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The faster-is-slower effect (FIS), which means that crowd at a high enough velocity could significantly increase the evacuation time to escape through an exit, is an interesting phenomenon in pedestrian dynamics. Such phenomenon had been studied widely and has been experimentally verified in different systems of discrete particles flowing through a centre exit. To experimentally validate this phenomenon by using people under high pressure is difficult due to ethical issues. A mouse, similar to a human, is a kind of self-driven and soft body creature with competitive behaviour under stressed conditions. Therefore, mice are used to escape through an exit at a corner. A number of repeated tests are conducted and the average escape time per mouse at different levels of stimulus are analysed. The escape times do not increase obviously with the level of stimulus for the corner exit, which is contrary to the experiment with the center exit. The experimental results show that the FIS effect is not necessary a universal law for any discrete system. The observation could help the design of buildings by relocating their exits to the corner in rooms to avoid the formation of FIS effect.

We construct twelve infinite families of pseudocyclic and non-amorphic association schemes, in which each nontrivial relation is a strongly regular graph. Three of the twelve families generalize the counterexamples to A. V. Ivanov's conjecture by Ikuta and Munemasa [15].1 |X| J, E 1 , . . . , E d be the primitive idempotents of the Bose-Mesner algebra of the scheme (X, {R i } 0≤i≤d ), where J is the all-one matrix of size |X| × |X|. The basis transition matrix from {E 0 , E 1 , . . . , E d } to {A 0 , A 1 , . . . , A d } is denoted by P = (p j (i)) 0≤i,j≤d , and usually called the first eigenmatrix (or character table) of the scheme. Explicitly P is the (d + 1) × (d + 1) matrix with rows and columns indexed by 0, 1, 2, . . . , d such thatLet k i = p i (0) and m i = rank(E i ). The k i 's and m i 's are called valencies and multiplicities of the scheme, respectively. We say that the scheme (X, {R i } 0≤i≤d ) is pseudocyclic if there exists an integer t such that m i = t for all i ∈ {1, . . . , d}. A classical example of pseudocyclic association schemes is the cyclotomic association scheme over a finite field, which we define below.

In this paper, generalizing the result in [9], I construct strongly regular Cayley graphs by using union of cyclotomic classes of Fq and Gauss sums of index w, where w≥2 is even. In particular, we obtain three infinite families of strongly regular graphs with new parameters.

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