Spatial Relationships among Hydroacoustic, Hydrographic and Top Predator Patterns: Cetacean Distributions in the Mid-Atlantic Bight

Effective conservation and management of top predators requires a comprehensive understanding of their distributions and of the underlying biological and physical processes that affect these distributions. The Mid-Atlantic Bight shelf break system is a dynamic and productive region where at least 32 species of cetaceans have been recorded through various systematic and opportunistic marine mammal surveys from the 1970s through 2012. My dissertation characterizes the spatial distribution and habitat of cetaceans in the Mid-Atlantic Bight shelf break system by utilizing marine mammal line-transect survey data, synoptic multi-frequency active acoustic data, and fine-scale hydrographic data collected during the 2011 summer Atlantic Marine Assessment Program for Protected Species (AMAPPS) survey. Although studies describing cetacean habitat and distributions have been previously conducted in the Mid-Atlantic Bight, my research specifically focuses on the shelf break region to elucidate both the physical and biological processes that influence cetacean distribution patterns within this cetacean hotspot.

In Chapter One I review biologically important areas for cetaceans in the Atlantic waters of the United States. I describe the study area, the shelf break region of the Mid-Atlantic Bight, in terms of the general oceanography, productivity and biodiversity. According to recent habitat-based cetacean density models, the shelf break region is an area of high cetacean abundance and density, yet little research is directed at understanding the mechanisms that establish this region as a cetacean hotspot.

In Chapter Two I present the basic physical principles of sound in water and describe the methodology used to categorize opportunistically collected multi-frequency active acoustic data using frequency responses techniques. Frequency response classification methods are usually employed in conjunction with net-tow data, but the logistics of the 2011 AMAPPS survey did not allow for appropriate net-tow data to be collected. Biologically meaningful information can be extracted from acoustic scattering regions by comparing the frequency response curves of acoustic regions to theoretical curves of known scattering models. Using the five frequencies on the EK60 system (18, 38, 70, 120, and 200 kHz), three categories of scatterers were defined: fish-like (with swim bladder), nekton-like (e.g., euphausiids), and plankton-like (e.g., copepods). I also employed a multi-frequency acoustic categorization method using three frequencies (18, 38, and 120 kHz) that has been used in the Gulf of Maine and Georges Bank which is based the presence or absence of volume backscatter above a threshold. This method is more objective than the comparison of frequency response curves because it uses an established backscatter value for the threshold. By removing all data below the threshold, only strong scattering information is retained.

In Chapter Three I analyze the distribution of the categorized acoustic regions of interest during the daytime cross shelf transects. Over all transects, plankton-like acoustic regions of interest were detected most frequently, followed by fish-like acoustic regions and then nekton-like acoustic regions. Plankton-like detections were the only significantly different acoustic detections per kilometer, although nekton-like detections were only slightly not significant. Using the threshold categorization method by Jech and Michaels (2006) provides a more conservative and discrete detection of acoustic scatterers and allows me to retrieve backscatter values along transects in areas that have been categorized. This provides continuous data values that can be integrated at discrete spatial increments for wavelet analysis. Wavelet analysis indicates significant spatial scales of interest for fish-like and nekton-like acoustic backscatter range from one to four kilometers and vary among transects.

In Chapter Four I analyze the fine scale distribution of cetaceans in the shelf break system of the Mid-Atlantic Bight using corrected sightings per trackline region, classification trees, multidimensional scaling, and random forest analysis. I describe habitat for common dolphins, Risso’s dolphins and sperm whales. From the distribution of cetacean sightings, patterns of habitat start to emerge: within the shelf break region of the Mid-Atlantic Bight, common dolphins were sighted more prevalently over the shelf while sperm whales were more frequently found in the deep waters offshore and Risso’s dolphins were most prevalent at the shelf break. Multidimensional scaling presents clear environmental separation among common dolphins and Risso’s dolphins and sperm whales. The sperm whale random forest habitat model had the lowest misclassification error (0.30) and the Risso’s dolphin random forest habitat model had the greatest misclassification error (0.37). Shallow water depth (less than 148 meters) was the primary variable selected in the classification model for common dolphin habitat. Distance to surface density fronts and surface temperature fronts were the primary variables selected in the classification models to describe Risso’s dolphin habitat and sperm whale habitat respectively. When mapped back into geographic space, these three cetacean species occupy different fine-scale habitats within the dynamic Mid-Atlantic Bight shelf break system.

In Chapter Five I present a summary of the previous chapters and present potential analytical steps to address ecological questions pertaining the dynamic shelf break region. Taken together, the results of my dissertation demonstrate the use of opportunistically collected data in ecosystem studies; emphasize the need to incorporate middle trophic level data and oceanographic features into cetacean habitat models; and emphasize the importance of developing more mechanistic understanding of dynamic ecosystems.

Learning and Exploiting Camera Geometry for Computer Vision

This work explores the use of statistical methods in describing and estimating camera poses, as well as the information feedback loop between camera pose and object detection. Surging development in robotics and computer vision has pushed the need for algorithms that infer, understand, and utilize information about the position and orientation of the sensor platforms when observing and/or interacting with their environment.

The first contribution of this thesis is the development of a set of statistical tools for representing and estimating the uncertainty in object poses. A distribution for representing the joint uncertainty over multiple object positions and orientations is described, called the mirrored normal-Bingham distribution. This distribution generalizes both the normal distribution in Euclidean space, and the Bingham distribution on the unit hypersphere. It is shown to inherit many of the convenient properties of these special cases: it is the maximum-entropy distribution with fixed second moment, and there is a generalized Laplace approximation whose result is the mirrored normal-Bingham distribution. This distribution and approximation method are demonstrated by deriving the analytical approximation to the wrapped-normal distribution. Further, it is shown how these tools can be used to represent the uncertainty in the result of a bundle adjustment problem.

Another application of these methods is illustrated as part of a novel camera pose estimation algorithm based on object detections. The autocalibration task is formulated as a bundle adjustment problem using prior distributions over the 3D points to enforce the objects' structure and their relationship with the scene geometry. This framework is very flexible and enables the use of off-the-shelf computational tools to solve specialized autocalibration problems. Its performance is evaluated using a pedestrian detector to provide head and foot location observations, and it proves much faster and potentially more accurate than existing methods.

Finally, the information feedback loop between object detection and camera pose estimation is closed by utilizing camera pose information to improve object detection in scenarios with significant perspective warping. Methods are presented that allow the inverse perspective mapping traditionally applied to images to be applied instead to features computed from those images. For the special case of HOG-like features, which are used by many modern object detection systems, these methods are shown to provide substantial performance benefits over unadapted detectors while achieving real-time frame rates, orders of magnitude faster than comparable image warping methods.

The statistical tools and algorithms presented here are especially promising for mobile cameras, providing the ability to autocalibrate and adapt to the camera pose in real time. In addition, these methods have wide-ranging potential applications in diverse areas of computer vision, robotics, and imaging.

Experimental detection of sudden stiffness change in a structural system employing Laser Doppler Vibrometry

Sudden changes in the stiffness of a structure are often indicators of structural damage. Detection of such sudden stiffness change from the vibrations of structures is important for Structural Health Monitoring (SHM) and damage detection. Non-contact measurement of these vibrations is a quick and efficient way for successful detection of sudden stiffness change of a structure. In this paper, we demonstrate the capability of Laser Doppler Vibrometry to detect sudden stiffness change in a Single Degree Of Freedom (SDOF) oscillator within a laboratory environment. The dynamic response of the SDOF system was measured using a Polytec RSV-150 Remote Sensing Vibrometer. This instrument employs Laser Doppler Vibrometry for measuring dynamic response. Additionally, the vibration response of the SDOF system was measured through a MicroStrain G-Link Wireless Accelerometer mounted on the SDOF system. The stiffness of the SDOF system was experimentally determined through calibrated linear springs. The sudden change of stiffness was simulated by introducing the failure of a spring at a certain instant in time during a given period of forced vibration. The forced vibration on the SDOF system was in the form of a white noise input. The sudden change in stiffness was successfully detected through the measurements using Laser Doppler Vibrometry. This detection from optically obtained data was compared with a detection using data obtained from the wireless accelerometer. The potential of this technique is deemed important for a wide range of applications. The method is observed to be particularly suitable for rapid damage detection and health monitoring of structures under a model-free condition or where information related to the structure is not sufficient.

Design, fabrication and characterization of resonant waveguide grating based optical biosensors

The absence of rapid, low cost and highly sensitive biodetection platform has hindered the implementation of next generation cheap and early stage clinical or home based point-of-care diagnostics. Label-free optical biosensing with high sensitivity, throughput, compactness, and low cost, plays an important role to resolve these diagnostic challenges and pushes the detection limit down to single molecule. Optical nanostructures, specifically the resonant waveguide grating (RWG) and nano-ribbon cavity based biodetection are promising in this context. The main element of this dissertation is design, fabrication and characterization of RWG sensors for different spectral regions (e.g. visible, near infrared) for use in label-free optical biosensing and also to explore different RWG parameters to maximize sensitivity and increase detection accuracy. Design and fabrication of the waveguide embedded resonant nano-cavity are also studied. Multi-parametric analyses were done using customized optical simulator to understand the operational principle of these sensors and more important the relationship between the physical design parameters and sensor sensitivities. Silicon nitride (SixNy) is a useful waveguide material because of its wide transparency across the whole infrared, visible and part of UV spectrum, and comparatively higher refractive index than glass substrate. SixNy based RWGs on glass substrate are designed and fabricated applying both electron beam lithography and low cost nano-imprint lithography techniques. A Chromium hard mask aided nano-fabrication technique is developed for making very high aspect ratio optical nano-structure on glass substrate. An aspect ratio of 10 for very narrow (~60 nm wide) grating lines is achieved which is the highest presented so far. The fabricated RWG sensors are characterized for both bulk (183.3 nm/RIU) and surface sensitivity (0.21nm/nm-layer), and then used for successful detection of Immunoglobulin-G (IgG) antibodies and antigen (~1μg/ml) both in buffer and serum. Widely used optical biosensors like surface plasmon resonance and optical microcavities are limited in the separation of bulk response from the surface binding events which is crucial for ultralow biosensing application with thermal or other perturbations. A RWG based dual resonance approach is proposed and verified by controlled experiments for separating the response of bulk and surface sensitivity. The dual resonance approach gives sensitivity ratio of 9.4 whereas the competitive polarization based approach can offer only 2.5. The improved performance of the dual resonance approach would help reducing probability of false reading in precise bio-assay experiments where thermal variations are probable like portable diagnostics.

Development of a Surface-Enhanced Raman Spectroscopy Method for the Detection of Benzodiazepines in Urine

Benzodiazepines are among the most prescribed compounds for anti-anxiety and are present in many toxicological screens. These drugs are also prominent in the commission of drug facilitated sexual assaults due their effects on the central nervous system. Due to their potency, a low dose of these compounds is often administered to victims; therefore, the target detection limit for these compounds in biological samples is 10 ng/mL. Currently these compounds are predominantly analyzed using immunoassay techniques; however more specific screening methods are needed. The goal of this dissertation was to develop a rapid, specific screening technique for benzodiazepines in urine samples utilizing surface-enhanced Raman spectroscopy (SERS), which has previously been shown be capable of to detect trace quantities of pharmaceutical compounds in aqueous solutions. Surface enhanced Raman spectroscopy has the advantage of overcoming the low sensitivity and fluorescence effects seen with conventional Raman spectroscopy. The spectra are obtained by applying an analyte onto a SERS-active metal substrate such as colloidal metal particles. SERS signals can be further increased with the addition of aggregate solutions. These agents cause the nanoparticles to amass and form hot-spots which increase the signal intensity. In this work, the colloidal particles are spherical gold nanoparticles in aqueous solution with an average size of approximately 30 nm. The optimum aggregating agent for the detection of benzodiazepines was determined to be 16.7 mM MgCl2, providing the highest signal intensities at the lowest drug concentrations with limits of detection between 0.5 and 127 ng/mL. A supported liquid extraction technique was utilized as a rapid clean extraction for benzodiazepines from urine at a pH of 5.0, allowing for clean extraction with limits of detection between 6 and 640 ng/mL. It was shown that at this pH other drugs that are prevalent in urine samples can be removed providing the selective detection of the benzodiazepine of interest. This technique has been shown to provide rapid (less than twenty minutes), sensitive, and specific detection of benzodiazepines at low concentrations in urine. It provides the forensic community with a sensitive and specific screening technique for the detection of benzodiazepines in drug facilitated assault cases.

Variables Affecting the Collection and Preservation of Human Scent Components through Instrumental and Biological Evaluations

In certain European countries and the United States of America, canines have been successfully used in human scent identification. There is however, limited scientific knowledge on the composition of human scent and the detection mechanism that produces an alert from canines. This lack of information has resulted in successful legal challenges to human scent evidence in the courts of law. The main objective of this research was to utilize science to validate the current practices of using human scent evidence in criminal cases. The goals of this study were to utilize Headspace Solid Phase Micro Extraction Gas Chromatography Mass Spectrometry (HS-SPME-GC/MS) to determine the optimum collection and storage conditions for human scent samples, to investigate whether the amount of DNA deposited upon contact with an object affects the alerts produced by human scent identification canines, and to create a prototype pseudo human scent which could be used for training purposes. Hand odor samples which were collected on different sorbent materials and exposed to various environmental conditions showed that human scent samples should be stored without prolonged exposure to UVA/UVB light to allow minimal changes to the overall scent profile. Various methods of collecting human scent from objects were also investigated and it was determined that passive collection methods yields ten times more VOCs by mass than active collection methods. Through the use of polymerase chain reaction (PCR) no correlation was found between the amount of DNA that was deposited upon contact with an object and the alerts that were produced by human scent identification canines. Preliminary studies conducted to create a prototype pseudo human scent showed that it is possible to produce fractions of a human scent sample which can be presented to the canines to determine whether specific fractions or the entire sample is needed to produce alerts by the human scent identification canines.

Quantitative Analysis and Determination of Microcystin in water by Capillary Electrophoresis Mass Spectrometry

The presence of harmful algal blooms (HAB) is a growing concern in aquatic environments. Among HAB organisms, cyanobacteria are of special concern because they have been reported worldwide to cause environmental and human health problem through contamination of drinking water. Although several analytical approaches have been applied to monitoring cyanobacteria toxins, conventional methods are costly and time-consuming so that analyses take weeks for field sampling and subsequent lab analysis. Capillary electrophoresis (CE) becomes a particularly suitable analytical separation method that can couple very small samples and rapid separations to a wide range of selective and sensitive detection techniques. This paper demonstrates a method for rapid separation and identification of four microcystin variants commonly found in aquatic environments. CE coupled to UV and electrospray ionization time-of-flight mass spectrometry (ESI-TOF) procedures were developed. All four analytes were separated within 6 minutes. The ESI-TOF experiment provides accurate molecular information, which further identifies analytes.

Terrigenous input and marine productivity for the Pacific sector of the Southern Ocean based on lipid biomarkers

In this study, we present a new multiproxy data set of terrigenous input, marine productivity and sea surface temperature (SST) from 52 surface sediment samples collected along E-W transects in the Pacific sector of the Southern Ocean. Allochtonous terrigenous input was characterized by the distribution of plant wax n-alkanes and soil-derived branched glycerol dialkyl glycerol tetraethers (brGDGTs). 230Th-normalized burial rates of both compound groups were highest close to the potential sources in Australia and New Zealand and are strongly related to lithogenic contents, indicating common sources and transport. Detection of both long-chain n-alkanes and brGDGTs at the most remote sites in the open ocean strongly suggests a primarily eolian transport mechanism to at least 110°W, i.e. by prevailing westerly winds. Two independent organic SST proxies were used, the UK'37 based on long-chain alkenones, and the TEX86 based on isoprenoid GDGTs. Both, UK'37 and TEX86 indices show robust relationships with temperature over a temperature range between 0.5 and 20°C, likely implying different seasonal and regional imprints on the temperature signal. While alkenone-based temperature estimates reliably reflect modern SST even at the low temperature end, large temperature residuals are observed for the polar ocean using the TEX86 index. 230Th-normalized burial rates of alkenones are highest close to the Subtropical Front and are positively related to lithogenic fluxes throughout the study area. In contrast, highest isoGDGT burial south of the Antarctic Polar Front is not related with dust flux but may be largely controlled by diatom blooms, and thus high opal fluxes during austral summer.

Dissolved Iron, Aluminium, and Dissolved Inorganic Phosphorus in the (Sub-)Tropical Atlantic Surface Ocean

Inorganic nitrogen depletion restricts productivity in much of the low-latitude oceans, generating a selective advantage for diazotrophic organisms capable of fixing atmospheric dinitrogen (N2). However, the abundance and activity of diazotrophs can in turn be controlled by the availability of other potentially limiting nutrients, including phosphorus (P) and iron (Fe). Here we present high-resolution data (~0.3°) for dissolved iron, aluminum, and inorganic phosphorus that confirm the existence of a sharp north-south biogeochemical boundary in the surface nutrient concentrations of the (sub)tropical Atlantic Ocean. Combining satellite-based precipitation data with results from a previous study, we here demonstrate that wet deposition in the region of the intertropical convergence zone acts as the major dissolved iron source to surface waters. Moreover, corresponding observations of N2 fixation and the distribution of diazotrophic Trichodesmium spp. indicate that movement in the region of elevated dissolved iron as a result of the seasonal migration of the intertropical convergence zone drives a shift in the latitudinal distribution of diazotrophy and corresponding dissolved inorganic phosphorus depletion. These conclusions are consistent with the results of an idealized numerical model of the system. The boundary between the distinct biogeochemical systems of the (sub)tropical Atlantic thus appears to be defined by the diazotrophic response to spatial-temporal variability in external Fe inputs. Consequently, in addition to demonstrating a unique seasonal cycle forced by atmospheric nutrient inputs, we suggest that the underlying biogeochemical mechanisms would likely characterize the response of oligotrophic systems to altered environmental forcing over longer timescales.

Communication-efficient decentralized sequential detection

The problem of decentralized sequential detection is studied in this thesis, where local sensors are memoryless, receive independent observations, and no feedback from the fusion center. In addition to traditional criteria of detection delay and error probability, we introduce a new constraint: the number of communications between local sensors and the fusion center. This metric is able to reflect both the cost of establishing communication links as well as overall energy consumption over time. A new formulation for communication-efficient decentralized sequential detection is proposed where the overall detection delay is minimized with constraints on both error probabilities and the communication cost. Two types of problems are investigated based on the communication-efficient formulation: decentralized hypothesis testing and decentralized change detection. In the former case, an asymptotically person-by-person optimum detection framework is developed, where the fusion center performs a sequential probability ratio test based on dependent observations. The proposed algorithm utilizes not only reported statistics from local sensors, but also the reporting times. The asymptotically relative efficiency of proposed algorithm with respect to the centralized strategy is expressed in closed form. When the probabilities of false alarm and missed detection are close to one another, a reduced-complexity algorithm is proposed based on a Poisson arrival approximation. In addition, decentralized change detection with a communication cost constraint is also investigated. A person-by-person optimum change detection algorithm is proposed, where transmissions of sensing reports are modeled as a Poisson process. The optimum threshold value is obtained through dynamic programming. An alternative method with a simpler fusion rule is also proposed, where the threshold values in the algorithm are determined by a combination of sequential detection analysis and constrained optimization. In both decentralized hypothesis testing and change detection problems, tradeoffs in parameter choices are investigated through Monte Carlo simulations.

From traditional resource to global commodities: a comparison of Rhodiola species using NMR spectroscopy - metabolomics and HPTLC

The fast developing international trade of products based on traditional knowledge and their value chains has become an important aspect of the ethnopharmacological debate. The structure and diversity of value chains and their impact on the phytochemical composition of herbal medicinal products has been overlooked in the debate about quality problems in transnational trade. Different government policies and regulations governing trade in herbal medicinal products impact on such value chains. Medicinal Rhodiola species, including Rhodiola rosea L. and Rhodiola crenulata (Hook.f. & Thomson) H.Ohba, have been used widely in Europe and Asia as traditional herbal medicines with numerous claims for their therapeutic effects. Faced with resource depletion and environment destruction, R. rosea and R. crenulata are becoming endangered, making them more economically valuable to collectors and middlemen, and also increasing the risk of adulteration and low quality. We compare the phytochemical differences among Rhodiola raw materials available on the market to provide a practical method for Rhodiola authentication and the detection of potential adulterant compounds. Samples were collected from Europe and Asia and nuclear magnetic resonance spectroscopy coupled with multivariate analysis software and high performance thin layer chromatography techniques were used to analyse the samples. A method was developed to quantify the amount of adulterant species contained within mixtures. We compared the phytochemical composition of collected Rhodiola samples to authenticated samples. Rosavin and rosarin were mainly present in R. rosea whereas crenulatin was only present in R. crenulata. 30% of the Rhodiola samples purchased from the Chinese market were adulterated by other Rhodiola spp. Moreover, 7 % of the raw-material samples were not labelled satifactorily. The utilisation of both 1H-NMR and HPTLC methods provided an integrated analysis of the phytochemical differences and novel identification method for R. rosea and R. crenulata. Using 1H-NMR spectroscopy it was possible to quantify the presence of R. crenulata in admixtures with R. rosea. This quantitative technique could be used in the future to assess a variety of herbal drugs and products. This project also highlights the need to further study the links between producers and consumers in national and trans-national trade.

Electrochemical RNA genosensors for toxic algal species: enhancing selectivity and sensitivity

Harmful algal blooms (HABs) are becoming more frequent as climate changes, with tropical species moving northward. Monitoring programs detecting the presence of toxic algae before they bloom are of paramount importance to protect aquatic ecosystems, aquaculture, human health and local economies. Rapid and reliable species identification methods using molecular barcodes coupled to biosensor detection tools have received increasing attention over the past decade as an alternative to the impractical standard microscopic counting-based techniques. This work reports on a PCR amplification-free electrochemical genosensor for the enhanced selective and sensitive detection of RNA from multiple Mediterranean toxic algal species. For a sandwich hybridization (SHA), we designed longer capture and signal probes for more specific target discrimination against a single base-pair mismatch from closely related species and for reproducible signals. We optimized experimental conditions, viz., minimal probe concentration in the SHA on a screen-printed gold electrode and selected the best electrochemical mediator. Probes from 13 Mediterranean dinoflagellate species were tested under optimized conditions and the format further tested for quantification of RNA from environmental samples. We not only enhanced the selectivity and sensitivity of the state-of-the-art toxic algal genosensors but also increased the repertoire of toxic algal biosensors in the Mediterranean, towards an integral and automatic monitoring system.

Electrochemical RNA genosensors for toxic algal species: enhancing selectivity and sensitivity

Harmful algal blooms (HABs) are becoming more frequent as climate changes, with tropical species moving northward. Monitoring programs detecting the presence of toxic algae before they bloom are of paramount importance to protect aquatic ecosystems, aquaculture, human health and local economies. Rapid and reliable species identification methods using molecular barcodes coupled to biosensor detection tools have received increasing attention over the past decade as an alternative to the impractical standard microscopic counting-based techniques. This work reports on a PCR amplification-free electrochemical genosensor for the enhanced selective and sensitive detection of RNA from multiple Mediterranean toxic algal species. For a sandwich hybridization (SHA), we designed longer capture and signal probes for more specific target discrimination against a single base-pair mismatch from closely related species and for reproducible signals. We optimized experimental conditions, viz., minimal probe concentration in the SHA on a screen-printed gold electrode and selected the best electrochemical mediator. Probes from 13 Mediterranean dinoflagellate species were tested under optimized conditions and the format further tested for quantification of RNA from environmental samples. We not only enhanced the selectivity and sensitivity of the state-of-the-art toxic algal genosensors but also increased the repertoire of toxic algal biosensors in the Mediterranean, towards an integral and automatic monitoring system.

Invisible Victims: Recorded Crime and Children in the UK

While violence against children is a common occurrence only a minority of incidents come to the attention of the authorities. Low reporting rates notwithstanding, official data such as child protection referrals and recorded crime statistics provide valuable information on the numbers of children experiencing harm which come to the attention of professionals in any given year. In the UK, there has been a strong tendency to focus on child protection statistics while children as victims of crime remain largely invisible in annual crime reports and associated compendia. This is despite the implementation of a raft of policies aimed at improving the system response to victims and witnesses of crime across the UK. This paper demonstrates the utility of a more detailed analysis of crime statistics in providing information on the patterns of crime against children and examining case outcomes. Based on data made available by the Police Service for Northern Ireland, it highlights how violent crime differentially impacts on older children and how detection rates vary depending on case characteristics. It makes an argument for developing recorded crime practice to make child victims of crime more visible and to facilitate assessment of the effectiveness of current initiatives and policy developments. Copyright © 2013 John Wiley & Sons, Ltd.

Achievable rates and outage probability of cognitive radio with dynamic frequency hopping under imperfect spectrum sensing

In this study, the authors propose simple methods to evaluate the achievable rates and outage probability of a cognitive radio (CR) link that takes into account the imperfectness of spectrum sensing. In the considered system, the CR transmitter and receiver correlatively sense and dynamically exploit the spectrum pool via dynamic frequency hopping. Under imperfect spectrum sensing, false-alarm and miss-detection occur which cause impulsive interference emerged from collisions due to the simultaneous spectrum access of primary and cognitive users. That makes it very challenging to evaluate the achievable rates. By first examining the static link where the channel is assumed to be constant over time, they show that the achievable rate using a Gaussian input can be calculated accurately through a simple series representation. In the second part of this study, they extend the calculation of the achievable rate to wireless fading environments. To take into account the effect of fading, they introduce a piece-wise linear curve fitting-based method to approximate the instantaneous achievable rate curve as a combination of linear segments. It is then demonstrated that the ergodic achievable rate in fast fading and the outage probability in slow fading can be calculated to achieve any given accuracy level.