The Extended Regularized Dual Averaging Method for Composite Optimization

We present a new algorithm, extended regularized dual averaging (XRDA), for solving composite optimization problems, which are a generalization of the regularized dual averaging (RDA) method. The main novelty of the method is that it allows more flexible control of the backward step size. For instance, the backward step size for RDA grows without bound, while XRDA the backward step size can be kept bounded

The Andre-Oort conjecture for the moduli space of Abelian Surfaces

We provide an unconditional proof of the Andr\'e-Oort conjecture for the coarse moduli space $\mathcal{A}_{2,1}$ of principally polarized Abelian surfaces, following the strategy outlined by Pila-Zannier.Comment: 14 page

Brain Volume Differences and Proactive Interference: A VBM Investigation of Healthy Cognitive Aging.

Research on aging and memory has consistently demonstrated decreased memory performance in older adults, specifically on tasks measuring verbal and spatial memory. Memory decline in aging is partially related to interference from competing information. In older adults, the learning of new information is more adversely affected by already-formed memories (i.e. proactive interference) than in younger adults. However, interference of new information on already- formed memories (retroactive interference) is less affected by age. The present investigation examined the association between proactive and retroactive interference, and brain volume in young and older adults. Proactive and retroactive interference were assessed with a Modified modified free recall (MMFR) test. Participants (n=39) first studied AB and DE word pairs three times before undergoing a cued recall test. Following AB-DE testing, participants had only one study-test cycle of AC and FG word pairs. Finally, participants completed the MMFR test to evaluate their memory for all previously studied and tested words. Results revealed that older adults experienced significantly more proactive interference than younger adults (performance on MMFR-AC minus MMFR-FG), but both age groups performed similarly on the retroactive interference measures. It was hypothesized that brain volume, and specifically Hippocampal and prefrontal volume, would be significantly correlated to memory performance; however no significant correlations were found with any specific brain regions

Capital Gains Realizations of the Rich and Sophisticated

This paper attempts to bring theoretical and empirical research on capital gains realization behavior closer together by considering whether investors who appear to engage more in strategic tax avoidance activity also respond differently to tax rates. We find that such investors exhibit significantly smaller responses to permanent tax rate changes than other investors. Put another way, a larger part of their response to capital gains tax rates reflects timing, consistent with their closer adherence to tax avoidance strategies emphasizing arbitrage based on tax rate differentials. This finding holds for two alternative specifications of realization behavior, one of which suggests larger permanent responses to capital gains tax rates than those of previous panel studies.

The Use of Legislative History in a System of Separated Powers, Putting Legislative History to a Vote: A Response to Professor Siegel, Timing and Delegation: A Reply

The debate over the legitimacy of judicial use of legislative history has significant legal and political ramifications that have long sparked controversy. As additional commentators join this long-running engagement, the focus of the debate necessarily changes. In a previous article, John Manning argued that the use of legislative history violates the constitutional rule barring congressional self-delegation. Jonathan Siegel argues here that judicial reliance on legislative history does not implicate that rule, because a statute\u27s legislative history already exists at the time of the statute\u27s passage, and statutory incorporation of preexisting materials operates as an adoption of those materials, not as a delegation of legislative power. To illustrate this point, Professor Siegel introduces, as a thought experiment, a hypothetical Interpretation of Statutes Act. The Act provides that the legislative history of every future statute will be automatically incorporated into the statute, without express adoption, and instructs courts to give customary weight to that incorporated legislative history. Siegel concludes that, because legislatures are permitted to incorporate, by reference, preenactment legislative history into statutes, such an Act would be constitutional. Disagreeing with that conclusion, Professor Manning responds that Siegel\u27s Act would only formalize an unconstitutional delegation of power. He argues that the resulting arrangement-of the Act or of judicial reliance on legislative history-would allow members of Congress to subvert the aims of bicameralism and presentment. He posits that the hypothetical Act would effectively enable them to vote for a statute without taking full responsibility for legislative history that resulted from factional logrolling. This separation of the legislators\u27 responsibility from the legislative result (viz. statutory text), Manning concludes, permits Congress to enact binding statutory details through a process condemned by Supreme Court jurisprudence because it is not prescribed by the Constitution. In a brief reply, Professor Siegel argues that the hypothetical Interpretation of Statutes Act would not allow law-makers to evade responsibility, because Congress would still be obligated to ratify agent-prepared legislative history when voting for each statute. Because of this chronology, Siegel concludes, the Act would take legislative history out of the delegation doctrine altogether

Waivers of State Sovereign Immunity and the Ideology of the Eleventh Amendment

States normally enjoy immunity from suit by private parties, but they may waive this immunity. The Supreme Court\u27s steady contraction of other exceptions to the rule of state sovereign immunity has renewed interest in the previously little-discussed possibilities of waiver. This Article explores the boundaries of waiver doctrine. This Article shows that, prior to 1945, the Supreme Court-even as it enforced a broad, substantive rule of state sovereign immunity-applied a sensible doctrine of waiver that balanced the interests of states with those of private parties and the federal judicial system. The Court\u27s traditional doctrine treated state sovereign immunity like the defense of personal jurisdiction. Failure to assert immunity in a timely fashion waived the immunity defense. This rule prevented unfair gamesmanship. Beginning in 1945, the traditional rules concerning waiver of state sovereign immunity got swept away by the overall ideological tide of state sovereign immunity doctrine. The immunity became so important that it overrode all other considerations, including the need to run the federal judicial system in a sensible way. The new rules of waiver permitted states to abuse their immunity and waste federal judicial resources by litigating the merits of a case while holding an immunity defense in reserve. The Supreme Court\u27s most recent decisions suggest that the Court has returned to its traditional rules concerning waiver. The Court should make clear that it has fully reinstated the traditional, sensible, non-ideologized rules of waiver. Such rules respect the states\u27 prerogative of refusing to be sued in a federal forum, while at the same time requiring states to assert their prerogative in an orderly way that respects the needs of the federal judicial system

Optimal Approximation of Zonoids and Uniform Approximation by Shallow Neural Networks

We study the following two related problems. The first is to determine to what error an arbitrary zonoid in $\mathbb{R}^{d+1}$ can be approximated in the Hausdorff distance by a sum of $n$ line segments. The second is to determine optimal approximation rates in the uniform norm for shallow ReLU$^k$ neural networks on their variation spaces. The first of these problems has been solved for $d\neq 2,3$, but when $d=2,3$ a logarithmic gap between the best upper and lower bounds remains. We close this gap, which completes the solution in all dimensions. For the second problem, our techniques significantly improve upon existing approximation rates when $k\geq 1$, and enable uniform approximation of both the target function and its derivatives