On the complexity of posets

AbstractThe purpose of this paper is to discuss several invariants each of which provides a measure of the intuitive notion of complexity for a finite partially ordered set. For a poset X the invariants discussed include cardinality, width, length, breadth, dimension, weak dimension, interval dimension and semiorder dimension denoted respectively X, W(X), L(X), B(X), dim(X). Wdim(X), Idim(X) and Sdim(X). Among these invariants the following inequalities hold. B(X)⩽Idim(X)⩽Sdim(X)⩽Wdim(X)⩽dim(X)⩽W(X). We prove that every poset X with three of more points contains a partly with Idim(X) Idim(X) {x,v}). If M denotes the set of maximal elements and A an arbitrary anticham of X we show that Idim(X)⩽W(X-M) and Idim(X)⩽2W(X-A). We also show that there exist functions f(n,t) and (gt) such that I(X)⩽n and Idim(X)⩽tsimply dim(X)⩽f(n,t and Sdim(X)⩽t implies dim(X)⩽g(t)

Capital Gains Taxation and Realizations: Evidence from Interstate Comparisons

Despite numerous studies of the relation between income taxes and capital garns realizations, the revenue consequences of reducing capital gains tax rates remain unclear. However, an important source of cross-sectional variation has been neglected in this line of research: since both the tax base and the tax rate vary among states, the marginal tax rate on capital gains differs among otherwise identical individuals located in different states. The interstate variation in the tax consequences of realizing capital gains implies that the incentive to realize gains varies across states. This paper documents the interstate variation in capital gains taxation and examines the relation between capital gains taxes and aggregated state-level realizations. For each state, we construct marginal tax rates on capital gains for the highest state income tax bracket for 1982 through 1990. Using state-level aggregated data rather than data on individual taxpayers alleviates the problem that the marginal tax rate is endogenous to the amount of capital gains realized. Panel estimates indicate that capital gains realizations are negatively related to capital gains tax rates. The estimated elasticity is smaller than that found by most researchers using panel data, with a point estimate of - 0.67 in our basic specification.

Green Jobs Myths

A rapidly growing literature promises that a massive program of government mandates, subsidies, and forced technological interventions will reward the nation with an economy brimming with green jobs. Not only will these jobs improve the environment, but they will be high paying, interesting, and provide collective rights. This literature is built on mythologies about economics, forecasting, and technology. In this Article, we survey the green jobs literature, analyze its assumptions, and show how the special interest groups promoting the idea of green jobs have embedded dubious assumptions and techniques within their analyses. Before undertaking efforts to restructure and possibly impoverish our society, careful analysis and informed public debate about these assumptions and prescriptions are necessary

Incidence and Allocation Effects of a State Fiscal Policy Shift: The Florio Initiatives in New Jersey

We calculate the incidence of recent changes to the New Jersey state tax system on a sample of homeowners. Our analysis distinguishes between business-as-usual responses to an evolving fiscal situation and tax changes that constitute a surprise. The latter have incidence effects; the former do not. We conclude that, if the changes carried out by NJ Governor Jim Florio are regarded as permanent, they effected a one-time wealth redistribution from, on average, higher-income homeowners toward lower-income homeowners and from owners of suburban residential property toward owners of urban residential property. Although effects on the averages for identifiable groups are clear and significant there is very considerable variation in the effects on individual homeowners within groups. We also estimate the allocation effects of the tax changes using a general equilibrium model that incorporates the option of in-and out migration. The results suggest that the changes will induce a sizable migration of weal thy and high-income people out of the state.

LSST: from Science Drivers to Reference Design and Anticipated Data Products

(Abridged) We describe here the most ambitious survey currently planned in the optical, the Large Synoptic Survey Telescope (LSST). A vast array of science will be enabled by a single wide-deep-fast sky survey, and LSST will have unique survey capability in the faint time domain. The LSST design is driven by four main science themes: probing dark energy and dark matter, taking an inventory of the Solar System, exploring the transient optical sky, and mapping the Milky Way. LSST will be a wide-field ground-based system sited at Cerro Pach\'{o}n in northern Chile. The telescope will have an 8.4 m (6.5 m effective) primary mirror, a 9.6 deg$^2$ field of view, and a 3.2 Gigapixel camera. The standard observing sequence will consist of pairs of 15-second exposures in a given field, with two such visits in each pointing in a given night. With these repeats, the LSST system is capable of imaging about 10,000 square degrees of sky in a single filter in three nights. The typical 5$\sigma$ point-source depth in a single visit in $r$ will be $\sim 24.5$ (AB). The project is in the construction phase and will begin regular survey operations by 2022. The survey area will be contained within 30,000 deg$^2$ with $\delta<+34.5^\circ$, and will be imaged multiple times in six bands, $ugrizy$, covering the wavelength range 320--1050 nm. About 90\% of the observing time will be devoted to a deep-wide-fast survey mode which will uniformly observe a 18,000 deg$^2$ region about 800 times (summed over all six bands) during the anticipated 10 years of operations, and yield a coadded map to $r\sim27.5$. The remaining 10\% of the observing time will be allocated to projects such as a Very Deep and Fast time domain survey. The goal is to make LSST data products, including a relational database of about 32 trillion observations of 40 billion objects, available to the public and scientists around the world.Comment: 57 pages, 32 color figures, version with high-resolution figures available from https://www.lsst.org/overvie

The Relative Role of Perceived Partner Risks in Promoting Condom Use in a Three-City Sample of High-Risk, Low-Income Women

We examined the effect of women’s perceptions of sexual partner risks on condom use. Women from three US cities (n = 1,967) were recruited to provide data on HIV risks. In univariate models, increased odds of condom use were associated with perceiving that partners had concurrent partners and being unaware of partners': (a) HIV status, (b) bisexuality, (c) concurrency; and/or (d) injection drug use. In multivariate models, neither being unaware of the four partner risk factors nor perceiving a partner as being high risk was associated with condom use. Contextual factors associated with decreased odds of condom use were having sex with a main partner, homelessness in the past year, alcohol use during sex, and crack use in the past 30 days. Awareness of a partner’s risks may not be sufficient for increasing condom use. Contextual factors, sex with a main partner in particular, decrease condom use despite awareness of partner risk factors

Chromosome evolution in Cophomantini (Amphibia, Anura, Hylinae)

The hylid tribe Cophomantini is a diverse clade of Neotropical treefrogs composed of the genera Aplastodiscus, Boana, Bokermannohyla, Hyloscirtus, and Myersiohyla. The phylogenetic relationships of Cophomantini have been comprehensively reviewed in the literature, providing a suitable framework for the study of chromosome evolution. Employing different banding techniques, we studied the chromosomes of 25 species of Boana and 3 of Hyloscirtus; thus providing, for the first time, data for Hyloscirtus and for 15 species of Boana. Most species showed karyotypes with 2n = 2x = 24 chromosomes; some species of the B. albopunctata group have 2n = 2x = 22, and H. alytolylax has 2n = 2x = 20. Karyotypes are all bi-armed in most species presented, with the exception of H. larinopygion (FN = 46) and H. alytolylax (FN = 38), with karyotypes that have a single pair of small telocentric chromosomes. In most species of Boana, NORs are observed in a single pair of chromosomes, mostly in the small chromosomes, although in some species of the B. albopunctata, B. pulchella, and B. semilineata groups, this marker occurs on the larger pairs 8, 1, and 7, respectively. In Hyloscirtus, NOR position differs in the three studied species: H. alytolylax (4p), H. palmeri (4q), and H. larinopygion (1p). Heterochromatin is a variable marker that could provide valuable evidence, but it would be necesserary to understand the molecular composition of the C-bands that are observed in different species in order to test its putative homology. In H. alytolylax, a centromeric DAPI+ band was observed on one homologue of chromosome pair 2. The band was present in males but absent in females, providing evidence for an XX/XY sex determining system in this species. We review and discuss the importance of the different chromosome markers (NOR position, C-bands, and DAPI/CMA3 patterns) for their impact on the taxonomy and karyotype evolution in Cophomantini