age or exposure to oxidative stress and was further reduced in AMD. Irak3-knockout mice exhibited an increased incidence of outer retinal degeneration at earlier ages, which was further exacerbated by oxidative stressors. The absence of IRAK-M led to a disruption in RPE cell homeostasis, characterized by compromised mitochondrial function, cellular senescence, and aberrant cytokine production. IRAK-M overexpression protected RPE cells against oxidative or immune stressors. Subretinal delivery of adeno-associated virus (AAV)-expressing human IRAK3 rescued light-induced outer retinal degeneration in wild-type mice and attenuated age-related spontaneous retinal degeneration in Irak3-knockout mice. Our data show that replenishment of IRAK-M in the RPE may redress dysregulated pro-inflammatory processes in AMD, suggesting a potential treatment for retinal degeneration

Histological Evaluation of Diabetic Neurodegeneration in the Retina of Zucker Diabetic Fatty (ZDF) Rats

In diabetes, retinal dysfunctions exist prior to clinically detectable vasculopathy, however the pathology behind these functional deficits is still not fully established. Previously, our group published a detailed study on the retinal histopathology of type 1 diabetic (T1D) rat model, where specific alterations were detected. Although the majority of human diabetic patients have type 2 diabetes (T2D), similar studies on T2D models are practically absent. To fill this gap, we examined Zucker Diabetic Fatty (ZDF) rats - a model for T2D - by immunohistochemistry at the age of 32 weeks. Glial reactivity was observed in all diabetic specimens, accompanied by an increase in the number of microglia cells. Prominent outer segment degeneration was detectable with changes in cone opsin expression pattern, without a decrease in the number of labelled elements. The immunoreactivity of AII amacrine cells was markedly decreased and changes were detectable in the number and staining of some other amacrine cell subtypes, while most other cells examined did not show any major alterations. Overall, the retinal histology of ZDF rats shows a surprising similarity to T1D rats indicating that despite the different evolution of the disease, the neuroretinal cells affected are the same in both subtypes of diabetes

Finite-Ring Combinatorics and MacWilliams' Equivalence Theorem

AbstractF. J. MacWilliams proved that Hamming isometries between linear codes extend to monomial transformations. This theorem has recently been genera- lized by J. Wood who proved it for Frobenius rings using character theoretic methods. The present paper provides a combinatorial approach: First we extend I. Constantinescu's concept of homogeneous weights on arbitrary finite rings and prove MacWilliams' equivalence theorem to hold with respect to these weights for all finite Frobenius rings. As a central tool we then establish a general inversion principle for real functions on finite modules that involves Möbius inversion on partially ordered sets. An application of the latter yields the aforementioned result of Wood