Expansion Trees with Cut

Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information which instances have been chosen for which quantifiers, known in the literature as expansion trees. Such a representation is inherently analytic and hence corresponds to a cut-free sequent calculus proof. Recently several extensions of such proof representations to proofs with cut have been proposed. These extensions are based on graphical formalisms similar to proof nets and are limited to prenex formulas. In this paper we present a new approach that directly extends expansion trees by cuts and covers also non-prenex formulas. We describe a cut-elimination procedure for our expansion trees with cut that is based on the natural reduction steps. We prove that it is weakly normalizing using methods from the epsilon-calculus

On the Estimation of Nonrandom Signal Coefficients from Jittered Samples

This paper examines the problem of estimating the parameters of a bandlimited signal from samples corrupted by random jitter (timing noise) and additive iid Gaussian noise, where the signal lies in the span of a finite basis. For the presented classical estimation problem, the Cramer-Rao lower bound (CRB) is computed, and an Expectation-Maximization (EM) algorithm approximating the maximum likelihood (ML) estimator is developed. Simulations are performed to study the convergence properties of the EM algorithm and compare the performance both against the CRB and a basic linear estimator. These simulations demonstrate that by post-processing the jittered samples with the proposed EM algorithm, greater jitter can be tolerated, potentially reducing on-chip ADC power consumption substantially.Comment: 11 pages, 8 figure

Cheap, Easy, or Connected: The Conditions for Creating Group Coordination

In both legal and political settings there has been a push toward adopting institutions that encourage consensus. The key feature of these institutions is that they bring interested parties together to communicate with each other. Existing research about the success or failure of particular institutions is ambiguous. Therefore, we turn our attention to understanding the general conditions when consensus is achievable, and we test experimentally three crucial factors that affect a group\u27s ability to achieve consensus: (1) the difficulty of the problem, (2) the costs of communication, and (3) the structure of communication. Using multiple experimental approaches, we find that difficult problems impede consensus, costs make consensus less likely (even relatively very small costs), and the structure of communication has significant effects and interacts with both problem difficulty and costs. In particular, the structure of communication can reduce the negative effect of costs and facilitate consensus. Together these results imply that consensus is only likely to occur if problems are easy, costs to communicate are low, or the communication structure helps overcome the other two problems. These findings can provide insight about the institutional designs that can be utilized to promote consensual outcomes