On Plane Wave Solutions in Lorentz-Violating Extensions of Gravity

In this paper, we obtain dispersion relations corresponding to plane wave solutions in Lorentz-breaking extensions of gravity with dimension 3, 4, 5 and 6 operators. We demonstrate that these dispersion relations display a usual Lorentz-invariant mode when the corresponding additive term involves higher derivatives.

Constrained versus Unconstrained Rational Inattention

The rational inattention literature is split between two versions of the model: in one, mutual information of states and signals are bounded by a hard constraint, while, in the other, it appears as an additive term in the decision maker’s utility function. The resulting constrained and unconstrained maximization problems are closely related, but, nevertheless, their solutions differ in certain aspects. In particular, movements in the decision maker’s prior belief and utility function lead to opposite comparative statics conclusions.

Changes in future precipitation mean and variability across scales

Changes in precipitation variability can have large societal consequences, whether at the short timescales of flash floods or the longer timescales of multi-year droughts. Recent studies have suggested that in future climate projections, precipitation variability rises more steeply than does its mean, leading to concerns about societal impacts. This work evaluates changes in mean precipitation over a broad range of spatial and temporal scales using a range of models from high-resolution regional simulations to millennial-scale global simulations. Results show that changes depend on the scale of aggregation and involve strong regional differences. On local scales that resolve individual rainfall events (hours and tens of kilometers), changes in precipitation distributions are complex and variances rise substantially more than means, as is required given the well-known disproportionate rise in precipitation intensity. On scales that aggregate across many events, distributional changes become simpler and variability changes smaller. At regional scale, future precipitation distributions can be largely reproduced by a simple transformation of present-day precipitation involving a multiplicative shift and a small additive term. The “extra” broadening is negatively correlated with changes in mean precipitation: in strongly “wetting” areas, distributions broaden less than expected from a simple multiplicative mean change; in “drying” areas, distributions narrow less. Precipitation variability changes are therefore of especial concern in the subtropics, which tend to dry under climate change. Outside the tropics, variability changes are similar on timescales from days to decades, i.e. show little frequency dependence. This behavior is highly robust across models, suggesting it may stem from some fundamental constraint.

A General Chaotic Circuit Design and Hardware Implementation via the Inductance Integrators

This paper presents a scheme for the modified chaotic circuits based on inductance integration. In view of the fact that the DC resistance of an inductor in the circuit cannot be ignored, this way of constructing the circuits is provided that can eliminate its influence on the integral circuits. By means of cascading an inverting adder circuit and inductance integral circuit, the output signal of the integral circuit is fed back to the inverting adder circuit, and its additive term is artificially added to match the actual inductance integrated circuit to achieve integral circuit based on the actual inductor which can offset the effect of its DC resistance. In order to verify the generality of the design, the process of designing Lorenz chaotic circuit is given and its attractors can also be observed from the oscilloscope.

Strain-rate effects associated with the HJC concrete model

The Holmquist-Johnson-Cook (HJC) model for concrete was presented in 1993 and has been used extensively since that time. Since then a third invariant effect has been added and the shear modulus has been revised to vary such that Poisson's ratio is held constant. It has always been diffcult, however, to determine the appropriate constant for the strain-rate effect as most of the published data are for the net stress as a function of the strain rate. Because concrete is both pressure dependent and strain-rate dependent, it is necessary to separate the individual effects. Recently strain-rate data for three concrete materials were presented by Piotrowska and others [1, 2], where the data are presented as equivalent stress versus confining pressure for a high strain rate and a quasi-static strain rate. This is the form necessary to determine the appropriate strain-rate effect, and the data show that the strain-rate effect is larger than used in the initial publication of the HJC model, and also that the strain-rate effect is a function of the confining pressure. For lower pressures the strain-rate effect is a factor to be applied to the quasi-static data (which is the effect represented in the original HJC model), but for higher pressures the strain rate effect is better represented by an additive term. With the addition of an another HJC constant (the pressure at which the strain rate effect transitions from a multiplied factor to an additive term) it is possible to more accurately represent the response of concrete under high pressures and high strain rates, and it is possible to compute more accurate results for projectile penetration into concrete targets. The paper presents the modified form of the HJC model, an analysis of the strain-rate effects, and results of penetration computations that are compared to experimental data in the literature.

A simple approach to estimate isotropic displacement parameters for hydrogen atoms

A simple combination of riding motion and an additive term is sufficient to estimate the temperature-dependent isotropic displacement parameters of hydrogen atoms, for use in X-ray structure refinements. The approach is validated against neutron diffraction data, and gives reasonable estimates in a very large temperature range (10–300 K). The model can be readily implemented in common structure refinement programs without auxiliary software.

Adaptive Estimation Using Multiagent Network Identifiers With Undirected and Directed Graph Topologies

In this paper, we present an adaptive estimation framework predicated on multiagent network identifiers with undirected and directed graph topologies. Specifically, the system state and plant parameters are identified online using N agents implementing adaptive observers with an interagent communication architecture. The adaptive observer architecture includes an additive term which involves a penalty on the mismatch between the state and parameter estimates. The proposed architecture is shown to guarantee state and parameter estimate consensus. Furthermore, the proposed adaptive identifier architecture provides a measure of agreement of the state and parameter estimates that is independent of the network topology and guarantees that the deviation from the mean estimate for both the state and parameter estimates converge to zero. Finally, an illustrative numerical example is provided to demonstrate the efficacy of the proposed approach.

Constant-optimized quantum circuits for modular multiplication and exponentiation

Reversible circuits for modular multiplication $Cx\%M$ with $x<M$ arise as components of modular exponentiation in Shor's quantum number-factoring algorithm. However, existing generic constructions focus on asymptotic gate count and circuit depth rather than actual values, producing fairly large circuits not optimized for specific $C$ and $M$ values. In this work, we develop such optimizations in a bottom-up fashion, starting with most convenient $C$ values. When zero-initialized ancilla registers are available, we reduce the search for compact circuits to a shortest-path problem. Some of our modular-multiplication circuits are asymptotically smaller than previous constructions, but worst-case bounds and average sizes remain $\Theta(n^2)$. In the context of modular exponentiation, we offer several constant-factor improvements, as well as an improvement by a constant additive term that is significant for few-qubit circuits arising in ongoing laboratory experiments with Shor's algorithm.

An Efficient Algorithm for Computing Hypervolume Contributions

The hypervolume indicator serves as a sorting criterion in many recent multi-objective evolutionary algorithms (MOEAs). Typical algorithms remove the solution with the smallest loss with respect to the dominated hypervolume from the population. We present a new algorithm which determines for a population of size n with d objectives, a solution with minimal hypervolume contribution in time [Formula: see text](nd/2 log n) for d > 2. This improves all previously published algorithms by a factor of n for all d > 3 and by a factor of [Formula: see text] for d = 3. We also analyze hypervolume indicator based optimization algorithms which remove λ > 1 solutions from a population of size n = μ + λ. We show that there are populations such that the hypervolume contribution of iteratively chosen λ solutions is much larger than the hypervolume contribution of an optimal set of λ solutions. Selecting the optimal set of λ solutions implies calculating [Formula: see text] conventional hypervolume contributions, which is considered to be computationally too expensive. We present the first hypervolume algorithm which directly calculates the contribution of every set of λ solutions. This gives an additive term of [Formula: see text] in the runtime of the calculation instead of a multiplicative factor of [Formula: see text]. More precisely, for a population of size n with d objectives, our algorithm can calculate a set of λ solutions with minimal hypervolume contribution in time [Formula: see text](nd/2 log n + nλ) for d > 2. This improves all previously published algorithms by a factor of nmin{λ,d/2} for d > 3 and by a factor of n for d = 3.

On the concept of model structural error

A consideration of model structural error leads to some particularly interesting tensions in the model calibration/conditioning process. In applying models we can usually only assess the total error on some output variable for which we have observations. This total error may arise due to input and boundary condition errors, model structural errors and error on the output observation itself (not only measurement error but also as a result of differences in meaning between what is modelled and what is measured). Statistical approaches to model uncertainty generally assume that the errors can be treated as an additive term on the (possibly transformed) model output. This allows for compensation of all the sources of error, as if the model predictions are correct and the total error can be treated as “measurement error.” Model structural error is not easily evaluated within this framework. An alternative approach to put more emphasis on model evaluation and rejection is suggested. It is recognised that model success or failure within this framework will depend heavily on an assessment of both input data errors (the “perfect” model will not produce acceptable results if driven with poor input data) and effective observation error (including a consideration of the meaning of observed variables relative to those predicted by a model).