Behavior of Friedmann-Robertson-Walker Cosmological Models in Scalar-Tensor Gravity

We analyze solutions to Friedmann-Robertson-Walker cosmologies in Brans-Dicke theory, where a scalar field is coupled to gravity. Matter is modelled by a $\gamma$-law perfect fluid, including false-vacuum energy as a special case. Through a change of variables, we reduce the field equations from fourth order to second order, and they become equivalent to a two-dimensional dynamical system. We then analyze the entire solution space of this dynamical system, and find that many qualitative features of these cosmologies can be gleaned, including standard non-inflationary or extended inflationary expansion, but also including bifurcations of stable or unstable expansion or contraction, noninflationary vacuum-energy dominated models, and several varieties of ``coasting," ``bouncing," ``hesitating," and ``vacillating" universes. It is shown that inflationary dogma, which states that a universe with curvature and dominated by inflationary matter will always approach a corresponding flat-space solution at late times, does not hold in general for the scalar-tensor theory, but rather that the occurence of inflation depends upon the initial energy of the scalar field relative to the expansion rate. In the case of flat space ($k=0$), the dynamical system formalism generates some previously known exact power-law solutions.Comment: Slight stylistic changes and some references added. This version to be published in {\sl Annals of Physics

What do we need for robust and quantitative health impact assessment?

Health impact assessment (HIA) aims to make the health consequences of decisions explicit. Decision-makers need to know that the conclusions of HIA are robust. Quantified estimates of potential health impacts may be more influential but there are a number of concerns. First, not everything that can be quantified is important. Second, not everything that is being quantified at present should be, if this cannot be done robustly. Finally, not everything that is important can be quantified; rigorous qualitative HIA will still be needed for a thorough assessment. This paper presents the first published attempt to provide practical guidance on what is required to perform robust, quantitative HIA. Initial steps include profiling the affected populations, obtaining evidence from for postulated impacts, and determining how differences in subgoups' exposures and suscepibilities affect impacts. Using epidemiological evidence for HIA is different from carrying out a new study. Key steps in quantifying impacts are mapping the causal pathway, selecting appropriate outcome measures and selecting or developing a statistical model. Evidence from different sources is needed. For many health impacts, evidence of an effect may be scarce and estimates of the size and nature of the relationship may be inadequate. Assumptions and uncertainties must therefore be explicit. Modelled data can sometimes be tested against empirical data but sensitivity analyses are crucial. When scientific problems occur, discontinuing the study is not an option, as HIA is usually intended to inform real decisions. Both qualitative and quantitative elements of HIA must be performed robustly to be of value

Exclusionary Discipline Highest in New Hampshire’s Urban Schools Suspension and Expulsion Found to Disproportionately Affect Disadvantaged Students

This research brief follows up on a joint Carsey/NH Kids Count publication from 2009. The 2009 study focused on larger disciplinary trends in New Hampshire schools and contextualized them in the policies, laws, and procedures that may have resulted in increased use of exclusionary discipline. The present study reports on rates of exclusionary discipline from 2010 through 2014 by school and student characteristics to better understand how and to what extent exclusionary discipline has been applied across the state in recent years. Authors Douglas Gagnon, Eleanor Jaffee, and Reeve Kennedy report that although rates of out-of-school suspension among secondary school students in New Hampshire are nearly as high as national trends, rates of expulsion are far below the national average. In urban secondary schools, the rate of in-school suspension is twice that of non-urban schools, while out-of-school suspension rates are three times higher. Male students, students of color, students eligible for free or reduced-price lunch, students with disabilities, and homeless students are more likely to experience exclusionary school discipline, although racial disparities appear to stem largely from the greater racial diversity at the urban schools that use this type of discipline at higher rates with all students. Statewide, 3.5 percent of New Hampshire’s middle and high school students are suspended out of school for a total of five days or more and/or expelled in a given year. Given the notably higher rates of use of exclusionary discipline in New Hampshire’s urban school districts, the authors recommend that school policies and environments be assessed for opportunities to reverse these trends and provide more students with consistent classroom time and instruction

Social Choice and Cultural Bias

These three essays are the fruits of a little Winter Study, in December 1981, which enabled Mary Douglas and James Douglas (both of Northwestern University, Illinois, USA) to visit the System and Decision Sciences area at IIASA, there to collaborate on an interdisciplinary (or, more properly, non-disciplinary) task. 'Institutional bias' was the provisional title for what we had in mind and our aim was to try to wrap some cultural and political context around the paradoxes of social choice. The Western liberal tradition holds rationality and individuality in high regard. It has to; otherwise it would not be liberal, nor would it cohere long enough to become a tradition. But too high a regard for reason may exaggerate the part played by conscious design in the conduct of human affairs, and too high a regard for the individual may exaggerate both his ability to identify the things that he values and his scope to arrange them in an order of his own choosing. The unity of these essays lies in their common critical theme; all three, in their different ways, take issue with the liberal tradition. James Douglas' point of departure is the recognition that actual political systems coped very effectively with the paradoxes of social choice long before Condorcet and Arrow revealed that those paradoxes existed. Since they could not have been consciously designed to do this, these systems must have evolved. The lowly dung beetle, as it decides whether to try to find a new and untenanted cow-pat or to stick with the ever crustier one that it has, follows a personal strategy so subtle as to require integral calculus in its solution. Could it be that we are no better equipped to design our political institutions than is the dung beetle up to doing 'A level' mathematics? Trial and error -- success and failure over countless generations -- we conclude, is what has led the individual dung beetle to the so-sensible strategy that it shares with every other dung beetle. The rational-choice theorist, if he could bring himself to study so distasteful a subject, would have to conclude that, with such a lack of variation in the preference orderings of cow-pats as we go from one individual to another, there is some form of dictatorship operating within the dung beetles' social system. Of course, in the dung beetle case, the lack of individuality -- the dictatorship -- is about as extreme as it could possibly be and it would be foolish to pretend that it provides a more valid model of human social life than does the theory of rational choice. No, our aim is not to jump to the dung beetle's extreme but, rather, to ask: 'extreme from what?' The answer has to be: 'from a situation in which, because the individual preference orderings are so gloriously varied that no parallelisms -- no little clumpings or mutual alignments -- can exist, there can be no dictatorship'. We would argue that such a situation, though intellectually intriguing, has nothing to do with the description of the life of man in society...apart, that is, from saying that it is not like that. The "invisible dictators"' that the rational-choice theorist conjures up in response to the parallelisms -- the departures from individual perfection -- that he continually bumps up against are, collectively, an old friend of the anthropologist. They are culture. The only trouble is that invisible dictators are plural and culture is singular. To resolve this paradox we begin by defining our extreme at the opposite pole to that defined by the theory of rational choice. Instead of the fine independence of the individual we take as our model the dung beetle. 'To what extent, and in what ways, does our behavior distance us from it?' we ask, rather than 'to what extent does our behavior fall short of the individualist ideal?'. But are not these differences, like a knot in a length of string, simply different ways of measuring the same thing? No, because there is no continuum -- no measuring scale -- between these two extremes. Total dictatorship is attainable; perfect individuality is not. We can measure our divergence from the attainable but not from the unattainable, and the attempt to do the latter we label 'the individualist fallacy ' . The dung beetle has, over the generations, adapted so as to take advantage of the adoptive possibilities of an environment within which certain laws (such as the progressive drying out of cow-pats) hold inexorable sway. In much the same way, actual political systems have evolved to take advantage of an environment wherein Arrow's impossibility theorem holds away. But what is particularly interesting is that, though all these systems cope with the paradoxes of social choice, they do not all cope with them in the same way. Mary Douglas comes in at this point and, venturing into the untrodden terrain that lies between cultural anthropology and organization theory, sketches out a three-fold typology of socially viable organizations, each one of which stabilizes itself with the aid of its appropriate and distinctive cultural bias. So it is culture -- man's self-reflexive ability -- that distances him from the dung beetle. At the same time, this idea of cultural biases stabilizing their appropriate social organizations ('departures from individual perfection' from the rational-choice viewpoint) allows us to reconcile a plurality of invisible dictators with a singular culture. The final essay explores the way in which these two levels -- the cultural biases that always intervene to prevent the attainment of perfect individuality and the political systems that cope with the paradoxes of social choice -- fit together. Cultural biases, it argues, are in perpetual contention. One organizational form may, for a time, gain dominance but it can never permanently eliminate the others. Within this flux certain conjunctions of cultural biases (and of their associated organizations) are stabilizable (or, at any rate, change only in slow time) and these persistent regularities we label 'political regimes

Applications of Hilbert Module Approach to Multivariable Operator Theory

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space \clh associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: $$\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h,$$where $p \in \mathbb{C}[z_1, \ldots, z_n]$ and $h \in \mathcal{H}$. A companion survey provides an introduction to the theory of Hilbert modules and some (Hilbert) module point of view to multivariable operator theory. The purpose of this survey is to emphasize algebraic and geometric aspects of Hilbert module approach to operator theory and to survey several applications of the theory of Hilbert modules in multivariable operator theory. The topics which are studied include: generalized canonical models and Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert spaces, a class of simple submodules and quotient modules of the Hardy modules over polydisc, commutant lifting theorem, similarity and free Hilbert modules, left invertible multipliers, inner resolutions, essentially normal Hilbert modules, localizations of free resolutions and rigidity phenomenon. This article is a companion paper to "An Introduction to Hilbert Module Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in Handbook of Operator Theory, Springe

Uniqueness of the minimum of the free energy of the 2D Yang-Mills theory at large N

There has been some controversies at the large $N$ behaviour of the 2D Yang-Mills and chiral 2D Yang-Mills theories. To be more specific, is there a one parameter family of minima of the free energy in the strong region, or the minimum is unique. We show that there is a missed equation which, added to the known equations, makes the minimum unique.Comment: 8 pages,Late

The effect of elevated hydrostatic pressure on the spectral absorption of deep-sea fish visual pigments

The effect of hydrostatic pressure (0.1-54 MPa, equivalent to pressures experienced by fish from the ocean's surface to depths of ca. 5400 m) on visual pigment absorption spectra was investigated for rod visual pigments extracted from the retinae of 12 species of deep-sea fish of diverse phylogeny and habitat. The wavelength of peak absorption (λmax) was shifted to longer wavelengths by an average of 1.35 nm at 40 MPa (a pressure approximately equivalent to average ocean depth) relative to measurements made at one atmosphere (ca. 0.1 MPa), but with little evidence of a change in absorbance at the λmax. We conclude that previousλ max measurements of deep-sea fish visual pigments, made at a pressure close to 0.1 MPa, provide a good indication ofλ max values at higher pressures when considering the ecology of vision in the deep-sea. Although not affecting the spectral sensitivity of the animal to any important degree, the observed shift inλ max may be of interest in the context of understanding opsin-chromophore interaction and spectral tuning of visual pigments

More on Phase Structure of Nonlocal 2D Generalized Yang-Mills Theories (nlgYM2_2's)

We study the phase structure of nonlocal two dimensional generalized Yang - Mills theories (nlgYM$_2$) and it is shown that all order of $\phi^{2k}$ model of these theories has phase transition only on compact manifold with $g = 0$(on sphere), and the order of phase transition is 3. Also it is shown that the $\phi^2 + \frac{2\alpha}{3}\phi^3$ model of nlgYM$_2$ has third order phase transition on any compact manifold with $1 < g < 1+ \frac{\hat{A}}{|\eta_c|}$, and has no phase transition on sphere.Comment: 11 pages, no figure