Thomas M. A. Fink

Beach Cusps as Self-Organized Patterns

Computer simulations of flow and sediment transport in the swash zone on a beach demonstrate that a model that couples local flow acceleration and alongshore surface gradient is sufficient to produce uniformly spaced beach cusps. The characteristics of the simulated cusps and the conditions under which they form are in reasonable agreement with observations of natural cusps. The self-organization mechanism in the model is incompatible with an accepted model in which standing alongshore waves drive the regular pattern of erosion and deposition that gives rise to beach cusps. Because the models make similar predictions, it is concluded that currently available observational data are insufficient for discrimination between them.

Comparison of pattern detection methods in microarray time series of the segmentation clock.

While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns.

How much non-coding DNA do eukaryotes require?

Despite tremendous advances in the field of genomics, the amount and function of the large non-coding part of the genome in higher organisms remains poorly understood. Here we report an observation, made for 37 fully sequenced eukaryotic genomes, which indicates that eukaryotes require a certain minimum amount of non-coding DNA (ncDNA). This minimum increases quadratically with the amount of DNA located in exons. Based on a simple model of the growth of regulatory networks, we derive a theoretical prediction of the required quantity of ncDNA and find it to be in excellent agreement with the data. The amount of additional ncDNA (in basepairs) which eukaryotes require obeys N(DEF)=1/2 (N(C)/N(P)) (N(C)-N(P)), where N(C) is the amount of exonic DNA, and N(P) is a constant of about 10 Mb. This value N(DEF) corresponds to a few percent of the genome in Homo sapiens and other mammals, and up to half the genome in simpler eukaryotes. Thus, our findings confirm that eukaryotic life depends on a substantial fraction of ncDNA and also make a prediction of the size of this fraction, which matches the data closely.

Identifying genes from up--down properties of microarray expression series

MOTIVATION We consider any collection of microarrays that can be ordered to form a progression; for example, as a function of time, severity of disease or dose of a stimulant. By plotting the expression level of each gene as a function of time, or severity, or dose, we form an expression series, or curve, for each gene. While most of these curves will exhibit random fluctuations, some will contain a pattern, and these are the genes that are most likely associated with the quantity used to order them. RESULTS We introduce a method of identifying the pattern and hence genes in microarray expression curves without knowing what kind of pattern to look for. Key to our approach is the sequence of ups and downs formed by pairs of consecutive data points in each curve. As a benchmark, we blindly identified genes from yeast cell cycles without selecting for periodic or any other anticipated behaviour. CONTACT tmf20@cam.ac.uk SUPPLEMENTARY INFORMATION The complete versions of Table 2 and Figure 4, as well as other material, can be found at http://www.lps.ens.fr/~willbran/up-down/ or http://www.tcm.phy.cam.ac.uk/~tmf20/up-down/

Unbiased pattern detection in microarray data series

MOTIVATION Following the advent of microarray technology in recent years, the challenge for biologists is to identify genes of interest from the thousands of genetic expression levels measured in each microarray experiment. In many cases the aim is to identify pattern in the data series generated by successive microarray measurements. RESULTS Here we introduce a new method of detecting pattern in microarray data series which is independent of the nature of this pattern. Our approach provides a measure of the algorithmic compressibility of each data series. A series which is significantly compressible is much more likely to result from simple underlying mechanisms than series which are incompressible. Accordingly, the gene associated with a compressible series is more likely to be biologically significant. We test our method on microarray time series of yeast cell cycle and show that it blindly selects genes exhibiting the expected cyclic behaviour as well as detecting other forms of pattern. Our results successfully predict two independent non-microarray experimental studies.

Noise spectroscopy using correlations of single-shot qubit readout.

A better understanding of the noise causing qubit decoherence is crucial for improving qubit performance. The noise spectrum affecting the qubit may be extracted by measuring dephasing under the application of pulse sequences but requires accurate qubit control and sufficiently long relaxation times, which are not always available. Here, we describe an alternative method to extract the spectrum from correlations of single-shot measurement outcomes of successive free induction decays. This method only requires qubit initialization and readout with a moderate fidelity and also allows independent tuning of both the overall sensitivity and the frequency region over which it is sensitive. Thus, it is possible to maintain a good detection contrast over a very wide frequency range. We discuss using our method for measuring both 1/f noise and the fluctuation spectrum of the nuclear bath of GaAs spin qubits.

Tie knots, random walks and topology

Necktie knots are inherently topological structures; what makes them tractable is the particular manner in which they are constructed. This observation motivates a map between tie knots and persistent walks on a triangular lattice. The topological structure embedded in a tie knot may be determined by appropriately manipulating its projection; we derive corresponding rules for tie knot sequences. We classify knots according to their size and shape and quantify the number of knots in a class. Aesthetic knots are characterised by the conditions of symmetry and balance. Of the 85 knots which may be tied with conventional tie, we recover the four traditional knots and introduce nine new aesthetic ones. For large (though impractical) half-winding number, we present some asymptotic results.

Designing tie knots by random walks

The simplest of conventional tie knots, the four-in-hand, has its origins in late-nineteenth-century England. The Duke of Windsor, as King Edward VIII became after abdicating in 1936, is credited with introducing what is now known as the Windsor knot, from which its smaller derivative, the half-Windsor, evolved. In 1989, the Pratt knot, the first new knot to appear in fifty years, was revealed on the front page of The New York Times.

Low-Temperature Behaviour of Social and Economic Networks

Real-world social and economic networks typically display a number of particular topological properties, such as a giant connected component, a broad degree distribution, the small-world property and the presence of communities of densely interconnected nodes. Several models, including ensembles of networks, also known in social science as Exponential Random Graphs, have been proposed with the aim of reproducing each of these properties in isolation. Here, we define a generalized ensemble of graphs by introducing the concept of graph temperature, controlling the degree of topological optimization of a network. We consider the temperature-dependent version of both existing and novel models and show that all the aforementioned topological properties can be simultaneously understood as the natural outcomes of an optimized, low-temperature topology. We also show that seemingly different graph models, as well as techniques used to extract information from real networks are all found to be particular low-temperature cases of the same generalized formalism. One such technique allows us to extend our approach to real weighted networks. Our results suggest that a low graph temperature might be a ubiquitous property of real socio-economic networks, placing conditions on the diffusion of information across these systems.

1-D random landscapes and non-random data series

We study the simplest random landscape, the curve formed by joining consecutive data points f1 ,...,f N+1 with line segments, where the fi are i.i.d. random numbers and fifj. We label each segment increasing (+) or decreasing (−) and call this string of +s and −s the up-down signature σ. We calculate the probability P (σ(f )) for a random curve and use it to bound the algorithmic information content of f . We show that f can be compressed byk =l og2 1/P (σ) − N bits, where k is a universal currency for comparing the amount of pattern in different curves. By applying our results to microarray time series data, we blindly identify regulatory genes. Copyright c � EPLA, 2007 Introduction. - Random landscapes are central to the disciplines of spin glasses, drainage networks, protein fold- ing, neural networks and combinatorial optimisation (1,2). Properties of these systems are related to simple ques- tions about their landscapes: How many minima are there? What is the size of their basins of attraction? What is the pattern of rises and falls? The large-scale analysis of data series has become increasingly important in the study of financial and biolog- ical systems. Identifying trends or pattern, for example, in currency exchange rates or microarray expression data can identify market inefficiencies or the regulatory function of a specific gene. Often the pattern in question is weak (close to random) and it must be identified from amongst a large ensemble of other random data series. In this letter we show that that there are fruitful underlying connections between the dynamical properties of a 1-D landscape and the presence of pattern in a series of data. Considering a series as a sequence of increases and decreases provides a method of compressing a curve, in the sense that the size of the file needed to store instructions for generating the curve is less than it would be by storing the curve outright. We derive a formal relation between the up-down properties of a curve and the algorithmic information content (AIC) of the equivalent data series, or size of the smallest file needed to store it, which is the