Designing Optimal Quantum Detectors Via Semidefinite Programming

We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of density operators. We show that the design of the optimal detector can be formulated as a semidefinite programming problem. Based on this formulation, we derive a set of necessary and sufficient conditions for an optimal quantum measurement. We then show that the optimal measurement can be found by solving a standard (convex) semidefinite program followed by the solution of a set of linear equations or, at worst, a standard linear programming problem. By exploiting the many well-known algorithms for solving semidefinite programs, which are guaranteed to converge to the global optimum, the optimal measurement can be computed very efficiently in polynomial time. Using the semidefinite programming formulation, we also show that the rank of each optimal measurement operator is no larger than the rank of the corresponding density operator. In particular, if the quantum state ensemble is a pure-state ensemble consisting of (not necessarily independent) rank-one density operators, then we show that the optimal measurement is a pure-state measurement consisting of rank-one measurement operators.Comment: Submitted to IEEE Transactions on Information Theor

മത്സ്യബന്ധനത്തിനുളള വിവിധതരം ട്രോള്‍ വലകള്‍ (Different kinds of trawl nets for power fishing)

Trawl net is a bag-shaped gear towed through water, the mouth of which is kept open either by a frame or beam or otter boards and floats or kites and sinkers or weight. Sometimes the opening is effected by dragging the net with two boats

Redundancy relations and robust failure detection

All failure detection methods are based on the use of redundancy, that is on (possible dynamic) relations among the measured variables. Consequently the robustness of the failure detection process depends to a great degree on the reliability of the redundancy relations given the inevitable presence of model uncertainties. The problem of determining redundancy relations which are optimally robust in a sense which includes the major issues of importance in practical failure detection is addressed. A significant amount of intuition concerning the geometry of robust failure detection is provided

Model reduction for analysis of cascading failures in power systems

In this paper, we apply a principal-orthogonal decomposition based method to the model reduction of a hybrid, nonlinear model of a power network. The results demonstrate that the sequence of fault events can be evaluated and predicted without necessarily simulating the whole system

Mass fluctuation kinetics: analysis and computation of equilibria and local dynamics

The mass fluctuation kinetics (MFK) model is a set of coupled ordinary differential equations approximating the time evolution of means and covariances of species concentrations in chemical reaction networks. It generalises classical mass action kinetics (MAK), in which fluctuations around the mean are ignored. MFK may be used to approximate stochasticity in system trajectories when stochastic simulation methods are prohibitively expensive computationally. This study presents a set of tools to aid in the analysis of systems within the MFK framework. A closed-form expression for the MFK Jacobian matrix is derived. This expression facilitates the computation of MFK equilibria and the characterisation of the dynamics of small deviations from the equilibria (i.e. local dynamics). Software developed in MATLAB to analyse systems within the MFK framework is also presented. The authors outline a homotopy continuation method that employs the Jacobian for bifurcation analysis, that is, to generate a locus of steady-state Jacobian eigenvalues corresponding to changing a chosen MFK parameter such as system volume or a rate constant. This method is applied to study the effect of small-volume stochasticity on local dynamics at equilibria in a pair of example systems, namely the formation and dissociation of an enzyme-substrate complex and a genetic oscillator. For both systems, this study reveals volume regimes where MFK provides a quantitatively and/or qualitatively correct description of system behaviour, and regimes where the MFK approximation is inaccurate. Moreover, our analysis provides evidence that decreasing volume from the MAK regime (infinite volume) has a destabilising effect on system dynamics

Structural Analysis of Laplacian Spectral Properties of Large-Scale Networks

Using methods from algebraic graph theory and convex optimization, we study the relationship between local structural features of a network and spectral properties of its Laplacian matrix. In particular, we derive expressions for the so-called spectral moments of the Laplacian matrix of a network in terms of a collection of local structural measurements. Furthermore, we propose a series of semidefinite programs to compute bounds on the spectral radius and the spectral gap of the Laplacian matrix from a truncated sequence of Laplacian spectral moments. Our analysis shows that the Laplacian spectral moments and spectral radius are strongly constrained by local structural features of the network. On the other hand, we illustrate how local structural features are usually not enough to estimate the Laplacian spectral gap.Comment: IEEE Automatic Control, accepted for publicatio

On the operation of small shrimp trawls in shallow waters-scope-ratio and size-depth relation

Studies on small trawls seem to be comparatively less. These trawls are generally operated in shallower waters, where due to the limitations in the length of warp that could be released, size restrictions have to be considered for their efficient functioning. An attempt has been made to assess the effective scope-ratio of length of warp required for the operation of trawls at shallower depth and to a judge the size of trawl suitable for use at lower depths

Operating Regimes of Signaling Cycles: Statics, Dynamics, and Noise Filtering

A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input–output characteristic in a certain steady-state regime. Here, we systematically study the cycle's steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four different regimes, each with its specific input–output characteristics. These results are obtained using the total quasi–steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions. We invoke experimental data that suggest the possibility of signaling cycles operating in one of the new regimes. We then consider the cycle's dynamic behavior, which has so far been relatively neglected. We demonstrate that the intrinsic architecture of the cycles makes them act—in all four regimes—as tunable low-pass filters, filtering out high-frequency fluctuations or noise in signals and environmental cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical simulations show that our analytical results hold well even for noise of large amplitude. We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways

Operating Regimes of Signaling Cycles: Statics, Dynamics, and Noise Filtering

A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input–output characteristic in a certain steady-state regime. Here, we systematically study the cycle's steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four different regimes, each with its specific input–output characteristics. These results are obtained using the total quasi–steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions. We invoke experimental data that suggest the possibility of signaling cycles operating in one of the new regimes. We then consider the cycle's dynamic behavior, which has so far been relatively neglected. We demonstrate that the intrinsic architecture of the cycles makes them act—in all four regimes—as tunable low-pass filters, filtering out high-frequency fluctuations or noise in signals and environmental cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical simulations show that our analytical results hold well even for noise of large amplitude. We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways