The Point Evaluation Method for Approximating Function Means,Variances and Covariances

A perennial problem in statistics is the determination of biases, variances and covariances for functions of random variables X₁, X₂, …, X_n which themselves have a known distribution. A common approach is through equations based upon Taylor series approximations but a “point evaluation” method may sometimes be a useful alternative. This involves approximating the multivariate distribution of the X variables by the 2ⁿ points given by X₁=μ₁±₁, X₂ = μ₂ ±₂, …, X_n = = μ_n μ_n, where μ_i is the mean and σ_i the standard deviation of Xi, with appropriate point weights. An advantage over the Taylor series approach is that function derivatives do not have to be explicitely calculated. The point evaluation method is particularly useful in cases where the X variables are uncorrelated. Then the evaluation of the 2ⁿ points can be replaced by the evaluation of 2n points. The point evaluation method is illustrated with powers of a normally distributed variable, and with estimation of gene frequencies from ABO blood group frequencies.     

Adaptive variation in structure and function of kidneys of speciating subterranean mole rats

Summary We report on kidney structure and function in subterranean mammals of four chromosomal species (2n=52, 54, 58 and 60) belonging to the Spalax ehrenbergi superspecies, in relation to their speciation and adaptive radiation from mesic (2n=52) to xeric (2n=60) environments in Israel. Structural variables measured involved: (1) Relative Medullary Thickness, (RMT); (2) Relative Kidney Weight. (RKW); and (3) Percentage of Kidney out of Body Weight (PKW). Functional variables involved: (i) Urine Solid Concentration, (USC); and (ii) Urine Osmotic Concentration (UOC). The results for chromosomal species 2n=52, 54, 58 and 60 indicated nonsignificant increase southward for RMT, but displayed significant increase along the same transect for RKW, PKW, and USC. The UOC was significantly lower in mesic 2n=52 as compared to the other three species when experimental animals were fed in the laboratory on regular carrot food. However, protein stress food (soybean) and salt stress of 0.45 mol NaCl, caused significant, three and a half fold increase of UOC in 2n=52, 54 and 58; but four and a half fold increase in 2n=60, significantly higher than in the other three species. We conclude that both structurally and functionally, the kidneys differentiated adaptively during the Pleistocene evolution of S. ehrenbergi in Israel, in accordance with aridity stress and halophyte food resources towards the desert. Nevertheless, Spalax generally shows clear upper limits in kidney structural and functional capacities, preventing it from colonizing the true desert, south of the 100 mm isohyete.     

Detecting controlling nodes of boolean regulatory networks

Boolean models of regulatory networks are assumed to be tolerant to perturbations. That qualitatively implies that each function can only depend on a few nodes. Biologically motivated constraints further show that functions found in Boolean regulatory networks belong to certain classes of functions, for example, the unate functions. It turns out that these classes have specific properties in the Fourier domain. That motivates us to study the problem of detecting controlling nodes in classes of Boolean networks using spectral techniques. We consider networks with unbalanced functions and functions of an average sensitivity less than ?k, where k is the number of controlling variables for a function. Further, we consider the class of 1-low networks which include unate networks, linear threshold networks, and networks with nested canalyzing functions. We show that the application of spectral learning algorithms leads to both better time and sample complexity for the detection of controlling nodes compared with algorithms based on exhaustive search. For a particular algorithm, we state analytical upper bounds on the number of samples needed to find the controlling nodes of the Boolean functions. Further, improved algorithms for detecting controlling nodes in large-scale unate networks are given and numerically studied.     

Calculations of the circular dichroism of double-helical nucleic acids. II. Effects involving n leads to pi transitions

The circular dichroism of double-helical nucleic acids was calculated as a function of geometry, including terms involving n → π* transitions. The “nonbonding” n or σ orbitals were of the azine type, delocalized, but concentrated at the nitrogen atoms of the purines and pyrimidines. Dynamic coupling of the magnetic moments of the n → π* transitions with the electric moments of π → π* transitions generated important terms. Mixing of electric dipole character into n → π* transitions by the static electric field perturbation of the molecule is of lesser importance. The largest contributions of n → π* transitions to the circular dichroism of double-helical nucleic acids are comparable in magnitude to the sum of π → π* terms only for geometries where the circular dichroism is weak. Using both n → π* and π → π* contributions one is able to match experimental and calculated circular dichroism spectra for DNA's over a much wider range of conditions than was possible previously.     

MORPHOLOGY OF SOME MAIZE-TRIPSACUM HYBRIDS

Diploid (2n = 20) and tetraploid (2n = 40) Zea mays L. were crossed with diploid (2n = 36) and tetraploid (2n = 72) Tripsacum dactyloides (L.) L. to produce a series of hybrids combining different numbers of haploid genomes from each parent. Eight hybrid groups and three parental groups were studied morphologically. Twenty-nine quantitative characters were recorded for each sample. Data were analyzed by univariate analysis of variance, multivariate analysis of variance, and discriminant function analysis, in an attempt to evaluate hybrid differences objectively and determine which morphological characters contribute statistically to group separation. The overall MANOVA F test was significant, establishing the presence of real differences between the hybrids; discriminant function analysis indicated that the percent of paired pistillate spikelets/cupule in the lateral inflorescence was the main variable which differentiated hybrids. Duncan's Multiple Range Tests for significant differences between means were applied to five variables contributing maximally to group discrimination, using the appropriate univariate ANOVAs. Pronounced maize-like attributes of backcross hybrids, as compared with corresponding F₁'s possessing similar genome constitutions, gave possible evidence of gene transfer between Zea mays and Tripsacum during backcrossing to maize.     

Tuned solutions in dynamic neural fields as building blocks for extended EEG models

The most prominent functional property of cortical neurons in sensory areas are their tuned receptive fields which provide specific responses of the neurons to external stimuli. Tuned neural firing indeed reflects the most basic and best worked out level of cognitive representations. Tuning properties can be dynamic on a short time-scale of fractions of a second. Such dynamic effects have been modeled by localised solutions (also called “bumps” or “peaks”) in dynamic neural fields. In the present work we develop an approximation method to reduce the dynamics of localised activation peaks in systems of n coupled nonlinear d-dimensional neural fields with transmission delays to a small set of delay differential equations for the peak amplitudes and widths only. The method considerably simplifies the analysis of peaked solutions as demonstrated for a two-dimensional example model of neural feature selectivity in the brain. The reduced equations describe the effective interaction between pools of local neurons of several (n) classes that participate in shaping the dynamic receptive field responses. To lowest order they resemble neural mass models as they often form the base of EEG-models. Thereby they provide a link between functional small-scale receptive field models and more coarse-grained EEG-models. More specifically, they connect the dynamics in feature-selective cortical microcircuits to the more abstract local elements used in coarse-grained models. However, beside amplitudes the reduced equations also reflect the sharpness of tuning of the activity in a d-dimensional feature space in response to localised stimuli.     

Partitioning the variation in a plot‐by‐species data matrix that is related to n sets of explanatory variables

Abstract. Variation partitioning by (partial) constrained ordination is a popular method for exploratory data analysis, but applications are mostly restricted to simple ecological questions only involving two or three sets of explanatory variables, such as climate and soil, this because of the rapid increase in complexity of calculations and results with an increasing number of explanatory variable sets. The existence is demonstrated of a unique algorithm for partitioning the variation in a set of response variables on n sets of explanatory variables; it is shown how the 2n– 1 non‐overlapping components of variation can be calculated. Methods for evaluation and presentation of variation partitioning results are reviewed, and a recursive algorithm is proposed for distributing the many small components of variation over simpler components. Several issues related to the use and usefulness of variation partitioning with n sets of explanatory variables are discussed with reference to a worked example.     

Galerkin-Ritz procedures for approximate solutions to systems of reaction-diffusion equations

For any essentially nonlinear system of reaction-diffusion equations of the generic form ∂c_i/∂t=D_i∇²c_i+Q_i(c,x,t) supplemented with Robin type boundary conditions over the surface of a closed bounded three-dimensional region, it is demonstrated that all solutions for the concentration distributionn-tuple function c=(c ₁(x,t),...,c _n (x,t)) satisfy a differential variational condition. Approximate solutions to the reaction-diffusion intial-value boundary-value problem are obtainable by employing this variational condition in conjunction with a Galerkin-Ritz procedure. It is shown that the dynamical evolution from a prescribed initial concentrationn-tuple function to a final steady-state solution can be determined to desired accuracy by such an approximation method. The variational condition also admits a systematic Galerkin-Ritz procedure for obtaining approximate solutions to the multi-equation elliptic boundary-value problem for steady-state distributions c=−c(x). Other systems of phenomenological (non-Lagrangian) field equations can be treated by Galerkin-Ritz procedures based on analogues of the differential variational condition presented here. The method is applied to derive approximate nonconstant steady-state solutions for ann-species symbiosis model.     

Template-based intervention in Boolean network models of biological systems

Motivation

A grand challenge in the modeling of biological systems is the identification of key variables which can act as targets for intervention. Boolean networks are among the simplest of models, yet they have been shown to adequately model many of the complex dynamics of biological systems. In our recent work, we utilized a logic minimization approach to identify quality single variable targets for intervention from the state space of a Boolean network. However, as the number of variables in a network increases, the more likely it is that a successful intervention strategy will require multiple variables. Thus, for larger networks, such an approach is required in order to identify more complex intervention strategies while working within the limited view of the network’s state space. Specifically, we address three primary challenges for the large network arena: the first challenge is how to consider many subsets of variables, the second is to design clear methods and measures to identify the best targets for intervention in a systematic way, and the third is to work with an intractable state space through sampling.

Results

We introduce a multiple variable intervention target called a template and show through simulation studies of random networks that these templates are able to identify top intervention targets in increasingly large Boolean networks. We first show that, when other methods show drastic loss in performance, template methods show no significant performance loss between fully explored and partially sampled Boolean state spaces. We also show that, when other methods show a complete inability to produce viable intervention targets in sampled Boolean state spaces, template methods maintain significantly consistent success rates even as state space sizes increase exponentially with larger networks. Finally, we show the utility of the template approach on a real-world Boolean network modeling T-LGL leukemia.

Conclusions

Overall, these results demonstrate how template-based approaches now effectively take over for our previous single variable approaches and produce quality intervention targets in larger networks requiring sampled state spaces.

     

Sex Hormones and Sexual Function in Obese Men Losing Weight

Objective: To study the impact of a weight‐loss program on sex hormones and sexual function among 38 middle‐aged obese men (BMI ≥35 kg/m²). Research Methods and Procedures: A randomized controlled clinical trial was conducted. The treatment group (n = 19) participated in a 4‐month weight‐loss program including 10 weeks on a very‐low‐energy diet (VLED) and 17 behavior modification visits. There was no intervention in the control group (n = 19). Both groups were followed for 8 months, i.e., 22 weeks after the active weight loss in the treatment group. The outcome measures (weight, sex hormones, sexual function, leptin, and metabolic variables) were obtained at baseline and at three time‐points during follow‐up. Results: The mean weight loss in the treatment group was 21 kg at the end of the 10‐week VLED. At the end of follow‐up, the maintained weight loss was 17 kg of baseline weight. The control group was weight stable throughout the study. In the treatment group, increases in sex hormone‐binding globulin, testosterone, and high‐density lipoprotein‐cholesterol, as well as decreases in insulin and leptin, were maintained until the end of follow‐up, although with VLED, the level of several hormones and metabolic variables improved transiently during the rapid weight loss. There were no significant changes in the questionnaire scores on sexual function in either group. Discussion: We conclude that obese men lose weight and increase their serum testosterone level on a weight‐loss program with VLED and behavior modification. However, they do not change their sexual function scores.     

A genetic code Boolean structure. I. The meaning of Boolean deductions

This paper proposes a genetic code Boolean structure derived from hydrogen bond numbers and chemical types of bases, purines and pyrimidines. It shows that in such Boolean structure, deductions comprise physico-chemical meaning. In particular, codons with adenine as a second base coding to hydrophilic amino acids are not deductible from codons with uracil in the same position, which code to hydrophobic amino acids. Boolean deductions could help us describe the gene evolution process. For instance, most of the reported mutations that confer drug resistance to the HIV protease gene correspond to deductions. What is more, in the human beta-globin gene a similar situation appears where most of the single codon mutations correspond to Boolean deductions from the respective wild-type codon.     

Nondestructive,simple, and accurate model for estimation of the individual leaf area of som (<Emphasis Type="Italic">Persea bombycina</Emphasis>)

Nondestructive approach of modeling leaf area could be useful for plant growth estimation especially when number of available plants is limited and/or experiment demands repeated estimation of leaf area over a time scale. A total of 1,280 leaves were selected randomly from eight different morphotypes of som (Persea bombycina) established at randomized complete block design under recommended cultural regimes in field. Maximum leaf laminar width (B), length (L) and their squares B², L²; leaf area (LA), and lamina length × width (L×B) were determined over two successive seasons. Leaf parameters were significantly affected by morphotypes; but seasons had nonsignificant impacts on tested features. Therefore, pooled seasonal morphotype means of each parameter were used to establish relationship with LA. L and its square L² did not provide accurate models for LA predictions. Considerably better models were obtained by using B (y = 2.984 + 7.9664 x, R ² = 0.615, P≥0.001, n = 119) and B² (y = 12.784+ 0.9604 x, R ² = 0.605, P≥0.001, n = 119) as independent variables. However, maximum accuracy of prediction of LA could be achieved through a simple linear relationship of L×B (y = 8.2203 + 0.4224 x, R ² = 0.843, P≥0.0001, n = 119). The model (LA:L×B) was validated with randomly selected leaf samples (n = 360) of som morphotypes and highly significant (P≤0.001) linear function was found between actual and predicted LAs. Therefore, the last model may consider adequate to predict leaf area of all cultivars of som with sufficient fidelity.     

Characterizations of the Exponential Distribution by Local Maximum Random Variables

Let {X_n, n≧1} be a sequence of independent and identically distributed random variables. Suppose n(K)=min n for which X_n>X_k, with K fixed and n>K. We will characterize the exponential distribution by considering the distributional properties of X_k and X_k and X_n(k).     

Optimal control of batch processes involving simultaneous enzymatic and microbial reactions

Optimal enzyme feed rate profiles have been calculated, based on a model for a fed-batch simultaneous enzymatic and microbial reaction (SEMR) process. The model parameters corresponded to a relatively slow citric acid fermentation. The profiles were calculated using an iterative algorithm based on the minimum principle. Penalty functions were used to enforce inequality constraints on the enzyme feed rate. Significant improvements in the objective function relative to that for the best constant enzyme feed rate were found. The effect on the optimal profiles of changes in the parameters of the model and the objective function were investigated, as was the effect of introducing the stationary state assumption to eliminate glucose concentration as a state variable. Major differences between bang-bang control variable profiles and singular arcs were found, with the singular arc solution slightly better than the optimal bang-bang control.List of Symbols a N-vector of initial conditions - b ₁–b₁₀ parameters defined in Table 2 - c vector of cost parameters - c ₁–c₆ penalty function parameters - E enzyme concentration (U/l) - f N-vector of functions - F enzyme feed rate (U/l-h) - g N-vector of functions - G glucose concentration (g/l) - H Hamiltonian - J objective function - J ^* modified objective function - L number of integration steps per time interval - L number of control variables - M number of time intervals - n iteration index - N number of state variables - P product concentration (g/l) - r ₁ glucose formation rate (g/l-h) - r ₂ product formation rate (g/l-h) - t time (h) - T final time (h) - u L-vector of control variables - x N-vector of state variables - z N-vector of adjoint variables - Z total enzyme fed (U/l) Greek convergence parameter The support of one of the authors by the National Science Foundation (Grant CBT-84-20552) is gratefully acknowledged.     

On multipole representation of current generators

In Yeh, Martinek, and de Beaumont (Bull. Math. Biophysics,20, 203–216, 1958), multipole representations of current generators in a volume conductor are used, based upon the Taylor series expansion of the potential function. In Yeh, (Bull. Math. Biophysics,23, 263–276, 1961) multipole representations of current generators in a spherical volume conductor are used, based upon the spherical harmonic expansion. This paper correlates these two systems of multipole representations so that formulations in terms of one system of the representations may be readily transformed into formulations in terms of the other system. Since the Taylor series representation is more graphic, whereas the spherical harmonic representation is more compact, such a transformation between these two systems of formulations can serve useful purposes in the application of the theory of electrocardiography. This investigation was supported by the National Heart Institute under Research Grant H-2263 (c-4).     

Mining TCGA Data Using Boolean Implications

Boolean implications (if-then rules) provide a conceptually simple, uniform and highly scalable way to find associations between pairs of random variables. In this paper, we propose to use Boolean implications to find relationships between variables of different data types (mutation, copy number alteration, DNA methylation and gene expression) from the glioblastoma (GBM) and ovarian serous cystadenoma (OV) data sets from The Cancer Genome Atlas (TCGA). We find hundreds of thousands of Boolean implications from these data sets. A direct comparison of the relationships found by Boolean implications and those found by commonly used methods for mining associations show that existing methods would miss relationships found by Boolean implications. Furthermore, many relationships exposed by Boolean implications reflect important aspects of cancer biology. Examples of our findings include cis relationships between copy number alteration, DNA methylation and expression of genes, a new hierarchy of mutations and recurrent copy number alterations, loss-of-heterozygosity of well-known tumor suppressors, and the hypermethylation phenotype associated with IDH1 mutations in GBM. The Boolean implication results used in the paper can be accessed at http://crookneck.stanford.edu/microarray/TCGANetworks/.     

Cytotaxonomy in distinct populations of Hoplias aff. malabaricus (Characiformes,Erythrinidae) from lower Paranapanema River basin

Cytogenetic and morphometric analyses were carried out in Hoplias aff. malabaricus specimens from six distinct populations from the lower Paranapanema River basin, located between the states of Paraná and São Paulo, Brazil. Measurements were also taken from a specimen collected in Surinam. In a population from a fish farm station at Universidade do Norte do Parana (EPUNOPAR), two sympatric cytotypes (2n = 40 and 2n = 42 chromosomes) are found. A population from a fish farm station at Universidade Estadual de Londrina (EPUEL) shows 2n = 42 meta–submetacentric chromosomes for males and females with a simple sex chromosome system of XX/XY type. Populations from the Vermelho and Rancho Alegre Rivers, Três Bocas Stream and Paranapanema River have 2n = 39 chromosomes in males and 2n = 40 chromosomes in females, showing a multiple sex chromosome system of X₁X₁X₂X₂/X₁X₂Y type. Twenty morphological variables were studied. These measurements were used for an analysis of the canonical variables and standard analysis of proportional measurements. The most variable measurements among the specimens are the maxilla length (MXL) and the pre‐dorsal distance (PDD). Analysis of canonical variables indicates three distinct groups in the first canonical axis formed by: (1) Três Bocas Stream, (2) Rancho Alegre + Vermelho River + EPUNOPAR and (3) EPUEL + Paranapanema River. This axis retained 79·4% of information from the original matrix. Analysis of morphometrics reveals differences among populations from the Paranapanema River basin and between these and the specimen from Surinam. The morphometric and cytogenetic differences among the studied populations suggest a species complex.     

A geometric synthesis method to realize a switching function

Frequently in threshold logic it is necessary to realize a switching function f of n variables in a two or more stages realization, both because it is not possible to realize f in a single gate and for reliability considerations. This means that the given function must be decomposed into a certain number of threshold functions, each of them having a number of variables less than n. When a geometric representation of switching functions is considered, the problem is equivalent to that of looking for functions whose patterns (on-sets) cover, in an adequate way, the on-set of the function f to be realized. In this paper a heuristic covering approach has been introduced which provides a manageable method for searching for a two stage realization of f. Furthermore a class of switching functions whose patterns possess a particular geometric shape (shell structure) has been considered. It has been proved that such functions (shell functions) are linearly separable and that one of their separating systems strictly depends on the centre and on the diameter of the shell structure. Gates implementing shell functions have been considered and their use has been revealed more convenient than that of majority gates in the solution of the problem of network synthesis. To clarify this advantage an example has been discussed in detail.     

Children with Avoidant or Disorganized Attachment Relate Differently to a Dog and to Humans During a Socially Stressful Situation

ABSTRACT

Human attachment representations are shaped in interaction with the primary caregiver and are generally transferred to further bonding/ social partners later in life. According to previous evidence, primary attachment representations acquired with humans do not seem to be transferred to companion animals. This was held as a major factor why such animals would effectively provide social support also to persons with insecure attachment. The aim of this study in 19 male children, 7–11 years of age and with insecure-avoidant or disorganized attachment, was to investigate differences in their social behavior and in physiological responses when socially supported by an unfamiliar therapy dog in a socially stressful situation. The Trier Social Stress Test for Children (TSST-C) was conducted to elicit stress in the children when in the presence of the dog and a female human investigator. We found that boys with disorganized attachment (n=11) communicated more intensely than avoidantly attached boys (n=8) with both the dog and humans present. Boys with a disorganized attachment had more physical contact with the dog during the TSST-C and talked more to the dog during and after the TSST-C than did boys with an insecure-avoidant attachment. While the prevailing wisdom holds that attachment representations acquired with the primary human caregiver would not transfer to companion animals, our data indicate otherwise. At least components of attachment-related interaction styles, such as degree of contact seeking in verbal and tactile interactions are also displayed in interaction with animal partners.     

Dynamical machinery of a biochemical clock

Closed positive feedback loops of catalytic reactions between macromolecules, or hypercycles, provide a kinetic mechanism whereby each Species serves to catalyze selfreproduction of its successor in the loop. Hypercycles of five members or more evolve into limit cycles characteristic of a biochemical clock. Computer study of the coupled non-linear differential equations which describe these systems shows that the periodT _n of then-species limit cycle is given byT _n=nτ_n, where τ_n is an elemental repeat period reflecting translational time invariance. Analytic solutions of the equations are developed so that the time evolution of elementaryn-hypercycles can be traced in dynamical detail. It is shown that the magnitude of τ_n is, to good approximation, a linear function ofn. For a givenn, τ_n is a very sensitive function of the relative concentration a given member of the loop has at the time its predecessor dominates the state of the hypercycle. These concentrations decrease with increasingn. Aroundn=15 they become so small that elementary hypercycles become unstable against disruptive concentration fluctuations. Species concentrations for more realistic hypercycles tend not to be as small, so that the present estimate of a maximum number of components is a lower bound.