Discrete phase-space structure of nn-qubit mutually unbiased bases

We work out the phase-space structure for a system of $n$ qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field \Gal{2^n} and investigate the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We provide a simple classification of such curves and study in detail the four- and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for $n$ qubits.Comment: Title changed. Improved version. Accepted for publication in Annals of Physic

Interactive Statistical Computing For Undergraduate Liberal Arts Education

St. Olaf College at Northfield, Minnesota, has an Interactive Statistical Analysis System for classroom research usage. SODAS (St. Olaf Data Analysis System) operates on a Minicomputer Time Sharing System (DEC PDP / 1140 has 15 terminals, 64K of core, and 3 disks). SODAS is used extensively by students for study of statistics, course projects, and research. In addition, it is used for faculty research . This system has increased student interest by involving them in realistic problems. In addition, student sophistication in problem solving has increased. The paper discusses the system design, the philosophy of interactive computing, and the pedagogical applications in an undergraduate curriculum

The relationship between mental toughness and cognitive control: evidence from the item-method directed forgetting task

Previous research by the authors found that mental toughness, as measured by the Mental Toughness Questionnaire 48 (MTQ48; Clough, P.J., Earle, K., & Sewell, D. [2002]. Mental toughness: the concept and its measurement. In I. Cockerill (Ed.), Solutions in sport psychology [pp. 32–43]. London: Thomson Publishing), was significantly associated with performance on the list-method directed forgetting task. The current study extends this finding to the item-method directed forgetting task in which the instruction to Remember or Forget is given after each item in the study list. A significant positive association was found between the correct recognition of Remember words and the emotional control subscale of the MTQ48. No significant associations were observed with other measures of mental toughness or personality. The findings are discussed in terms of the relationship between mental toughness and cognitive control

Direct measurements of DOCO isomers in the kinetics of OD+CO

Quantitative and mechanistically-detailed kinetics of the reaction of hydroxyl radical (OH) with carbon monoxide (CO) have been a longstanding goal of contemporary chemical kinetics. This fundamental prototype reaction plays an important role in atmospheric and combustion chemistry, motivating studies for accurate determination of the reaction rate coefficient and its pressure and temperature dependence at thermal reaction conditions. This intricate dependence can be traced directly to details of the underlying dynamics (formation, isomerization, and dissociation) involving the reactive intermediates cis- and trans-HOCO, which can only be observed transiently. Using time-resolved frequency comb spectroscopy, comprehensive mechanistic elucidation of the kinetics of the isotopic analogue deuteroxyl radical (OD) with CO has been realized. By monitoring the concentrations of reactants, intermediates, and products in real-time, the branching and isomerization kinetics and absolute yields of all species in the OD+CO reaction are quantified as a function of pressure and collision partner.Comment: 19 pages, 4 figure

Trinity University\u27s Summer Bridge Program: Navigating the Changing Demographics in Higher Education

Our article is divided into five sections. First, our study explores the demographic, economic, and cultural changes influencing higher education. We also explain the tangible and intangible benefits of a college education for first-generation, underrepresented students (FGUS). Second, we provide a brief discussion of the history of Trinity University and our Summer Bridge program. Third, our study describes our Summer Bridge program. Fourth, the data we collected examines how our Summer Bridge students’ grades and retention rates compare to our other first-year students. And, fifth, our article concludes with a discussion of future directions for our Summer Bridge program and how it may apply to other higher educational institutions. In particular, we offer recommendations for other student affairs professionals who also will be experiencing an increase in first-generation, underrepresented students

Implied Filtering Densities on Volatility's Hidden State

We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using Bayesian filtering. However, derivative data can be considered as conditional expectations that are already observed in the market, and which can be used as input to an inverse problem whose solution is an implied conditional density on volatility. Our analysis relies on a specification of the martingale change of measure, which we refer to as \textit{separability}. This specification has a multiplicative component that behaves like a risk premium on volatility uncertainty in the market. When applied to SPX options data, the estimated model and implied densities produce variance-swap rates that are consistent with the VIX volatility index. The implied densities are relatively stable over time and pick up some of the monthly effects that occur due to the options' expiration, indicating that the volatility-uncertainty premium could experience cyclic effects due to the maturity date of the options

Adolescents, Adults and Rewards: Comparing Motivational Neurocircuitry Recruitment Using fMRI

Background: Adolescent risk-taking, including behaviors resulting in injury or death, has been attributed in part to maturational differences in mesolimbic incentive-motivational neurocircuitry, including ostensible oversensitivity of the nucleus accumbens (NAcc) to rewards. Methodology/Principal Findings: To test whether adolescents showed increased NAcc activation by cues for rewards, or by delivery of rewards, we scanned 24 adolescents (age 12–17) and 24 adults age (22–42) with functional magnetic resonance imaging while they performed a monetary incentive delay (MID) task. The MID task was configured to temporally disentangle potential reward or potential loss anticipation-related brain signal from reward or loss notification-related signal. Subjects saw cues signaling opportunities to win or avoid losing $0,$.50, or $5 for responding quickly to a subsequent target. Subjects then viewed feedback of their trial success after a variable interval from cue presentation of between 6 to17 s. Adolescents showed reduced NAcc recruitment by reward-predictive cues compared to adult controls in a linear contrast with non-incentive cues, and in a volume-of-interest analysis of signal change in the NAcc. In contrast, adolescents showed little difference in striatal and frontocortical responsiveness to reward deliveries compared to adults. Conclusions/Significance: In light of divergent developmental difference findings between neuroimaging incentive paradigms (as well as at different stages within the same task), these data suggest that maturational differences i

Quantum concepts in optical polarization

We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincaré sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincaré space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored and their potential applications in quantum technologies are discussed

The effects of water velocity on the Ceratomyxa shasta infectious cycle

Ceratomyxa shasta is a myxozoan parasite identified as a contributor to salmon mortality in the Klamath River, USA. The parasite has a complex life cycle involving a freshwater polychaete, Manayunkia speciosa and a salmonid. As part of ongoing research on how environmental parameters influence parasite establishment and replication, we designed a laboratory experiment to examine the effect of water flow (velocity) on completion of the C. shasta infectious cycle. The experiment tested the effect of two water velocities, 0.05 and 0.01 m/s, on survival and infection of M. speciosa as well as transmission to susceptible rainbow trout and comparatively resistant Klamath River Chinook salmon. The faster water velocity facilitated the greatest polychaete densities, but the lowest polychaete infection prevalence. Rainbow trout became infected in all treatments, but at the slower velocity had a shorter mean day to death, indicating a higher infectious dose. Infection was not detected in Chinook salmon even at a dose estimated to be as high as 80,000 actinospores per fish. The higher water velocity resulted in lower C. shasta infection prevalence in M. speciosa and decreased infection severity in fish. Another outcome of our experiment is the description of a system for maintaining and infecting M. speciosa in the laboratory.This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by the author(s) and published by John Wiley & Sons Ltd. The article can be found at: http://onlinelibrary.wiley.com/journal/10.1111/%28ISSN%291365-2761.Keywords: Ceratomyxa shasta, Water velocity, Salmonids, Manayunkia speciosa, Infection, Parasite ecolog