A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

Processus de coalescence dans une population subdivisée avec possibilité de coalescences multiples

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

A finite-rate-of-innovation signal sampling perspective of the source-filter model of speech production

We consider the speech production mechanism and the asso- ciated linear source-filter model. For voiced speech sounds in particular, the source/glottal excitation is modeled as a stream of impulses and the filter as a cascade of second-order resonators. We show that the process of sampling speech signals can be modeled as filtering a stream of Dirac impulses (a model for the excitation) with a kernel function (the vocal tract response),and then sampling uniformly. We show that the problem of esti- mating the excitation is equivalent to the problem of recovering a stream of Dirac impulses from samples of a filtered version. We present associated algorithms based on the annihilating filter and also make a comparison with the classical linear prediction technique, which is well known in speech analysis. Results on synthesized as well as natural speech data are presented.

Sediment and organic matter properties, and molecular formula from sampling locations in the Northern Black Sea

Remineralization of organic matter in reactive marine sediments releases nutrients and dissolved organic matter (DOM) into the ocean. Here we focused on the molecular-level characterization of DOM by high-resolution Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS) in sediment pore waters and bottom waters from contrasting redox regimes in the northern Black Sea with particular emphasis on nitrogen-bearing compounds to derive an improved understanding of the molecular transformations involved in nitrogen release. The number of nitrogen-bearing molecules is generally higher in pore waters than in bottom waters. This suggests intensified degradation of nitrogen-bearing precursor molecules such as proteins in anoxic sediments: No significant difference was observed between sediments deposited under oxic vs anoxic conditions (average O/C ratios of 0.55) suggesting that the different organic matter quality induced by contrasting redox conditions does not impact protein diagenesis in the subseafloor. Compounds in the pore waters were on average larger, less oxygenated, and had a higher number of unsaturations. Applying a mathematical model, we could show that the assemblages of nitrogen-bearing molecular formulas are potential products of proteinaceous material that was transformed by the following reactions: (a) hydrolysis and deamination, both reducing the molecular size and nitrogen content of the products and intermediates; (b) oxidation and hydration of the intermediates; and (c) methylation and dehydration.

The credit risk(+) model with general sector correlations

We consider an enhancement of the credit risk+ model to incorporate correlations between sectors. We model the sector default rates as linear combinations of a common set of independent variables that represent macro-economic variables or risk factors. We also derive the formula for exact VaR contributions at the obligor level.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Sampling and learning the Mallows model under the Ulam distance

[EN]In this paper we deal with probability distributions over permutation spaces. The Probability model in use is the Mallows model. The distance for permutations that the model uses in the Ulam distance.

Exact solution of the XXZ Gaudin model with generic open boundaries

The XXZ Gaudin model with generic integrable boundaries specified by generic non-diagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained. (C) 2004 Elsevier B.V. All rights reserved.

Asymptotically exact probability distribution for the Sinai model with finite drift

We obtain the exact asymptotic result for the disorder-averaged probability distribution function for a random walk in a biased Sinai model and show that it is characterized by a creeping behavior of the displacement moments with time, similar to v(mu n), where mu <1 is dimensionless mean drift. We employ a method originated in quantum diffusion which is based on the exact mapping of the problem to an imaginary-time Schrodinger equation. For nonzero drift such an equation has an isolated lowest eigenvalue separated by a gap from quasicontinuous excited states, and the eigenstate corresponding to the former governs the long-time asymptotic behavior.

Unpacking Japan's 21st century "National Conversation" : images of the future beyond the iron cage of the "Catch Up" model

How does the image of the future operate upon history, and upon national and individual identities? To what extent are possible futures colonized by the image? What are the un-said futurecratic discourses that underlie the image of the future? Such questions inspired the examination of Japan’s futures images in this thesis. The theoretical point of departure for this examination is Polak’s (1973) seminal research into the theory of the ‘image of the future’ and seven contemporary Japanese texts which offer various alternative images for Japan’s futures, selected as representative of a ‘national conversation’ about the futures of that nation. These seven images of the future are: 1. Report of the Prime Minister’s Commission on Japan’s Goals in the 21st Century—The Frontier Within: Individual Empowerment and Better Governance in the New Millennium, compiled by a committee headed by Japan’s preeminent Jungian psychologist Kawai Hayao (1928-2007); 2. Slow Is Beautiful—a publication by Tsuji Shinichi, in which he re-images Japan as a culture represented by the metaphor of the sloth, concerned with slow and quality-oriented livingry as a preferred image of the future to Japan’s current post-bubble cult of speed and economic efficiency; 3. MuRatopia is an image of the future in the form of a microcosmic prototype community and on-going project based on the historically significant island of Awaji, and established by Japanese economist and futures thinker Yamaguchi Kaoru; 4. F.U.C.K, I Love Japan, by author Tanja Yujiro provides this seven text image of the future line-up with a youth oriented sub-culture perspective on that nation’s futures; 5. IMAGINATION / CREATION—a compilation of round table discussions about Japan’s futures seen from the point of view of Japan’s creative vanguard; 6. Visionary People in a Visionless Country: 21 Earth Connecting Human Stories is a collection of twenty one essays compiled by Denmark born Tokyo resident Peter David Pedersen; and, 7. EXODUS to the Land of Hope, authored by Murakami Ryu, one of Japan’s most prolific and influential writers, this novel suggests a future scenario portraying a massive exodus of Japan’s youth, who, literate with state-of-the-art information and communication technologies (ICTs) move en masse to Japan’s northern island of Hokkaido to launch a cyber-revolution from the peripheries. The thesis employs a Futures Triangle Analysis (FTA) as the macro organizing framework and as such examines both pushes of the present and weights from the past before moving to focus on the pulls to the future represented by the seven texts mentioned above. Inayatullah’s (1999) Causal Layered Analysis (CLA) is the analytical framework used in examining the texts. Poststructuralist concepts derived primarily from the work of Michel Foucault are a particular (but not exclusive) reference point for the analytical approach it encompasses. The research questions which reflect the triangulated analytic matrix are: 1. What are the pushes—in terms of current trends—that are affecting Japan’s futures? 2. What are the historical and cultural weights that influence Japan’s futures? 3. What are the emerging transformative Japanese images of the future discourses, as embodied in actual texts, and what potential do they offer for transformative change in Japan? Research questions one and two are discussed in Chapter five and research question three is discussed in Chapter six. The first two research questions should be considered preliminary. The weights outlined in Chapter five indicate that the forces working against change in Japan are formidable, structurally deep-rooted, wide-spread, and under-recognized as change-adverse. Findings and analyses of the push dimension reveal strong forces towards a potentially very different type of Japan. However it is the seven contemporary Japanese images of the future, from which there is hope for transformative potential, which form the analytical heart of the thesis. In analyzing these texts the thesis establishes the richness of Japan’s images of the future and, as such, demonstrates the robustness of Japan’s stance vis-à-vis the problem of a perceived map-less and model-less future for Japan. Frontier is a useful image of the future, whose hybrid textuality, consisting of government, business, academia, and creative minority perspectives, demonstrates the earnestness of Japan’s leaders in favour of the creation of innovative futures for that nation. Slow is powerful in its aim to reconceptualize Japan’s philosophies of temporality, and build a new kind of nation founded on the principles of a human-oriented and expanded vision of economy based around the core metaphor of slowness culture. However its viability in Japan, with its post-Meiji historical pushes to an increasingly speed-obsessed social construction of reality, could render it impotent. MuRatopia is compelling in its creative hybridity indicative of an advanced IT society, set in a modern day utopian space based upon principles of a high communicative social paradigm, and sustainability. IMAGINATION / CREATION is less the plan than the platform for a new discussion on Japan’s transformation from an econo-centric social framework to a new Creative Age. It accords with emerging discourses from the Creative Industries, which would re-conceive of Japan as a leading maker of meaning, rather than as the so-called guzu, a term referred to in the book meaning ‘laggard’. In total, Love Japan is still the most idiosyncratic of all the images of the future discussed. Its communication style, which appeals to Japan’s youth cohort, establishes it as a potentially formidable change agent in a competitive market of futures images. Visionary People is a compelling image for its revolutionary and subversive stance against Japan’s vision-less political leadership, showing that it is the people, not the futures-making elite or aristocracy who must take the lead and create a new vanguard for the nation. Finally, Murakami’s Exodus cannot be ruled out as a compelling image of the future. Sharing the appeal of Tanja’s Love Japan to an increasingly disenfranchised youth, Exodus portrays a near-term future that is achievable in the here and now, by Japan’s teenagers, using information and communications technologies (ICTs) to subvert leadership, and create utopianist communities based on alternative social principles. The principal contribution from this investigation in terms of theory belongs to that of developing the Japanese image of the future. In this respect, the literature reviews represent a significant compilation, specifically about Japanese futures thinking, the Japanese image of the future, and the Japanese utopia. Though not exhaustive, this compilation will hopefully serve as a useful starting point for future research, not only for the Japanese image of the future, but also for all image of the future research. Many of the sources are in Japanese and their English summations are an added reason to respect this achievement. Secondly, the seven images of the future analysed in Chapter six represent the first time that Japanese image of the future texts have been systematically organized and analysed. Their translation from Japanese to English can be claimed as a significant secondary contribution. What is more, they have been analysed according to current futures methodologies that reveal a layeredness, depth, and overall richness existing in Japanese futures images. Revealing this image-richness has been one of the most significant findings of this investigation, suggesting that there is fertile research to be found from this still under-explored field, whose implications go beyond domestic Japanese concerns, and may offer fertile material for futures thinkers and researchers, Japanologists, social planners, and policy makers.

Stochastic models and simulation of ion channel dynamics

The behaviour of ion channels within cardiac and neuronal cells is intrinsically stochastic in nature. When the number of channels is small this stochastic noise is large and can have an impact on the dynamics of the system which is potentially an issue when modelling small neurons and drug block in cardiac cells. While exact methods correctly capture the stochastic dynamics of a system they are computationally expensive, restricting their inclusion into tissue level models and so approximations to exact methods are often used instead. The other issue in modelling ion channel dynamics is that the transition rates are voltage dependent, adding a level of complexity as the channel dynamics are coupled to the membrane potential. By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. While such a model is more computationally efficient than exact methods we show that there are analytical problems with the resulting SDE as well as issues in using current numerical schemes to solve such an equation. We therefore make two contributions: develop a different model to describe the stochastic ion channel dynamics that analytically behaves in the correct manner and also discuss numerical methods that preserve the analytical properties of the model.

The hard-particle model for a dense granular flow down an inclined plane

Perfectly hard particles are those which experience an infinite repulsive force when they overlap, and no force when they do not overlap. In the hard-particle model, the only static state is the isostatic state where the forces between particles are statically determinate. In the flowing state, the interactions between particles are instantaneous because the time of contact approaches zero in the limit of infinite particle stiffness. Here, we discuss the development of a hard particle model for a realistic granular flow down an inclined plane, and examine its utility for predicting the salient features both qualitatively and quantitatively. We first discuss Discrete Element simulations, that even very dense flows of sand or glass beads with volume fraction between 0.5 and 0.58 are in the rapid flow regime, due to the very high particle stiffness. An important length scale in the shear flow of inelastic particles is the `conduction length' delta = (d/(1 - e(2))(1/2)), where d is the particle diameter and e is the coefficient of restitution. When the macroscopic scale h (height of the flowing layer) is larger than the conduction length, the rates of shear production and inelastic dissipation are nearly equal in the bulk of the flow, while the rate of conduction of energy is O((delta/h)(2)) smaller than the rate of dissipation of energy. Energy conduction is important in boundary layers of thickness delta at the top and bottom. The flow in the boundary layer at the top and bottom is examined using asymptotic analysis. We derive an exact relationship showing that the a boundary layer solution exists only if the volume fraction in the bulk decreases as the angle of inclination is increased. In the opposite case, where the volume fraction increases as the angle of inclination is increased, there is no boundary layer solution. The boundary layer theory also provides us with a way of understanding the cessation of flow when at a given angle of inclination when the height of the layer is decreased below a value h(stop), which is a function of the angle of inclination. There is dissipation of energy due to particle collisions in the flow as well as due to particle collisions with the base, and the fraction of energy dissipation in the base increases as the thickness decreases. When the shear production in the flow cannot compensate for the additional energy drawn out of the flow due to the wall collisions, the temperature decreases to zero and the flow stops. Scaling relations can be derived for h(stop) as a function of angle of inclination.

The advection-condensation model and water-vapour probability density functions

The statistically steady humidity distribution resulting from an interaction of advection, modelled as an uncorrelated random walk of moist parcels on an isentropic surface, and a vapour sink, modelled as immediate condensation whenever the specific humidity exceeds a specified saturation humidity, is explored with theory and simulation. A source supplies moisture at the deep-tropical southern boundary of the domain and the saturation humidity is specified as a monotonically decreasing function of distance from the boundary. The boundary source balances the interior condensation sink, so that a stationary spatially inhomogeneous humidity distribution emerges. An exact solution of the Fokker-Planck equation delivers a simple expression for the resulting probability density function (PDF) of the wate-rvapour field and also the relative humidity. This solution agrees completely with a numerical simulation of the process, and the humidity PDF exhibits several features of interest, such as bimodality close to the source and unimodality further from the source. The PDFs of specific and relative humidity are broad and non-Gaussian. The domain-averaged relative humidity PDF is bimodal with distinct moist and dry peaks, a feature which we show agrees with middleworld isentropic PDFs derived from the ERA interim dataset. Copyright (C) 2011 Royal Meteorological Society