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In the process of items delivery, the map of the destination locations is represented as a network. The network is used to facilitate vehicles for items delivery. This paper provides an overview of the importance of the clustering method in items delivery optimization. The simulation compares the minimum distance between items delivery using the clustering method and the classic method. The results show that optimization using the clustering method has the total minimum distance.

Morphology and functional aspects of the tool have been proposed to be critical factors modulating tool use-induced plasticity. However, how these aspects contribute to changing body representation has been underinvestigated. In the arm bisection task, participants have to estimate the length of their own arm by indicating its midpoint, a paradigm used to investigate the representation of the metric properties of the body. We employed this paradigm to investigate the impact of different actions onto tool embodiment. Our findings suggest that a training requiring actions mostly with proximal (shoulder) or distal (wrist) parts induces a different shift in the perceived arm midpoint. This effect is independent of, but enhanced by, the use of the tool during the training and in part influenced by specific demands of the task. These results suggest that specific motor patterns required by the training can induce different changes of body representation, calling for rethinking the concept of tool embodiment, which would be characterized not simply by the morphology of the tools, but also by the actions required for their specific use.

Alertness, or one’s general readiness to respond to stimulation, has previously been shown to affect spatial attention. However, most of this previous research focused on speeded, laboratory-based reaction tasks, as opposed to the classical line bisection task typically used to diagnose deficits of spatial attention in clinical settings. McIntosh et al. (Cogn Brain Res 25:833–850, 2005) provide a form of line bisection task which they argue can more sensitively assess spatial attention. Ninety-eight participants were presented with this line bisection task, once with and once without spatial cues, and both before and after a 50-min vigilance task that aimed to decrease alertness. A single participant was excluded due to potentially inconsistent behaviour in the task, leaving 97 participants for the full analyses. While participants were, on a group level, less alert after the 50-min vigilance task, they showed none of the hypothesised effects of reduced alertness on spatial attention in the line bisection task, regardless of with or without spatial cues. Yet, they did show the proposed effect of decreased alertness leading to a lower level of general attention. This suggests that alertness has no effect on spatial attention, as measured by a line bisection task, in neurotypical participants. We thus conclude that, in neurotypical participants, the effect of alertness on spatial attention can be examined more sensitively with tasks requiring a speeded response compared to unspeeded tasks.

Despite having relatively accurate timing, subjective time can be influenced by various contexts, such as stimulus spacing and sample frequency. Several electroencephalographic (EEG) components have been associated with timing, including the contingent negative variation (CNV), offset P2, and late positive component of timing (LPCt). However, the specific role of these components in the contextual modulation of perceived time remains unclear. In this study, we conducted two temporal bisection experiments to investigate this issue. Participants had to judge whether a test duration was close to a short or long standard. Unbeknownst to them, we manipulated the stimulus spacing (Experiment 1) and sample frequency (Experiment 2) to create short and long contexts while maintaining consistent test ranges and standards across different sessions. The results revealed that the bisection threshold shifted towards the ensemble mean, and both CNV and LPCt were sensitive to context modulation. In the short context, the CNV exhibited an increased climbing rate compared to the long context, whereas the LPCt displayed reduced amplitude and latency. These findings suggest that the CNV represents an expectancy wave preceding a temporal decision process, while the LPCt reflects the decision-making process itself, with both components influenced by the temporal context.

Major evidence for a right-hemisphere dominance of the brain in spatial and/or attentional tasks comes from lesion studies in patients with spatial neglect. However, the neuroanatomy of the different forms of neglect remains a matter of debate, and it remains unclear how dysfunctions in neglect relate to intact processes. In the healthy brain, perceptual pseudoneglect has been considered to be a phenomenon complementary to specific subtypes of neglect as observed in paradigms such as the line bisection task. Therefore, the current study investigated the intact functional anatomy of perceptual pseudoneglect using a meta-analysis to compensate for some of the limitations of individual imaging studies. We collated the data from 24 articles that tested 952 participants with a range of paradigms (landmark task, line bisection, grating-scales task, and number line task) obtaining 337 foci. Using Activation Likelihood Estimation (ALE) we identified a right-hemisphere biased network of cortical areas, including superior and intraparietal regions, the intraoccipital sulcus together with other occipital regions, as well as inferior frontal areas that were associated with perceptual pseudoneglect in partial agreement with lesion studies in patients with neglect. Our study is the first meta-analysis on the mechanisms underlying perceptual judgments which have been shown to give rise to perceptual pseudoneglect.

In many Western cultures, the processing of temporal words related to the past and to the future is associated with left and right space, respectively – a phenomenon known as the horizontal Mental Time Line (MTL). While this mapping is apparently quite ubiquitous, its regularity and consistency across different types of temporal concepts remain to be determined. Moreover, it is unclear whether such spatial mappings are an essential and early constituent of concept activation. In the present study, we used words denoting time units at different scales (hours of the day, days of the week, months of the year) associated with either left space (e.g., 9 a.m. , Monday , February ) or right space (e.g., 8 p.m. , Saturday , November ) as cues in a line bisection task. Fifty-seven healthy adults listened to temporal words and then moved a mouse cursor to the perceived midpoint of a horizontally presented line. We measured movement trajectories, initial line intersection coordinates, and final bisection response coordinates. We found movement trajectory displacements for left- vs. right-biasing hour and day cues. Initial line intersections were biased specifically by month cues, while final bisection responses were biased specifically by hour cues. Our findings offer general support to the notion of horizontal space-time associations and suggest further investigation of the exact chronometry and strength of this association across individual time units.

Several studies have shown that space immediately surrounding the body, or the peripersonal space is represented differently in the brain from the more distant extra-personal space. Moreover, the boundary of peripersonal space can be extended to space surrounding the tip of a tool held by the hand. However, it is not known if tools need to be connected to the body to modulate the peripersonal space. We used a line bisection task to investigate whether peripersonal space representation surrounds a virtual hand avatar that is disconnected from the body. Healthy participants conducted a line bisection task by responding with either a virtual hand avatar or a laser pointer. The to-be-bisected lines were presented either in peripersonal or extra-personal space. When the lines were placed in extra-personal space, the virtual hand avatar was presented near the line such that the hand avatar was far from participants and disconnected from their bodies. Results indicated a shift in the line bisection bias from the left to the right as the line presentation distance increased when using the laser pointer, whereas no shift in bias was observed when using the virtual hand avatar. This result indicates that objects resembling human hands presented even at a distance and disconnected from the body can be integrated into the peripersonal space, which suggests that peripersonal space representation is more flexible than previously reported.

For Erdős-Rényi random graphs with average degree γ, and uniformly random γ-regular graph on n vertices, we prove that with high probability the size of both the Max-Cut and maximum bisection are $n\\left( {\\frac{\\gamma }{4} + P * \\sqrt {\\frac{\\gamma }{4}} + o\\left( {\\sqrt \\gamma } \\right)} \\right) + o\\left( n \\right)$ while the size of the minimum bisection is $n\\left( {\\frac{\\gamma }{4} - P * \\sqrt {\\frac{\\gamma }{4}} + o\\left( {\\sqrt \\gamma } \\right)} \\right) + o\\left( n \\right)$. Our derivation relates the free energy of the anti-ferromagnetic Ising model on such graphs to that of the Sherrington-Kirkpatrick model, with P*≈0.7632 standing for the ground state energy of the latter, expressed analytically via Parisi's formula.

Previous studies have found reduced leftward bias of facial processing in individuals with Autism Spectrum Disorder (ASD). However, it is not clear whether they manifest a leftward bias in general visual processing. To shed light on this issue, the current study used the manual line bisection task to assess children 5 to 15 years of age with ASD as well as typically developing (TD) children. Results showed that children with ASD, similar to TD children, demonstrate a leftward bias in general visual processing, especially for bisecting long lines (≧ 80 mm). In both groups, participant performance in line bisection was affected by the hand used, the length of the line, the cueing symbol, and the location of the symbol. The ASD group showed a rightward bias when bisecting short lines (30 mm) with their left hands, which slightly differed from the TD group. These results indicate that while ASD individuals and TD individuals share a similar leftward bias in general visual processing, when using their left hands to bisect short lines, ASD individuals may show an atypical bias pattern.

Let G be a graph. A bisection of G is a bipartition of V ( G ) with V ( G ) = V 1 ∪ V 2 , V 1 ∩ V 2 = ∅ and | | V 1 | - | V 2 | | ≤ 1 . Bollobás and Scott conjectured that every graph admits a bisection such that for every vertex, its external degree is greater than or equal to its internal degree minus one. In this paper, we confirm this conjecture for some regular graphs. Our results extend a result given by Ban and Linial (J Graph Theory 83:5–18, 2016). We also give an upper bound of the maximum bisection of graphs.