Geometrical complexity of data approximators

There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types of principal curves and principal trees, and so on. For each type of approximators the measure of the approximator complexity was developed too. These measures are necessary to find the balance between accuracy and complexity and to define the optimal approximations of a given type. We propose a measure of complexity (geometrical complexity) which is applicable to approximators of several types and which allows comparing data approximations of different types.Comment: 10 pages, 3 figures, minor correction and extensio

The Case for Discontinuity in the Diffusion of Process Innovations: The Problem of Small Firms in Maturing Industries

The diffusion of innovations is at the core of the pattern of technological change. Many attempts to explain and describe this process have been undertaken during the last decade and a vast bibliography of publications on this subject is presented in Rogers, 1962 and 1983; and Rogers and Shoemaker, 1971. The theory of innovation is an important part of economic and social science, and is both conceptual and formal. Their unity is a necessary premise for the success of any scientific theory

Lithographically Defined Micropost Arrays for Programmable Actuation and Interfacial Hydrodynamics

Magnetically actuating surface-attached post (ASAP) arrays have great potential in microfluidic flow control, including mixing and pumping. Both passive (nonactuating) and active (actuating) micropillar arrays can also be used to control pressure-driven flow and the motion of microscopic particles carried by the fluid through microfluidic channels. Molding techniques are popular for generating these microstructures. However, fabricating high aspect ratio elastomeric microstructures over large surface areas suffers from practical problems such as damage incurred in the demolding process. Here, we report on a fabrication protocol that generates ASAP with an aspect ratio as high as 23:1 and a cross-sectional area less than 1 μm2 using straightforward photolithography processes. We generated 50 unique ASAP arrays, each occupying an area of 1 mm2 on a silicon mold; these arrays have varied cross-sectional shape and size, aspect ratio, and spacings between neighboring posts. Our protocol also controls the level of magnetic material in the ASAP tips with a centrifugation step. Using a herringbone pattern ASAP array, we have demonstrated control over the relative phase of actuation between neighboring posts. Such ASAP serve as an experimental platform to test current models predicting that reciprocal actuators in close proximity can successfully drive flow in a low Reynolds (Re) number environment

Time Parameters of the Blink Reflex in Normal Subjects

Our study was aimed at estimating normal time values for the EMG waves recorded in the blink reflex test. The group examined included 400 healthy subjects (226 women and 174 men, with mean age about 50 years). There was no significant difference between the ages of the male and female subjects. The mean latency of the R1 wave in the response was 10.3 msec, while R2 was obtained after 32.5 msec, on average. The contralateral response component R2c was observed after 34.4 msec, on average. Gender did not influence the results, while age had a significant effect on R1 (P = 0.029) and R2c (P = 0.0003). The older the subject, the longer the latencies of the above waves. The data obtained on a rather large sampling of the tested subjects can be useful as normography for medical and neurophysiological purposes.У своєму дослідженні ми оцінювали нормальні часові параметри хвиль ЕМГ, що реєструвалися при тестуванні рефлексу кліпання. До обстеженої групи ввійшли 400 здорових осіб (226 жінок та 174 чоловіки, середній вік близько 50 років) без істотної різниці віку в групах чоловіків і жінок. Середній латентний період (ЛП) хвилі R1 у складі досліджуваної рефлекторної відповіді складав 10.30, а хвилі R2 – 32.51 мс. Контралатеральний компонент відповіді R2c виникав із середнім ЛП 34.43 мс. Стать обстежених не впливала істотно на ці значення; в той же час останні демонстрували значну залежність від віку (R1, P = 0.029; R2c, P = 0.0003; чим старші були обстежені, тим довші були вказані ЛП). Результати, отримані на досить великій дослідженій групі здорових осіб, можуть бути корисними як нормографічні дані для медичних та нейрофизіологічних цілей

Semiconductive and Photoconductive Properties of the Single Molecule Magnets Mn12_{12}-Acetate and Fe8_8Br8_8

Resistivity measurements are reported for single crystals of Mn$_{12}$-Acetate and Fe$_8$Br$_8$. Both materials exhibit a semiconductor-like, thermally activated behavior over the 200-300 K range. The activation energy, $E_a$, obtained for Mn$_{12}$-Acetate was 0.37 $\pm$ 0.05 eV, which is to be contrasted with the value of 0.55 eV deduced from the earlier reported absorption edge measurements and the range of 0.3-1 eV from intramolecular density of states calculations, assuming $2E_a$= $E_g$, the optical band gap. For Fe$_8$Br$_8$, $E_a$ was measured as 0.73 $\pm$ 0.1 eV, and is discussed in light of the available approximate band structure calculations. Some plausible pathways are indicated based on the crystal structures of both lattices. For Mn$_{12}$-Acetate, we also measured photoconductivity in the visible range; the conductivity increased by a factor of about eight on increasing the photon energy from 632.8 nm (red) to 488 nm (blue). X-ray irradiation increased the resistivity, but $E_a$ was insensitive to exposure.Comment: 7 pages, 8 figure

Controversies and priorities in amyotrophic lateral sclerosis

Two decades after the discovery that 20% of familial amyotrophic lateral sclerosis (ALS) cases were linked to mutations in the superoxide dismutase-1 (SOD1) gene, a substantial proportion of the remainder of cases of familial ALS have now been traced to an expansion of the intronic hexanucleotide repeat sequence in C9orf72. This breakthrough provides an opportunity to re-evaluate longstanding concepts regarding the cause and natural history of ALS, coming soon after the pathological unification of ALS with frontotemporal dementia through a shared pathological signature of cytoplasmic inclusions of the ubiquitinated protein TDP-43. However, with profound clinical, prognostic, neuropathological, and now genetic heterogeneity, the concept of ALS as one disease appears increasingly untenable. This background calls for the development of a more sophisticated taxonomy, and an appreciation of ALS as the breakdown of a wider network rather than a discrete vulnerable population of specialised motor neurons. Identification of C9orf72 repeat expansions in patients without a family history of ALS challenges the traditional division between familial and sporadic disease. By contrast, the 90% of apparently sporadic cases and incomplete penetrance of several genes linked to familial cases suggest that at least some forms of ALS arise from the interplay of multiple genes, poorly understood developmental, environmental, and age-related factors, as well as stochastic events

The Complexity of the Empire Colouring Problem

We investigate the computational complexity of the empire colouring problem (as defined by Percy Heawood in 1890) for maps containing empires formed by exactly $r > 1$ countries each. We prove that the problem can be solved in polynomial time using $s$ colours on maps whose underlying adjacency graph has no induced subgraph of average degree larger than $s/r$. However, if $s \geq 3$, the problem is NP-hard even if the graph is a forest of paths of arbitrary lengths (for any $r \geq 2$, provided $s < 2r - \sqrt(2r + 1/4+ 3/2)$. Furthermore we obtain a complete characterization of the problem's complexity for the case when the input graph is a tree, whereas our result for arbitrary planar graphs fall just short of a similar dichotomy. Specifically, we prove that the empire colouring problem is NP-hard for trees, for any $r \geq 2$, if $3 \leq s \leq 2r-1$ (and polynomial time solvable otherwise). For arbitrary planar graphs we prove NP-hardness if $s<7$ for $r=2$, and $s < 6r-3$, for $r \geq 3$. The result for planar graphs also proves the NP-hardness of colouring with less than 7 colours graphs of thickness two and less than $6r-3$ colours graphs of thickness $r \geq 3$.Comment: 23 pages, 12 figure

Ocean forests: breakthrough yields for macroalgae

The US Department of Energy Advanced Research Projects Agency - Energy (ARPA-E) MacroAlgae Research Inspiring Novel Energy Research (MARINER) program is encouraging technologies for the sustainable harvest of large funding research of macroalgae for biofuels at less than $80 per dry metric ton (DMT). The Ocean Forests team, led by the University of Southern Mississippi, is developing a complete managed ecosystem where nutrients are transformed and recycled. The team’s designs address major bottlenecks in profitability of offshore aquaculture systems including economical moored structures that can withstand storms, efficient planting, managing and harvesting systems, and sustainable nutrient supply. The work is inspired by Lapointe who reported yields of Gracilaria tikvahiae equivalent to 127 DMT per hectare per year (compared with standard aquaculture systems in the range of 20 to 40 DMT/ha/yr). This approach offers the potential for breakthrough yields for many macroalgae species. Moreover, mini-ecosystems in offshore waters create communities of macroalgae, shellfish, and penned finfish, supplemented by visiting free-range fish that can increase productivity, produce quality products, and create jobs and income for aquafarmers. Additional benefits include reduced disease in fish pens, cleaning contaminated coastal waters, and maximizing nutrient recycling. Cost projections for a successful, intensive, scaled system are competitive with current prices for fossil fuels