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Concept: Elementary mathematics


The combinatorial nature of many important mathematical problems, including nondeterministic-polynomial-time (NP)-complete problems, places a severe limitation on the problem size that can be solved with conventional, sequentially operating electronic computers. There have been significant efforts in conceiving parallel-computation approaches in the past, for example: DNA computation, quantum computation, and microfluidics-based computation. However, these approaches have not proven, so far, to be scalable and practical from a fabrication and operational perspective. Here, we report the foundations of an alternative parallel-computation system in which a given combinatorial problem is encoded into a graphical, modular network that is embedded in a nanofabricated planar device. Exploring the network in a parallel fashion using a large number of independent, molecular-motor-propelled agents then solves the mathematical problem. This approach uses orders of magnitude less energy than conventional computers, thus addressing issues related to power consumption and heat dissipation. We provide a proof-of-concept demonstration of such a device by solving, in a parallel fashion, the small instance {2, 5, 9} of the subset sum problem, which is a benchmark NP-complete problem. Finally, we discuss the technical advances necessary to make our system scalable with presently available technology.

Concepts: Mathematics, Quantum computer, Computer, Computation, Problem solving, Computational complexity theory, Elementary mathematics, Knapsack problem


(1) To investigate whether a daily acute:chronic workload ratio informs injury risk in Australian football players; (2) to identify which combination of workload variable, acute and chronic time window best explains injury likelihood.

Concepts: Ratio, Algebra, Elementary mathematics, Football, Australian rules football


Photochemical derivatization is proposed for the spectrofluorimetric determination of tetrabenazine (TBZ). A central composite design was used to adjust experimental conditions (60min of UV in a 0.45molL(-1) NaOH solution) enabling the improvement of the analyte signal-to-blank ratio of one order of magnitude, when compared to the TBZ original fluorescence. Limit of quantification was 4.7×10(-8)molL(-1) but the detection power can be improved at least 10 times using solid phase extraction that also allows the separation of the analyte from matrix components, enabling the analysis of biologic fluids. Linear range covered at least three orders of magnitude. The combined uncertainty of the determination (at a 5×10(-6)molL(-1)) was 16%. Recoveries of TBZ in the analyses of a pharmaceutical formulation were in agreement with the ones obtained using a HPLC method. Recovery in saliva (5×10(-7)molL(-1) of TBZ) was 90±3% (n=3). The procedure minimizes the use of toxic chemical derivatization reagents and the generation of hazardous waste.

Concepts: Condensed matter physics, Chemistry, Solubility, Mathematical analysis, Analytical chemistry, Elementary mathematics, Hazardous waste, Solid phase extraction


Body size is a salient marker of physical health, with extremes implicated in various mental and physical health issues. It is therefore important to understand the mechanisms of perception of body size of self and others. We report a novel technique we term the bodyline, based on the numberline technique in numerosity studies. One hundred and three young women judged the size of sequentially presented female body images by positioning a marker on a line, delineated with images of extreme sizes. Participants performed this task easily and well, with average standard deviations less than 6% of the total scale. Critically, judgments of size were biased towards the previously viewed body, demonstrating that serial dependencies occur in the judgment of body size. The magnitude of serial dependence was well predicted by a simple Kalman-filter ideal-observer model, suggesting that serial dependence occurs in an optimal, adaptive way to improve performance in size judgments.

Concepts: Standard deviation, Choice, Dependency, Female body shape, Elementary mathematics, Judgment, Concepts in aesthetics, Extremes


We demonstrate the ability to record a tomographic tilt series containing 3487 images in only 3.5 s by using a direct electron detector in a transmission electron microscope. The electron dose is lower by at least one order of magnitude when compared with that used to record a conventional tilt series of fewer than 100 images in 15-60 minutes and the overall signal-to-noise ratio is greater than 4. Our results, which are illustrated for an inorganic nanotube, are important for ultra-low-dose electron tomography of electron-beam-sensitive specimens and real-time dynamic electron tomography of nanoscale objects with sub-ms temporal resolution.

Concepts: Electron, Electron microscope, Optics, Tomographic reconstruction, Tomography, Scanning electron microscope, Signal-to-noise ratio, Elementary mathematics


The action of rivers within valleys is fundamentally important in controlling landscape morphology, and how it responds to tectonic or climate change. The response of landscapes to external forcing usually results in sequential changes to river long profiles and the upstream migration of waterfalls. Currently, models of this response assume a relationship between waterfall retreat rate and drainage area at the location of the waterfall. Using an experimental study, we show that this assumption has limited application. Due to a self-regulatory response of channel geometry to higher discharge through increasing channel width, the bed shear stress at the lip of the experimental waterfall remains almost constant, so there was no observed change in the upstream retreat rate despite an order of magnitude increase in discharge. Crucially, however, the strength of the bedrock material exhibits a clear control on the magnitude of the mean retreat rate, highlighting the importance of lithology in setting the rate at which landscapes respond to external forcing. As a result existing numerical models of landscape evolution that simulate the retreat of waterfalls as a function of drainage area with a fixed erodibility constant should be re-evaluated to consider spatial heterogeneity in erodibility and channel self-organisation.

Concepts: Water, River, Force, Shear strength, Elementary mathematics, Geomorphology, Fluvial landforms


Deficits in ambulatory function progress at heterogeneous rates among individuals with Duchenne muscular dystrophy (DMD). The resulting inherent variability in ambulatory outcomes has complicated the design of drug efficacy trials and clouded the interpretation of trial results. We developed a prediction model for 1-year change in the six minute walk distance (6MWD) among DMD patients, and compared its predictive value to that of commonly used prognostic factors (age, baseline 6MWD, and steroid use).

Concepts: Electromyography, Efficacy, Genetic disorders, Muscular dystrophy, Duchenne muscular dystrophy, Muscular Dystrophy Association, Thought experiment, Elementary mathematics


Vocal sequences - utterances consisting of calls produced in close succession - are common phenomena in animal communication. While many studies have explored the adaptive benefits of producing such sequences, very little is known about how the costs and constraints involved in their production affect their form. Here, we investigated this issue in the chimpanzee (Pan troglodytes schweinfurthii) pant hoot, a long and structurally complex vocal sequence comprising four acoustically distinct phases - introduction, build-up, climax and let-down.

Concepts: Human, Structure, Hominidae, Set, Elementary mathematics, Real analysis, Common Chimpanzee, Chimpanzees


Several lines of evidence suggest that the striatum has an important role in spatial working memory. The neural dynamics in the striatum have been described in tasks with short delay periods (1-4s), but remain largely uncharacterized for tasks with longer delay periods. We collected and analyzed single unit recordings from the dorsomedial striatum of rats performing a spatial working memory task with delays up to 10s. We found that neurons were activated sequentially, with the sequences spanning the entire delay period. Surprisingly, this sequential activity was dissociated from stimulus encoding activity, which was present in the same neurons, but preferentially appeared towards the onset of the delay period. These observations contrast with descriptions of sequential dynamics during similar tasks in other brains areas, and clarify the contribution of the striatum in spatial working memory.

Concepts: Time, Series, Topology, Sequence, Activity, Task, Working memory, Elementary mathematics


The mechanical properties of ordinary materials degrade substantially with reduced density because their structural elements bend under applied load. We report a class of microarchitected materials that maintain a nearly constant stiffness per unit mass density, even at ultralow density. This performance derives from a network of nearly isotropic microscale unit cells with high structural connectivity and nanoscale features, whose structural members are designed to carry loads in tension or compression. Production of these microlattices, with polymers, metals, or ceramics as constituent materials, is made possible by projection microstereolithography (an additive micromanufacturing technique) combined with nanoscale coating and postprocessing. We found that these materials exhibit ultrastiff properties across more than three orders of magnitude in density, regardless of the constituent material.

Concepts: Density, Volume, Uranium, Materials science, Osmium, Kilogram, Iridium, Elementary mathematics