Bad News for Chordal Partitions

Reed and Seymour [1998] asked whether every graph has a partition into induced connected non-empty bipartite subgraphs such that the quotient graph is chordal. If true, this would have significant ramifications for Hadwiger's Conjecture. We prove that the answer is `no'. In fact, we show that the answer is still `no' for several relaxations of the question

Regulation and design of taxicab markets

This dissertation examines metropolitan areas subject to exclusive cruising regulations which prevent taxis affiliated with one city from picking up passengers in other neighboring cities. It examines the regulatory structure that evolved in North America, compares exclusive cruising regulation to a combined regulatory regime, and proposes a market-based mechanism to improve upon existing regulations. The first chapter examines the evolution of regulation of the taxicab industry in different metropolitan areas in North America. It provides an explanation for the prevalence of price and quantity regulations at the local level, and why the industry remains heavily regulated despite numerous attempts at deregulation. The second chapter theoretically investigates the efficiency of exclusive cruising regulation when there are multiple exclusive cruising locations in close proximity. Conventional wisdom suggests it is better to operate a combined regulatory regime, thereby eliminating the empty return trips that occur under exclusive cruising regulation. Under combined regulation, however, drivers have an incentive to be in the location with the highest expected revenue. It is shown that this can undermine regulators' control over the allocation of taxis across disparate locations, outweighing losses from empty return trips. In such situations exclusive cruising regulation would be preferred to combined regulation. When locations are sufficiently similar, it is shown that combined regulation will be preferred to exclusive cruising. The third chapter proposes a regulatory exchange market as an alternative to existing regulatory structures. The proposed mechanism maintains separate affiliations, but allows taxi drivers to exchange the right to pick up passengers in each others' affiliated location by participating in a bilateral market. In this market, taxis can exchange the right to pick up passengers in each others' affiliated locations, for a price paid by market participants affiliated with one location to those affiliated with the other location. It is shown that such an exchange market can be designed to achieve superior outcomes to both exclusive cruising regulation and combined regulation modes. We describe situations where the regulatory exchange market cannot be dominated by any other conceivable regulatory mechanism

Clustered Colouring in Minor-Closed Classes

The "clustered chromatic number" of a class of graphs is the minimum integer $k$ such that for some integer $c$ every graph in the class is $k$-colourable with monochromatic components of size at most $c$. We prove that for every graph $H$, the clustered chromatic number of the class of $H$-minor-free graphs is tied to the tree-depth of $H$. In particular, if $H$ is connected with tree-depth $t$ then every $H$-minor-free graph is $(2^{t+1}-4)$-colourable with monochromatic components of size at most $c(H)$. This provides the first evidence for a conjecture of Ossona de Mendez, Oum and Wood (2016) about defective colouring of $H$-minor-free graphs. If $t=3$ then we prove that 4 colours suffice, which is best possible. We also determine those minor-closed graph classes with clustered chromatic number 2. Finally, we develop a conjecture for the clustered chromatic number of an arbitrary minor-closed class

Critical theories of antisemitism

Distinguishing between different ways of thinking about antisemitism, this study concentrates on those theories that understand antisemitism as a uniquely modern phenomenon. Covering the period from the mid-19th century to the present day, it first examines the work of Marx and Nietzsche and then moves on to those theorists who wrote in the immediate aftermath of the holocaust and concludes with the postmodern writings of Bauman and Lyotard. It argues that these critical theories of antisemitism all relate the emergence of antisemitism to modern forms of political emancipation and questions the impact of the holocaust upon this body of thought. The study argues that the fluidity and open-endedness by which the early writers characterise modernity - most notably the ambivalence within modernity itself between the possibility of full emancipation and barbarity - comes to be replaced by an increasing pessimism that sees antisemitism as modernity's only possible outcome. It argues that this change is accompanied first by increasing the centrality of antisemitism to modernity, and also by defining more rigidly the concepts by which antisemitism is explained, most noticeably, the concept of "the Jews". This study argues that as a result of these interrelated developments, critical theories replicate many of the assumptions of the antisemitic worldview identified in the early works. By calling for a cautious and critical return to these earlier ways of explaining antisemitism, the study concludes by pointing to an approach that remains within the tradition of critical theory, but which re-establishes the critical distance between ways of accounting for antisemitism and the phenomenon itself - one in which the "Jewish question" is de-centred, the explanatory concepts reopened to question and the promise of emancipation reinvigorated

Functional characterisation of a predicted chloroplastic plant protein phosphatase

The phosphatase AtPTPKISI is involved in the control of starch metabolism in Arabidopsis thaliana leaves at night. The SEX4 (Starch Excess 4) mutants, lacking this predicted phosphatase, have strongly reduced rates of starch metabolism. It is shown that this chloroplastic protein can bind to glucans through a carbohydrate binding domain (CBM) located within its previously predicted kinase interaction sequence (KIS), while another novel KIS containing protein (AKINβy) shows no such interaction. Further analysis of the CBM identifies conserved residues vital for carbohydrate binding and common to CBMs, as well as sugar tongs, not present in similar CBMs or the GBD/KIS domain of the previously studies AMPKβ, but found within the binding domain of the PTPKIS family proteins. While PTPKIS 1 shows activity to generic phosphatase substrates, it is unable to dephosphorylate either phosphotyrosine or phosphothreonine containing peptides. It does however show phosphatase activity towards phosphorylated starch and amylopectin, comparable to that of the mammalian protein laforin. Remarkably, the most closely related protein to PTPKIS 1 outside the plant kingdom is laforin, required for the metabolism of the mammalian storage carbohydrate glycogen and implicated in a severe form of epilepsy (Lafora disease) in humans, through the formation of insoluble starch like polyglucans (lafora bodies). In addition to PTPKIS 1, PTPKIS 2 (At3g015180) is identified, a predicted phosphatase, with a domain structure homologous to that of PTPKIS 1, termed. The PTPKIS2-SALK (PTPKIS2 knockout) mutant, lacking this predicted phosphatase, has a reduced rate of starch metabolism. It is shown that this mutant causes a phenotype similar to SEX4, but less extreme. It is further shown that this protein can bind to glucans through a carbohydrate binding domain (CBM), but unlike PTPKIS 1 shows no activity towards any phosphate substrates. PTPKIS2 does however modulate the activity of PTPKIS 1, causing a 4-fold increase in the activity of PTPKIS 1 against phosphorylated starch, when both enzymes are present in equimolar concentrations. Finally, a hypothesis is proposed as to the roles of PTPKIS 1 and PTPKIS 2 in starch metabolism, and the similarity of function seen in the mammalian protein Laforin

The multiple roles of A-type lamins in cellular aging, cell cycle progression and the DNA damage response.

A-type lamins are a group of type V intermediate filaments whose main members are lamin A and C. Lamins A/C are components of the nuclear lamina and are encoded by the LMNA gene. Lamins A/C have a variety of cellular functions, including maintaining the structural integrity of the nucleus and the regulation of signal transduction pathways, transcription factors and DNA replication. Mutations in LMNA give rise to a diverse spectrum of diseases, termed laminopathies, which include premature aging syndromes. In Chapter 3, I sought to understand the role of wild type lamin A in normal cellular aging. Lamin A C-terminal cysteine residues were irreversibly oxidized during the in vitro aging of human dermal fibroblasts (HDFs), which impaired the ability of lamin A to form disulfide bonds, causing loss of function. Furthermore, loss of these cysteine residues induced premature senescence, suggesting that these cysteine residues are important for lamin A function during cellular aging. In Chapter 4, I extended previous findings implicating A-type lamins in the control of cell cycle progression. Loss of A-type lamins or its nucleoplasmic binding partner, LAP2α, caused delayed G1/S-phase progression, reduced cellular proliferation and cell cycle exit. Proliferative defects could not be rescued via treatment with anti-oxidants. In Chapters 5 and 6, I addressed the role of wild type mature lamin A/C in the DNA damage response (DDR). A-type lamins interact with the DDR mediator protein 53BP1 via its Tudor domain. Loss of LMNA caused endogenous DNA damage and loss of 53BP1 protein levels. Furthermore, loss of LMNA resulted in defective DNA repair that ultimately led to increased sensitivity to DNA damage. Together, the data presented here extends previous findings implicating A-type lamins in cell cycle progression and provides novel insights into the cellular roles of A-type lamins in cellular aging and the DNA damage response

Alternative Conceptions of Poverty and their Implications for Income Maintenance

This paper speaks to the problem of designing income maintenance programs from the perspective of sociological theory. First, the underlying logic of situational and cultural theories of poverty is delineated, and some of their general implications are explored. Afterwards, the predictions of these theories with respect to the response by poor persons to an income maintenance program are examined. It is argued that, in place of seeking whether one or the other type of explanation is valid in general, we ascertain for which groups in poverty and for what types of response a particular theory is likely to be more useful. The discussion is illustrated by a consideration of how an individual's response to income maintenance is likely to vary with ethnicity and neighborhood organization

This is the Piece that Everyone Here Has Come to Experience: The Challenges to Copyright of John Cage’s 4’33”

Framed within the broader context of law's engagement with modernism, this paper offers an argument in defence of copyright protection of John Cage's 4′33″ as a ‘musical work’ under the Copyright, Designs and Patents Act 1988. This argument approaches the issues involved analytically and contextually. In doing so, it draws on both legal and non-legal sources. Throughout the paper, the underlying question remains as to whether Cage's 4′33″ really is – or is not – a challenge to law (and to music)