The Magnus expansion and some of its applications

Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to built up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of preserving at any order certain symmetries of the exact solution. The goal of this review is threefold. First, to collect a number of developments scattered through half a century of scientific literature on Magnus expansion. They concern the methods for the generation of terms in the expansion, estimates of the radius of convergence of the series, generalizations and related non-perturbative expansions. Second, to provide a bridge with its implementation as generator of especial purpose numerical integration methods, a field of intense activity during the last decade. Third, to illustrate with examples the kind of results one can expect from Magnus expansion in comparison with those from both perturbative schemes and standard numerical integrators. We buttress this issue with a revision of the wide range of physical applications found by Magnus expansion in the literature.Comment: Report on the Magnus expansion for differential equations and its applications to several physical problem

Dental approach of orofacial pain in head and neck cancer patients

Orofacial pain (OFP) is an undesirable sensation frequently associated with head and neck cancer (HNC) and its treatment. OFP negatively impacts the quality of life of oncological patients. The approach to OFP diagnosis and management can differ if the patient visits a dentist or physician. The aim of this study was to present a case series of HNC with OFP managed by a dentist team and to discuss its role in the management of OFP. We recruited twenty-two adult patients with OFP and previous diagnosis of HNC referred to an academic dental clinic from 2015 to 2017. Nociceptive was more frequent than mixed and neuropathic pain, however 54,4% of the cases showed a neurological component. All types of pain were managed by dentist through removal of pain?s cause and appropriated local and systemic treatment. The intensity of pain was reduced in 86,3% of patients, and 45,4% of them reported absence of pain at the end of treatment. Dentist?s assessment plays a distinct and crucial role in the diagnosis and management of OFP in HNC patients throughout the oncological treatment

Impact of typhoon disturbance on the diversity of key ecosystem engineers in a monoculture mangrove forest plantation, Can Gio Biosphere Reserve, Vietnam

Mangrove crabs as key ecosystem engineers may play an important role in the recovery process of storm-damaged forests. Yet, their response to storm disturbance is largely unknown. Here we compare the ground-dwelling brachyuran crab community of intact mangrove stands with that of typhoon gaps having experienced 100% tree mortality. Field work was conducted in two adjacent areas in Can Gio Biosphere Reserve, southern Vietnam. In each area, an 18–20 yr old monoculture Rhizophora apiculata stand served as control and was compared with typhoon gaps where downed stems had been removed or left on-site. The gaps were 14 and 20 months old when studied in the dry and rainy season 2008, respectively. Time-based sampling of ground-dwelling crabs with hand or shovel was conducted by 4 persons inside 100 m2 plots for 30 min (7 replicate plots per area, treatment and month). Abiotic (sediment pH, salinity, temperature, grain size, water content, carbon and nitrogen content), and biotic measures (e.g. canopy coverage, woody debris, number of trees, leaf litter) were also taken. Despite complete canopy loss, total crab abundance has not changed significantly (in contrast to biomass) and all 12 species found in the forest were also found in the gaps, demonstrating their robustness. Another 9 gap-exclusive species were recorded and average species number and Shannon diversity were thus higher in the gaps. Perisesarma eumolpe was the most abundant species, both in the forest and in the gaps, and a shift from sesarmids (typical forest species) to ocypodids (generally more prominent in open areas) has not occurred. The persistence of litter-feeding sesarmid crabs prior to the re-establishment of a mangrove canopy is likely to depend on the availability of woody debris on the ground of the gaps, fuelling a mangrove detritus based food web, rather than one based on microphytobenthos and deposit-feeding ocypodids. The presence of burrowing crabs in the gaps suggests that important ecosystem engineering activities are still performed. However, bioturbation may be reduced as crab biomass and body size were smaller in the gaps. Follow-up assessments and field experiments are needed to understand the crabs' role in processing the woody debris, their long-term community dynamics and possible feed-backs between species shifts and gap regeneration

Tracking the little ones: use of fluorescent powder to follow a leaf litter lizard (Coleodactylus meridionalis, Squamata: Sphaerodactylidae) in the Atlantic Forest of southern Bahia, Brazil

Abstract The ecology of movement is an expanding area, marked by the diversity of analytical methods and protocols, which enables this integrative reading. We investigated movement ecology aspects of Coleodactylus meridionalis in southern Bahia, northeastern Brazil, using fluorescent powder with mineral oil to track individuals. We monitored 69 individuals of C. meridionalis that walked an average distance of 148 cm in 2h. We identified this movement as foraging due to the orientation of the step sequence and microenvironments used. We find no significant differences between walking distance and weight. However, we found a decrease in activity over the follow-up period. Most of the lizard’s movements were directed north, while south, east, and west were followed equally. The individuals stayed predominantly on the ground (leaf litter), but it was possible to observe the use of other surfaces, such as trunks and burrows on the ground. Therefore, we studied the movement in three dimensions (ground height, distance traveled, and orientation of steps). We observed the lizard’s foraging, one of the most common and least investigated movements in small lizards like C. meridionalis. This involves not only the species’ activity schedule but other intrinsic and extrinsic factors that shape the movement decisions of individuals

Mangroves support an estimated annual abundance of over 700 billion juvenile fish and invertebrates

Mangroves are a critical habitat that provide a suite of ecosystem services and support livelihoods. Here we undertook a global analysis to model the density and abundance of 37 commercially important juvenile fish and juvenile and resident invertebrates that are known to extensively use mangroves, by fitting expert-identified drivers of density to fish and invertebrate density data from published field studies. The numerical model predicted high densities throughout parts of Southeast and South Asia, the northern coast of South America, the Red Sea, and the Caribbean and Central America. Application of our model globally estimates that mangroves support an annual abundance of over 700 billion juvenile fish and invertebrates. While abundance at the early life-history stage does not directly equate to potential economic or biomass gains, this estimate indicates the critical role of mangroves globally in supporting fish and fisheries, and further builds the case for their conservation and restoration