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Diabetic Retinopathy (DR) is a complication of long-standing, unchecked diabetes and one of the leading causes of blindness in the world. This paper focuses on improved and robust methods to extract some of the features of DR, viz. Blood Vessels and Exudates. Blood vessels are segmented using multiple morphological and thresholding operations. For the segmentation of exudates, k-means clustering and contour detection on the original images are used. Extensive noise reduction is performed to remove false positives from the vessel segmentation algorithm's results. The localization of Optic Disc using k-means clustering and template matching is also performed. Lastly, this paper presents a Deep Convolutional Neural Network (DCNN) model with 14 Convolutional Layers and 2 Fully Connected Layers, for the automatic, binary diagnosis of DR. The vessel segmentation, optic disc localization and DCNN achieve accuracies of 95.93%, 98.77% and 75.73% respectively. The source code and pre-trained model are available https://github.com/Sohambasu07/DR_2021, RAAI 2020, 11 pages, 12 figures, 2 tables

Achieving large bandwidth at strong mode conversion strengths is a central problem in few-mode optical waveguides. The most uncomplicated modification of a standard mode-converting grating is to incorporate a single extra gap. Such simple design has not been applied yet for broadening conversion spectrum between core modes of any few-mode waveguide e.g. few-mode fiber, possibly due to lacking knowledge of critical parameter control: (a) phase shift value at resonance wavelength, and (b) deterministic method for placement of the phase shift(s) accommodating the change in waveguide properties during grating writing. From semi-analytical considerations, we show in full generality that our design of a single-phase-shifted grating increases the bandwidth at 99 % conversion strength by more than 2.9 times, together with elucidating crucial parameter tolerances. The phase-shift placement is determinable on-the-go from the conversion spectra, thereby obviating any estimation of modified waveguide properties during grating-writing. This offers the longed on-demand in-fiber solution for dispersion control in fiber laser cavities and communication systems.

Dynamics of underground water in floodplain forest in the Morava river alluvium in South Moravia is primarily dependent on hydrological conditions as main recipient of Morava, Kyjovka & Spářavka. Hydrological measures carried out in 2nd half of 20th century have caused a negative impact on this floodplain groundwater. Increasing climatic extremes (low precipitation, high evapotranspiration) caused decreasing moisture content in surface soil layers. The aim of the study was to evaluate the underground water dynamics of 2018 in model area of Mikulčice forest using GIS and compare the result with previous studies to get the long term trend of changing underground water and soil moisture regime. Results show that the underground water level dropped to more than 2m from the surface in the sand and gravel layer almost throughout the year which interrupted capillarity of the soil profile. The underground water dynamics in the vegetation period was only on average 0.75m which is almost flat. Soil moisture dropped to lower than hydrolimits of availability of water for plants in the vegetation period. Measured tree increment of main trees was very low and some trees are permanently in stress. Finishing of revitalization in this area with the aim of improving the negative situation is Important for future years.

Given any polynomial with real coefficients, the existence of a real quadratic polynomial factor is proven using only basic real analysis. The aim is to provide an approachable proof to anybody who is familiar with the least upper bound property for real numbers, continuity and growth property of polynomials, and unfamiliar with complex numbers, field extension or advanced topology.

Carl Friedrich Gauss is often given credit for providing the first correct proof of the fundamental theorem of algebra in his 1799 doctoral dissertation. However, Gauss's proof contained a significant gap. In this paper, we give an elementary way of filling the gap in Gauss's proof., 9 pages, 1 figure. To appear in American Mathematical Monthly

Resonant and non-resonant effects in few-mode fibers have found use in versatile devices. From sensing perspective, extensive research has been done on fringe sensitivity of nonresonant two-mode interference. Resonant mode converter gratings are promising candidates for the fields of mode division multiplexing and active devices based on few-mode fibers. This thesis explores multi-parameter sensing using two effects of two-mode interference (TMI), namely fringe shift and shift of group-velocity equalization (GVE) wavelength. The following sensing parameters were achieved: a) TMI fringe shift can be used for measuring the effect of changes in temperature and strain on intermodal dispersion. For exposure of the fiber with a scanning laser spot of constant velocity, the change in intermodal dispersion due to such particular exposure can also be measured using TMI fringes. b) GVE wavelength shift can be used for straightforward sensing of temperature and strain, without suffering from any dependency on the fiber length like TMI fringes. Using the shift of GVE wavelength during exposure of the full fiber with a scanning laser spot, the change in core index can be estimated due to a simple model. This allows measurement of small index changes due to irradiation, which is not possible with FBGs due to imperceptible strength of FBGs for small index changes and lower sensitivity. Combining the GVE and FBG resonance wavelengths provides a method for differentiating strain and temperature. The GVE wavelength also has an approximately three times higher temperature sensitivity compared to FBG resonance at similar wavelengths. The strain sensitivity of GVE and FBG resonance wavelengths are of similar magnitude but of opposite sign. TMI fringe shift can also be used to measure the extra phase added between two modes by each mark of laser irradiation. Two methods have been developed for completely characterizing the intermodal dispersion, which were verified experimentally for the LP01-LP02 dispersion. Intermodal and intramodal reflection peaks of two excited modes from an FBG written in the few-mode fiber can be used to approximately estimate the offset of the intermodal dispersion of the pristine fiber. Combining this with TMI phase unwrapping provides estimate of complete intermodal dispersion including offset. Measuring the resonance wavelength for a mode converter written using marks already characterized using TMI provides a precise estimate of the offset of the intermodal dispersion of the pristine fiber. From the estimate of extra phase added by each mark and intermodal dispersion of the pristine fiber, the intermodal dispersion experienced by resonantly interacting modes in an MC can be predicted. Fabrication of broadband mode converter gratings at any desired wavelength is an ongoing field of research. Different strategies were evaluated for making broadband MCs: a) Partial core irradiation with a tightly focussed laser spot was simulated with simple approximate models. In was concluded that the losses might be too high due to poor mode overlaps. b) It was determined using simulations that phase-shifted mode converter gratings can provide broader than 35 nm bandwidth at 20 dB conversion strength using reasonable irradiation parameters. The method was verified by achieving 41 nm bandwidth at 16 dB conversion strength.