Stochastic competitive learning in complex networks

Competitive learning is an important machine learning approach which is widely employed in artificial neural networks. In this paper, we present a rigorous definition of a new type of competitive learning scheme realized on large-scale networks. The model consists of several particles walking within the network and competing with each other to occupy as many nodes as possible, while attempting to reject intruder particles. The particle's walking rule is composed of a stochastic combination of random and preferential movements. The model has been applied to solve community detection and data clustering problems. Computer simulations reveal that the proposed technique presents high precision of community and cluster detections, as well as low computational complexity. Moreover, we have developed an efficient method for estimating the most likely number of clusters by using an evaluator index that monitors the information generated by the competition process itself. We hope this paper will provide an alternative way to the study of competitive learning.

Using complex networks concepts to assess approaches for citations in scientific papers

The number of citations received by authors in scientific journals has become a major parameter to assess individual researchers and the journals themselves through the impact factor. A fair assessment therefore requires that the criteria for selecting references in a given manuscript should be unbiased with regard to the authors or journals cited. In this paper, we assess approaches for citations considering two recommendations for authors to follow while preparing a manuscript: (i) consider similarity of contents with the topics investigated, lest related work should be reproduced or ignored; (ii) perform a systematic search over the network of citations including seminal or very related papers. We use formalisms of complex networks for two datasets of papers from the arXiv and the Web of Science repositories to show that neither of these two criteria is fulfilled in practice. By representing the texts as complex networks we estimated a similarity index between pieces of texts and found that the list of references did not contain the most similar papers in the dataset. This was quantified by calculating a consistency index, whose maximum value is one if the references in a given paper are the most similar in the dataset. For the areas of "complex networks" and "graphenes", the consistency index was only 0.11-0.23 and 0.10-0.25, respectively. To simulate a systematic search in the citation network, we employed a traditional random walk search (i.e. diffusion) and a random walk whose probabilities of transition are proportional to the number of the ingoing edges of the neighbours. The frequency of visits to the nodes (papers) in the network had a very small correlation with either the actual list of references in the papers or with the number of downloads from the arXiv repository. Therefore, apparently the authors and users of the repository did not follow the criterion related to a systematic search over the network of citations. Based on these results, we propose an approach that we believe is fairer for evaluating and complementing citations of a given author, effectively leading to a virtual scientometry.

Network-based stochastic semisupervised learning

Semisupervised learning is a machine learning approach that is able to employ both labeled and unlabeled samples in the training process. In this paper, we propose a semisupervised data classification model based on a combined random-preferential walk of particles in a network (graph) constructed from the input dataset. The particles of the same class cooperate among themselves, while the particles of different classes compete with each other to propagate class labels to the whole network. A rigorous model definition is provided via a nonlinear stochastic dynamical system and a mathematical analysis of its behavior is carried out. A numerical validation presented in this paper confirms the theoretical predictions. An interesting feature brought by the competitive-cooperative mechanism is that the proposed model can achieve good classification rates while exhibiting low computational complexity order in comparison to other network-based semisupervised algorithms. Computer simulations conducted on synthetic and real-world datasets reveal the effectiveness of the model.

Atomically resolved study of the morphology change of InAs/GaAs quantum dot layers induced by rapid thermal annealing

The optoelectronic properties of InAs/GaAs quantum dots can be tuned by rapid thermal annealing. In this study, the morphology change of InAs/GaAs quantum dots layers induced by rapid thermal annealing was investigated at the atomic-scale by cross-sectional scanning tunneling microscopy. Finite elements calculations that model the outward relaxation of the cleaved surface were used to determine the indium composition profile of the wetting layer and the quantum dots prior and post rapid thermal annealing. The results show that the wetting layer is broadened upon annealing. This broadening could be modeled by assuming a random walk of indium atoms. Furthermore, we show that the stronger strain gradient at the location of the quantum dots enhances the intermixing. Photoluminescence measurements show a blueshift and narrowing of the photoluminescence peak. Temperature dependent photoluminescence measurements show a lower activation energy for the annealed sample. These results are in agreement with the observed change in morphology. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770371]

Model for the Dynamics of the Cytoskeleton.

Particle tracking of microbeads attached to the cytoskeleton (CSK) reveals an intermittent dynamic. The mean squared displacement (MSD) is subdiffusive for small Δt and superdiffusive for large Δt, which are associated with periods of traps and periods of jumps respectively. The analysis of the displacements has shown a non-Gaussian behavior, what is indicative of an active motion, classifying the cells as a far from equilibrium material. Using Langevin dynamics, we reconstruct the dynamic of the CSK. The model is based on the bundles of actin filaments that link themself with the bead RGD coating, trapping it in an harmonic potential. We consider a one- dimensional motion of a particle, neglecting inertial effects (over-damped Langevin dynamics). The resultant force is decomposed in friction force, elastic force and random force, which is used as white noise representing the effect due to molecular agitation. These description until now shows a static situation where the bead performed a random walk in an elastic potential. In order to modeling the active remodeling of the CSK, we vary the equilibrium position of the potential. Inserting a motion in the well center, we change the equilibrium position linearly with time with constant velocity. The result found exhibits a MSD versus time ’tau’ with three regimes. The first regime is when ‘tau’ < ‘tau IND 0’, where ‘tau IND 0’ is the relaxation time, representing the thermal motion. At this regime the particle can diffuse freely. The second regime is a plateau, ‘tau IND 0’ < ‘tau’ < ‘tau IND 1’, representing the particle caged in the potential. Here, ‘tau IND 1’ is a characteristic time that limit the confinement period. And the third regime, ‘tau’ > ‘tau IND 1’, is when the particles are in the superdiffusive behavior. This is where most of the experiments are performed, under 20 frames per second (FPS), thus there is no experimental evidence that support the first regime. We are currently performing experiments with high frequency, up to 100 FPS, attempting to visualize this diffusive behavior. Beside the first regime, our simple model can reproduce MSD curves similar to what has been found experimentally, which can be helpful to understanding CSK structure and properties.

Rotational diffusion membrane and fluorescence anisotropy.

Structural properties of model membranes, such as lipid vesicles, may be investigated through the addition of fluorescent probes. After incorporation, the fluorescent molecules are excited with linearly polarized light and the fluorescence emission is depolarized due to translational as well as rotational diffusion during the lifetime of the excited state. The monitoring of emitted light is undertaken through the technique of time-resolved fluorescence: the intensity of the emitted light informs on fluorescence decay times, and the decay of the components of the emitted light yield rotational correlation times which inform on the fluidity of the medium. The fluorescent molecule DPH, of uniaxial symmetry, is rather hydrophobic and has collinear transition and emission moments. It has been used frequently as a probe for the monitoring of the fluidity of the lipid bilayer along the phase transition of the chains. The interpretation of experimental data requires models for localization of fluorescent molecules as well as for possible restrictions on their movement. In this study, we develop calculations for two models for uniaxial diffusion of fluorescent molecules, such as DPH, suggested in several articles in the literature. A zeroth order test model consists of a free randomly rotating dipole in a homogeneous solution, and serves as the basis for the study of the diffusion of models in anisotropic media. In the second model, we consider random rotations of emitting dipoles distributed within cones with their axes perpendicular to the vesicle spherical geometry. In the third model, the dipole rotates in the plane of the of bilayer spherical geometry, within a movement that might occur between the monolayers forming the bilayer. For each of the models analysed, two methods are used by us in order to analyse the rotational diffusion: (I) solution of the corresponding rotational diffusion equation for a single molecule, taking into account the boundary conditions imposed by the models, for the probability of the fluorescent molecule to be found with a given configuration at time t. Considering the distribution of molecules in the geometry proposed, we obtain the analytical expression for the fluorescence anisotropy, except for the cone geometry, for which the solution is obtained numerically; (II) numerical simulations of a restricted rotational random walk in the two geometries corresponding to the two models. The latter method may be very useful in the cases of low-symmetry geometries or of composed geometries.

Theoretical studies of microfluidics: "walking" drops and "melting" snowflakes.

The present PhD thesis summarizes two examples of research in microfluidics. Both times water was the subject of interest, once in the liquid state (droplets adsorbed on chemically functionalized surfaces), the other time in the solid state (ice snowflakes and their fractal behaviour). The first problem deals with a slipping nano-droplet of water adsorbed on a surface with photo-switchable wettability characteristics. Main focus was on identifying the underlying driving forces and mechanical principles at the molecular level of detail. Molecular Dynamics simulation was employed as investigative tool owing to its record of successfully describing the microscopic behaviour of liquids at interfaces. To reproduce the specialized surface on which a water droplet can effectively “walk”, a new implicit surface potential was developed. Applying this new method the experimentally observed droplet slippage could be reproduced successfully. Next the movement of the droplet was analyzed at various conditions emphasizing on the behaviour of the water molecules in contact with the surface. The main objective was to identify driving forces and molecular mechanisms underlying the slippage process. The second part of this thesis is concerned with theoretical studies of snowflake melting. In the present work snowflakes are represented by filled von Koch-like fractals of mesoscopic beads. A new algorithm has been developed from scratch to simulate the thermal collapse of fractal structures based on Monte Carlo and Random Walk Simulations (MCRWS). The developed method was applied and compared to Molecular Dynamics simulations regarding the melting of ice snowflake crystals and new parameters were derived from this comparison. Bigger snow-fractals were then studied looking at the time evolution at different temperatures again making use of the developed MCRWS method. This was accompanied by an in-depth analysis of fractal properties (border length and gyration radius) in order to shed light on the dynamics of the melting process.

Mutually catalytic branching at infinite rate

The purpose of this doctoral thesis is to prove existence for a mutually catalytic random walk with infinite branching rate on countably many sites. The process is defined as a weak limit of an approximating family of processes. An approximating process is constructed by adding jumps to a deterministic migration on an equidistant time grid. As law of jumps we need to choose the invariant probability measure of the mutually catalytic random walk with a finite branching rate in the recurrent regime. This model was introduced by Dawson and Perkins (1998) and this thesis relies heavily on their work. Due to the properties of this invariant distribution, which is in fact the exit distribution of planar Brownian motion from the first quadrant, it is possible to establish a martingale problem for the weak limit of any convergent sequence of approximating processes. We can prove a duality relation for the solution to the mentioned martingale problem, which goes back to Mytnik (1996) in the case of finite rate branching, and this duality gives rise to weak uniqueness for the solution to the martingale problem. Using standard arguments we can show that this solution is in fact a Feller process and it has the strong Markov property. For the case of only one site we prove that the model we have constructed is the limit of finite rate mutually catalytic branching processes as the branching rate approaches infinity. Therefore, it seems naturalto refer to the above model as an infinite rate branching process. However, a result for convergence on infinitely many sites remains open.

Statistical arbitrage on commodities

Questa tesi è incentrata sull'analisi dell'arbitraggio statistico, strategia di trading che cerca di trarre profitto dalle fluttuazioni statistiche di prezzo di uno o più asset sulla base del loro valore atteso. In generale, si creano opportunità di arbitraggio statistico quando si riescono ad individuare delle componenti sistematiche nelle dinamiche dei prezzi di alcuni asset che si muovono con regolarità persistenti e prevalenti. Perturbazioni casuali della domanda e dell’offerta nei mercati possono causare divergenze nei prezzi, dando luogo a opportunità di intermarket spread, ossia simultanei acquisto e vendita di commodities correlate tra loro. Vengono approfonditi vari test econometrici, i test unit root utilizzati per verificare se una serie storica possa essere modellizzata con un processo random walk. Infine viene costruita una strategia di trading basata sull'arbitraggio statistico e applicata numericamente alle serie storiche dal 2010 al 2014 di due titoli azionari sul petrolio: Brent e WTI.

Statistical methods for the analysis of DNA sequences: application to dinucleotide distribution in the human genome

Questa tesi si inserisce nell'ambito delle analisi statistiche e dei metodi stocastici applicati all'analisi delle sequenze di DNA. Nello specifico il nostro lavoro è incentrato sullo studio del dinucleotide CG (CpG) all'interno del genoma umano, che si trova raggruppato in zone specifiche denominate CpG islands. Queste sono legate alla metilazione del DNA, un processo che riveste un ruolo fondamentale nella regolazione genica. La prima parte dello studio è dedicata a una caratterizzazione globale del contenuto e della distribuzione dei 16 diversi dinucleotidi all'interno del genoma umano: in particolare viene studiata la distribuzione delle distanze tra occorrenze successive dello stesso dinucleotide lungo la sequenza. I risultati vengono confrontati con diversi modelli nulli: sequenze random generate con catene di Markov di ordine zero (basate sulle frequenze relative dei nucleotidi) e uno (basate sulle probabilità di transizione tra diversi nucleotidi) e la distribuzione geometrica per le distanze. Da questa analisi le proprietà caratteristiche del dinucleotide CpG emergono chiaramente, sia dal confronto con gli altri dinucleotidi che con i modelli random. A seguito di questa prima parte abbiamo scelto di concentrare le successive analisi in zone di interesse biologico, studiando l’abbondanza e la distribuzione di CpG al loro interno (CpG islands, promotori e Lamina Associated Domains). Nei primi due casi si osserva un forte arricchimento nel contenuto di CpG, e la distribuzione delle distanze è spostata verso valori inferiori, indicando che questo dinucleotide è clusterizzato. All’interno delle LADs si trovano mediamente meno CpG e questi presentano distanze maggiori. Infine abbiamo adottato una rappresentazione a random walk del DNA, costruita in base al posizionamento dei dinucleotidi: il walk ottenuto presenta caratteristiche drasticamente diverse all’interno e all’esterno di zone annotate come CpG island. Riteniamo pertanto che metodi basati su questo approccio potrebbero essere sfruttati per migliorare l’individuazione di queste aree di interesse nel genoma umano e di altri organismi.

Sistemi dinamici stocastici su network

L'obiettivo della tesi è studiare la dinamica di un random walk su network. Essa è inoltre suddivisa in due parti: la prima è prettamente teorica, mentre la seconda analizza i risultati ottenuti mediante simulazioni. La parte teorica è caratterizzata dall'introduzione di concetti chiave per comprendere i random walk, come i processi di Markov e la Master Equation. Dopo aver fornito un esempio intuitivo di random walk nel caso unidimensionale, tale concetto viene generalizzato. Così può essere introdotta la Master Equation che determina l'evoluzione del sistema. Successivamente si illustrano i concetti di linearità e non linearità, fondamentali per la parte di simulazione. Nella seconda parte si studia il comportamento di un random walk su network nel caso lineare e non lineare, studiando le caratteristiche della soluzione stazionaria. La non linearità introdotta simula un comportamento egoista da parte di popolazioni in interazioni. In particolare si dimostra l'esistenza di una Biforcazione di Hopf.

Proprietà statistiche di network dinamici

L'obbiettivo di questa tesi è quello di studiare alcune proprietà statistiche di un random walk su network. Dopo aver definito il concetto di network e di random walk su network, sono state studiate le caratteristiche dello stato stazionario di questo sistema, la loro dipendenza dalla topologia della rete e l'andamento del sistema verso l'equilibrio, con particolare interesse per la distribuzione delle fluttuazioni delle popolazioni sui differenti nodi, una volta raggiunto lo stato stazionario. In seguito, si è voluto osservare il comportamento del network sottoposto ad una forzatura costante, rappresentata da sorgenti e pozzi applicati in diversi nodi, e quindi la sua suscettività a perturbazioni esterne. Tramite alcune simulazioni al computer, viene provato che una forzatura esterna modifica in modo diverso lo stato del network in base alla topologia di quest'ultimo. Dai risultati si è trovato quali sono i nodi che, una volta perturbati, sono in grado di cambiare ampiamente lo stato generale del sistema e quali lo influenzano in minima parte.

Caratterizzazione di sequenze di DNA mediante catene di Markov

Questa tesi si inserisce nell’ambito di studio dei modelli stocastici applicati alle sequenze di DNA. I random walk e le catene di Markov sono tra i processi aleatori che hanno trovato maggiore diffusione in ambito applicativo grazie alla loro capacità di cogliere le caratteristiche salienti di molti sistemi complessi, pur mantenendo semplice la descrizione di questi. Nello specifico, la trattazione si concentra sull’applicazione di questi nel contesto dell’analisi statistica delle sequenze genomiche. Il DNA può essere rappresentato in prima approssimazione da una sequenza di nucleotidi che risulta ben riprodotta dal modello a catena di Markov; ciò rappresenta il punto di partenza per andare a studiare le proprietà statistiche delle catene di DNA. Si approfondisce questo discorso andando ad analizzare uno studio che si ripropone di caratterizzare le sequenze di DNA tramite le distribuzioni delle distanze inter-dinucleotidiche. Se ne commentano i risultati, al fine di mostrare le potenzialità di questi modelli nel fare emergere caratteristiche rilevanti in altri ambiti, in questo caso quello biologico.

Early bursts of body size and shape evolution are rare in comparative data

George Gaylord Simpson famously postulated that much of life's diversity originated as adaptive radiations-more or less simultaneous divergences of numerous lines from a single ancestral adaptive type. However, identifying adaptive radiations has proven difficult due to a lack of broad-scale comparative datasets. Here, we use phylogenetic comparative data on body size and shape in a diversity of animal clades to test a key model of adaptive radiation, in which initially rapid morphological evolution is followed by relative stasis. We compared the fit of this model to both single selective peak and random walk models. We found little support for the early-burst model of adaptive radiation, whereas both other models, particularly that of selective peaks, were commonly supported. In addition, we found that the net rate of morphological evolution varied inversely with clade age. The youngest clades appear to evolve most rapidly because long-term change typically does not attain the amount of divergence predicted from rates measured over short time scales. Across our entire analysis, the dominant pattern was one of constraints shaping evolution continually through time rather than rapid evolution followed by stasis. We suggest that the classical model of adaptive radiation, where morphological evolution is initially rapid and slows through time, may be rare in comparative data.

How do indirect measures of evaluation work? Evaluating the inference of prejudice in the Implicit Association Test

There has been significant interest in indirect measures of attitudes like the Implicit Association Test (IAT), presumably because of the possibility of uncovering implicit prejudices. The authors derived a set of qualitative predictions for people's performance in the IAT on the basis of random walk models. These were supported in 3 experiments comparing clearly positive or negative categories to nonwords. They also provided evidence that participants shift their response criterion when doing the IAT. Because of these criterion shifts, a response pattern in the IAT can have multiple causes. Thus, it is not possible to infer a single cause (such as prejudice) from IAT results. A surprising additional result was that nonwords were treated as though they were evaluated more negatively than obviously negative items like insects, suggesting that low familiarity items may generate the pattern of data previously interpreted as evidence for implicit prejudice.