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

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

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

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

Model-Based Noninvasive Estimation of Intracranial Pressure from Cerebral Blood Flow Velocity and Arterial Pressure

Intracranial pressure (ICP) is affected in many neurological conditions. Clinical measurement of pressure on the brain currently requires placing a probe in the cerebrospinal fluid compartment, the brain tissue, or other intracranial space. This invasiveness limits the measurement to critically ill patients. Because ICP is also clinically important in conditions ranging from brain tumors and hydrocephalus to concussions, noninvasive determination of ICP would be desirable. Our model-based approach to continuous estimation and tracking of ICP uses routinely obtainable time-synchronized, noninvasive (or minimally invasive) measurements of peripheral arterial blood pressure and blood flow velocity in the middle cerebral artery (MCA), both at intra-heartbeat resolution. A physiological model of cerebrovascular dynamics provides mathematical constraints that relate the measured waveforms to ICP. Our algorithm produces patient-specific ICP estimates with no calibration or training. Using 35 hours of data from 37 patients with traumatic brain injury, we generated ICP estimates on 2665 nonoverlapping 60-beat data windows. Referenced against concurrently recorded invasive parenchymal ICP that varied over 100 millimeters of mercury (mmHg) across all records, our estimates achieved a mean error (bias) of 1.6 mmHg and SD of error (SDE) of 7.6 mmHg. For the 1673 data windows over 22 hours in which blood flow velocity recordings were available from both the left and the right MCA, averaging the resulting bilateral ICP estimates reduced the bias to 1.5 mmHg and SDE to 5.9 mmHg. This accuracy is already comparable to that of some invasive ICP measurement methods in current clinical use.National Institutes of Health (U.S.) (R01 EB001659)CIMIT: Center for Integration of Medicine and Innovative Technolog

Infrared spectra and thermal decompositions of metal acetates and dicarboxylates

The infrared spectra of rare earth acetates have been studied to examine the metal-acetate bonding. The thermal decomposition of rare earth acetates as well as lead and copper acetates have been investigated in detail by employing thermogravimetric analysis and differential thermal analysis. Thermal decomposition of calcium dicarboxylates (malonate to sebacate) have been studied employing t.g.a. and d.t.a. Infrared spectra of the dicarboxylates have also been studied. Preliminary results on the products of decomposition of dicarboxylates have been reported

Continuous quantitative monitoring of cerebral oxygen metabolism in neonates by ventilator-gated analysis of NIRS recordings

Oxidative stress during fetal development, delivery, or early postnatal life is a major cause of neuropathology, as both hypoxic and hyperoxic insults can significantly damage the developing brain. Despite the obvious need for reliable cerebral oxygenation monitoring, no technology currently exists to monitor cerebral oxygen metabolism continuously and noninvasively in infants at high risk for developing brain injury. Consequently, a rational approach to titrating oxygen supply to cerebral oxygen demand – and thus avoiding hyperoxic or hypoxic insults – is currently lacking. We present a promising method to close this crucial technology gap in the important case of neonates on conventional ventilators. By using cerebral near-infrared spectroscopy and signals from conventional ventilators, along with arterial oxygen saturation, we derive continuous (breath-by-breath) estimates of cerebral venous oxygen saturation, cerebral oxygen extraction fraction, cerebral blood flow, and cerebral metabolic rate of oxygen. The resultant estimates compare very favorably to previously reported data obtained by non-continuous and invasive means from preterm infants in neonatal critical care.National Institutes of Health (U.S.) (Grant R01EB001659)National Institutes of Health (U.S.) (Grant K24NS057568)National Institutes of Health (U.S.) (Grant R21HD056009

Chronic elevation of pulmonary microvascular pressure in chronic heart failure reduces bi-directional pulmonary fluid flux

Aims. Chronic heart failure leads to pulmonary vascular remodelling and thickening of the alveolar–capillary barrier. We examined whether this protective effect may slow resolution of pulmonary oedema consistent with decreased bi-directional fluid flux. Methods and results. Seven weeks following left coronary artery ligation, we measured both fluid flux during an acute rise in left atrial pressure (n = 29) and intrinsic alveolar fluid clearance (n = 45) in the isolated rat lung. Chronic elevation of pulmonary microvascular pressure prevented pulmonary oedema and decreased lung compliance when left atrial pressure was raised to 20 cmH2O, and was associated with reduced expression of endothelial aquaporin 1 (P = 0.03). However, no other changes were found in mediators of fluid flux or cellular fluid channels. In isolated rat lungs, chronic LV dysfunction (LV end-diastolic pressure and infarct circumference) was also inversely related to alveolar fluid clearance (P ≤ 0.001). The rate of pulmonary oedema reabsorption was estimated by plasma volume expansion in eight patients with a previous clinical history of chronic heart failure and eight without, who presented with acute pulmonary oedema. Plasma volume expansion was reduced at 24 h in those with chronic heart failure (P = 0.03). Conclusions. Chronic elevation of pulmonary microvascular pressure in CHF leads to decreased intrinsic bi-directional fluid flux at the alveolar–capillary barrier. This adaptive response defends against alveolar flooding, but may delay resolution of alveolar oedema.A National Health and Medical Research Council (NHMRC) grant (#375129); Australian and New Zealand College of Anaesthetists (ANZCA) grant (#08/020); the Flinders Medical Centre Foundation