Tracking chains revisited

The structure ${\cal C}_2:=(1^\infty,\le,\le_1,\le_2)$, introduced and first analyzed in Carlson and Wilken 2012 (APAL), is shown to be elementary recursive. Here, $1^\infty$ denotes the proof-theoretic ordinal of the fragment $\Pi^1_1$-$\mathrm{CA}_0$ of second order number theory, or equivalently the set theory $\mathrm{KPl}_0$, which axiomatizes limits of models of Kripke-Platek set theory with infinity. The partial orderings $\le_1$ and $\le_2$ denote the relations of $\Sigma_1$- and $\Sigma_2$-elementary substructure, respectively. In a subsequent article we will show that the structure ${\cal C}_2$ comprises the core of the structure ${\cal R}_2$ of pure elementary patterns of resemblance of order $2$. In Carlson and Wilken 2012 (APAL) the stage has been set by showing that the least ordinal containing a cover of each pure pattern of order $2$ is $1^\infty$. However, it is not obvious from Carlson and Wilken 2012 (APAL) that ${\cal C}_2$ is an elementary recursive structure. This is shown here through a considerable disentanglement in the description of connectivity components of $\le_1$ and $\le_2$. The key to and starting point of our analysis is the apparatus of ordinal arithmetic developed in Wilken 2007 (APAL) and in Section 5 of Carlson and Wilken 2012 (JSL), which was enhanced in Carlson and Wilken 2012 (APAL) specifically for the analysis of ${\cal C}_2$.Comment: The text was edited and aligned with reference [10], Lemma 5.11 was included (moved from [10]), results unchanged. Corrected Def. 5.2 and Section 5.3 on greatest immediate $\le_1$-successors. Updated publication information. arXiv admin note: text overlap with arXiv:1608.0842

Pure patterns of order 2

We provide mutual elementary recursive order isomorphisms between classical ordinal notations, based on Skolem hulling, and notations from pure elementary patterns of resemblance of order $2$, showing that the latter characterize the proof-theoretic ordinal of the fragment $\Pi^1_1$-$\mathrm{CA}_0$ of second order number theory, or equivalently the set theory $\mathrm{KPl}_0$. As a corollary, we prove that Carlson's result on the well-quasi orderedness of respecting forests of order $2$ implies transfinite induction up to the ordinal of $\mathrm{KPl}_0$. We expect that our approach will facilitate analysis of more powerful systems of patterns.Comment: corrected Theorem 4.2 with according changes in section 3 (mainly Definition 3.3), results unchanged. The manuscript was edited, aligned with reference [14] (moving former Lemma 3.5 there), and argumentation was revised, with minor corrections in (the proof of) Theorem 4.2; results unchanged. Updated revised preprint; to appear in the APAL (2017

Controlling Improper Financial Gain in International Adoptions

When I went with the lawyer to pick up Kate--some part of town I could never find again--her mother was lying there, not in a house really, more like a stall with a bed in it. . . . It was like we were going baby shopping. 1 Although once rarely contemplated, international adoption has become a realistic option for couples in the United States. In fact, the United States has received more foreign children for adoption than any other country in the world. 2 Since the first wave of international adoptions in the late 1940s, 3 over 130,000 children have been adopted into this country. 4 As international adoptions have grown in popularity, both licensed agencies and private individuals have appeared in great numbers as adoption intermediaries. 5 High demand for adoptable children encourages these intermediaries to trade children for large amounts of money. 6 Informally, this practice is known as baby selling. 7 While there is no clear consensus that the exchange of some money in an adoption process is morally wrong, the exchange of large amounts of money for children may create improper incentives for birth mothers to release their children for adoption. Most international adoptions are arranged through agencies licensed by administrative or judicial bodies of a particular country to place children from that country. 8 However, adoptions are also handled through independent agents who may be private adoption lawyers, social workers, or other persons acting as liaisons between the adoptive parents ..

Pure Σ2\Sigma_2-Elementarity beyond the Core

We display the entire structure ${\cal R}_2$ coding $\Sigma_1$- and $\Sigma_2$-elementarity on the ordinals. This will enable the analysis of pure $\Sigma_3$-elementary substructures.Comment: Extensive rewrite of the introduction. Mathematical content of sections 2 and 3 unchanged, extended introduction to section 2. Removed section 4. Theorem 4.3 to appear elsewhere with corrected proo

Decoupled Solar Thermal Chemical Electrolysis of Water to Produce Hydrogen

Solar thermal chemical research at Valparaiso University focuses on using concentrated solar energy to produce hydrogen, which can be used to generate electricity in fuel cells. A two-step solar electrolytic process has been proposed for chemical systems such as Fe2O3/Fe3O4, Co3O4/CoO, and Mn2O3/MnO. This new process produces hydrogen using ideally 63-82% less electricity than the traditional electrolytic process. Theoretical solar-to-electrical efficiencies are approximately 19-40%, a range comparable to similar solar thermal chemical processes. Preliminary experimental work with the Fe2O3/Fe3O4 system has validated the chemical possibility of each step of the process. Future work seeks to determine if the proposed processes are all chemically possible, optimize their operation on a small scale and explore their viability on an industrial scale

A detection theory account of change detection

Previous studies have suggested that visual short-term memory (VSTM) has a storage limit of approximately four items. However, the type of high-threshold (HT) model used to derive this estimate is based on a number of assumptions that have been criticized in other experimental paradigms (e.g., visual search). Here we report findings from nine experiments in which VSTM for color, spatial frequency, and orientation was modeled using a signal detection theory (SDT) approach. In Experiments 1-6, two arrays composed of multiple stimulus elements were presented for 100 ms with a 1500 ms ISI. Observers were asked to report in a yes/no fashion whether there was any difference between the first and second arrays, and to rate their confidence in their response on a 1-4 scale. In Experiments 1-3, only one stimulus element difference could occur (T = 1) while set size was varied. In Experiments 4-6, set size was fixed while the number of stimuli that might change was varied (T = 1, 2, 3, and 4). Three general models were tested against the receiver operating characteristics generated by the six experiments. In addition to the HT model, two SDT models were tried: one assuming summation of signals prior to a decision, the other using a max rule. In Experiments 7-9, observers were asked to directly report the relevant feature attribute of a stimulus presented 1500 ms previously, from an array of varying set size. Overall, the results suggest that observers encode stimuli independently and in parallel, and that performance is limited by internal noise, which is a function of set size