Equitable Labelings of Caterpillar Graphs

The Graceful Tree Conjecture in graph theory has been open for almost half a century. The conjecture states that the vertices of any tree can be labeled with distinct integers between 0 and the number of edges of the tree in a way that the edges can be uniquely identified by the absolute value of the difference between their vertex labels. One possible approach to prove the conjecture is to prove the more general k-equitable tree conjecture. In a k-equitable labeling we assign integers from the set {0,1,2,…,k-1} to the vertices. Each edge will receive a label that is the absolute value of the difference of its vertex labels. We want to distribute the labels as equally as possible both for the edges and for the vertices. The conjecture states that this kind of labeling is possible for every tree and every k. This conjecture is equivalent to the graceful tree conjecture when k is the number of vertices of the tree. It has already been proven that every tree is 2-equitable and 3-equitable. We attempt to show a part of the k-equitable tree conjecture by choosing a large collection of trees called caterpillars, and examining different values of k

ROCK signalling induced gene expression changes in mouse pancreatic ductal adenocarcinoma cells

The RhoA and RhoC GTPases act via the ROCK1 and ROCK2 kinases to promote actomyosin contraction, resulting in directly induced changes in cytoskeleton structures and altered gene transcription via several possible indirect routes. Elevated activation of the Rho/ROCK pathway has been reported in several diseases and pathological conditions, including disorders of the central nervous system, cardiovascular dysfunctions and cancer. To determine how increased ROCK signalling affected gene expression in pancreatic ductal adenocarcinoma (PDAC) cells, we transduced mouse PDAC cell lines with retroviral constructs encoding fusion proteins that enable conditional activation of ROCK1 or ROCK2, and subsequently performed RNA sequencing (RNA-Seq) using the Illumina NextSeq 500 platform. We describe how gene expression datasets were generated and validated by comparing data obtained by RNA-Seq with RT-qPCR results. Activation of ROCK1 or ROCK2 signalling induced significant changes in gene expression that could be used to determine how actomyosin contractility influences gene transcription in pancreatic cancer

The Collateral Source Rule: Double Recovery and Indifference to Societal Interests in the Law of Tort Damages

This comment analyzes the present utility of the collateral source rule and finds the rule unjustified as a means of ensuring either punishment of the defendant or just compensation for the plaintiff. It further examines the efficacy of subrogation in eliminating the collateral source rule\u27s vice of double recovery. The comment concludes that legislative reform abolishing the collateral source rule and subrogation in medical malpractice suits should extend to all tort actions for personal injury, thereby entirely eliminating double recovery and the consequent higher societal costs in insurance premiums, taxes, and prices

Norwegians, Socialism and the Nonpartisan League in North Dakota, 1904-1920: How Red was their Protest?

Although its history has been largely ignored by scholars, North Dakota’s radical period, the socialist and Nonpartisan League years between 1904 and 1920, has been the exception. To explain the success of these left-wing movements, scholars have developed a number of theories. One of the most popular theories attributes the success of leftist political movements to the large number of Norwegians who resided in the state. According to this interpretation, Norwegian immigrants brought socialism and radicalism from Norway and transplanted it to the New World. Norwegians in North Dakota, this theory explains, were particularly radical and they became the vanguard of the protest movement during the early decades of the twentieth century. Although this interpretation has become the orthodox one among many scholars of North Dakota history, the hard evidence necessary to support this claim has been lacking. Therefore, the purpose of this thesis is to test the left of center interpretation for Norwegians in North Dakota. Using extensive voting analyses of both Norwegian and North Dakota elections, this thesis tests whether first, Norwegian immigrants acquired political leftism in Norway and second, whether they voted uniformly leftist in North Dakota. This thesis concludes that Norwegians naither brought leftism with them from Norway nor were they particularly radical in North Dakota. Instead, this thesis concludes that Norwegians tended to vote like other North Dakotans. This political behavior marked Norwegians in North Dakota as moderately conservative and not left of center

Somatotopic Organization Of The Mammalian Pain System And Developmental Mechanisms

Commonly, different regions of sensory maps are used to meet separate functional requirements. For the somatosensory system (which mediates sensation from the skin including touch, pain, and related modalities), the distal limbs have special behavioral importance for exploration and object manipulation. Accordingly, the hands and fingertips show heightened sensitivity for both touch and pain sensation in human subjects. In contrast to the touch system, the neural mechanisms for region-specific pain sensation are poorly understood. Despite over a century of research into the neural basis of pain, past work has not clearly defined the functional organization of the pain system across the body (somatotopic) map. In Chapter 2, we use a novel genetic mouse line to map the organization of one major class of mammalian pain-sensory neurons (the Mrgprd+ non-peptidergic nociceptors) across the body map. While we find no obvious peripheral mechanisms for high sensitivity in the distal limbs (mouse plantar paw skin has a low density of Mrgprd+ terminals, and single-cell arbor areas are comparable between paw and trunk skin), we reveal a novel region-specific organization in the spinal cord terminal arbors of these neurons. Specifically, paw and trunk neurons grow ‘round’ and ‘long’ arbor morphologies, respectively, such that paw neurons have a wider mediolateral spread in the spinal cord. We show that this region-specific morphology closely correlates with increased signal transmission for paw pain circuits. We conclude that region-specific organization of Mrgprd+ spinal cord terminals provides a possible mechanism for the high pain sensitivity of the distal limbs. In Chapter 3, we investigate potential developmental mechanisms for region-specific arbor morphologies. Disruption of peripheral target innervation does not alter their central arbor morphologies, suggesting that this central somatotopic difference develops independent of cues/processes from the periphery. However, this difference is present from very early developmental stages, suggesting that pre-programming mechanisms might govern this somatotopic pattern. Collectively, this work reveals that region-specific organization is a fundamental principle for the pain system with clear implications for our understanding of pain in both normal and pathological conditions

The Collateral Source Rule: Double Recovery and Indifference to Societal Interests in the Law of Tort Damages

This comment analyzes the present utility of the collateral source rule and finds the rule unjustified as a means of ensuring either punishment of the defendant or just compensation for the plaintiff. It further examines the efficacy of subrogation in eliminating the collateral source rule\u27s vice of double recovery. The comment concludes that legislative reform abolishing the collateral source rule and subrogation in medical malpractice suits should extend to all tort actions for personal injury, thereby entirely eliminating double recovery and the consequent higher societal costs in insurance premiums, taxes, and prices

Reliability of the Minnesota vocational interest inventory with hospitalized mental patients.

Thesis (M.S.