Hyperconnected Research Articles

A method for extracting period~10 modulations from DNA sequence correlations applied to the Drosophila melanogaster genome

Nucleosome DNA packaging and positioning within the Drosophila melanogaster genome imposes a weak modulation, with a period of about 10 bp in the genomic composition correlations. We present formalism for extracting such modulations from an irreducible set of six correlation functions calculated along the D. melanogaster genome. These modulations were seen to be stronger for the irreducible self-correlation C(zz)(k) (strong-weak binding). Using an FFT procedure, we show that the period~10 modulation extracted from such self-correlation is viewed to be an oscillation with period~10.9 overmodulated by an oscillation with period~153. This behavior of the modulation reflects the organization of the eukaryotic genomic DNA. But, since the period~10 modulation dies for k ~150, the constraints imposed by the nucleosome arrangement over the nucleosome sequence composition must be weak, provided that such constraints are the sources for the modulations.

The study of the solvability of the genome annotation problem on sets of elementary motifs

The problem of genome annotation (i.e., the establishment of the biological roles of proteins and corresponding genes) is one of the major tasks of postgenomic bioinformatics. This paper reports the development of the previously proposed formalism for the study of the local solvability of the genome annotation problem. Here, we introduce the concepts of elementary motifs, positional independence of motifs, heuristic evaluation of informativeness, and solvability on the sets of elementary motifs. We show that introduction of a linear order in a set of elementary motifs allows us to calculate the irreducible motif sets. The formalism was used in experiments to compute the sets of the most informative motifs for several protein functions.

Feasibility in reverse convex mixed-integer programming

In this paper we address the problem of the infeasibility of systems defined by reverse convex inequality constraints, where some or all of the variables are integer. In particular, we provide a polynomial algorithm that identifies a set of all constraints critical to feasibility ( CF ) , that is constraints that may affect a feasibility status of the system after some perturbation of the right-hand sides. Furthermore, we will investigate properties of the irreducible infeasible sets and infeasibility sets, showing in particular that every irreducible infeasible set as well as infeasibility sets in the considered system, are subsets of the set CF of constraints critical to feasibility.

Downward causation by information control in micro-organisms

The concepts of functional equivalence classes and information control in living systems are useful to characterize downward (or top-down) causation by feedback information control in synthetic biology. Herein, we re-analyse published experiments of microbiology and synthetic biology that demonstrate the existence of several classes of functional equivalence in microbial organisms. Classes of functional equivalence from the bacterial operating system, which processes and controls the information encoded in the genome, can readily be interpreted as strong evidence, if not demonstration, of top-down causation (TDC) by information control. The proposed biological framework reveals how this type of causality is put in action in the cellular operating system. Considerations on TDC by information control and adaptive selection can be useful for synthetic biology by delineating the irreducible set of properties that characterizes living systems. Through a 'retro-synthetic' biology approach, these considerations could contribute to identifying the constraints behind the emergence of molecular complexity during the evolution of an ancient RNA/peptide world into a modern DNA/RNA/protein world. In conclusion, we propose TDCs by information control and adaptive selection as the two types of downward causality absolutely necessary for life.

Introduction to the Fractality Principle of Consciousness and the Sentyon Postulate

Recently, consciousness research has gained much attention. Indeed, the question at stake is significant: why is the brain not just a computing device, but generates a perception from within? Ambitious endeavors trying to simulate the entire human brain assume that the algorithm will do the trick: as soon as we assemble the brain in a computer and increase the number of operations per time, consciousness will emerge by itself. I disagree with this simplistic representation. My argument emerges from the "atomism paradox": the irreducible space of the consciously perceived world, the endospace is incompatible with the reducible and decomposable architecture of the brain or a computer. I will first discuss the fundamental challenges in current consciousness models and then propose a new model based on the fractality principle: "the whole is in each of its parts". This new model copes with the atomism paradox by implementing an iterative mapping of information from higher order brain structures to smaller scales on the cellular and molecular level, which I will refer to as "fractalization". This information fractalization gives rise to a new form of matter that is conscious ("bright matter"). Bright matter is composed of conscious particles or units named "sentyons". The internal fractality of these sentyons will close a loop (the "psychic loop") in a recurrent fractal neural network (RFNN) that allows for continuous and complete information transformation and sharing between higher order brain structures and the endpoint substrate of consciousness at the molecular level.

The skew-torsion holonomy theorem and naturally reductive spaces

We prove a Simons-type holonomy theorem for totally skew 1-forms with values in a Lie algebra of linear isometries. The only transitive case, for this theorem, is the full orthogonal group. We only use geometric methods and we do not use any classification (not even that of transitive isometric actions on the sphere or the list of rank one symmetric spaces). This result was independently proved, by using an algebraic approach, by Paul-Andy Nagy. We apply this theorem to prove that the canonical connection of a compact naturally reductive space is unique, provided the space does not split off, locally, a sphere or a compact Lie group with a bi-invariant metric. From this it follows easily how to obtain the full isometry group of a naturally reductive space. This generalizes known classification results of Onishchick, for normal homogeneous spaces with simple group of isometries, and Shankar, for homogeneous spaces of positive curvature. This also answers a question posed by J. Wolf and Wang-Ziller. Namely, to explain why the presentation group of an isotropy irreducible space, strongly or not, cannot be enlarged (unless for spheres, or for compact simple Lie groups with a bi-invariant metric).

SU-E-T-726: Validation of ProACTive, an Irreducible Vector Space Method of Dose Calculation

Purpose: Monte Carlo dose calculations are considered to be the gold standard by which other techniques are compared, particularly for complex geometries with regions of electronic disequilibrium. The major disadvantage of Monte Carlo is the associated long calculation times. This necessitates limiting the number of histories and/or using interpolative techniques, potentially reducing accuracy. ProACTive is an irreducible vector space method of dose calculation with computation times significantly faster than Monte Carlo. The purpose of the work is to validate ProACTiveˈs accuracy.Method: ProACTive calculations were compared to measurement and/or EGS4/PRESTA Monte Carlo for both homogenous and heterogeneous geometries for 6MV and 18MV. Sufficient Monte Carlo histories were run to minimize statistical uncertainty. Depth dose and profile measurements were taken from an average of measurements obtained on 40 Varian linear accelerators commissioned in the last several years. Heterogeneous phantoms included a complex phantom consisting of water, aluminum and lung irradiated by a 2×2 cm2 18 MV x-ray beam as described by Mohan and Rogers (ICCR2000 Proceedings). Results: ProACTive calculation times were significantly faster than Monte Carlo run with a large number of histories. For homogenous geometries, ProACTive calculations showed good agreement with measurement for a wide range of depths and beam sizes, both on and off axis. For the ICCR2000 phantom, ProACTive and Monte Carlo showed overall good agreement. Both calculation methods showed some difference compared to measurement, especially at a density boundary. It is not clear whether the differences are real or due to uncertainty in the measurements and their interpretation for this extreme geometry. Conclusions: For the geometries tested, ProACTive shows good agreement with measurement and similar computational accuracy to Monte Carlo when the latter is run with sufficient histories to minimize statistical uncertainty. ProACTiveˈs accuracy and computational time make it a feasible clinical solution to accurate dose calculation.

Phononic conductance of quasi-one-dimensional waveguides with an atomic hole defect

A theoretical approach based on the matching method has been developed to investigate the local phonon density of states (DOS) and the coherent phonon transmission near the atomic hole defect. The model system containing the defect is composed of three monatomic triple parallel chains, with atomic hole defect introducing them in the central chain. The matching method is used, in the harmonic approximation, to calculate the local Green's functions for the irreducible set of sites that constitute the inhomogeneous perturbed domain. The model system is studied for different cases of elastic hardening and softening in the perturbed zone. The purpose is to investigate how the local dynamics can respond to changes in the microscopic environment on the perturbed domain. The analysis of the total phonon conductance spectra and the densities of vibration states identify characteristic features and demonstrate the central role of the atomic hole defect localized in the perfect structure and the possible use, of them, as filters of phonon.

Polar actions on certain principal bundles over symmetric spaces of compact type

We study polar actions with horizontal sections on the total space of certain principal bundles G/K → G/H with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In particular, we exhibit examples of hyperpolar actions with cohomogeneity greater than one on locally irreducible homogeneous spaces with nonnegative curvature which are not homeomorphic to symmetric spaces.

A relaxation scheme for computation of the joint spectral radius of matrix sets

The problem of computation of the joint (generalized) spectral radius of matrix sets has been discussed in a number of publications. In this paper, an iteration procedure is considered that allows to build numerically Barabanov norms for the irreducible matrix sets and simultaneously to compute the joint spectral radius of these sets.

Free divisors in prehomogeneous vector spaces

We study linear free divisors, that is, free divisors arising as discriminants in prehomogeneous vector spaces, and in particular in quiver representation spaces. We give a characterization of the prehomogeneous vector spaces containing such linear free divisors. For reductive linear free divisors, we prove that the numbers of geometric and representation theoretic irreducible components coincide. As a consequence, we find that a quiver can only give rise to a linear free divisor if it has no (oriented or unoriented) cycles. We also deduce that the linear free divisors which appear in Sato and Kimura's list of irreducible prehomogeneous vector spaces are the only irreducible reductive linear free divisors. Furthermore, we show that all quiver linear free divisors are strongly Euler homogeneous, that they are locally weakly quasihomogeneous at points whose corresponding representation is not regular, and that all tame quiver linear free divisors are locally weakly quasihomogeneous. In particular, the latter satisfy the logarithmic comparison theorem.

Equations and algebraic geometry over profinite groups

The notion of an equation over a profinite group is defined, as well as the concepts of an algebraic set and of a coordinate group. We show how to represent the coordinate group as a projective limit of coordinate groups of finite groups. It is proved that if the set π(G) of prime divisors of the profinite period of a group G is infinite, then such a group is not Noetherian, even with respect to one-variable equations. For the case of Abelian groups, the finiteness of a set π(G) gives rise to equational Noetherianness. The concept of a standard linear pro-p-group is introduced, and we prove that such is always equationally Noetherian. As a consequence, it is stated that free nilpotent pro-p-groups and free metabelian pro-p-groups are equationally Noetherian. In addition, two examples of equationally non-Noetherian pro-p-groups are constructed. The concepts of a universal formula and of a universal theory over a profinite group are defined. For equationally Noetherian profinite groups, coordinate groups of irreducible algebraic sets are described using the language of universal theories and the notion of discriminability.

Terminal contributions for duplex oligonucleotide thermodynamic properties in the context of nearest neighbor models

Additive physical properties of DNA polymer duplexes have been expanded in terms of eight irreducible parameters that ultimately lead to consistency relations among the corresponding 10 duplex dimer contributions. End parameters are often added to allow for oligomer analysis which would add four extra degrees of freedom to the aforementioned parameters. Analysis of sufficient experimental data on oligomer duplexes allows for the unambiguous recovery of irreducible parameters. Values for free energy, enthalpy, and entropy are thus obtained, in terms of either irreducible or dimer decomposition sets. Here, a better adjust for the entropic (and enthalpic) irreducible parameters are obtained as we consider the more precise melting temperature data for the sequences of a given dataset. However, still large error estimates, and no clear distinction between the orientations of the terminal base pairs could yet be found. Finally, statistical mechanics approaches are applied for to connect the nearest neighbor approach to the two states model. Ad hoc end effects can be thus correlated to nucleation phenomena, leading to a critique for its role in nearest neighbor modeling.

Minimal Sets of Turns for Breaking Cycles in Graphs Modeling Networks

The problem of preventing deadlocks and livelocks in computer communication networks, in particular, those with wormhole routing, is considered. The method to prevent deadlocks is to prohibit certain turns (i.e., the use of certain pairs of connected edges) in the routing process, in such a way that eliminates all cycles in the graph. We propose a new algorithm that constructs a minimal (irreducible) set of turns that breaks all cycles and preserves connectivity of the graph. The algorithm is tree-free and is considerably simpler than earlier cycle-breaking algorithms. We prove its properties and present lower and upper bounds for minimum cardinalities of cycle-breaking connectivity preserving sets for graphs of general topology as well as for planar graphs. In particular, the algorithm guarantees that not more than 1/3 of all turns in the network become prohibited. We also present experimental results on the fraction of prohibited turns, the distance dilation, as well as on the message delivery times and saturation loads for the proposed algorithm in comparison with known tree-based algorithms. The proposed algorithm outperforms substantially the tree-based algorithms in all characteristics considered.

Ideal-triangularizability of nil-algebras generated by positive operators

R. Drnov�ek, D. Kokol-Bukov�ek, L. Livshits, G. MacDonald, M. Omladic, and H. Radjavi constructed an irreducible set of positive nilpotent operators on which is closed under multiplication, addition and multiplication by positive real scalars with the property that any finite subset is ideal-triangularizable. In this paper we prove the following: every algebra of nilpotent operators which is generated by a set of positive operators on a Banach lattice is ideal-triangularizable whenever the nilpotency index of its operators is bounded; every finite subset of an algebra of nilpotent operators which is generated by a set of positive operators on a Banach lattice is ideal-triangularizable.

Dirichlet forms associated with linear diffusions

One-dimensional local Dirichlet spaces associated with linear diffusions are studied. The first result is to give a representation for any 1-dim local, irreducible and regular Dirichlet space. The second result is a necessary and sufficient condition for a Dirichlet space to be regular subspace of another Dirichlet space.

Criteria for the stability of the finiteness property and for the uniqueness of Barabanov norms

A set of matrices is said to have the finiteness property if the maximal rate of exponential growth of long products of matrices drawn from that set is realised by a periodic product. The extent to which the finiteness property is prevalent among finite sets of matrices is the subject of ongoing research. In this article, we give a condition on a finite irreducible set of matrices which guarantees that the finiteness property holds not only for that set, but also for all sufficiently nearby sets of equal cardinality. We also prove a theorem giving conditions under which the Barabanov norm associated to a finite irreducible set of matrices is unique up to multiplication by a scalar, and show that in certain cases these conditions are also persistent under small perturbations.

Elements of Algebraic Geometry and the Positive Theory of Partially Commutative Groups

AbstractThe first main result of the paper is a criterion for a partially commutative group 𝔾 to be a domain. It allows us to reduce the study of algebraic sets over 𝔾 to the study of irreducible algebraic sets, and reduce the elementary theory of 𝔾 (of a coordinate group over 𝔾) to the elementary theories of the direct factors of 𝔾 (to the elementary theory of coordinate groups of irreducible algebraic sets).Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group ℍ. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of ℍ has quantifier elimination and that arbitrary first-order formulas lift from ℍ to ℍ * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Hybrid functionals within the all-electron FLAPW method: Implementation and applications of PBE0

We present an efficient implementation of the PBE0 hybrid functional within the full-potential linearized augmented-plane-wave (FLAPW) method. The Hartree-Fock exchange term, which is a central ingredient of hybrid functionals, gives rise to a computationally expensive nonlocal potential in the one-particle Schroedinger equation. The matrix elements of this exchange potential are calculated with the help of an auxiliary basis that is constructed from products of FLAPW basis functions. By representing the Coulomb interaction in this basis the nonlocal exchange term becomes a Brillouin-zone (BZ) sum over vector-matrix-vector products. We show that the Coulomb matrix can be made sparse by a suitable unitary transformation of the auxiliary basis, which accelerates the computation of the vector-matrix-vector products considerably. Additionally, we exploit spatial and time-reversal symmetry to identify the nonvanishing exchange matrix elements in advance and to restrict the k summations for the nonlocal potential to an irreducible set of k points. Favorable convergence of the self-consistent-field cycle is achieved by a nested density-only and density-matrix iteration scheme. We discuss the convergence with respect to the parameters of our numerical scheme and show results for a variety of semiconductors and insulators, including oxide materials, where the PBE0 hybrid functional improves the band gaps and the description of localized states in comparison with the PBE functional. Furthermore, we find that in contrast to conventional local exchange-correlation functionals ferromagnetic EuO is correctly predicted to be a semiconductor.

Visible Actions on Reducible Multiplicity-Free Spaces

The notion of (strongly) visible actions was introduced by T. Kobayashi [10, 11] for the biholomorphic action on a complex manifold with (possibly) infinitely many orbits. A holomorphic action of a Lie group G on a complex manifold D is strongly visible with a slice S if D = G ⋅ S, and there exists an anti-holomorphic and orbit preserving diffeomorphism σ on D such that σ|S = idS. Generalizing our previous result [22] about strongly visible actions on irreducible multiplicity-free spaces à la Kac, we treat reducible multiplicity-free spaces classified by Benson–Ratcliff and Leahy and prove that any multiplicity-free space naturally admits a strongly visible action. Further, we give an explicit description of S and σ. Our result gives an evidence to Kobayashi's conjecture [12, Conjecture 3.2] in the case of linear actions, asserting that we can take S to have the same dimension with the rank of V .