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Detecting the interaction between humans and objects in images is a critical problem for obtaining a deeper understanding of the visual relationship in a scene and also a critical technology in many practical applications, such as augmented reality, video surveillance and information retrieval. Be that as it may, due to the fine-grained actions and objects in the real scene and the coexistence of multiple interactions in one scene, the problem is far from being solved. This paper differs from prior approaches, which focused only on the features of instances, by proposing a method that utilizes a four-stream CNNs network for human-object interaction (HOI) detection. More detailed visual features, spatial features and pose features from human-object pairs are extracted to solve the challenging task of detection in images. Specially, the core idea is that the region where people interact with objects contains important identifying cues for specific action classes, and the detailed cues can be fused to facilitate HOI recognition. Experiments on two large-scale HOI public benchmarks, V-COCO and HICO-DET, are carried out and the results show the effectiveness of the proposed method.

In real traffic, the right-turn vehicles at intersections are not controlled by signal lights and their effects are neglected. In this paper, we develop a cellular automaton model to formulate the complicated turning behaviors of vehicles at intersections. Simulation results are quite in accord with the observation on the Beijing's 4th ring road. It is found that the right-turn vehicles may produce queue near the intersection, a short lane designed for right-turn has prominent effect in improving traffic flow, but, a too long lane for right-turn cannot further decrease the stop ratio as expected. These findings deepen our understanding on the effects of right-turn vehicles and may help the design and management of intersections.

Using cellular automata (CA) Nagel–Schreckenberg (NaSch) model, we numerically study the probability P_ac of the occurrence of car accidents at nonsignalized intersection when drivers do not respect the priority rules. We also investigated the impact of mixture lengths and velocities of vehicles on this probability. It is found that in the first case, where vehicles distinguished only by their lengths, the car accidents start to occur above a critical density ρ_c. Furthermore, the increase of the fraction of long vehicles (F_L) delays the occurrence of car accidents (increasing ρ_c) and increases the risk of collisions when ρ > ρ_c. In other side, the mixture of maximum velocities (with same length for all vehicles) leads to the appearance of accidents at the intersection even in the free flow regime. Moreover, the increase of the fraction of fast vehicles (F_f) reduces the accident probability (P_ac). The influence of roads length is also studied. We found that the decrease of the roads length enhance the risk of collision.

Using the cellular automata Nagel–Schreckenberg (NaSch) model, we numerically study the impact of traffic lights on the probability of car accidents ($P_{\mathrm{\text{ac}}}$) at the intersection of two roads. It is found that, the probability $P_{\mathrm{\text{ac}}}$ is more stable with variation of the green light ($T$) when the symmetric lights are adopted. Moreover, simulation results show the existence of a critical time $T_c$, below which ($T<T_c$) $P_{\mathrm{\text{ac}}}$ increases as the injection rate ($\alpha$) increases, however, above which ($T>T_c$) the growing of $\alpha$ has for effect the decrease of $P_{\mathrm{\text{ac}}}$. Furthermore, the decrease of $P_{\mathrm{\text{ac}}}$ is almost always accompanied by a loss of the flux, especially with asymmetrical lights. To overcome this problem, we proposed a strategy that can greatly increase the flux and keep the probability $P_{\mathrm{\text{ac}}}$ as small as possible, especially for the low and high injection rates.

Differential equations that switch between different modes of behavior across a surface of discontinuity are used to model, for example, electronic switches, mechanical contact, predator–prey preference changes, and genetic or cellular regulation. Switching in such systems is unlikely to occur precisely at the ideal discontinuity surface, but instead can involve various spatiotemporal delays or noise. If a system switches between more than two modes, across a boundary formed by the intersection of discontinuity surfaces, then its motion along that intersection becomes highly sensitive to such nonidealities. If switching across the surfaces is affected by hysteresis, time delay, or discretization, then motion along the intersection can be affected by erratic variations that we characterize as “jitter”. Introducing noise, or smoothing out the discontinuity, instead leads to steady motion along the intersection well described by the so-called canopy extension of Filippov’s sliding concept (which applies when the discontinuity surface is a simple hypersurface). We illustrate the results with numerical experiments and an example from power electronics, providing explanations for the phenomenon as far as they are known.

Evaluating the intersection of two rational parametric surfaces is a recurring operation in solid modeling. However, surface intersection is not an easy problem and continues to be an active topic of research. The main reason lies in the fact that any good surface intersection technique has to balance three conflicting goals of accuracy, robustness and efficiency. In this paper, we formulate the problems of curve and surface intersections using algebraic sets in a higher dimensional space. Using results from Elimination theory, we project the algebraic set to a lower dimensional space. The projected set can be expressed as a matrix determinant. The matrix itself, rather than its symbolic determinant, is used as the representation for the algebraic set in the lower dimensional space. This is a much more compact and efficient representation. Given such a representation, we perform matrix operations for evaluation and use results from linear algebra for geometric operations on the intersection curve. Most of the operations involve evaluating numeric determinants and computing the rank, kernel and eigenvalues of matrices. The accuracy of such operations can be improved by pivoting or other numerical techniques. We use this representation for inversion operation, computing the intersection of curves and surfaces and tracing the intersection curve of two surfaces in lower dimension.

We propose Asymmetric Simple Exclusion Processes to analyze the traffic states around a T-shaped intersection. The system consists of six roadways connected by the intersection. There are nine control-parameters separated into three categories: injection α_i, removal β_i, and turning P_i, (where i = 1, 2, 3). As these nine parameters change, traffic states on each roadway reveal a two-phase transition: free flow (F) and jam (J). Together, there can be 64 (=2⁶) possible combinations for the traffic phases. We observe 63 distinct phases. We analyze three major causes of congestion:

(1) increase of traffic demand simulated by injection α_i;

(2) decrease of roadway capacity simulated by removal β_i;

(3) redistribution of traffic pattern simulated by turning P_i.

In case (1), congestion can be confined to the roadways heading toward the intersection. In case (2), spillovers can be observed and congestion will pervade the whole system. In case (3), congestion can be triggered by both increasing P_i and decreasing P_i. The phase diagram can be a convenient tool to summarize the results of numerical simulations. We also compare the unsignalized intersection to an intersection regulated by traffic signals. We find that the operation of traffic signals is very inefficient in resolving the congestion around a T-shaped intersection.

In this paper, we proposed a model based on the connected vehicles to control the traffic flow at the intersection. To evaluate this model, we studied its impact on the flux and the probability of accidents at the intersection. On the one hand, simulation results showed that the increase in the number of connected vehicles decreases the congestion coefficient and enhances the traffic situation in the system. On the other hand, connected vehicles reduce the probability of accidents at the intersection. In this way, the vehicle intersection (central controller) communication can decrease the congestion and enhance road safety, especially in the intermediate and high traffic conditions.

This paper explored the impacts of vehicle-to-infrastructure (V2I) communication on the mixed traffic flow consisting of connected vehicles (CVs) and human-driven vehicles (HVs). We developed a cellular automaton model for mixed flow at the signalized intersection. In addition to considering the motion characteristics of CVs and the influence of HVs on the motion behavior of CVs, the model also considered the influence of signal lights. CVs determine their velocities via V2I communication in order to pass the signal light with less delay and avoid stopping. Through simulations, we found that the presence, frequency and range of V2I communication all make a difference in the mixed flow. Also, 1-Hz communication reduces the number of vehicles within 300 m before the red light from 36 to 26, and the 10-Hz communication reduces one more; 1-Hz communication increases the number of accelerations, but when the frequency increases to 10 Hz, the number of accelerations decreases to the same value as without V2I communication, but the value of number of accelerations increases monotonously with the frequency; traffic delay decreases and capacity increases as the frequency increases. However, as the communication range increases, except that the number of accelerations first decreases and then increases, other traffic characteristics remain unchanged. The number of accelerations reaches a minimum at about 500 m.

In this paper, we propose new rules of advancing edges for computing the intersection of a pair of convex polygons in the plane. These rules have no ambiguities when extended into the spherical surface, differently from those of O'Rourke et al.⁴ Finally, we design a linear-time algorithm for computing the intersection of a pair of spherical convex polygons, and prove its correctness.

We prove that the finite representation property holds for representation by partial functions for the signature consisting of composition, intersection, domain and range and for any expansion of this signature by the antidomain, fixset, preferential union, maximum iterate and opposite operations. The proof shows that, for all these signatures, the size of base required is bounded by a double-exponential function of the size of the algebra. This establishes that representability of finite algebras is decidable for all these signatures. We also give an example of a signature for which the finite representation property fails to hold for representation by partial functions.

It is well known that any two longest paths in a connected graph share a vertex. It is also known that there are connected graphs where 7 longest paths do not share a common vertex. It was conjectured that any three longest paths in a connected graph have a vertex in common. In this note we prove the conjecture for outerplanar graphs and give sufficient conditions for the conjecture to hold in general.