Counting Partial Spread Functions in Eight Variables

4 - Recursive Enumerability

The simultaneous matching-to-sample procedures that are widely used to study stimulus equivalence in human participants have generally been unsuccessful in animals. However, functional equivalence classes have been demonstrated in pigeons and sea lions using a concurrent repeated reversal discrimination procedure. In this procedure, responding to one set of stimuli is reinforced but responding to a different set is not and the set associated with reinforcement is changed with multiple reversals during the experiment. The experiments reported here were designed to assess whether functional equivalence classes could be demonstrated in rats using similar techniques. Rats were initially trained with two sets of olfactory stimuli (six odors/set). Following many reversals, probe reversal sessions were conducted in which rats were exposed to a subset of the members of each set and, later in the session, the withheld stimuli were introduced. Responding to these delayed probe trials in accord with the reversed contingencies constituted transfer of function. There was some evidence of transfer in Experiment 1, but the effects were relatively weak and variable. Experiment 2 introduced procedural changes and found strong evidence of transfer of function consistent with the formation of functional equivalence classes. These procedures offer a promising strategy to study symbolic behavior in rodents.

Partial functions of the k-valued logic monotone with respect to an arbitrary partially ordered set with the least and largest elements and distinct from a lattice are considered. It is shown that the set of closed classes of partial monotone functions containing a precomplete in Pk class of everywhere determined monotone function is infinite.

In this study, we employed the advanced reactive force field (ReaxFF) molecular dynamics (MD) simulations to investigate the adsorption mechanisms of acetone, ethanol, methanol and propanol molecules on newly-designed tubular helix nanostructure doped by sulfur substituting carbon atoms. The adsorption processes of four different volatile organic compounds (VOCs) on tubular helix nanostructure are simulated at temperature of 300 K, containing fixed 100 adsorbate molecules. The adsorption energy of acetone is calculated as -4.4 eV which is higher than that of other molecules and it exhibits very strong adsorption of acetone on active sites of tubular helix nanostructure attracting this molecule. Moreover, some MD structural analysis methods, such as partial correlation function (PCF) and diffusion coefficients from mean square displacement (MSD) reveal that O atom in acetone molecule strongly interactions with C and S atoms on tubular helix nanostructure in short distance of 1.17 Å. Addition, the diffusion coefficient of acetone molecule into tubular helix nanostructure is more than that of other molecules indicating faster and easier movement in helical environment. Finally, molecular entrapment capability of tubular helix nanostructure and the surrounding level of acetone molecules the tubular helix nanostructure were revealed by computational method. The computational results help understand the great potential of gas sensor device of newly-designed tubular helix nanostructure in the context of pioneer experimental studies.

Let Vn be the number of equivalence classes of invertible maps from {0,1}n to {0,1}n, under action of permutation of variables on domain and range. So far, the values Vn have been known for n ? 6. This paper describes the procedure by which the values of Vn are calculated for n ? 30.

In Experiments 1 and 2 a match-to-sample procedure was used to establish the prerequisite conditional discriminations for two 3-member equivalence classes (A1, B1, C1 & A2, B2, C2) where stimuli A1 and A2 were written instructions. In Experiment 1 tests for transitivity confirmed the emergence of derived relations. Following this, an off-the-baseline test was given to verify the existence of functional equivalence classes. During off-the-baseline testing stimuli B and C from both classes controlled responding appropriate to the instructions contained in A1 and A2 respectively. In Experiment 2, the omission of tests for transitivity and the reversal of instructions contained in A1 and A2 did not impede the emergence of functional equivalence classes. In Experiment 3, classes A1, B1, C1 and E1, F1, G1 were linked via D1 to produce one class (A1, B1, C1, D1, E1, F1, G1); another two classes (A2, B2, C2 & E2, F2, G2) were linked with D2 to produce A2, B2, C2, D2, E2, F2, G2. The A and G stimuli in each class contained competing sets of instructions. When transformation of function was examined in the first class, the functions at C1 and E1 were controlled by the rules at A1 and G1 respectively; D1 controlled responding in accordance with the instructions at A1. Results from all experiments are discussed in the context of procedures designed to investigate transfer/transformation of function.

Minimization and NP multifunctions

This study extended previous research on equivalence classes that contain more than one function. Initially, separate equivalence classes were established (A1, B1, C1 and A3, B3, C3) using a one-to-many matching-to-sample procedure where A1 and A3 were the sample stimuli. These classes then were transformed into functional equivalence classes by training unique functions at A1 and A3; using modelling clay, a ball was made at A1 and an oblong was made at A3. These two classes then were joined together using another matching-to-sample procedure to establish the class X1-A1-A3. Tests were conducted to see what behaviours occurred in the presence of A1, X1, and A3. Of seven participants, three produced entirely new behaviours at X1, while the others produced the behaviours previously taught at A1 and A3. Results are discussed in the context of variables affecting the generation of novel behaviour.

This SAND report provides the technical progress through April 2005 of the Sandia-led project, "Carbon Sequestration in Synechococcus Sp.: From Molecular Machines to Hierarchical Modeling," funded by the DOE Office of Science Genomics:GTL Program. Understanding, predicting, and perhaps manipulating carbon fixation in the oceans has long been a major focus of biological oceanography and has more recently been of interest to a broader audience of scientists and policy makers. It is clear that the oceanic sinks and sources of CO2 are important terms in the global environmental response to anthropogenic atmospheric inputs of CO2 and that oceanic microorganisms play a key role in this response. However, the relationship between this global phenomenon and the biochemical mechanisms of carbon fixation in these microorganisms is poorly understood. In this project, we will investigate the carbon sequestration behavior of Synechococcus Sp., an abundant marine cyanobacteria known to be important to environmental responses to carbon dioxide levels, through experimental and computational methods. This project is a combined experimental and computational effort with emphasis on developing and applying new computational tools and methods. Our experimental effort will provide the biology and data to drive the computational efforts and include significant investment in developing new experimental methods for uncovering protein partners, characterizing protein complexes, identifying new binding domains. We will also develop and apply new data measurement and statistical methods for analyzing microarray experiments. Computational tools will be essential to our efforts to discover and characterize the function of the molecular machines of Synechococcus. To this end, molecular simulation methods will be coupled with knowledge discovery from diverse biological data sets for high-throughput discovery and characterization of protein-protein complexes. In addition, we will develop a set of novel capabilities for inference of regulatory pathways in microbial genomes across multiple sources of information through the integration of computational and experimental technologies. These capabilities will be applied to Synechococcus regulatory pathways to characterize their interaction map and identify component proteins in these - 4 -pathways. We will also investigate methods for combining experimental and computational results with visualization and natural language tools to accelerate discovery of regulatory pathways. The ultimate goal of this effort is develop and apply new experimental and computational methods needed to generate a new level of understanding of how the Synechococcus genome affects carbon fixation at the global scale. Anticipated experimental and computational methods will provide ever-increasing insight about the individual elements and steps in the carbon fixation process, however relating an organism's genome to its cellular response in the presence of varying environments will require systems biology approaches. Thus a primary goal for this effort is to integrate the genomic data generated from experiments and lower level simulations with data from the existing body of literature into a whole cell model. We plan to accomplish this by developing and applying a set of tools for capturing the carbon fixation behavior of complex of Synechococcus at different levels of resolution. Finally, the explosion of data being produced by high-throughput experiments requires data analysis and models which are more computationally complex, more heterogeneous, and require coupling to ever increasing amounts of experimentally obtained data in varying formats. These challenges are unprecedented in high performance scientific computing and necessitate the development of a companion computational infrastructure to support this effort. More information about this project can be found at www.genomes-to-life.org Acknowledgment We want to gratefully acknowledge the contributions of: Grant Heffelfinger1*, Anthony Martino2, Brian Palenik6, Andrey Gorin3, Ying Xu10,3, Mark Daniel Rintoul1, Al Geist3, Matthew Ennis1, with Pratul Agrawal3, Hashim Al-Hashimi8, Andrea Belgrano12, Mike Brown1, Xin Chen9, Paul Crozier1, PguongAn Dam10, Jean-Loup Faulon2, Damian Gessler12, David Haaland1, Victor Havin4, C.F. Huang5, Tao Jiang9, Howland Jones1, David Jung3, Katherine Kang14, Michael Langston15, Shawn Martin1, Shawn Means1, Vijaya Natarajan4, Roy Nielson5, Frank Olken4, Victor Olman10, Ian Paulsen14, Steve Plimpton1, Andreas Reichsteiner5, Nagiza Samatova3, Arie Shoshani4, Michael Sinclair1, Alex Slepoy1, Shawn Stevens8, Charlie Strauss5, Zhengchang Su10, Ed Thomas1, Jerilyn Timlin1, WimVermaas13, Xiufeng Wan11, HongWei Wu10, Dong Xu11, Grover Yip8, Erik Zuiderweg8 *Author to whom correspondence should be addressed (gsheffe@sandia.gov) 1. Sandia National Laboratories, Albuquerque, NM 2. Sandia National Laboratories, Livermore, CA 3. Oak Ridge National Laboratory, Oak Ridge, TN 4. Lawrence Berkeley National Laboratory, Berkeley, CA 5. Los Alamos National Laboratory, Los Alamos, NM 6. University of California, San Diego 7. University of Illinois, Urbana/Champaign 8. University of Michigan, Ann Arbor 9. University of California, Riverside 10. University of Georgia, Athens 11. University of Missouri, Columbia 12. National Center for Genome Resources, Santa Fe, NM 13. Arizona State University 14. The Institute for Genomic Research 15. University of Tennessee 5 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL8500.

An asymptotic estimate is established for the number of equivalence classes of Boolean functions of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> variables under transformations of the form <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f(x) \rightarrow f(Ax+b)+ L(x)</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x=(x_{l}, \cdots ,x_{n}), A</tex> is a nonsingular <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> matrix, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</tex> is a vector, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L(x)</tex> is a linear function.

Two rational functions $f,g\in \mathbb F_q(X)$ are said to be <em>equivalent</em> if there exist $\phi ,\psi \in \mathbb F_q(X)$ of degree $1$ such that $g=\phi \circ f\circ \psi $. We give an explicit formula for the number of equivalence classes of rati

The present study examined the effects of including stimuli previously trained as members of functional classes or equivalence classes on subsequent equivalence class formation, and isolated the effects of preliminary training from those of the acquired function stimuli. Fifty-six adults were assigned to 1 of 5 conditions. The control group (CONT) received no preliminary training prior to the terminal phase. Participants in the other 4 groups learned two 3-member functional classes and two 3-member equivalence classes during the preliminary phase. The terminal equivalence phase trained two 5-member classes (A → B → C → D → E) comprising abstract forms; the C stimuli in the terminal phase were (a) from the preliminary functional classes for 1 group (ACQ-F), (b) from the preliminary equivalence classes for the second experimental group (ACQ-E), (c) pictures of everyday objects for the picture control group (PIC), and (d) novel, unfamiliar stimuli for the preliminary training control group (PRE-CONT). Class formation yields were 100% in the PIC condition and 11% in the CONT condition; however, low yields in the PRE-CONT, ACQ-F, and ACQ-E conditions were unexpected, suggesting that procedural variables in preliminary training account for more of the subsequent effects on class formation than the stimulus control properties of the acquired function stimuli.

It has been claimed that different types of causes must be considered in biological systems, including top-down as well as same-level and bottom-up causation, thus enabling the top levels to be causally efficacious in their own right. To clarify this issue, the important distinctions between information and signs are introduced here and the concepts of information control and functional equivalence classes in those systems are rigorously defined and used to characterize when top-down causation by feedback control happens, in a way that is testable. The causally significant elements we consider are equivalence classes of lower level processes, realized in biological systems through different operations having the same outcome within the context of information control and networks.

As preparation for a duality theory for saddle programs, a partial conjugacy correspondence is developed among equivalence classes of saddle functions. Three known conjugacy correspondences, including Fenchel’s correspondence among convex functions and Rockafellar’s extension of it to equivalence classes of saddle functions, are shown to be degenerate special cases. Additionally, two new correspondences are brought to light as further special cases. Various questions are answered concerning the lower and upper closures and effective domain of the resulting equivalence class, as well as the effect the correspondence has on the related purely convex function and the subdifferential mapping.

With the recent trend of analysing the process of computation through the linear logic looking glass, it is well understood that the ability to copy and erase data is essential in order to obtain a Turingcomplete computation model. However, erasing and copying don't need to be explicitly included in Turing-complete computation models: in this paper we show that the class of partial recursive functions that are syntactically linear (that is, partial recursive functions where no argument is erased or copied) is Turing-complete