Cantor set fiber Bragg grating

The theory of fractals has already been applied to many fields in science, such as physics, biology, and chemistry. One of the most commonly used fractals in these applications is the Cantor set. Novel fiber Bragg gratings are proposed that combine the present technology of fiber Bragg gratings with the theory of Cantor sets. The principal goal of this work is to analyze how Cantor sets, applied to gratings, can alter their reflectivity spectra. Specifically, it is observed that, as the order of the Cantor set increases, the bandpass reflectivity spectra of these gratings broaden and evolve into more-complex patterns. Also, self-similarity properties can be observed in the spectra of these gratings. Numerical examples demonstrate variations in the spectra of these structures as the fractal order increases.     

Growth and ellipsometric studies of periodic and cantor aperiodic amorphous Ge/Si superlattices

Artificial superlattices of amorphous germanium (a-Ge) and amorphous silicon (a-Si) were deposited using dual-target magnetron d.c. sputtering on Si(001) substrates. The superlattices were fabricated with modulations according to deterministic aperiodic sequences as well as periodic sequences. The deterministic aperiodic sequences were made according to the generation of generalized Cantor sets. Optical characterization of the superlattices were carried out with spectroscopic ellipsometry. The optical properties of the Cantor and periodic superlattices with equal a-Ge:a-Si volume ratios were compared. We found that the interference peaks from the Cantor superlattices are more pronounced compared with the interference peaks from the periodic superlattices. The periodic superlattices could be modelled with both multilayer and effective-medium models, in contrast to the Cantor superlattices for which only multilayer models were appropriate. This is, to our knowledge, the first study of Cantor superlattices.     

Disordered animal multilayer reflectors and the localization of light

Multilayer optical reflectors constructed from ‘stacks’ of alternating layers of high and low refractive index dielectric materials are present in many animals. For example, stacks of guanine crystals with cytoplasm gaps occur within the skin and scales of fish, and stacks of protein platelets with cytoplasm gaps occur within the iridophores of cephalopods. Common to all these animal multilayer reflectors are different degrees of random variation in the thicknesses of the individual layers in the stack, ranging from highly periodic structures to strongly disordered systems. However, previous discussions of the optical effects of such thickness disorder have been made without quantitative reference to the propagation of light within the reflector. Here, we demonstrate that Anderson localization provides a general theoretical framework to explain the common coherent interference and optical properties of these biological reflectors. Firstly, we illustrate how the localization length enables the spectral properties of the reflections from more weakly disordered ‘coloured’ and more strongly disordered ‘silvery’ reflectors to be explained by the same physical process. Secondly, we show how the polarization properties of reflection can be controlled within guanine–cytoplasm reflectors, with an interplay of birefringence and thickness disorder explaining the origin of broadband polarization-insensitive reflectivity.     

A search game model of the scatter hoarder's problem

Scatter hoarders are animals (e.g. squirrels) who cache food (nuts) over a number of sites for later collection. A certain minimum amount of food must be recovered, possibly after pilfering by another animal, in order to survive the winter. An optimal caching strategy is one that maximizes the survival probability, given worst case behaviour of the pilferer. We modify certain ‘accumulation games’ studied by Kikuta & Ruckle (2000 J. Optim. Theory Appl.) and Kikuta & Ruckle (2001 Naval Res. Logist.), which modelled the problem of optimal diversification of resources against catastrophic loss, to include the depth at which the food is hidden at each caching site. Optimal caching strategies can then be determined as equilibria in a new ‘caching game’. We show how the distribution of food over sites and the site-depths of the optimal caching varies with the animal''s survival requirements and the amount of pilfering. We show that in some cases, ‘decoy nuts’ are required to be placed above other nuts that are buried further down at the same site. Methods from the field of search games are used. Some empirically observed behaviour can be shown to be optimal in our model.     

Honeybee combs: how the circular cells transform into rounded hexagons

We report that the cells in a natural honeybee comb have a circular shape at ‘birth’ but quickly transform into the familiar rounded hexagonal shape, while the comb is being built. The mechanism for this transformation is the flow of molten visco-elastic wax near the triple junction between the neighbouring circular cells. The flow may be unconstrained or constrained by the unmolten wax away from the junction. The heat for melting the wax is provided by the ‘hot’ worker bees.     

Stochastic analysis of biochemical reaction networks with absolute concentration robustness

It has recently been shown that structural conditions on the reaction network, rather than a ‘fine-tuning’ of system parameters, often suffice to impart ‘absolute concentration robustness’ (ACR) on a wide class of biologically relevant, deterministically modelled mass-action systems. We show here that fundamentally different conclusions about the long-term behaviour of such systems are reached if the systems are instead modelled with stochastic dynamics and a discrete state space. Specifically, we characterize a large class of models that exhibit convergence to a positive robust equilibrium in the deterministic setting, whereas trajectories of the corresponding stochastic models are necessarily absorbed by a set of states that reside on the boundary of the state space, i.e. the system undergoes an extinction event. If the time to extinction is large relative to the relevant timescales of the system, the process will appear to settle down to a stationary distribution long before the inevitable extinction will occur. This quasi-stationary distribution is considered for two systems taken from the literature, and results consistent with ACR are recovered by showing that the quasi-stationary distribution of the robust species approaches a Poisson distribution.     

Dichotomous feedback: a signal sequestration-based feedback mechanism for biocontroller design

We introduce a new design framework for implementing negative feedback regulation in synthetic biology, which we term ‘dichotomous feedback’. Our approach is different from current methods, in that it sequesters existing fluxes in the process to be controlled, and in this way takes advantage of the process’s architecture to design the control law. This signal sequestration mechanism appears in many natural biological systems and can potentially be easier to realize than ‘molecular sequestration’ and other comparison motifs that are nowadays common in biomolecular feedback control design. The loop is closed by linking the strength of signal sequestration to the process output. Our feedback regulation mechanism is motivated by two-component signalling systems, where a second response regulator could be competing with the natural response regulator thus sequestering kinase activity. Here, dichotomous feedback is established by increasing the concentration of the second response regulator as the level of the output of the natural process increases. Extensive analysis demonstrates how this type of feedback shapes the signal response, attenuates intrinsic noise while increasing robustness and reducing crosstalk.     

Properties of neuronal facilitation that improve target tracking in natural pursuit simulations

Although flying insects have limited visual acuity (approx. 1°) and relatively small brains, many species pursue tiny targets against cluttered backgrounds with high success. Our previous computational model, inspired by electrophysiological recordings from insect ‘small target motion detector’ (STMD) neurons, did not account for several key properties described from the biological system. These include the recent observations of response ‘facilitation’ (a slow build-up of response to targets that move on long, continuous trajectories) and ‘selective attention’, a competitive mechanism that selects one target from alternatives. Here, we present an elaborated STMD-inspired model, implemented in a closed loop target-tracking system that uses an active saccadic gaze fixation strategy inspired by insect pursuit. We test this system against heavily cluttered natural scenes. Inclusion of facilitation not only substantially improves success for even short-duration pursuits, but it also enhances the ability to ‘attend’ to one target in the presence of distracters. Our model predicts optimal facilitation parameters that are static in space and dynamic in time, changing with respect to the amount of background clutter and the intended purpose of the pursuit. Our results provide insights into insect neurophysiology and show the potential of this algorithm for implementation in artificial visual systems and robotic applications.     

Diffraction from fractal grating Cantor sets

In this paper, we have generalized the F^α-calculus by suggesting Fourier and Laplace transformations of the function with support of the fractals set which are the subset of the real line. Using this generalization, we have found the diffraction fringes from the fractal grating Cantor sets.     

Design of dynamic genetic memory

In electronic systems, dynamic random access memory (DRAM) is one of the core modules in the modern silicon computer. As for a bio‐computer, one would need a mechanism for storage of bio‐information named ‘data’, which, in binary logic, has two levels, logical high and logical low, or in the normalised form, ‘1’ and ‘0’. This study proposes a possible genetic DRAM based on the modified electronic configuration, which uses the biological reaction to fulfil an equivalent RC circuit constituting a memory cell. The authors implement fundamental functions of the genetic DRAM by incorporating a genetic toggle switch for data hold. The results of simulation verify that the basic function can be used on a bio‐storage module for the future bio‐computer.Inspec keywords: DRAM chips, genetic engineering, biocomputers, bioinformatics, equivalent circuits, RC circuitsOther keywords: dynamic genetic memory design, electronic systems, dynamic random access memory, modern silicon computer, biocomputer, bioinformation, binary logic, logical high level, logical low level, normalised form, genetic DRAM, modified electronic configuration, biological reaction, equivalent RC circuit, memory cell, fundamental functions, genetic toggle switch, data hold, biostorage module     

Preventable H5N1 avian influenza epidemics in the British poultry industry network exhibit characteristic scales

Epidemics are frequently simulated on redundantly wired contact networks, which have many more links between sites than are minimally required to connect all. Consequently, the modelled pathogen can travel numerous alternative routes, complicating effective containment strategies. These networks have moreover been found to exhibit ‘scale-free’ properties and percolation, suggesting resilience to damage. However, realistic H5N1 avian influenza transmission probabilities and containment strategies, here modelled on the British poultry industry network, show that infection dynamics can additionally express characteristic scales. These system-preferred scales constitute small areas within an observed power law distribution that exhibit a lesser slope than the power law itself, indicating a slightly increased relative likelihood. These characteristic scales are here produced by a network-pervading intranet of so-called hotspot sites that propagate large epidemics below the percolation threshold. This intranet is, however, extremely vulnerable; targeted inoculation of a mere 3–6% (depending on incorporated biosecurity measures) of the British poultry industry network prevents large and moderate H5N1 outbreaks completely, offering an order of magnitude improvement over previously advocated strategies affecting the most highly connected ‘hub’ sites. In other words, hotspots and hubs are separate functional entities that do not necessarily coincide, and hotspots can make more effective inoculation targets. Given the ubiquity and relevance of networks (epidemics, Internet, power grids, protein interaction), recognition of this spreading regime elsewhere would suggest a similar disproportionate sensitivity to such surgical interventions.     

Moiré by fractal structures

Abstract

The theoretical and experimental results of the Moiré effect observed by superposing two grids containing fractal Cantor structures are presented in this paper. It is also analysed the equivalence between the information obtained by the Fraunhofer diffraction through those fractal grids and that obtained through Moiré. In a recently published paper [1] it was verified that the diffraction pattern is highly sensitive to variations in dimension, order of growth and lacunarity of the Cantor fractal, becoming a powerful tool to analyse and determine these parameters. So, in this paper it is intended to determine the effect that the order of growth, the dimension, and the lacunarity of one-dimensional fractal Cantor structures have over the Moiré patterns that result from superposing these structures over replicas of themselves which have been rotated through a small angle α. The main goal is to verify if there exists an intimate relation between the resulting Moiré pattern and the parameters that describe this fractal structure, as occurs in the case of the diffraction pattern.     

The feasibility of coherent energy transfer in microtubules

It was once purported that biological systems were far too ‘warm and wet’ to support quantum phenomena mainly owing to thermal effects disrupting quantum coherence. However, recent experimental results and theoretical analyses have shown that thermal energy may assist, rather than disrupt, quantum coherent transport, especially in the ‘dry’ hydrophobic interiors of biomolecules. Specifically, evidence has been accumulating for the necessary involvement of quantum coherent energy transfer between uniquely arranged chromophores in light harvesting photosynthetic complexes. The ‘tubulin’ subunit proteins, which comprise microtubules, also possess a distinct architecture of chromophores, namely aromatic amino acids, including tryptophan. The geometry and dipolar properties of these aromatics are similar to those found in photosynthetic units indicating that tubulin may support coherent energy transfer. Tubulin aggregated into microtubule geometric lattices may support such energy transfer, which could be important for biological signalling and communication essential to living processes. Here, we perform a computational investigation of energy transfer between chromophoric amino acids in tubulin via dipole excitations coupled to the surrounding thermal environment. We present the spatial structure and energetic properties of the tryptophan residues in the microtubule constituent protein tubulin. Plausibility arguments for the conditions favouring a quantum mechanism of signal propagation along a microtubule are provided. Overall, we find that coherent energy transfer in tubulin and microtubules is biologically feasible.     

Unilateral contact problems with fractal geometry and fractal friction laws: methods of calculation

The present paper deals with two interrelated subjects: the fractal geometry and the fractal behaviour in unilateral contact problems. More specifically, throughout this paper both the interfaces and the friction laws holding on these interfaces are modelled by means of the fractal geometry. It is important to notice here that the fractality of the induced friction laws takes into account the randomness of the interface asperities causing the friction forces. According to the fractal model introduced in this paper, both the fractal law and the fractal interface are considered to be graphs of two different fractal interpolation functions which are the “fixed points” of two contractive operators. Using this method, the fractal friction law is approximated by a sequence of nonmonotone possibly multivalued classical C ⁰-curves. The numerical treatment of each arizing nonmonotone problem is accomplished by an advanced solution method which approximates the nonmonotone problem by a sequence of monotone subproblems. Numerical applications from the static analysis of cracked structures with a prescribed fractal geometry and fractal interface laws are included in order to illustrate the theory.     

Phase transitions and assortativity in models of gene regulatory networks evolved under different selection processes

We study a simplified model of gene regulatory network evolution in which links (regulatory interactions) are added via various selection rules that are based on the structural and dynamical features of the network nodes (genes). Similar to well-studied models of ‘explosive’ percolation, in our approach, links are selectively added so as to delay the transition to large-scale damage propagation, i.e. to make the network robust to small perturbations of gene states. We find that when selection depends only on structure, evolved networks are resistant to widespread damage propagation, even without knowledge of individual gene propensities for becoming ‘damaged’. We also observe that networks evolved to avoid damage propagation tend towards disassortativity (i.e. directed links preferentially connect high degree ‘source’ genes to low degree ‘target’ genes and vice versa). We compare our simulations to reconstructed gene regulatory networks for several different species, with genes and links added over evolutionary time, and we find a similar bias towards disassortativity in the reconstructed networks.     

The evolution of developmental patterning under genetic duplication constraints

Of considerable interest are the evolutionary and developmental origins of complex, adaptive structures and the mechanisms that stabilize these structures. We consider the relationship between the evolutionary process of gene duplication and deletion and the stability of morphogenetic patterns produced by interacting activators and inhibitors. We compare the relative stability of patterns with a single activator and inhibitor (two-dimensional system) against a ‘redundant’ system with two activators or two inhibitors (three-dimensional system). We find that duplication events can both expand and contract the space of patterns. We study developmental robustness in terms of stochastic escape times from this space, also known as a ‘canalization potential’. We embed the output of pattern formation into an explicit evolutionary model of gene duplication, gene loss and variation in the steepness of the canalization potential. We find that under all constant conditions, the system evolves towards a preference for steep potentials associated with low phenotypic variability and longer lifespans. This preference leads to an overall decrease in the density of redundant genotypes as developmental robustness neutralizes the advantages of genetic robustness.     

On the reliability of seasonal climate forecasts

Seasonal climate forecasts are being used increasingly across a range of application sectors. A recent UK governmental report asked: how good are seasonal forecasts on a scale of 1–5 (where 5 is very good), and how good can we expect them to be in 30 years time? Seasonal forecasts are made from ensembles of integrations of numerical models of climate. We argue that ‘goodness’ should be assessed first and foremost in terms of the probabilistic reliability of these ensemble-based forecasts; reliable inputs are essential for any forecast-based decision-making. We propose that a ‘5’ should be reserved for systems that are not only reliable overall, but where, in particular, small ensemble spread is a reliable indicator of low ensemble forecast error. We study the reliability of regional temperature and precipitation forecasts of the current operational seasonal forecast system of the European Centre for Medium-Range Weather Forecasts, universally regarded as one of the world-leading operational institutes producing seasonal climate forecasts. A wide range of ‘goodness’ rankings, depending on region and variable (with summer forecasts of rainfall over Northern Europe performing exceptionally poorly) is found. Finally, we discuss the prospects of reaching ‘5’ across all regions and variables in 30 years time.     

Asymptotic burnout and homeostatic awakening: a possible solution to the Fermi paradox?

Previous studies show that city metrics having to do with growth, productivity and overall energy consumption scale superlinearly, attributing this to the social nature of cities. Superlinear scaling results in crises called ‘singularities’, where population and energy demand tend to infinity in a finite amount of time, which must be avoided by ever more frequent ‘resets’ or innovations that postpone the system''s collapse. Here, we place the emergence of cities and planetary civilizations in the context of major evolutionary transitions. With this perspective, we hypothesize that once a planetary civilization transitions into a state that can be described as one virtually connected global city, it will face an ‘asymptotic burnout’, an ultimate crisis where the singularity-interval time scale becomes smaller than the time scale of innovation. If a civilization develops the capability to understand its own trajectory, it will have a window of time to affect a fundamental change to prioritize long-term homeostasis and well-being over unyielding growth—a consciously induced trajectory change or ‘homeostatic awakening’. We propose a new resolution to the Fermi paradox: civilizations either collapse from burnout or redirect themselves to prioritizing homeostasis, a state where cosmic expansion is no longer a goal, making them difficult to detect remotely.     

Construction and characterization of rectal cancer‐related lncRNA‐mRNA ceRNA network reveals prognostic biomarkers in rectal cancer

Rectal cancer is an important cause of cancer‐related deaths worldwide. In this study, the differentially expressed (DE) lncRNAs/mRNAs were first identified and the correlation level between DE lncRNAs and mRNAs were calculated. The results showed that genes of highly correlated lncRNA‐mRNA pairs presented strong prognosis effects, such as GPM6A, METTL24, SCN7A, HAND2‐AS1 and PDZRN4. Then, the rectal cancer‐related lncRNA‐mRNA network was constructed based on the ceRNA theory. Topological analysis of the network revealed that the network was maintained by hub nodes and a hub subnetwork was constructed, including the hub lncRNA MIR143HG and MBNL1‐SA1. Further analysis indicated that the hub subnetwork was highly related to cancer pathways, such as ‘Focal adhesion’ and ‘Wnt signalling pathway’. Hub subnetwork also had significant prognosis capability. A closed lncRNA‐mRNA module was identified by bilateral network clustering. Genes in modules also showed high prognosis effects. Finally, a core lncRNA‐TF crosstalk network was identified to uncover the crosstalk and regulatory mechanisms of lncRNAs and TFs by integrating ceRNA crosstalks and TF binding affinities. Some core genes, such as MEIS1, GLI3 and HAND2‐AS1 were considered as the key regulators in tumourigenesis. Based on the authors’ comprehensive analysis, all these lncRNA‐mRNA crosstalks provided promising clues for biological prognosis of rectal cancer.