Bertrand competition with intertemporal demand

In the text-book model of dynamic Bertrand competition, competing firms meet the same demand function every period. This is not a satisfactory model of the demand side if consumers can make intertemporal substitution between periods. Each period then leaves some residual demand to future periods, and consumers who observe price under-cutting may correctly anticipate an ensuing price war and therefore postpone their purchases. Accordingly, the interaction between the firms no longer constitutes a repeated game, and hence falls outside the domain of the usual Folk theorems. We analyze collusive pricing in such situations, and study cases when consumers have perfect and imperfect foresight and varying degrees of patience. It turns out that collusion against patient and forward-looking consumers is easier to sustain than collusion in the text-book model

A Survey on Retrieval of Mathematical Knowledge

We present a short survey of the literature on indexing and retrieval of mathematical knowledge, with pointers to 72 papers and tentative taxonomies of both retrieval problems and recurring techniques.Comment: CICM 2015, 20 page

Adaptive response and enlargement of dynamic range

Many membrane channels and receptors exhibit adaptive, or desensitized, response to a strong sustained input stimulus, often supported by protein activity-dependent inactivation. Adaptive response is thought to be related to various cellular functions such as homeostasis and enlargement of dynamic range by background compensation. Here we study the quantitative relation between adaptive response and background compensation within a modeling framework. We show that any particular type of adaptive response is neither sufficient nor necessary for adaptive enlargement of dynamic range. In particular a precise adaptive response, where system activity is maintained at a constant level at steady state, does not ensure a large dynamic range neither in input signal nor in system output. A general mechanism for input dynamic range enlargement can come about from the activity-dependent modulation of protein responsiveness by multiple biochemical modification, regardless of the type of adaptive response it induces. Therefore hierarchical biochemical processes such as methylation and phosphorylation are natural candidates to induce this property in signaling systems.Comment: Corrected typos, minor text revision

Fusion of secretory vesicles isolated from rat liver

Secretory vesicles isolated from rat liver were found to fuse after exposure to Ca2+. Vescle fusion is characterized by the occurrence of twinned vesicles with a continuous cleavage plane between two vesicles in freeze-fracture electron microscopy. The number of fused vesicles increases with increasing Ca2+-concentrations and is half maximal around 10–6 m. Other divalent cations (Ba2+, Sr2+, and Mg2+) were ineffective. Mg2+ inhibits Ca2+-induced fusion. Therefore, the fusion of secretory vesiclesin vitro is Ca2+ specific and exhibits properties similar to the exocytotic process of various secretory cells. Various substances affecting secretionin vivo (microtubular inhibitors, local anethetics, ionophores) were tested for their effect on membrane fusion in our system. The fusion of isolated secretory vesicles from liver was found to differ from that of pure phospholipid membranes in its temperature dependence, in its much lower requirement for Ca2+, and in its Ca2+-specificity. Chemical and enzymatic modifications of the vesicle membrane indicate that glycoproteins may account for these differences

The BRAIN Initiative: developing technology to catalyse neuroscience discovery

The evolution of the field of neuroscience has been propelled by the advent of novel technological capabilities, and the pace at which these capabilities are being developed has accelerated dramatically in the past decade. Capitalizing on this momentum, the United States launched the Brain Research through Advancing Innovative Neurotechnologies (BRAIN) Initiative to develop and apply new tools and technologies for revolutionizing our understanding of the brain. In this article, we review the scientific vision for this initiative set forth by the National Institutes of Health and discuss its implications for the future of neuroscience research. Particular emphasis is given to its potential impact on the mapping and study of neural circuits, and how this knowledge will transform our understanding of the complexity of the human brain and its diverse array of behaviours, perceptions, thoughts and emotions