One-dimensional Spatial Model Research Articles

A Dodgson-Hare synthesis

In 1876, Charles Dodgson (better known as Lewis Carroll) proposed a committee election procedure that chooses the Condorcet winner when one exists and otherwise eliminates candidates outside the Smith set, then allows for re-votes until a Condorcet winner emerges. The present paper discusses Dodgson’s work in the context of strategic election behavior and suggests a “Dodgson-Hare” method: a variation on Dodgson’s procedure, for use in public elections. This method allows for candidate withdrawal and employs Hare’s plurality-loser-elimination method to resolve persistent cycles. Given plausible assumptions about how candidates decide whether to withdraw when there is a cycle, Dodgson-Hare outperforms Hare, Condorcet-Hare, and 12 other voting rules in a series of spatial-model simulations that count how often each rule is vulnerable to coalitional manipulation. In the case of a one-dimensional spatial model, all coalitional voting strategies that are possible under Condorcet-Hare can be undone in Dodgson-Hare, by the withdrawal of candidates who have incentive to withdraw.

A robust mathematical model of adaxial–abaxial patterning

AbstractBiological development results from intricate and dynamic interactions between members of gene regulatory networks. This is exemplified by the production of flat leaf architecture. Leaves flatten by driving growth along the boundary between their adaxial (top) and abaxial (bottom) domains. These domains are generated by interactions between a complex network of transcription factors and small RNAs. Despite its complexity, flat leaf production is robust to genetic and environmental noise. To identify factors contributing to this robustness, we mathematically modelled the determinants and interactions that pattern the adaxial–abaxial axis in leaves of Arabidopsis thaliana. Model parameters were estimated almost exclusively using experimental data. Our model recapitulates observations of adaxial–abaxial patterning and small RNA-target interactions. Positioning of the adaxial–abaxial boundary is stable across a wide range of small RNA source values and is highly robust to noise in the model. The successful application of our one-dimensional spatial model will enable higher-dimension modelling of the complex and mechanistically challenging process of flat leaf production.

Experimental and Numerical Analysis of Start-Up of a Capillary Pumped Loop for Terrestrial Applications

Abstract A study on the start-up phases of a capillary pumped loop for terrestrial application (CPLTA) is proposed in this paper. Experimental analysis and numerical modeling, using a one-dimensional spatial discretization model, based on thermohydraulic equations and solved by nodal network/electrical analogy, are presented to study the thermal and hydraulic behavior of the loop for methanol and n-pentane as working fluids, during start-up transient phases. The experimental observations are backed up by the numerical model to help the transient and steady analysis of this kind of loop. The precise numerical study allows to have a better understanding of the complicated phenomena happening during the start-up and to have a global view of the behavior of the capillary pumped loop for integrated power (CPLIP) during these phases. In this study, it will be also shown the influence of vapor line solid walls thermal inertia and its impact on the dynamic behavior and on the success of the start-up of the loop.

Multifractal Desynchronization of the Cardiac Excitable Cell Network During Atrial Fibrillation. II. Modeling.

In a companion paper (I. Multifractal analysis of clinical data), we used a wavelet-based multiscale analysis to reveal and quantify the multifractal intermittent nature of the cardiac impulse energy in the low frequency range ≲ 2Hz during atrial fibrillation (AF). It demarcated two distinct areas within the coronary sinus (CS) with regionally stable multifractal spectra likely corresponding to different anatomical substrates. The electrical activity also showed no sign of the kind of temporal correlations typical of cascading processes across scales, thereby indicating that the multifractal scaling is carried by variations in the large amplitude oscillations of the recorded bipolar electric potential. In the present study, to account for these observations, we explore the role of the kinetics of gap junction channels (GJCs), in dynamically creating a new kind of imbalance between depolarizing and repolarizing currents. We propose a one-dimensional (1D) spatial model of a denervated myocardium, where the coupling of cardiac cells fails to synchronize the network of cardiac cells because of abnormal transjunctional capacitive charging of GJCs. We show that this non-ohmic nonlinear conduction 1D modeling accounts quantitatively well for the “multifractal random noise” dynamics of the electrical activity experimentally recorded in the left atrial posterior wall area. We further demonstrate that the multifractal properties of the numerical impulse energy are robust to changes in the model parameters.

The stepping stone model in a random environment and the effect of local heterogneities on isolation by distance patterns

We study a one-dimensional spatial population model where the population sizes at each site are chosen according to a translation invariant and ergodic distribution and are uniformly bounded away from 0 and infinity. We suppose that the frequencies of a particular genetic type in the colonies evolve according to a system of interacting diffusions, following the stepping stone model of Kimura. We show that, over large spatial and temporal scales, this model behaves like the solution to a stochastic heat equation with Wright-Fisher noise with constant coefficients. These coefficients are the effective diffusion rate of genes within the population and the effective local population density. We find that, in our model, the local heterogeneity leads to a slower effective diffusion rate and a larger effective population density than in a uniform population. Our proof relies on duality techniques, an invariance principle for reversible random walks in a random environment and a convergence result for a system of coalescing random walks in a random environment.

One-dimensional spatial model for self-heating in compost piles: Investigating effects of moisture and air flow

This paper considers the self-heating process which occurs within a compost pile using a one-dimensional spatially-dependent model incorporating terms that account for self-heating due to both biological and oxidation mechanisms. As the moisture content within a compost pile and the air flow through it are the two crucial factors in the degradation process, we use a model which incorporates four mass-balance equations, namely, energy, oxygen, vapour and liquid water concentrations, to investigate the behaviour of a compost pile when these two factors interact. Analyses of different initial water contents and air-flow velocities within a compost pile show that they can determine the efficiency of the biodegradation process. For an intermediate water content range and air-flow rate, the biological reaction is shown to be at its optimal value but there is also a possibility of spontaneous ignition within the compost pile.

A Search for the General Will in a Spatial Model

In Book IV, Chapter II of The Social Contract, Jean-Jacques Rousseau argued that the nearer opinion approaches unanimity in an assembly, the greater is the dominance of the general will. The present study revisits this classical argument in a one-dimensional spatial model with variable agendas. The study obtains a sufficient condition under which the Borda winner and the Condorcet winner almost coincide so that we can unambiguously find an alternative that conforms to the general will. This condition describes the existence of certain sympathy among voters on the evaluation of alternatives, and it is much weaker than the unanimity requirement.

A folk theorem for the one-dimensional spatial bargaining model

We show that in the one-dimensional bargaining model based on the protocol of Baron and Ferejohn (Am Polit Sci Rev 83:1181–1206, 1989), if voting is simultaneous, publicly observed, and no agent has the power to unilaterally impose a choice, then arbitrary policies can be supported by subgame perfect equilibria in stage-undominated voting strategies when agents are patient. Moreover, in the model with a bad status quo, arbitrary outcomes can be supported for arbitrary positive discount factors. We formulate sufficient conditions for supporting arbitrary alternatives in terms of a system of equations. The system has a straightforward solution in the model with no discounting, and after verifying non-singularity of this system, we use the implicit function theorem to derive the folk theorem when agents are sufficiently patient.

Spatially induced disparities in users' and non-users' WTP for water quality improvements—Testing the effect of multiple substitutes and distance decay

Costs and benefits of water restoration projects are not necessarily evenly spread out over the entire area affected by the project. The physical distribution of benefits is, therefore, an important parameter when conducting economic analyses of water restoration projects. Two particularly relevant spatial issues relate to 1) the location of the population relative to the location of the waterbody, and 2) the availability and characteristics of substitute water bodies.Based on a contingent valuation (CV) study of the demand for restoring Odense River in Denmark a spatial demand model which accounts for travel time both to the river subject for valuation and to potential substitute sites is estimated. It is concluded that the spatial distribution of benefits is unlikely to be homogeneously determined by a one-dimensional spatial model. Moreover, the results suggest that the effect of spatial issues on preferences varies between users and non-users. For non-users the spatial impacts from potential substitutes significantly reduce demand for improvements in Odense River. This indicates that focus on estimation of distance decay effects may be an important tool in relation to ensuring proper geographical delimitation of the population in a given context.

A spatial model of the relationship between seats and votes

The empirical relationship between votes received and seats won in an election is widely used to infer whether district boundaries and other election rules benefit one party or type of voter. Specifically, the electoral system is said to be biased against one party or group if, when that party or group wins 50% of the vote it receives less than 50% of the seats. However, a definitive interpretation of the empirical relationship between seats and votes presents substantial difficulties, which owes much to the absence of the linkage between this relationship and individual voter’s preferences and behavior. We offer such a linkage and derive a particular form of it from the one-dimensional spatial model of voting, the most widely used model of voting in Political Science. We show that under this model the methods commonly used to estimate the relationship between seats and votes do not properly identify the electoral bias caused by districting. We use the model to develop a new approach for estimating the electoral bias and apply the techniques to the US Senate during the period 2002–2006 and the US Presidential race of 2004. We find evidence of bias against Democratic voters in the US Senate but not in the Electoral College.

Accurate Inference and Estimation in Population Genomics

Both intra- and interspecific genomic comparisons have revealed local similarities in the level and frequency of mutational variation, as well as in patterns of gene expression. This autocorrelation between measurements leads to violations of assumptions of independence in many statistical methods, resulting in misleading and incorrect inferences. Here I show that autocorrelation can be due to many factors and is present across the genome. Using a one-dimensional spatial stochastic model, I further show how previous results can be employed to correct for autocorrelation along chromosomes in population and comparative genomics research. When multiple hypothesis tests are autocorrelated, I demonstrate that a simple correction can lead to increased power in statistical inference. I present a preliminary analysis of population genomic data from Drosophila simulans to show the ubiquity of autocorrelation and applicability of the methods proposed here.

Voter Uncertainty Can Produce Preferences with More Than One Peak, but Not Preference Cycles: A Clue to the Fate of Ross Perot?

The one-dimensional Downsian spatial model entails single-peaked preferences for each voter. Consequently, the preference ranking of the electorate as a whole is also single-peaked, and Condorcet cycles in the preferences of the electorate are not possible. Our main theoretical results herein are that, if the model is generalized to allow for voter uncertainty about candidates' positions, then single-peakedness no longer exists invariably, either for individual voters or for the electorate as a whole. However, cyclical preference majorities remain impossible. We examine how well the generalized model may fit preference and variability data from the 1992 United States Presidential election.

Entry-deterring policy differentiation by electoral candidates

This paper studies the equilibria of a one-dimensional spatial model in which three candidates seek to maximize their probabilities of winning, are uncertain about the voters’ preferences, and may move whenever they wish. In the presence of enough uncertainty there is an equilibrium in which two candidates enter simultaneously at distinct positions in the first period and either the third candidate does not enter or enters between the first two in the second period.

Rupture Process of the 1995 Antofagasta Subduction Earthquake ( M w = 8.1)

A finite-source rupture model of the July 30, 1995, M w = 8.1 Antofagasta (Northern Chile) subduction earthquake is developed using body and surface waves that span periods from 20 to 290 s. A long-period (150–290 s) surface-wave spectral inversion technique is applied to estimate the average finite-fault source properties. Deconvolutions of broadband body waves using theoretical Green’s functions, and deconvolutions of broadband fundamental mode surface waves using empirical Green’s functions provided by a large aftershock, yield effective source time functions containing periods from 20 to 200 s for many directivity parameters. The source time functions are used in an inverse radon transform to image a one-dimensional spatial model of the moment rate history. The event produced a predominantly unilateral southward rupture, yielding strong directivity effects on all seismic waves with periods less than a few hundred seconds. The aftershock information, spectral analysis, and moment rate distribution indicate a rupture length of 180-200 km, with the largest slip concentrated in the first 120 km, a rupture azimuth of 205° ± 10° along the Chilean coastline, and a rupture duration of 60–68 s with a corresponding average rupture velocity of 3.0–3.2 km/s. The overall rupture character is quite smooth, accentuating the directivity effects and reducing the shaking intensity, however there are three regions with enhanced moment rate distributed along the rupture zone: near the epicenter, 50 to 80 km south of the epicenter, and 110 to 140 km south of the epicenter.

Optimal Recycling and the Location of Waste Facilities

In this paper, we consider a waste management program in a local economy. There are two kinds of facilities: waste processing facilities and landfills. The local government plans the waste management program to minimize the costs of transportation, disposal, and negative externalities. In order to examine the optimal location problem of waste facilities and landfills and the optimal recycling system, a one-dimensional spatial model is constructed. We derive the optimal spatial structure of waste facilities and show the critical point of the recycling ratio.

A modelling analysis on dynamics of hilly sandy grassland landscapes using spatial simulation

A one-dimensional spatial simulation model, SLOPE, was developed to simulate the dynamics of soil water and vegetation biomass of semi-arid hilly sandy grasslands. The model stressed interactions between soil water and plant growth for variable geographical locations, slope angle, aspect angle, soil hydraulic properties as well as plant assimilation and transpiration characteristics. Climatic and field-experimental data on plant biomass and transpiration as well as soil water characteristics, conducted in the Erdos Plateau in northern China, were used to parameterize the model. A simulation was run for variable soil hydraulic conductivity and slope and aspect angles to obtain steady state solutions. The results indicated that soil water and biomass production strongly depended on slope and aspect angles, but were not so sensitive to soil hydraulic conductivity. Soil water was, but biomass production was not, sensitive to aspect angle.

Wave trains in a model of gypsy moth population dynamics.

A recent model of gypsy moth [Lymantria dispar (Lepidoptera: Lymantriidae)] populations led to the observation of traveling waves in a one-dimensional spatial model. In this work, these waves are studied in more detail and their nature investigated. It was observed that when there are no spatial effects the model behaves chaotically under certain conditions. Under the same conditions, when diffusion is allowed, traveling waves develop. The biomass densities involved in the model, when examined at one point in the spatial domain, are found to correspond to a limit cycle lying on the surface of the chaotic attractor of the spatially homogeneous model. Also observed are wave trains that have modulating maxima, and which when examined at one point in the spatial domain show a quasiperiodic temporal behavior. This complex behavior is determined to be due to the interaction of the traveling wave and the chaotic background dynamics. (c) 1995 American Institute of Physics.

Spatial duopoly and residential structure

This paper studies a (one-dimensional) spatial duopoly model with an endogenous residential structure. Depending on the primitives of the model, we can observe one of the following urban configurations: (i) if the area under study is small enough, the two firms locate at the center and the residential pattern is that of a monocentric city; (ii) if the area is sufficiently large, the firms locate separately with a residential pattern of a bicentric city; (iii) if the area is very large, the two firms and residential patterns are completely separated, thus corresponding to two distinct monocentric cities. Although we consider the case in which two retail firms compete for consumers, the model can be reinterpreted, mutatis mutandis, as two manufacturing firms competing for workers.

Multi-party competition with exit: A comment on Duverger's Law

Contrary to Duverger's Law, there exist multi-party systems in conjunction with simple majority single-ballot systems. At least three exceptions exist to this “law”. Rae (1971) and Riker (1976; 1982) offer explanations for two of the most prominent exceptions, i.e. Canada and India. I also discuss another exception, Great Britain. In this paper, I use a simple one-dimensional spatial model to show that a multi-party system can be supported under a simple majority single-ballot system. This explanation depends on the way political parties exit the system. If parties decide sequentially whether or not to exit, a multi-party system can not be maintained. If political parties make this decision simultaneously, a multi-party system may be able to sustain itself.

Throughflow effects on the transient and stability characteristics of a thermosyphon

Throughflow effects on the flow in a natural circulation loop are investigated analytically. The loop consists of two vertical insulated branches with a point heat source at the bottom and a point heat sink at the top. Hot liquid is extracted continuously at the hottest spot (just downstream of the heat source) and replaced by cold liquid injection just downstream of the heat sink. A one-dimensional spatial model is employed to calculate flow rates and temperature distributions for various loop parameters and through-flow rates. Steady state, transient behavior, and stability characteristics are studied. It is found that the throughflow stabilizes the motion in the loop.