Partitioning variability in animal behavioral videos using semi-supervised variational autoencoders

Recent neuroscience studies demonstrate that a deeper understanding of brain function requires a deeper understanding of behavior. Detailed behavioral measurements are now often collected using video cameras, resulting in an increased need for computer vision algorithms that extract useful information from video data. Here we introduce a new video analysis tool that combines the output of supervised pose estimation algorithms (e.g. DeepLabCut) with unsupervised dimensionality reduction methods to produce interpretable, low-dimensional representations of behavioral videos that extract more information than pose estimates alone. We demonstrate this tool by extracting interpretable behavioral features from videos of three different head-fixed mouse preparations, as well as a freely moving mouse in an open field arena, and show how these interpretable features can facilitate downstream behavioral and neural analyses. We also show how the behavioral features produced by our model improve the precision and interpretation of these downstream analyses compared to using the outputs of either fully supervised or fully unsupervised methods alone.     

A precise error bound for quantum phase estimation

Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers.     

Self-illuminating quantum dot conjugates for in vivo imaging

Fluorescent semiconductor quantum dots hold great potential for molecular imaging in vivo. However, the utility of existing quantum dots for in vivo imaging is limited because they require excitation from external illumination sources to fluoresce, which results in a strong autofluorescence background and a paucity of excitation light at nonsuperficial locations. Here we present quantum dot conjugates that luminesce by bioluminescence resonance energy transfer in the absence of external excitation. The conjugates are prepared by coupling carboxylate-presenting quantum dots to a mutant of the bioluminescent protein Renilla reniformis luciferase. We show that the conjugates emit long-wavelength (from red to near-infrared) bioluminescent light in cells and in animals, even in deep tissues, and are suitable for multiplexed in vivo imaging. Compared with existing quantum dots, self-illuminating quantum dot conjugates have greatly enhanced sensitivity in small animal imaging, with an in vivo signal-to-background ratio of > 10(3) for 5 pmol of conjugate.     

N-player quantum games in an EPR setting

The N-player quantum games are analyzed that use an Einstein-Podolsky-Rosen (EPR) experiment, as the underlying physical setup. In this setup, a player's strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical choice between two directions along which spin or polarization measurements are made. The players' strategies thus remain identical to their strategies in the mixed-strategy version of the classical game. In the EPR setting the quantum game reduces itself to the corresponding classical game when the shared quantum state reaches zero entanglement. We find the relations for the probability distribution for N-qubit GHZ and W-type states, subject to general measurement directions, from which the expressions for the players' payoffs and mixed Nash equilibrium are determined. Players' N x N payoff matrices are then defined using linear functions so that common two-player games can be easily extended to the N-player case and permit analytic expressions for the Nash equilibrium. As a specific example, we solve the Prisoners' Dilemma game for general N ≥ 2. We find a new property for the game that for an even number of players the payoffs at the Nash equilibrium are equal, whereas for an odd number of players the cooperating players receive higher payoffs. By dispensing with the standard unitary transformations on state vectors in Hilbert space and using instead rotors and multivectors, based on Clifford's geometric algebra (GA), it is shown how the N-player case becomes tractable. The new mathematical approach presented here has wide implications in the areas of quantum information and quantum complexity, as it opens up a powerful way to tractably analyze N-partite qubit interactions.     

Protonation status of metal-bound ligands can be determined by quantum refinement

The protonation status of key residues and bound ligands are often important for the function of a protein. Unfortunately, protons are not discerned in normal protein crystal structures, so their positions have to be determined by more indirect methods. We show that the recently developed quantum refinement method can be used to determine the position of protons in crystal structures. By replacing the molecular-mechanics potential, normally used in crystallographic refinement, by more accurate quantum chemical calculations, we get information about the ideal structure of a certain protonation state. By comparing the refined structures of different protonation states, the one that fits the crystallographic raw data best can be decided using four criteria: the R factors, electron density maps, strain energy, and divergence from the unrestrained quantum chemical structure. We test this method on alcohol dehydrogenase, for which the pK(a) of the zinc-bound solvent molecule is experimentally known. We show that we can predict the correct protonation state for both a deprotonated alcohol and a neutral water molecule.     

Employing ICA and SOM for spike sorting of multielectrode recordings from CNS

For classification of action potential shapes in multineuron recordings, we present a spike sorting system employing independent component analysis (ICA) and an unsupervised artificial neural network (Kohonen's self-organizing map, SOM). We focus on how ICA in the first stage of the spike sorting system can be used to address specific problems arising in recordings using multielectrode arrays in the CNS. Using real data recorded from the pontine nuclei in rats and simulated data, we evaluate the performance of several ICA algorithms to remove cross-talk between electrodes using data from continuous recording (or simulation). When using cut-out data, the standard format of extracellular spike recordings, new problems emerge and robust algorithms are needed. We demonstrate that several ICA algorithms show a good performance on cut-out data from multielectrode array recordings (simulated and real data). In tetrode recordings the same neuron is purposely recorded by several electrodes simultaneously and we show, how independent component analysis can be used in this case to identify redundant information and hence to compress relevant information, improving subsequent clustering of a SOM.     

Verification of phylogenetic inference programs using metamorphic testing

Many phylogenetic inference programs are available to infer evolutionary relationships among taxa using aligned sequences of characters, typically DNA or amino acids. These programs are often used to infer the evolutionary history of species. However, in most cases it is impossible to systematically verify the correctness of the tree returned by these programs, as the correct evolutionary history is generally unknown and unknowable. In addition, it is nearly impossible to verify whether any non-trivial tree is correct in accordance to the specification of the often complicated search and scoring algorithms. This difficulty is known as the oracle problem of software testing: there is no oracle that we can use to verify the correctness of the returned tree. This makes it very challenging to test the correctness of any phylogenetic inference programs. Here, we demonstrate how to apply a simple software testing technique, called Metamorphic Testing, to alleviate the oracle problem in testing phylogenetic inference programs. We have used both real and randomly generated test inputs to evaluate the effectiveness of metamorphic testing, and found that metamorphic testing can detect failures effectively in faulty phylogenetic inference programs with both types of test inputs.     

Efficient algorithms for quantitative trait loci mapping problems.

Rapid advances in molecular genetics push the need for efficient data analysis. Advanced algorithms are necessary for extracting all possible information from large experimental data sets. We present a general linear algebra framework for quantitative trait loci (QTL) mapping, using both linear regression and maximum likelihood estimation. The formulation simplifies future comparisons between and theoretical analyses of the methods. We show how the common structure of QTL analysis models can be used to improve the kernel algorithms, drastically reducing the computational effort while retaining the original analysis results. We have evaluated our new algorithms on data sets originating from two large F(2) populations of domestic animals. Using an updating approach, we show that 1-3 orders of magnitude reduction in computational demand can be achieved for matrix factorizations. For interval-mapping/composite-interval-mapping settings using a maximum likelihood model, we also show how to use the original EM algorithm instead of the ECM approximation, significantly improving the convergence and further reducing the computational time. The algorithmic improvements makes it feasible to perform analyses which have previously been deemed impractical or even impossible. For example, using the new algorithms, it is reasonable to perform permutation testing using exhaustive search on populations of 200 individuals using an epistatic two-QTL model.     

A quantum mechanical model of adaptive mutation

The principle that mutations occur randomly with respect to the direction of evolutionary change has been challenged by the phenomenon of adaptive mutations. There is currently no entirely satisfactory theory to account for how a cell can selectively mutate certain genes in response to environmental signals. However, spontaneous mutations are initiated by quantum events such as the shift of a single proton (hydrogen atom) from one site to an adjacent one. We consider here the wave function describing the quantum state of the genome as being in a coherent linear superposition of states describing both the shifted and unshifted protons. Quantum coherence will be destroyed by the process of decoherence in which the quantum state of the genome becomes correlated (entangled) with its surroundings. Using a very simple model we estimate the decoherence times for protons within DNA and demonstrate that quantum coherence may be maintained for biological time-scales. Interaction of the coherent genome wave function with environments containing utilisable substrate will induce rapid decoherence and thereby destroy the superposition of mutant and non-mutant states. We show that this accelerated rate of decoherence may significantly increase the rate of production of the mutated state.     

Creating self-illuminating quantum dot conjugates

Semiconductor quantum dots are inorganic fluorescent nanocrystals that, because of their unique optical properties compared with those of organic fluorophores, have become popular as fluorescent imaging probes. Although external light excitation is typically required for imaging with quantum dots, a new type of quantum dot conjugate has been reported that can luminesce with no need for external excitation. These self-illuminating quantum dot conjugates can be prepared by coupling of commercially available carboxylate-presenting quantum dots to the light-emitting protein Renilla luciferase. When the conjugates are exposed to the luciferase's substrate coelenterazine, the energy released by substrate catabolism is transferred to the quantum dots through bioluminescence resonance energy transfer, leading to quantum dot light emission. This protocol describes step-by-step procedures for the preparation and characterization of these self-illuminating quantum dot conjugates. The preparation process is relatively simple and can be done in less than 2 hours. The availability of self-illuminating quantum dot conjugates will provide many new possibilities for in vivo imaging and detection, such as monitoring of in vivo cell trafficking, multiplex bioluminescence imaging and new quantum dot-based biosensors.     

External cross-validation for unbiased evaluation of protein family detectors: application to allergens

Key issues in protein science and computational biology are design and evaluation of algorithms aimed at detection of proteins that belong to a specific family, as defined by structural, evolutionary, or functional criteria. In this context, several validation techniques are often used to compare different parameter settings of the detector, and to subsequently select the setting that yields the smallest error rate estimate. A frequently overlooked problem associated with this approach is that this smallest error rate estimate may have a large optimistic bias. Based on computer simulations, we show that a detector's error rate estimate can be overly optimistic and propose a method to obtain unbiased performance estimates of a detector design procedure. The method is founded on an external 10-fold cross-validation (CV) loop that embeds an internal validation procedure used for parameter selection in detector design. The designed detector generated in each of the 10 iterations are evaluated on held-out examples exclusively available in the external CV iterations. Notably, the average of these 10 performance estimates is not associated with a final detector, but rather with the average performance of the design procedure used. We apply the external CV loop to the particular problem of detecting potentially allergenic proteins, using a previously reported design procedure. Unbiased performance estimates of the allergen detector design procedure are presented together with information about which algorithms and parameter settings that are most frequently selected.     

Development of a concentric water-displacement model lung

Simulation of lung ventilation using a model lung can provide a means of evaluating lung function tests, mathematical models and computer algorithms. We describe a new water-displacement lung model, which can simulate lung volumes up to 3.8 l and tidal volumes up to 1 l. Gas mixing is ensured by using a ring of venturi devices. Model compliance and airways resistance are described.     

Photosynthetic quantum yield dynamics: from photosystems to leaves

The mechanisms underlying the wavelength dependence of the quantum yield for CO(2) fixation (α) and its acclimation to the growth-light spectrum are quantitatively addressed, combining in vivo physiological and in vitro molecular methods. Cucumber (Cucumis sativus) was grown under an artificial sunlight spectrum, shade light spectrum, and blue light, and the quantum yield for photosystem I (PSI) and photosystem II (PSII) electron transport and α were simultaneously measured in vivo at 20 different wavelengths. The wavelength dependence of the photosystem excitation balance was calculated from both these in vivo data and in vitro from the photosystem composition and spectroscopic properties. Measuring wavelengths overexciting PSI produced a higher α for leaves grown under the shade light spectrum (i.e., PSI light), whereas wavelengths overexciting PSII produced a higher α for the sun and blue leaves. The shade spectrum produced the lowest PSI:PSII ratio. The photosystem excitation balance calculated from both in vivo and in vitro data was substantially similar and was shown to determine α at those wavelengths where absorption by carotenoids and nonphotosynthetic pigments is insignificant (i.e., >580 nm). We show quantitatively that leaves acclimate their photosystem composition to their growth light spectrum and how this changes the wavelength dependence of the photosystem excitation balance and quantum yield for CO(2) fixation. This also proves that combining different wavelengths can enhance quantum yields substantially.     

Challenging the classical notion of time in cognition: a quantum perspective

All mental representations change with time. A baseline intuition is that mental representations have specific values at different time points, which may be more or less accessible, depending on noise, forgetting processes, etc. We present a radical alternative, motivated by recent research using the mathematics from quantum theory for cognitive modelling. Such cognitive models raise the possibility that certain possibilities or events may be incompatible, so that perfect knowledge of one necessitates uncertainty for the others. In the context of time-dependence, in physics, this issue is explored with the so-called temporal Bell (TB) or Leggett–Garg inequalities. We consider in detail the theoretical and empirical challenges involved in exploring the TB inequalities in the context of cognitive systems. One interesting conclusion is that we believe the study of the TB inequalities to be empirically more constrained in psychology than in physics. Specifically, we show how the TB inequalities, as applied to cognitive systems, can be derived from two simple assumptions: cognitive realism and cognitive completeness. We discuss possible implications of putative violations of the TB inequalities for cognitive models and our understanding of time in cognition in general. Overall, this paper provides a surprising, novel direction in relation to how time should be conceptualized in cognition.     

Universal polyethylene glycol linkers for attaching receptor ligands to quantum dots

Biologically active small molecule derivatives that can be conjugated to quantum dots have the promise of revolutionizing fluorescent imaging in biology. In order to achieve this several technical hurdles have to be surmounted, one of which is non-specific adsorption of quantum dots to cell membranes. Pegylating quantum dots has been shown to eliminate non-specific binding. Consequently it is necessary to develop a universal synthetic methodology to attach small molecule ligands to polyethylene glycol. These pegylated small molecules may then be conjugated to the surfaces of quantum dots. Ideally this universal strategy should be adaptable and be applicable to PEG chains of varying lengths. This paper describes the development of one such methodology and the synthesis of a pegylated derivative of the known 5HT₂ agonist 1-(2-aminopropyl)-2,5-dimethoxy benzene. This compound was tested and found to be an agonist for the 5HT_2A and 5HT_2C receptor having EC₅₀ values of 250 and 50 nM, respectively.     

Real-time nanoscopy by using blinking enhanced quantum dots

Superresolution optical microscopy (nanoscopy) is of current interest in many biological fields. Superresolution optical fluctuation imaging, which utilizes higher-order cumulant of fluorescence temporal fluctuations, is an excellent method for nanoscopy, as it requires neither complicated optics nor illuminations. However, it does need an impractical number of images for real-time observation. Here, we achieved real-time nanoscopy by modifying superresolution optical fluctuation imaging and enhancing the fluctuation of quantum dots. Our developed quantum dots have higher blinking than commercially available ones. The fluctuation of the blinking improved the resolution when using a variance calculation for each pixel instead of a cumulant calculation. This enabled us to obtain microscopic images with 90-nm and 80-ms spatial-temporal resolution by using a conventional fluorescence microscope without any optics or devices.     

Orgons andbiolons in theoretical biology: Phenomenological analysis and quantum analogies

In this paper we define two types of formal biological entities corresponding to biological levels of organization, thebiolons and theorgons, the properties of which are phenomenologically analyzed and discussed.We examine then, in a rather speculative manner, how some characteristics of these entities may suggest analogies between properties of biological systems and some special features of quantum systems.These analogies are principally related to the specific roles played by these entities (relatively to matter-energy, for orgons, and to information, for biolons) in a biological system. They are funded on the formal equivalence between the temporal variations associated to the development of the orgons and the biolons, respectively, and the statistical distribution over the available energy levels of the two main types of quantum entities, the fermions and the bosons (the former being associated to the constitution of matter and the latter to the effects of interactions).This formal comparison leads us to put into correspondences the developmental duration in biological systems with the energetic structuration in quantum ones and the related characteristic times of the former with the temperature of the latter. We discuss briefly these correspondences.     

dsDNA-coated quantum dots

Because of their unique spectral properties, quantum dots (QDs) have recently proved useful as fluorescent labels for biosensing probes. We developed a versatile QD label by modifying dsDNA with biotin and thiol groups at opposite ends and attaching it to quantum dots via a metal-thiol bond. These dsDNA-coated QDs fluorescently label their targets through biotin-streptavidin binding and show excellent histological results when used to detect biotin-labeled chromosome probes. The dsDNA coating also circumvented the common problems of aggregation and steric hindrance that occur with other QD probes.     

A biomolecular implementation of logically reversible computation with minimal energy dissipation

Energy dissipation associated with logic operations imposes a fundamental physical limit on computation and is generated by the entropic cost of information erasure, which is a consequence of irreversible logic elements. We show how to encode information in DNA and use DNA amplification to implement a logically reversible gate that comprises a complete set of operators capable of universal computation. We also propose a method using this design to connect, or 'wire', these gates together in a biochemical fashion to create a logic network, allowing complex parallel computations to be executed. The architecture of the system permits highly parallel operations and has properties that resemble well known genetic regulatory systems.