Un ni iv ve er rs si it ty y o of f P Pr re et to or ri ia a SynopsisThe simplicial homology global optimisation (SHGO) algorithm is a general purpose global optimisation algorithm based on applications of simplicial integral homology and combinatorial topology. SHGO approximates the homology groups of a complex built on a hypersurface homeomorphic to a complex on the objective function. This provides both approximations of locally convex subdomains in the search space through Sperner's lemma (Sperner, 1928) and a useful visual tool for characterising and efficiently solving higher dimensional black and grey box optimisation problems. This complex is built up using sampling points within the feasible search space as vertices. The algorithm is specialised in finding all the local minima of an objective function with expensive function evaluations efficiently which is especially suitable to applications such as energy landscape exploration. SHGO was initially developed as an improvement on the topographical global optimisation (TGO) method first proposed by Törn (1986;1990;1992). It is proven that the SHGO algorithm will always outperform TGO on function evaluations if the objective function is Lipschitz smooth. In this dissertation SHGO is applied to non-convex problems with linear and box constraints with bounds placed on the variables. Numerical experiments on linearly constrained test problems show that SHGO gives competitive results compared to TGO and the recently developed Lc-DISIMPL algorithm (Paulavičius anď Zilinskas, 2016) as well as the PSwarm and DIRECT-L1 algorithms. Furthermore SHGO is compared with the TGO, basinhopping (BH) and differential evolution (DE) global optimisation algorithms over a large selection of black-box problems with bounds placed on the variables from the SciPy (Jones, Oliphant, Peterson, et al., 2001-) benchmarking test suite. A Python implementation of the SHGO and TGO algorithms published under a MIT license can be found from https://bitbucket.org/upiamcompthermo/shgo/.

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BackgroundDegenerative spinal stenosis and instability requiring multilevel spine surgery has been associated with large blood losses. Factors that affect perioperative blood loss include time of surgery, surgical procedure, patient height, combined anterior/posterior approaches, number of levels fused, blood salvage techniques, and the use of anti-fibrinolytic medications. This study was done to evaluate the efficacy of tranexamic acid in reducing blood loss in spine surgery.MethodsThis retrospective case control study includes 97 patients who had to undergo surgery because of degenerative lumbar spinal stenosis and instability. All operations included spinal decompression, interbody fusion and posterior instrumentation (4-5 segments). Forty-six patients received 1 g tranexamic acid intravenous, preoperative and six hours and twelve hours postoperative; 51 patients without tranexamic acid administration were evaluated as a control group. Based on the records, the intra- and postoperative blood losses were measured by evaluating the drainage and cell saver systems 6, 12 and 24 hours post operation. Additionally, hemoglobin concentration and platelet concentration were reviewed. Furthermore, the number of red cell transfusions given and complications associated with tranexamic acid were assessed.ResultsThe postoperative hemoglobin concentration demonstrated a statistically significant difference with a p value of 0.0130 showing superiority for tranexamic acid use (tranexamic acid group: 11.08 g/dl, SD: 1.68; control group: 10.29 g/dl, SD: 1.39). The intraoperative cell saver volume and drainage volume after 24 h demonstrated a significant difference as well, which indicates a less blood loss in the tranexamic acid group than the control group. The postoperative drainage volume at12 hours showed no significant differences; nor did the platelet concentration Allogenic blood transfusion (two red cell units) was needed for eight patients in the tranexamic acid group and nine in the control group because of postoperative anemia. Complications associated with the administration of tranexamic acid, e.g. renal failure, deep vein thrombosis or pulmonary embolism did not occur.ConclusionsThis study suggests a less blood loss when administering tranexamic acid in posterior lumbar spine surgery as demonstrated by the higher postoperative hemoglobin concentration and the less blood loss. But given the relatively small volume of blood loss in the patients of this study it is underpowered to show a difference in transfusion rates.

Our results demonstrate that CCL22 is expressed in human placenta. Decidual expression was only observed in miscarriage conditions and correlates with Treg infiltration. Thus, CCL22 plays a role in human pregnancy and may occur as a negative feedback response to pro-inflammatory events during miscarriage conditions.