On the Floquet Theory of Delay Differential Equations

We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the Poincar'e Lindstedt and the Shohat expansions which were originally developed for ordinary differential equations. Then we systematically elaborate a linear stability analysis around a time periodic reference state. This allows to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions

Geometric Friction Directs Cell Migration

In the absence of environmental cues, a migrating cell performs an isotropic random motion. Recently, the breaking of this isotropy has been observed when cells move in the presence of asymmetric adhesive patterns. However, up to now the mechanisms at work to direct cell migration in such environments remain unknown. Here, we show that a nonadhesive surface with asymmetric microgeometry consisting of dense arrays of tilted micropillars can direct cell motion. Our analysis reveals that most features of cell trajectories, including the bias, can be reproduced by a simple model of active Brownian particle in a ratchet potential, which we suggest originates from a generic elastic interaction of the cell body with the environment. The observed guiding effect, independent of adhesion, is therefore robust and could be used to direct cell migration both in vitro and in vivo

Spatiotemporal communication with synchronized optical chaos

We propose a model system that allows communication of spatiotemporal information using an optical chaotic carrier waveform. The system is based on broad-area nonlinear optical ring cavities, which exhibit spatiotemporal chaos in a wide parameter range. Message recovery is possible through chaotic synchronization between transmitter and receiver. Numerical simulations demonstrate the feasibility of the proposed scheme, and the benefit of the parallelism of information transfer with optical wavefronts.Comment: 4 pages, 5 figure

Generalized Totalizer Encoding for Pseudo-Boolean Constraints

Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are used to model many real-world problems. A common approach to solve these constraints is to encode them into a SAT formula. The runtime of the SAT solver on such formula is sensitive to the manner in which the given pseudo-Boolean constraints are encoded. In this paper, we propose generalized Totalizer encoding (GTE), which is an arc-consistency preserving extension of the Totalizer encoding to pseudo-Boolean constraints. Unlike some other encodings, the number of auxiliary variables required for GTE does not depend on the magnitudes of the coefficients. Instead, it depends on the number of distinct combinations of these coefficients. We show the superiority of GTE with respect to other encodings when large pseudo-Boolean constraints have low number of distinct coefficients. Our experimental results also show that GTE remains competitive even when the pseudo-Boolean constraints do not have this characteristic.Comment: 10 pages, 2 figures, 2 tables. To be published in 21st International Conference on Principles and Practice of Constraint Programming 201

A logical approach for behavioural composition of scenario-based models

As modern systems become more complex, design approaches model different aspects of the system separately. When considering (intra and inter) system interactions, it is usual to model individual scenarios using UML’s sequence diagrams. Given a set of scenarios we then need to check whether these are consistent and can be combined for a better understanding of the overall behaviour. This paper addresses this by presenting a novel formal technique for composing behavioural models at the metamodel level through exact metamodel restriction (EMR). In our approach a sequence diagram can be completely described by a set of logical constraints at the metamodel level. When composing sequence diagrams we take the union of the sets of logical constraints for each diagram and additional behavioural constraints that describe the matching composition glue. A formal semantics for composition in accordance with the glue guides our model transformation to Alloy. Alloy’s fully automated constraint solver gives us the solution. Our technique has been implemented as an Eclipse plugin SD2Alloy.Postprin

Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed

On Tackling the Limits of Resolution in SAT Solving

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for formulas in conjunctive normal form (CNF) to the problem of solving maximum satisfiability over Horn formulas. Given the new transformation, the paper proves a polynomial bound on the number of MaxSAT resolution steps for pigeonhole formulas. This result is in clear contrast with earlier results on the length of proofs of MaxSAT resolution for pigeonhole formulas. The paper also establishes the same polynomial bound in the case of modern core-guided MaxSAT solvers. Experimental results, obtained on CNF formulas known to be hard for CDCL SAT solvers, show that these can be efficiently solved with modern MaxSAT solvers

Polarization coupling and pattern selection in a type-II optical parametric oscillator

We study the role of a direct intracavity polarization coupling in the dynamics of transverse pattern formation in type-II optical parametric oscillators. Transverse intensity patterns are predicted from a stability analysis, numerically observed, and described in terms of amplitude equations. Standing wave intensity patterns for the two polarization components of the field arise from the nonlinear competition between two concentric rings of unstable modes in the far field. Close to threshold a wavelength is selected leading to standing waves with the same wavelength for the two polarization components. Far from threshold the competition stabilizes patterns in which two different wavelengths coexist.Comment: 14 figure

Adaptive evolution of a recombinant lactose-consuming Saccharomyces cerevisiae strain

In previous work, a recombinant S. cerevisiae flocculent strain (NCYC869-A3/T1, or simply T1) with the ability to express both the LAC4 (coding for beta-galactosidase) and LAC12 (lactose permease) genes of Kluyveromyces lactis was constructed (Domingues et al., Appl Microbiol Biotechnol 51:621–626, 1999). The original recombinant obtained (T1) was able to metabolise lactose but slowly. Thus, it was subjected to an adaptation period, where the recombinant yeast was kept in liquid lactose medium, refreshed periodically. Cells collected after the adaptation process presented improved fermentative characteristics compared to the original transformant, namely higher growth rate and higher ethanol productivity. This evolved strain was named T1-E. The fermentative parameters (shake-flask cultivations with buffered lactose defined mineral medium) of strain T1-E are similar to K. lactis wild-type strain CBS2359 (NRRLY1140). We aim at elucidating what happened during the process of adaptation/evolution that the yeast went through. The plasmid used for transformation (pKR1B-Lac4-1), which harbors a 13 kb region of the K. lactis genome including LAC4 and LAC12 genes, remained autonomous in the recombinant strain. Plasmid isolated from T1 (before adaptation) was identical to pKR1B-Lac4-1. However, we found that the plasmid isolated from T1-E carries a 1594 bp deletion (positions -518 to -2111 from the 5' end of LAC4) in the promoter region between LAC4 and LAC12 genes. This deletion may have improved the transcription of one or both of the genes, which may be the cause for the improved lactose consumption phenotype of the evolved strain. In lactose cultivations, the intracellular beta-galactosidase activity of strain T1-E is about 40 times higher when compared to T1. Moreover, the level of beta-galactosidase activity in strain T1-E is comparable to K. lactis CBS2359. Microarray analysis showed increased expression of genes related with transposable elements in T1-E compared to T1, which reflects the selective pressure that the yeast suffered during the adaptation process. The transcriptome (S. cerevisiae) analysis did not revealed other important differences between T1 and T1-E