Asymptotic Probability of Incidence Relations Over Finite Fields

Given four generic lines in FP3, we ask, How many lines meet the four? The answer depends on the field. When F = C, the answer is two. When F = R, the answer is either zero or two. If we work over a finite field there are only finitely many projective lines. We compute the probability four lines are met by two. The main result is that as q approaches infinity, this probability approaches 1/2. Asymptotically, the other half of the time zero lines will meet the four

Love Me, Phoebe, Love Me : Plantation Song And Chorus

https://digitalcommons.library.umaine.edu/mmb-vp/3993/thumbnail.jp

Little Cotton Dolly : Plantation Lullaby

https://digitalcommons.library.umaine.edu/mmb-vp/4651/thumbnail.jp

Investigations of an On-body Reflectometer Probe

Radar can be utilized to detect the mechanical heart activity and is a potential alternative to today’s heartbeat monitoring techniques in medicine. It can detect details of the heart activity, such as filling and ejection of heart chambers and opening and closing of heart valves. This is due to the radars ability to detect movements and direction of motion. Compared to electrocardiogram and ultrasound it has the advantage that it is a contactless measurement. The objective of this thesis is the development of a proof-of-concept prototype of a novel microwave on-body sensor for heartbeat detection, which can be used inside an MRI system and which could provide prospective triggering information. The main idea is to use a microwave sensor (reflectometer) with an on-body antenna illuminating the heart and detecting the reflected signal. The measurement is based on the evaluation of the heart-related time-dependent reflection coefficient of the antenna, by minimizing the static and respiration-related components of the reflection coefficient. In a first step, this is done by minimizing the antenna mismatch with an automatic impedance matching circuit after the placement of the antenna on the chest of an individual; the antenna mismatch is dependent on the position and the individual body properties. In a second step the residual static and slow variation signal from respiration is suppressed by a canceller circuit (well-known from CW radar technology as reflected power canceller). With the reflectometer sensor system consisting of a CW signal generator (transmitter, Tx), on-body antenna, adaptive impedance matching circuit and demodulator circuit as part of the reflected signal canceller, the performance of each component influences the performance of the sensor system. Thus, the thesis concentrates on the design of the circuits and the antenna but also investigates the wave propagation scenario of the sensor applied to a human chest. The signals measured with the microwave sensor are compared with a standard measurement method for heart activity, a heart sound measurement. This is used in order to assess the obtained signal and relate the signal states to certain heart states. The measured radar signals are found to be sensitive to position of the sensor, the individual and the posture of the individual, making the interpretation of the signals challenging

Nano-Imprinted Thin Films of Reactive, Azlactone-Containing Polymers: Combining Methods for the Topographic Patterning of Cell Substrates with Opportunities for Facile Post-Fabrication Chemical Functionalization

Approaches to the fabrication of surfaces that combine methods for the topographic patterning of soft materials with opportunities for facile, post-fabrication chemical functionalization could contribute significantly to advances in biotechnology and a broad range of other areas. Here, we report methods that can be used to introduce well defined nano- and microscale topographic features to thin films of reactive polymers containing azlactone functionality using nanoimprint lithography (NIL). We demonstrate that NIL can be used to imprint topographic patterns into thin films of poly(2-vinyl-4,4- dimethylazlactone) and a copolymer of methyl methacrylate and 2-vinyl- 4,4-dimethylazlactone using silicon masters having patterns of grooves and ridges ranging in width from 400 nm to 2μm, demonstrating the potential f this method to transfer patterns to films of these reactive polymers over a range of feature sizes and densities. We demonstrate further that the azlactone functionality of these polymers survives temperatures and pressures associated with NIL, and that topographically patterned films can be readily functionalized post-fabrication by treatment of surface-accessible azlactone functionality with small molecules and polymers containing primary amines. The results of experiments in which NIH-3T3 cells were seeded onto films imprinted with lined patterns having a pitch of 4 demonstrated that cells attach and proliferate on these azlactone-containing films and that they align in the direction of the imprinted pattern. Finally, we demonstrate that the treatment of these materials with amine-functionalized poly(ethylene glycol) (PEG) can be used to create regions of topographically patterned films that prevent cell adhesion. The results of this study suggest approaches to the functionalization of topographically patterned surfaces with a broad range of chemical functionality (e.g., peptides, proteins, carbohydrates, etc.) of biotechnological interest. The ability to manipulate and define both the physical topography and chemical functionality of these reactive materials could provide opportunities to investigate the combined effects of substrate topography and chemical functionality on cell behavior and may also be useful in a broad range of other applications

The Sloan Digital Sky Survey Stripe 82 Imaging Data: Depth-Optimized Co-adds Over 300 Deg^2 in Five Filters

We present and release co-added images of the Sloan Digital Sky Survey (SDSS) Stripe 82. Stripe 82 covers an area of 300 deg^2 on the Celestial Equator, and has been repeatedly scanned 70-90 times in the ugriz bands by the SDSS imaging survey. By making use of all available data in the SDSS archive, our co-added images are optimized for depth. Input single-epoch frames were properly processed and weighted based on seeing, sky transparency, and background noise before co-addition. The resultant products are co-added science images and their associated weight images that record relative weights at individual pixels. The depths of the co-adds, measured as the 5 sigma detection limits of the aperture (3.2 arcsec diameter) magnitudes for point sources, are roughly 23.9, 25.1, 24.6, 24.1, and 22.8 AB magnitudes in the five bands, respectively. They are 1.9-2.2 mag deeper than the best SDSS single-epoch data. The co-added images have good image quality, with an average point-spread function FWHM of ~1 arcsec in the r, i, and z bands. We also release object catalogs that were made with SExtractor. These co-added products have many potential uses for studies of galaxies, quasars, and Galactic structure. We further present and release near-IR J-band images that cover ~90 deg^2 of Stripe 82. These images were obtained using the NEWFIRM camera on the NOAO 4-m Mayall telescope, and have a depth of about 20.0--20.5 Vega magnitudes (also 5 sigma detection limits for point sources).Comment: 19 pages, 17 figures, accepted for publication in ApJ

Flattened Stirling Permutations

Recall that a Stirling permutation is a permutation on the multiset $\{1,1,2,2,\ldots,n,n\}$ such that any numbers appearing between repeated values of $i$ must be greater than $i$. We call a Stirling permutation ``flattened'' if the leading terms of maximal chains of ascents (called runs) are in weakly increasing order. Our main result establishes a bijection between flattened Stirling permutations and type $B$ set partitions of $\{0,\pm1,\pm2,\ldots,\pm (n-1)\}$, which are known to be enumerated by the Dowling numbers, and we give an independent proof of this fact. We also determine the maximal number of runs for any flattened Stirling permutation, and we enumerate flattened Stirling permutations with a small number of runs or with two runs of equal length. We conclude with some conjectures and generalizations worthy of future investigation.Comment: 15 pages, 1 figure, 2 tabl

Fabrication and Selective Functionalization of Amine-Reactive Polymer Multilayers on Topographically Patterned Microwell Cell Culture Arrays

We report an approach to the fabrication and selective functionalization of amine-reactive polymer multilayers on the surfaces of 3-D polyurethane-based microwell cell culture arrays. Reactive layer-by-layer assembly of multilayers using branched polyethyleneimine (BPEI) and the azlactone- functionalized polymer poly(2-vinyl-4,4′-dimethylazlactone) (PVDMA) yielded film-coated microwell arrays that could be chemically functionalized postfabrication by treatment with different amine-functionalized macromolecules or small molecule primary amines. Treatment of film-coated arrays with the small molecule amine d-glucamine resulted in microwell surfaces that resisted the adhesion and proliferation of mammalian fibroblast cells in vitro. These and other experiments demonstrated that it was possible to functionalize different structural features of these arrays in a spatially resolved manner to create dual-functionalized substrates (e.g., to create arrays having either (i) azlactone-functionalized wells, with regions between the wells functionalized with glucamine or (ii) substrates with spatially resolved regions of two different cationic polymers). In particular, spatial control over glucamine functionalization yielded 3-D substrates that could be used to confine cell attachment and growth to microwells for periods of up to 28 days and support the 3-D culture of arrays of cuboidal cell clusters. These approaches to dual functionalization could prove useful for the long-term culture and maintenance of cell types for which the presentation of specific and chemically well-defined 3-D culture environments is required for control over cell growth, differentiation, and other important behaviors. More generally, our approach provides methods for the straightforward chemical functionalization of otherwise unreactive topographically patterned substrates that could prove to be useful in a range of other fundamental and applied contexts. © 2011 American Chemical Society