Embedded minimal surfaces

The study of embedded minimal surfaces in \RR^3 is a classical problem, dating to the mid 1700's, and many people have made key contributions. We will survey a few recent advances, focusing on joint work with Tobias H. Colding of MIT and Courant, and taking the opportunity to focus on results that have not been highlighted elsewhere.Comment: To appear in proceedings of Madrid ICM200

Androgen receptor-dependent and -independent mechanisms driving prostate cancer progression: Opportunities for therapeutic targeting from multiple angles.

Despite aggressive treatment for localized cancer, prostate cancer (PC) remains a leading cause of cancer-related death for American men due to a subset of patients progressing to lethal and incurable metastatic castrate-resistant prostate cancer (CRPC). Organ-confined PC is treated by surgery or radiation with or without androgen deprivation therapy (ADT), while options for locally advanced and disseminated PC include radiation combined with ADT, or systemic treatments including chemotherapy. Progression to CRPC results from failure of ADT, which targets the androgen receptor (AR) signaling axis and inhibits AR-driven proliferation and survival pathways. The exact mechanisms underlying the transition from androgen-dependent PC to CRPC remain incompletely understood. Reactivation of AR has been shown to occur in CRPC despite depletion of circulating androgens by ADT. At the same time, the presence of AR-negative cell populations in CRPC has also been identified. While AR signaling has been proposed as the primary driver of CRPC, AR-independent signaling pathways may represent additional mechanisms underlying CRPC progression. Identification of new therapeutic strategies to target both AR-positive and AR-negative PC cell populations and, thereby, AR-driven as well as non-AR-driven PC cell growth and survival mechanisms would provide a two-pronged approach to eliminate CRPC cells with potential for synthetic lethality. In this review, we provide an overview of AR-dependent and AR-independent molecular mechanisms which drive CRPC, with special emphasis on the role of the Jak2-Stat5a/b signaling pathway in promoting castrate-resistant growth of PC through both AR-dependent and AR-independent mechanisms

Limit Pricing and Predation in the Antitrust Laws: Economic and Legal Aspects

The overwhelming view in the economic literature is that limit pricing, the practice of establishing a non-profit-maximizing price with the intention of deterring entry of others into the market, either does not make economic sense or, in any event, does not have anticompetitive effects. This article will take a systematic look at the legal status of the limit price doctrine and propose its proper role

Comparison of continuous and discontinuous collisional bumpers: Dimensionally scaled impact experiments into single wire meshes

An experimental inquiry into the utility of discontinuous bumpers was conducted to investigate the collisional outcomes of impacts into single grid-like targets and to compare the results with more traditional bumper designs that employ continuous sheet stock. We performed some 35 experiments using 6.3 and 3.2 mm diameter spherical soda-lime glass projectiles at low velocities (less than 2.5 km/s) and 13 at velocities between 5 and 6 km/s, using 3.2 mm spheres only. The thrust of the experiments related to the characterization of collisional fragments as a function of target thickness or areal shield mass of both bumper designs. The primary product of these experiments was witness plates that record the resulting population of collisional fragments. Substantial interpretive and predictive insights into bumper performance were obtained. All qualitative observations (on the witness plates) and detailed measurements of displaced masses seem simply and consistently related only to bumper mass available for interaction with the impactor. This renders the grid bumper into the superior shield design. These findings present evidence that discontinuous bumpers are a viable concept for collisional shields, possibly superior to continuous geometries

Case Reports : Rheumatoid pleural effusions and trapped lung : An uncommon complication of rheumatoid arthritis

Rheumatoid arthritis (RA) is a disease affecting approximately 1[percent] of the population. It is familiarly defined as "chronic, symmetric, debilitating and destructive inflammatory polyarthritis characterized by proliferative synovial tissue (pannus) formation in affected joints" (1). Pain symptoms are typically worse in the morning, thedisease affects females more than males, and ulnar deviation and swan neck deformities are common. Perhaps less well known is the extensive list of extra-articular manifestations (EAMs) that can occur at any time duringthe course of the disease. EAMs affect an estimated 18-41[percent] of patients with RA (1). Renal, pulmonary cardiovascular, nervous, and integumentary system manifestations have all been described. Our case is that of anRA patient with shortness of breath and pleural effusions

Global standards of Constitutional law : epistemology and methodology

Just as it led the philosophy of science to gravitate around scientific practice, the abandonment of all foundationalist aspirations has already begun making political philosophy into an attentive observer of the new ways in which constitutional law is practiced. Yet paradoxically, lawyers and legal scholars are not those who understand this the most clearly. Beyond analyzing the jurisprudence that has emerged from the expansion of constitutional justice, and taking into account the development of international and regional law, the ongoing globalization of constitutional law requires comparing the constitutional laws of individual nations. Following Waldron, the product of this new legal science can be considered as ius gentium. This legal science is not as well established as one might like to think. But it can be developed on the grounds of the practice that consists in ascertaining standards. As abstract types of best “practices” (and especially norms) of constitutional law from around the world, these are only a source of law in a substantive, not a formal, sense. They thus belong to what I should like to call a “second order legal positivity.” In this article I will undertake, both at a methodological and an epistemological level, the development of a model for ascertaining global standards of constitutional law