The 3-Good Neighbor Edge-Fault-Tolerant Strong Menger Edge Connectivity on the Class of BC Networks

A graph [Formula: see text] is called strongly Menger edge connected (SM-[Formula: see text] for short) if the number of disjoint paths between any two of its vertices equals the minimum degree of these two vertices. In this paper, we focus on the maximally edge-fault-tolerant of the class of BC-networks (contain hypercubes, twisted cubes, Möbius cubes, crossed cubes, etc.) concerning the SM-[Formula: see text] property. Under the restricted condition that each vertex is incident with at least three fault-free edges, we show that even if there are [Formula: see text] faulty edges, all BC-networks still have SM-[Formula: see text] property and the bound [Formula: see text] is sharp.

Experimental Study and Numerical Study on Shear Bearing Capacity of Shear Key Joints of Reinforced Concrete Open-Web Sandwich Plates

The shear key in the reinforced concrete open-web sandwich plate (RCOSP) is a block joint that connects with the top chord and the bottom chord. In order to understand the failure mode of the shear key and verify the accuracy of the current algorithm, a total of 9 test pieces are prepared and classified 3 groups were assigned longitudinal reinforcement (LR) ratios of 0.49%, 0.82%, and 1.24%, respectively. The horizontal concentrated static loading under simple support condition is carried out. The test results show that the shear key is horizontally cut and the concrete is pulled apart or crushed along the direction of chord width at the shear key-chords area; the strain level of the concrete and stirrup of the shear key is lower averagely; the development of the horizontal displacement and the strain of the longitudinal bars of the test pieces goes through elastic, elastoplastic, and plastic stages; the ultimate load of the test pieces has almost no relationship with the reinforcement ratio of shear key but is controlled by the degree of crack development in the area where shear key connects with the chords. To avoid the current algorithm overestimating the shear capacity of shear key, the restricted condition of shear section is proposed. The finite element analysis (FEA) further verifies that the restricted condition of shear section proposed in this paper is reasonable and necessary.

Lattice-Based Linearly Homomorphic Signature Scheme over F 2

In this paper, we design a new lattice-based linearly homomorphic signature scheme over F 2 . The existing schemes are all constructed based on hash-and-sign lattice-based signature framework, where the implementation of preimage sampling function is Gaussian sampling, and the use of trapdoor basis needs a larger dimension m ≥ 5 n log q . Hence, they cannot resist potential side-channel attacks and have larger sizes of public key and signature. Under Fiat–Shamir with aborting signature framework and general SIS problem restricted condition m ≥ n log q , we use uniform sampling of filtering technology to design the scheme, and then, our scheme has a smaller public key size and signature size than the existing schemes and it can resist side-channel attacks.

Fault-Tolerant Maximal Local-Edge-Connectivity of Augmented Cubes

An interconnection network is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively. Connectivity is an important metric for fault tolerance of interconnection networks. A connected graph [Formula: see text] is said to be maximally local-edge-connected if each pair of vertices [Formula: see text] and [Formula: see text] of [Formula: see text] are connected by [Formula: see text] pairwise edge-disjoint paths. In this paper, we show that the [Formula: see text]-dimensional augmented cube [Formula: see text] is [Formula: see text]-edge-fault-tolerant maximally local-edge-connected and the bound [Formula: see text] is sharp; under the restricted condition that each vertex has at least three fault-free adjacent vertices, [Formula: see text] is [Formula: see text]-edge-fault-tolerant maximally local-edge-connected and the bound [Formula: see text] is sharp; and under the restricted condition that each vertex has at least [Formula: see text] fault-free adjacent vertices, [Formula: see text] is [Formula: see text]-edge-fault-tolerant maximally local-edge-connected. Furthermore, we show that a [Formula: see text]-regular graph [Formula: see text] is [Formula: see text]-fault-tolerant one-to-many maximally local-connected if [Formula: see text] does not contain [Formula: see text] and is super [Formula: see text]-vertex-connected of order 1, a [Formula: see text]-regular graph [Formula: see text] is [Formula: see text]-fault-tolerant one-to-many maximally local-connected if [Formula: see text] does not contain [Formula: see text] and is super [Formula: see text]-vertex-connected of order 1.

Do exploratory arm movements contribute to maximum reach distance judgements?

Exploratory movements provide information about agents’ action capabilities in a given environment. However, little is known about the specifics of these exploratory movements, such as which movements are necessary to perceive a given action capability. This experiment tested whether arm movements contributed to judgements of maximum reach distance. Participants made judgements about their maximum reach distance by walking to the point farthest from an object from which they still perceived the object to be reachable. Over the course of two sets of nine judgements, participants’ arms either swung naturally by their sides (Unrestricted Condition) or were held together behind their backs (Restricted Condition). Arm movement restriction increased maximum reach distance judgement error when compared with unrestricted judgements. In addition, judgement error improved over trials only when exploratory arm movements were unrestricted, and the improvements did not carry over to subsequent judgements made when exploratory arm movements were restricted. Arm movement restriction did not increase the variability of judgement error when compared with unrestricted judgements. The results indicate that exploration is necessary to generate affordance information, show that restricted exploration degrades affordance perception, and suggest that maximum reach distance exists at the global array level. In addition, they have practical implications for operational situations in which actors’ arm movements are restricted, such as when military personnel wear body armour.

On the twisted Dorfman-Courant like brackets

There are completely described all \(\mathcal{VB}_{m,n}\)-gauge-natural operators \(C\) which, like to the Dorfman-Courant bracket, send closed linear \(3\)-forms \(H\in\Gamma^{l-\rm{clos}}_E(\bigwedge^3T^*E)\) on a smooth (\(\mathcal{C}^{\infty}\)) vector bundle \(E\) into \(\mathbf{R}\)-bilinear operators \[C_H:\Gamma^l_E(TE\oplus T^*E)\times \Gamma^l_E(TE\oplus T^*E)\to \Gamma^l_E(TE\oplus T^*E)\] transforming pairs of linear sections of \(TE\oplus T^*E\to E\) into linear sections of \(TE\oplus T^*E\to E\). Then all such \(C\) which also, like to the twisted Dorfman-Courant bracket, satisfy both some "restricted" condition and the Jacobi identity in Leibniz form are extracted.

Fault-Tolerant Maximal Local-Connectivity on Cayley Graphs Generated by Transpositions

An interconnection network is usually modeled as a graph, in which vertices and edges correspond to processors and communication links, respectively. Connectivity is an important metric for fault tolerance of interconnection networks. A graph [Formula: see text] is said to be maximally local-connected if each pair of vertices [Formula: see text] and [Formula: see text] are connected by [Formula: see text] vertex-disjoint paths. In this paper, we show that Cayley graphs generated by [Formula: see text]([Formula: see text]) transpositions are [Formula: see text]-fault-tolerant maximally local-connected and are also [Formula: see text]-fault-tolerant one-to-many maximally local-connected if their corresponding transposition generating graphs have a triangle, [Formula: see text]-fault-tolerant one-to-many maximally local-connected if their corresponding transposition generating graphs have no triangles. Furthermore, under the restricted condition that each vertex has at least two fault-free adjacent vertices, Cayley graphs generated by [Formula: see text]([Formula: see text]) transpositions are [Formula: see text]-fault-tolerant maximally local-connected if their corresponding transposition generating graphs have no triangles.

Does Restricting an Observer’s Arm Movements Degrade Their Judgments of Others’ Reaching Abilities?

Summary Observers can perceive others’ action capabilities. These actions include observers’ abilities to perceive the maximum height that an actor can sit, step across a gap, climb in a bipedal manner, or reach an object (Stoffregen et al., 1999; Mark, 2007; Ramenzoni et al., 2008a, 2008b). While observers’ abilities to perceive others’ action capabilities have been widely studied, researchers debate the information to which observers attend when making such judgments. Some have argued observers attend to actor-environment relations when perceiving others’ action capabilities (e.g., Stoffregen et al., 1999; Mark, 2007; Ramenzoni et al., 2008a). From this perspective, observers attend to relations between relevant characteristics of the actor’s body (e.g., leg length) and their environment (e.g., step height) to perceive actors’ action capabilities (e.g., stair-climbing ability). This perspective has empirical support. For example, observers differentiated short and tall actors’ maximum sitting heights but only when the actors and sitting apparatus were presented in the same scale (Stoffregen et al., 1999). Others have argued observers attend to observer-environment relations when perceiving others’ capabilities (e.g., Knoblich & Sebanz, 2006; Ramenzoni et al., 2008b; Gallese & Sinigaglia, 2011). From this perspective, observers perceive their own action capabilities (Step 1), which serve as a model for the actor’s action capabilities and then adjust that model (Step 2) to account for observer-actor differences (Knoblich & Sebanz, 2006; Gallese & Sinigaglia, 2011). This perspective also has empirical support. For example, observers wearing ankle weights underestimated actors’ maximum jump-to-reach heights (Ramenzoni et al., 2008b). The present study further investigated whether observers attend to observer-environment relations when perceiving others’ maximum reach capabilities. Participants ( n = 34) made judgments about a confederate’s maximum reach capability while participants’ arms were held either freely by their sides (Unrestricted Condition) or placed behind their back (Restricted Condition). Widlus and Jones (2017) demonstrated that such arm restriction led to more erroneous judgments about one’s own reaching capabilities. To make judgments, participants directed the confederate to the farthest point from a hanging object that would still afford the confederate the ability to reach the object. If observers attend to observer-environment relations when judging the confederate’s maximum reach capability, then 1) judgment error would be greater in the Restricted condition than in the Unrestricted condition, 2) judgments would align with observers’ capabilities better than with the confederate’s, and 3) judgment error would positively correlate with the degree of dissimilarity between observers’ and the confederate’s action capabilities. The experiment used a within-subjects design. The independent variable was observer arm exploration, which consisted of two levels: unrestricted and restricted arm exploration. The dependent variable was the participant’s judgment of the farthest distance the confederate could reach. This was operationalized as the distance between the confederate’s clavicle and the to-be-reached object, once participants had directed the confederate to the position where they believed the confederate could just reach the object. Those judgments served as the basis for several measures. The present study’s results suggested arm restriction did not increase judgment error. Second, judgments did not align with observers’ capabilities better than with the confederate’s. Third, judgment error did not positively correlate with the degree of dissimilarity between observers’ and the confederate’s action capabilities. Collectively, these outcomes provide consistent evidence that observers did not base their judgments of the confederate’s reaching capabilities on observer-environment relations. Instead, these results are consistent with previous studies that support the possibility that observers based their judgments on actor-environment relations (Stoffregen et al., 1999; Ramenzoni et al., 2008a). Understanding how observers judge others’ action capabilities allows us to better predict errors that may occur in operational settings, e.g., whether a firefighter will inaccurately judge whether their partner can accomplish a given task. Human factors professionals can then develop solutions to mitigate such errors, e.g., equipment redesign to better reveal actor-environment relations.

Modelling of Ship’s Trajectory Planning in Collision Situations by Hybrid Genetic Algorithm

Ship collision-avoidance trajectory planning aims at searching for a theoretical safe-critical trajectory in accordance with COLREGs and good seamanship. In this paper, a novel optimal trajectory planning based on hybrid genetic algorithm is presented for ship collision avoidance in the open sea. The proposed formulation is established based on the theory of the Multiple Genetic Algorithm (MPGA) and Nonlinear Programming, which not only overcomes the inherent deficiency of the Genetic Algorithm (GA) for premature convergence, but also guarantees the practicality and consistency of the optimal trajectory. Meanwhile, the encounter type as well as the obligation of collision avoidance is determined according to COLREGs, which is then considered as the restricted condition for the operation of population initialization. Finally, this trajectory planning model is evaluated with a set of test cases simulating various traffic scenarios to demonstrate the feasibility and superiority of the optimal trajectory.

Do Exploratory Arm Movements Contribute to Reach-Ability Judgments?

Gibson (1979/1986) argued that exploratory movements generate information about agents’ action-capabilities within a given environment, that is, about the agent-environment system’s affordances. To date, the scant literature on exploratory movements has revealed two important findings. First, restricting exploratory movements degrades the accuracy of affordance judgments (Mark et al., 1990; Yu, Bardy, & Stoffregen, 2011). Second, exploratory movements can be very subtle (Stoffregen, Yang, & Bardy, 2005; Yu, Bardy, & Stoffregen, 2011). However, many questions regarding exploratory movements have yet to be answered. For example, what exploratory movements are necessary to perceive a given affordance, and how do exploratory movements differ from related movements? Our long-term goal is to address such gaps in the literature. We decided to begin by examining what exploratory movements must be executed in order to perceive whether the actor can reach an object. Reaching exploratory movements likely have two key components: 1) head movements and 2) shoulder movements. The former can generate information about the absolute distance between the actor and the to-be-reached object (Bingham & Stassen, 1994), and have been confirmed to be necessary to produce accurate reaching judgments (Mantel, Stoffregen, Campbell & Bardy, 2015). The latter generates information about the actor’s arm length (Anderson & Turvey, 1998; Shibata, Gyoba, & Takeshima, 2012;), but their necessity to the reach-ability judgment has yet to be studied. The current experiment used a restriction paradigm to determine whether exploratory arm movements are necessary to make accurate reaching judgments. Participants (n = 32) judged their maximum reaching ability either while holding their arms behind their backs with their dominant hand grasping their non-dominant wrist (the Restricted condition), or while their arms swung naturally at their sides (the Unrestricted condition). Judgments were made actively, by walking forward or backward, in order to allow participants to generate the exploratory movements they would normally create (with the exception of arm movements in the Restricted condition) when moving toward an object with the intention to perform a reach (Mantel, Bardy, & Stoffregen, 2010). The study utilized a within-subjects design, with starting condition counterbalanced. For each condition, participants completed 1 practice trial followed by 9 experimental trials. Starting distances (from object) and angles were drawn equally and randomly from ranges of 1 – 24”, 25 – 48”, 49 – 72”, and 0 - 29o, 30 - 59o, 60 - 89o, respectively. Distances and angles were not repeated to prevent memorization. In line with previous affordance perception research, the dependent variable, Accuracy, was computed in terms of percentage of absolute error (|[judged maximum reach / actual maximum reach] -1| *100) (Oudejans, Michaels, Bakker, & Dolné, 1996). Accuracy was significantly greater when arm movements were unrestricted as compared to restricted, supporting the theory that exploratory arm movements are a component of reach-ability judgments. Reaching judgments in neither condition were perfectly accurate, which may have been due to the reaching judgment being the focal task (Heft, 1993). The present results have practical implications for operational situations in which actors’ arm movements might be restricted. For example, U.S. police and military personnel sometimes wear body armor that covers their shoulders, mounts ballistic plates to their upper arms, or some combination thereof. To the extent that such body armor restricts arm movements, then our results suggest that their reach-ability judgments would be degraded.