Affine quantum super Schur-Weyl duality

The Schur-Weyl duality, which started as the study of the commuting actions of the symmetric group $S_d$ and $\mathrm{GL}(n,\mathbb{C})$ on $V^{\otimes d}$ where $V=\mathbb{C}^n$, was extended by Drinfeld and Jimbo to the context of the finite Iwahori-Hecke algebra $H_d(q^2)$ and quantum algebras $U_q(\mathrm{gl}(n))$, on using universal $R$-matrices, which solve the Yang-Baxter equation. There were two extensions of this duality in the Hecke-quantum case: to the affine case, by Chari and Pressley, and to the super case, by Moon and by Mitsuhashi. We complete this chain of works by completing the cube, dealing with the general affine super case, relating the commuting actions of the affine Iwahori-Hecke algebra $H^a_d(q^2)$ and of the affine quantum Lie superalgebra $U_{q,a}^\sigma(\mathrm{sl}(m,n))$ using the presentation by Yamane in terms of generators and relations, acting on the $d$th tensor power of the superspace $V=\mathbb{C}^{m+n}$. Thus we construct a functor and show it is an equivalence of categories of $H_d^a(q^2)$ and $U_{q,a}^\sigma(\mathrm{sl}(m,n))$-modules when $d<n'=m+n$

Time Quasilattices in Dissipative Dynamical Systems

We establish the existence of `time quasilattices' as stable trajectories in dissipative dynamical systems. These tilings of the time axis, with two unit cells of different durations, can be generated as cuts through a periodic lattice spanned by two orthogonal directions of time. We show that there are precisely two admissible time quasilattices, which we term the infinite Pell and Clapeyron words, reached by a generalization of the period-doubling cascade. Finite Pell and Clapeyron words of increasing length provide systematic periodic approximations to time quasilattices which can be verified experimentally. The results apply to all systems featuring the universal sequence of periodic windows. We provide examples of discrete-time maps, and periodically-driven continuous-time dynamical systems. We identify quantum many-body systems in which time quasilattices develop rigidity via the interaction of many degrees of freedom, thus constituting dissipative discrete `time quasicrystals'.Comment: 38 pages, 14 figures. This version incorporates "Pell and Clapeyron Words as Stable Trajectories in Dynamical Systems", arXiv:1707.09333. Submission to SciPos

Transient twinkle perception is induced by sequential presentation of stimuli that flicker at frequencies above the critical fusion frequency

The critical fusion frequency (CFF) is a threshold that represents the temporal limits of the human visual system. If two flickering stimuli with equal subjective luminances are presented simultaneously at different locations, the CFF is the temporal frequency above which they cannot be distinguished. However, when the stimuli are presented sequentially at the same position, a transient twinkle can be perceived around the moment of the changeover. To investigate the mechanism underlying this transient twinkle perception (TTP), we independently manipulated the luminance contrast and temporal frequency of the flicker, as well as the inter-stimulus interval (ISI). We found that TTP was greater as the luminance step was larger, it was stably perceived for flicker frequencies up to 200 Hz, and it was robust for all ISIs if flicker frequencies were below 250 Hz. For 250 and 300 Hz flicker, TTP was attenuated in the condition that 1-frame and 2-frame ISIs were inserted. These results can be explained by a simple filtering model that TTP occurs if the temporal change in a weighted moving average of stimulus luminance exceeds a certain threshold. TTP gives additional evidence that human visual system can detect the transient change of flicker stimuli at much higher temporal frequency than the CFF, by averaging mechanism of luminance

On a Relation between the Flicker value and the Working Condition

The appropriate disposition of the worker improves the ability of the worker and the efficiency of the labor and further decreases the rate of inferior goods and the rate of accidents. In previous paper, the variation of the flicker value, the trend of the miss frequency and the relation between them under the condition which has one surveillance point and one back-ground condition are analyzed. In this paper, the surveillance point is increased to two points and the back ground condition also two in order to examine which condition influences strongly to the flicker value in the working time. It was found that the variation of the flicker value is strongly connected with the qualification, the number of the surveillance and its miss-frequency