Rapid and high-sensitivity detections of biological analytes are critically important to ensure timely diagnosis of disease and effective monitoring of public health. Although various new biosensing platforms have been established as alternatives to conventional laboratory methods, most of these biosensing platforms suffer from insufficient sensitivities that severely limit their wide applications. To improve the detection sensitivities of these biosensors, surface modifications based on poly(amidoamine) (PAMAM) dendrimers and rolling circle amplification (RCA) have been proven to be effective methods. In this thesis, surface modification strategies based on PAMAM dendrimers and RCA have been applied on three biosensing platforms, including enzyme-linked immunosorbent assay (ELISA), localized surface plasmon resonance (LSPR) sensor chip, and affinity membrane, to improve their detection sensitivities. For the ELISA platform, glass-bottom and poly(styrene) 96-well plates are surface modified by dendrimer-aptamer conjugates to improve detection performances of human platelet-derived growth factor-BB using ELISA. The results show that the ELISA performed using the modified 96-well plates presents a much broader linear detection range and a significantly lower limit of detection (LOD) than conventional ELISA plates. For the LSPR platform, the dendrimer and aptamer modification strategy is employed to surface modify LSPR sensor chips for sensitive detection of the SARS-CoV-2 virus, and an RCA-AuNPs complex is developed to amplify the detection signals. The results show that the modified chip can sensitively detect the SARS-CoV-2 virus with a LOD of 148 vp/mL, suggesting that the modified LSPR chip and signal amplification method can be used for early diagnosis of Covid-19. For the affinity membrane platform, nylon membranes with dendrimer and dual-RCA surface modifications are developed to detect Escherichia coli O157:H7 in food samples. The surface-modified membranes significantly reduce the detection time of the target bacteria to two hours instead of several days using traditional bacterial detection methods. In addition, the new membranes achieve higher sample throughputs (around 4-5 mL/s) with a lower LOD (10 cells/ 250 mL) in processing real-world food samples compared to other similar detection platforms. The excellent properties of our surface modification approaches may provide further advantages when employed in other platforms, such as target separation and enrichment, antifouling and antibacterial, and drug delivery applications.

The Gauss circle problem in classical number theory concerns the estimation of N(x) = { (m1;m2) in ZxZ : m1^2 + m2^2 <= x }, the number of integer lattice points inside a circle of radius sqrt(x). Gauss showed that P(x) = N(x)- pi * x satisfi es P(x) = O(sqrt(x)). Later Hardy and Landau independently proved that P(x) = Omega_(x1=4(log x)1=4). It is conjectured that inf{e in R : P(x) = O(x^e )}= 1/4. I. K atai showed that the integral from 0 to X of |P(x)|^2 dx = X^(3/2) + O(X(logX)^2). Similar results to those of the circle have been obtained for regions D in R^2 which contain the origin and whose boundary dD satis fies suff cient smoothness conditions. Denote by P_D(x) the similar error term to P(x) only for the domain D. W. G. Nowak showed that, under appropriate conditions on dD, P_D(x) = Omega_(x1=4(log x)1=4) and that the integral from 0 to X of |P_D(x)|^2 dx = O(X^(3/2)). A result similar to Nowak's mean square estimate is given in the case where only "primitive" lattice points, {(m1;m2) in Z^2 : gcd(m1;m2) = 1 }, are counted in a region D, on assumption of the Riemann Hypothesis.

Real-time multi-circle detection has been a challenging problem in the field of biomedical image processing, due to the variable sizes and non-ideal shapes of cells in microscopic images. In this study, two new multi-circle detection algorithms are developed to facilitate an automatic bladder cancer diagnosis system: one is a modified circular Hough Transform algorithm integrated with edge gradient information; and the other one is a stochastic search approach based on real valued artificial immune systems. Computer simulation results show both algorithms outperform traditional methods such as the Hough Transform and the geometric feature based method, in terms of both precision and speed.

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Background The Circle of Willis (CoW) is an arterial anastomotic circle located at the skull base thatmaintains collateral circulation in the brain. Variations in CoW anatomy are commonly presentin the general population. Absent or hypoplastic segments of the CoW have been linked to anincreased stroke risk. Aim To determine whether CoW completeness is related to future ischemic stroke in the elderlypopulation after adjustment for relevant clinical risk factors. Methods Consecutive patients that underwent computed tomography angiography (CTA) of the headbetween 2014-2015 (60 years or older) were included. CoW-integrity was determined on CTAimages. Patient journals were retrospectively examined for ischemic stroke events followingthe CTA. Cox proportional hazard regression analysis was performed to determine hazard forischemic stroke in patients with incomplete CoW. Results 147 patients were included. The median follow-up time was 6.4 years (interquartile range 3.0years). 17 ischemic stroke events occurred during the follow-up period. Age (hazard ratio, HR1.10, p=0.03) and gender (HR 0.25, p=0.04) were statistically significant risk factors forischemic stroke. Complete anterior and posterior CoW was associated with lower strokehazards, however, the association was not statistically significant (HR 0.36, p=0.34 and HR0.67, p=0.45, respectively). Conclusions No significant risk reduction could be observed for either complete posterior or anterior CoW.Sex and age were significant risk factors for ischemic stroke. Further research is necessary toinvestigate how CoW integrity influences stroke risk after adjustment for other risk factors.

Geographical profiling (GP) is a method used to determine an offender’s most likely area of residence. GP helps to better understand the spatial behaviour of an offender, by connecting series of crimes in a specific area. Research have shown that the geographic space plays an important part when solving crimes, especially with respect to serial offenders that tend to offend closer to their home. Despite the fact that GP has had some success, the field has received criticism, and speculations regarding its applicability for actual investigations. This thesis seeks to evaluate whether a specific method within GP could have been applied for an actual investigation. Thus, the aim of this study is to explore if it is possible to apply the Circle Theory of Environmental Range to the case of Marcel Lychau Hansen, ‘Amagermanden’, who is a famous Danish serial offender, and whether the theory could have contributed to the investigation at the time. By conducting a case study, the results showed that Hansen was operating as a commuter, and the theory was therefore not able to predict a narrowed area for his residence, since it was not possible to perform the Hypothesis of Environmental Range. However, the study showed that he had several of his daily routines on Amager – and this finding highlights, that considering the geographical factors would have been an important factor for the investigation. The study concludes the theory to be applicable to the case, though it was found limited in how it could have contributed to the investigation, and the geographical profile could not stand alone for this specific investigation.