Completely bounded kernels

We introduce completely bounded kernels taking values in L(A,B) where A and B are C*-algebras. We show that if B is injective such kernels have a Kolmogorov decomposition precisely when they can be scaled to be completely contractive, and that this is automatic when the index set is countable.Comment: 22 pages. Fixed oversight in previous version. To appear in Acta Scientiarum Mathematicarum (Szeged) for the 100th anniversary of the birth of Bela Sz.-Nag

Validating Predictions of Unobserved Quantities

The ultimate purpose of most computational models is to make predictions, commonly in support of some decision-making process (e.g., for design or operation of some system). The quantities that need to be predicted (the quantities of interest or QoIs) are generally not experimentally observable before the prediction, since otherwise no prediction would be needed. Assessing the validity of such extrapolative predictions, which is critical to informed decision-making, is challenging. In classical approaches to validation, model outputs for observed quantities are compared to observations to determine if they are consistent. By itself, this consistency only ensures that the model can predict the observed quantities under the conditions of the observations. This limitation dramatically reduces the utility of the validation effort for decision making because it implies nothing about predictions of unobserved QoIs or for scenarios outside of the range of observations. However, there is no agreement in the scientific community today regarding best practices for validation of extrapolative predictions made using computational models. The purpose of this paper is to propose and explore a validation and predictive assessment process that supports extrapolative predictions for models with known sources of error. The process includes stochastic modeling, calibration, validation, and predictive assessment phases where representations of known sources of uncertainty and error are built, informed, and tested. The proposed methodology is applied to an illustrative extrapolation problem involving a misspecified nonlinear oscillator

Spatial and temporal variability in the relative contribution of king mackerel (Scomberomorus cavalla) stocks to winter mixed fisheries off South Florida

King mackerel (Scomberomorus cavalla) are ecologically and economically important scombrids that inhabit U.S. waters of the Gulf of Mexico (GOM) and Atlantic Ocean (Atlantic). Separate migratory groups, or stocks, migrate from eastern GOM and southeastern U.S. Atlantic to south Florida waters where the stocks mix during winter. Currently, all winter landings from a management-defined south Florida mixing zone are attributed to the GOM stock. In this study, the stock composition of winter landings across three south Florida sampling zones was estimated by using stock-specific otolith morphological variables and Fourier harmonics. The mean accuracies of the jackknifed classifications from stepwise linear discriminant function analysis of otolith shape variables ranged from 66−76% for sex-specific models. Estimates of the contribution of the Atlantic stock to winter landings, derived from maximum likelihood stock mixing models, indicated the contribution was highest off southeastern Florida (as high as 82.8% for females in winter 2001−02) and lowest off southwestern Florida (as low as 14.5% for females in winter 2002−03). Overall, results provided evidence that the Atlantic stock contributes a certain, and perhaps a significant (i.e., ≥50%), percentage of landings taken in the management-defined winter mixing zone off south Florida, and the practice of assigning all winter mixing zone landings to the GOM stock shoul

Prospects for detecting proto-neutron star rotation and spindown using supernova neutrinos

After a successful supernova, a proto-neutron star (PNS) cools by emitting neutrinos on $\sim 1-100$ s timescales. Provided that there are neutrino emission `hot-spots' or `cold-spots' on the surface of the rotating PNS, we can expect a periodic modulation in the number of neutrinos observable by detectors. We show that Fourier transform techniques can be used to determine the frequency of rotation of the PNS from the neutrino arrival times. Provided there is no spindown, a 1-parameter Discrete Fourier Transform (DFT) is sufficient to determine the spin period of the PNS. If the PNS is born as a magnetar with polar magnetic field strength $B_0 \gtrsim 10^{15}$ G and is `slowly' rotating with an initial spin period $\gtrsim 100$ ms, then it can spin down to periods of the order of seconds during the cooling phase. We propose a modified DFT technique with three parameters to detect spindown. Due to lack of neutrino data from a nearby supernova except the $\sim20$ neutrinos detected from SN1987A, we use toy models and one physically motivated modulating function to generate neutrino arrival times. We use the false alarm rate (FAR) to quantify the significance of the Fourier power spectrum peaks. We show that PNS rotation and spindown are detected with $\rm FAR<2\%$ ($2\sigma$) for periodic signal content $\rm M\gtrsim 13-15\%$ if $5\times 10^{3}$ neutrinos are detected in 3 s and with $\rm FAR<1\%$ for $\rm M\geq 5\%$ if $5\times 10^{4}$ neutrinos are detected in 3 s. Since we can expect $\sim 10^{4}-10^{5}$ neutrino detections from a supernova at 10 kpc, detection of PNS rotation and spindown is possible using the neutrinos from the next Galactic supernova.Comment: 18 pages, 16 figure

Effects of Elevated H\u3csup\u3e+\u3c/sup\u3e And P\u3csub\u3ei\u3c/sub\u3e on The Contractile Mechanics of Skeletal Muscle Fibres From Young and Old Men: Implications for Muscle Fatigue in Humans

The present study aimed to identify the mechanisms responsible for the loss in muscle power and increased fatigability with ageing by integrating measures of whole‐muscle function with single fibre contractile mechanics. After adjusting for the 22% smaller muscle mass in old (73–89 years, n = 6) compared to young men (20–29 years, n = 6), isometric torque and power output of the knee extensors were, respectively, 38% and 53% lower with age. Fatigability was ∼2.7‐fold greater with age and strongly associated with reductions in the electrically‐evoked contractile properties. To test whether cross‐bridge mechanisms could explain age‐related decrements in knee extensor function, we exposed myofibres (n = 254) from the vastus lateralis to conditions mimicking quiescent muscle and fatiguing levels of acidosis (H+) (pH 6.2) and inorganic phosphate (Pi) (30 mm). The fatigue‐mimicking condition caused marked reductions in force, shortening velocity and power and inhibited the low‐ to high‐force state of the cross‐bridge cycle, confirming findings from non‐human studies that these ions act synergistically to impair cross‐bridge function. Other than severe age‐related atrophy of fast fibres (−55%), contractile function and the depressive effects of the fatigue‐mimicking condition did not differ in fibres from young and old men. The selective loss of fast myosin heavy chain II muscle was strongly associated with the age‐related decrease in isometric torque (r = 0.785) and power (r = 0.861). These data suggest that the age‐related loss in muscle strength and power are primarily determined by the atrophy of fast fibres, but the age‐related increased fatigability cannot be explained by an increased sensitivity of the cross‐bridge to H+ and Pi

The Population of Eccentric Binary Black Holes: Implications for mHz Gravitational Wave Experiments

The observed binary black hole (BBH) mergers indicate a large Galactic progenitor population continuously evolving from large orbital separations and low gravitational wave (GW) frequencies to the final merger phase. We investigate the equilibrium distribution of binary black holes in the Galaxy. Given the observed BBH merger rate, we contrast the expected number of systems radiating in the low-frequency $0.1-10\,$mHz GW band under two assumptions: (1) that all merging systems originate from near-circular orbits, as may be indicative of isolated binary evolution, and (2) that all merging systems originate at very high eccentricity, as predicted by models of dynamically-formed BBHs and triple and quadruple systems undergoing Lidov-Kozai eccentricity oscillations. We show that the equilibrium number of systems expected at every frequency is higher in the eccentric case (2) than in the circular case (1) by a factor of $\simeq 2-15$. This follows from the fact that eccentric systems spend more time than circular systems radiating in the low-frequency GW bands. The GW emission comes in pulses at periastron separated by the orbital period, which may be days to years. For a LISA-like sensitivity curve, we show that if eccentric systems contribute significantly to the observed merger rate, then $\simeq 10$ eccentric systems should be seen in the Galaxy.Comment: 12 pages, 6 figures, matches ApJ accepted versio

Enterprise Resource Planning Research: Where Are We Now and Where Should We Go From Here?

The research related to Enterprise Resource Planning (ERP) has grown over the past several years. This growing body of ERP research results in an increased need to review this extant literature with the intent of identifying gaps and thus motivate researchers to close this breach. Therefore, this research was intended to critique, synthesize and analyze both the content (e.g., topics, focus) and processes (i.e., methods) of the ERP literature, and then enumerates and discusses an agenda for future research efforts. To accomplish this, we analyzed 49 ERP articles published (1999-2004) in top Information Systems (IS) and Operations Management (OM) journals. We found an increasing level of activity during the 5-year period and a slightly biased distribution of ERP articles targeted at IS journals compared to OM. We also found several research methods either underrepresented or absent from the pool of ERP research. We identified several areas of need within the ERP literature, none more prevalent than the need to analyze ERP within the context of the supply chain

Reconciling ^(56)Ni Production in Type Ia Supernovae with Double Degenerate Scenarios

We combine the observed distribution of Type Ia supernova (SN Ia) ^(56)Ni yields with the results of sub-Chandrasekhar detonation and direct collision calculations to estimate what mass white dwarfs (WDs) should be exploding for each scenario. For collisions, the average exploding WD mass must be peaked at ≈0.75M_☉, significantly higher than the average field WD mass of ≈0.55–0.60M_☉. Thus, if collisions produce most SNe Ia, then a mechanism must exist that favours higher mass WDs. On the other hand, in old stellar populations, collisions would naturally result in low-luminosity SNe Ia, and we suggest these may be related to 1991bg-like events. For sub-Chandrasekhar detonations, the average exploding WD mass must be peaked at ≈1.1M_☉. This is similar to the average total mass in WD–WD binaries, but it is not clear whether double degenerate mergers would synthesize sufficient ^(56)Ni to match observed yields. If not, then actual ≈1.1M_☉ WDs would be needed for sub-Chandrasekhar detonations. Since such high-mass WDs are produced relatively quickly in comparison to the age of SN Ia environments, this would require either accretion on to lower mass WDs prior to ignition or a long time-scale between formation of the ≈1.1M_☉ WD and ignition