Some problems of edge waves and standing waves on beaches

Some problems of edge waves and standing waves on beaches are examined.

The nonlinear interaction of a wave normally incident on a sloping beach with a subharmonic edge wave is studied. A two-timing expansion is used in the full nonlinear theory to obtain the modulation equations which describe the evolution of the waves. It is shown how large amplitude edge waves are produced; and the results of the theory are compared with some recent laboratory experiments.

Traveling edge waves are considered in two situations. First, the full linear theory is examined to find the finite depth effect on the edge waves produced by a moving pressure disturbance. In the second situation, a Stokes' expansion is used to discuss the nonlinear effects in shallow water edge waves traveling over a bottom of arbitrary shape. The results are compared with the ones of the full theory for a uniformly sloping bottom.

The finite amplitude effects for waves incident on a sloping beach, with perfect reflection, are considered. A Stokes' expansion is used in the full nonlinear theory to find the corrections to the dispersion relation for the cases of normal and oblique incidence.

Finally, an abstract formulation of the linear water waves problem is given in terms of a self adjoint but nonlocal operator. The appropriate spectral representations are developed for two particular cases.

MicroRNA-132 is a physiological regulator of hematopoietic stem cell function and B-cell development

MicroRNAs are a class of small non-coding RNAs that negatively regulate gene expression. Several microRNAs have been implicated in altering hematopoietic cell fate decisions. Importantly, deregulation of many microRNAs can lead to deleterious consequences in the hematopoietic system, including the onset of cancer, autoimmunity, or a failure to respond effectively to infection. As such, microRNAs fine-tune the balance between normal hematopoietic output and pathologic consequences. In this work, we explore the role of two microRNAs, miR-132 and miR-125b, in regulating hematopoietic stem cell (HSC) function and B cell development. In particular, we uncover the role of miR-132 in maintaining the appropriate balance between self-renewal, differentiation, and survival in aging HSCs by buffering the expression of a critical transcription factor, FOXO3. By maintain this balance, miR-132 may play a critical role in preventing aging-associated hematopoietic conditions such as autoimmune disease and cancer. We also find that miR-132 plays a critical role in B cell development by targeting a key transcription factor, Sox4, that is responsible for the differentiation of pro-B cells into pre-B cells. We find that miR-132 regulates B cell apoptosis, and by delivering miR-132 to mice that are predisposed to developing B cell cancers, we can inhibit the formation of these cancers and improve the survival of these mice. In addition to miR-132, we uncovered the role of another critical microRNA, miR-125b, that potentiates hematopoietic stem cell function. We found that enforced expression of miR-125b causes an aggressive myeloid leukemia by downregulation of its target Lin28a. Importantly, miR-125b also plays a critical role in inhibiting the formation of pro-B cells. Thus, we have discovered two microRNAs with important roles in regulating normal hematopoiesis, and whose dregulation can lead to deleterious consequences such as cancer in the aging hematopoietic system. Both miR-132 and miR-125b may therefore be targeted for therapeutics to inhibit age-related immune diseases associated with the loss of HSC function and cancer progression.