Scalar CFTs and Their Large N Limits

We study scalar conformal field theories whose large $N$ spectrum is fixed by the operator dimensions of either Ising model or Lee-Yang edge singularity. Using numerical bootstrap to study CFTs with $S_N\otimes Z_2$ symmetry, we find a series of kinks whose locations approach $(\Delta^{\text{Ising}}_{\sigma},\Delta^{\text{Ising}}_{\epsilon})$ at $N\rightarrow \infty$. Setting $N=4$, we study the cubic anisotropic fixed point with three spin components. As byproducts of our numerical bootstrap work, we discover another series of kinks whose identification with previous known CFTs remains a mystery. We also show that "minimal models" of $\mathcal{W}_3$ algebra saturate the numerical bootstrap bounds of CFTs with $S_3$ symmetry.Comment: 29 pages, 5 figure

A weighted pair graph representation for reconstructibility of Boolean control networks

A new concept of weighted pair graphs (WPGs) is proposed to represent a new reconstructibility definition for Boolean control networks (BCNs), which is a generalization of the reconstructibility definition given in [Fornasini & Valcher, TAC2013, Def. 4]. Based on the WPG representation, an effective algorithm for determining the new reconstructibility notion for BCNs is designed with the help of the theories of finite automata and formal languages. We prove that a BCN is not reconstructible iff its WPG has a complete subgraph. Besides, we prove that a BCN is reconstructible in the sense of [Fornasini & Valcher, TAC2013, Def. 4] iff its WPG has no cycles, which is simpler to be checked than the condition in [Fornasini & Valcher, TAC2013, Thm. 4].Comment: 20 pages, 10 figures, accepted by SIAM Journal on Control and Optimizatio

Synthesis of Covert Actuator Attackers for Free

In this paper, we shall formulate and address a problem of covert actuator attacker synthesis for cyber-physical systems that are modelled by discrete-event systems. We assume the actuator attacker partially observes the execution of the closed-loop system and is able to modify each control command issued by the supervisor on a specified attackable subset of controllable events. We provide straightforward but in general exponential-time reductions, due to the use of subset construction procedure, from the covert actuator attacker synthesis problems to the Ramadge-Wonham supervisor synthesis problems. It then follows that it is possible to use the many techniques and tools already developed for solving the supervisor synthesis problem to solve the covert actuator attacker synthesis problem for free. In particular, we show that, if the attacker cannot attack unobservable events to the supervisor, then the reductions can be carried out in polynomial time. We also provide a brief discussion on some other conditions under which the exponential blowup in state size can be avoided. Finally, we show how the reduction based synthesis procedure can be extended for the synthesis of successful covert actuator attackers that also eavesdrop the control commands issued by the supervisor.Comment: The paper has been accepted for the journal Discrete Event Dynamic System