Parameterized Construction of Program Representations for Sparse Dataflow Analyses

Data-flow analyses usually associate information with control flow regions. Informally, if these regions are too small, like a point between two consecutive statements, we call the analysis dense. On the other hand, if these regions include many such points, then we call it sparse. This paper presents a systematic method to build program representations that support sparse analyses. To pave the way to this framework we clarify the bibliography about well-known intermediate program representations. We show that our approach, up to parameter choice, subsumes many of these representations, such as the SSA, SSI and e-SSA forms. In particular, our algorithms are faster, simpler and more frugal than the previous techniques used to construct SSI - Static Single Information - form programs. We produce intermediate representations isomorphic to Choi et al.'s Sparse Evaluation Graphs (SEG) for the family of data-flow problems that can be partitioned per variables. However, contrary to SEGs, we can handle - sparsely - problems that are not in this family

From Brownian Dynamics to Markov Chain: an Ion Channel Example

A discrete rate theory for general multi-ion channels is presented, in which the continuous dynamics of ion diffusion is reduced to transitions between Markovian discrete states. In an open channel, the ion permeation process involves three types of events: an ion entering the channel, an ion escaping from the channel, or an ion hopping between different energy minima in the channel. The continuous dynamics leads to a hierarchy of Fokker-Planck equations, indexed by channel occupancy. From these the mean escape times and splitting probabilities (denoting from which side an ion has escaped) can be calculated. By equating these with the corresponding expressions from the Markov model the Markovian transition rates can be determined. The theory is illustrated with a two-ion one-well channel. The stationary probability of states is compared with that from both Brownian dynamics simulation and the hierarchical Fokker-Planck equations. The conductivity of the channel is also studied, and the optimal geometry maximizing ion flux is computed.Comment: submitted to SIAM Journal on Applied Mathematic

A General Theory of Sample Complexity for Multi-Item Profit Maximization

The design of profit-maximizing multi-item mechanisms is a notoriously challenging problem with tremendous real-world impact. The mechanism designer's goal is to field a mechanism with high expected profit on the distribution over buyers' values. Unfortunately, if the set of mechanisms he optimizes over is complex, a mechanism may have high empirical profit over a small set of samples but low expected profit. This raises the question, how many samples are sufficient to ensure that the empirically optimal mechanism is nearly optimal in expectation? We uncover structure shared by a myriad of pricing, auction, and lottery mechanisms that allows us to prove strong sample complexity bounds: for any set of buyers' values, profit is a piecewise linear function of the mechanism's parameters. We prove new bounds for mechanism classes not yet studied in the sample-based mechanism design literature and match or improve over the best known guarantees for many classes. The profit functions we study are significantly different from well-understood functions in machine learning, so our analysis requires a sharp understanding of the interplay between mechanism parameters and buyer values. We strengthen our main results with data-dependent bounds when the distribution over buyers' values is "well-behaved." Finally, we investigate a fundamental tradeoff in sample-based mechanism design: complex mechanisms often have higher profit than simple mechanisms, but more samples are required to ensure that empirical and expected profit are close. We provide techniques for optimizing this tradeoff

Integrating Energy Markets: Does Sequencing Matter?

This paper addresses three questions that are relevant to integrating different regional transmission areas. Market integrating normally increases the number of competitors and should therefore reduce prices but the first section shows that prices could rise when the number of generators initially increases. Regulatory effort will also be affected by market integration. If the number of generators in either market is low, then our analysis suggests that the outcome depends on whether the regulators act independently or co-ordinate. Finally, if markets are gradually combined into larger units, the choice of transmission allocation (auctions or market coupling) will affect the prospects of making further gains and hence could lead to incomplete reform.Cambridge-MIT Institut

Charm, Beauty and Top at HERA

Results on open charm and beauty production and on the search for top production in high-energy electron-proton collisions at HERA are reviewed. This includes a discussion of relevant theoretical aspects, a summary of the available measurements and measurement techniques, and their impact on improved understanding of QCD and its parameters, such as parton density functions and charm- and beauty-quark masses. The impact of these results on measurements at the LHC and elsewhere is also addressed.Comment: 103 pages, 60 figures, to be published in Prog. Part. Nucl. Phy