Product Variety and Demand Uncertainty

We show that demand uncertainty leads to vertical product differentiation even when consumers are homogeneous. When a firm anticipates that its inventory or capacity may not be fully utilized, product variety can reduce its expected costs of excess capacity. When the firm offers a continuum of product varieties, the highest quality product has the highest profit margins but the lowest percentage margin, while the lowest quality product has the highest percentage margin but the lowest absolute margin. We derive these results in both a monopoly model and a variety of different competitive models. We conclude with a discussion of empirical predictions together with a brief discussion of supporting evidence available from marketing studies.

Identifying Patients Suitable for Discharge After a Single-Presentation High-Sensitivity Troponin Result: A Comparison of Five Established Risk Scores and Two High-Sensitivity Assays.

STUDY OBJECTIVE: We compare the ability of 5 established risk scores to identify patients with suspected acute coronary syndromes who are suitable for discharge after a modified single-presentation high-sensitivity troponin result. METHODS: This was a prospective observational study conducted in a UK district general hospital emergency department. Consecutive adults recruited with suspected acute coronary syndrome for whom attending physicians determined evaluation with serial troponin testing was required. Index tests were definitions of low risk applied to modified Goldman, Thrombolysis in Myocardial Infarction (TIMI), Global Registry of Acute Cardiac Events (GRACE), History, ECG, Age, Risk Factors, Troponin (HEART), and Vancouver Chest Pain Rule risk scores, incorporating either high-sensitivity troponin T or I results. The endpoint was acute myocardial infarction within 30 days. A test sensitivity threshold for acute myocardial infarction of 98% was chosen. Clinical utility was defined as a negative predictive value greater than or equal to 99.5% and identification of greater than 30% suitable for discharge. RESULTS: Nine hundred fifty-nine patients underwent high-sensitivity troponin T analysis and 867 underwent high-sensitivity troponin I analysis. In the high-sensitivity troponin T group, 79 of 959 (8.2%) had an acute myocardial infarction and 66 of 867 (7.6%) in the high-sensitivity troponin I group. Two risk scores (GRACE <80 and HEART ≤3) did not have the potential to achieve a sensitivity of 98% with high-sensitivity troponin T, and 3 scores (Goldman ≤1, TIMI ≤1, and GRACE <80) with high-sensitivity troponin I. A TIMI score of 0 or less than or equal to 1 and modified Goldman score less than or equal to 1 with high-sensitivity troponin T, and TIMI score of 0 and HEART score of less than or equal to 3 with high-sensitivity troponin I had the potential to achieve a negative predictive value greater than or equal to 99.5% while identifying greater than 30% of patients as suitable for immediate discharge. CONCLUSION: With established risk scores, it may be possible to identify greater than 30% of patients suitable for discharge, with a negative predictive value greater than or equal to 99.5% for the diagnosis of acute myocardial infarction, using a single high-sensitivity troponin test result at presentation. There is variation in high-sensitivity troponin assays, which may have implications in introducing rapid rule-out protocols

Product variety and demand uncertainty

We demonstrate that demand uncertainty alone can lead to equilibrium product variety. We consider a simple environment in which when demand is certain, a social planner, a competitive market, and a monopolist would all offer a single product, but when demand is uncertain, a social planner, a competitive market, and a monopolist will all offer vertically differentiated products. When a firm anticipates that its inventory or capacity may not be fully utilized, increasing product variety is efficient because it reduces the expected costs of excess capacity. We find that when the firm offers a continuum of product varieties, the highest quality product has the highest profit margins but the lowest percentage margin, while the lowest quality product has the highest percentage margin but the lowest absolute margin. We derive these results in both a monopoly model and a variety of different competitive models. We conclude with a discussion of empirical predictions together with a brief discussion of supporting evidence available from marketing studies

On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principle

The monitoring of a quantum-mechanical harmonic oscillator on which a classical force acts is important in a variety of high-precision experiments, such as the attempt to detect gravitational radiation. This paper reviews the standard techniques for monitoring the oscillator, and introduces a new technique which, in principle, can determine the details of the force with arbitrary accuracy, despite the quantum properties of the oscillator. The standard method for monitoring the oscillator is the "amplitude-and-phase" method (position or momentum transducer with output fed through a narrow-band amplifier). The accuracy obtainable by this method is limited by the uncertainty principle ("standard quantum limit"). To do better requires a measurement of the type which Braginsky has called "quantum nondemolition." A well known quantum nondemolition technique is "quantum counting," which can detect an arbitrarily weak classical force, but which cannot provide good accuracy in determining its precise time dependence. This paper considers extensively a new type of quantum nondemolition measurement—a "back-action-evading" measurement of the real part X_1 (or the imaginary part X_2) of the oscillator's complex amplitude. In principle X_1 can be measured "arbitrarily quickly and arbitrarily accurately," and a sequence of such measurements can lead to an arbitrarily accurate monitoring of the classical force. The authors describe explicit Gedanken experiments which demonstrate that X_1 can be measured arbitrarily quickly and arbitrarily accurately. In these experiments the measuring apparatus must be coupled to both the position (position transducer) and the momentum (momentum transducer) of the oscillator, and both couplings must be modulated sinusoidally. For a given measurement time the strength of the coupling determines the accuracy of the measurement; for arbitrarily strong coupling the measurement can be arbitrarily accurate. The "momentum transducer" is constructed by combining a "velocity transducer" with a "negative capacitor" or "negative spring." The modulated couplings are provided by an external, classical generator, which can be realized as a harmonic oscillator excited in an arbitrarily energetic, coherent state. One can avoid the use of two transducers by making "stroboscopic measurements" of X_1, in which one measures position (or momentum) at half-cycle intervals. Alternatively, one can make "continuous single-transducer" measurements of X_1 by modulating appropriately the output of a single transducer (position or momentum), and then filtering the output to pick out the information about X_1 and reject information about X_2. Continuous single-transducer measurements are useful in the case of weak coupling. In this case long measurement times are required to achieve good accuracy, and continuous single-transducer measurements are almost as good as perfectly coupled two-transducer measurements. Finally, the authors develop a theory of quantum nondemolition measurement for arbitrary systems. This paper (Paper I) concentrates on issues of principle; a sequel (Paper II) will consider issues of practice

Classical phase-space descriptions of continuous-variable teleportation

The nonnegative Wigner function of all quantum states involved in teleportation of Gaussian states using the standard continuous-variable teleportation protocol means that there is a local realistic phase-space description of the process. This includes the coherent states teleported up to now in experiments. We extend the phase-space description to teleportation of non-Gaussian states using the standard protocol and conclude that teleportation of non-Gaussian states with fidelity of 2/3 is a "gold standard" for this kind of teleportation.Comment: New version contains minor changes requested by journal referee

Qubit metrology and decoherence

Quantum properties of the probes used to estimate a classical parameter can be used to attain accuracies that beat the standard quantum limit. When qubits are used to construct a quantum probe, it is known that initializing $n$ qubits in an entangled "cat state," rather than in a separable state, can improve the measurement uncertainty by a factor of $1/\sqrt{n}$. We investigate how the measurement uncertainty is affected when the individual qubits in a probe are subjected to decoherence. In the face of such decoherence, we regard the rate $R$ at which qubits can be generated and the total duration $\tau$ of a measurement as fixed resources, and we determine the optimal use of entanglement among the qubits and the resulting optimal measurement uncertainty as functions of $R$ and $\tau$.Comment: 24 Pages, 3 Figure

Local Realistic Model for the Dynamics of Bulk-Ensemble NMR Information Processing

We construct a local realistic hidden-variable model that describes the states and dynamics of bulk-ensemble NMR information processing up to about 12 nuclear spins. The existence of such a model rules out violation of any Bell inequality, temporal or otherwise, in present high-temperature, liquid-state NMR experiments. The model does not provide an efficient description in that the number of hidden variables grows exponentially with the number of nuclear spins.Comment: REVTEX, 7 page

White Dwarfs in Globular Clusters: HST Observations of M4

Using WFPC2 on the Hubble Space Telescope, we have isolated a sample of 258 white dwarfs (WDs) in the Galactic globular cluster M4. Fields at three radial distances from the cluster center were observed and sizeable WD populations were found in all three. The location of these WDs in the color-magnitude diagram, their mean mass of 0.51($\pm 0.03$)M$_{\odot}$, and their luminosity function confirm basic tenets of stellar evolution theory and support the results from current WD cooling theory. The WDs are used to extend the cluster main-sequence mass function upward to stars that have already completed their nuclear evolution. The WD/red dwarf binary frequency in M4 is investigated and found to be at most a few percent of all the main-sequence stars. The most ancient WDs found are about 9 Gyr old, a level which is set solely by the photometric limits of our data. Even though this is less than the age of M4, we discuss how these cooling WDs can eventually be used to check the turnoff ages of globular clusters and hence constrain the age of the Universe.Comment: 46 pages, latex, no figures included, figures available at ftp://ftp.astro.ubc.ca/pub/richer/wdfig.uu size 2.7Mb. To be published in the Astrophysical Journa

Chaos for Liouville probability densities

Using the method of symbolic dynamics, we show that a large class of classical chaotic maps exhibit exponential hypersensitivity to perturbation, i.e., a rapid increase with time of the information needed to describe the perturbed time evolution of the Liouville density, the information attaining values that are exponentially larger than the entropy increase that results from averaging over the perturbation. The exponential rate of growth of the ratio of information to entropy is given by the Kolmogorov-Sinai entropy of the map. These findings generalize and extend results obtained for the baker's map [R. Schack and C. M. Caves, Phys. Rev. Lett. 69, 3413 (1992)].Comment: 26 pages in REVTEX, no figures, submitted to Phys. Rev.

Direct neutron capture of 48Ca at kT = 52 keV

The neutron capture cross section of 48Ca was measured relative to the known gold cross section at kT = 52 keV using the fast cyclic activation technique. The experiment was performed at the Van-de-Graaff accelerator, Universitaet Tuebingen. The new experimental result is in good agreement with a calculation using the direct capture model. The 1/v behaviour of the capture cross section at thermonuclear energies is confirmed, and the adopted reaction rate which is based on several previous experimental investigations remains unchanged.Comment: 9 pages (uses Revtex), 2 postscript figures, accepted for publication as Brief Report in Phys. Rev.