Western Chess: Endgame data

This spreadsheet contains key data about that part of the endgame of Western Chess for which Endgame Tables (EGTs) have been generated by computer. It is derived from the EGT work since 1969 of Thomas Ströhlein, Ken Thompson, Christopher Wirth, Eugene Nalimov, Marc Bourzutschky, John Tamplin and Yakov Konoval. The data includes %s of wins, draws and losses (wtm and btm), the maximum and average depths of win under various metrics (DTC = Depth to Conversion, DTM = Depth to Mate, DTZ = Depth to Conversion or Pawn-push), and examples of positions of maximum depth. It is essentially about sub-7-man Chess but is updated as news comes in of 7-man EGT computations.

The maximum rate of mammal evolution

How fast can a mammal evolve from the size of a mouse to the size of an elephant? Achieving such a large transformation calls for major biological reorganization. Thus, the speed at which this occurs has important implications for extensive faunal changes, including adaptive radiations and recovery from mass extinctions. To quantify the pace of large-scale evolution we developed a metric, clade maximum rate, which represents the maximum evolutionary rate of a trait within a clade. We applied this metric to body mass evolution in mammals over the last 70 million years, during which multiple large evolutionary transitions occurred in oceans and on continents and islands. Our computations suggest that it took a minimum of 1.6, 5.1, and 10 million generations for terrestrial mammal mass to increase 100-, and 1,000-, and 5,000- fold, respectively. Values for whales were down to half the length (i.e., 1.1, 3, and 5 million generations), perhaps due to the reduced mechanical constraints of living in an aquatic environment. When differences in generation time are considered, we find an exponential increase in maximum mammal body mass during the 35 million years following the Cretaceous–Paleogene (K–Pg) extinction event. Our results also indicate a basic asymmetry in macroevolution: very large decreases (such as extreme insular dwarfism) can happen at more than 10 times the rate of increases. Our findings allow more rigorous comparisons of microevolutionary and macroevolutionary patterns and processes. Keywords: haldanes, biological time, scaling, pedomorphosis

The unsteady flow of a weakly compressible fluid in a thin porous layer II: three-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a three-dimensional layer, composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Numerical solution of this three-dimensional evolution problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l, a situation which occurs frequently in the application to oil and gas reservoir recovery and which leads to significant stiffness in the numerical problem. Under the assumption that $\epsilon\propto h/l\ll 1$, we show that, to leading order in $\epsilon$, the pressure field varies only in the horizontal directions away from the wells (the outer region). We construct asymptotic expansions in $\epsilon$ in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive expressions for all significant process quantities. The only computations required are for the solution of non-stiff linear, elliptic, two-dimensional boundary-value, and eigenvalue problems. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the layer, $\epsilon$, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighbourhood of wells and away from wells.

An experiment in the Assimilation of Data in Dynamical Analysis

A system for continuous data assimilation is presented and discussed. To simulate the dynamical development a channel version of a balanced barotropic model is used and geopotential (height) data are assimilated into the models computations as data become available. In the first experiment the updating is performed every 24th, 12th and 6th hours with a given network. The stations are distributed at random in 4 groups in order to simulate 4 areas with different density of stations. Optimum interpolation is performed for the difference between the forecast and the valid observations. The RMS-error of the analyses is reduced in time, and the error being smaller the more frequent the updating is performed. The updating every 6th hour yields an error in the analysis less than the RMS-error of the observation. In a second experiment the updating is performed by data from a moving satellite with a side-scan capability of about 15°. If the satellite data are analysed at every time step before they are introduced into the system the error of the analysis is reduced to a value below the RMS-error of the observation already after 24 hours and yields as a whole a better result than updating from a fixed network. If the satellite data are introduced without any modification the error of the analysis is reduced much slower and it takes about 4 days to reach a comparable result to the one where the data have been analysed.

Information-based data selection for ensemble data assimilation

Ensemble-based data assimilation is rapidly proving itself as a computationally-efficient and skilful assimilation method for numerical weather prediction, which can provide a viable alternative to more established variational assimilation techniques. However, a fundamental shortcoming of ensemble techniques is that the resulting analysis increments can only span a limited subspace of the state space, whose dimension is less than the ensemble size. This limits the amount of observational information that can effectively constrain the analysis. In this paper, a data selection strategy that aims to assimilate only the observational components that matter most and that can be used with both stochastic and deterministic ensemble filters is presented. This avoids unnecessary computations, reduces round-off errors and minimizes the risk of importing observation bias in the analysis. When an ensemble-based assimilation technique is used to assimilate high-density observations, the data-selection procedure allows the use of larger localization domains that may lead to a more balanced analysis. Results from the use of this data selection technique with a two-dimensional linear and a nonlinear advection model using both in situ and remote sounding observations are discussed.

On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

We consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound-soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.

Atmospheric predictability revisited

This article examines the potential to improve numerical weather prediction (NWP) by estimating upper and lower bounds on predictability by re-visiting the original study of Lorenz (1982) but applied to the most recent version of the European Centre for Medium Range Weather Forecasts (ECMWF) forecast system, for both the deterministic and ensemble prediction systems (EPS). These bounds are contrasted with an older version of the same NWP system to see how they have changed with improvements to the NWP system. The computations were performed for the earlier seasons of DJF 1985/1986 and JJA 1986 and the later seasons of DJF 2010/2011 and JJA 2011 using the 500-hPa geopotential height field. Results indicate that for this field, we may be approaching the limit of deterministic forecasting so that further improvements might only be obtained by improving the initial state. The results also show that predictability calculations with earlier versions of the model may overestimate potential forecast skill, which may be due to insufficient internal variability in the model and because recent versions of the model are more realistic in representing the true atmospheric evolution. The same methodology is applied to the EPS to calculate upper and lower bounds of predictability of the ensemble mean forecast in order to explore how ensemble forecasting could extend the limits of the deterministic forecast. The results show that there is a large potential to improve the ensemble predictions, but for the increased predictability of the ensemble mean, there will be a trade-off in information as the forecasts will become increasingly smoothed with time. From around the 10-d forecast time, the ensemble mean begins to converge towards climatology. Until this point, the ensemble mean is able to predict the main features of the large-scale flow accurately and with high consistency from one forecast cycle to the next. By the 15-d forecast time, the ensemble mean has lost information with the anomaly of the flow strongly smoothed out. In contrast, the control forecast is much less consistent from run to run, but provides more detailed (unsmoothed) but less useful information.

A comparative review of dimension reduction methods in approximate Bayesian computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.

Computing Fresnel integrals via modified trapezium rules

In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule approximations to integrals on the real line, these trapezium rules modified to take into account poles of the integrand near the real axis. Our starting point is a method for computation of the error function of complex argument due to Matta and Reichel (J Math Phys 34:298–307, 1956) and Hunter and Regan (Math Comp 26:539–541, 1972). We construct approximations which we prove are exponentially convergent as a function of N , the number of quadrature points, obtaining explicit error bounds which show that accuracies of 10−15 uniformly on the real line are achieved with N=12 , this confirmed by computations. The approximations we obtain are attractive, additionally, in that they maintain small relative errors for small and large argument, are analytic on the real axis (echoing the analyticity of the Fresnel integrals), and are straightforward to implement.

On the determination of ion temperature in the auroral F-region ionosphere

Assessment is made of the effect of the assumed form for the ion velocity distribution function on estimates of three-dimensional ion temperature from one-dimensional observations. Incoherent scatter observations by the EISCAT radar at a variety of aspect angles are used to demonstrate features of ion temperature determination and to study the ion velocity distribution function. One form of the distribution function which has recently been widely used In the interpretation of EISCAT measurements, is found to be consistent with the data presented here, in that no deviation from a Maxwellian can be detected for observations along the magnetic field line and that the ion temperature and its anisotropy are accurately predicted. It is shown that theoretical predictions of the anisotropy by Monte Carlo computations are very accurate, the observed value being greater by only a few percent. It is also demonstrated for the case studied that errors of up to 93% are introduced into the ion temperature estimate if the anisotropy is neglected. Observations at an aspect angle of 54.7°, which are not subject to this error, have a much smaller uncertainty (less than 1%) due to the adopted form of the distribution of line-of-sight velocity.

Zombie mouse in a Chinese Room

John Searle’s Chinese Room Argument (CRA) purports to demonstrate that syntax is not sufficient for semantics, and, hence, because computation cannot yield understanding, the computational theory of mind, which equates the mind to an information processing system based on formal computations, fails. In this paper, we use the CRA, and the debate that emerged from it, to develop a philosophical critique of recent advances in robotics and neuroscience. We describe results from a body of work that contributes to blurring the divide between biological and artificial systems; so-called animats, autonomous robots that are controlled by biological neural tissue and what may be described as remote-controlled rodents, living animals endowed with augmented abilities provided by external controllers. We argue that, even though at first sight, these chimeric systems may seem to escape the CRA, on closer analysis, they do not. We conclude by discussing the role of the body–brain dynamics in the processes that give rise to genuine understanding of the world, in line with recent proposals from enactive cognitive science.

A Variance-Minimizing Filter for Large-Scale Applications

A truly variance-minimizing filter is introduced and its per for mance is demonstrated with the Korteweg– DeV ries (KdV) equation and with a multilayer quasigeostrophic model of the ocean area around South Africa. It is recalled that Kalman-like filters are not variance minimizing for nonlinear model dynamics and that four - dimensional variational data assimilation (4DV AR)-like methods relying on per fect model dynamics have dif- ficulty with providing error estimates. The new method does not have these drawbacks. In fact, it combines advantages from both methods in that it does provide error estimates while automatically having balanced states after analysis, without extra computations. It is based on ensemble or Monte Carlo integrations to simulate the probability density of the model evolution. When obser vations are available, the so-called importance resampling algorithm is applied. From Bayes’ s theorem it follows that each ensemble member receives a new weight dependent on its ‘ ‘distance’ ’ t o the obser vations. Because the weights are strongly var ying, a resampling of the ensemble is necessar y. This resampling is done such that members with high weights are duplicated according to their weights, while low-weight members are largely ignored. In passing, it is noted that data assimilation is not an inverse problem by nature, although it can be for mulated that way . Also, it is shown that the posterior variance can be larger than the prior if the usual Gaussian framework is set aside. However , i n the examples presented here, the entropy of the probability densities is decreasing. The application to the ocean area around South Africa, gover ned by strongly nonlinear dynamics, shows that the method is working satisfactorily . The strong and weak points of the method are discussed and possible improvements are proposed.