Approximating High-Dimensional Dynamic Models: Sieve Value Function Iteration

Many dynamic problems in economics are characterized by large state spaces which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of high-dimensional dynamic models based on sieves and establish results for the: (a) consistency, (b) rates of convergence, and (c) bounds on the error of approximation. We embed this method for approximating the solution to the dynamic problem within an estimation routine and prove that it provides consistent estimates of the model's parameters. We provide Monte Carlo evidence that our method can successfully be used to approximate models that would otherwise be infeasible to compute, suggesting that these techniques may substantially broaden the class of models that can be solved and estimated.

Division, adjoints, and dualities of bilinear maps

The distributive property can be studied through bilinear maps and various morphisms between these maps. The adjoint-morphisms between bilinear maps establish a complete abelian category with projectives and admits a duality. Thus the adjoint category is not a module category but nevertheless it is suitably familiar. The universal properties have geometric perspectives. For example, products are orthogonal sums. The bilinear division maps are the simple bimaps with respect to nondegenerate adjoint-morphisms. That formalizes the understanding that the atoms of linear geometries are algebraic objects with no zero-divisors. Adjoint-isomorphism coincides with principal isotopism; hence, nonassociative division rings can be studied within this framework. This also corrects an error in an earlier pre-print; see Remark 2.11

Combinatorial Alexander Duality -- a Short and Elementary Proof

Let X be a simplicial complex with the ground set V. Define its Alexander dual as a simplicial complex X* = {A \subset V: V \setminus A \notin X}. The combinatorial Alexander duality states that the i-th reduced homology group of X is isomorphic to the (|V|-i-3)-th reduced cohomology group of X* (over a given commutative ring R). We give a self-contained proof.Comment: 7 pages, 2 figure; v3: the sign function was simplifie

Dynamic Expression of Broad-Complex Isoforms Mediates Temporal Control of an Ecdysteroid Target Gene at the Onset of Drosophila Metamorphosis

AbstractMetamorphosis in Drosophila melanogaster is orchestrated by the steroid hormone ecdysone, which triggers a cascade of primary-response transcriptional regulators and secondary effector genes during the third larval instar and prepupal periods of development. The early ecdysone-response Broad-Complex (BR-C) gene, a key regulator of this cascade, is defined by three complementing functions (rbp, br, and 2Bc) and encodes several distinct zinc-finger-containing isoforms (Z1 to Z4). Using isoform-specific polyclonal antibodies we observe in the fat body a switch in BR-C isoform expression from the Z2 to the other three isoforms during the third instar. We show that the 2Bc+ function that corresponds presumably to the Z3 isoform is required for the larval fat body-specific expression of a transgenic construct (AE) in which the lacZ gene is under the control of the ecdysone-regulated enhancer and minimal promoter of the fat body protein 1 (Fbp1) gene. Using hs(BR-C) transgenes, we demonstrate that overexpression of Z1, Z3, or Z4, but not Z2, is able to rescue AE activity with faithful tissue specificity in a BR-C null (npr1) genetic context, demonstrating a partial functional redundancy between Z1, Z3, and Z4 isoforms. We also show that continuous overexpression of Z2 during the third instar represses AE, while conversely, expression of Z3 earlier than its normal onset induces precocious expression of the construct. This finding establishes a tight correlation between the dynamic pattern of expression of the BR-C isoforms and their individual repressive or inductive roles in AE regulation. Altogether our results demonstrate that the balance between BR-C protein isoforms in the fat body mediates, in part, the precise timing of the ecdysone activation of the AE construct but does not modulate its tissue specificity

Is sticky blood bad for the Brain? Hemostatic and inflammatory systems and dementia in the Caerphilly prospective study

Objective— Hemostasis and inflammation have been implicated in dementia. This study investigates the role of specific hemostatic and inflammatory pathways with incident vascular and nonvascular dementia.Methods and Results— This was a prospective study of a population sample of men aged 65 to 84 years, with baseline assessment of hemostatic and inflammatory factors and cognition measured 17 years later. The sample included 865 men (59 had dementia and 112 had cognitive impairment, not dementia), free of vascular disease at baseline and for whom hemostatic and inflammatory marker data were available and cognitive status was known. A total of 15 hemostatic and 6 inflammatory markers were assessed. Factor analysis was used to identify hemostatic subsystems. The National Institute of Neurological Disorders and Stroke–Association Internationale pour la Recherche et l’Enseignement en Neurologie criteria were used to identify vascular dementia. By using standardized (z) scores for hemostatic and inflammatory markers, and after adjustment for age and risk factors, vascular dementia was associated with fibrinogen (hazard ratio [HR], 1.68; 95% confidence interval [CI], 1.02–2.76), factor VIII (HR, 1.79; 95% CI, 1.09–3.00), and plasminogen activator inhibitor 1 (HR, 3.13; 95% CI, 1.73–5.70). For vascular dementia, the HR risk from high levels of all three hemostatic variables (fibrinogen, factor VIII, and plasminogen activator inhibitor 1) was 2.97 (P<0.001). Inflammatory factors were not associated with vascular dementia.Conclusion— The associations of these hemostatic markers with vascular dementia may implicate clot formation as the primary mechanism and are consistent with a microinfarct model of vascular dementia

Neurodevelopmental abnormalities in children with PHACE syndrome.

Prior case reports have identified neurodevelopmental abnormalities in children with PHACE syndrome, a neurocutaneous disorder first characterized in 1996. In this multicenter, retrospective study of a previously identified cohort of 93 children diagnosed with PHACE syndrome from 1999 to 2010, 29 children had neurologic evaluations at ≥ 1 year of age (median age: 4 years, 2 months). In all, 44% had language delay, 36% gross motor delay, and 8% fine motor delay; 52% had an abnormal neurological exam, with speech abnormalities as the most common finding. Overall, 20 of 29 (69%) had neurodevelopmental abnormalities. Cerebral, but not posterior fossa, structural abnormalities were identified more often in children with abnormal versus normal neurodevelopmental outcomes (35% vs. 0%, P = .04). Neurodevelopmental abnormalities in young children with PHACE syndrome referred to neurologists include language and gross motor delay, while fine motor delay is less frequent. Prospective studies are needed to understand long-term neurodevelopmental outcomes

Iron Isotope Fractionation during Fe(II) Oxidation Mediated by the Oxygen-Producing Marine Cyanobacterium Synechococcus PCC 7002

In this study, we couple iron isotope analysis to microscopic and mineralogical investigation of iron speciation during circumneutral Fe(II) oxidation and Fe(III) precipitation with photosynthetically produced oxygen. In the presence of the cyanobacterium Synechococcus PCC 7002, aqueous Fe(II) (Fe(II)aq) is oxidized and precipitated as amorphous Fe(III) oxyhydroxide minerals (iron precipitates, Feppt), with distinct isotopic fractionation (ε56Fe) values determined from fitting the δ56Fe(II)aq (1.79‰ and 2.15‰) and the δ56Feppt (2.44‰ and 2.98‰) data trends from two replicate experiments. Additional Fe(II) and Fe(III) phases were detected using microscopy and chemical extractions and likely represent Fe(II) and Fe(III) sorbed to minerals and cells. The iron desorbed with sodium acetate (FeNaAc) yielded heavier δ56Fe compositions than Fe(II)aq. Modeling of the fractionation during Fe(III) sorption to cells and Fe(II) sorption to Feppt, combined with equilibration of sorbed iron and with Fe(II)aq using published fractionation factors, is consistent with our resulting δ56FeNaAc. The δ56Feppt data trend is inconsistent with complete equilibrium exchange with Fe(II)aq. Because of this and our detection of microbially excreted organics (e.g., exopolysaccharides) coating Feppt in our microscopic analysis, we suggest that electron and atom exchange is partially suppressed in this system by biologically produced organics. These results indicate that cyanobacteria influence the fate and composition of iron in sunlit environments via their role in Fe(II) oxidation through O2 production, the capacity of their cell surfaces to sorb iron, and the interaction of secreted organics with Fe(III) minerals

A semiconductor source of triggered entangled photon pairs?

The realisation of a triggered entangled photon source will be of great importance in quantum information, including for quantum key distribution and quantum computation. We show here that: 1) the source reported in ``A semiconductor source of triggered entangled photon pairs''[1. Stevenson et al., Nature 439, 179 (2006)]} is not entangled; 2) the entanglement indicators used in Ref. 1 are inappropriate, relying on assumptions invalidated by their own data; and 3) even after simulating subtraction of the significant quantity of background noise, their source has insignificant entanglement.Comment: 5 pages in pre-print format, 1 tabl

Early effects of lipopolysaccharide-induced inflammation on foetal brain development in rat

Studies in humans and animal models link maternal infection and imbalanced levels of inflammatory mediators in the foetal brain to the aetiology of neuropsychiatric disorders. In a number of animal models, it was shown that exposure to viral or bacterial agents during a period that corresponds to the second trimester in human gestation triggers brain and behavioural abnormalities in the offspring. However, little is known about the early cellular and molecular events elicited by inflammation in the foetal brain shortly after maternal infection has occurred. In this study, maternal infection was mimicked by two consecutive intraperitoneal injections of 200 μg of LPS (lipopolysaccharide)/kg to timed-pregnant rats at GD15 (gestational day 15) and GD16. Increased thickness of the CP (cortical plate) and hippocampus together with abnormal distribution of immature neuronal markers and decreased expression of markers for neural progenitors were observed in the LPS-exposed foetal forebrains at GD18. Such effects were accompanied by decreased levels of reelin and the radial glial marker GLAST (glial glutamate transporter), and elevated levels of pro-inflammatory cytokines in maternal serum and foetal forebrains. Foetal inflammation elicited by maternal injections of LPS has discrete detrimental effects on brain development. The early biochemical and morphological changes described in this work begin to explain the sequelae of early events that underlie the neurobehavioural deficits reported in humans and animals exposed to prenatal insults

Bird records for the Saddle Bag Mountain area of Lincoln and Tillamook Counties

The results of 703 observations are given; most of these were made in the 1930's by James Macnab, Jane Claire Dirks-Edmunds, Dorothy McKey-Fender, and others. These results are the most comprehensive throughout the year for any site above 1,000 ft in Lincoln County and hint that bird communities at sites above 1,400 ft are less diverse than sites nearer sea level. However, many more systematic observations throughout the year are needed to elucidate the significance of elevation on bird diversity. Two marshes on Saddle Bag Mountain are the only locations where Common Snipe appear to nest in Lincoln County