Complementary approaches to understanding the plant circadian clock

Circadian clocks are oscillatory genetic networks that help organisms adapt to the 24-hour day/night cycle. The clock of the green alga Ostreococcus tauri is the simplest plant clock discovered so far. Its many advantages as an experimental system facilitate the testing of computational predictions. We present a model of the Ostreococcus clock in the stochastic process algebra Bio-PEPA and exploit its mapping to different analysis techniques, such as ordinary differential equations, stochastic simulation algorithms and model-checking. The small number of molecules reported for this system tests the limits of the continuous approximation underlying differential equations. We investigate the difference between continuous-deterministic and discrete-stochastic approaches. Stochastic simulation and model-checking allow us to formulate new hypotheses on the system behaviour, such as the presence of self-sustained oscillations in single cells under constant light conditions. We investigate how to model the timing of dawn and dusk in the context of model-checking, which we use to compute how the probability distributions of key biochemical species change over time. These show that the relative variation in expression level is smallest at the time of peak expression, making peak time an optimal experimental phase marker. Building on these analyses, we use approaches from evolutionary systems biology to investigate how changes in the rate of mRNA degradation impacts the phase of a key protein likely to affect fitness. We explore how robust this circadian clock is towards such potential mutational changes in its underlying biochemistry. Our work shows that multiple approaches lead to a more complete understanding of the clock

Ultrasensitive Negative Feedback Control: A Natural Approach for the Design of Synthetic Controllers

This is the final version of the article. Available from Public Library of Science via the DOI in this record.Many of the most important potential applications of Synthetic Biology will require the ability to design and implement high performance feedback control systems that can accurately regulate the dynamics of multiple molecular species within the cell. Here, we argue that the use of design strategies based on combining ultrasensitive response dynamics with negative feedback represents a natural approach to this problem that fully exploits the strongly nonlinear nature of cellular information processing. We propose that such feedback mechanisms can explain the adaptive responses observed in one of the most widely studied biomolecular feedback systems—the yeast osmoregulatory response network. Based on our analysis of such system, we identify strong links with a well-known branch of mathematical systems theory from the field of Control Engineering, known as Sliding Mode Control. These insights allow us to develop design guidelines that can inform the construction of feedback controllers for synthetic biological systems.This work was funded by the UK Engineering and Physical Sciences Research Council (EPSRC), grant number EP/I017445/1

Algorithms for Stable Matching and Clustering in a Grid

We study a discrete version of a geometric stable marriage problem originally proposed in a continuous setting by Hoffman, Holroyd, and Peres, in which points in the plane are stably matched to cluster centers, as prioritized by their distances, so that each cluster center is apportioned a set of points of equal area. We show that, for a discretization of the problem to an $n\times n$ grid of pixels with $k$ centers, the problem can be solved in time $O(n^2 \log^5 n)$, and we experiment with two slower but more practical algorithms and a hybrid method that switches from one of these algorithms to the other to gain greater efficiency than either algorithm alone. We also show how to combine geometric stable matchings with a $k$-means clustering algorithm, so as to provide a geometric political-districting algorithm that views distance in economic terms, and we experiment with weighted versions of stable $k$-means in order to improve the connectivity of the resulting clusters.Comment: 23 pages, 12 figures. To appear (without the appendices) at the 18th International Workshop on Combinatorial Image Analysis, June 19-21, 2017, Plovdiv, Bulgari

Lagrange structure and quantization

A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do \textit{not} necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the Lagrangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in $d+1$ dimensions, being localized on the boundary, are proved to be equivalent to the original theory in $d$ dimensions. As the topological sigma-model has a well defined action, it is path-integral quantized in the usual way that results in quantization of the original (not necessarily Lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The general quantization scheme is exemplified by several models including the ones whose classical dynamics are not variational.Comment: Minor corrections, format changed, 40 page

disk laser welding of ti 6al 4v titanium alloy plates in t joint configuration

Abstract Titanium alloys are employed in a wide range of applications, ranging from aerospace to medicine. In particular, Ti-6Al-4V is the most common, thanks to an excellent combination of low density, high specific strength and corrosion resistance. Laser welding has been increasingly considered as an alternative to traditional techniques to join titanium alloys. An increase in penetration depth and a reduction of possible welding defects is indeed achieved; moreover a smaller grain size in the fused zone is benefited in comparison to either TIG and plasma arc welding, thus providing an increase in the tensile strength of the welded structures. The aim of this work is to study disk-laser welding of 3.2mm thick Ti-6Al-4V plates in T-joint configuration without using a filler wire, defining the influence of different process parameters. The issue concerning the clamping of the plates is discussed and a proper device is developed to carry out welds. A structured plan has to be carried out in order to characterize the process thus discussing the response variables. Power and welding speed are considered as crucial input variables since they determine the thermal input to the work-piece; furthermore, given the particular configuration analyzed, tilt angle is considered as a further variable, whereas focus position is fixed below the upper surface to obtain a full penetration. Welding beads have been first examined with a coordinate measuring machine to study distortions, and then from a morphological point of view. Eventually, Vickers microhardness testing has been conducted to discuss structural changes in fusion and heat affected zone due to welding thermal cycles

Modelling Non-linear Crowd Dynamics in Bio-PEPA

Emergent phenomena occur due to the pattern of non-linear and distributed local interactions between the elements of a system over time. Surprisingly, agent based crowd models, in which the movement of each individual follows a limited set of simple rules, often re-produce quite closely the emergent behaviour of crowds that can be observed in reality. An example of such phenomena is the spontaneous self-organisation of drinking parties in the squares of cities in Spain, also known as "El Botellon" [20]. We revisit this case study providing an elegant stochastic process algebraic model in Bio-PEPA amenable to several forms of analyses, among which simulation and fluid flow analysis. We show that a fluid flow approximation, i.e. a deterministic reading of the average behaviour of the system, can provide an alternative and efficient way to study the same emergent behaviour as that explored in [20] where simulation was used instead. Besides empirical evidence, also an analytical justification is provided for the good correspondence found between simulation results and the fluid flow approximation

Simple sequence repeat-based assessment of genetic diversity in 'Dimrit' and 'Gemre' grapevine accessions from Turkey

It is widely believed that Turkey has played an important role in the evolution of modern day grapes due to its unique geographical location with close proximity to the regions of grape diversity. Despite this, the rich grape germplasm found in Turkey has not been sufficiently analyzed genetically. In this study, 31 grapevine accessions from 'Dimrit' (or 'Dilmit') and 'Gemre' grape groups were genetically analyzed at eight SSR (microsatellite) loci (VVS2, VVMD5, VVMD7, VVMD24, VVMD27, VVMD28, VrZAG62 and VrZAG79) and for a number of ampeolographic characteristics. These analyses identified sufficient genetic diversity between these two grape groups that, in general, clustered separately in the dendrogram constructed based on the SSR data. However, the ecogeographical distribution and genetic relationship of the genotypes did not show any significant correlation. Two 'Gemre' accessions were determined as genetically identical. In addition, one case of synonym and several cases of homonym genotypes were identified. The results reported here are important first steps towards better characterization of these grape genotypes and would aid future germplasm management and breeding efforts.

Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket

We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent \Delta operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra, and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie brackets with a fixed nilpotent Lie algebra element Q. We find the most general Jacobi-like identity that such a hierarchy satisfies. The numerical coefficients in front of each term in these generalized Jacobi identities are related to the Bernoulli numbers. We suggest that the definition of a homotopy Lie algebra should be enlarged to accommodate this important case. Finally, we consider the Courant bracket as an example of a derived bracket. We extend it to the "big bracket" of exterior forms and multi-vectors, and give closed formulas for the higher Courant brackets.Comment: 42 pages, LaTeX. v2: Added remarks in Section 5. v3: Added further explanation. v4: Minor adjustments. v5: Section 5 completely rewritten to include covariant construction. v6: Minor adjustments. v7: Added references and explanation to Section

Spontaneous ventral urethral fistula in a young diabetic man: a case report

We present the first case reported in the medical literature of a patient with a spontaneous ventral urethral fistula accompanied by severe infection due to diabetes mellitus. A 34-year-old man with poor controlled adult-onset diabetes mellitus was admitted to our hospital with a large subcutaneous abscess involving the complete penis, scrotum and perineum. The patient did not report any history of any penile trauma or local infection but has experienced transient swelling of the perineal region following urination. Initial surgical treatment consisted of surgical debridement of necrotic tissue. At this time reconstructive surgery was impossible and a suprapubic cystostomy was performed. After 4 months of suprapubic urinary diversion the urethral fistula resolved and function of external genitalia was reestablished. In a follow-up period of 40 months no recurrence occurred. Spontaneous diabetes-associated ventral urethral fistulas are extremely rare and we are not aware of any other published case report