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RISS 인기검색어
- 검색키워드
- 저자 : Katz, Marian Lisa (검색결과 83 건)
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On p-adic estimates of weights in Abelian codes over Galois rings
Katz, Daniel J California Institute of Technology 2005 해외박사(DDOD)
Let p be a prime. We prove various analogues and generalizations of McEliece's theorem on the p-divisibility of weights of words in cyclic codes over a finite field of characteristic p. Here we consider Abelian codes over various Galois rings. We present four new theorems on p-adic valuations of weights. For simplicity of presentation here, we assume that our codes do not contain constant words. The first result has two parts, both concerning Abelian codes over Z/pdZ . The first part gives a lower bound on the p-adic valuations of Hamming weights. This bound is shown to be sharp: for each code; we find the maximum k such that pk divides all Hamming weights. The second part of our result concerns the number of occurrences of a given nonzero symbol seZ/pd Z in words of our code; we call this number the s-count. We find aj such that pj divides the s-counts of all words in the code. Both our bounds are stronger than previous ones for infinitely many codes. The second result concerns Abelian codes over Z/4Z . We give a sharp lower bound on the 2-adic valuations of Lee weights. It improves previous bounds for infinitely many codes. The third result concerns Abelian codes over arbitrary Galois rings. We give a lower bound on the p-adic valuations of Hamming weights. When we specialize this result to finite fields, we recover the theorem of Delsarte and McEliece on the p-divisibility of weights in Abelian codes over finite fields. The fourth result generalizes the Delsarte-McEliece theorem. We consider the number of components in which a collection c1,..., ct of words all have the zero symbol; we call this the simultaneous zero count. Our generalized theorem p-adically estimates simultaneous zero counts in Abelian codes over finite fields, and we can use it to prove the theorem of N. M. Katz on the p-divisibility of the cardinalities of affine algebraic sets over finite fields.
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Sumfree subsets in cubes of arbitrary dimension
Katz, Daniel Jason Brown University 2009 해외박사(DDOD)
Abstract not available.
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Katz, Samuel Goddard Harvard University 2004 해외박사(DDOD)
GATA transcription factors control diverse aspects of development through interaction with the zinc-finger co-factors, Friend of GATA (FOG) proteins. Loss of GATA-1, FOG-1, or their interaction results in a developmental block in both erythropoiesis and megakaryopoiesis. Similarly, deletion of either FOG-2 or a knock-in mutation in GATA-4 that prevents binding to FOG-2, results in cardiac malformations, including tetrology of Fallot and double outlet right ventricle, respectively. Despite these crucial observations, little is currently known regarding the mechanisms by which FOG family proteins coordinate developmental decisions through GATA transcription factors. To address this concern a structure-function analysis of FOG-1 was undertaken in which the ability of various FOG-1 constructs to rescue a FOG-1 null hematopoietic cell line was assessed. From this assay we demonstrate that interaction through only one of FOG-1's four GATA binding zinc fingers is sufficient for rescue, providing evidence against a model in which FOG-1 acts to bridge multiple GATA-binding DNA elements. Furthermore, we find that megakaryocytic development, but not erythroid development, requires FOG-1's N-terminus, but is repressed by FOG-1's zinc fingers 1 through 4. The functional significance of a motif shared by all FOG family members and known to mediate interaction with the co-repressor C-terminal Binding Protein (CtBP) was explored by the generation and analysis of a mouse with a knock-in mutation at the FOG-1 locus that prevents FOG-1 from binding to CtBP. These mice develop normally, allowing us to conclude that interaction between FOG-1 and the corepressor CtBP is dispensable for normal erythropoiesis in vivo. Finally, we have generated a conditional knock-out FOG-1 allele and transgenic FOG-1 rescue of hematopoiesis in order to extend the GATA-FOG paradigm of hematopoietic differentiation to the development of multiple tissues that co-express FOG-1 with other GATA family members. In particular, we demonstrate that FOG-1 is essential for proper cardiac development. Hearts lacking FOG-1 display a common atrioventricular valve and Double Outlet Right Ventricle (DORV). These defects are not due to migration or function of neural crest cells. Further exploration of FOG family members within and outside of hematopoiesis will lead to a better understanding of how transcription factors control cellular differentiation as a crucial first step in understanding organogenesis and considering new approaches to organ repair.
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A molecular clock in the vomeronasal organ
Katz, Ron Columbia University 2006 해외박사(DDOD)
The orchestrated timing of physiology and behavior is critical for reproductive success with the timing of behavior and physiology synchronized to the 24-hour day through the activity of rhythmic oscillators. In mammals, reproductive behavior is initiated by mate recognition and attraction. Chemical cues, called pheromones, signal the sex and social status of individuals between the same species. Detection of chemosensory information relies in part on sensory neurons of the vomeronasal organ (VNO). While VNO-dependent behavior as assayed in a resident-intruder paradigm was not different at opposed times of day, circadian (endogenously rhythmic) mutant animals were more aggressive and inter-male mounting was not observed. We did find that a diurnal (entrained) rhythm in pheromone preference exists, with wild type male mice displaying a preference for female estrous urine at night. By identifying diurnal and circadian rhythms in clock genes expressed by the vomeronasal sensory neurons (VSNs) we also find that the VNO is a peripheral molecular clock. Importantly, our results suggest a mechanism whereby a molecular clock through circadian enhancer elements regulates daily rhythms in chemosensory specific transcripts, Trpc2 and Omp. Thus peripheral circadian regulation of pheromone detection ensures the coordinated timing of sexual receptivity and mate finding critical for reproductive success.
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