Graph Algorithms and Complexity Aspects on Special Graph Classes

Graphs are a very flexible tool within mathematics, as such, numerous problems can be solved by formulating them as an instance of a graph. As a result, however, some of the structures found in real world problems may be lost in a more general graph. An example of this is the 4-Colouring problem which, as a graph problem, is NP-complete. However, when a map is converted into a graph, we observe that this graph has structural properties, namely being (K_5, K_{3,3})-minor-free which can be exploited and as such there exist algorithms which can find 4-colourings of maps in polynomial time. This thesis looks at problems which are NP-complete in general and determines the complexity of the problem when various restrictions are placed on the input, both for the purpose of finding tractable solutions for inputs which have certain structures, and to increase our understanding of the point at which a problem becomes NP-complete. This thesis looks at four problems over four chapters, the first being Parallel Knock-Out. This chapter will show that Parallel Knock-Out can be solved in O(n+m) time on P_4-free graphs, also known as cographs, however, remains hard on split graphs, a subclass of P_5-free graphs. From this a dichotomy is shown on $P_k$-free graphs for any fixed integer $k$. The second chapter looks at Minimal Disconnected Cut. Along with some smaller results, the main result in this chapter is another dichotomy theorem which states that Minimal Disconnected Cut is polynomial time solvable for 3-connected planar graphs but NP-hard for 2-connected planar graphs. The third chapter looks at Square Root. Whilst a number of results were found, the work in this thesis focuses on the Square Root problem when restricted to some classes of graphs with low clique number. The final chapter looks at Surjective H-Colouring. This chapter shows that Surjective H-Colouring is NP-complete, for any fixed, non-loop connected graph H with two reflexive vertices and for any fixed graph H’ which can be obtained from H by replacing vertices with true twins. This result enabled us to determine the complexity of Surjective H-Colouring on all fixed graphs H of size at most 4

Fiber-Based Laser Transmitter at 1.57 Micrometers for Remote Sensing of Atmospheric Carbon Dioxide from Satellites

Over the past 20 years, NASA Goddard has successfully developed space-based lidar for remote sensing studies of the Earth and planets. The lidar in all missions to date have used diode pumped Nd:YAG laser transmitters. Recently we have been concentrating work on developing integrated path differential absorption (IPDA) lidar to measure greenhouse gases, with the goal of measurements from space. Due to the absorption spectrum of CO2 a fiber-based master oscillator power amplifier (MOPA) laser with a tunable seed source is an attractive laser choice. Fiber-based lasers offer a number of potential advantages for space, but since they are relatively new, challenges exist in developing them. In order to reduce risks for new missions using fiber-based lasers, we developed a 30- month plan to mature the technology of a candidate laser transmitter for space-based CO2 measurements to TRL-6. This work is also intended to reduce development time and costs and increase confidence in future mission success

Psychopathology and affect dysregulation across the continuum of psychosis: A multiple comparison group study

This is the peer reviewed version of the following article: Taylor, H. E., Stewart, S. L. K., Dunn, G., Parker, S., Bentall, R. P., Birchwood, M., & Morrison, A. P. (2014). Psychopathology and affect dysregulation across the continuum of psychosis: A multiple group comparison study. Early Intervention in Psychiatry, 8(3), 221-228. DOI: 10.1111/eip.12064, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/eip.12064/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-ArchivingAim: There is evidence that psychotic-like phenomena can be detected within the general population and that psychotic experiences lie on a continuum which also spans affective states. We aimed to investigate comparisons of a first episode psychosis group, an ‘at-risk mental state group’ and a help-seeking control group with non-patients to explore whether affective states lie on a continuum of psychosis. Method: Measures of psychotic-like experiences, social anxiety and depression were administered to 20 patients experiencing first episode psychosis (FEP), 113 patients experiencing an ‘at-risk’ mental state (ARMS), 28 patients who were help-seeking but not experiencing a FEP or ARMS (HSC) and 30 non-clinical participants (NC). Results: For distress in relation to psychotic-like experiences, the FEP, ARMS and HSC groups scored significantly higher than the NC group for the perceptual abnormalities and non-bizarre ideas. In terms of severity of psychotic experiences, the FEP scored the highest, followed by the ARMS group, followed by the HSC and NC group. The clinical groups scored significantly higher for depression than the non-clinical group. Interestingly, only the FEP and the ARMS group scored significantly higher than non-patients for social anxiety. Conclusions: These findings suggest that a psychosis continuum exists, however this does not suggest that both psychosis and affective symptoms lie on the same continuum, rather it would appear that the presence of such affective states that may affect help-seeking behavior and clinical status. The implications of these findings for clinical practice are discussed

Early detection and intervention evaluation for people at risk of psychosis: multisite randomised controlled trial

Objective To determine whether cognitive therapy is effective in preventing the worsening of emerging psychotic symptoms experienced by help seeking young people deemed to be at risk for serious conditions such as schizophrenia

Fiber-Based Laser MOPA Transmitter Packaging for Space Environment

NASAs Goddard Space Flight Center has been developing lidar to remotely measure CO2 and CH4 in the Earths atmosphere. The ultimate goal is to make space-based satellite measurements with global coverage. We are working on maturing the technology readiness of a fiber-based, 1.57-micron wavelength laser transmitter designed for use in atmospheric CO2 remote-sensing. To this end, we are building a ruggedized prototype to demonstrate the required power and performance and survive the required environment. We are building a fiber-based master oscillator power amplifier (MOPA) laser transmitter architecture. The laser is a wavelength-locked, single frequency, externally modulated DBR operating at 1.57-micron followed by erbium-doped fiber amplifiers. The last amplifier stage is a polarization-maintaining, very-large-mode-area fiber with ~1000 m2 effective area pumped by a Raman fiber laser. The optical output is single-frequency, one microsecond pulses with >450 J pulse energy, 7.5 KHz repetition rate, single spatial mode, and > 20 dB polarization extinction

Fiber-Based Laser Transmitter Technology Maturation for Spectroscopic Measurements from Space

NASA's Goddard Space Flight Center has been developing lidar to remotely measure CO2 in the Earth's atmosphere. We have advanced the tunable laser technology to enable high-fidelity measurements from space. In this paper, we will report on the progress of fiber-based, 1.57-micron wavelength, laser transmitter that has demonstrated the optical performance required for a low earth orbiting instrument. The laser transmitter has been packaged and is undergoing environmental testing to demonstrate its technology readiness for space

Restoring Pre-Industrial CO\u3csub\u3e2\u3c/sub\u3e Levels While Achieving Sustainable Development Goals

© 2020 by the authors. Unless humanity achieves United Nations Sustainable Development Goals (SDGs) by 2030 and restores the relatively stable climate of pre-industrial CO2 levels (as early as 2140), species extinctions, starvation, drought/floods, and violence will exacerbate mass migrations. This paper presents conceptual designs and techno-economic analyses to calculate sustainable limits for growing high-protein seafood and macroalgae-for-biofuel. We review the availability of wet solid waste and outline the mass balance of carbon and plant nutrients passing through a hydrothermal liquefaction process. The paper reviews the availability of dry solid waste and dry biomass for bioenergy with CO2 capture and storage (BECCS) while generating Allam Cycle electricity. Sufficient wet-waste biomass supports quickly building hydrothermal liquefaction facilities. Macroalgae-for-biofuel technology can be developed and straightforwardly implemented on SDG-achieving high protein seafood infrastructure. The analyses indicate a potential for (1) 0.5 billion tonnes/yr of seafood; (2) 20 million barrels/day of biofuel from solid waste; (3) more biocrude oil from macroalgae than current fossil oil; and (4) sequestration of 28 to 38 billion tonnes/yr of bio-CO2. Carbon dioxide removal (CDR) costs are between 25–33% of those for BECCS with pre-2019 technology or the projected cost of air-capture CDR

Core Schemas across the Continuum of Psychosis: A Comparison of Clinical and Non-Clinical Groups

This article has been accepted for publication and will appear in a revised form, subsequent to peer review and/or editorial input by Cambridge University Press, in Behavioural and Cognitive Psychotherapy published by Cambridge University Press. Copyright BABCP.Background: Research suggests that core schemas are important in both the development and maintenance of psychosis. Aims: The aim of the study was to investigate and compare core schemas in four groups along the continuum of psychosis and examine the relationships between schemas and positive psychotic symptomatology. Method: A measure of core schemas was distributed to 20 individuals experiencing first-episode psychosis (FEP), 113 individuals with “at risk mental states” (ARMS), 28 participants forming a help-seeking clinical group (HSC), and 30 non-help-seeking individuals who endorse some psychotic-like experiences (NH). Results: The clinical groups scored significantly higher than the NH group for negative beliefs about self and about others. No significant effects of group on positive beliefs about others were found. For positive beliefs about the self, the NH group scored significantly higher than the clinical groups. Furthermore, negative beliefs about self and others were related to positive psychotic symptomatology and to distress related to those experiences. Conclusions: Negative evaluations of the self and others appear to be characteristic of the appraisals of people seeking help for psychosis and psychosis-like experiences. The results support the literature that suggests that self-esteem should be a target for intervention. Future research would benefit from including comparison groups of people experiencing chronic psychosis and people who do not have any psychotic-like experiences