A probabilistic framework for next best view estimation in a cluttered environment

In this article, we present an information gain-based variant of the next best view problem for occluded environment. Our proposed method utilizes a belief model of the unobserved space to estimate the expected information gain of each possible viewpoint. More precise, this belief model allows a more precise estimation of the visibility of occluded space and with that a more accurate prediction of the potential information gain of new viewing positions. We present experimental evaluation on a robotic platform for active data acquisition, however due to the generality of our approach it also applies to a wide variety of 3D reconstruction problems. With the evaluation done in simulation and on a real robotic platform, exploring and acquiring data from different environments we demonstrate the generality and usefulness of our approach for next best view estimation and autonomous data acquisition.     

Low-energy points on the sphere and the real projective plane

We present a generalization of a family of points on ${\mathbb{S}}^2$, the Diamond ensemble, containing collections of N points on ${\mathbb{S}}^2$ with very small logarithmic energy for all $N\in \mathbb{N}$. We extend this construction to the real projective plane ${\mathbb{RP}}^2$ and we obtain upper and lower bounds with explicit constants for the Green and logarithmic energy on this last space.     

A Mixed Mann Iteration Process for Fixed Points of Mixed Increasing Operators in Ordered Banach Spaces

In this paper, we develop a new mixed Mann iteration process to approximate the fixed points of mixed increasing operators in ordered Banach spaces and discuss the convergence analysis of the iterative sequences generated by the iteration process. As an application, we develop a new iterative method for solving a class of nonlinear integral equations.     

Ratio-conjugation tool and its application in linear optimization models†

The ratio-conjugation-tool (RC) is constructed systematically, and its applicability for analysis of economic models is demonstrated. One of the main results establishes a general formula for RC of aggregative function. This tool is applied to the analysis of linear economic dynamics models of Neumann–Gale type which can be solved by a dynamic programming method: for each direct problem we construct the corresponding dual RC-problem. Moreover, we consider three examples of the most important economic dynamics models and look at these now from a unified general position.     

Derivation of invariant varieties of periodic points from singularity confinement in the case of Toda map

We have shown in [1] that the invariant varieties of periodic points (IVPP) of all periods of some higher dimensional rational maps can be derived, iteratively, from the singularity confinement (SC). We generalize this algorithm, in this paper, to apply to any birational map, which has more invariants than the half of the dimension.     

Double‐crosslinked reversible redox‐responsive hydrogels based on disulfide–thiol interchange

We present novel redox‐responsive hydrogels based on poly(N‐isopropylacrylamide) or poly(acrylamide), consisting of a reversible disulfide crosslinking agent N,N′‐bis(acryloyl)cystamine and a permanent crosslinking agent N,N′‐methylenebisacrylamide for microfluidic applications. The mechanism of swelling/deswelling behavior starts with the cleavage and reformation of disulfide bonds, leading to a change of crosslinking density and crosslinking points. Raman and ultraviolet‐visible spectroscopy confirm that conversion efficiency of thiol–disulfide interchange up to 99%. Rheological analysis reveals that the E modulus of hydrogel is dependent on the crosslinking density and can be repeatedly manipulated between high‐ and low‐stiffness states over at least 5 cycles without significant decrease. Kinetic studies showed that the mechanical strength of the gels changes as the redox reaction proceeds. This process is much faster than the autonomous diffusion in the hydrogel. Moreover, cooperative diffusion coefficient (D_coop) indicates that the swelling process of the hydrogel is affected by the reduction reaction. Finally, this reversibly switchable redox behavior of bulky hydrogel could be proven in microstructured hydrogel dots through short‐term photopatterning process. These hydrogel dots on glass substrates also showed the desired short response time on cyclic swelling and shrinking processes known from downsized hydrogel shapes. Such stimuli‐responsive hydrogels with redox‐sensitive crosslinkers open a new pathway in exchanging analytes for sensing and separating in microfluidics applications. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2590–2601     

Explicit maximal and minimal curves over finite fields of odd characteristics

In this work we present explicit classes of maximal and minimal Artin–Schreier type curves over finite fields having odd characteristics. Our results include the proof of Conjecture 5.9 given in [1] as a very special subcase. We use some techniques developed in [2], which were not used in [1].