Budget Imbalance Criteria for Auctions: A Formalized Theorem

We present an original theorem in auction theory: it specifies general conditions under which the sum of the payments of all bidders is necessarily not identically zero, and more generally not constant. Moreover, it explicitly supplies a construction for a finite minimal set of possible bids on which such a sum is not constant. In particular, this theorem applies to the important case of a second-price Vickrey auction, where it reduces to a basic result of which a novel proof is given. To enhance the confidence in this new theorem, it has been formalized in Isabelle/HOL: the main results and definitions of the formal proof are re- produced here in common mathematical language, and are accompanied by an informal discussion about the underlying ideas.Comment: 6th Podlasie Conference on Mathematics 2014, 11 page

Proving soundness of combinatorial Vickrey auctions and generating verified executable code

Using mechanised reasoning we prove that combinatorial Vickrey auctions are soundly specified in that they associate a unique outcome (allocation and transfers) to any valid input (bids). Having done so, we auto-generate verified executable code from the formally defined auction. This removes a source of error in implementing the auction design. We intend to use formal methods to verify new auction designs. Here, our contribution is to introduce and demonstrate the use of formal methods for auction verification in the familiar setting of a well-known auction

Improved Limit on theta_{13} and Implications for Neutrino Masses in Neutrino-less Double Beta Decay and Cosmology

We analyze the impact of a measurement, or of an improved bound, on theta_{13} for the determination of the effective neutrino mass in neutrino-less double beta decay and cosmology. In particular, we discuss how an improved limit on (or a specific value of) theta_{13} can influence the determination of the neutrino mass spectrum via neutrino-less double beta decay. We also discuss the interplay with improved cosmological neutrino mass searches.Comment: 22 pages, 5 figures. Minor corrections, matches version in PR

The light chain but not the heavy chain of botulinum A toxin inhibits exocytosis from permeabilized adrenal chromaffin cells

The heavy and light chains of botulinum A toxin were separated by anion exchange chromatography. Their intracellular actions were studied using bovine adrenal chromaffin cells permeabilized with streptolysin O. Purified light chain inhibited the Ca2+-stimulated [3H]noradrenaline release with a half-maximal effect at about 1.8 nM. The inhibition was incomplete. Heavy chain up to 28 nM was neither effective by itself nor did it enhance the inhibitory effect of light chain. It is concluded that the light chain of botulinum A toxin contains the functional domain responsible for the inhibition of exocytosis

Amylase release from streptolysin O-permeabilized pancreatic acinar cells. Effects of Ca2+, guanosine 5'-[gamma-thio]triphosphate, cyclic AMP, tetanus toxin and botulinum A toxin

The molecular requirements for amylase release and the intracellular effects of botulinum A toxin and tetanus toxin on amylase release were investigated using rat pancreatic acinar cells permeabilized with streptolysin O. Micromolar concentrations of free Ca2+ evoked amylase release from these cells. Maximal release was observed in the presence of 30 microM free Ca2+. Ca(2+)-stimulated, but not basal, amylase release was enhanced by guanosine 5'-[gamma-thio]triphosphate (GTP[S]) (3-4 fold) or cyclic AMP (1.5-2 fold). Neither the two-chain forms of botulinum A toxin and tetanus toxin, under reducing conditions, nor the light chains of tetanus toxin, inhibited amylase release triggered by Ca2+, or combinations of Ca2+ + GTP[S] or Ca2+ + cAMP. The lack of inhibition was not due to inactivation of botulinum A toxin or tetanus toxin by pancreatic acinar cell proteolytic enzymes, as toxins previously incubated with permeabilized pancreatic acinar cells inhibited Ca(2+)-stimulated [3H]noradrenaline release from streptolysin O-permeabilized adrenal chromaffin cells. These data imply that clostridial neurotoxins inhibit a Ca(2+)-dependent mechanism which promotes exocytosis in neural and endocrine cells, but not in exocrine cells