"Uniform Measures On Inverse Limit Spaces"

Motivated by problems from dynamic economic models, we consider the problem of defining a uniform measure on inverse limit spaces. Let f be a function from a compact metric space X into itself where f is continuous, onto and piecewise one-to-one. Let Y be the inverse limit of (X,f). Then starting with a measure m1 on the Borel sets of X, we recursively construct a sequence of probability measures (m1,m2,...) on the Borel sets of X satisfying mn(A)=mn+1[B] for each Borel set A and n=1,2,... and B is the preimage of A under f. This sequence of probability measures is then uniquely extended to a probability measure on the inverse limit space Y. If m1 is a uniform measure, we argue that the measure induced on the inverse limit space by the recursively constructed sequence of measures is a uniform measure. As such, the measure has uses in economic theory for policy evaluation and in dynamical systems in providing an ambient measure (when Lebesgue measure is not available) with which to define an SRB measure or a metric attractor for the shift map on the inverse limit space.Inverse Limits, probability measure, multiple equilibria, global indeterminancy

Chaos and Sector-specific Externalities

Benhabib and Farmer (1996) explore the possibility of local indeterminacy in a twosector model with sector-speci c externalities. They nd that very small sector-specific externalities are su cient for local indeterminacy. In this case, it is possible to construct sunspot equilibria where extrinsic uncertainty matters. In this paper, I provide a global analysis of their model revealing the existence of Euler equation branching. This branching allows for regime switching equilibria with cycles and chaotic behavior. These equilibria occur whether the \local dynamics" are determinate or indeterminate.two-sector model, regime switching, global indeterminacy, cycles and chaos

"Euler Equation Branching"

Some macroeconomic models exhibit a type of global indeterminacy known as Euler equation branching (e.g., the one-sector growth model with a production externality). The dynamics in such models are governed by a differential inclusion. In this paper, we show that in models with Euler equation branching there are multiple equilibria and that the dynamics are chaotic. In particular, we provide sufficient conditions for a dynamical system on the plane with Euler equation branching to be chaotic and show analytically that in a neighborhood of a steady state, these sufficient conditions will typically be satisfied. We also extend the results of Christiano and Harrison (JME, 1999) for the one-sector growth model with a production externality. In a more general setting, we provide necessary and sufficient conditions for Euler equation branching in this model. We show that chaotic and cyclic equilibria are possible and that this behavior is not dependent on the steady state being "locally" determinate or indeterminate.global indeterminacy, Euler equation branching, multiple equilibria, cycles,chaos, increasing returns to scale, externality, regime switching

Expected Utility in Models with Chaos

In this paper, we provide a framework for calculating expected utility in models with chaotic equilibria and consequently a framework for ranking chaos. Suppose that a dynamic economic model’s equilibria correspond to orbits generated by a chaotic dynamical system f : X ! X where X is a compact metric space and f is continuous. The map f could represent the forward dynamics xt+1 = f(xt) or the backward dynamics xt = f(xt+1). If f represents the forward/backward dynamics, the set of equilibria forms a direct/inverse limit space. We use a natural f-invariant measure on X to induce a measure on the direct/inverse limit space and show that this induced measure is a natural ¾-invariant measure where ¾ is the shift operator. We utilize this framework in the cash-in-advance model of money where f is the backward map to calculate expected utility when equilibria are chaotic.chaos, inverse limits, direct limits, natural invariant measure, cash-in-advance

The Relationship between Cost Analysis and Program Management

Cost analysis if often viewed as applying basic principles and cost methodologies to determine total system cost. These finished estimates then flow into a decision making process and the cost estimator leaves the stage. Reality shows that the cost estimator is actually one of the main contributors to the decision making process. Our introduction to this special issue explores the areas where cost estimating plays a major role in program management in areas beyond the normal program estimate. We have included articles that show the key role estimators can play in source selection strategies and evaluation; cost of delay analysis for management decisions, earned value management methods to predict program costs; decision criteria to rank competing projects that complement traditional cost-based methods; and a new methodology for determining research and development budget profiles

Is it Round? Spectropolarimetry of the Type II-P Supernova 1999em

We present the first multi-epoch spectropolarimetry of a type II plateau supernova (SN II-P), with optical observations of SN 1999em on days 7, 40, 49, 159, and 163 after discovery. These data are used to probe the geometry of the electron-scattering atmosphere before, during, and after the plateau phase, which ended roughly 90 days after discovery. Weak continuum polarization with an unchanging polarization angle (theta ~ 160 deg) is detected at all epochs, with p ~ 0.2% on day 7, p ~ 0.3% on days 40 and 49, and p ~ 0.5% in the final observations. Distinct polarization modulations across strong line features are present on days 40, 49, 159, and 163. Uncorrected for interstellar polarization (which is believed to be quite small), polarization peaks are associated with strong P Cygni absorption troughs and nearly complete depolarization is seen across the H-alpha emission profile. The temporal evolution of the continuum polarization and sharp changes across lines indicate polarization intrinsic to SN 1999em. When modeled in terms of the oblate, electron-scattering atmospheres of Hoeflich, the observed polarization implies anasphericity of at least 7% during the period studied. The temporal polarization increase may indicate greater asphericity deeper into the ejecta. We discuss the implications of asphericity on the use of type II-P supernovae as primary extragalactic distance indicators through the expanding photosphere method (EPM). If asphericity produces directionally dependant flux and peculiar galaxy motions are characterized by sigma_v_rec = 300 km/s, it is shown that the agreement between previous EPM measurements of SNe II and distances to the host galaxies predicted by a linear Hubble law restrict mean SN II asphericity to values less than 30% (3-sigma) during the photospheric phase.Comment: 65 pages (29 Figures, 4 Tables), Accepted for publication in the June 1, 2001 edition of ApJ. Revised statistical analysis of scatter in Hubble diagram of previous EPM distances and the implications for mean SN II asphericit

A two-directional approach to pyrrolizidines: total syntheses and biological evaluation of alkaloid cis-223B and (+/-)-xenovenine

Total syntheses of alkaloid cis-223B and xenovenine are reported in 3 and 4 steps respectively using a two-directional synthesis/triple reductive amination strategy, and their neurotoxic properties assessed

Two-directional synthesis and biological evaluation of alkaloid 5-epi-cis-275B′

The first total synthesis of myrmicine ant alkaloid 5-epi-cis-275B0 (4) is presented. A tandem cyclisation stablished the entire core of the structure in a single transformation as well as the required 2,5-anti stereochemistry. Two-directional synthesis was used to furnish the cyclisation precursor 2, as in each of the subsequent steps towards the natural product. The first electrophysiology studies for 4 (against nicotinic acetylcholine receptors) were also conducted, finding modest inhibition of current

The Brightness of Colour

Background: The perception of brightness depends on spatial context: the same stimulus can appear light or dark depending on what surrounds it. A less well-known but equally important contextual phenomenon is that the colour of a stimulus can also alter its brightness. Specifically, stimuli that are more saturated (i.e. purer in colour) appear brighter than stimuli that are less saturated at the same luminance. Similarly, stimuli that are red or blue appear brighter than equiluminant yellow and green stimuli. This non-linear relationship between stimulus intensity and brightness, called the Helmholtz-Kohlrausch (HK) effect, was first described in the nineteenth century but has never been explained. Here, we take advantage of the relative simplicity of this 'illusion' to explain it and contextual effects more generally, by using a simple Bayesian ideal observer model of the human visual ecology. We also use fMRI brain scans to identify the neural correlates of brightness without changing the spatial context of the stimulus, which has complicated the interpretation of related fMRI studies.Results: Rather than modelling human vision directly, we use a Bayesian ideal observer to model human visual ecology. We show that the HK effect is a result of encoding the non-linear statistical relationship between retinal images and natural scenes that would have been experienced by the human visual system in the past. We further show that the complexity of this relationship is due to the response functions of the cone photoreceptors, which themselves are thought to represent an efficient solution to encoding the statistics of images. Finally, we show that the locus of the response to the relationship between images and scenes lies in the primary visual cortex (V1), if not earlier in the visual system, since the brightness of colours (as opposed to their luminance) accords with activity in V1 as measured with fMRI.Conclusions: The data suggest that perceptions of brightness represent a robust visual response to the likely sources of stimuli, as determined, in this instance, by the known statistical relationship between scenes and their retinal responses. While the responses of the early visual system (receptors in this case) may represent specifically the statistics of images, post receptor responses are more likely represent the statistical relationship between images and scenes. A corollary of this suggestion is that the visual cortex is adapted to relate the retinal image to behaviour given the statistics of its past interactions with the sources of retinal images: the visual cortex is adapted to the signals it receives from the eyes, and not directly to the world beyond

Routine Antenatal Anti-D Prophylaxis in Women Who Are Rh(D) Negative: Meta-Analyses Adjusted for Differences in Study Design and Quality

Background: To estimate the effectiveness of routine antenatal anti-D prophylaxis for preventing sensitisation in pregnant Rhesus negative women, and to explore whether this depends on the treatment regimen adopted. Methods: Ten studies identified in a previous systematic literature search were included. Potential sources of bias were systematically identified using bias checklists, and their impact and uncertainty were quantified using expert opinion. Study results were adjusted for biases and combined, first in a random-effects meta-analysis and then in a random-effects metaregression analysis. Results: In a conventional meta-analysis, the pooled odds ratio for sensitisation was estimated as 0.25 (95 % CI 0.18, 0.36), comparing routine antenatal anti-D prophylaxis to control, with some heterogeneity (I 2 = 19%). However, this naïve analysis ignores substantial differences in study quality and design. After adjusting for these, the pooled odds ratio for sensitisation was estimated as 0.31 (95 % CI 0.17, 0.56), with no evidence of heterogeneity (I 2 = 0%). A meta-regression analysis wa