On the proper reconstruction of complex dynamical systems spoilt by strong measurement noise

This article reports on a new approach to properly analyze time series of dynamical systems which are spoilt by the simultaneous presence of dynamical noise and measurement noise. It is shown that even strong external measurement noise as well as dynamical noise which is an intrinsic part of the dynamical process can be quantified correctly, solely on the basis of measured times series and proper data analysis. Finally real world data sets are presented pointing out the relevance of the new approach

Finite size fluctuations and stochastic resonance in globally coupled bistable systems

The dynamics of a system formed by a finite number $N$ of globally coupled bistable oscillators and driven by external forces is studied focusing on a global variable defined as the arithmetic mean of each oscillator variable. Several models based on truncation schemes of a hierarchy of stochastic equations for a set of fluctuating cumulant variables are presented. This hierarchy is derived using It\^o stochastic calculus, and the noise terms in it are treated using an asymptotic approximation valid for large $N$. In addition, a simplified one-variable model based on an effective potential is also considered. These models are tested in the framework of the phenomenon of stochastic resonance. In turn, they are used to explain in simple terms the very large gains recently observed in these finite systems

The complex chemical Langevin equation

The chemical Langevin equation (CLE) is a popular simulation method to probe the stochastic dynamics of chemical systems. The CLE's main disadvantage is its break down in finite time due to the problem of evaluating square roots of negative quantities whenever the molecule numbers become sufficiently small. We show that this issue is not a numerical integration problem, rather in many systems it is intrinsic to all representations of the CLE. Various methods of correcting the CLE have been proposed which avoid its break down. We show that these methods introduce undesirable artefacts in the CLE's predictions. In particular, for unimolecular systems, these correction methods lead to CLE predictions for the mean concentrations and variance of fluctuations which disagree with those of the chemical master equation. We show that, by extending the domain of the CLE to complex space, break down is eliminated, and the CLE's accuracy for unimolecular systems is restored. Although the molecule numbers are generally complex, we show that the "complex CLE" predicts real-valued quantities for the mean concentrations, the moments of intrinsic noise, power spectra and first passage times, hence admitting a physical interpretation. It is also shown to provide a more accurate approximation of the chemical master equation of simple biochemical circuits involving bimolecular reactions than the various corrected forms of the real-valued CLE, the linear-noise approximation and a commonly used two moment-closure approximation.Comment: 47 pages, 8 figure

Approximation and inference methods for stochastic biochemical kinetics - a tutorial review

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the Chemical Master Equation. Despite its simple structure, no analytic solutions to the Chemical Master Equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.Comment: 73 pages, 12 figures in J. Phys. A: Math. Theor. (2016

A neuroanatomically grounded Hebbian-learning model of attention–language interactions in the human brain

Meaningful familiar stimuli and senseless unknown materials lead to different patterns of brain activation. A late major neurophysiological response indexing ‘sense’ is the negative component of event-related potential peaking at around 400 ms (N400), an event-related potential that emerges in attention-demanding tasks and is larger for senseless materials (e.g. meaningless pseudowords) than for matched meaningful stimuli (words). However, the mismatch negativity (latency 100–250 ms), an early automatic brain response elicited under distraction, is larger to words than to pseudowords, thus exhibiting the opposite pattern to that seen for the N400. So far, no theoretical account has been able to reconcile and explain these findings by means of a single, mechanistic neural model. We implemented a neuroanatomically grounded neural network model of the left perisylvian language cortex and simulated: (i) brain processes of early language acquisition and (ii) cortical responses to familiar word and senseless pseudoword stimuli. We found that variation of the area-specific inhibition (the model correlate of attention) modulated the simulated brain response to words and pseudowords, producing either an N400- or a mismatch negativity-like response depending on the amount of inhibition (i.e. available attentional resources). Our model: (i) provides a unifying explanatory account, at cortical level, of experimental observations that, so far, had not been given a coherent interpretation within a single framework; (ii) demonstrates the viability of purely Hebbian, associative learning in a multilayered neural network architecture; and (iii) makes clear predictions on the effects of attention on latency and magnitude of event-related potentials to lexical items. Such predictions have been confirmed by recent experimental evidence

Revenue Administration Reforms in anglophone Africa Since the Early 1990's

Despite positive but mixed progress over two decades, most lower income African countries need to enhance their low tax-to-GDP ratios by mobilizing domestic resources to complement debt relief, donor aid and to achieve the MDG and poverty reduction objectives. With these goals in mind, most African countries have undertaken revenue administration reforms and from the early 1990s, 16 of 19 Anglophone Africa countries established some form of revenue authority (RA) for greater governance, financing, and workforce autonomy. Changes in governance and HR practices are evident, but has revenue administration improved overall? Capacity limitations and integrity issues persist. The introduction of VAT heralded self-assessment, but in most instances without being integrated with income tax administration. Rather, VAT administration was assigned to a separate department. Special units for large taxpayers are now common following initial challenges, but programs for other taxpayer segments are still emerging.Tax administration;Customs administration;Revenue mobilization;Fiscal reforms;Natural resources;Resource mobilization;Revenue measures;Tax reforms;Value added tax;vat, large taxpayers, taxpayer services, tax administrations, domestic tax, tax type, domestic taxes, tax collections, tax departments, wave, indirect tax, vat rate, internal revenue, tax reform, indirect taxes, tariff reform, tax obligations, tax revenues, tax system, direct tax, trade taxes, direct taxes, tax department, tax audit, taxpayer compliance, taxpayer identification, tax purposes, revenue collection, tax return, tax officials, income taxpayers, press, large businesses, taxpayer education, tax administration strategies, government tax revenue, tax collection, corporate income tax, central government tax, spectrum, excise taxes, tax authorities, corporate income taxes, international trade taxes, tax liability, tax offices, taxpayer groups, income taxes, tax instruments, tax accounting, tax exempt organizations, tax assessment, telecommunications, tax rulings, state income tax, electronic media, sales tax, vat revenue, import taxes, tax administration reform, strategic planning, television, tax payments, tax assessments, income tax rates, tax administration reforms, packages, tax payment