Quantum adiabatic optimization and combinatorial landscapes

In this paper we analyze the performance of the Quantum Adiabatic Evolution algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, $\gamma=M/N$. We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (versus only energy) is used, and are able to show the existence of a dynamic threshold $\gamma=\gamma_d$ starting with some value of K -- the number of variables in each clause. Beyond dynamic threshold, the algorithm should take exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz. We have been able to map the ensemble of random graphs onto another ensemble with fluctuations significantly reduced. This enabled us to obtain tight upper bounds on satisfiability transition and to recompute the dynamical transition using the extended set of landscapes.Comment: 41 pages, 10 figures; added a paragraph on paper's organization to the introduction, fixed reference

The influence of moisture content and temperature on storage stability of freeze-dried biologics

Moisture and temperature are both critical factors that affect the long term storage stability of Freeze-dried (FD) biologics. Both physical structure and biological activity can be affected by the conditions that the FD material is subject to over a prolonged storage period. This project aimed to investigate how these key factors affected the long term storage stability of FD biologics. The relationship between moisture content, cake structure and the physical/biological stability for model proteins/antigen standards during long term storage was investigated. Novel techniques and procedures were developed to measure the effects of moisture and storage temperature in FD material. Dynamic vapour sorption (DVS) instrumentation, in conjunction with a real time video imaging, was used to measured visible collapse/shrinkage of FD materials. DVS data used in conjunction with video images for a series of temperatures were analysed to provide stability maps. These provided critical moisture content levels that should not be exceeded in order to retain structural cake stability. In addition, other novel techniques were utilised to measure morphological or physical changes with regards to moisture and temperature. Mechanical properties of the FD materials was measured with a flat punch indenter, while inverse gas chromatography (IGC) was used to measure the cake specific surface area (SSA). Mechanical indention data showed that increasing moisture and storage temperature lead to a reduction of mechanical properties and specifically Young’s modulus. IGC was shown to be suitable alternative to measure SSA of FD biologics, providing comparable SSA values to standard volumetric gas adsorption techniques. Advantages of IGC included being able to show and measure changes to SSA of FD materials conditioned at different relative humidities. A series of long term stability trials were also conducted for high protein concentration formulations (IgG) with a range of 10 - 200 mg/mL to further investigate mechanisms of protein stabilisation in regards to optimum moisture and temperature. Higher concentration proteins had lower SSA’s with larger Young’s Modulus but suffered from longer reconstitution times. IgG stability during 12 month storage trials showed evidence for both vitrification and water replacement theories. The data also provided further evidence for the bell shaped distribution theory of optimum moisture content for some materials and that over-drying with a low moisture cycle might not necessarily be the best option for long term storage stability of IgG. High moisture contents of up to 5% w/w did not seem to have any impact on stability until storage above 45°C. With high concertation FD proteins above 50 mg/mL, there was low of risk of structural collapse with increasing moisture content compared to lower concentration materials. Water ingress into vials during their long term storage is of huge concern especially for all FD materials, but especially so for low mass products such as FD Influenza antigens. Comparison of different closure storage formats for FD antigens was explored and it was found that vials with vacuum-oven dried stoppers had less moisture ingress than vials with unprocessed stoppers (straight out of manufacturers packaging). Vials with vacuum-oven dried stoppers were shown to give comparable potency and moisture content ingress as glass ampoules for reference standard influenza antigens over a 1 year period from -20°C to 45°C. Thus not only can vials with vacuum oven dried stoppers reduce moisture ingress compared to unprocessed stopper vials, but can also result in retaining greater potency and stability during long term storage. In summary, this thesis via use of prolonged stability trials, expanded and further consolidated knowledge on current theories of mechanisms of stability in context to moisture content and temperature during long term storage for real world commercial FD biological standards. This thesis also promoted and endorsed the adoption of novel techniques or practices (such as vacuum oven drying stoppers) to provide further aid and insight in optimising the long term storage stability of FD biologics for future use in industry.Open Acces

Middle Level Education Aims for Equity and Inclusion, but Do Our School Websites Meet ADA Compliance?

An often-overlooked component of a middle school website is the necessity for that website to be accessible to those with disabilities, while following the guidelines of the Americans with Disabilities Act (ADA) and Section 508 of the Workforce Rehabilitation Act. In support of the belief that support the belief that inclusive education and respect for diversity should be integrated throughout the school, this study investigated the accessibility of middle school websites in Indiana, Kentucky, and Ohio by selecting a random sample of 150 schools and analyzing their homepages using WAVE (Web Accessibility Versatile Evaluator), which reports accessibility violations by annotating a copy of the page that was evaluated and presenting embedded icons and indicators to disclose breaches with ADA. Out of 150 districts, 54% had errors that need immediate attention and all 150 schools had alerts of likely violations that ranged from alt-text omissions and empty or confusing links to issues with color contrast and keyboard-only navigation. The article proceeds to give practical suggestions for eliminating many of the errors, even for those shareholders with less than sophisticated technological expertise