Variational approach for learning Markov processes from time series data

Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly nonlinear dynamical systems is facilitated by the fact that we can often find a (generally nonlinear) transformation of the system coordinates to features in which the dynamics can be excellently approximated by a linear Markovian model. Moreover, the large number of system variables often change collectively on large time- and length-scales, facilitating a low-dimensional analysis in feature space. In this paper, we introduce a variational approach for Markov processes (VAMP) that allows us to find optimal feature mappings and optimal Markovian models of the dynamics from given time series data. The key insight is that the best linear model can be obtained from the top singular components of the Koopman operator. This leads to the definition of a family of score functions called VAMP-r which can be calculated from data, and can be employed to optimize a Markovian model. In addition, based on the relationship between the variational scores and approximation errors of Koopman operators, we propose a new VAMP-E score, which can be applied to cross-validation for hyper-parameter optimization and model selection in VAMP. VAMP is valid for both reversible and nonreversible processes and for stationary and non-stationary processes or realizations

Cooperative H-infinity Estimation for Large-Scale Interconnected Linear Systems

In this paper, a synthesis method for distributed estimation is presented, which is suitable for dealing with large-scale interconnected linear systems with disturbance. The main feature of the proposed method is that local estimators only estimate a reduced set of state variables and their complexity does not increase with the size of the system. Nevertheless, the local estimators are able to deal with lack of local detectability. Moreover, the estimators guarantee H-infinity-performance of the estimates with respect to model and measurement disturbances.Comment: Short version published in Proc. American Control Conference (ACC), pp.2119-2124. Chicago, IL, 201

Quantum Algorithm for Approximating Maximum Independent Sets

We present a quantum algorithm for approximating maximum independent sets of a graph based on quantum non-Abelian adiabatic mixing in the sub-Hilbert space of degenerate ground states, which generates quantum annealing in a secondary Hamiltonian. For both sparse and dense graphs, our quantum algorithm on average can find an independent set of size very close to $\alpha(G)$, which is the size of the maximum independent set of a given graph $G$. Numerical results indicate that an $O(n^2)$ time complexity quantum algorithm is sufficient for finding an independent set of size $(1-\epsilon)\alpha(G)$. The best classical approximation algorithm can produce in polynomial time an independent set of size about half of $\alpha(G)$

Resonant Quantum Search with Monitor Qubits

We present an algorithm for the generalized search problem (searching $k$ marked items among $N$ items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity $O(\sqrt{N/k})$ as the Grover algorithm. A natural extension of the algorithm, incorporating auxiliary "monitor" qubits, can determine $k$ precisely, if it is unknown. The time complexity of our counting algorithm is $O(\sqrt{N})$, similar to the best quantum approximate counting algorithm, or better, given appropriate physical resources.Comment: 12 pages, 1 figur

Flow Cell Characterisation: Flow Visualisation, Pressure Drop and Mass Transport at 2D Electrodes in a Rectangular Channel

The reaction environment in a C-Flow Lab 5 × 5® laboratory-scale electrochemical flow cell was characterised in terms of fluid flow, hydraulic pressure drop and space averaged mass transport coefficient. The cell was studied in flow-by configuration with smooth, planar electrodes within its rectangular flow channels. The effect of a turbulence promoter (a polymer mesh with a volumetric porosity of 0.84) placed next to the working electrode was also evaluated. Electrolyte volumetric flow rates ranged from 0.3 to 1.5 dm3 min-1, corresponding to mean linear velocities of 2 to 10 cm s-1 past the electrode surface and channel Reynolds numbers of 53 to 265. The pressure drop was measured both over the electrode channel and through the whole cell as a function of mean linear velocity. The electrochemical performance was quantified using the limiting current technique, which was used to determine the mass transport coefficient over the same range of flow rate. Results were compared to well-characterised electrochemical flow reactors found in the literature. The mass transport enhancement factor due to the presence of the turbulence promoter was between 1.6 and 3.9 under the studied conditions. Reactant conversion in batch recirculation mode and normalised space velocity were predicted from the electrochemical plug flow reactor equation