Arithmetic progressions of cycles in outer-planar graphs

AbstractA question of Erdős asks if every graph with minimum degree 3 must contain a pair of cycles whose lengths differ by 1 or 2. Some recent work of Häggkvist and Scott (see Arithmetic progressions of cycles in graphs, preprint), whilst proving this, also shows that minimum degree 500k2 guarantees the existence of cycles whose lengths are m,m+2,m+4,…,m+2k for some m—an arithmetic progression of cycles. In like vein, we prove that an outer-planar graph of order n, with bounded internal face size, and outer face a cycle, must contain a sequence of cycles whose lengths form an arithmetic progression of length exp((clogn)1/3−loglogn). Using this we give an answer for outer-planar graphs to a question of Erdős concerning the number of different sets which can be achieved as cycle spectra

Financial Analysis of Implementing an Anaerobic Digester and Free Stall Barn System on a Mississippi Dairy Farm

The installation of an anaerobic digestion system and a free stall barn on a Mississippi dairy farm is only feasible with the presence of a cost-share plan. A 60% cost-share plan is the minimum amount of support a farmer must receive in order to install both facilities.Anaerobic digester, Dairy farm, Cost-share plan, Farm Management,

The role of the systemic inflammatory response, the JAK STAT pathway and the MAPK pathway in the prognosis of resectable pancreatic cancer

Pancreatic cancer is a devastating disease with a five year survival of only 2-3%. Only 10-15% of patients have resectable disease at presentation and the only potential cure is major surgery with adjuvant chemotherapy. The outcomes of surgery are disappointing with a median survival of only15-17 months and operative mortality and morbidity figures of 5-10% and 40% respectively. This abysmal prognosis is likely due to the highly aggressive nature of the tumour, its resistance to adjuvant therapy, its late presentation and the likely presence of micro-metastases not detectable at staging or surgery. A pre-operative systemic inflammatory response (as measured by CRP) is known to be associated with a poor prognosis in a number of cancers including pancreatic cancer. The reasons behind this poor prognosis are not yet known. The main driver of plasma CRP levels is the cytokine IL-6, known to be elevated in the plasma of patients with pancreatic cancer. This thesis hypothesises that upregulation of two IL-6-dependent pathways, the JAK STAT and MAPK pathways is responsible for the poor prognosis associated with an inflammatory response in pancreatic cancer. Both of these pathways are known to be involved in cellular growth, differentiation and apoptosis and when activated they may confer a growth or survival advantage to tumour cells. The aims of this thesis were to establish the prognostic role of a systemic inflammatory response in resectable pancreatic cancer in both a retrospective and prospective cohort and establish whether increased protein expression in either the JAK STAT or MAPK pathways is associated with a poor prognosis in the same retrospective cohort. A retrospective database of 148 patients who had undergone Whipple resection for either pancreatic cancer (PC) or non-pancreatic peri-ampullary cancer (NPPC) was created with pre-operative CRP values and survival data. The author then created tissue micro-arrays (TMA’s) with both tumour and normal pancreatic duct tissue from each of the 148 patients in the retrospective cohort and carried out immunohistochemistry on 12 antibodies known to be crucial in IL-6 signalling (6 in the JAK STAT and 6 in the MAPK pathways). Following staining the author scored each of the antibodies using the weighted histoscore to allow analysis of antigen expression. During the period of research the author also created a prospective database of 36 patients who underwent surgery for either PC or NPPC. Plasma was stored pre-operatively from each of the patients and this was later thawed and using an ELISA kit another research fellow (JL) was able to establish plasma levels of IL-6 in the prospective cohort. On univariate analysis a raised pre-operative CRP was associated with poorer survival, 374 days versus 618 days (p=0.0001) in the retrospective PC group only. On multivariate analysis, only pre-operative CRP retained statistical significance amongst those factors shown to be significant on univariate analysis (P=0.009). In the prospective group, patients with low levels of IL-6 had a median survival of 799 days, against a median survival of 537 days in those with high plasma IL-6 levels (P=0.002) when all 36 patients were analysed together. On analysis of protein expression, no significant relationship between increased expression and poor survival was seen for any of the 12 proteins analysed. The results from this thesis confirm that a pre-operative inflammatory response is associated with poor survival in patients with resectable pancreatic cancer. Raised plasma levels of IL-6 are also associated with poorer survival in similar patients. However, the poor prognosis appears to be via a JAK STAT/ MAPK independent mechanism. Other possible explanations for this poor prognosis including the connection between inflammation and cachexia and other important inflammatory proteins such as NF-κB and SOCS are explored in the discussion of this thesis

A Generalization of a Theorem of Dirac

AbstractIn this paper, we give a generalization of a well-known result of Dirac that given any k vertices in a k-connected graph where k⩾2, there is a circuit containing all of them. We also generalize a result of Häggkvist and Thomassen. Our main result partially answers an open matroid question of Oxley

Completing some Partial Latin Squares

AbstractWe show that any partial 3 r× 3 r Latin square whose filled cells lie in two disjoint r×r sub-squares can be completed. We do this by proving the more general result that any partial 3 r by 3 r Latin square, with filled cells in the top left 2r× 2 r square, for which there is a pairing of the columns so that in each row there is a filled cell in at most one of each matched pair of columns, can be completed if and only if there is some way to fill the cells of the top left 2 r× 2 r square

I heard it through the grapevine : A Randomized Controlled Trial on the Direct and Vicarious Effects of Preventative Specific Deterrence Initiatives in Criminal Networks

A rich body of literature exists on deterrence, yet little is known about how deterrence messages are communicated through social networks. This is an important gap in our understanding, because such communication gives rise to the possibility that social institutions can utilize the vicarious effect of the threat of punishment against one individual to reduce the rate of reoffending amongst their criminal associates. To test this, we identified criminals with an extensive offending history (prolific offenders) and their co-offenders using social network analysis and then conducted a randomized controlled trial to measure the effect on both prolific offenders and their cooffenders of delivering a “specific deterrence” message. The treatment— preemptive engagements with prolific offenders by a police officer offering both ‘carrots’ (desistance pathways) and ‘sticks’ (increased sanction threat)—was applied to the prolific offenders, but not to their co-offenders. The outcomes suggest that a single officer–offender engagement leads to a crime suppression effect in all comparisons, with 21.3%, 11.0%, and 15.0% reductions for specific, vicarious, and total network deterrence effects, respectively. The findings suggest that (a) social network analysis based on in-house police records can be used to cartographically understand social networks of offenders, with an aim of preventing crime; (b) deterrence messages promulgated by the police have the capacity to reduce crime beyond what was previously assumed, as the cascading of threats in cooffending relationships carries a vicarious crime reduction impact; (c) unlike “reactive specific deterrence” (i.e., a threat of punishment following a specific and detected crime) which can have perverse effects on certain offenders, preventative specific deterrence is a promising crime policy

"I heard it through the grapevine": A Randomized Controlled Trial on the Direct and Vicarious Effects of Preventative Specific Deterrence Initiatives in Criminal Networks

A rich body of literature exists on deterrence, yet little is known about how deterrence messages are communicated through social networks. This is an important gap in our understanding, because such communication gives rise to the possibility that social institutions can utilize the vicarious effect of the threat of punishment against one individual to reduce the rate of reoffending amongst their criminal associates. To test this, we identified criminals with an extensive offending history (“prolific offenders”) and their co-offenders using social network analysis and then conducted a randomized controlled trial to measure the effect on both prolific offenders and their co-offenders of delivering a “specific deterrence” message. The treatment—preemptive engagements with prolific offenders by a police officer offering both ‘carrots’ (desistance pathways) and ‘sticks’ (increased sanction threat)—was applied to the prolific offenders, but not to their co-offenders. The outcomes suggest that a single officer–offender engagement leads to a crime suppression effect in all comparisons, with 21.3%, 11.0%, and 15.0% reductions for specific, vicarious, and total network deterrence effects, respectively. The findings suggest that (a) social network analysis based on in-house police records can be used to prevent crime; (b) deterrence messages promulgated by the police have the capacity to reduce crime beyond what was previously assumed, as the cascading of threats in co-offending relationships carries a vicarious crime reduction impact; (c) unlike “reactive specific deterrence” (i.e., a threat of punishment following a specific and detected crime) which can have perverse effects on certain offenders, preventative specific deterrence is a promising crime policy.N/