A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

Satisfaction in choice as a function of the number of alternatives: When "goods satiate" but "bads escalate"

Whereas people are typically thought to be better off with more choices, studiesshow that they often prefer to choose from small as opposed to large sets of alternatives.We propose that satisfaction from choice is an inverted U-shaped function of thenumber of alternatives. This proposition is derived theoretically by considering thebenefits and costs of different numbers of alternatives and is supported by fourexperimental studies. We also manipulate the perceptual costs of information processingand demonstrate how this affects the resulting satisfaction function. We furtherindicate that satisfaction when choosing from a given set is diminished if people aremade aware of the existence of other choice sets. The role of individual differences insatisfaction from choice is documented by noting effects due to gender and culture. Weconclude by emphasizing the need to have an explicit rationale for knowing how muchchoice is enough.

Executive Order Number Six, February 21, 2008

Establishes a Green Government Initiative for the State of Iowa.

Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation

This paper studies the rate of convergence of an appropriatediscretization scheme of the solution of the Mc Kean-Vlasovequation introduced by Bossy and Talay. More specifically,we consider approximations of the distribution and of thedensity of the solution of the stochastic differentialequation associated to the Mc Kean - Vlasov equation. Thescheme adopted here is a mixed one: Euler/weakly interactingparticle system. If $n$ is the number of weakly interactingparticles and $h$ is the uniform step in the timediscretization, we prove that the rate of convergence of thedistribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of theorder of $\frac 1{\sqrt n} + h $, while for the densities is ofthe order $ h +\frac 1 {\sqrt {nh}}$. This result is obtainedby carefully employing techniques of Malliavin Calculus.

Executive Order Number Seven, June 27, 2008

This Executive Order establishes an Iowa Task Force to Rebuild Iowa, after the storms and flood in May and June of 2008.

Executive Order Number Eight, July 16, 2008

This Executive Order establishes an Independent Contractor Reform Task Force.

Iowa Developments, Volume 17, Number 4

Business news from the Iowa Department of Economic Development

Iowa Developments, August 2008, Volume 17, Number 5

Business Development news from the Iowa Department of Economic Development

Iowa Developments, October 2008, Volume 17, Number 6

Business Development news from the Iowa Department of Economic Development

On bounds for network revenue management

The Network Revenue Management problem can be formulated as a stochastic dynamic programming problem (DP or the\optimal" solution V *) whose exact solution is computationally intractable. Consequently, a number of heuristics have been proposed in the literature, the most popular of which are the deterministic linear programming (DLP) model, and a simulation based method, the randomized linear programming (RLP) model. Both methods give upper bounds on the optimal solution value (DLP and PHLP respectively). These bounds are used to provide control values that can be used in practice to make accept/deny decisions for booking requests. Recently Adelman [1] and Topaloglu [18] have proposed alternate upper bounds, the affine relaxation (AR) bound and the Lagrangian relaxation (LR) bound respectively, and showed that their bounds are tighter than the DLP bound. Tight bounds are of great interest as it appears from empirical studies and practical experience that models that give tighter bounds also lead to better controls (better in the sense that they lead to more revenue). In this paper we give tightened versions of three bounds, calling themsAR (strong Affine Relaxation), sLR (strong Lagrangian Relaxation) and sPHLP (strong Perfect Hindsight LP), and show relations between them. Speciffically, we show that the sPHLP bound is tighter than sLR bound and sAR bound is tighter than the LR bound. The techniques for deriving the sLR and sPHLP bounds can potentially be applied to other instances of weakly-coupled dynamic programming.

Executive Order Number Nine, November 7, 2008

This Executive Order directs IFA to administer the allocation of additional tax-exempt bonding authority provided by the Disaster Relief Act, develop administrative rules to implement the allocation of this additional tax-exempt bonding authority, track the allocation of the additional tax-exempt bonding authority to ensure compliance with all applicable federal law, and provide all necessary reports to the IRS.

Executive Order Number Ten, December 22, 2008

This Executive Order aids the Governor to meet his Constitutional obligation to balance the state budget, announcing that he would order a 1.5 percent across-the-board reduction in state expenditures for the current fiscal year.

Genome-wide association analysis of copy number variation in recurrent depressive disorder.

Large, rare copy number variants (CNVs) have been implicated in a variety of psychiatric disorders, but the role of CNVs in recurrent depression is unclear. We performed a genome-wide analysis of large, rare CNVs in 3106 cases of recurrent depression, 459 controls screened for lifetime-absence of psychiatric disorder and 5619 unscreened controls from phase 2 of the Wellcome Trust Case Control Consortium (WTCCC2). We compared the frequency of cases with CNVs against the frequency observed in each control group, analysing CNVs over the whole genome, genic, intergenic, intronic and exonic regions. We found that deletion CNVs were associated with recurrent depression, whereas duplications were not. The effect was significant when comparing cases with WTCCC2 controls (P=7.7 × 10(-6), odds ratio (OR) =1.25 (95% confidence interval (CI) 1.13-1.37)) and to screened controls (P=5.6 × 10(-4), OR=1.52 (95% CI 1.20-1.93). Further analysis showed that CNVs deleting protein coding regions were largely responsible for the association. Within an analysis of regions previously implicated in schizophrenia, we found an overall enrichment of CNVs in our cases when compared with screened controls (P=0.019). We observe an ordered increase of samples with deletion CNVs, with the lowest proportion seen in screened controls, the next highest in unscreened controls and the highest in cases. This may suggest that the absence of deletion CNVs, especially in genes, is associated with resilience to recurrent depression.

Executive Order Number Eleven, February 17, 2009

This Executive Order creates a task force on dependent care.

Executive Order Number Twelve, April 14, 2009

This Executive Order made the creation of the Iowa Accountability and Transparency Board and the report of the State of Iowa's efforts to implement the AARA