First-order Approach Research Articles

ASPeRiX, a first-order forward chaining approach for answer set computing

AbstractThe natural way to use Answer Set Programming (ASP) to represent knowledge in Artificial Intelligence or to solve a combinatorial problem is to elaborate a first-order logic program with default negation. In a preliminary step, this program with variables is translated in an equivalent propositional one by a first tool: the grounder. Then, the propositional program is given to a second tool: the solver. This last one computes (if they exist) one or many answer sets (stable models) of the program, each answer set encoding one solution of the initial problem. Until today, almost all ASP systems apply this two steps computation. In this article, the projectASPeRiX. is presented as a first-order forward chaining approach for Answer Set Computing. This project was among the first to introduce an approach of answer set computing that escapes the preliminary phase of rule instantiation by integrating it in the search process. The methodology applies a forward chaining of first-order rules that are grounded on the fly by means of previously produced atoms. Theoretical foundations of the approach are presented, the main algorithms of the ASP solverASPeRiX. are detailed and some experiments and comparisons with existing systems are provided.

Moral hazard and the spanning condition without the first-order approach

The “spanning condition” describes a situation where the agent's effort determines the weights placed on two distinct technologies. Sufficient conditions are known under which the first-order approach (FOA) is valid when the spanning condition holds. In this paper, a complete solution to the problem is provided. Thus, the problem is solved even when the FOA is not valid. The solution has two main steps. The first step fully characterizes the set of implementable actions. The second step establishes that the optimal contract can be found by applying the FOA to the newly identified set of feasible actions. This procedure correctly solves a famous counterexample due to Mirrlees in which the standard FOA is not valid. A much simpler and economically more compelling counterexample is provided. Moreover, the model provides a tractable environment in which it is possible to study comparative statics even when the FOA is not justified.

A unifying approach to incentive compatibility in moral hazard problems

A new approach to moral hazard is presented. Once local incentive compatibility is satisfied, the problem of verifying global incentive compatibility is shown to be isomorphic to the problem of comparing two classes of distribution functions. Thus, tools from choice under uncertainty can be brought to bear on the problem. The approach allows classic justifications of the first-order approach (FOA) to be proven using the same unifying methodology. However, the approach is especially useful for analyzing higher-dimensional moral hazard problems. New and more tractable multi-signal justifications of the FOA are derived and implications for optimal monitoring are examined. The approach yields justifications of the FOA in certain settings where the action is multidimensional, as in the case when the agent is multitasking. Finally, a tractable multitasking model with richer predictions than the popular but simple linear-exponential-normal model is presented.

An Adaptive and Time-Efficient ECG R-Peak Detection Algorithm.

R-peak detection is crucial in electrocardiogram (ECG) signal analysis. This study proposed an adaptive and time-efficient R-peak detection algorithm for ECG processing. First, wavelet multiresolution analysis was applied to enhance the ECG signal representation. Then, ECG was mirrored to convert large negative R-peaks to positive ones. After that, local maximums were calculated by the first-order forward differential approach and were truncated by the amplitude and time interval thresholds to locate the R-peaks. The algorithm performances, including detection accuracy and time consumption, were tested on the MIT-BIH arrhythmia database and the QT database. Experimental results showed that the proposed algorithm achieved mean sensitivity of 99.39%, positive predictivity of 99.49%, and accuracy of 98.89% on the MIT-BIH arrhythmia database and 99.83%, 99.90%, and 99.73%, respectively, on the QT database. By processing one ECG record, the mean time consumptions were 0.872 s and 0.763 s for the MIT-BIH arrhythmia database and QT database, respectively, yielding 30.6% and 32.9% of time reduction compared to the traditional Pan-Tompkins method.

Mixed boundary value problems on cylindrical domains

We study second-order divergence-form systems on half-infinite cylindrical domains with a bounded and possibly rough base, subject to homogeneous mixed boundary conditions on the lateral boundary and square integrable Dirichlet, Neumann, or regularity data on the cylinder base. Assuming that the coefficients $A$ are close to coefficients $A_0$ that are independent of the unbounded direction with respect to the modified Carleson norm of Dahlberg, we prove a priori estimates and establish well-posedness if $A_0$ has a special structure. We obtain a complete characterization of weak solutions whose gradient either has an $L^2$-bounded non-tangential maximal function or satisfies a Lusin area bound. To this end, we combine the first-order approach to elliptic systems with the Kato square root estimate for operators with mixed boundary conditions.

An inertial proximal Peaceman-Rachford splitting method

The strictly contractive Peaceman-Rachford splitting method (SC-PRSM) is a very efficient first-order approach for linearly constrained separable convex optimization problems, and its convergence rate is faster than that of ADMM. Recently, a semi-proximal Peaceman-Rachford splitting method was proposed to modify SC-PRSM by introducing semi-proximal terms to the subproblems. In this paper, motivated by the idea of the inertial proximal ADMM, we improve the semi-proximal Peaceman-Rachford splitting method by employing an inertial technique to accelerate its convergence, i.e., at each iteration the semi-proximal Peaceman-Rachford splitting method is applied to a point extrapolated at the current iterate in the direction of last movement. The proposed algorithmic framework is very general so that SC-PRSM and semi-proximal Peaceman-Rachford splitting methods are covered as special cases. Based on the asymptotic feasibility of the iterative sequence and the convergence of the function values, we establish the convergence of the whole sequence generated by the proposed algorithm under very mild assumptions. We demonstrate the efficiency of the inertial extrapolation step via experimental results on least squares semi-definite programming problems and total variation based medical image reconstruction problems.

Quantifying risk to agriculture from volcanic ashfall: a case study from the Bay of Plenty, New Zealand

Quantitatively assessing long-term volcanic risk can be challenging due to the many variables associated with volcanic hazard and vulnerability. This study presents a structured first-order approach for considering variables in hazard and vulnerability analyses, such as eruption style and cyclic fragility, in order to quantitatively estimate risk. Probabilistic volcanic hazard data derived from advection–diffusion–sedimentation tephra fall model TEPHRA2 and probabilistic volcanic hazard analysis tool BET_VH (Bayesian Event Tree for Volcanic Hazards) are combined with fragility functions and seasonal vulnerability coefficients for agricultural production to calculate volcanic risk indices which represent the likelihood of damage or loss to farm production over a given time frame. The resulting dataset allows for approximations of quantitative risk over a continuous range of ash thickness thresholds, at multiple levels of uncertainty, and in the context of fluctuating hazard and vulnerability environments (e.g., seasonal wind patterns and crop phases). We illustrate this approach through a case study which evaluates the risk of incurring 90% damage to agricultural production at dairy and fruit farms in the Bay of Plenty region of New Zealand (BoP) due to ashfall from a Plinian eruption phase at the large local caldera volcano, the Okataina Volcanic Centre (OVC). Consideration of seasonal wind profiles, seasonal fluctuations in fruit and dairy farm vulnerability, multiple possible OVC eruption styles, different possible OVC vent locations, and a continuous distribution of ash thickness and damage thresholds enables a multi-dimensional analysis that aims to reflect the natural complexity and interdependencies associated with volcanic risk. A risk uncertainty matrix is introduced as a conceptual scheme to help guide evaluation and communication of the results of such quantitative risk analyses by showing how different types of uncertainty can yield “maximum”, “average”, or “minimum” estimates of risk. Results of this case study indicate that BoP fruit farms are at higher risk of experiencing damage and production loss from OVC ashfall than dairy farms, and farms to the east of the OVC are typically at higher risk than farms to the north of the OVC. Forecasts based on the annual maximum estimate of risk for fruit farms show a regional average of 2.3% probability (greater than 1 in 50 likelihood) of experiencing 90% damage from a basaltic or rhyolitic Plinian eruption from anywhere within the OVC over a period of 100 years. Seasonal-level analyses revealed that the risk of experiencing losses due to OVC ashfall at fruit farms is cyclic and fluctuates with time of year and harvest season, with the highest risk experienced during peak harvest season (15 October–14 April) when crop vulnerability is high and westerly winds dominate in the BoP.

A single-level reformulation of mixed integer bilevel programming problems

This paper focuses on the single-level reformulation of mixed integer bilevel programming problems (MIBLPP). Due to the existence of lower-level integer variables, the popular approaches in the literature such as the first-order approach are not applicable to the MIBLPP. In this paper, we reformulate the MIBLPP as a mixed integer mathematical program with complementarity constraints (MIMPCC) by separating the lower-level continuous and integer variables. In particular, we show that global and local minimizers of the MIBLPP correspond to those of the MIMPCC respectively under suitable conditions.

Confinement effects on the electron transfer cross section: a study of He2+ colliding on atomic H

In this work, the role of pressure produced by the surrounding conditions of neighboring atoms on the charge transfer cross section in the interaction of ions with atoms is studied. The effect of pressure on the target is simulated by a spherical confinement cavity model with the target atom at its center. The electron transfer probability is obtained by a time-dependent solution to the Schrödinger equation by means of a finite-difference approach and the Crank–Nicolson propagation method. Results are presented for the benchmark system HeH() under different confinement conditions. Within this first-order approach to pressure effects, it is found that the radial region of the electron capture probability is affected by the cavity, meanwhile the rotational part of the interaction is only slightly modified. Furthermore, Stückelberg oscillations are preserved as a function of the impact parameter and only its intensity is reduced with a slight shift towards low impact parameters as pressure is increased. The pressure effect is larger when the electron interaction on the target is restricted to within the cavity than when it acts also outside the cavity. In addition, the larger the pressure, the smaller the electron capture cross section. The numerical results are interpreted by an analytic two-state model that supports the numerical findings.

Robust tensor decomposition based on Cauchy distribution and its applications

Tensor analysis has reached a celebrity status in the areas of machine learning, computer vision, and artificial intelligence. Completing and recovering tensor is an important problem for tensor analysis. It involves recovering a tensor from either a subset of its entries or the whole entries contaminated by noise. Classical tensor completion/recovery methods are based mainly on l2-norm (Gaussian distribution noise) models, and are sensitive to noise of large magnitude. While l1-norm (Laplacian distribution noise) based methods are robust to noise of large magnitude, they do not deal with dense noise effectively. In this paper, we present a novel Cauchy tensor decomposition method for simultaneously recovering and completing a low rank tensor with both missing data and complex noise. We utilize the Cauchy distribution to model noise and derive the objective function of Cauchy tensor decomposition under the maximum likelihood estimation (MLE) framework. Then we developed a robust tensor decomposition framework that used first-order optimization approaches to optimize the objective function. Extensive numerical experiments are conducted and show that our method is able to successfully recover and complete tensors with large/dense noise and missing data. We further demonstrate the usefulness of Cauchy tensor decomposition on three real-world applications, image inpainting, traffic data process and foreground/background separation. The experimental results show that the method is applicable to a wide range of problems.

Two Conformers of N,N-Diethylpropionamide As Observed by Microwave Spectroscopy and Quantum Chemistry.

The microwave spectra of two conformers of N,N-diethylpropionamide were recorded using a molecular beam Fourier transform microwave spectrometer operating in the frequency range 2-26.5 GHz. Hyperfine splittings arising from the (14)N quadrupole coupling effect were observed and analyzed. Fits using a rigid rotor model with centrifugal distortion correction and first-order perturbation approach for the quadrupole coupling yielded highly accurate molecular parameters and standard deviations within the measurement accuracy for both conformers. Complementary quantum chemical calculations were carried out for a conformational analysis, theoretical values of the spectroscopic constants, and the (14)N nuclear quadrupole coupling constants.

A fast first-order optimization approach to elastoplastic analysis of skeletal structures

It is classical that, when the small deformation is assumed, the incremental analysis problem of an elastoplastic structure with a piecewise-linear yield condition and a linear strain hardening model can be formulated as a convex quadratic programming problem. Alternatively, this paper presents a different formulation, an unconstrained nonsmooth convex optimization problem, and proposes to solve it with an accelerated gradient-like method. Specifically, we adopt an accelerated proximal gradient method, that has been developed for a regularized least squares problem. Numerical experiments show that the presented algorithm is effective for large-scale elastoplastic analysis. Also, a simple warm-start strategy can speed up the algorithm when the path-dependent incremental analysis is carried out.

Phase angle calculation dynamics of type‐4 wind turbines in rms simulations during severe voltage dips

To conduct power system simulations with high shares of wind energy, standard wind turbine models, which are aimed to be generic rms models for a wide range of wind turbine types, have been developed. As a common practice of rms simulations, the power electronic interface of wind turbines is assumed to be ideally synchronised, i.e. grid synchronisation (e.g. phase locked loop (PLL)) is not included in simplified wind turbine models. As will be shown in this study, this practice causes simulation convergence problems during severe voltage dips and when the loss of synchronism occurs. In order to provide the simulation convergence without adding complexity to the generic models, a first-order filtering approach is proposed as a phase angle calculation algorithm in the grid synchronisation of the rms type-4 wind turbine models. The proposed approach provides robustness for the simulation of large-scale power systems with high shares of wind energy.

Colloid-Associated Groundwater Contaminant Transport in Homogeneous Saturated Porous Media: Mathematical and Numerical Modeling

During the past two decades, significant efforts have been made to study contaminant transport in the presence of colloids. Several researchers reported that colloidal particles could enhance the migration of contaminants in groundwater by reducing retardation factor. When the colloidal particles are present in the aquifer, the subsurface system can be considered as a three-phase system with two solid phases and an aqueous phase. The interaction between contaminants, colloids, and solid matrix should be considered in assessing the fate and transport of the contaminant in the groundwater flow system. In this study, a one-dimensional numerical model is developed by employing a fully implicit finite difference method. This model is based on mass balance equations and mass partition mechanisms between the carriers and solid matrix, as well as between the carriers and contaminants in a saturated homogeneous porous medium. This phenomenon is presented by two approaches: equilibrium approach and fully kinetic first-order approach. The formulation of the model can be simplified by employing equilibrium partitioning of particles. However, contaminant transport can be predicted more accurately in realistic situations by kinetic modeling. To test the sensitivity of the model, the effect of the various chemical and physical coefficients on the migration of contaminant was investigated. The results of numerical modeling matched favorably with experimental data reported in the literature.

A first-order hyperbolic system approach for dispersion

We propose a new first-order hyperbolic system approach for dispersive partial differential equations.We apply a compact 4th-order RD scheme, and solve time dependent dispersive PDEs.We demonstrate the performance of the high-order RD schemes on the proposed hyperbolic system, including dispersive shock cases.We verify that the predicted solution, its gradient and Hessian have the same order of accuracy on randomly distributed nodes.

Linking microbial immobilization of fertilizer nitrogen to in situ turnover of soil microbial residues in an agro-ecosystem

Understanding long-term microbial immobilization of nitrogen (N) fertilizer is essential for N management in agricultural soils. Evaluating the transformation and accumulation of N fertilizer into microbial residues is critical for developing such an understanding due to the requirement of time-integrated biomarkers and a 15N-labeling technique. By tracing the dynamics of amino sugars derived from annually applied fertilizer over 8 years, we investigated the influence of continuous maize residue mulching on the temporal immobilization of fertilizer N in an agricultural soil and quantified the turnover of microbial residues in situ. We found that the amino sugar transformation rate from fertilizer N was constant over time in both fertilization-only and maize residue mulching managements, but it was significantly higher in the upper cultivation layer (0–10cm) after maize residue mulching. Mulching with maize residue facilitated initial fertilizer N transformation, while the subsequent 7-year application maintained the increased transformation rate. Consequently, the accumulation of fertilizer-derived amino sugars increased linearly in both managements within the 8 years of our field experiment. The mean residence time (MRT) of soil amino sugar-N was estimated by using extrapolation and first-order kinetics approaches, respectively. The calculated MRT of amino sugar-N using first-order kinetics (78 and 154 years at 0–10 and 10–20cm, respectively) was slightly shorter than that estimated by the extrapolation (89 and 165 years at 0–10 and 10–20cm, respectively) in the fertilization-only management. Mulching with maize residue did not change the MRT of amino sugar-N because maize residue addition enhanced the immobilization of maize residue-derived N or the transformation of indigenous soil N in addition to those of fertilizer N, leading to the same proportion of new N assimilated in microbial residues.

Absorption of twisted light by a mesoscopic atomic target

The excitation of a hydrogen-atom target by a twisted Bessel light beam is investigated. The atoms are assumed to have a Gaussian spatial distribution in the target. Theoretical analysis is performed within a nonrelativistic framework using a first-order perturbation approach and density matrix formalism. By using this theory, we derive the expressions for excitation cross sections and for alignment parameters of the excited atomic state. In particular, we make calculations for the transition caused by the interaction of Bessel beams with the atomic target. For this transition, we analyze the population of magnetic sublevels for the excited state and study how it is affected by the projection of the total angular momentum of incident light. The calculations indicate that the projection of the total angular momentum of the incident Bessel beam affects the alignment of atoms for sufficiently small targets with size less than 200 nm. This can be observed experimentally by measuring the linear polarization of the subsequent fluorescent light.

From dwindling ice to headwater lakes: could dams replace glaciers in the European Alps?

The potential exploitation of areas becoming ice-free in response to ongoing climate change has rarely been addressed, although it could be of interest from the water management perspective. Here we present an estimate for the potential of mitigating projected changes in seasonal water availability from melting glaciers by managing runoff through reservoirs. For the European Alps we estimate that by the end of the century, such a strategy could offset up to 65% of the expected summer-runoff changes from presently glacierized surfaces. A first-order approach suggests that the retention volume potentially available in the areas becoming deglacierized is in excess of the volume required for achieving the maximal possible mitigation by more than one order of magnitude. Obviously, however, such a strategy cannot compensate for the reduction in annual runoff caused by glacier ice depletion. Our estimates indicate that by 2070–2099, 0.73 ± 0.67 km3 a−1 of this non-renewable component of the water cycle could be missing in Alpine water supplies.

Uniform vs Differential Excise Taxes Under the Second-Order Approach

This paper solves the lack of a monotonicity constraint in optimal taxation models describing second-order conditions for incentive compatibility. We conclude that most findings obtained under the first-order approach, and among them notably Mirrlees’s results on Pareto efficient taxation and Corlett and Hague’s tax rule, may no longer hold beyond the assumption that the gradient of the utility function is affine with respect to ability. This reduces the desirability of differential excise taxes to a special case, while providing an argument for uniform excise taxes since, for the derivation under the second-order approach of the Atkinson and Stiglitz theorem, no further assumption is needed other than the usual weak separability of preferences.

Distance computation of ontology vector for ontology similarity measuring and ontology mapping

In recent years, various kinds of learning techniques are applied in ontology similarity measuring and ontology mapping algorithms. The essence of these learning tricks is attributed to obtaining obtain a score function which is employed for calculating the similarity between vertices. Since each vertex’s related information is denoted as a p dimensional vector, the similarity between ontology vertices is equivalent to determine the distance between their correspond vectors in the high dimensional space. In this paper, we raise a new ontology learning algorithm for ontology similarity measuring and ontology mapping by means of distance computation for ontology vectors. The optimal ontology distance function is learned in terms of regularization and first-order approaches. Then, two experiments using two different kinds of ontology convex function are presented. The result data show the effectiveness of our new ontology learning algorithm in special engineering applications.