Deautonomization by singularity confinement: an algebro-geometric justification

The ‘deautonomization’ of an integrable mapping of the plane consists in treating the free parameters in the mapping as functions of the independent variable, the precise expressions of which are to be determined with the help of a suitable criterion for integrability. Standard practice is to use the singularity confinement criterion and to require that singularities be confined at the very first opportunity. An algebro-geometrical analysis will show that confinement at a later stage leads to a non-integrable deautonomized system, thus justifying the standard singularity confinement approach. In particular, it will be shown on some selected examples of discrete Painlevé equations, how their regularization through blow-up yields exactly the same conditions on the parameters in the mapping as the singularity confinement criterion. Moreover, for all these examples, it will be shown that the conditions on the parameters are in fact equivalent to a linear transformation on part of the Picard group, obtained from the blow-up.

Microbial degradation of microcystin in Florida's freshwaters

Presence of microcystin (MC), a predominant freshwater algal toxin and a suspected liver carcinogen, in Florida's freshwaters poses serious health threat to humans and aquatic species. Being recalcitrant to conventional physical and chemical water treatment methods, biological methods of MC removal is widely researched. Water samples collected from five sites of Lake Okeechobee (LO) frequently exposed to toxic Microcystis blooms were used as inoculum for enrichment with microcystin LR (MC-LR) supplied as sole C and N source. After 20 days incubation, MC levels were analyzed using high performance liquid chromatography (HPLC). A bacterial consortium consisting of two isolates DC7 and DC8 from the Indian Prairie Canal sample showed over 74% toxin degradation at the end of day 20. Optimal temperature requirement for biodegradation was identified and phosphorus levels did not affect the MC biodegradation. Based on 16S rRNA sequence similarity the isolate DC8 was found to have a match with Microbacterium sp. and the DC7 isolate with Rhizobium gallicum (AY972457).

Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature.

Estimation of the macromolecular proton fraction and bound pool T2 in multiple sclerosis

This study used a model for magnetization transfer (MT) to estimate two underlying parameters: the macromolecular proton fraction (f) and the bound pool T2 (T2b) in patients with multiple sclerosis (MS). Sixty patients with clinically definite MS and 27 healthy controls were imaged using: (1) a dual echo fast spin echo sequence, (2) a MT sequence (with ten MT power and offset frequency combinations) and (3) proton density and T1 weighted sequences (for T1 relaxation time estimation). Fourteen normal-appearing white matter (NAWM) regions of interest (ROI) and six normal-appearing gray matter (NAGM) ROIs were outlined in all subjects. Lesions were also contoured in subjects affected by MS. The model was fitted to the data leading to estimates of T2b and f. Results showed that T2b was increased in lesions whereas f was reduced. In NAWM, f was decreased while T2b was only increased in secondary progressive MS. NAWM f correlated modestly with disability. Further studies are needed to investigate the pathological basis of the abnormalities observed.

Another approach to protons with constricted mobility in white matter: pilot studies using wideline and high-resolution NMR spectroscopy

We report a new approach for the identification of an independent method of studying the semi-solid pool of protons, i.e., protons with constrained motion as a result of being bound to lipid and protein matrices. These protons cannot be observed using conventional imaging techniques since their transverse relaxation times are much shorter than the minimum echo times that are currently available on clinical scanners. In this pilot study, in vitro multicomponent transverse relaxation experiments were made on human white matter slices, fixed in formalin (7 normal and 5 with multiple sclerosis). The transverse relaxation decay curves were multiexponential and were decomposed to yield three primary components. The shortest T(2) component that we obtained (a component too short to be seen by in vivo methods) was of the order of microseconds. We hypothesize that this might correspond to the macromolecular pool of lipid protons trapped within the myelin sheaths. To our knowledge, this is the first attempt at extracting this ultra short T(2) component from human white matter. Subsequently, an attempt was made to directly detect the lipid protons in a proton NMR spectrum and, if possible, measure their concentration in some of the tissues, using the technique of magic angle spinning.

Quantitative magnetization transfer mapping of bound protons in multiple sclerosis

Quantitative analysis of magnetization transfer images has the potential to allow a more thorough characterization of the protons, both bound and free, in a tissue by extracting a number of parameters relating to the NMR properties of the protons and their local environment. This work develops previously presented techniques to produce estimates of parameters such as the bound proton fraction, f, and the transverse relaxation time of the bound pool, T(2B), for the whole brain in a clinically acceptable imaging time. This is achieved by limiting the number of data collected (typically to 10); to collect 28 5-mm slices with a reconstructed resolution of 0.94 x 0.94 mm. The protocol takes 82 sec per data point. The fitting technique is assessed against previous work and for fitting failures. Maps and analysis are presented from a group of seven controls and 20 multiple sclerosis patients. The maps show that the parameters are sensitive to tissue-specific differences and can detect pathological change within lesions. Statistically significant differences in parameters such as T(2B) and f are seen between normal-appearing white matter, multiple sclerosis lesions, and control white matter. Whole-brain histograms of these parameters are also presented, showing differences between patients and controls.

Preliminary magnetic resonance study of the macromolecular proton fraction in white matter: a potential marker of myelin?

We report on a new quantitative magnetization transfer (MT) technique that allows for the in vivo estimation of the macromolecular proton fraction (f) and the bound pool T2 relaxation time (T2b), whilst permitting whole brain coverage. In this pilot study, five subjects with multiple sclerosis (MS) and five healthy controls were studied. Both f and T2b were significantly different between MS lesions and normal control white matter (WM). Relationships between f and T1 relaxation time [Spearmans rank correlation coefficient (r(s)) = -0.97, P < 0.001] and f and the magnetization transfer ratio (MTR; r(s) = 0.80, P < 0.001) were observed. Compared with MTR, f and T2b have the potential advantage of relative independence from MT acquisition protocol while offering more pathologically specific information. In particular, f may provide a more direct indication of myelin content in WM.

Precise estimate of fundamental in-vivo MT parameters in human brain in clinically feasible times

A methodology is presented for extracting precise quantitative MT parameters using a magnetisation-prepared spoiled gradient echo sequence. This method, based on a new mathematical model, provides relaxation parameters for human brain in-vitro and in-vivo. The in-vivo parameters have been obtained from three different regions of normal white matter: occipital white matter, frontal white matter and centrum semiovale; two regions of normal grey matter: cerebral cortex and cerebellum, and from five regions with MS lesions. All this has been achieved using MT images collected within a timeframe that is clinically feasible. We hope that this new technique will shed light on the properties and dynamics of water compartments within the brain.

Rapid flow cytometric susceptibility testing of Candida albicans

A rapid flow cytometric assay for in vitro antifungal drug susceptibility testing was developed by adapting the proposed reference method for broth macrodilution testing of yeasts. Membrane permeability changes caused by the antifungal agent were measured by flow cytometry using propidium iodide, a nucleic acid-binding fluorochrome largely excluded by the intact cell membrane. We determined the in vitro susceptibility of 31 Candida albicans isolates and two quality control strains (Candida parapsilosis ATCC 22019 and Candida krusei ATCC 6258) to amphotericin B and fluconazole. Amphotericin B MICs ranged from 0.03 to 2.0 microg/ml, while fluconazole MICs ranged from 0.125 to 128 microg/ml. This method results in clear-cut endpoints that were reproducible. Four-hour incubation was required for fluconazole, whereas a 2-h incubation was sufficient for amphotericin B to provide MICs comparable to the reference macrodilution method developed by the National Committee for Clinical Laboratory Standards Subcommittee on Antifungal Susceptibility Tests. Results of these studies show that flow cytometry provides a rapid and sensitive in vitro method for antifungal susceptibility testing of C. albicans.