Bounds on Query Convergence

The problem of finding an optimum using noisy evaluations of a smooth cost function arises in many contexts, including economics, business, medicine, experiment design, and foraging theory. We derive an asymptotic bound E[ (x_t - x*)^2 ] >= O(1/sqrt(t)) on the rate of convergence of a sequence (x_0, x_1, >...) generated by an unbiased feedback process observing noisy evaluations of an unknown quadratic function maximised at x*. The bound is tight, as the proof leads to a simple algorithm which meets it. We further establish a bound on the total regret, E[ sum_{i=1..t} (x_i - x*)^2 ] >= O(sqrt(t)) These bounds may impose practical limitations on an agent's performance, as O(eps^-4) queries are made before the queries converge to x* with eps accuracy.Comment: 6 pages, 2 figure

Automatic Differentiation of Algorithms for Machine Learning

Automatic differentiation---the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately---dates to the origin of the computer age. Reverse mode automatic differentiation both antedates and generalizes the method of backwards propagation of errors used in machine learning. Despite this, practitioners in a variety of fields, including machine learning, have been little influenced by automatic differentiation, and make scant use of available tools. Here we review the technique of automatic differentiation, describe its two main modes, and explain how it can benefit machine learning practitioners. To reach the widest possible audience our treatment assumes only elementary differential calculus, and does not assume any knowledge of linear algebra.Comment: 7 pages, 1 figur

The Challenge of Co-Religionist Commerce

This Article addresses the rise of co-religionist commerce in the United States—that is, the explosion of commercial dealings that take place between co-religionists who intend their transactions to achieve both commercial and religious objectives. To remain viable, coreligionist commerce requires all the legal support necessary to sustain all other commercial relationships. Contracts must be enforced, parties must be protected against torts, and disputes must be reliably adjudicated. Under current constitutional doctrine, co-religionist commercial agreements must be translated into secular terminology if they are to be judicially enforced. But many religious goods and services cannot be accurately translated without religious terms and structures. To address this translation problem, courts could make use of contextual tools of contract interpretation, thereby providing the necessary evidence to give meaning to co-religionist commercial agreements. However, contextual approaches to co-religionist commerce have been undermined by two current legal trends—one in constitutional law, the other in commercial law. The first is New Formalism, which discourages courts from looking to customary norms and relational principles to interpret commercial instruments. The second is what we call Establishment Clause Creep, which describes a growing judicial reticence to adjudicate disputes situated within a religious context. Together, these two legal developments prevent courts from using context to interpret and enforce co-religionist commercial agreements. This Article proposes that courts preserve co-religionist commerce with a limited embrace of contextualism. A thorough inquiry into context, which is discouraged by both New Formalist and many Establishment Clause doctrines, would allow courts to surmise parties\u27 intents and distinguish commercial from religious substance. Empowering the intent of co-religionist parties and limiting the doctrinal developments that threaten to undermine co-religionist commerce can secure marketplace dealings without intruding upon personal faith

Overbilling and Informed Financial Consent — A Contractual Solution

U.S. hospitals and physicians regularly charge uninsured patients and patients receiving care outside their health-plan networks far more what most health insurers pay and far more than their actual costs. Such practices have triggered over 100 lawsuits and prompted calls for pricing transparency in Congress and price regulation in several states. This Perspective argues that the theory of implied contracts, a foundation in most first-year courses in contract law, offers a useful legal and ethical mechanism for handling these troubling problems in health care billing

AD in Fortran, Part 1: Design

We propose extensions to Fortran which integrate forward and reverse Automatic Differentiation (AD) directly into the programming model. Irrespective of implementation technology, embedding AD constructs directly into the language extends the reach and convenience of AD while allowing abstraction of concepts of interest to scientific-computing practice, such as root finding, optimization, and finding equilibria of continuous games. Multiple different subprograms for these tasks can share common interfaces, regardless of whether and how they use AD internally. A programmer can maximize a function F by calling a library maximizer, XSTAR=ARGMAX(F,X0), which internally constructs derivatives of F by AD, without having to learn how to use any particular AD tool. We illustrate the utility of these extensions by example: programs become much more concise and closer to traditional mathematical notation. A companion paper describes how these extensions can be implemented by a program that generates input to existing Fortran-based AD tools

The critical region of strong-coupling lattice QCD in different large-N limits

We study the critical behavior at nonzero temperature phase transitions of an effective Hamiltonian derived from lattice QCD in the strong-coupling expansion. Following studies of related quantum spin systems that have a similar Hamiltonian, we show that for large $N_c$ and fixed $g^2N_c$, mean field scaling is not expected, and that the critical region has a finite width at $N_c=\infty$. A different behavior rises for $N_f\to \infty$ and fixed $N_c$ and $g^2/N_f$, which we study in two spatial dimensions and for $N_c=1$. We find that the width of the critical region is suppressed by $1/N_f^p$ with $p=1/2$, and argue that a generalization to $N_c>1$ and to three dimensions will change this only in detail (e.g. the value of $p>0$), but not in principle. We conclude by stating under what conditions this suppression is expected, and remark on possible realizations of this phenomenon in lattice gauge theories in the continuum.Comment: 24 pages, 6 figures. New version includes: a more extensive discussion of strong-coupling expansions and their region of validity. Accordingly I have reworded the descriptions of the investigated limits. Removed typos and misprint

Lessons From India in Organizational Innovation: A Tale of Two Heart Hospitals

Recent discussions in health reform circles have pinned great hopes on the prospect of innovation as the solution to the high-cost, inadequate-quality U.S. health system. But U.S. health care institutions--insurers, providers and specialists--have ceded leadership in innovation to Indian hospitals such as Care Hospital in Hyderabad and the Fortis Hospitals around New Delhi, which have U.S.-trained doctors and can perform open heart surgery for $6000 (compared to$100,000 in the United States). The Indian success is a window into America\u27s stalemate with inflating costs and stagnant innovation

A Cautious Path Forward on Accountable Care Organizations

The wave of new Accountable Care Organizations (ACOs), spurred by financial incentives in the Affordable Care Act, could become the latest chapter in the steady accumulation of market power by hospitals, health care systems, and physician groups. The main purpose behind forming many ACOs may not be to achieve cost savings but instead to strengthen negotiating power over purchasers in the private sector. This would be an unfortunate sequel to the waves of mergers in the 1990s when health care entities sought to counter market pressure from managed care organizations. The possibility that ACOs might further concentrate health care markets brings new urgency to understanding why provider monopolies are pernicious and to considering how government can ensure that ACOs pursue efficiency rather than market power

Local sequence features that influence AP-1 cis-regulatory activity

In the genome, most occurrences of transcription factor binding sites (TFBS) have no cis-regulatory activity, which suggests that flanking sequences contain information that distinguishes functional from nonfunctional TFBS. We interrogated the role of flanking sequences near Activator Protein 1 (AP-1) binding sites that reside in DNase I Hypersensitive Sites (DHS) and regions annotated as Enhancers. In these regions, we found that sequence features directly adjacent to the core motif distinguish high from low activity AP-1 sites. Some nearby features are motifs for other TFs that genetically interact with the AP-1 site. Other features are extensions of the AP-1 core motif, which cause the extended sites to match motifs of multiple AP-1 binding proteins. Computational models trained on these data distinguish between sequences with high and low activity AP-1 sites and also predict changes in cis-regulatory activity due to mutations in AP-1 core sites and their flanking sequences. Our results suggest that extended AP-1 binding sites, together with adjacent binding sites for additional TFs, encode part of the information that governs TFBS activity in the genome.</jats:p