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

Failure of Autophagy-Lysosomal Pathways in Rod Photoreceptors Causes the Early Retinal Degeneration Phenotype Observed in Cln6nclf Mice

PURPOSE. Vision loss caused by photoreceptor death represents one of the first symptoms in neuronal ceroid lipofuscinosis, a condition characterized by accumulation of intracellular waste. Cln6nclf mice have a naturally occurring mutation in ceroid–lipofuscinosis neuronal (CLN) protein 6 and are a model of this disorder. In order to identify the effect intracellular waste (lipofuscin) accumulation plays in driving retinal degeneration, the time course of degeneration was carefully characterized functionally using the electroretinogram and structurally using histology. METHODS. Cln6nclf and C57BL/6J, wild-type, mice were studied at postnatal day 18 (P18), P30, P60, P120, and P240, and retinal degeneration was correlated with changes in the retinal pigment epithelial (RPE) and neuronal autophagy–lysosomal pathways using super-resolution microscopy. RESULTS. In Cln6nclf mice there was significant loss of rod photoreceptor function at P18, prior to photoreceptor nuclei loss at P60. In contrast, cone pathway function was not affected until P240. The loss of rod photoreceptor function correlated with significant disruption of the autophagy–lysosomal degradation pathways within photoreceptors, but not in the RPE or other retinal neurons. Additionally, there was cytosolic accumulation of P62 and undigested mitochondrial-derived, ATP synthase subunit C in the photoreceptor layers of Cln6nclf mice at P30. CONCLUSIONS. These results suggest that rod photoreceptors have an increased sensitivity to disturbances in the autophagy–lysosomal pathway and the subsequent failure of mitochondrial turnover, relative to other retinal cells. It is likely that primary failure of the rod photoreceptors rather than the RPE or other retinal neurons underlies the early visual dysfunction that occurs in the Cln6nclf mouse model

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

Construction of good LDPC codes using dilation matrices

This paper extends results that have been reported in [1],[6], and [5] for algebraic construction of a low-density matrix to be used as a parity-check matrix for an error-correcting code. After describing the basic idea and the results we finish with a performance diagram that suggests that these codes are as good as random constructions in the area of low SNR and perform better than an algebraic construction tested in [7] in the area of higher SNR. As has been noted in [8], codes with algebraic structure may be easier to implement. The flexibility of the construction we describe may also be advantageous