Real Intersection Research Articles

A behavioral multi-agent model for road traffic simulation

Multi-agent systems allow the simulation of complex phenomena that cannot easily be described analytically. Multi-agent approaches are often based on coordinating agents whose actions and interactions are related to the emergence of the phenomenon to be simulated. In this article, we focus on road traffic simulation, specifically the design of a road traffic simulation tool able to deal realistically with road junctions. We propose a multi-agent behavioral model based on (i) the opportunistic individual behaviors that describe the norm violation and (ii) the anticipatory individual abilities of simulated drivers that allow critical situations to be detected. Our proposition has been validated for different traffic scenarios. Specifically, we simulated the traffic in a real intersection and then compared the simulated traffic flow with the real flow to highlight the relevance of our approach.

Counting positive solutions for polynomial systems with real coefficients

Based on the subresultant polynomial chain and the method presented by Hongguang Fu and Lu Yang et al., we propose a practical algorithm for computing the number of sign changes of the leading coefficients and the constant terms of a generalized Sturm sequence (GSS). With the principal minors sequence of the discrimination matrix of the polynomial and the number of sign changes of the GSS, a formula determining the number of positive solutions of a given bivariate polynomial systems with real coefficients (with a finite number of complex solutions) and its algorithm are presented. Using the techniques of the B - net form of bivariate splines function, this algorithm can be used for computing the number of real intersection points of two piecewise algebraic curves and its distributions in all cells when common points are finite. A piecewise algebraic curve is defined by a bivariate spline function.

On the probability distribution of data at points in real complete intersection varieties

We show several estimates on the probability distribution of some data at points in real complete intersection varieties: norms of real affine solutions, condition number of real solution of real systems of multi-variate polynomial equations and convergence radius of Newton's operator for under-determined system of multi-variate polynomial equations.

Near-optimal parameterization of the intersection of quadrics: II. A classification of pencils

We present here the first classification of pencils of quadrics based on the type of their intersection in real projective space and we show how this classification can be used to compute efficiently the type of the real intersection. This classification is at the core of the design of the algorithms, presented in Part III, for computing, in all cases of singular intersection, a near-optimal parameterization with polynomial functions, that is a parameterization in projective space whose coordinate functions are polynomial and such that the number of distinct square roots appearing in the coefficients is at most one away from the minimum.

Validating a driving simulator using surrogate safety measures

Traffic crash statistics and previous research have shown an increased risk of traffic crashes at signalized intersections. How to diagnose safety problems and develop effective countermeasures to reduce crash rate at intersections is a key task for traffic engineers and researchers. This study aims at investigating whether the driving simulator can be used as a valid tool to assess traffic safety at signalized intersections. In support of the research objective, this simulator validity study was conducted from two perspectives, a traffic parameter (speed) and a safety parameter (crash history). A signalized intersection with as many important features (including roadway geometries, traffic control devices, intersection surroundings, and buildings) was replicated into a high-fidelity driving simulator. A driving simulator experiment with eight scenarios at the intersection were conducted to determine if the subjects’ speed behavior and traffic risk patterns in the driving simulator were similar to what were found at the real intersection. The experiment results showed that speed data observed from the field and in the simulator experiment both follow normal distributions and have equal means for each intersection approach, which validated the driving simulator in absolute terms. Furthermore, this study used an innovative approach of using surrogate safety measures from the simulator to contrast with the crash analysis for the field data. The simulator experiment results indicated that compared to the right-turn lane with the low rear-end crash history record (2 crashes), subjects showed a series of more risky behaviors at the right-turn lane with the high rear-end crash history record (16 crashes), including higher deceleration rate (1.80 ± 1.20 m/s 2 versus 0.80 ± 0.65 m/s 2), higher non-stop right-turn rate on red (81.67% versus 57.63%), higher right-turn speed as stop line (18.38 ± 8.90 km/h versus 14.68 ± 6.04 km/h), shorter following distance (30.19 ± 13.43 m versus 35.58 ± 13.41 m), and higher rear-end probability (9/59 = 0.153 versus 2/60 = 0.033). Therefore, the relative validity of driving simulator was well established for the traffic safety studies at signalized intersections.

Spaces of Polytopes and Cobordism of Quasitoric Manifolds

Our aim is to bring the theory of analogous polytopes to bear on the study of quasitoric manifolds, in the context of stably complex manifolds with compatible torus action. By way of application, we give an explicit construction of a quasitoric representative for every complex cobordism class as the quotient of a free torus action on a real quadratic complete intersection. We suggest a systematic description for omnioriented quasitoric manifolds in terms of combinatorial data, and explain the relationship with non-singular projective toric varieties (otherwise known as toric manifolds). By expressing the first and third authors' approach to the representability of cobordism classes in these terms, we simplify and correct two of their original proofs concerning quotient polytopes; the first relates to framed embeddings in the positive cone, and the second involves modifying the operation of connected sum to take account of orientations. Analogous polytopes provide an informative setting for several of the details.

An urban traffic network model via coloured timed Petri nets

This paper deals with modelling of traffic networks (TNs) for control purposes. A modular framework based on coloured timed Petri nets (CTPNs) is proposed to model the dynamics of signalized TN systems: places represent link cells and crossing sections, tokens are vehicles and token colours represent the routing of the corresponding vehicle. In addition, ordinary timed Petri nets model the signal timing plans of the traffic lights controlling the area. The proposed modelling framework is applied to a real intersection located in Bari, Italy. A discrete event simulation of the controlled intersection validates the model and tests the signal timing plan obtained by an optimization strategy presented in the related literature.

Coplanar circles, quasi-affine invariance and calibration

We define the lines associated with two coplanar circles, and give the distributions of any two coplanar circles and their associated lines. Further we prove that the distribution of two coplanar circles with no real intersection and their associated lines is a quasi-affine invariance. Then the results are applied to calibrating a camera. The calibration method has the advantages: (1) it is based on conic fitting; (2) it does not need any matching. Experiments with two separate circles validate our quasi-affine invariance and show that the estimated camera intrinsic parameters are as good as those obtained by Zhang's (2000) method.

ORTHOGONAL EXPANSION: A NEGLECTED FACTOR IN TILT ILLUSIONS

A broad collection of illusions belonging to the Zollner and the Poggendorff families, including new variants — in particular, tilted and tilting squares — are examined in the light of two possible formal principles : a principle of regression to right angles (RRA) and a principle of “orthogonal expansion”, which is a perceptual expansion of the extent perpendicularly to the inducing lines. The domains of validity of the two principles are compared. We propose that RRA is more pertinent when the target line is explicitely present and makes real intersections with the inducing lines. Orthogonal expansion can produce RRA as a side-effect. It would be more pertinent when there are several parallel or nearly parallel inducing lines, and it does not require the presence of a real target. Both principles may be grounded on neurophysiological mechanisms. Orientation detectors would influence each other in the orientation domain, generating RRA and accounting for the illusions of the Poggendorff family. They would also influence each other in the extent domain, generating orthogonal expansion, and accounting for the illusions of the Zollner family.

A robust algorithm for finding the real intersections of three quadric surfaces

By Bezout's theorem, three quadric surfaces have at most eight isolated intersections although they may have infinitely many intersections. In this paper, we present an efficient and robust algorithm, to obtain the isolated and the connected components of, or to determine the number of isolated real intersections of, three quadric surfaces by reducing the problem to computing the real intersections of two planar curves obtained by Levin's method.

Geometric view of the thermodynamics of adsorption at a line of three-phase contact.

We consider three fluid phases meeting at a line of common contact and study the linear excesses per unit length of the contact line (the linear adsorptions Lambda(i)) of the fluid's components. In any plane perpendicular to the contact line, the locus of choices for the otherwise arbitrary location of that line that makes one of the linear adsorptions, say Lambda(2), vanish, is a rectangular hyperbola. Two of the adsorptions Lambda(2) and Lambda(3) then both vanish when the contact line is chosen to pass through any of the intersections of the two corresponding hyperbolas Lambda(2)=0 and Lambda(3)=0. There may be two or four such real intersections. It is found most surprisingly, and confirmed in a numerical example, that Lambda(1(2,3)), the adsorption of component 1 in a frame of reference in which the adsorptions Lambda(2) and Lambda(3) are both 0, depends on which intersection of the hyperbolas Lambda(2)=0 and Lambda(3)=0 is chosen for the location of the contact line. This implies that what had long been taken to be the line analog of the Gibbs adsorption equation is incomplete; there must be additional, previously unanticipated terms in the relation, consistent with the invariance of the line tension to choice of location of the contact line. It is then not Lambda(1(2,3)) by itself but a related expression containing it that must be invariant, and this invariance is also confirmed in the numerical example. The presence of the additional terms in the adsorption equation is further confirmed and their origin clarified in a mean-field density-functional model. The supplemental terms vanish at a wetting transition, where one of the contact angles goes to 0.

An urban traffic network model via coloured timed petri nets

This paper deals with modelling of traffic networks for real time control purposes. A modular framework based on coloured timed Petri nets is proposed to model the dynamics of signalized traffic network systems: places represent link cells and crossing sections, tokens are vehicles and token colours represent the routing of the corresponding vehicle. In addition, an ordinary timed Petri net models the signal timing plan controlling the area. The proposed modelling framework is applied to a real intersection located in Bari, Italy. A discrete event simulation of the controlled intersection validates the model and tests the signal timing plan obtained by an optimization strategy presented in the related literature.

Investigations of Blocks in Foundations and Abutments of Concrete Dams

This paper discusses investigations of potential block hazards in ten existing American concrete arch and buttress dams. Block theory was used to identify and describe all removable blocks, based on the study of construction photos and logs, and new mapping, often done on steep valley sides. Water forces on the block faces were calculated for stability analysis using a map of the phreatic surface or an estimated flow regime along the subsurface boundary of the block. In some cases, block hazards were shown to be nonexistent because there were no real intersections of significant discontinuities of sufficient extent to cut out a block, or there was no kinematically possible mode of failure with the prevailing force system. Several dams had blocks that were removable but judged sufficiently safe with the applicable friction angles. Three structures demanded attention: A spillway structure was armored to prevent further erosion that diminished the resistance of a key block in its foundation; a dome and buttress structure received a reinforced concrete buttress to add passive support against a block critically located in the abutment; and a drainage adit and deep drains drilled from the surface and from the adit were constructed to raise the safety factor of a large block beneath the abutment of an arch dam.

Viro Method for the Construction of Real Complete Intersections

The Viro method is a powerful construction method of real nonsingular algebraic hypersurfaces with prescribed topology. It is based on polyhedral subdivisions of Newton polytopes. A combinatorial version of the Viro method is called combinatorial patchworking and arises when the considered subdivisions are triangulations. B. Sturmfels has generalized the combinatorial patchworking to the case of real complete intersections. We extend his result by generalizing the Viro method to the case of real complete intersections.

Intersection number and topology preservation within digital surfaces

In this paper, we prove a new result of digital topology which states that the digital fundamental group—a notion previously introduced by Kong (Comput. Graphics 13 (1989) 159–166)—is sufficient to characterize topology preservation within digital surfaces. This proof involves a new tool for proving theorems in this field: the intersection number which counts the number of real intersections between two surfels loops lying on a digital surface. The main property of the intersection number and the reason why it is useful is the following: the intersection number between two paths does not change after any continuous deformation applied to the paths.

Piecewise algebraic curve

A piecewise algebraic curve is defined by a bivariate spline function. Using the techniques of the B- net form of bivariate splines function, discriminant sequence of polynomial (cf. Yang Lu et al. (Sci. China Ser. E 39(6) (1996) 628) and Yang Lu et al. (Nonlinear Algebraic Equation System and Automated Theorem Proving, Shanghai Scientific and Technological Education Publishing House, Shanghai, 1996)) and the number of sign changes in the sequence of coefficients of the highest degree terms of sturm sequence, we determine the number of real intersection points of two piecewise algebraic curves whose common points are finite. A lower bound of the number of real intersection points is given in terms of the method of rotation degree of vector field.

Installation and experiences of field testing a fuzzy signal controller

This paper describes the installation of a fuzzy signal controller (FSC) at a real intersection. The results of a vehicle-actuated control system with a fuzzy-control system using microscopic simulation and field measurements have been compared. The results indicate that the fuzzy control is very competitive against traditional vehicle-actuated control, if traffic volumes are higher than low-demand. The benefit of fuzzy logic lies in its ability to handle linguistic information by representing it as a fuzzy set. The simple algorithm structure, the savings of material costs and the low installation and maintenance costs are important advantages. The results of this paper prove that the FSC can be installed in real infrastructure and that fuzzy algorithms can be more effective than traditional vehicle-actuated control.

Field Evaluation of Audible Traffic Signals for Blind Pedestrians

The project aims to single out an audible traffic signal or a pair of audible traffic signals that would enable blind pedestrians to cross intersections safely. This is carried out in three phases: 1) measuring walking alignment and crossing time of blind pedestrian subjects within a simulated corridor, with four different simultaneous traffic signals (cuckoo, peep-peep, 4-note melody and neo-cuckoo) presented in a quiet environment, 2) measuring alignment with audible traffic signals alternating on each end of the simulated corridor, in a quiet environment and 3) measuring alignment at a busy real intersection. This paper reports on the results of the first two phases. The 4-note melody originally proposed by Hall et al. (1996) and modified in a recent study (Laroche et al., 1999) gave better results in terms of localization and perception of safety than any other signals specified in the Canadian standard (Transportation Association of Canada, 1992). Audible traffic signals alternating back and forth on each side of the corridor gave better results than signals presented simultaneously from both sides.

Deformation of Complete Intersections in the Plane

We study deformations of zero-dimensional complete intersections in the plane, and prove the following results. (1) Two complex non-singular curves intersecting at r points with multiplicities d 1 , …, d r can be deformed into curves intersecting (at some points) with multiplicities d ′ 1 , …, d ′ s which are arbitrary prescribed partitions of the numbers d 1 , …, d r . (2) Two real curves intersecting with multiplicity at most 2 at each of their real common points can be deformed so that all real multiple intersection points split into real simple intersection points.

Towards a combinatorial intersection cohomology for fans

The real intersection cohomology of a toric variety is described in a purely combinatorial way using methods of elementary commutative algebra only. We define, for arbitrary fans, the notion of a ``minimal extension sheaf'' on the fan as an axiomatic characterization of the equivariant intersection cohomology sheaf. This provides a purely algebraic interpretation of Stanley's generalized f- and g-vector of an arbitrary polytope or complete fan under a natural vanishing condition. -- The results presented in this note originate from joint work with G.Barthel, J.-P.Brasselet and L.Kaup, continuing earlier research (see math.AG/9904159). A detailed exposition will appear elsewhere (see math.AG/0002181).