Symmetries of Electrostatic Interaction between DNA Molecules

We study a model for pair interaction $U$ of DNA molecules generated by the discrete dipole moments of base-pairs and the charges of phosphate groups, and find noncommutative group of eighth order ${\cal S}$ of symmetries that leave $U$ invariant. We classify the minima using group ${\cal S}$ and employ numerical methods for finding them. The minima may correspond to several cholesteric phases, as well as phases formed by cross-like conformations of molecules at an angle close to $\rm{90}^{o}$, "snowflake phase". The results depend on the effective charge $Q$ of the phosphate group which can be modified by the polycations or the ions of metals. The snowflake phase could exist for $Q$ above the threshold $Q_C$. Below $Q_C$ there could be several cholesteric phases. Close to $Q_C$ the snowflake phase could change into the cholesteric one at constant distance between adjacent molecules.Comment: 13 pages, 4 figure

Coordinated optimization of visual cortical maps (I) Symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of OP columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about an hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference.Comment: 90 pages, 16 figure

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

Fine-structured multi-scaling long-range correlations in completely sequenced genomes—features, origin, and classification

The sequential organization of genomes, i.e. the relations between distant base pairs and regions within sequences, and its connection to the three-dimensional organization of genomes is still a largely unresolved problem. Long-range power-law correlations were found using correlation analysis on almost the entire observable scale of 132 completely sequenced chromosomes of 0.5 × 106 to 3.0 × 107 bp from Archaea, Bacteria, Arabidopsis thaliana, Saccharomyces cerevisiae, Schizosaccharomyces pombe, Drosophila melanogaster, and Homo sapiens. The local correlation coefficients show a species-specific multi-scaling behaviour: close to random correlations on the scale of a few base pairs, a first maximum from 40 to 3,400 bp (for Arabidopsis thaliana and Drosophila melanogaster divided in two submaxima), and often a region of one or more second maxima from 105 to 3 × 105 bp. Within this multi-scaling behaviour, an additional fine-structure is present and attributable to codon usage in all except the human sequences, where it is related to nucleosomal binding. Computer-generated random sequences assuming a block organization of genomes, the codon usage, and nucleosomal binding explain these results. Mutation by sequence reshuffling destroyed all correlations. Thus, the stability of correlations seems to be evolutionarily tightly controlled and connected to the spatial genome organization, especially on large scales. In summary, genomes show a complex sequential organization related closely to their three-dimensional organization

Hierarchical Models in the Brain

This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of state-space or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of arbitrary complexity. Special cases range from the general linear model for static data to generalised convolution models, with system noise, for nonlinear time-series analysis. Crucially, all of these models can be inverted using exactly the same scheme, namely, dynamic expectation maximization. This means that a single model and optimisation scheme can be used to invert a wide range of models. We present the model and a brief review of its inversion to disclose the relationships among, apparently, diverse generative models of empirical data. We then show that this inversion can be formulated as a simple neural network and may provide a useful metaphor for inference and learning in the brain

Time Scale Hierarchies in the Functional Organization of Complex Behaviors

Traditional approaches to cognitive modelling generally portray cognitive events in terms of ‘discrete’ states (point attractor dynamics) rather than in terms of processes, thereby neglecting the time structure of cognition. In contrast, more recent approaches explicitly address this temporal dimension, but typically provide no entry points into cognitive categorization of events and experiences. With the aim to incorporate both these aspects, we propose a framework for functional architectures. Our approach is grounded in the notion that arbitrary complex (human) behaviour is decomposable into functional modes (elementary units), which we conceptualize as low-dimensional dynamical objects (structured flows on manifolds). The ensemble of modes at an agent’s disposal constitutes his/her functional repertoire. The modes may be subjected to additional dynamics (termed operational signals), in particular, instantaneous inputs, and a mechanism that sequentially selects a mode so that it temporarily dominates the functional dynamics. The inputs and selection mechanisms act on faster and slower time scales then that inherent to the modes, respectively. The dynamics across the three time scales are coupled via feedback, rendering the entire architecture autonomous. We illustrate the functional architecture in the context of serial behaviour, namely cursive handwriting. Subsequently, we investigate the possibility of recovering the contributions of functional modes and operational signals from the output, which appears to be possible only when examining the output phase flow (i.e., not from trajectories in phase space or time)

Four-Year Treatment Outcomes of Adult Patients Enrolled in Mozambique's Rapidly Expanding Antiretroviral Therapy Program

BACKGROUND: In Mozambique during 2004-2007 numbers of adult patients (≥15 years old) enrolled on antiretroviral therapy (ART) increased about 16-fold, from <5,000 to 79,500. All ART patients were eligible for co-trimoxazole. ART program outcomes, and determinants of outcomes, have not yet been reported. METHODOLOGY/PRINCIPAL FINDINGS: In a retrospective cohort study, we investigated rates of mortality, attrition (death, loss to follow-up, or treatment cessation), immunologic treatment failure, and regimen-switch, as well as determinants of selected outcomes, among a nationally representative sample of 2,596 adults initiating ART during 2004-2007. At ART initiation, median age of patients was 34 and 62% were female. Malnutrition and advanced disease were common; 18% of patients weighed <45 kilograms, and 15% were WHO stage IV. Median baseline CD4(+) T-cell count was 153/µL and was lower for males than females (139/µL vs. 159/µL, p<0.01). Stavudine, lamivudine, and nevirapine or efavirenz were prescribed to 88% of patients; only 31% were prescribed co-trimoxazole. Mortality and attrition rates were 3.4 deaths and 19.8 attritions per 100 patient-years overall, and 12.9 deaths and 57.2 attritions per 100 patient-years in the first 90 days. Predictors of attrition included male sex [adjusted hazard ratio (AHR) 1.5; 95% confidence interval (CI), 1.3-1.8], weight <45 kg (AHR 2.1; 95% CI, 1.6-2.9, reference group >60 kg), WHO stage IV (AHR 1.7; 95% CI, 1.3-2.4, reference group WHO stage I/II), lack of co-trimoxazole prescription (AHR 1.4; 95% CI, 1.0-1.8), and later calendar year of ART initiation (AHR 1.5; 95% CI, 1.2-1.8). Rates of immunologic treatment failure and regimen-switch were 14.0 and 0.6 events per 100-patient years, respectively. CONCLUSIONS: ART initiation at earlier disease stages and scale-up of co-trimoxazole among ART patients could improve outcomes. Research to determine reasons for low regimen-switch rates and increasing rates of attrition during program expansion is needed