We report the results of operator state fluctuations in gene expression for the entire bacterial growth cycle, using single-cell analysis and synthetic unregulated and negative-feedback transcription regulatory gene circuits. In the unregulated circuit, during the cell cycle, we observe a crossover from log-normal-to-normal distribution of expressed proteins and an unusual linear dependence of ...

Since Euclidean global AdS2 space represented as a strip has two boundaries, the state-operator correspondence in the dual CFT1 reduces to the standard map from the operators acting on a single copy of the Hilbert space to states in the tensor product of two copies of the Hilbert space. Using this picture we argue that the corresponding states in the dual string theory living on AdS2 × K are de...

In this expression ↠and â denote the creation and annihilation operators of the one-mode radiation field of frequency Ω, ωA the separation between the atomic levels, Ĵz denotes a collective atomic operator which counts the difference of population between the two atomic levels, Ĵ+ a collective atomic operator which promotes atoms from the lower level to the upper level, Ĵ− = Ĵ † +, and μ stan...

In the theory for continuous-time linear systems, the system Hankel operator plays an important role in a number of realization problems ranging from providing an abstract notion of state to yielding tests for state space minimality and algorithms for model reduction. But in the case of continuous-time nonlinear systems, Hankel theory is considerably less developed beyond a well known Hankel ma...

Many solid-state NMR experiments exploit interference effects between time dependencies in the system Hamiltonian to design an effective time-independent Hamiltonian with the desired properties. Effective Hamiltonians can be designed such that they contain only selected parts of the full system Hamiltonian while all other parts are averaged to zero. A general theoretical description of such exp...

New technologies are available for emergency management experts to help them cope with challenges such as information overload, multitasking and fatigue. Among these technologies, a wide variety of physiological sensors can now be deployed to measure the Operator Functional State (OFS). To be truly useful, such measures should not only characterize the overall OFS, but also the specific dimensi...

In the last 2 decades, the application of new technologies in process control caused a radical change in the role of the operator. To cope with these changes, the operator needs personalized support that can vary over time. To realize this support, we present the design and first testing of a framework for adaptive support. First an analysis was done which data is necessary for the framework. A...