Discounting the distant future: How much do uncertain rates increase valuations?

We demonstrate that when the future path of the discount rate is uncertain and highly correlated, the distant future should be discounted at significantly lower rates than suggested by the current rate. We then use two centuries of US interest rate data to quantify this effect. Using both random walk and mean-reverting models, we compute the "certainty-equivalent rate" that summarizes the effect of uncertainty and measures the appropriate forward rate of discount in the future. Under the random walk model we find that the certainty-equivalent rate falls continuously from 4% to 2% after 100 years, 1% after 200 years, and 0.5% after 300 years. At horizons of 400 years, the discounted value increases by a factor of over 40,000 relative to conventional discounting. Applied to climate change mitigation, we find that incorporating discount rate uncertainty almost doubles the expected present value of mitigation benefits. © 2003 Elsevier Science (USA). All rights reserved.

Agglomeration effects in foreign direct investment and the pollution haven hypothesis

Does environmental regulation impair international competitiveness of pollution-intensive industries to the extent that they relocate to countries with less stringent regulation, turning those countries into "pollution havens"? We test this hypothesis using panel data on outward foreign direct investment (FDI) flows of various industries in the German manufacturing sector and account for several econometric issues that have been ignored in previous studies. Most importantly, we demonstrate that externalities associated with FDI agglomeration can bias estimates away from finding a pollution haven effect if omitted from the analysis. We include the stock of inward FDI as a proxy for agglomeration and employ a GMM estimator to control for endogenous time-varying determinants of FDI flows. Furthermore, we propose a difference estimator based on the least polluting industry to break the possible correlation between environmental regulatory stringency and unobservable attributes of FDI recipients in the cross-section. When accounting for these issues we find robust evidence of a pollution haven effect for the chemical industry. © 2008 Springer Science+Business Media B.V.

A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Telomere disruption results in non-random formation of de novo dicentric chromosomes involving acrocentric human chromosomes.

Genome rearrangement often produces chromosomes with two centromeres (dicentrics) that are inherently unstable because of bridge formation and breakage during cell division. However, mammalian dicentrics, and particularly those in humans, can be quite stable, usually because one centromere is functionally silenced. Molecular mechanisms of centromere inactivation are poorly understood since there are few systems to experimentally create dicentric human chromosomes. Here, we describe a human cell culture model that enriches for de novo dicentrics. We demonstrate that transient disruption of human telomere structure non-randomly produces dicentric fusions involving acrocentric chromosomes. The induced dicentrics vary in structure near fusion breakpoints and like naturally-occurring dicentrics, exhibit various inter-centromeric distances. Many functional dicentrics persist for months after formation. Even those with distantly spaced centromeres remain functionally dicentric for 20 cell generations. Other dicentrics within the population reflect centromere inactivation. In some cases, centromere inactivation occurs by an apparently epigenetic mechanism. In other dicentrics, the size of the alpha-satellite DNA array associated with CENP-A is reduced compared to the same array before dicentric formation. Extra-chromosomal fragments that contained CENP-A often appear in the same cells as dicentrics. Some of these fragments are derived from the same alpha-satellite DNA array as inactivated centromeres. Our results indicate that dicentric human chromosomes undergo alternative fates after formation. Many retain two active centromeres and are stable through multiple cell divisions. Others undergo centromere inactivation. This event occurs within a broad temporal window and can involve deletion of chromatin that marks the locus as a site for CENP-A maintenance/replenishment.

Structure, function, and phylogeny of the mating locus in the Rhizopus oryzae complex.

The Rhizopus oryzae species complex is a group of zygomycete fungi that are common, cosmopolitan saprotrophs. Some strains are used beneficially for production of Asian fermented foods but they can also act as opportunistic human pathogens. Although R. oryzae reportedly has a heterothallic (+/-) mating system, most strains have not been observed to undergo sexual reproduction and the genetic structure of its mating locus has not been characterized. Here we report on the mating behavior and genetic structure of the mating locus for 54 isolates of the R. oryzae complex. All 54 strains have a mating locus similar in overall organization to Phycomyces blakesleeanus and Mucor circinelloides (Mucoromycotina, Zygomycota). In all of these fungi, the minus (-) allele features the SexM high mobility group (HMG) gene flanked by an RNA helicase gene and a TP transporter gene (TPT). Within the R. oryzae complex, the plus (+) mating allele includes an inserted region that codes for a BTB/POZ domain gene and the SexP HMG gene. Phylogenetic analyses of multiple genes, including the mating loci (HMG, TPT, RNA helicase), ITS1-5.8S-ITS2 rDNA, RPB2, and LDH genes, identified two distinct groups of strains. These correspond to previously described sibling species R. oryzae sensu stricto and R. delemar. Within each species, discordant gene phylogenies among multiple loci suggest an outcrossing population structure. The hypothesis of random-mating is also supported by a 50:50 ratio of plus and minus mating types in both cryptic species. When crossed with tester strains of the opposite mating type, most isolates of R. delemar failed to produce zygospores, while isolates of R. oryzae produced sterile zygospores. In spite of the reluctance of most strains to mate in vitro, the conserved sex locus structure and evidence for outcrossing suggest that a normal sexual cycle occurs in both species.

Assessing the homogenization of urban land management with an application to US residential lawn care.

Changes in land use, land cover, and land management present some of the greatest potential global environmental challenges of the 21st century. Urbanization, one of the principal drivers of these transformations, is commonly thought to be generating land changes that are increasingly similar. An implication of this multiscale homogenization hypothesis is that the ecosystem structure and function and human behaviors associated with urbanization should be more similar in certain kinds of urbanized locations across biogeophysical gradients than across urbanization gradients in places with similar biogeophysical characteristics. This paper introduces an analytical framework for testing this hypothesis, and applies the framework to the case of residential lawn care. This set of land management behaviors are often assumed--not demonstrated--to exhibit homogeneity. Multivariate analyses are conducted on telephone survey responses from a geographically stratified random sample of homeowners (n = 9,480), equally distributed across six US metropolitan areas. Two behaviors are examined: lawn fertilizing and irrigating. Limited support for strong homogenization is found at two scales (i.e., multi- and single-city; 2 of 36 cases), but significant support is found for homogenization at only one scale (22 cases) or at neither scale (12 cases). These results suggest that US lawn care behaviors are more differentiated in practice than in theory. Thus, even if the biophysical outcomes of urbanization are homogenizing, managing the associated sustainability implications may require a multiscale, differentiated approach because the underlying social practices appear relatively varied. The analytical approach introduced here should also be productive for other facets of urban-ecological homogenization.

The induced innovation hypothesis and energy-saving technological change

We develop a methodology for testing Hicks's induced innovation hypothesis by estimating a product-characteristics model of energy-using consumer durables, augmenting the hypothesis to allow for the influence of government regulations. For the products we explored, the evidence suggests that (i) the rate of overall innovation was independent of energy prices and regulations; (ii) the direction of innovation was responsive to energy price changes for some products but not for others; (iii) energy price changes induced changes in the subset of technically feasible models that were offered for sale; (iv) this responsiveness increased substantially during the period after energy-efficiency product labeling was required; and (v) nonetheless, a sizable portion of efficiency improvements were autonomous.

Gene selection using iterative feature elimination random forests for survival outcomes.

Although many feature selection methods for classification have been developed, there is a need to identify genes in high-dimensional data with censored survival outcomes. Traditional methods for gene selection in classification problems have several drawbacks. First, the majority of the gene selection approaches for classification are single-gene based. Second, many of the gene selection procedures are not embedded within the algorithm itself. The technique of random forests has been found to perform well in high-dimensional data settings with survival outcomes. It also has an embedded feature to identify variables of importance. Therefore, it is an ideal candidate for gene selection in high-dimensional data with survival outcomes. In this paper, we develop a novel method based on the random forests to identify a set of prognostic genes. We compare our method with several machine learning methods and various node split criteria using several real data sets. Our method performed well in both simulations and real data analysis.Additionally, we have shown the advantages of our approach over single-gene-based approaches. Our method incorporates multivariate correlations in microarray data for survival outcomes. The described method allows us to better utilize the information available from microarray data with survival outcomes.

Regularity of invariant densities for 1D systems with random switching

© 2015 IOP Publishing Ltd & London Mathematical Society.This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove the smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points.

Stochastic switching in infinite dimensions with applications to random parabolic PDE

© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.

The reappearance hypothesis revisited: recurrent involuntary memories after traumatic events and in everyday life.

Recurrent involuntary memories are autobiographical memories that come to mind with no preceding retrieval attempt and that are subjectively experienced as being repetitive. Clinically, they are classified as a symptom of posttraumatic stress disorder. The present work is the first to systematically examine recurrent involuntary memories outside clinical settings. Study 1 examines recurrent involuntary memories among survivors of the tsunami catastrophe in Southeast Asia in 2004. Study 2 examines recurrent involuntary memories in a large general population. Study 3 examines whether the contents of recurrent involuntary memories recorded in a diary study are duplicates of, or differ from, one another. We show that recurrent involuntary memories are not limited to clinical populations or to emotionally negative experiences; that they typically do not come to mind in a fixed and unchangeable form; and that they show the same pattern regarding accessibility as do autobiographical memories in general. We argue that recurrent involuntary memories after traumas and in everyday life can be explained in terms of general and well-established mechanisms of autobiographical memory.

Revisiting the monoamine hypothesis of depression: a new perspective.

As the incidence of depression increases, depression continues to inflict additional suffering to individuals and societies and better therapies are needed. Based on magnetic resonance spectroscopy and laboratory findings, gamma aminobutyric acid (GABA) may be intimately involved in the pathophysiology of depression. The isoelectric point of GABA (pI = 7.3) closely approximates the pH of cerebral spinal fluid (CSF). This may not be a trivial observation as it may explain preliminary spectrophotometric, enzymatic, and HPLC data that monoamine oxidase (MAO) deaminates GABA. Although MAO is known to deaminate substrates such as catecholamines, indoleamines, and long chain aliphatic amines all of which contain a lipophilic moiety, there is very good evidence to predict that a low concentration of a very lipophilic microspecies of GABA is present when GABA pI = pH as in the CSF. Inhibiting deamination of this microspecies of GABA could explain the well-established successful treatment of refractory depression with MAO inhibitors (MAOI) when other antidepressants that target exclusively levels of monoamines fail. If further experimental work can confirm these preliminary findings, physicians may consider revisiting the use of MAOI for the treatment of non-intractable depression because the potential benefits of increasing GABA as well as the monoamines may outweigh the risks associated with MAOI therapy.

Chronic opioid therapy and opioid tolerance: a new hypothesis.

Opioids are efficacious and cost-effective analgesics, but tolerance limits their effectiveness. This paper does not present any new clinical or experimental data but demonstrates that there exist ascending sensory pathways that contain few opioid receptors. These pathways are located by brain PET scans and spinal cord autoradiography. These nonopioid ascending pathways include portions of the ventral spinal thalamic tract originating in Rexed layers VI-VIII, thalamocortical fibers that project to the primary somatosensory cortex (S1), and possibly a midline dorsal column visceral pathway. One hypothesis is that opioid tolerance and opioid-induced hyperalgesia may be caused by homeostatic upregulation during opioid exposure of nonopioid-dependent ascending pain pathways. Upregulation of sensory pathways is not a new concept and has been demonstrated in individuals impaired with deafness or blindness. A second hypothesis is that adjuvant nonopioid therapies may inhibit ascending nonopioid-dependent pathways and support the clinical observations that monotherapy with opioids usually fails. The uniqueness of opioid tolerance compared to tolerance associated with other central nervous system medications and lack of tolerance from excess hormone production is discussed. Experimental work that could prove or disprove the concepts as well as flaws in the concepts is discussed.