Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors

In applied work economists often seek to relate a given response variable y to some causal parameter mu* associated with it. This parameter usually represents a summarization based on some explanatory variables of the distribution of y, such as a regression function, and treating it as a conditional expectation is central to its identification and estimation. However, the interpretation of mu* as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when mu* is modelled as a parametric function of explanatory variables because it is well known how instrumental variables techniques can be used to identify and estimate mu*. In contrast, handling endogenous regressors in nonparametric models, where mu* is regarded as fully unknown, presents di±cult theoretical and practical challenges. In this paper we consider an endogenous nonparametric model based on a conditional moment restriction. We investigate identification related properties of this model when the unknown function mu* belongs to a linear space. We also investigate underidentification of mu* along with the identification of its linear functionals. Several examples are provided in order to develop intuition about identification and estimation for endogenous nonparametric regression and related models.

Solving SAT in linear time with a neural-like membrane system

We present in this paper a neural-like membrane system solving the SAT problem in linear time. These neural Psystems are nets of cells working with multisets. Each cell has a finite state memory, processes multisets of symbol-impulses, and can send impulses (?excitations?) to the neighboring cells. The maximal mode of rules application and the replicative mode of communication between cells are at the core of the eficiency of these systems.

Self-consistent resonance absorption with two layer profile steepening

Resonance absorption of p-polarized light, incident at angle 6 on a flowing, stratified plasma, is analyzed; profile steepening within (i) a layer around the turning point, and (ii) a thinner,embedded sublayer at the critical surface is taken into account self-consistently. The entire steepened region is taken as collisionless and isothermal. The structure of the main layer shows a variety of regimes, depending on how the flow crosses a sonic point. The structure of the sublayer is also determined; it is entirely subsonic (with no wave breaking) for a well-defined,broad parameter range. Density changes across both layer and sublayer, and fractional absorption, are given in terms of [(wavelength)2 Xintensity/temperature], and (temperature/mec2). The flow outside the double structure is also analyzed for particular conditions.

Morphological Functions to Quantify Three-Dimensional Tomograms of Macropore Structure in a Vineyard Soil with Two Different Management Regimes

Soil tomography and morphological functions built over Minkowski functionals were used to describe the impact on pore structure of two soil management practices in a Mediterranean vineyard. Soil structure controls important physical and biological processes in soil–plant–microbial systems. Those processes are dominated by the geometry of soil pore structure, and a correct model of this geometry is critical for understanding them. Soil tomography has been shown to provide rich three-dimensional digital information on soil pore geometry. Recently, mathematical morphological techniques have been proposed as powerful tools to analyze and quantify the geometrical features of porous media. Minkowski functionals and morphological functions built over Minkowski functionals provide computationally efficient means to measure four fundamental geometrical features of three-dimensional geometrical objects, that is, volume, boundary surface, mean boundary surface curvature, and connectivity. We used the threshold and the dilation and erosion of three-dimensional images to generate morphological functions and explore the evolution of Minkowski functionals as the threshold and as the degree of dilation and erosion changes. We analyzed the three-dimensional geometry of soil pore space with X-ray computed tomography (CT) of intact soil columns from a Spanish Mediterranean vineyard by using two different management practices (conventional tillage versus permanent cover crop of resident vegetation). Our results suggested that morphological functions built over Minkowski functionals provide promising tools to characterize soil macropore structure and that the evolution of morphological features with dilation and erosion is more informative as an indicator of structure than moving threshold for both soil managements studied.

ORK1, a potassium-selective leak channel with two pore domains cloned from Drosophila melanogaster by expression in Saccharomyces cerevisiae

A K+ channel gene has been cloned from Drosophila melanogaster by complementation in Saccharomyces cerevisiae cells defective for K+ uptake. Naturally expressed in the neuromuscular tissues of adult flies, this gene confers K+ transport capacity on yeast cells when heterologously expressed. In Xenopus laevis oocytes, expression yields an ungated K+-selective current whose attributes resemble the “leak” conductance thought to mediate the resting potential of vertebrate myelinated neurons but whose molecular nature has long remained elusive. The predicted protein has two pore (P) domains and four membrane-spanning helices and is a member of a newly recognized K+ channel family. Expression of the channel in flies and yeast cells makes feasible studies of structure and in vivo function using genetic approaches that are not possible in higher animals.

Mitosis in vertebrate somatic cells with two spindles: Implications for the metaphase/anaphase transition checkpoint and cleavage

During mitosis an inhibitory activity associated with unattached kinetochores prevents PtK1 cells from entering anaphase until all kinetochores become attached to the spindle. To gain a better understanding of how unattached kinetochores block the metaphase/anaphase transition we followed mitosis in PtK1 cells containing two independent spindles in a common cytoplasm. We found that unattached kinetochores on one spindle did not block anaphase onset in a neighboring mature metaphase spindle 20 μm away that lacked unattached kinetochores. As in cells containing a single spindle, anaphase onset occurred in the mature spindles x̄ = 24 min after the last kinetochore attached regardless of whether the adjacent immature spindle contained one or more unattached kinetochores. These findings reveal that the inhibitory activity associated with an unattached kinetochore is functionally limited to the vicinity of the spindle containing the unattached kinetochore. We also found that once a mature spindle entered anaphase the neighboring spindle also entered anaphase x̄ = 9 min later regardless of whether it contained monooriented chromosomes. Thus, anaphase onset in the mature spindle catalyzes a “start anaphase” reaction that spreads globally throughout the cytoplasm and overrides the inhibitory signal produced by unattached kinetochores in an adjacent spindle. Finally, we found that cleavage furrows often formed between the two independent spindles. This reveals that the presence of chromosomes and/or a spindle between two centrosomes is not a prerequisite for cleavage in vertebrate somatic cells.

A transcriptional activating region with two contrasting modes of protein interaction

A C-terminal segment of the yeast activator Gal4 manifests two functions: When tethered to DNA, it elicits gene activation, and it binds the inhibitor Gal80. Here we examine the effects on these two functions of cysteine and proline substitutions. We find that, although certain cysteine substitutions diminish interaction with Gal80, those substitutions have little effect on the activating function in vivo and interaction with TATA box-binding protein (TBP) in vitro. Proline substitutions introduced near residues critical for Gal80 binding abolish that interaction but once again have no effect on the activating function. Crosslinking experiments show that a defined position in the activating peptide is in close proximity to TBP and Gal80 in the two separate reactions and show that binding of the inhibitor blocks binding to TBP. Thus, the same stretch of amino acids are involved in two quite different protein–protein interactions: binding to Gal80, which depends on a precise sequence and the formation of a defined secondary structure, or interactions with the transcriptional machinery in vivo, which are not impaired by perturbations of either sequence or structure.

Peptide hybrids containing α- and β-amino acids: Structure of a decapeptide β-hairpin with two facing β-phenylalanine residues

A β-hairpin conformation has been characterized in crystals of the decapeptide t-butoxycarbonyl-Leu-Val-βPhe-Val-DPro-Gly-Leu-βPhe-Val-Val-methyl ester [βPhe; (S)-β3 homophenylalanine] by x-ray diffraction. The polypeptide chain reversal is nucleated by the centrally positioned DPro-Gly segment, which adopts a type-I′ β-turn conformation. Four intramolecular cross-strand hydrogen bonds stabilize the peptide fold. The βPhe(3) and βPhe(8) residues occupy facing positions on the hairpin, with the side chains projecting on opposite faces of the β-sheet. At the site of insertion of β-residues, the polarity of the peptide units along each strand reverses, as compared with the α-peptide segments. In this analog, a small segment of a polar sheet is observed, where adjacent CO and NH groups line up in opposite directions in each strand. In the crystal, an extended β-sheet is formed by hydrogen bonding between strands of antiparallel pairs of β-hairpins. The crystallographic parameters for C65H102N10O13⋅ 3H2O are: space group P212121; a = 19.059(8) Å, b = 19.470(2) Å, c = 21.077(2) Å; Z = 4; agreement factor R1 = 9.12% for 3,984 data observed >4σ(F) and a resolution of 0.90 Å.

Isolation and Characterization of a Histidine Biosynthetic Gene in Arabidopsis Encoding a Polypeptide with Two Separate Domains for Phosphoribosyl-ATP Pyrophosphohydrolase and Phosphoribosyl-AMP Cyclohydrolase

Phosphoribosyl-ATP pyrophosphohydrolase (PRA-PH) and phosphoribosyl-AMP cyclohydrolase (PRA-CH) are encoded by HIS4 in yeast and by hisIE in bacteria and catalyze the second and the third step, respectively, in the histidine biosynthetic pathway. By complementing a hisI mutation of Escherichia coli with an Arabidopsis cDNA library, we isolated an Arabidopsis cDNA (At-IE) that possesses these two enzyme activities. The At-IE cDNA encodes a bifunctional protein of 281 amino acids with a calculated molecular mass of 31,666 D. Genomic DNA-blot analysis with the At-IE cDNA as a probe revealed a single-copy gene in Arabidopsis, and RNA-blot analysis showed that the At-IE gene was expressed ubiquitously throughout development. Sequence comparison suggested that the At-IE protein has an N-terminal extension of about 50 amino acids with the properties of a chloroplast transit peptide. We demonstrated through heterologous expression studies in E. coli that the functional domains for the PRA-CH (hisI) and PRA-PH (hisE) resided in the N-terminal and the C-terminal halves, respectively, of the At-IE protein.

Excitation transfer spectroscopy with two metastable 138Ba+ ions in same trap.

In the absence of lasers approaching trapped ion clock transitions in sharpness we propose to replace the 12.49 m laser field exciting the D3/2-D5/2 transition of the single Ba+ ion A in D3/2 with the near-field of a close by identical ion B in the excited D5/2 state. We tune the frequency of the near-field by the differential Stark shift generated when the center of mass of the tuned ions is slightly moved out of the trap center by a small bias voltage. We demonstrate that the resultant resonant energy exchange can be made considerably faster than the natural lifetime of either metastable level and show how it might be detected.

A gradient estimate to a degenerate parabolic equation with a singular absorption term: The global quenching phenomena

We prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term. We also show the global quenching phenomena for L1 initial datums. Moreover, the free boundary problem is considered in this paper.

Robust solutions to multi-objective linear programs with uncertain data

In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for the radius of robust feasibility guaranteeing constraint feasibility for all possible scenarios within a specified uncertainty set under affine data parametrization. We then present numerically tractable optimality conditions for minmax robust weakly efficient solutions, i.e., the weakly efficient solutions of the robust counterpart. We also consider highly robust weakly efficient solutions, i.e., robust feasible solutions which are weakly efficient for any possible instance of the objective matrix within a specified uncertainty set, providing lower bounds for the radius of highly robust efficiency guaranteeing the existence of this type of solutions under affine and rank-1 objective data uncertainty. Finally, we provide numerically tractable optimality conditions for highly robust weakly efficient solutions.