Strongly Regular Graphs as Laplacian Extremal Graphs

The Laplacian spread of a graph is the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of the graph. We find that the class of strongly regular graphs attains the maximum of largest eigenvalues, the minimum of second-smallest eigenvalues of Laplacian matrices and hence the maximum of Laplacian spreads among all simple connected graphs of fixed order, minimum degree, maximum degree, minimum size of common neighbors of two adjacent vertices and minimum size of common neighbors of two nonadjacent vertices. Some other extremal graphs are also provided.Comment: 11 pages, 4 figures, 1 tabl

Multimode optical feedback dynamics in InAs/GaAs quantum dot lasers emitting exclusively on ground or excited states: transition from short- to long-delay regimes

© 2018 Optical Society of America. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved.The optical feedback dynamics of two multimode InAs/GaAs quantum dot lasers emitting exclusively on sole ground or excited lasing states is investigated. The transition from long- to short-delay regimes is analyzed, while the boundaries associated to the birth of periodic and chaotic oscillations are unveiled to be a function of the external cavity length. The results show that depending on the initial lasing state, different routes to chaos are observed. These results are of importance for the development of isolator-free transmitters in short-reach networks

Characteristics of speed dispersion and its relationship to fundamental traffic flow parameters

[[abstract]]Speed dispersion is essential for transportation research but inaccessible to certain sensors that simply record density, mean speed, and/or flow. An alternative is to relate speed dispersion with these available parameters. This paper is compiled from nearly a quarter million observations on an urban freeway and a resulting data-set with two speed dispersion measures and the three fundamental parameters. Data are examined individually by lane and aggregately by direction. The first dispersion measure, coefficient of variation of speed, is found to be exponential with density, negative exponential with mean speed, and two-phase linear to flow. These empirical relationships are proven to be general for a variety of coefficient ranges under the above function forms. The second measure, standard deviation of speed, does not present any simple relationships to the fundamental parameters, and its maximum occurs at around a half to two-thirds of the free flow speed. Speed dispersion may be significantly different by lane.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[incitationindex]]EI[[ispeerreviewed]]Y[[booktype]]紙本[[booktype]]電子版[[countrycodes]]GB

Modular Properties of 3D Higher Spin Theory

In the three-dimensional sl(N) Chern-Simons higher-spin theory, we prove that the conical surplus and the black hole solution are related by the S-transformation of the modulus of the boundary torus. Then applying the modular group on a given conical surplus solution, we generate a 'SL(2,Z)' family of smooth constant solutions. We then show how these solutions are mapped into one another by coordinate transformations that act non-trivially on the homology of the boundary torus. After deriving a thermodynamics that applies to all the solutions in the 'SL(2,Z)' family, we compute their entropies and free energies, and determine how the latter transform under the modular transformations. Summing over all the modular images of the conical surplus, we write down a (tree-level) modular invariant partition function.Comment: 51 pages; v2: minor corrections and additions; v3: final version, to appear in JHE

Operational Assessment of Speed Priority for High-Occupancy Vehicle Lanes over General-Purpose Lanes

[[abstract]]Current guidelines arguably do not properly address how much high-occupancy vehicle (HOV) lanes should be prioritized over general-purpose (GP) lanes. This study develops two schemes for HOV and GP lanes by utilizing the concept of “speed equilibrium,” which determines whether HOV lanes are under-prioritized, over-prioritized, or well-prioritized. The first scheme incorporates average vehicle occupancy with speed priorities, reflecting the HOV core value of carrying more persons in fewer vehicles; HOV lanes maintain higher equilibrium speeds than GP lanes, but the differences decrease as traffic speeds decrease from free flow to jam states. The second scheme is a revision of the existing HOV principle: equilibrium built upon the principle of time saved leads to increasingly greater HOV speeds relative to GP lane speeds, as traffic volumes increase. Both schemes are visualized in three-dimensional data plots to illustrate the effects of individual traffic variables. Using only a single measure, i.e., speed, ensures inferior HOV priority with respect to mobility and reliability. Observed freeway data were applied to the two schemes, and the results can be used to determine the necessity of HOV policy adjustment. The schemes are complimentary to current HOV operational assessments.[[sponsorship]]Transportation Research Board[[conferencetype]]國際[[conferencedate]]20140112~20140116[[booktype]]電子版[[iscallforpapers]]Y[[conferencelocation]]Washington D.C., U.S.A