An analytic generalization of the rogers-ramanujan identities for odd moduli

A (k - 1)-fold Eulerian series expansion is given for II(1 - qⁿ)^-1, where the product runs over all positive integers n that are not congruent to 0,i or - i modulo 2k + 1. The Rogers-Ramanujan identities are the cases k = i = 2 and k = i + 1 = 2.     

Glomerular therapeutics: looking back, looking forward

Fifty years ago, the prospects for treatment of glomerulonephritis were dim. Beginning around 1950 the field of "glomerular therapeutics" was begun by the introduction of new agents (adrenocorticotrophic hormone, cortisone, nitrogen mustard) as possible disease-modifying therapies for the various forms of glomerular disease. For the next several decades these and other agents (azathioprine, cyclophosphamide, chlorambucil, prednisone) were used therapeutically in a largely uncontrolled and anecdotal fashion. The application of randomized, controlled trials led to the adoption of some forms of therapy as both effective and reasonably safe, and the rejection of others as either ineffective or hazardous. New regimens involving different routes of administration or dosing schedules were adopted. After about another two decades, new and increasingly selective agents began to be introduced into the therapeutic armamentarium (cyclosporine, mycophenolate mofetil). Diseases previously associated with a very poor outcome were transformed into manageable disorders. The consequences of glomerular disease (e.g., nephrotic syndrome, chronic renal failure) were now subject to control and alleviation in many circumstances. The next transformation of "glomerular therapeutics" is now under way. The revolution in molecular genetics and pharmacogenomics will allow new agents to be developed that target specific aspects of the pathogenic mechanisms underlying glomerular disease. This transformation will not be an easy one, because development, testing, approval, and application of these new concepts in therapeutics (e.g., somatic gene therapy) will be time consuming and expensive. Eventually, the understanding of the genetic basis of susceptibility to glomerular disease and its progression will allow a preventative and curative, rather than palliative, strategy to emerge.     

Fluorescent probes: looking backward and looking forward.

Probe technology has been advancing very rapidly but to study molecular events in real time, there has to be a discrete choice in the use of "probes" and the "labels" that they carry. In this minireview, we shed light on the use of fluorescent probes, especially the use of green fluorescent protein (GFP) and its variants as tools to cell biologists studying protein secretion and trafficking. The use of these GFP variants has further widened the application of Fluorescence Resonance Energy Transfer (FRET) in analyzing protein-protein interaction.     

An asian man with recurrent abdominal pain

Recurrent pyogenic cholangitis (RPC), or oriental cholangiohepatitis, is characterized by intrabiliary pigment stone formation, whose main manifestation consists of recurrent episodes of cholangitis, although other biliopancreatic complications can also occur. RPC develops mainly in Asian patients, in whom this entity is one of the main causes of acute abdominal pain. The differential diagnosis should be established with all other entities associated with intrahepatic stone formation, which is more common in Asian countries compared with the predominance of gallstone formation in the West. The diagnostic and therapeutic approach requires collaboration among gastroenterologists, radiologists and gastrointestinal surgeons. We review the most important clinical, diagnostic and therapeutic features of this entity, which, although clearly predominant in Asia, is increasingly diagnosed in our setting.