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In a standard Quantum Sensing (QS) task one aims at estimating an unknown parameter $\theta$, encoded into an $n$-qubit probe state, via measurements of the system. The success of this task hinges on the ability to correlate changes in the parameter to changes in the system response $\mathcal{R}(\theta)$ (i.e., changes in the measurement outcomes). For simple cases the form of $\mathcal{R}(\theta)$ is known, but the same cannot be said for realistic scenarios, as no general closed-form expression exists. In this work we present an inference-based scheme for QS. We show that, for a general class of unitary families of encoding, $\mathcal{R}(\theta)$ can be fully characterized by only measuring the system response at $2n+1$ parameters. In turn, this allows us to infer the value of an unknown parameter given the measured response, as well as to determine the sensitivity of the sensing scheme, which characterizes its overall performance. We show that inference error is, with high probability, smaller than $\delta$, if one measures the system response with a number of shots that scales only as $\Omega(\log^3(n)/\delta^2)$. Furthermore, the framework presented can be broadly applied as it remains valid for arbitrary probe states and measurement schemes, and, even holds in the presence of quantum noise. We also discuss how to extend our results beyond unitary families. Finally, to showcase our method we implement it for a QS task on real quantum hardware, and in numerical simulations., Comment: 5+10 pages, 3+5 figures

The task of learning a quantum circuit to prepare a given mixed state is a fundamental quantum subroutine. We present a variational quantum algorithm (VQA) to learn mixed states which is suitable for near-term hardware. Our algorithm represents a generalization of previous VQAs that aimed at learning preparation circuits for pure states. We consider two different ans\"{a}tze for compiling the target state; the first is based on learning a purification of the state and the second on representing it as a convex combination of pure states. In both cases, the resources required to store and manipulate the compiled state grow with the rank of the approximation. Thus, by learning a lower rank approximation of the target state, our algorithm provides a means of compressing a state for more efficient processing. As a byproduct of our algorithm, one effectively learns the principal components of the target state, and hence our algorithm further provides a new method for principal component analysis. We investigate the efficacy of our algorithm through extensive numerical implementations, showing that typical random states and thermal states of many body systems may be learnt this way. Additionally, we demonstrate on quantum hardware how our algorithm can be used to study hardware noise-induced states., Comment: 17 main + 17 appendix pages, 6 main + 9 appendix figures

Trotterization-based, iterative approaches to quantum simulation are restricted to simulation times less than the coherence time of the quantum computer, which limits their utility in the near term. Here, we present a hybrid quantum-classical algorithm, called Variational Fast Forwarding (VFF), for decreasing the quantum circuit depth of quantum simulations. VFF seeks an approximate diagonalization of a short-time simulation to enable longer-time simulations using a constant number of gates. Our error analysis provides two results: (1) the simulation error of VFF scales at worst linearly in the fast-forwarded simulation time, and (2) our cost function's operational meaning as an upper bound on average-case simulation error provides a natural termination condition for VFF. We implement VFF for the Hubbard, Ising, and Heisenberg models on a simulator. Additionally, we implement VFF on Rigetti's quantum computer to demonstrate simulation beyond the coherence time. Finally, we show how to estimate energy eigenvalues using VFF., 13 + 7 pages, 7 figures

Non-von Neumann computational hardware, based on neuron-inspired, non-linear elements connected via linear, weighted synapses—so-called neuromorphic systems—is a viable computational substrate. Since neuromorphic systems have been shown to use less power than CPUs for many applications, they are of potential use in autonomous systems such as robots, drones, and satellites, for which power resources are at a premium. The power used by neuromorphic systems is approximately proportional to the number of spiking events produced by neurons on-chip. However, typical information encoding on these chips is in the form of firing rates that unarily encode information. That is, the number of spikes generated by a neuron is meant to be proportional to an encoded value used in a computation or algorithm. Unary encoding is less efficient (produces more spikes) than binary encoding. For this reason, here we present neuromorphic computational mechanisms for implementing binary two’s complement operations. We use the mechanisms to construct a neuromorphic, binary matrix multiplication algorithm that may be used as a primitive for linear differential equation integration, deep networks, and other standard calculations. We also construct a random walk circuit and apply it in Brownian motion simulations. We study how both algorithms scale in circuit size and iteration time.

Quantum neural networks (QNNs) have generated excitement around the possibility of efficiently analyzing quantum data. But this excitement has been tempered by the existence of exponentially vanishing gradients, known as barren plateau landscapes, for many QNN architectures. Recently, Quantum Convolutional Neural Networks (QCNNs) have been proposed, involving a sequence of convolutional and pooling layers that reduce the number of qubits while preserving information about relevant data features. In this work we rigorously analyze the gradient scaling for the parameters in the QCNN architecture. We find that the variance of the gradient vanishes no faster than polynomially, implying that QCNNs do not exhibit barren plateaus. This provides an analytical guarantee for the trainability of randomly initialized QCNNs, which highlights QCNNs as being trainable under random initialization unlike many other QNN architectures. To derive our results we introduce a novel graph-based method to analyze expectation values over Haar-distributed unitaries, which will likely be useful in other contexts. Finally, we perform numerical simulations to verify our analytical results., Comment: 9 + 20 pages, 7 + 8 figures, 3 tables. Updated to published version

Currently available quantum hardware allows for small-scale implementations of quantum machine learning algorithms. Such experiments aid the search for applications of quantum computers by benchmarking the near-term feasibility of candidate algorithms. Here we demonstrate the quantum learning of a two-qubit unitary by a sequence of three parameterized quantum circuits containing a total of 21 variational parameters. Moreover, we variationally diagonalize the unitary to learn its spectral decomposition, i.e., its eigenvalues and eigenvectors. We illustrate how this can be used as a subroutine to compress the depth of dynamical quantum simulations. One can view our implementation as a demonstration of entanglement-enhanced machine learning, as only a single (entangled) training data pair is required to learn a $4\ifmmode\times\else\texttimes\fi{}4$ unitary matrix.

The capabilities of natural neural systems have inspired new generations of machine learning algorithms as well as neuromorphic very large-scale integrated (VLSI) circuits capable of fast, low-power information processing. However, it has been argued that most modern machine learning algorithms are not neurophysiologically plausible. In particular, the workhorse of modern deep learning, the backpropagation algorithm, has proven difficult to translate to neuromorphic hardware. In this study, we present a neuromorphic, spiking backpropagation algorithm based on synfire-gated dynamical information coordination and processing, implemented on Intel's Loihi neuromorphic research processor. We demonstrate a proof-of-principle three-layer circuit that learns to classify digits from the MNIST dataset. To our knowledge, this is the first work to show a Spiking Neural Network (SNN) implementation of the backpropagation algorithm that is fully on-chip, without a computer in the loop. It is competitive in accuracy with off-chip trained SNNs and achieves an energy-delay product suitable for edge computing. This implementation shows a path for using in-memory, massively parallel neuromorphic processors for low-power, low-latency implementation of modern deep learning applications., arXiv

Quantum compiling, where a parameterized quantum circuit is trained to learn a target unitary, is an important primitive for quantum computing that can be used as a subroutine to obtain optimal circuits or as a tomographic tool to study the dynamics of an experimental system. While much attention has been paid to quantum compiling on discrete variable hardware, less has been paid to compiling in the continuous variable paradigm. Here we motivate several, closely related, short depth continuous variable algorithms for quantum compilation. We analyse the trainability of our proposed cost functions and numerically demonstrate our algorithms by learning arbitrary Gaussian operations and Kerr non-linearities. We further make connections between this framework and quantum learning theory in the continuous variable setting by deriving No-Free-Lunch theorems. These generalization bounds demonstrate a linear resource reduction for learning Gaussian unitaries using entangled coherent-Fock states and an exponential resource reduction for learning arbitrary unitaries using Two-Mode-Squeezed states., Comment: 20 pages, 7 figures

Scrambling processes, which rapidly spread entanglement through many-body quantum systems, are difficult to investigate using standard techniques, but are relevant to quantum chaos and thermalization. In this Letter, we ask if quantum machine learning (QML) could be used to investigate such processes. We prove a no-go theorem for learning an unknown scrambling process with QML, showing that any variational ansatz is highly probable to have a barren plateau landscape, i.e., cost gradients that vanish exponentially in the system size. This implies that the required resources scale exponentially even when strategies to avoid such scaling (e.g., from ansatz-based barren plateaus or No-Free-Lunch theorems) are employed. Furthermore, we numerically and analytically extend our results to approximate scramblers. Hence, our work places generic limits on the learnability of unitaries when lacking prior information., 5 pages, 3 figures in the main text. 6 pages, 1 figure in the supplementary information. Comments welcome

Sparse coding algorithms have been used to model the acquisition of V1 simple cell receptive fields as well as to accomplish the unsupervised acquisition of features for a variety of machine learning applications. The Locally Competitive Algorithm (LCA) provides a biologically plausible implementation of sparse coding based on lateral inhibition. LCA can be reformulated to support dictionary learning via an online local Hebbian rule that reduces predictive coding error. Although originally formulated in terms of leaky integrator rate-coded neurons, LCA based on lateral inhibition between leaky integrate-and-fire (LIF) neurons has been implemented on spiking neuromorphic processors but such implementations preclude local online learning. We previously reported that spiking LCA can be expressed in terms of predictive coding error in a manner that allows for unsupervised dictionary learning via a local Hebbian rule but the issue of stability has not previously been addressed. Here, we use the Nengo simulator to show that unsupervised dictionary learning in a spiking LCA model can be made stable by incorporating epochs of sinusoidally-modulated noise that we hypothesize are analogous to slow-wave sleep. In the absence of slow-wave sleep epochs, the |L| 2 norm of individual features tends to increase over time during unsupervised dictionary learning until the corresponding neurons can be activated by random Gaussian noise. By inserting epochs of sinusoidally-modulated Gaussian noise, however, the |L| 2 norms of any activated neurons are down regulated such | that individual neurons are no longer activated by noise. Our results suggest that slow-wave sleep may act, in part, to ensure that cortical neurons do not "hallucinate" their target features in pure noise, thus helping to maintain dynamical stability.

A new class of neuromorphic processors promises to provide fast and power-efficient execution of spiking neural networks with on-chip synaptic plasticity. This efficiency derives in part from the fine-grained parallelism as well as event-driven communication mediated by spatially and temporally sparse spike messages. Another source of efficiency arises from the close spatial proximity between synapses and the sites where their weights are applied and updated. This proximity of compute and memory elements drastically reduces expensive data movements but imposes the constraint that only local operations can be efficiently performed, similar to constraints present in biological neural circuits. Efficient weight update operations should therefore only depend on information available locally at each synapse as non-local operations that involve copying, taking a transpose, or normalizing an entire weight matrix are not efficiently supported by present neuromorphic architectures. Moreover, spikes are typically non-negative events, which imposes additional constraints on how local weight update operations can be performed. The Locally Competitive Algorithm (LCA) is a dynamical sparse solver that uses only local computations between non-spiking leaky integrator neurons, allowing for massively parallel implementations on compatible neuromorphic architectures such as Intel's Loihi research chip. It has been previously demonstrated that non-spiking LCA can be used to learn dictionaries of convolutional kernels in an unsupervised manner from raw, unlabeled input, although only by employing non-local computation and signed non-spiking outputs. Here, we show how unsupervised dictionary learning with spiking LCA (S-LCA) can be implemented using only local computation and unsigned spike events, providing a promising strategy for constructing self-organizing neuromorphic chips.

For some time, it has been thought that backpropagation of errors could not be implemented in biophysiologically realistic neural circuits. This belief was largely due to either 1) the need for symmetric replication of feedback and feedforward weights, 2) the need for differing forms of activation between forward and backward propagating sweeps, and 3) the need for a separate network for error gradient computation and storage, on the one hand, or 4) nonphysiological backpropagation through the forward propagating neurons themselves, on the other. In this paper, we present spiking neuron mechanisms for gating pulses to maintain short-term memories, controlling forward inference and backward error propagation, and coordinating learning of feedback and feedforward weights. These neural mechanisms are synthesized into a new backpropagation algorithm for neuromorphic circuits.

The brain has a central, short-term learning module, the hippocampus, which transfers what it has learned to long-term memory in cortex during non-REM sleep. The putative mechanism responsible for this type of memory consolidation invokes hierarchically nested hippocampal ripples (100-250 Hz), thalamo-cortical spindles (7-15 Hz), and cortical slow oscillations (< 1 Hz) to enable transfer. Suppression of, for instance, thalamic spindles has been shown to impair hippocampus-dependent memory consolidation. Cortical oscillations are central to information transfer in neural systems. Significant evidence supports the idea that coincident spike input can allow the neural threshold to be overcome, and spikes to be propagated downstream in a circuit. Thus, an observation of oscillations in neural circuits would be an indication that repeated synchronous spiking is enabling information transfer. However, for memory transfer, in which synaptic weights must be being transferred from one neural circuit (region) to another, what is the mechanism? Here, we present a synaptic transfer mechanism whose structure provides some understanding of the phenomena that have been implicated in memory transfer, including the nested oscillations at various frequencies. The circuit is based on the principle of pulse-gated, graded information transfer between neural populations.PACS numbers: 87.18.Sn,87.19.lj,87.19.lm,87.19.lq

One of the most promising applications of an error-corrected universal quantum computer is the efficient simulation of complex quantum systems such as large molecular systems. In this application, one is interested in both the electronic structure such as the ground state energy and dynamical properties such as the scattering cross section and chemical reaction rates. However, most theoretical work and experimental demonstrations have focused on the quantum computation of energies and energy surfaces. In this work, we attempt to make the prethreshold (not error-corrected) quantum simulation of dynamical properties practical as well. We show that the use of precomputed potential energy surfaces and couplings enables the gate-based simulation of few-channel but otherwise realistic molecular collisions. Our approach is based on the widely used Born---Oppenheimer approximation for the structure problem coupled with a semiclassical method for the dynamics. In the latter the electrons are treated quantum mechanically but the nuclei are classical, which restricts the collisions to high energy or temperature (typically above $$\approx 10$$?10 eV). By using operator splitting techniques optimized for the resulting time-dependent Hamiltonian simulation problem, we give several physically realistic collision examples, with 3---8 channels and circuit depths < 1000.

Zebrafish are a promising vertebrate model for elucidating how neural circuits generate behavior under normal and pathological conditions. The Baraban group first demonstrated that zebrafish larvae are valuable for investigating seizure events and can be used as a model for epilepsy in humans. Because of their small size and transparency, zebrafish embryos are ideal for imaging seizure activity using calcium indicators. Light-sheet microscopy is well suited to capturing neural activity in zebrafish because it is capable of optical sectioning, high frame rates, and low excitation intensities. We describe work in our lab to use light-sheet microscopy for high-speed long-time imaging of neural activity in wildtype and mutant zebrafish to better understand the connectivity and activity of inhibitory neural networks when GABAergic signaling is altered in vivo. We show that, with light-sheet microscopy, neural activity can be recorded at 23 frames per second in twocolors for over 10 minutes allowing us to capture rare seizure events in mutants. We have further implemented structured illumination to increase resolution and contrast in the vertical and axial directions during high-speed imaging at an effective frame rate of over 7 frames per second.

Light Sheet Microscopy is well suited for imaging model organisms and tissue sections that are hundreds of microns thick. Adaptive Optics is needed to correct aberrations in these samples. Here we describe our design of a scene based Shack Hartmann Wavefront Sensor for Light Sheet Microscopy.

Coherent neuronal activity is believed to underlie the transfer and processing of information in the brain. Coherent activity in the form of synchronous firing and oscillations has been measured in many brain regions and has been correlated with enhanced feature processing and other sensory and cognitive functions. In the theoretical context, synfire chains and the transfer of transient activity packets in feedforward networks have been appealed to in order to describe coherent spiking and information transfer. Recently, it has been demonstrated that the classical synfire chain architecture, with the addition of suitably timed gating currents, can support the graded transfer of mean firing rates in feedforward networks (called synfire-gated synfire chains-SGSCs). Here we study information propagation in SGSCs by examining mutual information as a function of layer number in a feedforward network. We explore the effects of gating and noise on information transfer in synfire chains and demonstrate that asymptotically, two main regions exist in parameter space where information may be propagated and its propagation is controlled by pulse-gating: a large region where binary codes may be propagated, and a smaller region near a cusp in parameter space that supports graded propagation across many layers.

Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach for discovering such algorithms. We apply our method to a ubiquitous primitive: computing the overlap ${\rm Tr}(\rho\sigma)$ between two quantum states $\rho$ and $\sigma$. The standard algorithm for this task, known as the Swap Test, is used in many applications such as quantum support vector machines, and, when specialized to $\rho = \sigma$, quantifies the Renyi entanglement. Here, we find algorithms that have shorter depths than the Swap Test, including one that has a constant depth (independent of problem size). Furthermore, we apply our approach to the hardware-specific connectivity and gate sets used by Rigetti's and IBM's quantum computers and demonstrate that the shorter algorithms that we derive significantly reduce the error - compared to the Swap Test - on these computers., Comment: 12 pages, 11 figures

Objective To evaluate examiner variability in a superficial skin marker model of canine stifle kinematics. Study Design Experimental. Animals Six clinically normal dogs. Methods Dogs had 11 retroreflective markers fixed to the skin on the right hindlimb. Dogs were trotted 5 times through the calibrated testing space and this was repeated on 4 different testing days. Examiner A applied all markers to a dog and collected 6 good trials for analysis. The markers were then removed and Examiner B immediately repeated the process on the same dog. This was repeated for each dog on the 4 testing days. The dogs were trotted at a velocity of 1.70–2.10 m/s through the testing space to obtain the dynamic data sets. Comparisons were performed with Fourier analysis and Generalized Indicator Function Analysis (GIFA). Significance was set at P

Neural data analysis has increasingly incorporated causal information to study circuit connectivity. Dimensional reduction forms the basis of most analyses of large multivariate time series. Here, we present a new, multitaper-based decomposition for stochastic, multivariate time series that acts on the covariance of the time series at all lags, $C(\tau)$, as opposed to standard methods that decompose the time series, $\mathbf{X}(t)$, using only information at zero-lag. In both simulated and neural imaging examples, we demonstrate that methods that neglect the full causal structure may be discarding important dynamical information in a time series., Comment: This invited paper was presented at the Asilomar 50th Conference on Signals, Systems, and Computers

Recent evidence suggests that neural information is encoded in packets and may be flexibly routed from region to region. We have hypothesized that neural circuits are split into sub-circuits where one sub-circuit controls information propagation via pulse gating and a second sub-circuit processes graded information under the control of the first sub-circuit. Using an explicit pulse-gating mechanism, we have been able to show how information may be processed by such pulse-controlled circuits and also how, by allowing the information processing circuit to interact with the gating circuit, decisions can be made. Here, we demonstrate how Hebbian plasticity may be used to supplement our pulse-gated information processing framework by implementing a machine learning algorithm. The resulting neural circuit has a number of structures that are similar to biological neural systems, including a layered structure and information propagation driven by oscillatory gating with a complex frequency spectrum., This invited paper was presented at the 50th Asilomar Conference on Signals, Systems and Computers

Line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse-gating in feedforward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, non-linear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and thus, dynamically control the processing of graded information., Comment: 7 pages, 5 figures

Compiling quantum algorithms for near-term quantum computers (accounting for connectivity and native gate alphabets) is a major challenge that has received significant attention both by industry and academia. Avoiding the exponential overhead of classical simulation of quantum dynamics will allow compilation of larger algorithms, and a strategy for this is to evaluate an algorithm's cost on a quantum computer. To this end, we propose a variational hybrid quantum-classical algorithm called quantum-assisted quantum compiling (QAQC). In QAQC, we use the overlap between a target unitary $U$ and a trainable unitary $V$ as the cost function to be evaluated on the quantum computer. More precisely, to ensure that QAQC scales well with problem size, our cost involves not only the global overlap ${\rm Tr} (V^\dagger U)$ but also the local overlaps with respect to individual qubits. We introduce novel short-depth quantum circuits to quantify the terms in our cost function, and we prove that our cost cannot be efficiently approximated with a classical algorithm under reasonable complexity assumptions. We present both gradient-free and gradient-based approaches to minimizing this cost. As a demonstration of QAQC, we compile various one-qubit gates on IBM's and Rigetti's quantum computers into their respective native gate alphabets. Furthermore, we successfully simulate QAQC up to a problem size of 9 qubits, and these simulations highlight both the scalability of our cost function as well as the noise resilience of QAQC. Future applications of QAQC include algorithm depth compression, black-box compiling, noise mitigation, and benchmarking., Comment: 19 + 10 pages, 14 figures. Added larger scale implementations and proof that cost function is DQC1-hard

Light sheet fluorescence microscopy (LSFM) is a powerful tool for investigating model organisms including zebrafish. However, due to scattering and refractive index variations within the sample, the resulting image often suffers from low contrast. Structured illumination (SI) has been combined with scanned LSFM to remove out-of-focus and scattered light using square-law detection. Here, we demonstrate that the combination of LSFM with linear reconstruction SI can further increase resolution and contrast in the vertical and axial directions compared to the widely adopted root-mean square reconstruction method while using the same input images. We apply this approach to imaging neural activity in 7-day postfertilization zebrafish larvae. We imaged two-dimensional sections of the zebrafish central nervous system in two colors at an effective frame rate of 7 frames per second.

The efficiency and accuracy of cortical maps from optical imaging experiments have been improved using periodic stimulation protocols. The resulting data analysis requires the detection and estimation of periodic information in a multivariate dataset. To date, these analyses have relied on discrete Fourier transform (DFT) sinusoid estimates. Multitaper methods have become common statistical tools in the analysis of univariate time series that can give improved estimates. Here, we extend univariate multitaper harmonic analysis methods to the multivariate, imaging context. Given the hypothesis that a coherent oscillation across many pixels exists within a specified bandwidth, we investigate the problem of its detection and estimation in noisy data by constructing Hotelling's generalized T2-test. We then extend the investigation of this problem in two contexts, that of standard canonical variate analysis (CVA) and that of generalized indicator function analysis (GIFA) which is often more robust in extracting a signal in spatially correlated noise. We provide detailed information on the fidelities of the mean estimates found with our methods and comparison with DFT estimates. Our results indicate that GIFA provides particularly good estimates of harmonic signals in spatially correlated noise and is useful for detecting small amplitude harmonic signals in applications such as biological imaging measurements where spatially correlated noise is common. We demonstrate the power of our methods with an optical imaging dataset of the periodic response to a periodically rotating oriented drifting grating stimulus experiment in cat visual cortex.

In this paper, we extend our framework for constructing low-dimensional dynamical system models of large-scale neuronal networks of mammalian primary visual cortex. Our dimensional reduction procedure consists of performing a suitable linear change of variables and then systematically truncating the new set of equations. The extended framework includes modeling the effect of neglected modes as a stochastic process. By parametrizing and including stochasticity in one of two ways we show that we can improve the systems-level characterization of our dimensionally reduced neuronal network model. We examined orientation selectivity maps calculated from the firing rate distribution of large-scale simulations and stochastic dimensionally reduced models and found that by using stochastic processes to model the neglected modes, we were able to better reproduce the mean and variance of firing rates in the original large-scale simulations while still accurately predicting the orientation preference distribution.

The use of nondestructive NMR spectroscopy for enzymatic studies offers unique opportunities to identify nearly all enzymatic byproducts and detect unstable short-lived products or intermediates at the molecular level; however, numerous challenges must be overcome before it can become a widely used tool. The biosynthesis of acetyl-coenzyme A (acetyl-CoA) by acetyl-CoA synthetase is used here as a case study for the development of an analytical NMR-based time-course assay platform. We describe an algorithm to deconvolve superimposed spectra into spectra for individual molecules, and further develop a model to simulate the acetyl-CoA synthetase enzyme reaction network using the data derived from time-course NMR. Simulation shows indirectly that synthesis of acetyl-CoA is mediated via an enzyme-bound intermediate (possibly acetyl-AMP) and is accompanied by a nonproductive loss from an intermediate. The ability to predict enzyme function based on partial knowledge of the enzymatic pathway topology is also discussed.

Objective: To model the kinematics of the canine stifle in 3 dimensions using the Joint Coordinate System (JCS) and compare the JCS method with linear and segmental models. Study Design: In vivo biomechanical study. Animals: Normal adult mixed breed dogs (n=6). Methods: Dogs had 10 retroreflective markers affixed to the skin on the right pelvic limb. Dogs were walked and trotted 5 times through the calibrated space and the procedure was repeated 5 days later. Sagittal flexion and extension angle waveforms acquired during each trial with all 3 models (JCS, Linear, and Segmental) were produced simultaneously during each gait. The JCS method provided additional internal/external and abduction/adduction angles. Comparison of sagittal flexion and extension angle waveforms was performed with generalized indicator function analysis (GIFA) and Fourier analysis. A normalization procedure was performed. Results: Each model provided consistent equivalent sagittal flexion–extension data. The JCS provided consistent additional internal/external and abduction/adduction. Sagittal waveform differences were found between methods and testing days for each dog at a walk and a trot with both GIFA and Fourier analysis. After normalization, differences were less with Fourier analysis and were unaltered with GIFA. Conclusions: Whereas all methods produced similar flexion–extension waveforms, JCS provided additional valuable data. Clinical Relevance: The JCS model provided sagittal plane flexion/extension data as well as internal/external rotation and abduction/adduction data.