Using Functional Programming to recognize Named Structure in an Optimization Problem: Application to Pooling

Branch-and-cut optimization solvers typically apply generic algorithms, e.g., cutting planes or primal heuristics, to expedite performance for many mathematical optimization problems. But solver software receives an input optimization problem as vectors of equations and constraints containing no structural information. This article proposes automatically detecting named special structure using the pattern matching features of functional programming. Specifically, we deduce the industrially-relevant nonconvex nonlinear Pooling Problem within a mixed-integer nonlinear optimization problem and show that we can uncover pooling structure in optimization problems which are not pooling problems. Previous work has shown that preprocessing heuristics can find network structures; we show that we can additionally detect nonlinear pooling patterns. Finding named structures allows us to apply, to generic optimization problems, cutting planes or primal heuristics developed for the named structure. To demonstrate the recognition algorithm, we use the recognized structure to apply primal heuristics to a test set of standard pooling problems

Data Structures for Representing Symmetry in Quadratically Constrained Quadratic Programs

Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the Branch and Bound algorithm. Symmetry may induce large search trees with multiple equivalent solutions, i.e. with the same optimal value. Dealing with symmetry requires detecting and classifying it first. This paper develops several methods for detecting symmetry in quadratically constrained quadratic optimisation problems via adjacency matrices. Using graph theory, we transform these matrices into binary layered graphs and enter them into the software package nauty. Nauty generates important symmetric properties of the original problem

The impact of government measures and human mobility trend on COVID-19 related deaths in the UK

The COVID-19 global pandemic has rapidly expanded, with the UK being one of the countries with the highest number of cases and deaths in proportion to its population. Major clinical and human behavioural measures have been taken by the UK government to control the spread of the epidemic and to support the health system. It remains unclear how exactly human mobility restrictions have affected the virus spread in the UK. This research uses driving, walking and transit real-time data to investigate the impact of government control measures on human mobility reduction, as well as the connection between trends in human-mobility and severe COVID-19 outcomes. Human mobility was observed to gradually decrease as the government was announcing more measures and it stabilized at a scale of around 80 % after a lockdown was imposed. The study shows that human-mobility reduction had a significant impact on reducing COVID-19-related deaths, thus providing crucial evidence in support of such government measures

A modified speculum for transsphenoidal surgery: Technical note

This technical note presents the advantages of a modified nasal speculum for the translabial-endonasal transsphenoidal approach to the sphenoid sinus and sella for surgery on lesions of the pituitary. The width of the upper lateral wings of the speculum was reduced by half over approximately three fourths of their length. This increases interior clearance and makes it easier to introduce the instruments used during transsphenoidal operations. We performed 50 transsphenoidal procedures for pituitary adenomas using the remodeled speculum. Three experienced surgeons evaluated the visual field and instrument passage through it, and they found it superior to the conventional design. The modification resulted in marked reduction of the overall operation duration. In conclusion, the more open translabial-transnasal speculum described here definitely facilitates the transsphenoidal approach to the pituitary. © 2009 Springer-Verlag

Selection of cranial site for shunting debilitated patients

Background-objective. The optimum cranial site for ventricular catheter insertion in CSF shunts is still under debate and there has been no general consensus as far as surgical technicalities are concerned. Furthermore, there have been no reports dealing with appropriate cranial site selection in debilitated patients. The aim of this report is to stress the need to utilize a frontal approach when dealing with patients who are likely to remain bed-bound for long periods and to emphasize the well-known prerequisites such as meticulous surgical technique and perioperative general and local care. Method. A retrospective analysis of all shunt operations and revisions performed in our department during the last 6 years. Findings. This analysis revealed 8 long-term recumbent patients with late valve extrusion (N1 = 5) or primary wound breakdown (N2 = 3), all through the occipital area. Extended periods of bed rest due to neurological disease combined with poor nursing and dietary intake had led to either chronic valve extrusion or wound breakdown. Shunt revision was performed successfully by a frontal approach in 5 whereas 2 tolerated shunt removal and one died of meningitis. Conclusion. In debilitated patients or those who are likely to remain bed-bound for long periods, a frontal approach for proximal catheter insertion may help prevent immediate postoperative wound breakdown or late valve extrusion

Arachnoiditis ossificans with progressive syringomyelia and spinal arachnoid cyst

We present a 30-year-old man with progressive spastic paraparesis. Spinal imaging revealed extensive calcification of the thoracic cord and cauda equina arachnoid, an intradural extramedullary cyst and evidence of rapidly progressing syringomyelia. Radiological diagnosis was arachnoiditis ossificans and an attempt at surgical decompression was made because of progressive neurologic deterioration. Due to tenacious adhesion of the calcified plaques to the cord and roots, only cyst drainage was achieved; the patient had no clinical improvement. A literature review revealed only two other cases reported in the literature with co-existence of arachnoiditis ossificans and syringomyelia. In none of the previous cases was there an intradural extramedullary arachnoid cyst, nor did the syrinx progress in such a rapid fashion. An attempt is made to explain possible pathophysiological mechanisms leading to this unusual pathology. (c) 2006 Elsevier Ltd. All rights reserved

CT-guided stereotactic biopsies of brain stem lesions: personal experience and literature review

Appropriate therapy of brain stem lesions should be guided by an accurate diagnosis. Clinical evaluation combined with modem neuroimaging techniques may nowadays approach the diagnosis but not always with accuracy, thus leading to erroneous treatment. We report a series of 11 patients who underwent stereotactic biopsy for brain stem lesions. In 8 patients, the lesion was approached transfrontally. In the remaining 3 patients, the lesion was approached via the suboccipital transcerebellar route. There was no surgical mortality. Precise histological diagnosis was achieved in all patients. Three patients (27.2%) suffered complications attributed to the procedure and were successfully treated conservatively. Histological results were in accordance with preoperative diagnosis in 9 patients (81.8%). Despite the limited number of patients, our data suggest that stereotactic biopsy of brain stem lesions is a safe technique that can obtain adequate tissue for histological diagnosis, thus providing each patient with the best available treatment