Metabolic pathway analysis in presence of biological constraints

Metabolic pathway analysis is a key method to study metabolism at steady state and the elementary fluxes (EFs) is one major concept allowing one to analyze the network in terms of non-decomposable pathways. The supports of the EFs contain in particular the supports of the elementary flux modes (EFMs), which are the support-minimal pathways, and EFs coincide with EFMs when the only flux constraints are given by the irreversibility of certain reactions. Practical use of both EFMs and EFs has been hampered by the combinatorial explosion of their number in large, genome-scale, systems. The EFs give the possible pathways at steady state but the real pathways are limited by biological constraints, such as thermodynamic or, more generally, kinetic constraints and regulatory constraints from the genetic network. We provide results about the mathematical structure and geometrical characterization of the solutions space in presence of such biological constraints and revisit the concept of EFMs and EFs in this framework. We show that most of those results depend only on a very general property of compatibility of the constraints with sign: either sign-based for regulatory constraints or sign-monotone (a stronger property) for thermodynamic and kinetic constraints. We show in particular that EFs for sign-monotone constraints are just those original EFs that satisfy the constraint and show how to efficiently integrate their computation in the double description method, the most widely used method in the tools dedicated to EFMs computation.

Optimal Dynamic Auctions Are Virtual Welfare Maximizers

We are interested in the setting where a seller sells sequentially arriving items, one per period, via a dynamic auction. At the beginning of each period, each buyer draws a private valuation for the item to be sold in that period and this valuation is independent across buyers and periods. The auction can be dynamic in the sense that the auction at period t can be conditional on the bids in that period and all previous periods, subject to certain appropriately defined incentive compatible and individually rational conditions. Perhaps not surprisingly, the revenue optimal dynamic auctions are computationally hard to find and existing literatures that aim to approximate the optimal auctions are all based on solving complex dynamic programs. It remains largely open on the structural interpretability of the optimal dynamic auctions. In this paper, we show that any optimal dynamic auction is a virtual welfare maximizer subject to some monotone allocation constraints. In particular, the explicit definition of the virtual value function above arises naturally from the primal-dual analysis by relaxing the monotone constraints. We further develop an ironing technique that gets rid of the monotone allocation constraints. Quite different from Myerson’s ironing approach, our technique is more technically involved due to the interdependence of the virtual value functions across buyers. We nevertheless show that ironing can be done approximately and efficiently, which in turn leads to a Fully Polynomial Time Approximation Scheme of the optimal dynamic auction.

Constraint-Based Sequential Pattern Mining with Decision Diagrams

Constraint-based sequential pattern mining aims at identifying frequent patterns on a sequential database of items while observing constraints defined over the item attributes. We introduce novel techniques for constraint-based sequential pattern mining that rely on a multi-valued decision diagram (MDD) representation of the database. Specifically, our representation can accommodate multiple item attributes and various constraint types, including a number of non-monotone constraints. To evaluate the applicability of our approach, we develop an MDD-based prefix-projection algorithm and compare its performance against a typical generate-and-check variant, as well as a state-of-the-art constraint-based sequential pattern mining algorithm. Results show that our approach is competitive with or superior to these other methods in terms of scalability and efficiency.