Bias and learning in temporal binding: intervals between actions and outcomes are compressed by prior bias

It has consistently been shown that agents judge the intervals between their actions and outcomes as compressed in time, an effect named intentional binding. In the present work, we investigated whether this effect is result of prior bias volunteers have about the timing of the consequences of their actions, or if it is due to learning that occurs during the experimental session. Volunteers made temporal estimates of the interval between their action and target onset (Action conditions), or between two events (No-Action conditions). Our results show that temporal estimates become shorter throughout each experimental block in both conditions. Moreover, we found that observers judged intervals between action and outcomes as shorter even in very early trials of each block. To quantify the decrease of temporal judgments in experimental blocks, exponential functions were fitted to participants’ temporal judgments. The fitted parameters suggest that observers had different prior biases as to intervals between events in which action was involved. These findings suggest that prior bias might play a more important role in this effect than calibration-type learning processes.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Posterior Simulation in the Generalized Linear Model with Semiparmetric Random Effects

Generalized linear mixed models with semiparametric random effects are useful in a wide variety of Bayesian applications. When the random effects arise from a mixture of Dirichlet process (MDP) model, normal base measures and Gibbs sampling procedures based on the Pólya urn scheme are often used to simulate posterior draws. These algorithms are applicable in the conjugate case when (for a normal base measure) the likelihood is normal. In the non-conjugate case, the algorithms proposed by MacEachern and Müller (1998) and Neal (2000) are often applied to generate posterior samples. Some common problems associated with simulation algorithms for non-conjugate MDP models include convergence and mixing difficulties. This paper proposes an algorithm based on the Pólya urn scheme that extends the Gibbs sampling algorithms to non-conjugate models with normal base measures and exponential family likelihoods. The algorithm proceeds by making Laplace approximations to the likelihood function, thereby reducing the procedure to that of conjugate normal MDP models. To ensure the validity of the stationary distribution in the non-conjugate case, the proposals are accepted or rejected by a Metropolis-Hastings step. In the special case where the data are normally distributed, the algorithm is identical to the Gibbs sampler.

DEVELOPMENT AND APPLICATIONS OF GENOMIC RESOURCES FOR TWO NORTH AMERICAN HARDWOOD TAXA

Hardwoods comprise about half of the biomass of forestlands in North America and present many uses including economic, ecological and aesthetic functions. Forest trees rely on the genetic variation within tree populations to overcome the many biotic, abiotic, anthropogenic factors which are further worsened by climate change, that threaten their continued survival and functionality. To harness these inherent genetic variations of tree populations, informed knowledge of the genomic resources and techniques, which are currently lacking or very limited, are imperative for forest managers. The current study therefore aimed to develop genomic microsatellite markers for the leguminous tree species, honey locust, Gleditsia triacanthos L. and test their applicability in assessing genetic variation, estimation of gene flow patterns and identification of a full-sib mapping population. We also aimed to test the usefulness of already developed nuclear and gene-based microsatellite markers in delineation of species and taxonomic relationships between four of the taxonomically difficult Section Lobatae species (Quercus coccinea, Q. ellipsoidalis, Q. rubra and Q. velutina. We recorded 100% amplification of G. triacanthos genomic microsatellites developed using Illumina sequencing techniques in a panel of seven unrelated individuals with 14 of these showing high polymorphism and reproducibility. When characterized in 36 natural population samples, we recorded 20 alleles per locus with no indication for null alleles at 13 of the 14 microsatellites. This is the first report of genomic microsatellites for this species. Honey locust trees occur in fragmented populations of abandoned farmlands and pastures and is described as essentially dioecious. Pollen dispersal if the main source of gene flow within and between populations with the ability to offset the effects of random genetic drift. Factors known to influence gene include fragmentation and degree of isolation, which make the patterns gene flow in fragmented populations of honey locust a necessity for their sustainable management. In this follow-up study, we used a subset of nine of the 14 developed gSSRs to estimate gene flow and identify a full-sib mapping population in two isolated fragments of honey locust. Our analyses indicated that the majority of the seedlings (65-100% - at both strict and relaxed assignment thresholds) were sired by pollen from outside the two fragment populations. Only one selfing event was recorded confirming the functional dioeciousness of honey locust and that the seed parents are almost completely outcrossed. From the Butternut Valley, TN population, pollen donor genotypes were reconstructed and used in paternity assignment analyses to identify a relatively large full-sib family comprised of 149 individuals, proving the usefulness of isolated forest fragments in identification of full-sib families. In the Ames Plantation stand, contemporary pollen dispersal followed a fat-tailed exponential-power distribution, an indication of effective gene flow. Our estimate of δ was 4,282.28 m, suggesting that insect pollinators of honey locust disperse pollen over very long distances. The high proportion of pollen influx into our sampled population implies that our fragment population forms part of a large effectively reproducing population. The high tendency of oak species to hybridize while still maintaining their species identity make it difficult to resolve their taxonomic relationships. Oaks of the section Lobatae are famous in this regard and remain unresolved at both morphological and genetic markers. We applied 28 microsatellite markers including outlier loci with potential roles in reproductive isolation and adaptive divergence between species to natural populations of four known interfertile red oaks, Q. coccinea, Q. ellpsoidalis, Q. rubra and Q. velutina. To better resolve the taxonomic relationships in this difficult clade, we assigned individual samples to species, identified hybrids and introgressive forms and reconstructed phylogenetic relationships among the four species after exclusion of genetically intermediate individuals. Genetic assignment analyses identified four distinct species clusters, with Q. rubra most differentiated from the three other species, but also with a comparatively large number of misclassified individuals (7.14%), hybrids (7.14%) and introgressive forms (18.83%) between Q. ellipsoidalis and Q. velutina. After the exclusion of genetically intermediate individuals, Q. ellipsoidalis grouped as sister species to the largely parapatric Q. coccinea with high bootstrap support (91 %). Genetically intermediate forms in a mixed species stand were located proximate to both potential parental species, which supports recent hybridization of Q. velutina with both Q. ellipsoidalis and Q. rubra. Analyses of genome-wide patterns of interspecific differentiation can provide a better understanding of speciation processes and taxonomic relationships in this taxonomically difficult group of red oak species.

A generalized anisotropic quadric yield criterion and its application to bone tissue at multiple length scales

Nonlinear computational analysis of materials showing elasto-plasticity or damage relies on knowledge of their yield behavior and strengths under complex stress states. In this work, a generalized anisotropic quadric yield criterion is proposed that is homogeneous of degree one and takes a convex quadric shape with a smooth transition from ellipsoidal to cylindrical or conical surfaces. If in the case of material identification, the shape of the yield function is not known a priori, a minimization using the quadric criterion will result in the optimal shape among the convex quadrics. The convexity limits of the criterion and the transition points between the different shapes are identified. Several special cases of the criterion for distinct material symmetries such as isotropy, cubic symmetry, fabric-based orthotropy and general orthotropy are presented and discussed. The generality of the formulation is demonstrated by showing its degeneration to several classical yield surfaces like the von Mises, Drucker–Prager, Tsai–Wu, Liu, generalized Hill and classical Hill criteria under appropriate conditions. Applicability of the formulation for micromechanical analyses was shown by transformation of a criterion for porous cohesive-frictional materials by Maghous et al. In order to demonstrate the advantages of the generalized formulation, bone is chosen as an example material, since it features yield envelopes with different shapes depending on the considered length scale. A fabric- and density-based quadric criterion for the description of homogenized material behavior of trabecular bone is identified from uniaxial, multiaxial and torsional experimental data. Also, a fabric- and density-based Tsai–Wu yield criterion for homogenized trabecular bone from in silico data is converted to an equivalent quadric criterion by introduction of a transformation of the interaction parameters. Finally, a quadric yield criterion for lamellar bone at the microscale is identified from a nanoindentation study reported in the literature, thus demonstrating the applicability of the generalized formulation to the description of the yield envelope of bone at multiple length scales.

Influence of Gestational Age and Parental Education on Executive Functions of Children Born Very Preterm

Background: Children born very preterm (<32 weeks’ gestational age; VPT) and/or very low birth weight (<1500 g; VLBW) are at high risk of deficits in executive functions, namely inhibition, working memory, and shifting. Both, gestational age and socioeconomic factors, such as parental education, are known to influence executive functions, with children born at lower gestational age and with lower educated parents displaying worse executive skills. This study aimed to investigate if maternal and paternal education moderated the relationship between gestational age and executive functions in VPT/VLBW children aged 8-12 years. It was hypothesised that the disadvantageous effect of low gestational age could be buffered more easily in families with higher educational background. Methods: Sixty VPT/VLBW children born in the cohort of 1998-2003 were recruited. All children completed executive function tasks (inhibition, working memory, and shifting). Results: There was a significant dose-response-relationship between gestational age and inhibition, with children being born at earlier gestational age showing worse inhibition. However, neither maternal nor paternal education moderated the relationship between gestational age and executive functions significantly. Conclusion: children than parental education. The disadvantageous effect of low gestational age was equal in children with higher and lower educated parents. However, the impact of gestational age and parental education on executive functions may differ depending on the socioeconomic spectrum of the study sample.

FUNCTIONS OF DEADENYLATION FACTORS IN MRNA DECAY AND MRNA PROCESSING BODY FORMATION

Most newly synthesized messenger RNAs possess a 5’ cap and a 3’ poly(A) tail. The process of poly(A) tail shortening, also termed deadenylation, is important for post-transcriptional gene regulation, because deadenylation not only leads to mRNA translational inhibition but also is the first step of major mRNA degradation. Translationally inhibited mRNAs can be stored and/or degraded in dynamic cytoplasmic foci termed mRNA processing bodies, or P bodies, which are conserved in eukaryotes. To shed new light on the mechanisms of P body formation and P body functions, I focused on the link between deadenylation factors and P bodies. I found that the two major deadenylation complexes, Pan3-Pan2 and Ccr4-Caf1, can both be enriched in P bodies. The deadenylase activity of the Ccr4-Caf1 complex is prerequisite for P body formation. Pan3, but not the deadenylase Pan2, is essential for P body formation. While the C-terminal domain of Pan3 is important for interaction with Pan2, Pan3 N-terminal domain is important for Pan3 to form cytoplasmic foci colocalizing with P bodies and to promote mRNA decay. Interestingly, Pan3 N-terminal domain may be phosphorylated to regulate Pan3 localization and functions. Aside from the functions of the two deadenylation complexes in P bodies, I also studied all reported human P body proteins as a whole using bioinformatics. This effort not only has generated a comprehensive picture of the functions of and interactions among human P body proteins, but also has predicted proteins that may regulate P body formation and/or functions. In summary, my study has established a direct link between mRNA deadenylation and P body formation and has also led to new hypotheses to guide future research on how P body dynamics are controlled.

Prospective memory, executive functions, and metacognition are already differentiated in young elementary school children: Evidence from latent factor modelling

This study investigated the empirical differentiation of prospective memory, executive functions, and metacognition and their structural relationships in 119 elementary school children (M = 95 months, SD = 4.8 months). These cognitive abilities share many characteristics on the theoretical level and are all highly relevant in many everyday contexts when intentions must be executed. Nevertheless, their empirical relationships have not been examined on the latent level, although an empirical approach would contribute to our knowledge concerning the differentiation of cognitive abilities during childhood. We administered a computerized event-based prospective memory task, three executive function tasks (updating, inhibition, shifting), and a metacognitive control task in the context of spelling. Confirmatory factor analysis revealed that the three cognitive abilities are already empirically differentiable in young elementary school children. At the same time, prospective memory and executive functions were found to be strongly related, and there was also a close link between prospective memory and metacognitive control. Furthermore, executive functions and metacognitive control were marginally significantly related. The findings are discussed within a framework of developmental differentiation and conceptual similarities and differences.

Molecular basis of salt tolerance in Physcomitrella Patens model plant: potassium homeostasis and physiological roles of chx transporters

El suelo salino impone un estrés abiótico importante que causa graves problemas en la agricultura ya que la mayoría de los cultivos se ven afectados por la salinidad debido a efectos osmóticos y tóxicos. Por ello, la contaminación y la escasez de agua dulce, la salinización progresiva de tierras y el aumento exponencial de la población humana representan un grave problema que amenaza la seguridad alimentaria mundial para las generaciones futuras. Por lo tanto, aumentar la tolerancia a la salinidad de los cultivos es un objetivo estratégico e ineludible para garantizar el suministro de alimentos en el futuro. Mantener una óptima homeostasis de K+ en plantas que sufren estrés salino es un objetivo importante en el proceso de obtención de plantas tolerantes a la salinidad. Aunque el modelo de la homeostasis de K+ en las plantas está razonablemente bien descrito en términos de entrada de K+, muy poco se sabe acerca de los genes implicados en la salida de K+ o de su liberación desde la vacuola. En este trabajo se pretende aclarar algunos de los mecanismos implicados en la homeostasis de K+ en plantas. Para ello se eligió la briofita Physcomitrella patens, una planta no vascular de estructura simple y de fase haploide dominante que, entre muchas otras cualidades, hacen que sea un modelo ideal. Lo más importante es que no sólo P. patens es muy tolerante a altas concentraciones de Na+, sino que también su posición filogenética en la evolución de las plantas abre la posibilidad de estudiar los cambios claves que, durante el curso de la evolución, se produjeron en las diversas familias de los transportadores de K+. Se han propuesto varios transportadores de cationes como candidatos que podrían tener un papel en la salida de K+ o su liberación desde la vacuola, especialmente miembros de la familia CPA2 que contienen las familias de transportadores KEA y CHX. En este estudio se intenta aumentar nuestra comprensión de las funciones de los transportadores de CHX en las células de las plantas usando P. patens, como ya se ha dicho. En esta especie, se han identificado cuatro genes CHX, PpCHX1-4. Dos de estos genes, PpCHX1 y PpCHX2, se expresan aproximadamente al mismo nivel que el gen PpACT5, y los otros dos genes muestran una expresión muy baja. La expresión de PpCHX1 y PpCHX2 en mutantes de Escherichia coli defectivos en el transporte de K+ restauraron el crecimiento de esta cepa en medios con bajo contenido de K+, lo que viii sugiere que la entrada de K+ es energizada por un mecanismo de simporte con H+. Por otra parte, estos transportadores suprimieron el defecto asociado a la mutación kha1 en Saccharomyces cerevisiae, lo que sugiere que podrían mediar un antiporte en K+/H+. La proteína PpCHX1-GFP expresada transitoriamente en protoplastos de P. patens co-localizó con un marcador de Golgi. En experimentos similares, la proteína PpCHX2-GFP localizó aparentemente en la membrana plasmática y tonoplasto. Se construyeron las líneas mutantes simples de P. patens ΔPpchx1 y ΔPpchx2, y también el mutante doble ΔPpchx2 ΔPphak1. Los mutantes simples crecieron normalmente en todas las condiciones ensayadas y mostraron flujos de entrada normales de K+ y Rb+; la mutación ΔPpchx2 no aumentó el defecto de las plantas ΔPphak1. En experimentos a largo plazo, las plantas ΔPpchx2 mostraron una retención de Rb+ ligeramente superior que las plantas silvestres, lo que sugiere que PpCHX2 promueve la transferencia de Rb+ desde la vacuola al citosol o desde el citosol al medio externo, actuando en paralelo con otros transportadores. Sugerimos que transportadores de K+ de varias familias están involucrados en la homeostasis de pH de orgánulos ya sea mediante antiporte K+/H+ o simporte K+-H+.ix ABSTRACT Soil salinity is a major abiotic stress causing serious problems in agriculture as most crops are affected by it. Moreover, the contamination and shortage of freshwater, progressive land salinization and exponential increase of human population aggravates the problem implying that world food security may not be ensured for the next generations. Thus, a strategic and an unavoidable goal would be increasing salinity tolerance of plant crops to secure future food supply. Maintaining an optimum K+ homeostasis in plants under salinity stress is an important trait to pursue in the process of engineering salt tolerant plants. Although the model of K+ homeostasis in plants is reasonably well described in terms of K+ influx, very little is known about the genes implicated in K+ efflux or release from the vacuole. In this work, we aim to clarify some of the mechanisms involved in K+ homeostasis in plants. For this purpose, we chose the bryophyte plant Physcomitrella patens, a nonvascular plant of simple structure and dominant haploid phase that, among many other characteristics, makes it an ideal model. Most importantly, not only P. patens is very tolerant to high concentrations of Na+, but also its phylogenetic position in land plant evolution opens the possibility to study the key changes that occurred in K+ transporter families during the course of evolution. Several cation transporter candidates have been proposed to have a role in K+ efflux or release from the vacuole especially members of the CPA2 family which contains the KEA and CHX transporter families. We intended in this study to increase our understanding of the functions of CHX transporters in plant cells using P. patens, in which four CHX genes have been identified, PpCHX1-4. Two of these genes, PpCHX1 and PpCHX2, are expressed at approximately the same level as the PpACT5 gene, but the other two genes show an extremely low expression. PpCHX1 and PpCHX2 restored growth of Escherichia coli mutants on low K+-containing media, suggesting they mediated K+ uptake that may be energized by symport with H+. In contrast, these genes suppressed the defect associated to the kha1 mutation in Saccharomyces cerevisiae, which suggest that they might mediate K+/H+ antiport. PpCHX1-GFP protein transiently expressed in P. patens protoplasts co-localized with a Golgi marker. In similar experiments, the PpCHX2-GFP protein appeared to localize to tonoplast and plasma x membrane. We constructed the ΔPpchx1 and ΔPpchx2 single mutant lines, and the ΔPpchx2 ΔPphak1 double mutant. Single mutant plants grew normally under all the conditions tested and exhibited normal K+ and Rb+ influxes; the ΔPpchx2 mutation did not increase the defect of ΔPphak1 plants. In long-term experiments, ΔPpchx2 plants showed a slightly higher Rb+ retention than wild type plants, which suggests that PpCHX2 mediates the transfer of Rb+ from either the vacuole to the cytosol or from the cytosol to the external medium in parallel with other transporters. We suggest that K+ transporters of several families are involved in the pH homeostasis of organelles by mediating either K+/H+ antiport or K+-H+ symport.

Functions of FKBP12 and Mitochondrial Cyclophilin Active Site Residues In Vitro and In Vivo in Saccharomyces cerevisiae

Cyclophilin and FK506 binding protein (FKBP) accelerate cis–trans peptidyl-prolyl isomerization and bind to and mediate the effects of the immunosuppressants cyclosporin A and FK506. The normal cellular functions of these proteins, however, are unknown. We altered the active sites of FKBP12 and mitochondrial cyclophilin from the yeast Saccharomyces cerevisiae by introducing mutations previously reported to inactivate these enzymes. Surprisingly, most of these mutant enzymes were biologically active in vivo. In accord with previous reports, all of the mutant enzymes had little or no detectable prolyl isomerase activity in the standard peptide substrate-chymotrypsin coupled in vitro assay. However, in a variation of this assay in which the protease is omitted, the mutant enzymes exhibited substantial levels of prolyl isomerase activity (5–20% of wild-type), revealing that these mutations confer sensitivity to protease digestion and that the classic in vitro assay for prolyl isomerase activity may be misleading. In addition, the mutant enzymes exhibited near wild-type activity with two protein substrates, dihydrofolate reductase and ribonuclease T1, whose folding is accelerated by prolyl isomerases. Thus, a number of cyclophilin and FKBP12 “active-site” mutants previously identified are largely active but protease sensitive, in accord with our findings that these mutants display wild-type functions in vivo. One mitochondrial cyclophilin mutant (R73A), and also the wild-type human FKBP12 enzyme, catalyze protein folding in vitro but lack biological activity in vivo in yeast. Our findings provide evidence that both prolyl isomerase activity and other structural features are linked to FKBP and cyclophilin in vivo functions and suggest caution in the use of these active-site mutations to study FKBP and cyclophilin functions.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Flows of knowledge from universities and federal laboratories: Modeling the flow of patent citations over time and across institutional and geographic boundaries

The extent to which new technological knowledge flows across institutional and national boundaries is a question of great importance for public policy and the modeling of economic growth. In this paper we develop a model of the process generating subsequent citations to patents as a lens for viewing knowledge diffusion. We find that the probability of patent citation over time after a patent is granted fits well to a double-exponential function that can be interpreted as the mixture of diffusion and obsolescense functions. The results indicate that diffusion is geographically localized. Controlling for other factors, within-country citations are more numerous and come more quickly than those that cross country boundaries.

Behaviours, Processes and Probabilistic Environmental Functions in H-Open Systems

The Patten’s Theory of the Environment, supposes an impotent contribution to the Theoretical Ecology. The hypothesis of the duality of environments, the creaon and genon functions and the three developed propositions are so much of great importance in the field of the Applied Mathematical as Ecology. The authors have undertaken an amplification and revision of this theory, developing the following steps: 1) A theory of processes. 2) A definition of structural and behavioural functions. 3) A probabilistic definition of the environmental functions. In this paper the authors develop the theory of behavioural functions, begin the theory of environmental functions and give a complementary focus to the theory of processes that has been developed in precedent papers.

Table of hyperbolic sines and cosines; x=2 to x=10.

Mode of access: Internet.

Higher mathematics. A text-book for classical and engineering colleges.

"Bibliography ... general works on the history of mathematics in the nineteenth century": p. 568-570.