In this paper I introduce some background for subtraction games and explore the Sprague-Grundy functions defined on them. I exhibit some subtraction games where the functions are guaranteed to be strictly periodic. I also exhibit a class of subtraction games which have bounded range, and show there are uncountably many of these.

This thesis is focused on understanding of addition and subtraction by pupils during maths lessons by Hejný. The aim of the thesis was fulfilled using analysis of pupil's solutions of some chosen exercises from publisher's Fraus textbooks. For the information survey, a combination of action and qualitative research methods. The research was carried out in the school year 2017/2018 at the primary school in the Prague - east district.

<p>Foreground segmentation is a common first step in tracking and surveillance applications.  The purpose of foreground segmentation is to provide later stages of image processing with an indication of where interesting data can be found.  This thesis is an investigation of how foreground segmentation can be performed in two contexts: as a pre-step to trajectory tracking and as a pre-step in indoor surveillance applications.</p><p>Three methods are selected and detailed: a single Gaussian method, a Gaussian mixture model method, and a codebook method.  Experiments are then performed on typical input video using the methods.  It is concluded that the Gaussian mixture model produces the output which yields the best trajectories when used as input to the trajectory tracker.  An extension is proposed to the Gaussian mixture model which reduces shadow, improving the performance of foreground segmentation in the surveillance context.</p>

Ground penetrating radar (GPR) is a promising technique for humanitarian demining applications as it permits providing useful information about the subsurface based on wave reflections produced by electromagnetic (EM) contrasts. Yet, landmine detection using GPR can suffer from: (1) clutter, i.e, undesirable effects from antenna coupling, system ringing and soil surface and subsurface reflections; (2) false alarms, e.g., reflections from buried mine-like objects such as stones or metallic debris; (3) effects of soil properties on the GPR performance, such as attenuation. This thesis addresses these topics in an integrated approach aiming at reducing clutter, identifying landmines from false alarms and analysing GPR performance. For subtracting undesirable reflections, a new physically-based filtering algorithm is developed, which takes into account major antenna effects and soil surface reflection. It is applied in conjunction with a change detection algorithm for enhancing landmine detection. Landmine identification is performed using discriminant characteristics extracted from the pre-filtered data by a novel feature extraction approach in the time-frequency domain. For analysing the effects of soil properties, in particular soil dielectric permittivity, an EM model is coupled to pedotransfer functions for estimating the GPR performance on a given soil. The developed algorithms are validated using data acquired by two different hand-held GPR systems. Promising results are obtained under laboratory and outdoor conditions, where different types of soil (including real mine-affected soils) and landmines (including improvised explosive devices) are considered.

Several factors contribute to the failure of the central nervous system (CNS) to regenerate after injury. These include inhibition of axonal growth by myelin and glial scar associated molecules, as well as the intrinsic inability of adult CNS neurons to grow long axons in environments that are permissive for younger neurons. Neurons in the peripheral nervous system (PNS) display a much higher capacity to regenerate after injury than CNS neurons, as shown by conditioning lesion experiments and by microtransplantation of dorsal root ganglia neurons into CNS white matter tracts. Our central hypothesis is that neurons of the PNS express specific regeneration associated genes that mediate their enhanced growth response after injury. We have employed a combination of subtractive hybridization, microarray comparison and promoter analysis to probe for genes specific to neurons of the dorsal root ganglia (DRG), using cerebellar granule neurons (CGN) as a reference. We have identified over a thousand different genes, many of whose products form interaction networks and signaling pathways. Moreover, we have identified several dozen transcription factors that may play a role in establishing DRG neuron identity and shape their responses after injury. One of these transcription factors is Signal Transducer and Activator of Transcription 3 (STAT3), previously known to be upregulated in the PNS after a conditioning lesion but not known to be specific to the PNS. Using a real time PCR and immunochemical approaches we have shown that STAT3 is constitutively expressed and selectively active in DRG neurons both in culture and in vivo. We show that the overexpression of wild type STAT3 in cerebellar granule neurons leads to the formation of supernumerary neurites, whereas the overexpression of constitutively active STAT3-C leads to a 20% increase in total neurite outgrowth. It is hoped that the genetic delivery of STAT3-C, potentially combined with co-activators of transcription, will improve functional regeneration of CNS axons in vivo.

Ground penetrating radar (GPR) is a promising technique for humanitarian demining applications as it permits providing useful information about the subsurface based on wave reflections produced by electromagnetic (EM) contrasts. Yet, landmine detection using GPR can suffer from: (1) clutter, i.e, undesirable effects from antenna coupling, system ringing and soil surface and subsurface reflections; (2) false alarms, e.g., reflections from buried mine-like objects such as stones or metallic debris; (3) effects of soil properties on the GPR performance, such as attenuation. This thesis addresses these topics in an integrated approach aiming at reducing clutter, identifying landmines from false alarms and analysing GPR performance. For subtracting undesirable reflections, a new physically-based filtering algorithm is developed, which takes into account major antenna effects and soil surface reflection. It is applied in conjunction with a change detection algorithm for enhancing landmine detection. Landmine identification is performed using discriminant characteristics extracted from the pre-filtered data by a novel feature extraction approach in the time-frequency domain. For analysing the effects of soil properties, in particular soil dielectric permittivity, an EM model is coupled to pedotransfer functions for estimating the GPR performance on a given soil. The developed algorithms are validated using data acquired by two different hand-held GPR systems. Promising results are obtained under laboratory and outdoor conditions, where different types of soil (including real mine-affected soils) and landmines (including improvised explosive devices) are considered.

Students with emotional and behavioral disorders (E/BD) display severe social and academic deficits that can adversely affect their academic performance in mathematics and result in higher rates of failure throughout their schooling compared to other students with disabilities (U.S. Department of Education, 2005; Webber & Plotts, 2008). Furthermore, students with E/BD are at a greater risk of being served in more exclusionary and restrictive settings compared to their peers as a result of their poor social skills and chronic disruptive behaviors (Gagnon & Leone, 2005; Furney, Hasazi, Clark-Keefe, & Hartnett, 2003; U.S. Department of Education, 2005; Whorton, Siders, Fowler, & Naylor, 2000). This is of great concern as students with E/BD often receive lower grades, fail more classes, have higher drop-out rates, have fewer employment opportunities, and have increased involvement in the legal system (Bullock & Gable, 2006; Cullinan & Sabornie, 2004; Jolivette, Stichter, Nelson, Scott, & Liaupsin, 2000; Kauffman, 2001). The purpose of this study was to analyze the effect of the equal additions algorithm on subtraction with regrouping on the subtraction performance of fourth-grade students with E/BD and mathematics difficulties. The equal additions algorithm was taught using a direct instruction technique. This study investigated 3 participants at the fourth grade level in a residential treatment facility which serves students with E/BD. A multiprobe multiple baseline across participants design was used for this study. Assessments used for this study included (a) Woodcock Johnson III (WJIII), (b) the ENRIGHT, (c) a student questionnaire, (d) baseline probes, and (e) an error analysis student profile. Data was analyzed by visual analysis. The results suggest that when the equal additions algorithm was systematically implemented students were able to successfully complete subtraction with regrouping problems and errors dramatically decreased. Limitations and future for research directions are discussed.

There has been a growth in demand for advancing algorithms in surveillance applications concerning moving vehicles where analysis of traffic has a potential application to security, traffic management (congestion and accident detection), speed measurement, car counting and statistics, as well as turning movement at intersections. This research focuses on multiple-vehicle detection, recognition, and tracking in urban environments based on video sequences obtained from a single CCD camera mounted on a pole at urban highways and crossroads. The proposed system integrates several modules including segmentation, object detection, object recognition and classification, and tracking. Background segmentation, based on Gaussian Mixture models, is used to extract moving objects from images using the respective foreground object information such as location, size, and color distribution. To recognize vehicles, a 3D polyhedral car model described by a set of parameters is built and mapped to the 2D edge information attained from the video sequence. The matching process is then used to classify the foreground object obtained into vehicles and non-vehicles. The output from the recognition model is used in tracking multiple cars based on a deterministic data association method that takes place between consecutive frame information. The multiple-vehicle surveillance system developed in this thesis, based on integrating different modules, provides a novel approach for vehicle monitoring. Furthermore, the system makes use of minimal a priori knowledge about vehicle location, size, type, numbers, and pathways. The system implemented in this work functions well under various camera perspectives, background clutter, vehicle viewpoints, road types, scale changes, image noise, image resolutions, and lighting conditions.

There has been a growth in demand for advancing algorithms in surveillance applications concerning moving vehicles where analysis of traffic has a potential application to security, traffic management (congestion and accident detection), speed measurement, car counting and statistics, as well as turning movement at intersections. This research focuses on multiple-vehicle detection, recognition, and tracking in urban environments based on video sequences obtained from a single CCD camera mounted on a pole at urban highways and crossroads. The proposed system integrates several modules including segmentation, object detection, object recognition and classification, and tracking. Background segmentation, based on Gaussian Mixture models, is used to extract moving objects from images using the respective foreground object information such as location, size, and color distribution. To recognize vehicles, a 3D polyhedral car model described by a set of parameters is built and mapped to the 2D edge information attained from the video sequence. The matching process is then used to classify the foreground object obtained into vehicles and non-vehicles. The output from the recognition model is used in tracking multiple cars based on a deterministic data association method that takes place between consecutive frame information. The multiple-vehicle surveillance system developed in this thesis, based on integrating different modules, provides a novel approach for vehicle monitoring. Furthermore, the system makes use of minimal a priori knowledge about vehicle location, size, type, numbers, and pathways. The system implemented in this work functions well under various camera perspectives, background clutter, vehicle viewpoints, road types, scale changes, image noise, image resolutions, and lighting conditions.

Syftet med denna studie var att undersöka elevers användning av lösningsstrategier i subtraktion samt lärares och läromedlens framställning av dessa, för att kunna komma fram till hur en framgångsrik undervisning i subtraktion, med fokus på lösningsstrategier, kan se ut. Undersökningen genomfördes i tre klasser i åk 3. Metoder i studien var elevenkät, intervju med lärare och läromedelsgranskning. Data bearbetades med hjälp av en egenkonstruerad begreppsmodell utifrån olika lösningsstrategier. Resultatet visar på en större variation av lösningsstrategier i undervisningen än i elevernas uträkningar. Eleverna använder sig oftast av enbart en av lösningsstrategierna, så kallad ”talsortsvis beräkning”. Strategin leder till många fel i elevernas uträkningar. / The purpose of this study was to investigate how pupils use solution strategies for subtraction, and how those are presented by teachers and textbooks in order to find out how successful teaching in subtraction, with focus on solution strategies, might look. The study was carried out on three groups in the 3rd grade. The methods of this study consisted of a pupil survey, interviews with teachers and a review of textbooks. The data were processed using a self-constructed conceptual model based on different solution strategies. The results indicate a larger variation of solution strategies in the teaching than in the pupils´ calculations. The pupils typically use only one of the solution strategies, a so-called "number-splitting calculation". This strategy leads to many errors in the pupils' calculations.