Undirected Process Research Articles

Phase transition in the majority-vote model on time-varying networks.

Social interactions may affect the update of individuals' opinions. The existing models such as the majority-vote (MV) model have been extensively studied in different static networks. However, in reality, social networks change over time and individuals interact dynamically. In this work, we study the behavior of the MV model on temporal networks to analyze the effects of temporality on opinion dynamics. In social networks, people are able to both actively send connections and passively receive connections, which leads to different effects on individuals' opinions. In order to compare the impact of different patterns of interactions on opinion dynamics, we simplify them into two processes, that is, the single directed (SD) process and the undirected (UD) process. The former only allows each individual to adopt an opinion by following the majority of actively interactive neighbors, while the latter allows each individual to flip opinion by following the majority of both actively interactive and passively interactive neighbors. By borrowing the activity-driven time-varying network with attractiveness (ADA model), the two opinion update processes, i.e., the SD and the UD processes, are related with the network evolution. With the mean-field approach, we derive the critical noise threshold for each process, which is also verified by numerical simulations. Compared with the SD process, the UD process reaches a larger consensus level below the same critical noise. Finally, we also verify the main results in real networks.

Exploratory search during directed navigation in C. elegans and Drosophila larva.

Many organisms-from bacteria to nematodes to insect larvae-navigate their environments by biasing random movements. In these organisms, navigation in isotropic environments can be characterized as an essentially diffusive and undirected process. In stimulus gradients, movement decisions are biased to drive directed navigation toward favorable environments. How does directed navigation in a gradient modulate random exploration either parallel or orthogonal to the gradient? Here, we introduce methods originally used for analyzing protein folding trajectories to study the trajectories of the nematode Caenorhabditis elegans and the Drosophila larva in isotropic environments, as well as in thermal and chemical gradients. We find that the statistics of random exploration in any direction are little affected by directed movement along a stimulus gradient. A key constraint on the behavioral strategies of these organisms appears to be the preservation of their capacity to continuously explore their environments in all directions even while moving toward favorable conditions.

Simultaneous characterization of sense and antisense genomic processes by the double-stranded hidden Markov model.

Hidden Markov models (HMMs) have been extensively used to dissect the genome into functionally distinct regions using data such as RNA expression or DNA binding measurements. It is a challenge to disentangle processes occurring on complementary strands of the same genomic region. We present the double-stranded HMM (dsHMM), a model for the strand-specific analysis of genomic processes. We applied dsHMM to yeast using strand specific transcription data, nucleosome data, and protein binding data for a set of 11 factors associated with the regulation of transcription.The resulting annotation recovers the mRNA transcription cycle (initiation, elongation, termination) while correctly predicting strand-specificity and directionality of the transcription process. We find that pre-initiation complex formation is an essentially undirected process, giving rise to a large number of bidirectional promoters and to pervasive antisense transcription. Notably, 12% of all transcriptionally active positions showed simultaneous activity on both strands. Furthermore, dsHMM reveals that antisense transcription is specifically suppressed by Nrd1, a yeast termination factor.

An Analysis of Cumulative Selection and Random Drift in the Evolutionary Origination of Novel Protein Motifs

Despite the fact that all-important protein motifs encoded in gene sequences are generally considered to have been generated solely through a gradual and undirected process of change, the idea lacks empirical evidence and also suffers from theoretical difficulties. More recently, sudden developments such as through the exonization of non-coding DNA, as well as frameshift mutation, have been suggested as another source of evolutionary innovation. A mathematical model was used here to describe the combined action of both cumulative natural selection and random drift, relative to that of an alternative mechanism of artificial selection, in the origination of a hypothetical multi-residue sequence motif. A computer simulation of the model quantifiably demonstrates the marked inefficacy of standard forces in developing these molecular features when compared to the power of a directed or self-organizing process. An examination of how natural population shifts, including migration and isolation, as well as intragenic recombination, may serve to facilitate this particular case is also explored. An evolutionary accretion for novel motifs is concluded as being eminently feasible, although not one wholly reliant on the outcome of chance and differential reproduction.

Scale-free graphs of increasing degree

We study a scale-free random graph process in which the number of edges added at each step increases. This differs from the standard model in which a fixed number, m, of edges are added at each step. Let f(t) be the number of edges added at step t. In the standard scale-free model, f(t) = m constant, whereas in this paper we consider f(t) = [tc],c > 0. Such a graph process, in which the number of edges grows non-linearly with the number of vertices is said to have accelerating growth. We analyze both an undirected and a directed process. The power law of the degree sequence of these processes exhibits widely differing behavior. For the undirected process, the terminal vertex of each edge is chosen by preferential attachment based on vertex degree. When f(t) = m constant, this is the standard scale-free model, and the power law of the degree sequence is 3. When f(t) = [tc],c < 1, the degree sequence of the process exhibits a power law with parameter x = (3 − c)/(1 − c). As c → 0, x → 3, which gives a value of x = 3, as in standard scale-free model. Thus no more slowly growing monotone function f(t) alters the power law of this model away from x = 3. When c = 1, so that f(t) = t, the expected degree of all vertices is t, the vertex degree is concentrated, and the degree sequence does not have a power law. For the directed process, the terminal vertex is chosen proportional to in-degree plus an additive constant, to allow the selection of vertices of in-degree zero. For this process when f(t) = m is constant, the power law of the degree sequence is x = 2 + 1/m. When f(t) = [tc], c > 0, the power law becomes x = 1 + 1/(1 + c), which naturally extends the power law to [1,2]. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 38, 396–421, 2011

In the shadow of Intelligent Design: the teaching of evolution

The theory of evolution by natural selection is contrasted in the media, and in some schools, with creationist ideas, in which the diversity of life on Earth is said to be the result of direct species-by-species creation, not of evolution. More recently, the Intelligent Design movement has claimed that “certain features of the universe and of living things are best explained by an intelligent cause rather than an undirected process such as natural selection” (Intelligent Design Network website). A sample of 35 trainee and 29 experienced teachers from secondary schools in England were interviewed about their views, teaching and school policies regarding Darwin's theory of evolution and challenges to it, shortly before an organisation promoting Intelligent Design sent resources to all science departments in the United Kingdom. Data were grouped according to responses to creationist views, school policies and the value of the theory of evolution by natural selection. The majority of the teachers and trainees would use existing evidence that makes it highly probable that evolution has occurred, but for some there was a failure to recognise the nature of scientific enquiry. Aspects of practice and viewpoint gave serious concern about whether all science teachers and prospective science teachers have a scientific view of evolution or have sufficient training to respond to ‘alternative theories’ in science lessons. Professional development and curriculum guidance for both trainee and experienced teachers is indicated.

Distribution of Vertex Degree in Web-Graphs

We give results for the age-dependent distribution of vertex degree and number of vertices of given degree in the undirected web-graph process, a discrete random graph process introduced in [8]. For such processes we show that as $k \rightarrow \infty$, the expected proportion of vertices of degree $k$ has power law parameter $1+1/\eta$ where $\eta$ is the limiting ratio of the expected number of edge endpoints inserted by preferential attachment to the expected total degree. The proof for the undirected process generalizes naturally to give similar results for the directed hub-authority process, and an undirected hypergraph process.

Chemistry in Motion—Unidirectional Rotating Molecular Motors

Molecules are in constant motion, if not frozen around 0 K, but their Brownian motion is random. Overcoming this randomizing effect and generating directional motion at the molecular level with artificial systems is still a challenge. Research in this area is inspired by the vision of transferring the concept of an engine or a motor to the molecular level. That this is possible is illustrated by the directional processes found in nature: cell division, translocation of organelles, and membrane transport all rely on directional movement, while processes such as replication, transcription, and translation require encoded information sequences to be read and copied in a directional manner. Macroscopic engines and molecular motors both convert chemical, electrical, or light energy into mechanical work, yet their mode of operation is very different. Because of their dimensions molecular motors must operate at energies only slightly higher than those of the thermal bath surrounding them. They are actuated by Brownian motion and the key to their function is to give a direction to these undirected processes. Chemistry's role is to select one direction from all possible movements by lowering the energy profile of this directional movement compared to all the others. This makes this movement happen preferentially. Chemical or photochemical steps fuel these selection processes. Leigh et al. recently reported a net relative unidirectional circumrotation in a mechanically interlocked molecular rotor. The [2]catenane system (Scheme 1) consists of a larger macro-

Validated sizing rule against chatter of relief valves during gas service

Abstract Spring loaded relief valves are commonly used for protecting pressure loaded vessels, piping, etc. against overpressure. If the relief valve is installed improperly it may chatter while discharging. This behaviour is defined as an extremely rapid full opening and closing of the valve. The associated mechanical loads can damage the piping, equipment and the relief valve with the result of loss of pressure relief protection, undirected process fluid release, danger of fire and/or explosion, etc. In the technical guidelines and in the literature, sizing rules for the proper installation of relief valves are recommended. Most commonly applied is the 3% pressure loss rule for the allowable inlet pipe pressure drop as recommended in the API RP 520 (API RP 520: Sizing, selection and installation of pressure-relieving systems in refineries, 1993) or AD A2 ( AD-Merkblatt A2 : Sicherheitseinrichtungen gegen Druckuberschreitung—Sicherheitsventile, 1993). Another recommendation is based on the transmission time and the amplitude of the pressure waves generated by the abrupt safety valve opening and closing. In addition to these elementary rules, sophisticated computer codes for numerical simulation of the valve behaviour during the discharge process need to include the interrelationship between the flow in the pipe and that in the safety valve. Experiments have been performed with the objective of checking the validity of the rules. Based also on results taken from the literature a modified pressure surge sizing method is recommended. The usefulness of supplementary measures to establish in industrial installations a posteriore valve stability, e.g., by increasing the inlet pipe diameter, reducing the safety valve lift or installation of an oscillation damper are also evaluated.

Mitochondrial DNA of Chenopodium album (L): a comparison of leaves and suspension cultures

The mitochondrial genome (mt genome) of Chenopodium album was analysed. It was found to have a size of about 270 kb and a GC content of 46%. The genomes of plant cells and suspension cultures were compared. Restriction fragment pattern analyses and hybridization experiments revealed quantitative and qualitative alterations. However, a comparison of the restriction fragment patterns of two independently established in vitro cultures did not reveal differences as far as the mt chromosomal DNA is concerned. Therefore, alterations in mtDNA induced by in vitro culture seem not to be caused by an entirely undirected process in Chenopodium. A plasmid-like DNA molecule was amplified in only one of the cultures investigated and not in the other or in the plant cells. This molecule has a length of 1,083 by and is referred to as Ca1 mp1.

Some theoretical aspects of protein coevolution in the ecosystem “phage-bacteria” II. The deterministic model of microevolution

The deterministic model of microevolutionary dynamics of “phagebacteria” ecosystem is analyzed. Primary (and after all decisive) events that determine the dynamics are direct interactions between bacterial reception and viral adsorption proteins. Structure of the model is that under real parameters of adsorption, lysis and reproduction each separate ( ith) stage of microevolution comes to end with total lysis of ith population of bacteria by ith population of phage. It is shown however that in the course of joint microevolution both populations pass over some critical sizes when a new pair of antagonistic strains arises with certainty from mutations. As a result it is easy to visualize and simulate by computer the process of successive fixations of such pairs of mutants. This coevolution is the original example of a locally adaptive but globally undirected process which is characterized also by: (1) constant average rate, (2) neutrality of mutations at the moment of their emergence and during the period of “anticipation” of ecological changes, (3) pure adaptivity of the same mutations at the moment of proper fixation and (4) “intrinsic origin” (from the ecosystem dynamics itself) of selective constraints.