Online Relaxation Refinement for Satisficing Planning: On Partial Delete Relaxation, Complete Hill-Climbing, and Novelty Pruning

In classical AI planning, heuristic functions typically base their estimates on a relaxation of the input task. Such relaxations can be more or less precise, and many heuristic functions have a refinement procedure that can be iteratively applied until the desired degree of precision is reached. Traditionally, such refinement is performed offline to instantiate the heuristic for the search. However, a natural idea is to perform such refinement online instead, in situations where the heuristic is not sufficiently accurate. We introduce several online-refinement search algorithms, based on hill-climbing and greedy best-first search. Our hill-climbing algorithms perform a bounded lookahead, proceeding to a state with lower heuristic value than the root state of the lookahead if such a state exists, or refining the heuristic otherwise to remove such a local minimum from the search space surface. These algorithms are complete if the refinement procedure satisfies a suitable convergence property. We transfer the idea of bounded lookaheads to greedy best-first search with a lightweight lookahead after each expansion, serving both as a method to boost search progress and to detect when the heuristic is inaccurate, identifying an opportunity for online refinement. We evaluate our algorithms with the partial delete relaxation heuristic hCFF, which can be refined by treating additional conjunctions of facts as atomic, and whose refinement operation satisfies the convergence property required for completeness. On both the IPC domains as well as on the recently published Autoscale benchmarks, our online-refinement search algorithms significantly beat state-of-the-art satisficing planners, and are competitive even with complex portfolios.

Modeling a unit cell: crystallographic refinement procedure using the biomolecular MD simulation platform Amber

A procedure has been developed for the refinement of crystallographic protein structures based on the biomolecular simulation program Amber. The procedure constructs a model representing a crystal unit cell, which generally contains multiple protein molecules and is fully hydrated with TIP3P water. Periodic boundary conditions are applied to the cell in order to emulate the crystal lattice. The refinement is conducted in the form of a specially designed short molecular-dynamics run controlled by the Amber ff14SB force field and the maximum-likelihood potential that encodes the structure-factor-based restraints. The new Amber-based refinement procedure has been tested on a set of 84 protein structures. In most cases, the new procedure led to appreciably lower R free values compared with those reported in the original PDB depositions or obtained by means of the industry-standard phenix.refine program. In particular, the new method has the edge in refining low-accuracy scrambled models. It has also been successful in refining a number of molecular-replacement models, including one with an r.m.s.d. of 2.15 Å. In addition, Amber-refined structures consistently show superior MolProbity scores. The new approach offers a highly realistic representation of protein–protein interactions in the crystal, as well as of protein–water interactions. It also offers a realistic representation of protein crystal dynamics (akin to ensemble-refinement schemes). Importantly, the method fully utilizes the information from the available diffraction data, while relying on state-of-the-art molecular-dynamics modeling to assist with those elements of the structure that do not diffract well (for example mobile loops or side chains). Finally, it should be noted that the protocol employs no tunable parameters, and the calculations can be conducted in a matter of several hours on desktop computers equipped with graphical processing units or using a designated web service.

Recommended X-ray single-crystal structure refinement and Rietveld refinement procedure for tremolite

A detailed description of the structure of the amphibole-supergroup minerals is very challenging owing to their complex chemical composition that renders the process of cation partition extremely difficult, particularly because of the occurrence of multivalent elements. Since amphiboles naturally occur under a fibrous morphology and have largely been used to produce asbestos, there is a growing demand for detailed and accurate structural data in order to study the relationships between structure, composition and toxicity. The present study proposes a recommended refinement procedure for both X-ray single-crystal structure refinement (SREF) and Rietveld analysis for tremolite, selected as a test case. The corresponding structural results are compared to estimate the `degree of confidence' of the Rietveld refinement with regard to SREF. In particular, it is shown that the interpretation of the electron density of the tremolite structure by SREF is model dependent. By assuming that the site-scattering values from SREF should be as close as possible to those from electron microprobe analysis, as a crucial constraint for the correct description of the final crystal-chemical model, it is found that it is best satisfied by using partially ionized scattering curves (SCs) for O and Si, and neutral SCs (neutral oxygen curves or NOCs) for other atoms. This combination leads to the best fit to the diffraction data. Moreover, it is found that Rietveld refinement using NOCs produces the best structural results, in excellent agreement with SREF. It is worth noting that, due to the complexity of the diffraction pattern and the fairly large number of freely refinable parameters, refinements with different combinations of SCs produce results almost indistinguishable from a statistical point of view, albeit showing significant differences from a structural point of view.

On refinement strategies for solving $${\textsc {MINLP}\mathrm{s}}$$ by piecewise linear relaxations: a generalized red refinement

We investigate the generalized red refinement for n-dimensional simplices that dates back to Freudenthal (Ann Math 43(3):580–582, 1942) in a mixed-integer nonlinear program ($${\textsc {MINLP}}$$ MINLP ) context. We show that the red refinement meets sufficient convergence conditions for a known $${\textsc {MINLP}}$$ MINLP solution framework that is essentially based on solving piecewise linear relaxations. In addition, we prove that applying this refinement procedure results in piecewise linear relaxations that can be modeled by the well-known incremental method established by Markowitz and Manne (Econometrica 25(1):84–110, 1957). Finally, numerical results from the field of alternating current optimal power flow demonstrate the applicability of the red refinement in such $${\textsc {MIP}}$$ MIP -based $${\textsc {MINLP}}$$ MINLP solution frameworks.

Robust Extrinsic Calibration of Multiple RGB-D Cameras with Body Tracking and Feature Matching

RGB-D cameras have been commercialized, and many applications using them have been proposed. In this paper, we propose a robust registration method of multiple RGB-D cameras. We use a human body tracking system provided by Azure Kinect SDK to estimate a coarse global registration between cameras. As this coarse global registration has some error, we refine it using feature matching. However, the matched feature pairs include mismatches, hindering good performance. Therefore, we propose a registration refinement procedure that removes these mismatches and uses the global registration. In an experiment, the ratio of inliers among the matched features is greater than 95% for all tested feature matchers. Thus, we experimentally confirm that mismatches can be eliminated via the proposed method even in difficult situations and that a more precise global registration of RGB-D cameras can be obtained.

Wastewater Treatment using Magnetic Nanoparticles and Nanocomposites

The application of magnetic nano-photocatalysts in clean water technologies, has been widely studied due to their improved chemical and physical properties. Due to the incorporation of magnetic materials into the nano-photocatalysts, the separation of the resultant nanocomposite can be facilitated via an applied external magnetic field, leading to more economic and also more ecologically friendly water refinement procedure. This paper presents a short review of magnetic nanomaterials in the purification of contaminated water/wastewater.

A Three-valued Approach to Strategic Abilities under Imperfect Information

A major challenge for logics for strategies is represented by their verification in contexts of imperfect information. In this contribution we advance the state of the art by approximating the verification of Alternating-time Temporal Logic (ATL) under imperfect information by using perfect information and a three-valued semantics. In particular, we develop novel automata-theoretic techniques for the linear-time logic LTL, then apply these to finding “failure” states, where the ATL specification to be model checked is undefined. Such failure states can then be fed into a refinement procedure, thus providing a sound, albeit incomplete, verification procedure.

A Computational Method for Subdivision Depth of Ternary Schemes

Subdivision schemes are extensively used in scientific and practical applications to produce continuous shapes in an iterative way. This paper introduces a framework to compute subdivision depths of ternary schemes. We first use subdivision algorithm in terms of convolution to compute the error bounds between two successive polygons produced by refinement procedure of subdivision schemes. Then, a formula for computing bound between the polygon at k-th stage and the limiting polygon is derived. After that, we predict numerically the number of subdivision steps (depths) required for smooth limiting shape based on the demand of user specified error (distance) tolerance. In addition, extensive numerical experiments were carried out to check the numerical outcomes of this new framework. The proposed methods are more efficient than the method proposed by Song et al.

Distinguishing space groups by electron channelling: centrosymmetric full-Heusler or non-centrosymmetric half-Heusler?

X-ray emission under electron-channelling conditions is used to distinguish between a non-centrosymmetric half-Heusler and a centrosymmetric full-Heusler crystal. For TiCo1.5+x Sn the space-group determination based on a Rietveld refinement procedure became challenging for increasing Co content (x > 0.2), while electron channelling proved successful for higher Co content (x = 0.35). This technique can be used on crystals as small as (10 nm)3.