Dynamic Decomposition of Spatiotemporal Neural Signals

Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to specific types of information processing. Here we present a data analysis framework that uses a linearized model of these dynamic states in order to decompose the measured neural signal into a series of components that capture both rhythmic and non-rhythmic neural activity. The method is based on stochastic differential equations and Gaussian process regression. Through computer simulations and analysis of magnetoencephalographic data, we demonstrate the efficacy of the method in identifying meaningful modulations of oscillatory signals corrupted by structured temporal and spatiotemporal noise. These results suggest that the method is particularly suitable for the analysis and interpretation of complex temporal and spatiotemporal neural signals

Phosphoenolpyruvate Carboxykinase as the Sole Anaplerotic Enzyme in Saccharomyces cerevisiae

Pyruvate carboxylase is the sole anaplerotic enzyme in glucose-grown cultures of wild-type Saccharomyces cerevisiae. Pyruvate carboxylase-negative (Pyc–) S. cerevisiae strains cannot grow on glucose unless media are supplemented with C4 compounds, such as aspartic acid. In several succinate-producing prokaryotes, phosphoenolpyruvate carboxykinase (PEPCK) fulfills this anaplerotic role. However, the S. cerevisiae PEPCK encoded by PCK1 is repressed by glucose and is considered to have a purely decarboxylating and gluconeogenic function. This study investigates whether and under which conditions PEPCK can replace the anaplerotic function of pyruvate carboxylase in S. cerevisiae. Pyc– S. cerevisiae strains constitutively overexpressing the PEPCK either from S. cerevisiae or from Actinobacillus succinogenes did not grow on glucose as the sole carbon source. However, evolutionary engineering yielded mutants able to grow on glucose as the sole carbon source at a maximum specific growth rate of ca. 0.14 h–1, one-half that of the (pyruvate carboxylase-positive) reference strain grown under the same conditions. Growth was dependent on high carbon dioxide concentrations, indicating that the reaction catalyzed by PEPCK operates near thermodynamic equilibrium. Analysis and reverse engineering of two independently evolved strains showed that single point mutations in pyruvate kinase, which competes with PEPCK for phosphoenolpyruvate, were sufficient to enable the use of PEPCK as the sole anaplerotic enzyme. The PEPCK reaction produces one ATP per carboxylation event, whereas the original route through pyruvate kinase and pyruvate carboxylase is ATP neutral. This increased ATP yield may prove crucial for engineering of efficient and low-cost anaerobic production of C4 dicarboxylic acids in S. cerevisiae

Quantum rejection sampling

Rejection sampling is a well-known method to sample from a target distribution, given the ability to sample from a given distribution. The method has been first formalized by von Neumann (1951) and has many applications in classical computing. We define a quantum analogue of rejection sampling: given a black box producing a coherent superposition of (possibly unknown) quantum states with some amplitudes, the problem is to prepare a coherent superposition of the same states, albeit with different target amplitudes. The main result of this paper is a tight characterization of the query complexity of this quantum state generation problem. We exhibit an algorithm, which we call quantum rejection sampling, and analyze its cost using semidefinite programming. Our proof of a matching lower bound is based on the automorphism principle which allows to symmetrize any algorithm over the automorphism group of the problem. Our main technical innovation is an extension of the automorphism principle to continuous groups that arise for quantum state generation problems where the oracle encodes unknown quantum states, instead of just classical data. Furthermore, we illustrate how quantum rejection sampling may be used as a primitive in designing quantum algorithms, by providing three different applications. We first show that it was implicitly used in the quantum algorithm for linear systems of equations by Harrow, Hassidim and Lloyd. Secondly, we show that it can be used to speed up the main step in the quantum Metropolis sampling algorithm by Temme et al.. Finally, we derive a new quantum algorithm for the hidden shift problem of an arbitrary Boolean function and relate its query complexity to "water-filling" of the Fourier spectrum.Comment: 19 pages, 5 figures, minor changes and a more compact style (to appear in proceedings of ITCS 2012

Wasserstein Variational Inference

This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and the Wasserstein distance as special cases. The gradients of the Wasserstein variational loss are obtained by backpropagating through the Sinkhorn iterations. This technique results in a very stable likelihood-free training method that can be used with implicit distributions and probabilistic programs. Using the Wasserstein variational inference framework, we introduce several new forms of autoencoders and test their robustness and performance against existing variational autoencoding techniques.Comment: 8 pages, 1 figur

Weak Acid Permeation in Synthetic Lipid Vesicles and Across the Yeast Plasma Membrane

We present a fluorescence-based approach for determination of the permeability of small molecules across the membranes of lipid vesicles and living cells. With properly designed experiments, the method allows us to assess the membrane physical properties both in vitro and in vivo. We find that the permeability of weak acids increases in the order of benzoic > acetic > formic > lactic, both in synthetic lipid vesicles and the plasma membrane of Saccharomyces cerevisiae, but the permeability is much lower in yeast (one to two orders of magnitude). We observe a relation between the molecule permeability and the saturation of the lipid acyl chain (i.e., lipid packing) in the synthetic lipid vesicles. By analyzing wild-type yeast and a manifold knockout strain lacking all putative lactic acid transporters, we conclude that the yeast plasma membrane is impermeable to lactic acid on timescales up to ∼2.5 h.BT/Industrial Microbiolog

Forward Amortized Inference for Likelihood-Free Variational Marginalization

In this paper, we introduce a new form of amortized variational inference by using the forward KL divergence in a joint-contrastive variational loss. The resulting forward amortized variational inference is a likelihood-free method as its gradient can be sampled without bias and without requiring any evaluation of either the model joint distribution or its derivatives. We prove that our new variational loss is optimized by the exact posterior marginals in the fully factorized mean-field approximation, a property that is not shared with the more conventional reverse KL inference. Furthermore, we show that forward amortized inference can be easily marginalized over large families of latent variables in order to obtain a marginalized variational posterior. We consider two examples of variational marginalization. In our first example we train a Bayesian forecaster for predicting a simplified chaotic model of atmospheric convection. In the second example we train an amortized variational approximation of a Bayesian optimal classifier by marginalizing over the model space. The result is a powerful meta-classification network that can solve arbitrary classification problems without further training.Comment: 9 pages, 3 figure