Compact reduction in Lipschitz-free spaces

We prove a general principle satisfied by weakly precompact sets of Lipschitz-free spaces. By this principle, certain infinite dimensional phenomena in Lipschitz-free spaces over general metric spaces may be reduced to the same phenomena in free spaces over their compact subsets. As easy consequences we derive several new and some known results. The main new results are: $\mathcal {F}(X)$ is weakly sequentially complete for every superreflexive Banach space $X$, and $\mathcal {F}(M)$ has the Schur property and the approximation property for every scattered complete metric space $M$.

Football player dominant region determined by a novel model based on instantaneous kinematics variables

Dominant regions are defined as regions of the pitch where a player can reach before any other and are commonly determined without considering the free-spaces in the pitch. We presented an approach to football players’ dominant regions analysis, based on movement models created from players’ positions, displacement, velocity, and acceleration vectors. 109 Brazilian male professional football players were analysed during official matches, computing over 15 million positional data obtained by video-based tracking system. Movement models were created based on players’ instantaneous vectorial kinematics variables, then probabilities models and dominant regions were determined. Accuracy in determining dominant regions by the proposed model was tested for different time-lag windows. We calculated the areas of dominant, free-spaces, and Voronoi regions. Mean correct predictions of dominant region were 96.56%, 88.64%, and 72.31% for one, two, and three seconds, respectively. Dominant regions areas were lower than the ones computed by Voronoi, with median values of 73 and 171 m2, respectively. A median value of 5537 m2 was presented for free-space regions, representing a large part of the pitch. The proposed movement model proved to be more realistic, representing the match dynamics and can be a useful method to evaluate the players’ tactical behaviours during matches.

Enhancing Mechanical Properties of Various Sintered Pellets with Nano-Additives

The impact of Fe, Co, Ni nano-additives on the density, microhardness and bending strength was investigated for several sintered pellets. Fe, Co, Ni nanopowders (NP) were prepared in the size range 67-94 nm using chemical metallurgy techniques. These powders (0.5 wt. %) were dispersed into three sets of micron powders: Co (+0.5 wt. % Co NP); Fe (+0.5 wt. % Fe NP); Fe+0.5wt. % C (+0.5 wt. % Co and 0.5 wt. % Ni NP). Mixtures were further mixed and processed using a magnetic mill and a turbulent mixer. Sintering was carried out using spark plasma sintering (SPS) as well as pressureless sintering (PS). The densities of sintered pellets were found to increase by 2.5-3% (SPS) and 3-5% (PS) in the presence of nano-additives; corresponding increases in microhardness and bending strength were determined to be 7.9-11.1% and 17.9-38.7%, respectively. These results are discussed in terms enhanced packing due to interparticle sliding and the filling of free spaces with the nanodisperse phase.

Agoraphilic navigation algorithm in dynamic environment with obstacles motion tracking and prediction

This paper presents a new algorithm to navigate robots in dynamically cluttered environments. The proposed algorithm uses basic concepts of space attraction (hence the term Agoraphilic) to navigate robots through dynamic obstacles. The new algorithm in this paper is an advanced development of the original Agoraphilic navigation algorithm that was only able to navigate robots in static environments. The Agoraphilic algorithm does not look for obstacles (problems) to avoid but rather for a free space (solutions) to follow. Therefore, it is also described as an optimistic navigation algorithm. This algorithm uses only one attractive force created by the available free space. The free-space concept allows the Agoraphilic algorithm to overcome inherited challenges of general navigation algorithms. However, the original Agoraphilic algorithm has the limitation in navigating robots only in static, not in dynamic environments. The presented algorithm was developed to address this limitation of the original Agoraphilic algorithm. The new algorithm uses a developed object tracking module to identify the time-varying free spaces by tracking moving obstacles. The capacity of the algorithm was further strengthened by the new prediction module. Future space prediction allowed the algorithm to make decisions considering future growing/diminishing free spaces. This paper also includes a bench-marking study of the new algorithm compared with a recently published APF-based algorithm under a similar operating environment. Furthermore, the algorithm was validated based on experimental tests and simulation tests.

Enabling engagement: an exploration of accessibility planning from Berlin to Toronto

The Accessibility for Ontarians with Disabilities Act (AODA) is a landmark piece of legislation that removes both physical and social barriers faced by people with disabilities. This Act will make Ontario fully accessible to people with disabilities by 2025 through the development of accessibility standards, all while changing the perceptions of accessibility and people with disabilities. This research paper will explore accessibility planning in Toronto. Given that planners work in communicative roles, there is little direction in AODA that discuss engagement activities. Planners must utilize a mix of high- and low-tech methods when engaging with vulnerable communities, especially with people with disabilities. A case study of methods and planning policies in Berlin, Germany is presented to illustrate strong efforts in designing barrier-free spaces. Examples from Berlin will be then compared to Toronto’s efforts in addressing issues of accessibility and engagement with people with disabilities.