Williams College

This is the classic work upon which modern-day game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.

An unknown quantum state \ensuremath{\Vert}\ensuremath{\varphi}〉 can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Einstein-Podolsky-Rosen (EPR) correlations. To do so the sender, ``Alice,'' and the receiver, ``Bob,'' must prearrange the sharing of an EPR-correlated pair of particles. Alice makes a joint measurement on her EPR particle and the unknown quantum system, and sends Bob the classical result of this measurement. Knowing this, Bob can convert the state of his EPR particle into an exact replica of the unknown state \ensuremath{\Vert}\ensuremath{\varphi}〉 which Alice destroyed.

The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state $\ensuremath{\rho}$ is the minimum average entanglement of an ensemble of pure states that represents \ensuremath{\rho}. An earlier paper conjectured an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix, and proved the formula for special states. The present paper extends the proof to arbitrary states of this system and shows how to construct entanglement-minimizing decompositions.

We examine properties of residual-based tests for the null of no cointegration for dynamic panels in which both the short-run dynamics and the long-run slope coefficients are permitted to be heterogeneous across individual members of the panel. The tests also allow for individual heterogeneous fixed effects and trend terms, and we consider both pooled within dimension tests and group mean between dimension tests. We derive limiting distributions for these and show that they are normal and free of nuisance parameters. We also provide Monte Carlo evidence to demonstrate their small sample size and power performance, and we illustrate their use in testing purchasing power parity for the post–Bretton Woods period.I thank Rich Clarida, Bob Cumby, Mahmoud El-Gamal, Heejoon Kang, Chiwha Kao, Andy Levin, Klaus Neusser, Masao Ogaki, David Papell, Pierre Perron, Abdel Senhadji, Jean-Pierre Urbain, Alan Taylor, and three anonymous referees for helpful comments on various earlier versions of this paper. The paper has also benefited from presentations at the 1994 North American Econometric Society Summer Meetings in Quebec City, the 1994 European Econometric Society Summer Meetings in Maastricht, and workshop seminars at the Board of Governors of the Federal Reserve, INSEE-CREST Paris, IUPUI, Ohio State, Purdue, Queens University Belfast, Rice University–University of Houston, and Southern Methodist University. Finally, I thank the following students who provided assistance in the earlier stages of the project: Younghan Kim, Rasmus Ruffer, and Lining Wan.

Entanglement purification protocols (EPPs) and quantum error-correcting codes (QECCs) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a mixed state M shared by two parties; with a QECC, an arbitrary quantum state |\ensuremath{\xi}〉 can be transmitted at some rate Q through a noisy channel \ensuremath{\chi} without degradation. We prove that an EPP involving one-way classical communication and acting on mixed state M^(\ensuremath{\chi}) (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel \ensuremath{\chi}) yields a QECC on \ensuremath{\chi} with rate Q=D, and vice versa. We compare the amount of entanglement E(M) required to prepare a mixed state M by local actions with the amounts ${\mathit{D}}_{1}$(M) and ${\mathit{D}}_{2}$(M) that can be locally distilled from it by EPPs using one- and two-way classical communication, respectively, and give an exact expression for E(M) when M is Bell diagonal. While EPPs require classical communication, QECCs do not, and we prove Q is not increased by adding one-way classical communication. However, both D and Q can be increased by adding two-way communication. We show that certain noisy quantum channels, for example a 50% depolarizing channel, can be used for reliable transmission of quantum states if two-way communication is available, but cannot be used if only one-way communication is available. We exhibit a family of codes based on universal hashing able to achieve an asymptotic Q (or D) of 1-S for simple noise models, where S is the error entropy. We also obtain a specific, simple 5-bit single-error-correcting quantum block code. We prove that iff a QECC results in high fidelity for the case of no error then the QECC can be recast into a form where the encoder is the matrix inverse of the decoder. \textcopyright{} 1996 The American Physical Society.

We describe an open-source toolkit for statistical machine translation whose novel contributions are (a) support for linguistically motivated factors, (b) confusion network decoding, and (c) efficient data formats for translation models and language models. In addition to the SMT decoder, the toolkit also includes a wide variety of tools for training, tuning and applying the system to many translation tasks.

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Two separated observers, by applying local operations to a supply of not-too-impure entangled states (e.g., singlets shared through a noisy channel), can prepare a smaller number of entangled pairs of arbitrarily high purity (e.g., near-perfect singlets). These can then be used to faithfully teleport unknown quantum states from one observer to the other, thereby achieving faithful transmission of quantum information through a noisy channel. We give upper and lower bounds on the yield $D\left(M\right)$ of pure singlets $(|{\ensuremath{\Psi}}^{\ensuremath{-}}〉)$ distillable from mixed states $M$, showing $D\left(M\right)>0$ if $〈{\ensuremath{\Psi}}^{\ensuremath{-}}|M|{\ensuremath{\Psi}}^{\ensuremath{-}}〉>\frac{1}{2}$.

The ``entanglement of formation'' of a mixed state \ensuremath{\rho} of a bipartite quantum system can be defined as the minimum number of singlets needed to create an ensemble of pure states that represents \ensuremath{\rho}. We find an exact formula for the entanglement of formation for all mixed states of two qubits having no more than two nonzero eigenvalues, and we report evidence suggesting that the formula is valid for all states of this system.

Consider three qubits A, B, and C which may be entangled with each other. We show that there is a trade-off between A's entanglement with B and its entanglement with C. This relation is expressed in terms of a measure of entanglement called the concurrence, which is related to the entanglement of formation. Specifically, we show that the squared concurrence between A and B, plus the squared concurrence between A and C, cannot be greater than the squared concurrence between A and the pair BC. This inequality is as strong as it could be, in the sense that for any values of the concurrences satisfying the corresponding equality, one can find a quantum state consistent with those values. Further exploration of this result leads to a definition of an essential three-way entanglement of the system, which is invariant under permutations of the qubits.

We summarize the findings of a recently completed study of the productivity impacts of international crop genetic improvement research in developing countries. Over the period 1960 to 2000, international agricultural research centers, in collaboration with national research programs, contributed to the development of "modern varieties" for many crops. These varieties have contributed to large increases in crop production. Productivity gains, however, have been uneven across crops and regions. Consumers generally benefited from declines in food prices. Farmers benefited only where cost reductions exceeded price reductions.

Many widely used economic models implicitly assume that income shares should be identical across time and space. Although time-series data from industrial countries appear consistent with this notion, cross-section data generally appear to contradict the assumption. A commonly used calculation suggests that labor shares of national income vary from about .05 to about .80 in international cross-section data. This paper suggests that the usual approach underestimates labor income in small firms. Several adjustments for calculating labor shares are identified and compared. They all yield labor shares for most countries in the range of .65.80.

ABSTRACT The concentration of radiocarbon ( 14 C) differs between ocean and atmosphere. Radiocarbon determinations from samples which obtained their 14 C in the marine environment therefore need a marine-specific calibration curve and cannot be calibrated directly against the atmospheric-based IntCal20 curve. This paper presents Marine20, an update to the internationally agreed marine radiocarbon age calibration curve that provides a non-polar global-average marine record of radiocarbon from 0–55 cal kBP and serves as a baseline for regional oceanic variation. Marine20 is intended for calibration of marine radiocarbon samples from non-polar regions; it is not suitable for calibration in polar regions where variability in sea ice extent, ocean upwelling and air-sea gas exchange may have caused larger changes to concentrations of marine radiocarbon. The Marine20 curve is based upon 500 simulations with an ocean/atmosphere/biosphere box-model of the global carbon cycle that has been forced by posterior realizations of our Northern Hemispheric atmospheric IntCal20 14 C curve and reconstructed changes in CO 2 obtained from ice core data. These forcings enable us to incorporate carbon cycle dynamics and temporal changes in the atmospheric 14 C level. The box-model simulations of the global-average marine radiocarbon reservoir age are similar to those of a more complex three-dimensional ocean general circulation model. However, simplicity and speed of the box model allow us to use a Monte Carlo approach to rigorously propagate the uncertainty in both the historic concentration of atmospheric 14 C and other key parameters of the carbon cycle through to our final Marine20 calibration curve. This robust propagation of uncertainty is fundamental to providing reliable precision for the radiocarbon age calibration of marine based samples. We make a first step towards deconvolving the contributions of different processes to the total uncertainty; discuss the main differences of Marine20 from the previous age calibration curve Marine13; and identify the limitations of our approach together with key areas for further work. The updated values for ΔR , the regional marine radiocarbon reservoir age corrections required to calibrate against Marine20, can be found at the data base http://calib.org/marine/ .

Fifty-six heroin addicts and 60 age-matched controls were offered choices between monetary rewards ($11-$80) available immediately and larger rewards ($25-$85) available after delays ranging from 1 week to 6 months. Participants had a 1-in-6 chance of winning a reward that they chose on one randomly selected trial. Delay-discounting rates were estimated from the pattern of participants' choices. The discounting model of impulsiveness (Ainslie, 1975) implies that delay-discounting rates are positively correlated with impulsiveness. On average, heroin addicts' discount rates were twice those of controls (p = .004), and discount rates were positively correlated with impulsivity as measured by self-report questionnaires (p < .05). The results lend external validity to the delay-discounting rate as a measure of impulsiveness, a characteristic associated with substance abuse.

Ocean-going ships carry, as ballast, seawater that is taken on in port and released at subsequent ports of call. Plankton samples from Japanese ballast water released in Oregon contained 367 taxa. Most taxa with a planktonic phase in their life cycle were found in ballast water, as were all major marine habitat and trophic groups. Transport of entire coastal planktonic assemblages across oceanic barriers to similar habitats renders bays, estuaries, and inland waters among the most threatened ecosystems in the world. Presence of taxonomically difficult or inconspicuous taxa in these samples suggests that ballast water invasions are already pervasive.

Today’s data centers offer tremendous aggregate bandwidth to clusters of tens of thousands of machines. However, because of limited port densities in even the highest-end switches, data center topologies typically consist of multi-rooted trees with many equal-cost paths between any given pair of hosts. Existing IP multipathing protocols usually rely on per-flow static hashing and can cause substantial bandwidth losses due to longterm collisions. In this paper, we present Hedera, a scalable, dynamic flow scheduling system that adaptively schedules a multi-stage switching fabric to efficiently utilize aggregate network resources. We describe our implementation using commodity switches and unmodified hosts, and show that for a simulated 8,192 host data center, Hedera delivers bisection bandwidth that is 96 % of optimal and up to 113 % better than static load-balancing methods. 1

Koehn, Philipp; Hoang, Hieu; Birch, Alexandra; Callison-Burch, Chris; Federico, Marcello; Bertoldi, Nicola; Cowan, Brooke; Shen, Wade; Moran, Christine; Zens, Richard; Bojar, Ondrej; Constantin, Alexandra; Herbst, Evan

Knowing how to manage one's own learning has become increasingly important in recent years, as both the need and the opportunities for individuals to learn on their own outside of formal classroom settings have grown. During that same period, however, research on learning, memory, and metacognitive processes has provided evidence that people often have a faulty mental model of how they learn and remember, making them prone to both misassessing and mismanaging their own learning. After a discussion of what learners need to understand in order to become effective stewards of their own learning, we first review research on what people believe about how they learn and then review research on how people's ongoing assessments of their own learning are influenced by current performance and the subjective sense of fluency. We conclude with a discussion of societal assumptions and attitudes that can be counterproductive in terms of individuals becoming maximally effective learners.

Abstract This paper documents the 16th data release (DR16) from the Sloan Digital Sky Surveys (SDSS), the fourth and penultimate from the fourth phase (SDSS-IV). This is the first release of data from the Southern Hemisphere survey of the Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2); new data from APOGEE-2 North are also included. DR16 is also notable as the final data release for the main cosmological program of the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), and all raw and reduced spectra from that project are released here. DR16 also includes all the data from the Time Domain Spectroscopic Survey and new data from the SPectroscopic IDentification of ERosita Survey programs, both of which were co-observed on eBOSS plates. DR16 has no new data from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey (or the MaNGA Stellar Library “MaStar”). We also preview future SDSS-V operations (due to start in 2020), and summarize plans for the final SDSS-IV data release (DR17).

Sequencing of the genome of the butterfly Heliconius melpomene shows that closely related Heliconius species exchange protective colour-pattern genes promiscuously. Heliconius butterflies are an excellent system in which to study ecology, behaviour, mimicry and speciation. The genome of the postman butterfly Heliconius melpomene has now been sequenced. Using genomic resequencing of individuals from distinct lineages, the authors document heterogenous patterns of genomic diversity associated with adaptively divergent wing-colour patterns. As the second lepidopteran genome to be sequenced, Heliconius offers novel opportunities for comparative genomics within this economically significant insect order, which includes many pest species, as well as the only domesticated insect, the silkmoth Bombyx mori. The evolutionary importance of hybridization and introgression has long been debated1. Hybrids are usually rare and unfit, but even infrequent hybridization can aid adaptation by transferring beneficial traits between species. Here we use genomic tools to investigate introgression in Heliconius, a rapidly radiating genus of neotropical butterflies widely used in studies of ecology, behaviour, mimicry and speciation2,3,4,5. We sequenced the genome of Heliconius melpomene and compared it with other taxa to investigate chromosomal evolution in Lepidoptera and gene flow among multiple Heliconius species and races. Among 12,669 predicted genes, biologically important expansions of families of chemosensory and Hox genes are particularly noteworthy. Chromosomal organization has remained broadly conserved since the Cretaceous period, when butterflies split from the Bombyx (silkmoth) lineage. Using genomic resequencing, we show hybrid exchange of genes between three co-mimics, Heliconius melpomene, Heliconius timareta and Heliconius elevatus, especially at two genomic regions that control mimicry pattern. We infer that closely related Heliconius species exchange protective colour-pattern genes promiscuously, implying that hybridization has an important role in adaptive radiation.