Predictability, entropy and information of infinite transformations

We show that a certain type of quasi finite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving transformation which is not quasi finite; and consider distribution asymptotics of information showing that e.g. for Boole's transformation, information is asymptotically mod-normal with square root normalization. Lastly we see that certain ergodic, probability preserving transformations with zero entropy have analogous properties and consequently entropy dimension of at most 1/2.Comment: typos corrected, clarifications added, unproved result remove

The recurrence time for ergodic systems of infinite measures

We investigate quantitative recurrence in systems having an infinite measure. We extend the Ornstein-Weiss theorem for a general class of infinite systems estimating return time in decreasing sequences of cylinders. Then we restrict to a class of one dimensional maps with indifferent fixed points and calculate quantitative recurrence in sequences of balls, obtaining that this is related to the behavior of the map near the fixed points

The functional role of Th-POK in lineage commitment during T-cell development

T lymphocytes develop in the thymus through multiple stages (DN, DP and SP) during which their survival and lineage are determined. During thymocyte maturation, T-cell Receptor (TCR) signaling induces important downstream mediators of differentiation. ThPOK (T-helper inducing POZ-Kruppel factor) has been identified as a master regulator of lineage commitment at the CD4/CD8 branch point, and is selectively induced in class II-restricted thymocytes, suggesting that it is upregulated by strong TCR signals. In order to identify upstream signaling pathways responsible for ThPOK induction, we mapped key transcriptional control elements at the ThPOK locus. These studies show that a dual silencer/enhancer element is primarily responsible for selective induction of ThPOK. We are currently attempting to identify key factors that bind to and regulate activity of this element during thymocytedevelopment. Given that γδ lineage commitment, like CD4 commitment, may be decided by relative TCR signal strength, it is possible that the same downstream effectors may be involved in both processes. However, the potential role of ThPOK in γδ commitment has not yet been explored. By carrying out in vitro stimulation of γδ thymocytes with anti-TCR antibody and varying ligand affinity for the transgenic KN6 γδTCR in vivo, we have now established that ThPOK induction in γδTCR+ thymocytes is controlled by TCR signaling and specifically requires a strong/ high affinity TCR ligand. Strikingly, ThPOK deficient mice show a severe reduction in mature γδ thymocytes as well as altered V region usage in γδ thymocytes, showing that ThPOK is important for maturation/selection of γδ cells. ThPOK is particularly important for development of a subset of γδ thymocytes that express Vγ1.1 and the NK1.1 surface marker, which has been previously referred to as NKTγδ cells and appears to be enriched for self-reactive specificities. Conversely, in mice that express ThPOK constitutively, the proportion of mature γδ thymocytes is greatly increased, as is the proportion of Vγ1.1+ thymocytes. These results demonstrate a new role for ThPOK in development of γδ thymocytes. Future work will distinguish whether ThPOK is important for differentiation, proliferation and our lineage commitment of the γδ subset.Ph.D., Biomedical Engineering -- Drexel University, 201

Spatial determinism for a free Z2-action

We extend the idea of bilateral determinism of a free Z-action by D. Ornstein and B. Weiss to a free Z²-action. We show that we have a 'stronger' spatial determinism for Z²-actions: to determine the complete Z²-name of a point, it is enough to know the name of a fraction of the orbit whose density can be made arbitrarily small. Moreover, for zero-entropy Z²-actions, we prove that there exists a partition (P) over tilde such that the (P) over tilde -names of an arbitrarily small one-sided cone determine the points.Keywords: Transformations, Amenable groups, Dimensions, Entrop