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 Quantitative Biology , 2014, Abstract: Electrocorticogram (ECoG)-based brain computer interfaces (BCI) can potentially control upper extremity prostheses to restore independent function to paralyzed individuals. However, current research is mostly restricted to the offline decoding of finger or 2D arm movement trajectories, and these results are modest. This study seeks to improve the fundamental understanding of the ECoG signal features underlying upper extremity movements to guide better BCI design. Subjects undergoing ECoG electrode implantation performed a series of elementary upper extremity movements in an intermittent flexion and extension manner. It was found that movement velocity, $\dot\theta$, had a high positive (negative) correlation with the instantaneous power of the ECoG high-$\gamma$ band (80-160 Hz) during flexion (extension). Also, the correlation was low during idling epochs. Visual inspection of the ECoG high-$\gamma$ band revealed power bursts during flexion/extension events that have a waveform that strongly resembles the corresponding flexion/extension event as seen on $\dot\theta$. These high-$\gamma$ bursts were present in all elementary movements, and were spatially distributed in a somatotopic fashion. Thus, it can be concluded that the high-$\gamma$ power of ECoG strongly encodes for movement trajectories, and can be used as an input feature in future BCIs.
 Physics , 2014, DOI: 10.1038/ncomms7210 Abstract: Ensemble averaging of molecular states is fundamental for the experimental determination of thermodynamic quantities. A special case occurs for single-molecule investigations under equilibrium conditions, for which free energy, entropy and enthalpy at finite-temperatures are challenging to determine with ensemble-averaging alone. Here, we provide a method to access single-molecule thermodynamics, by confining an individual molecule to a nanoscopic pore of a two-dimensional metal-organic nanomesh, where we directly record finite-temperature time-averaged statistical weights using temperature-controlled scanning tunneling microscopy. The obtained patterns represent a real space equilibrium probability distribution. We associate this distribution with a partition function projection to assess spatially resolved thermodynamic quantities, by means of computational modeling. The presented molecular dynamics based Boltzmann weighting model is able to reproduce experimentally observed molecular states with high accuracy. By an in-silico customized energy landscape we demonstrate that distinct probability distributions can be encrypted at different temperatures. Such modulation provides means to encode and decode information into position-temperature space or to realize nanoscopic thermal probes.
 Frontiers in Behavioral Neuroscience , 2013, DOI: 10.3389/fnbeh.2013.00008 Abstract: Many neurons in the macaque ventral intraparietal area (VIP) are multimodal, i.e., they respond not only to visual but also to tactile, auditory and vestibular stimulation. Anatomical studies have shown distinct projections between area VIP and a region of premotor cortex controlling head movements. A specific function of area VIP could be to guide movements in order to head for and/or to avoid objects in near extrapersonal space. This behavioral role would require a consistent representation of visual motion within 3-D space and enhanced activity for nearby motion signals. Accordingly, in our present study we investigated whether neurons in area VIP are sensitive to moving visual stimuli containing depth signals from horizontal disparity. We recorded single unit activity from area VIP of two awake behaving monkeys (Macaca mulatta) fixating a central target on a projection screen. Sensitivity of neurons to horizontal disparity was assessed by presenting large field moving images (random dot fields) stereoscopically to the two eyes by means of LCD shutter goggles synchronized with the stimulus computer. During an individual trial, stimuli had one of seven different disparity values ranging from 3° uncrossed- (far) to 3° crossed- (near) disparity in 1° steps. Stimuli moved at constant speed in all simulated depth planes. Different disparity values were presented across trials in pseudo-randomized order. Sixty-one percent of the motion sensitive cells had a statistically significant selectivity for the horizontal disparity of the stimulus (p < 0.05, distribution free ANOVA). Seventy-five percent of them preferred crossed-disparity values, i.e., moving stimuli in near space, with the highest mean activity for the nearest stimulus. At the population level, preferred direction of visual stimulus motion was not affected by horizontal disparity. Thus, our findings are in agreement with the behavioral role of area VIP in the representation of movement in near extrapersonal space.
 Mathematics , 2001, Abstract: We study M(n,k,r), the number of orbits of {(a_1,...,a_k)\in Z_n^k | a_1+...+a_k = r (mod n)} under the action of S_k. Equivalently, M(n,k,r) sums the partition numbers of an arithmetic sequence: M(n,k,r) = sum_{t \geq 0} p(n-1,k,r+nt), where p(a,b,t) denotes the number of partitions of t into at most b parts, each of which is at most a. We derive closed formulas and various identities for such arithmetic partition sums. These results have already appeared in Elashvili/Jibladze/Pataraia, Combinatorics of necklaces and "Hermite reciprocity", J. Alg. Combin. 10 (1999) 173-188, and the main result was also published by Von Sterneck in Sitzber. Akad. Wiss. Wien. Math. Naturw. Class. 111 (1902), 1567-1601 (see Lemma 2 and references in math.NT/9909121). Thanks to Don Zagier and Robin Chapman for bringing these references to our attention.
 PLOS Biology , 2012, DOI: 10.1371/journal.pbio.0020045 Abstract: Many recent studies describe learning-related changes in sensory and motor areas, but few have directly probed for improvement in neuronal coding after learning. We used information theory to analyze single-cell activity from the primary motor cortex of monkeys, before and after learning a local rotational visuomotor task. We show that after learning, neurons in the primary motor cortex conveyed more information about the direction of movement and did so with relation to their directional sensitivity. Similar to recent findings in sensory systems, this specific improvement in encoding is correlated with an increase in the slope of the neurons' tuning curve. We further demonstrate that the improved information after learning enables a more accurate reconstruction of movement direction from neuronal populations. Our results suggest that similar mechanisms govern learning in sensory and motor areas and provide further evidence for a tight relationship between the locality of learning and the properties of neurons; namely, cells only show plasticity if their preferred direction is near the training one. The results also suggest that simple learning tasks can enhance the performance of brain–machine interfaces.
 PLOS Biology , 2004, DOI: 10.1371/journal.pbio.0020045 Abstract: Many recent studies describe learning-related changes in sensory and motor areas, but few have directly probed for improvement in neuronal coding after learning. We used information theory to analyze single-cell activity from the primary motor cortex of monkeys, before and after learning a local rotational visuomotor task. We show that after learning, neurons in the primary motor cortex conveyed more information about the direction of movement and did so with relation to their directional sensitivity. Similar to recent findings in sensory systems, this specific improvement in encoding is correlated with an increase in the slope of the neurons' tuning curve. We further demonstrate that the improved information after learning enables a more accurate reconstruction of movement direction from neuronal populations. Our results suggest that similar mechanisms govern learning in sensory and motor areas and provide further evidence for a tight relationship between the locality of learning and the properties of neurons; namely, cells only show plasticity if their preferred direction is near the training one. The results also suggest that simple learning tasks can enhance the performance of brain–machine interfaces.
 Henk Don Mathematics , 2011, Abstract: We study the geometry of billiard orbits on rectangular billiards. A truncated billiard orbit induces a partition of the rectangle into polygons. We prove that thirteen is a sharp upper bound for the number of different areas of these polygons.
 Physics , 2004, DOI: 10.1137/040612877 Abstract: Symbolic codes for rotational orbits and "islands-around-islands" are constructed for the quadratic, area-preserving Henon map. The codes are based upon continuation from an anti-integrable limit, or alternatively from the horseshoe. Given any sequence of rotation numbers we obtain symbolic sequences for the corresponding elliptic and hyperbolic rotational orbits. These are shown to be consistent with numerical evidence. The resulting symbolic partition of the phase space consists of wedges constructed from images of the symmetry lines of the map.
 S. Fuhrmann In die Skriflig , 2011, DOI: 10.4102/ids.v45i2&3.35 Abstract: The letters of Ignatius represent one of the key texts for the emergence of martyrdom during the second century AD in Christianity. This article is concerned with the question whether Ignatius contributed to a “theology of martyrdom” or whether he rather relied on previous traditions. The author argues, by undertaking an analysis of certain pragmatics and semantics, that the motif of martyrdom is solely used to buttress Ignatius’ claim for authority among his intended addressees by referring to an understanding of martyrdom that has its roots in the New Testament. An identification of the author of the letters with a historical martyr is regarded as unlikely.
 Computer Science , 2007, DOI: 10.1142/S0218348X96000029 Abstract: We show that the predictability of letters in written English texts depends strongly on their position in the word. The first letters are usually the least easy to predict. This agrees with the intuitive notion that words are well defined subunits in written languages, with much weaker correlations across these units than within them. It implies that the average entropy of a letter deep inside a word is roughly 4 times smaller than the entropy of the first letter.
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