Parabolic movement primitives and cortical states: merging optimality with geometric invariance

Previous studies have suggested that several types of rules govern the generation of complex arm movements. One class of rules consists of optimizing an objective function (e.g., maximizing motion smoothness). Another class consists of geometric and kinematic constraints, for instance the coupling between speed and curvature during drawing movements as expressed by the two-thirds power law. It has also been suggested that complex movements are composed of simpler elements or primitives. However, the ability to unify the different rules has remained an open problem. We address this issue by identifying movement paths whose generation according to the two-thirds power law yields maximally smooth trajectories. Using equi-affine differential geometry we derive a mathematical condition which these paths must obey. Among all possible solutions only parabolic paths minimize hand jerk, obey the two-thirds power law and are invariant under equi-affine transformations (which preserve the fit to the two-thirds power law). Affine transformations can be used to generate any parabolic stroke from an arbitrary parabolic template, and a few parabolic strokes may be concatenated to compactly form a complex path. To test the possibility that parabolic elements are used to generate planar movements, we analyze monkeys’ scribbling trajectories. Practiced scribbles are well approximated by long parabolic strokes. Of the motor cortical neurons recorded during scribbling more were related to equi-affine than to Euclidean speed. Unsupervised segmentation of simulta- neously recorded multiple neuron activity yields states related to distinct parabolic elements. We thus suggest that the cortical representation of movements is state-dependent and that parabolic elements are building blocks used by the motor system to generate complex movements.     

A Compact Representation of Drawing Movements with Sequences of Parabolic Primitives

Some studies suggest that complex arm movements in humans and monkeys may optimize several objective functions, while others claim that arm movements satisfy geometric constraints and are composed of elementary components. However, the ability to unify different constraints has remained an open question. The criterion for a maximally smooth (minimizing jerk) motion is satisfied for parabolic trajectories having constant equi-affine speed, which thus comply with the geometric constraint known as the two-thirds power law. Here we empirically test the hypothesis that parabolic segments provide a compact representation of spontaneous drawing movements. Monkey scribblings performed during a period of practice were recorded. Practiced hand paths could be approximated well by relatively long parabolic segments. Following practice, the orientations and spatial locations of the fitted parabolic segments could be drawn from only 2–4 clusters, and there was less discrepancy between the fitted parabolic segments and the executed paths. This enabled us to show that well-practiced spontaneous scribbling movements can be represented as sequences (“words”) of a small number of elementary parabolic primitives (“letters”). A movement primitive can be defined as a movement entity that cannot be intentionally stopped before its completion. We found that in a well-trained monkey a movement was usually decelerated after receiving a reward, but it stopped only after the completion of a sequence composed of several parabolic segments. Piece-wise parabolic segments can be generated by applying affine geometric transformations to a single parabolic template. Thus, complex movements might be constructed by applying sequences of suitable geometric transformations to a few templates. Our findings therefore suggest that the motor system aims at achieving more parsimonious internal representations through practice, that parabolas serve as geometric primitives and that non-Euclidean variables are employed in internal movement representations (due to the special role of parabolas in equi-affine geometry).     

Compositionality of arm movements can be realized by propagating synchrony

We present a biologically plausible spiking neuronal network model of free monkey scribbling that reproduces experimental findings on cortical activity and the properties of the scribbling trajectory. The model is based on the idea that synfire chains can encode movement primitives. Here, we map the propagation of activity in a chain to a linearly evolving preferred velocity, which results in parabolic segments that fulfill the two-thirds power law. Connections between chains that match the final velocity of one encoded primitive to the initial velocity of the next allow the composition of random sequences of primitives with smooth transitions. The model provides an explanation for the segmentation of the trajectory and the experimentally observed deviations of the trajectory from the parabolic shape at primitive transition sites. Furthermore, the model predicts low frequency oscillations (<10 Hz) of the motor cortex local field potential during ongoing movements and increasing firing rates of non-specific motor cortex neurons before movement onset.     

A model of handwriting

The research reported here is concerned with hand trajectory planning for the class of movements involved in handwriting. Previous studies show that the kinematics of human two-joint arm movements in the horizontal plane can be described by a model which is based on dynamic minimization of the square of the third derivative of hand position (jerk), integrated over the entire movement. We extend this approach to both the analysis and the synthesis of the trajectories occurring in the generation of handwritten characters. Several basic strokes are identified and possible stroke concatenation rules are suggested. Given a concise symbolic representation of a stroke shape, a simple algorithm computes the complete kinematic specification of the corresponding trajectory. A handwriting generation model based on a kinematics from shape principle and on dynamic optimization is formulated and tested. Good qualitative and quantitative agreement was found between subject recordings and trajectories generated by the model. The simple symbolic representation of hand motion suggested here may permit the central nervous system to learn, store and modify motor action plans for writing in an efficient manner.     

Calibration of pneumotachographs using a calibrated syringe.

Pneumotachograph require frequent calibration. Constant-flow methods allow polynomial calibration curves to be derived but are time consuming. The iterative syringe stroke technique is moderately efficient but results in discontinuous conductance arrays. This study investigated the derivation of first-, second-, and third-order polynomial calibration curves from 6 to 50 strokes of a calibration syringe. We used multiple linear regression to derive first-, second-, and third-order polynomial coefficients from two sets of 6-50 syringe strokes. In part A, peak flows did not exceed the specified linear range of the pneumotachograph, whereas flows in part B peaked at 160% of the maximum linear range. Conductance arrays were derived from the same data sets by using a published algorithm. Volume errors of the calibration strokes and of separate sets of 70 validation strokes (part A) and 140 validation strokes (part B) were calculated by using the polynomials and conductance arrays. Second- and third-order polynomials derived from 10 calibration strokes achieved volume variability equal to or better than conductance arrays derived from 50 strokes. We found that evaluation of conductance arrays using the calibration syringe strokes yields falsely low volume variances. We conclude that accurate polynomial curves can be derived from as few as 10 syringe strokes, and the new polynomial calibration method is substantially more time efficient than previously published conductance methods.     

Character complexity and redundancy in writing systems over human history

A writing system is a visual notation system wherein a repertoire of marks, or strokes, is used to build a repertoire of characters. Are there any commonalities across writing systems concerning the rules governing how strokes combine into characters; commonalities that might help us identify selection pressures on the development of written language? In an effort to answer this question we examined how strokes combine to make characters in more than 100 writing systems over human history, ranging from about 10 to 200 characters,and including numerals, abjads, abugidas, alphabets and syllabaries from five major taxa: Ancient Near-Eastern, European, Middle Eastern, South Asian, Southeast Asian. We discovered underlying similarities in two fundamental respects. (i) The number of strokes per characters is approximately three, independent of the number of characters in the writing system; numeral systems are the exception, having on average only two strokes per character. (ii) Characters are ca. 50% redundant, independent of writing system size; intuitively, this means that acharacter's identity can be determined even when half of its strokes are removed. Because writing systems are under selective pressure to have characters that are easy for the visual system to recognize and for the motor system to write, these fundamental commonalities may be a fingerprint of mechanisms underlying the visuo-motor system.     

A deterministic mechanism producing the loose coupling phenomenon observed in an actomyosin system

Myosins are molecular motors that convert the chemical energy of ATP into mechanical work called a power stroke. Class II myosin engaged in muscle contraction is reported to show a "loose coupling phenomenon", in which the number of power strokes is greater than the number of ATP hydrolyses. This phenomenon cannot be explained by the lever-arm hypothesis, which is currently accepted as a standard theory for myosin motility. In this paper, a model is proposed to reproduce the loose coupling phenomenon. The model is based on a mechanochemical process called "Driven by Detachment (DbD)" mechanism, which assumes that the energy of the power strokes originates from the potential energy generated by the attractive force between myosin and actin. During the docking process, the potential energy is converted into an intramolecular strain in a myosin molecule, which drives the power stroke after the myosin is firmly attached to an actin filament. The energy of ATP is used to temporarily reduce the attractive force and to increase the potential energy. Therefore, it is not directly linked to the power strokes. When myosin molecules work as an aggregate, the sliding movement of a myosin filament driven by the power strokes of some myosin heads makes other myosin heads that have completed their power strokes detach from the actin without consuming ATP. Under the DbD mechanism, these passively detached myosins can be again engaged in power strokes after the next attachment to actin. As a result, the number of power strokes becomes greater than the number of ATP hydrolyses, and the loose coupling phenomenon will be observed. A theoretical analysis indicates that the efficiency of converting the potential energy into intramolecular elastic energy determines the number of power strokes per each ATP hydrolysis. Computer simulations showed that the DbD mechanism actually produced the loose coupling phenomenon. A critical requirement for this mechanism is that ATP must preferentially facilitate the detachment of myosins that have completed their power strokes, but are still strongly attached to the actin. This requirement may be fulfilled by ATP hydrolysis tightly depending on the conformation of a myosin molecule.     

Identifying Change Points in a Covariate Effect on Time-to-Event Analysis with Reduced Isotonic Regression

Isotonic regression is a useful tool to investigate the relationship between a quantitative covariate and a time-to-event outcome. The resulting non-parametric model is a monotonic step function of a covariate X and the steps can be viewed as change points in the underlying hazard function. However, when there are too many steps, over-fitting can occur and further reduction is desirable. We propose a reduced isotonic regression approach to allow combination of small neighboring steps that are not statistically significantly different. In this approach, a second stage, the reduction stage, is integrated into the usual monotonic step building algorithm by comparing the adjacent steps using appropriate statistical testing. This is achieved through a modified dynamic programming algorithm. We implemented the approach with the simple exponential distribution and then its extension, the Weibull distribution. Simulation studies are used to investigate the properties of the resulting isotonic functions. We apply this methodology to the Diabetes Control and Complication Trial (DCCT) data set to identify potential change points in the association between HbA1c and the risk of severe hypoglycemia.     

Methodology for rigorous modeling of protein conformational changes by Rosetta using DEER distance restraints

We describe an approach for integrating distance restraints from Double Electron-Electron Resonance (DEER) spectroscopy into Rosetta with the purpose of modeling alternative protein conformations from an initial experimental structure. Fundamental to this approach is a multilateration algorithm that harnesses sets of interconnected spin label pairs to identify optimal rotamer ensembles at each residue that fit the DEER decay in the time domain. Benchmarked relative to data analysis packages, the algorithm yields comparable distance distributions with the advantage that fitting the DEER decay and rotamer ensemble optimization are coupled. We demonstrate this approach by modeling the protonation-dependent transition of the multidrug transporter PfMATE to an inward facing conformation with a deviation to the experimental structure of less than 2Å C_α RMSD. By decreasing spin label rotamer entropy, this approach engenders more accurate Rosetta models that are also more closely clustered, thus setting the stage for more robust modeling of protein conformational changes.     

Bidirectional power stroke by ncd kinesin

Optical trapping experiments reveal details of molecular motor dynamics. In noisy data, temporal structure within the power stroke of motors can be analyzed by ensemble averaging, but this obscures infrequent subcategories of events. We have here developed an analysis method that uses Kalman filtering of measurements, model-based estimation of the power strokes produced by the motor head, and automatic event classification to discriminate between different types of motor events. This method was applied to optical trap measurements of power strokes of the Drosophila kinesin-14 ncd in a three-bead geometry. We found the majority of events to be consistent with the previously discovered minus-end directed power stroke of ncd, occurring with ATP binding. Unexpectedly, 30% of apparent power strokes were plus-directed and 6% of binding events did not terminate in a discernible stroke. Ensemble averaging for each event category revealed that plus- and minus-directed strokes have different size and occur at different instants within the ncd-MT attachment sequence.     

A Bayesian joint model of recurrent events and a terminal event

Recurrent events could be stopped by a terminal event, which commonly occurs in biomedical and clinical studies. In this situation, dependent censoring is encountered because of potential dependence between these two event processes, leading to invalid inference if analyzing recurrent events alone. The joint frailty model is one of the widely used approaches to jointly model these two processes by sharing the same frailty term. One important assumption is that recurrent and terminal event processes are conditionally independent given the subject‐level frailty; however, this could be violated when the dependency may also depend on time‐varying covariates across recurrences. Furthermore, marginal correlation between two event processes based on traditional frailty modeling has no closed form solution for estimation with vague interpretation. In order to fill these gaps, we propose a novel joint frailty‐copula approach to model recurrent events and a terminal event with relaxed assumptions. Metropolis–Hastings within the Gibbs Sampler algorithm is used for parameter estimation. Extensive simulation studies are conducted to evaluate the efficiency, robustness, and predictive performance of our proposal. The simulation results show that compared with the joint frailty model, the bias and mean squared error of the proposal is smaller when the conditional independence assumption is violated. Finally, we apply our method into a real example extracted from the MarketScan database to study the association between recurrent strokes and mortality.     

Extending networks of protected areas to optimize connectivity and population growth rate

Protected areas (PAs) are recognized as the flagship tool to offset biodiversity loss on Earth. Spatial conservation planning seeks optimal designs of PAs that meet multiple targets such as biodiversity representation and population persistence. Since connectivity between PAs is a fundamental requirement for population persistence, several methods have been developed to include connectivity into PA design algorithms. Among these, the eigenvalue decomposition of the connectivity matrix allows for identifying clusters of strongly connected sites and selecting the sites contributing the most to population persistence. So far, this method was only suited to optimize an entire network of PAs without considering existing PAs in the new design. However, a more cost‐effective and realistic approach is to optimize the design of an extended network to improve its connectivity and thus population persistence. Here, we develop a flexible algorithm based on eigenvalue decomposition of connectivity matrices to extend existing networks of PAs while optimizing connectivity and population growth rate. We also include a splitting algorithm to improve cluster identification. The new algorithm accounts for the change in connectivity due to the increased biological productivity often observed in existing PAs. We illustrate the potential of our algorithm by proposing an extension of the network of ～100 Mediterranean marine PAs to reach the targeted 10% surface area protection from the current 1.8%. We identify differences between the clean slate scenario, where all sites are available for protection, irrespective of their current protection status, and the scenario where existing PAs are forced to be included into the optimized solution. By integrating this algorithm to existing multi‐objective and multi‐specific algorithms of PA selection, the demographic effects of connectivity can be explicitly included into conservation planning.     

A new method of evaluation of the masticatory function in humans

A method is proposed to estimate mastication by three indices: chewing effect, chewing performance, chewing efficiency. Definitions are given for these terms. A new chewing test is described, permits studying the influence of the number of chewing strokes, chewing force and volume of test portion on the mastication using a group of 25 dentate persons aged 17-25 years with class I occlusion. A new approach to the estimation of chewing efficiency changes traditional views. A strong positive correlation is first found between chewing effect (A) and integrated bioelectrical activity (J) of chewing muscles with the constant number of chewing strokes. A relation between A and J is established when the number of chewing strokes increases.     

Improving strand pairing prediction through exploring folding cooperativity

The topology of $beta$-sheets is defined by the pattern of hydrogen-bonded strand pairing. Therefore, predicting hydrogen bonded strand partners is a fundamental step towards predicting $beta$-sheet topology. At the same time, finding the correct partners is very difficult due to long range interactions involved in strand pairing. Additionally, patterns of aminoacids involved, in $beta$-sheet formations are very general and therefore difficult to use for computational recognition of specific contacts between strands. In this work, we report a new strand pairing algorithm. To address above mentioned difficulties, our algorithm attempts to mimic elements of the folding process. Namely, in addition to ensuring that the predicted hydrogen bonded strand pairs satisfy basic global consistency constraints, it takes into account hypothetical folding pathways. Consistently with this view, introducing hydrogen bonds between a pair of strands changes the probabilities of forming hydrogen bonds between other pairs of strand. We demonstrate that this approach provides an improvement over previously proposed algorithms. We also compare the performance of this method to that of a global optimization algorithm that poses the problem as integer linear programming optimization problem and solves it using ILOG CPLEXtexttrademark package.     

Efficient selection of tagging single-nucleotide polymorphisms in multiple populations

Common genetic polymorphism may explain a portion of the heritable risk for common diseases, so considerable effort has been devoted to finding and typing common single-nucleotide polymorphisms (SNPs) in the human genome. Many SNPs show correlated genotypes, or linkage disequilibrium (LD), suggesting that only a subset of all SNPs (known as tagging SNPs, or tagSNPs) need to be genotyped for disease association studies. Based on the genetic differences that exist among human populations, most tagSNP sets are defined in a single population and applied only in populations that are closely related. To improve the efficiency of multi-population analyses, we have developed an algorithm called MultiPop-TagSelect that finds a near-minimal union of population-specific tagSNP sets across an arbitrary number of populations. We present this approach as an extension of LD-select, a tagSNP selection method that uses a greedy algorithm to group SNPs into bins based on their pairwise association patterns, although the MultiPop-TagSelect algorithm could be used with any SNP tagging approach that allows choices between nearly equivalent SNPs. We evaluate the algorithm by considering tagSNP selection in candidate-gene resequencing data and lower density whole-chromosome data. Our analysis reveals that an exhaustive search is often intractable, while the developed algorithm can quickly and reliably find near-optimal solutions even for difficult tagSNP selection problems. Using populations of African, Asian, and European ancestry, we also show that an optimal multi-population set of tagSNPs can be substantially smaller (up to 44%) than a typical set obtained through independent or sequential selection.Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Inferring protein interactions from phylogenetic distance matrices

Finding the interacting pairs of proteins between two different protein families whose members are known to interact is an important problem in molecular biology. We developed and tested an algorithm that finds optimal matches between two families of proteins by comparing their distance matrices. A distance matrix provides a measure of the sequence similarity of proteins within a family. Since the protein sets of interest may have dozens of proteins each, the use of an efficient approximate solution is necessary. Therefore the approach we have developed consists of a Metropolis Monte Carlo optimization algorithm which explores the search space of possible matches between two distance matrices. We demonstrate that by using this algorithm we are able to accurately match chemokines and chemokine-receptors as well as the tgfbeta family of ligands and their receptors.     

The fragment assembly string graph

We present a concept and formalism, the string graph, which represents all that is inferable about a DNA sequence from a collection of shotgun sequencing reads collected from it. We give time and space efficient algorithms for constructing a string graph given the collection of overlaps between the reads and, in particular, present a novel linear expected time algorithm for transitive reduction in this context. The result demonstrates that the decomposition of reads into kmers employed in the de Bruijn graph approach described earlier is not essential, and exposes its close connection to the unitig approach we developed at Celera. This paper is a preliminary piece giving the basic algorithm and results that demonstrate the efficiency and scalability of the method. These ideas are being used to build a next-generation whole genome assembler called BOA (Berkeley Open Assembler) that will easily scale to mammalian genomes.     

Revisiting wavefront construction with collective agents: an approach to foraging

We consider the problem of coordinating a team of agents that have to collect disseminated resources in an unknown environment. We are interested in approaches in which agents collectively explore the environment and build paths between home and resources. The originality of our approach is to simultaneously build an artificial potential field (APF) around the agents’ home while foraging. We propose a multi-agent model defining a distributed and asynchronous version of Barraquand et al. Wavefront algorithm. Agents need only to mark and read integers locally on a grid, that is, their environment. We prove that the construction converges to the optimal APF. This allows the definition of a complete parameter-free foraging algorithm, called c-marking agents. The algorithm is evaluated by simulation, while varying the foraging settings. Then we compare our approach to a pheromone-based algorithm. Finally, we discuss requirements for implementation in robotics.     

GPS-free Positioning in Mobile Ad Hoc Networks

We consider the problem of node positioning in ad hoc networks. We propose a distributed, infrastructure-free positioning algorithm that does not rely on GPS (Global Positioning System). Instead, the algorithm uses the distances between the nodes to build a relative coordinate system in which the node positions are computed in two dimensions. Despite the distance measurement errors and the motion of the nodes, the algorithm provides sufficient location information and accuracy to support basic network functions. Examples of applications where this algorithm can be used include Location Aided Routing [10] and Geodesic Packet Forwarding [2]. Another example are sensor networks, where mobility is less of a problem. The main contribution of this work is to define and compute relative positions of the nodes in an ad hoc network without using GPS. We further explain how the proposed approach can be applied to wide area ad hoc networks.     

Plato: a genetic algorithm approach to run-time reconfiguration in?autonomic computing systems

Increasingly, applications need to be able to self-reconfigure in response to changing requirements and environmental conditions. Autonomic computing has been proposed as a means for automating software maintenance tasks. As the complexity of adaptive and autonomic systems grows, designing and managing the set of reconfiguration rules becomes increasingly challenging and may produce inconsistencies. This paper proposes an approach to leverage genetic algorithms in the decision-making process of an autonomic system. This approach enables a system to dynamically evolve target reconfigurations at run time that balance tradeoffs between functional and non-functional requirements in response to changing requirements and environmental conditions. A key feature of this approach is incorporating system and environmental monitoring information into the genetic algorithm such that specific changes in the environment automatically drive the evolutionary process towards new viable solutions. We have applied this genetic-algorithm based approach to the dynamic reconfiguration of a collection of remote data mirrors, demonstrating an effective decision-making method for diffusing data and minimizing operational costs while maximizing data reliability and network performance, even in the presence of link failures.