Vitamin A, one of the earliest vitamins to be discovered, has so far eluded attempts to uncover i... more Vitamin A, one of the earliest vitamins to be discovered, has so far eluded attempts to uncover its function in metabolism. Its role in vision, brilliantly elucidated by Wald and his group, though important, cannot be its only function, since an animal dies from vitamin A deficiency but not necessarily from blindness. A great deal of effort and research has been expended in the field of the morphological changes caused by a deficiency of the vitamin, such as epithelial keratinization. However, this work has not led to any clues concerning the changes occurring on the molecular level, and indeed the observed morphological lesions may be only the final and distant manifestations of an originally molecular lesion. Comparatively little is known about the metabolic effects of vitamin A deficiency, Oxygen uptake in. vitro was shown to be lowered somewhat in vitamin A deficiency (1). Total carcass fat was found to be decreased in vitamin A-deficient rats compared to that of pair-fed rats (2) ; cholesterol levels were shown to be unaffected (3). Rather than study the change in level of a particular metabolite, a more dynamic approach to the problem was sought in the present work. The level of incorporation of radioactivity from administered radioactive substrates into the members of a known chain of intermediary metabolites was determined in order to discover a possible block caused by the vitamin deficiency. In this way, the enzymatic step requiring the vitamin may be located. Ideally, in a reaction sequence A 4 B-+ C-+ D, if a vitamin is required for step B + C, then, starting with radioactive A, in deficiency, radioactivity will appear in B, but not in C and D. Starting with radioactive B, no radioactivity will appear in C and D, but with radioactive C radioactivity will appear in D, in spite of the deficiency. In order to explore as wide a range of metabolic reactions as possible, * This investigation was supported by a grant from the National Vitamin Foundation and by United States Atomic Energy Commission contract No. AT(ll-1).67 with the University of Illinois. Based on a thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy,
A secret sharing scheme is non-perfect if some subsets of participants that cannot recover the se... more A secret sharing scheme is non-perfect if some subsets of participants that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes. To this end, we extend the known connections between polymatroids and perfect secret sharing schemes to the non-perfect case. In order to study non-perfect secret sharing schemes in all generality, we describe their structure through their access function, a real function that measures the amount of information that every subset of participants obtains about the secret value. We prove that there exists a secret sharing scheme for every access function. Uniform access functions, that is, the ones whose values depend only on the number of participants, generalize the threshold access structures. Our main result is to determine the optimal information ratio of the uniform access functions. Moreover, we present a construction of linear secret sharing schemes with optimal information ratio for the rational uniform access functions.
Vitamin A, one of the earliest vitamins to be discovered, has so far eluded attempts to uncover i... more Vitamin A, one of the earliest vitamins to be discovered, has so far eluded attempts to uncover its function in metabolism. Its role in vision, brilliantly elucidated by Wald and his group, though important, cannot be its only function, since an animal dies from vitamin A deficiency but not necessarily from blindness. A great deal of effort and research has been expended in the field of the morphological changes caused by a deficiency of the vitamin, such as epithelial keratinization. However, this work has not led to any clues concerning the changes occurring on the molecular level, and indeed the observed morphological lesions may be only the final and distant manifestations of an originally molecular lesion. Comparatively little is known about the metabolic effects of vitamin A deficiency, Oxygen uptake in. vitro was shown to be lowered somewhat in vitamin A deficiency (1). Total carcass fat was found to be decreased in vitamin A-deficient rats compared to that of pair-fed rats (2) ; cholesterol levels were shown to be unaffected (3). Rather than study the change in level of a particular metabolite, a more dynamic approach to the problem was sought in the present work. The level of incorporation of radioactivity from administered radioactive substrates into the members of a known chain of intermediary metabolites was determined in order to discover a possible block caused by the vitamin deficiency. In this way, the enzymatic step requiring the vitamin may be located. Ideally, in a reaction sequence A 4 B-+ C-+ D, if a vitamin is required for step B + C, then, starting with radioactive A, in deficiency, radioactivity will appear in B, but not in C and D. Starting with radioactive B, no radioactivity will appear in C and D, but with radioactive C radioactivity will appear in D, in spite of the deficiency. In order to explore as wide a range of metabolic reactions as possible, * This investigation was supported by a grant from the National Vitamin Foundation and by United States Atomic Energy Commission contract No. AT(ll-1).67 with the University of Illinois. Based on a thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy,
A secret sharing scheme is non-perfect if some subsets of participants that cannot recover the se... more A secret sharing scheme is non-perfect if some subsets of participants that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes. To this end, we extend the known connections between polymatroids and perfect secret sharing schemes to the non-perfect case. In order to study non-perfect secret sharing schemes in all generality, we describe their structure through their access function, a real function that measures the amount of information that every subset of participants obtains about the secret value. We prove that there exists a secret sharing scheme for every access function. Uniform access functions, that is, the ones whose values depend only on the number of participants, generalize the threshold access structures. Our main result is to determine the optimal information ratio of the uniform access functions. Moreover, we present a construction of linear secret sharing schemes with optimal information ratio for the rational uniform access functions.
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Papers by Connor Johnson