Tractable Level Research Articles

Asymptotic theory for damped dynamics of gas-filled bubbles

The small-amplitude damped oscillations of a gas-filled spherical bubble surrounded by a viscous liquid is studied analytically using a symbolically computable version of the two-time scale expansion (“two-timing”) technique. The developed uniformly valid asymptotic expansions have closed analytical forms under arbitrary specifications for the ideal gas polytropic exponent and the damping coefficient. Heretofore, a comparable level of analytical tractability has been afforded only by a linearized mass-spring-damper model; the corresponding regular perturbation expansion is, however, nonuniform for weak damping. Predictions from the two-timing and the mass-spring-damper models are compared with the full-scale numerical solution of the Rayleigh-Plesset equation. The two-scale analysis resolves several characteristics of the numerical data, such as the disparately large/small acceleration of the bubble wall near the most compressed/expanded states of the bubble, which the linearized model does not. The predictions of the two-scale model are shown to perform favorably against experimental data from the literature. New asymptotic predictions, which are very accurate for overdamped settings, are also developed by extending the mass-spring-damper model.

High-resolution analysis of individual Drosophila melanogaster larvae uncovers individual variability in locomotion and its neurogenetic modulation.

Neuronally orchestrated muscular movement and locomotion are defining faculties of multicellular animals. Due to its simple brain and genetic accessibility, the larva of the fruit fly Drosophila melanogaster allows one to study these processes at tractable levels of complexity. However, although the faculty of locomotion clearly pertains to the individual, most studies of locomotion in larvae use measurements aggregated across animals, or animals tested one by one, an extravagance for larger-scale analyses. This prevents grasping the inter- and intra-individual variability in locomotion and its neurogenetic determinants. Here, we present the IMBA (individual maggot behaviour analyser) for analysing the behaviour of individual larvae within groups, reliably resolving individual identity across collisions. We use the IMBA to systematically describe the inter- and intra-individual variability in locomotion of wild-type animals, and how the variability is reduced by associative learning. We then report a novel locomotion phenotype of an adhesion GPCR mutant. We further investigated the modulation of locomotion across repeated activations of dopamine neurons in individual animals, and the transient backward locomotion induced by brief optogenetic activation of the brain-descending 'mooncrawler' neurons. In summary, the IMBA is an easy-to-use toolbox allowing an unprecedentedly rich view of the behaviour and its variability of individual larvae, with utility in multiple biomedical research contexts.

Outage in Motorway Multi-Lane VANETs With Hardcore Headway Distance Using Synthetic Traces

In this paper we analyze synthetic mobility traces generated for three-lane unidirectional motorway traffic to find that the locations of vehicles along a lane are better modeled by a hardcore point process instead of the widely-accepted Poisson point process (PPP). In order to capture the repulsion between successive vehicles while maintaining a level of analytical tractability, we make a simple extension to PPP: We model the inter-vehicle distance along a lane equal to the sum of a constant hardcore distance and an exponentially distributed random variable. We calculate the J-function and the Ripley's K-function for this hardcore point process. We fit its parameters to the available traces, and we illustrate that the higher the average speed along a lane, the more prominent the hardcore component becomes. In addition, we consider a transmitter-receiver link on the same lane, and we generate simple formulae for the moments of interference under reduced Palm measure for that lane, and without conditioning for other lanes. We illustrate that under Rayleigh fading a shifted-gamma approximation for the distribution of interference per lane provides a very good fit to the simulated outage probability using the synthetic traces, while the fit using the PPP is poor.

Multiplicative background risk models: Setting a course for the idiosyncratic risk factors distributed phase-type

Multiplicative background risk models in which the idiosyncratic risk factors are assumed to be distributed exponentially, and the systemic risk factor has an arbitrary distribution on the non-negative half of the real line have seen a great variety of applications in actuarial science. Admittedly, these structures, which are well-known to mathematical statisticians under the name of exponential mixtures, enjoy remarkable level of technical tractability and so are a convenient tool for modelling risk components in a portfolio of an insurer. That said, the assumption of exponentiality is merely a mathematical nicety and does not have to reflect reality, yet the works that loosen this assumption are rare. The goals of this paper are two-fold. Firstly, we pursue a holistic approach and discuss in detail the multiplicative background risk models with arbitrarily distributed idiosyncratic and systemic risk factors. In this respect, we systematize the existing results and report some new ones. Secondly, and more importantly, we focus on the special case when the distribution of the idiosyncratic risk factors is phase-type. The novel theory, which allows to introduce significant heterogeneity in the idiosyncratic risk factors, is illustrated by numerous numerical examples borrowed from the context of the determination and allocation of economic capital. The examples suggest that a little departure from exponentiality can have substantial impact on the outcome of risk analysis.

Development of a Mesoscale Inversion System for Estimating Continental‐Scale CO2 Fluxes

AbstractComputational requirements often impose limitations on the spatial and temporal resolutions of atmospheric CO2 inversions, increasing aggregation and representation errors. This study enables higher spatial and temporal resolution inversions with spatial and temporal error structures similar to those used in other published inversions by representing the prior flux error covariances as a Kronecker product of spatial and temporal covariances and by using spectral methods for the spatial correlations. Compared to existing inversion systems that are forced to degrade the resolution of the problem in order to bring the dimensionality down to computationally tractable levels, this inversion framework is able to take advantage of mesoscale transport simulations and more of the complexity of spatial and temporal covariances in the surface CO2 fluxes. This approach was successfully implemented over one month with an identical‐twin observing system simulation experiment (OSSE) using a set of assumptions about the prior flux uncertainties compatible both with continental‐scale uncertainty estimates and with comparisons of vegetation models to flux towers. The demonstration illustrates the potential of the newly developed inversion system to use high‐temporal‐resolution information from the North American tower network, to extract high‐resolution information about CO2 fluxes that is inaccessible to coarser resolution inversion systems, and to simultaneously optimize an ensemble of prior estimates. This demonstration sets the stage for regional flux inversions that can take full advantage of the high‐resolution data available in tower CO2 records and mesoscale atmospheric transport reanalyses, include more realistic prior error structures, and explore specifying prior fluxes with ensembles.

Relativistic formalism of nonadiabatic electron-nucleus-radiation dynamics in molecules: Path-integral approach

Many-electron relativistic quantum theories of stationary molecular electronic states have been developed in so-called quantum chemistry, in which nuclear configuration is frozen in space-time under the Born-Oppenheimer approximation. These time-independent methods are concerned with energetics, which are supposed to determine molecular structures and dominate low-energy chemical reactions. Yet, rapid progress in laser technology demands that theoretical chemistry should get prepared for relativistic electron-nucleus coupled dynamics driven by unconventional ultrastrong laser pulses. We therefore generalize our previously developed path-integral formalism of nonadiabatic electron dynamics [Hanasaki and Takatsuka, Phys. Rev. A 81, 052514 (2010)] to cover the relativistic regime in radiation fields. Starting from a formal relativistic path-integral formulation of electron-nucleus coupled systems interacting with quantum radiation fields, we reduce it to a tractable level of approximations to set a theoretical foundation for future applications.

Neuroimaging endophenotypes of type 2 diabetes mellitus: a discordant sibling pair study.

Type 2 diabetes mellitus (T2DM) is characterized by notable familial aggregation involving common variants of many genes, and its heritability leads to a high prevalence in the siblings of affected individuals compared with the general population. Endophenotypes are objective, heritable, quantitative traits that appear to reflect the genetic risk for polygenic disorders at more biologically tractable levels. Based on a sibling pair design, we aimed to find the neuroimaging endophenotypes of T2DM and investigate the role of inherent neurological disorders in the pathogenesis and deterioration of T2DM. Twenty-six pairs of diagnosed T2DM patients with unaffected siblings and 26 unrelated controls were included in this study. Both high-resolution structural MRI and three-dimensional pseudo-continuous arterial spin labelling (3D-pCASL) MRI data were acquired with a 3.0 T MRI system. Voxel-based morphometry (VBM) analysis was performed on the structural T1W images, and cerebral blood flow (CBF) maps were obtained. All data were processed with the SPM8 package under the MATLAB 7.6 operation environment. The T2DM patients and their unaffected siblings shared significant atrophy in the right inferior/middle temporal gyrus, and left insula, in addition to elevated CBF in the right prefrontal lobe. Several regions with abnormal CBF in siblings, including the right inferior/middle temporal gyrus, left insula, left operculum, right supramarginal gyrus, right prefrontal lobe, and bilateral anterior cingulate cortex, also presented significant atrophy in T2DM patients. The shared brain regions with grey matter (GM) loss and CBF increases may serve as neuroimaging endophenotypes of T2DM, and the regions with abnormal CBF in siblings indicate an increased risk for T2DM.

Engineering Translational Resource Allocation Controllers: Mechanistic Models, Design Guidelines, and Potential Biological Implementations.

The use of orthogonal ribosomes in combination with dynamic resource allocation controllers is a promising approach for relieving the negative effects of cellular resource limitations on the modularity of synthetic gene circuits. Here, we develop a detailed mechanistic model of gene expression and resource allocation, which when simplified to a tractable level of complexity, allows the rational design of translational resource allocation controllers. Analysis of this model reveals a fundamental design trade-off: that reducing coupling acts to decrease gene expression. Through a sensitivity analysis of the experimentally tunable controller parameters, we identify how each controller design parameter affects the overall closed-loop behavior of the system, leading to a detailed set of design guidelines for optimally managing this trade-off. On the basis of our designs, we evaluated a number of alternative potential experimental implementations of the proposed system using commonly available biological components. Finally, we show that the controller is capable of dynamically allocating ribosomes as needed to restore modularity in a number of more complex synthetic circuits, such as the repressilator, and activation cascades composed of multiple interacting modules.

Hybrid machine learning and optimisation method to solve a tri‐level road network protection problem

In this study, the authors employ machine learning to develop a new solution method for solving a tri-level network protection problem. In the upper-level, the planner aims to minimise the impact of the interdictor's attempt to disrupt a road network through protection activities. At the middle-level, however, the interdictor seeks to maximise the network's cost function, that is total travel time while the user equilibrium assignment models the road users behaviour at the lower-level. The proposed solution algorithm combines implicit enumeration with machine learning for faster performance. In so doing, four machine learning methods are evaluated among which the artificial neural network model shows the best performance and thereby to be exploited. Principal component analysis is also employed as part of the data pre-processing to perform dimensionality reduction. The proposed solution algorithm exhibits a reasonable level of tractability when employed to solve large problems in which a real-world network is under investigation. Although it cannot guarantee global optimality, it is argued that this is an essential compromise for the application of the network optimisation problems on extensive real-world networks and the large solution space that they generate.

Financial statement networks: an application of network theory in audit

Auditors use predictive models to estimate financial account values in a financial statement. Prior studies suggest that incorporating organizational knowledge into these models yields better predictive accuracy. We propose a novel method to con- struct a financial statement network in order to gain insight into the organizational structure of a company using real financial transaction data from ten companies. We show that real data yields financial statement networks of varying complexity. We introduce a method to aggregate the nodes and edges of the financial statement net- work, which results in its visualization at the right level of tractability. We also show that this visualization enables the auditor to assess the complexity of the organizational structure of a company and to use it as a risk indicator for the audit. Further, the obtained network yields insights into the monetary flow between financial accounts and business processes. We show that this information can be used to add organizational knowledge to predictive models for the purpose of obtaining audit evidence.

COHERENT FOREIGN EXCHANGE MARKET MODELS

A model describing the dynamics of a foreign exchange (FX) rate should preserve the same level of analytical tractability when the inverted FX process is considered. We show that affine stochastic volatility models satisfy such a requirement. Such a finding allows us to use affine stochastic volatility models as a building block for FX dynamics that are functionally-invariant with respect to the construction of suitable products/ratios of rates, thus generalizing the model of [A. De Col, A. Gnoatto & M. Grasselli (2013) Smiles all around: FX joint calibration in a multi-Heston model, Journal of Banking and Finance 37 (10), 3799–3818.].

Pricing Exotic Discrete Variance Swaps under the 3/2-Stochastic Volatility Models

We consider pricing of various types of exotic discrete variance swaps, like the gamma swaps and corridor variance swaps, under the 3/2-stochastic volatility models (SVMs) with jumps in asset price. The class of SVMs that use a constant-elasticity-of-variance (CEV) process for the instantaneous variance exhibits good analytical tractability only when the CEV parameter takes just a few special values (namely 0, 1/2, 1 and 3/2). The popular Heston model corresponds to the choice of the CEV parameter to be 1/2. However, the stochastic volatility dynamics implied by the Heston model fails to capture some important empirical features of the market data. The choice of 3/2 for the CEV parameter in the SVM shows better agreement with empirical studies while it maintains a good level of analytical tractability. Using the partial integro-differential equation (PIDE) formulation, we manage to derive quasi-closed-form pricing formulas for the fair strike prices of various types of exotic discrete variance swaps with various weight processes and different return specifications under the 3/2-model. Pricing properties of these exotic discrete variance swaps with respect to various model parameters are explored.

A nearly-optimal algorithm for the Fredholm problem of the second kind over a non-tensor product Sobolev space

In a previous paper, the authors showed that the information complexity of the Fredholm problem of the second kind is essentially the same as that of the approximation problems over the spaces of kernels and right-hand sides. This allowed us to give necessary and sufficient conditions for the Fredholm problem to exhibit a particular level of tractability (for information complexity) over weighted tensor product (\textsc{wtp}) spaces, as well as over an important class of \textit{not} necessarily tensor product weighted Sobolev spaces. Furthermore, we addressed the overall complexity of this Fredholm problem for the case in which the kernels and right-hand sides belong to a \textsc{wtp} space. For this case, we showed that a nearly-minimal-error interpolatory algorithm is easily implementable, with cost very close (to within a logarithmic factor) to the information cost. As a result, tractability results, which had previously only held for the information complexity, now hold for the overall complexity--provided that our kernels and right-hand sides belong to \textsc{wtp} spaces. This result does not hold for the weighted Sobolev spaces mentioned above, since they are not necessarily tensor product spaces. In this paper, we close this gap. We exhibit an easily implementable iterative approximation to a nearly minimal error interpolatory algorithm for this family of weighted Sobolev spaces. This algorithm exhibits the same good properties as the algorithm presented in the previous paper.

Automatic selection of candidate investments for Transmission Expansion Planning

This paper deals explicitly with the problem of proposing candidate lines (sometimes referred to as technical alternatives) for Transmission Expansion Planning (TEP). Candidate lines have been traditionally regarded as expert-provided system information. However, given the need to plan larger networks, identifying interesting candidates is an issue of increasing relevance and complexity. This paper proposes a consistent method to tackle this problem.First, an automatic and objective candidate discovery mechanism based on sensitivities proposes potentially interesting investments. Then, a candidate management strategy filters the list of candidates to keep problem size within tractable levels in a Mathematical Programming context without compromising global optimality. Finally, a candidate analysis tool reveals the relationships among investments from a relatively fast and simple power flow study. This information can be interesting to provide support for expansion decisions. These theoretical developments are complemented by a realistic case study which illustrates the applicability of the method.

Pricing Exotic Variance Swaps Under 3/2-Stochastic Volatility Models

We consider pricing of various types of exotic discrete variance swaps, like the gamma swaps and corridor swaps, under the 3/2-stochastic volatility models with jumps. The class of stochastic volatility models (SVM) that use a constant-elasticity-of-variance (CEV) process for the instantaneous variance exhibit nice analytical tractability when the CEV parameter takes just a few special values (namely, 0, 1/2, 1 and 3/2). The popular Heston model corresponds to the choice of the CEV parameter to be 1/2. However, the stochastic volatility dynamics derived from the Heston model fails to agree with empirical findings from actual market data. The choice of 3/2 for the CEV parameter in the SVM shows better agreement with empirical studies while it maintains a good level of analytical tractability. By using the partial integro-differential equation formulation, we manage to derive quasi-closed form pricing formulas for the fair strike values of various types of discrete variance swaps. Pricing properties of these exotic discrete variance swaps under different market conditions are explored.

Towards optimal allocation of computer resources: Trade-offs between uncertainty quantification, discretization and model reduction

The computational complexity of numerical models can be broken down into contributions ranging from spatial, temporal and stochastic resolution, e.g., spatial grid resolution, time step size and number of repeated simulations dedicated to quantify uncertainty. Controlling these resolutions allows keeping the computational cost at a tractable level whilst still aiming at accurate and robust predictions. The objective of this work is to introduce a framework that optimally allocates the available computational resources in order to achieve highest accuracy associated with a given prediction goal. Our analysis is based on the idea to jointly consider the discretization errors and computational costs of all individual model dimensions (physical space, time, parameter space). This yields a cost-to-error surface which serves to aid modelers in finding an optimal allocation of the computational resources (ORA). As a pragmatic way to proceed, we propose running small cost-efficient pre-investigations in order to estimate the joint cost-to-error surface, then fit underlying complexity and error models, decide upon a computational design for the full simulation, and finally to perform the designed simulation at near-optimal costs-to-accuracy ratio. We illustrate our approach with three examples from subsurface hydrogeology and show that the computational costs can be substantially reduced when allocating computational resources wisely and in a situation-specific and task-specific manner. We conclude that the ORA depends on a multitude of parameters, assumptions and problem-specific features and, hence, ORA needs to be determined carefully prior to each investigation.

Modelling facial expressions: A framework for simulating nonlinear soft tissue deformations using embedded 3D muscles

Human face can be seen as a soft tissue organ complex with a large investing network of musculature. Due to its complexity, most existing computational models approximate these muscular structures using simple geometries such as 1-D curves or primitive 3-D shapes. This paper presents a new approach to evaluate muscle contribution from anatomically accurate geometries while maintaining the computational complexity at a tractable level. In the proposed method, 3-D muscle structures are embedded inside a facial continuum (encompassing all superficial soft tissue structures), where mechanical contribution of muscles is evaluated independently and transferred to the facial computational domain through a finite element mapping procedure. Muscle forces are decomposed into an array of discrete point loads that are determined at the integration points of an appropriate quadrature scheme. As a result, muscle meshes can be constructed independent from the facial mesh giving two main advantages: (i) the muscle geometries can be refined independent of the facial computational domain, and (ii) it is not required for the computational domain to conform to complex topology of muscle structures.

Automatized Decision Making for Autonomous Agents

Utility theory and the principle of maximising the expected utility have, within the multi-agent community, had a great influence on multi-agent based decision. Even though this principle is often useful when evaluating a decision situation it is virtually impossible, except in very artificial situations, to use the more basic decision rules with its unrealistically strong requirements for the input data, and other candidate methods must be considered instead. This article provides an overview and brings attention to some of the possibilities to utilize more elaborated decision methods, while still keeping the computational issues at a tractable level.

Computing galled networks from real data.

Motivation: Developing methods for computing phylogenetic networks from biological data is an important problem posed by molecular evolution and much work is currently being undertaken in this area. Although promising approaches exist, there are no tools available that biologists could easily and routinely use to compute rooted phylogenetic networks on real datasets containing tens or hundreds of taxa. Biologists are interested in clades, i.e. groups of monophyletic taxa, and these are usually represented by clusters in a rooted phylogenetic tree. The problem of computing an optimal rooted phylogenetic network from a set of clusters, is hard, in general. Indeed, even the problem of just determining whether a given network contains a given cluster is hard. Hence, some researchers have focused on topologically restricted classes of networks, such as galled trees and level-k networks, that are more tractable, but have the practical draw-back that a given set of clusters will usually not possess such a representation.Results: In this article, we argue that galled networks (a generalization of galled trees) provide a good trade-off between level of generality and tractability. Any set of clusters can be represented by some galled network and the question whether a cluster is contained in such a network is easy to solve. Although the computation of an optimal galled network involves successively solving instances of two different NP-complete problems, in practice our algorithm solves this problem exactly on large datasets containing hundreds of taxa and many reticulations in seconds, as illustrated by a dataset containing 279 prokaryotes.Availability: We provide a fast, robust and easy-to-use implementation of this work in version 2.0 of our tree-handling software Dendroscope, freely available from http://www.dendroscope.org.Contact: huson@informatik.uni-tuebingen.de

Neurocognitive endophenotypes of obsessive-compulsive disorder

Endophenotypes (intermediate phenotypes) are objective, heritable, quantitative traits hypothesized to represent genetic risk for polygenic disorders at more biologically tractable levels than distal behavioural and clinical phenotypes. It is theorized that endophenotype models of disease will help to clarify both diagnostic classification and aetiological understanding of complex brain disorders such as obsessive-compulsive disorder (OCD). To investigate endophenotypes in OCD, we measured brain structure using magnetic resonance imaging (MRI), and behavioural performance on a response inhibition task (Stop-Signal) in 31 OCD patients, 31 of their unaffected first-degree relatives, and 31 unrelated matched controls. Both patients and relatives had delayed response inhibition on the Stop-Signal task compared with healthy controls. We used a multivoxel analysis method (partial least squares) to identify large-scale brain systems in which anatomical variation was associated with variation in performance on the response inhibition task. Behavioural impairment on the Stop-Signal task, occurring predominantly in patients and relatives, was significantly associated with reduced grey matter in orbitofrontal and right inferior frontal regions and increased grey matter in cingulate, parietal and striatal regions. A novel permutation test indicated significant familial effects on variation of the MRI markers of inhibitory processing, supporting the candidacy of these brain structural systems as endophenotypes of OCD. In summary, structural variation in large-scale brain systems related to motor inhibitory control may mediate genetic risk for OCD, representing the first evidence for a neurocognitive endophenotype of OCD.