Algorithmic Interpretations of Fractal Dimension

We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several well-studied notions of fractal dimension for sets and measures in Euclidean space. We consider a definition of fractal dimension for finite metric spaces which agrees with standard notions used to empirically estimate the fractal dimension of various sets. We define the fractal dimension of some metric space to be the infimum delta>0, such that for any eps>0, for any ball B of radius r >= 2eps, and for any eps-net N, we have |B cap N|=O((r/eps)^delta). Using this definition we obtain faster algorithms for a plethora of classical problems on sets of low fractal dimension in Euclidean space. Our results apply to exact and fixed-parameter algorithms, approximation schemes, and spanner constructions. Interestingly, the dependence of the performance of these algorithms on the fractal dimension nearly matches the currently best-known dependence on the standard Euclidean dimension. Thus, when the fractal dimension is strictly smaller than the ambient dimension, our results yield improved solutions in all of these settings. We remark that our definition of fractal definition is equivalent up to constant factors to the well-studied notion of doubling dimension. However, in the problems that we consider, the dimension appears in the exponent of the running time, and doubling dimension is not precise enough for capturing the best possible such exponent for subsets of Euclidean space. Thus our work is orthogonal to previous results on spaces of low doubling dimension; while algorithms on spaces of low doubling dimension seek to extend results from the case of low dimensional Euclidean spaces to more general metric spaces, our goal is to obtain faster algorithms for special pointsets in Euclidean space

A spectrum deconvolution method based on grey relational analysis

The extensive usage of X ray spectroscopies in studying complex material systems is not only intended to reveal underlying mechanisms that govern physical phenomena, but also used in applied studies focused on an insight driven performance improvement of a wide range of devices. However, the traditional analysis methods for X ray spectroscopic data are rather time consuming and sensitive to errors in data pre processing e.g., normalization or background subtraction . In this study, a method based on grey relational analysis, a multi variable statistical method, is proposed to analyze and extract information from X ray spectroscopic data. As a showcase, the valence bands of microcrystalline silicon suboxides probed by hard X ray photoelectron spectroscopy HAXPES were investigated. The results obtained by the proposed method agree well with conventionally derived composition information e.g., curve fit of Si 2p core level of the silicon suboxides . Furthermore, the uncertainty of chemical compositions derived by the proposed method is smaller than that of traditional analysis methods e.g., the least square fit , when artificial linear functions are introduced to simulate the errors in data pre processing. This suggests that the proposed method is capable of providing more reliable and accurate results, especially for data containing significant noise contributions or that is subject to inconsistent data pre processing. Since the proposed method is less experience driven and error prone, it offers a novel approach for automate data analysis, which is of great interest for various applications, such as studying combinatorial material librarie

Paramagnetic centers in amorphous and microcrystalline silicon irradiated with 2 МeV electrons

Amorphous and microcrystalline silicon are well known materials for thin film large area electronics. The defects in the material are an important issue for the device quality and the manufacturing process optimization. We study defects in thin film silicon with electron spin resonance (ESR). In order to vary the defect density in a wide range 2 MeV electron bombardment at 100 K was applied with dose as high as 10¹⁸ e*cm⁻². Samples were investigated after deposition, after irradiation and between the annealing steps. The spin density (Ns) in the material was varied over 3 orders of magnitude. Strong satellites with g≈2.010 and g≈2.000 were observed on the shoulders of the dangling bond line. The initial Ns and the shape of the resonance line were restored after annealing.Аморфний і мікрокристалічний кремній є широко відомими матеріалами для виробництва тонкоплівкової електроники великої площі. Дефекти у даних матеріалах відіграють вирішальну роль для якості пристроїв і оптимізації виробничих процесів. Ми досліджували тонкоплівковий гідрогенований кремній методом вимірів електронного парамагнитного резонансу (ЕПР). Для зміни щільності дефектів у широкому диапазоні зразки було опромінено електронами з енергією 2 МеВ. Зразки було досліджено після осадження, після опромінення і між етапами відпалу. Щільність спинів (Ns) в матеріалі змінювалась в межах 3-х порядків величини. З обох боків від центрального резонансу, що характеризує обірвані зв’язки кремнію, спостеригались потужні додаткові резонансні лінії (g≈2.010 и g≈2.000). Після відпалу форма резонансних ліній і щільність спинів поверталися до вихідних показників.Аморфный и микрокристаллический кремний являются широко известными материалами для производства тонкопленочной электроники большой площади. Дефекты в данных материалах играют решающую роль для качества приборов и оптимизации производственных процессов. Мы исследовали тонкопленочный гидрогенированный кремний методом измерений электронного парамагнитного резонанса (ЭПР). Для изменения плотности дефектов в широких пределах образцы облучались электронами с энергией 2 МэВ. Образцы исследовались после осаждения, после облучения и между стадиями отжига. Плотность спинов (Ns) в материале изменялась в пределах 3-х порядков величины. По обе стороны от центрального резонанса, характеризующего оборванные связи кремния, наблюдались мощные дополнительные резонансные линии (g≈2.010 и g≈2.000). После отжига форма резонансных линий и плотность спинов возвращались к исходным значениям

The Effect of 7,12-dimethylbenz[a]-anthracene (DMBA) on Physical Activity in Female Mice

BACKGROUND: Regular exercise has been shown to reduce the risk of occurrence for certain cancers. In animal models, DMBA is a synthetic carcinogen that has been established as the gold standard for inducing cancerous tumors in rodents. However, it has yet to be established whether DMBA has an effect on voluntary wheel running in mice. If there is an effect, it would confound any experiment which investigates exercise effects on tumor growth. PURPOSE: The overall purpose of this project was to determine if DMBA altered voluntary wheel running in mice. METHODS: All procedures were approved by TAMU IACUC. SENCAR mice breeder pairs (Charles River) and offspring at 3 weeks of age were group housed and randomly assigned to a group receiving the DMBA (n=69) or not receiving the DMBA treatment (n=22). At 4 weeks of age, two running wheels were placed inside the cages and connected to a computer that measured distance and time. The running wheels were mounted to the cage tops of standard rat cages and equipped with a cycling computer (BC8.12, Sigma Sport) to record running distance and duration. The running wheels were plastic and had a 410mm circumference with a solid running surface. From 8 to 14 weeks of age, mice in the DMBA group were gavaged daily with a DMBA dose (20 µg/mouse) dissolved in corn oil. A two way ANOVA was employed to determine the effect of DMBA on activity with factors of time and treatment. RESULTS: DMBA had no effect on the distance (p=0.51) or duration ran (p=0.12), but significantly decreased the speed at which the mice ran (p=0.02). A post-hoc analysis indicated that significant decreases in speed occurred at weeks 12 (35.2 ±9.2 vs. 46.4 ± 14.6; p=0.0002) and 20 (35.4 ±10.3 vs. 46.2 ± 14.1; p\u3c0.0001) of age. CONCLUSION: Our data suggest that DMBA does not affect the distance or time spent running on a wheel, but does affect the speed at which the mice run. While DMBA decreased speed, the significant effects on speed are minor given that neither distance nor duration were different between the groups. Therefore, we can conclude that DMBA does not prevent voluntary wheel running in mice

Functional near infrared spectroscopy (fNIRS) to assess cognitive function in infants in rural Africa

Cortical mapping of cognitive function during infancy is poorly understood in low-income countries due to the lack of transportable neuroimaging methods. We have successfully piloted functional near infrared spectroscopy (fNIRS) as a neuroimaging tool in rural Gambia. Four-to-eight month old infants watched videos of Gambian adults perform social movements, while haemodynamic responses were recorded using fNIRS. We found distinct regions of the posterior superior temporal and inferior frontal cortex that evidenced either visual-social activation or vocally selective activation (vocal > non-vocal). The patterns of selective cortical activation in Gambian infants replicated those observed within similar aged infants in the UK. These are the first reported data on the measurement of localized functional brain activity in young infants in Africa and demonstrate the potential that fNIRS offers for field-based neuroimaging research of cognitive function in resource-poor rural communities

Precursors to Natural Grammar Learning: Preliminary Evidence from 4-Month-Old Infants

When learning a new language, grammar—although difficult—is very important, as grammatical rules determine the relations between the words in a sentence. There is evidence that very young infants can detect rules determining the relation between neighbouring syllables in short syllable sequences. A critical feature of all natural languages, however, is that many grammatical rules concern the dependency relation between non-neighbouring words or elements in a sentence i.e. between an auxiliary and verb inflection as in is singing. Thus, the issue of when and how children begin to recognize such non-adjacent dependencies is fundamental to our understanding of language acquisition. Here, we use brain potential measures to demonstrate that the ability to recognize dependencies between non-adjacent elements in a novel natural language is observable by the age of 4 months. Brain responses indicate that 4-month-old German infants discriminate between grammatical and ungrammatical dependencies in auditorily presented Italian sentences after only brief exposure to correct sentences of the same type. As the grammatical dependencies are realized by phonologically distinct syllables the present data most likely reflect phonologically based implicit learning mechanisms which can serve as a precursor to later grammar learning

Functional near infrared spectroscopy (fNIRS) to assess cognitive function in infants in rural Africa

Cortical mapping of cognitive function during infancy is poorly understood in low-income countries due to the lack of transportable neuroimaging methods. We have successfully piloted functional near infrared spectroscopy (fNIRS) as a neuroimaging tool in rural Gambia. Four-to-eight month old infants watched videos of Gambian adults perform social movements, while haemodynamic responses were recorded using fNIRS. We found distinct regions of the posterior superior temporal and inferior frontal cortex that evidenced either visual-social activation or vocally selective activation (vocal > non-vocal). The patterns of selective cortical activation in Gambian infants replicated those observed within similar aged infants in the UK. These are the first reported data on the measurement of localized functional brain activity in young infants in Africa and demonstrate the potential that fNIRS offers for field-based neuroimaging research of cognitive function in resource-poor rural communities

Over 65% sunlight absorption in a 1 mu m Si slab with hyperuniform texture

Thin, flexible, and invisible solar cells will be a ubiquitous technology in the near future. Ultrathin crystalline silicon (c-Si) cells capitalize on the success of bulk silicon cells while being lightweight and mechanically flexible, but suffer from poor absorption and efficiency. Here we present a new family of surface texturing, based on correlated disordered hyperuniform patterns, capable of efficiently coupling the incident spectrum into the silicon slab optical modes. We experimentally demonstrate 66.5% solar light absorption in free-standing 1 μm c-Si layers by hyperuniform nanostructuring for the spectral range of 400 to 1050 nm. The absorption equivalent photocurrent derived from our measurements is 26.3 mA/cm2, which is far above the highest found in literature for Si of similar thickness. Considering state-of-the-art Si PV technologies, we estimate that the enhanced light trapping can result in a cell efficiency above 15%. The light absorption can potentially be increased up to 33.8 mA/cm2 by incorporating a back-reflector and improved antireflection, for which we estimate a photovoltaic efficiency above 21% for 1 μm thick Si cells