Practical Stability and Vector-Lyapunov Functions for Impulsive Differential Equations with "Supremum"

Stability of nonlinear impulsive differential equations with "supremum" is studied. A special type of stability, combining two different measures and a dot product on a cone, is defined. Perturbing cone-valued piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed.

Properties of Lp (K)-Solutions of Linear Nonhomogeneous Impulsive Differential Equations with Unbounded Linear Operator

Sufficient conditions for the existence of Lp(k)-solutions of linear nonhomogeneous impulsive differential equations with unbounded linear operator are found. An example of the theory of the linear nonhomogeneous partial impulsive differential equations of parabolic type is given.

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

Anti-Periodic Boundary Value Problem for Impulsive Fractional Integro Differential Equations

MSC 2010: 34A37, 34B15, 26A33, 34C25, 34K37

APP controls the formation of PI(3,5)P2 vesicles through its binding of the PIKfyve complex

Phosphoinositides are signalling lipids that are crucial for major signalling events as well as established regulators of membrane trafficking. Control of endosomal sorting and endosomal homeostasis requires phosphatidylinositol-3-phosphate (PI(3)P) and phosphatidylinositol-3,5-bisphosphate (PI(3,5)P2), the latter a lipid of low abundance but significant physiological relevance. PI(3,5)P2 is formed by phosphorylation of PI(3)P by the PIKfyve complex which is crucial for maintaining endosomal homeostasis. Interestingly, loss of PIKfyve function results in dramatic neurodegeneration. Despite the significance of PIKfyve, its regulation is still poorly understood. Here we show that the Amyloid Precursor Protein (APP), a central molecule in Alzheimer’s disease, associates with the PIKfyve complex (consisting of Vac14, PIKfyve and Fig4) and that the APP intracellular domain directly binds purified Vac14. We also show that the closely related APP paralogues, APLP1 and 2 associate with the PIKfyve complex. Whether APP family proteins can additionally form direct protein–protein interaction with PIKfyve or Fig4 remains to be explored. We show that APP binding to the PIKfyve complex drives formation of PI(3,5)P2 positive vesicles and that APP gene family members are required for supporting PIKfyve function. Interestingly, the PIKfyve complex is required for APP trafficking, suggesting a feedback loop in which APP, by binding to and stimulating PI(3,5)P2 vesicle formation may control its own trafficking. These data suggest that altered APP processing, as observed in Alzheimer’s disease, may disrupt PI(3,5)P2 metabolism, endosomal sorting and homeostasis with important implications for our understanding of the mechanism of neurodegeneration in Alzheimer’s disease.

Notes on the Solution of Dynamic Optimization Problems with Explicit Controls in Discrete-Time Economic Models

Йордан Йорданов, Андрей Василев - В работата се изследват методи за решаването на задачи на оптималното управление в дискретно време с безкраен хоризонт и явни управления. Дадена е обосновка на една процедура за решаване на такива задачи, базирана на множители на Лагранж, коята често се употребява в икономическата литература. Извеждени са необходимите условия за оптималност на базата на уравнения на Белман и са приведени достатъчни условия за оптималност при допускания, които често се използват в икономиката.

Method of Averaging for Impulsive Differential Inclusions

AMS subject classification: Primary 49N25, Secondary 49J24, 49J25.

High-accuracy discrimination of Parkinson’s Disease participants from healthy controls using smartphones

Objective: To test the practicality and effectiveness of cheap, ubiquitous, consumer-grade smartphones to discriminate Parkinson’s disease (PD) subjects from healthy controls, using self-administered tests of gait and postural sway. Background: Existing tests for the diagnosis of PD are based on subjective neurological examinations, performed in-clinic. Objective movement symptom severity data, collected using widely-accessible technologies such as smartphones, would enable the remote characterization of PD symptoms based on self-administered, behavioral tests. Smartphones, when backed up by interviews using web-based videoconferencing, could make it feasible for expert neurologists to perform diagnostic testing on large numbers of individuals at low cost. However, to date, the compliance rate of testing using smart-phones has not been assessed. Methods: We conducted a one-month controlled study with twenty participants, comprising 10 PD subjects and 10 controls. All participants were provided identical LG Optimus S smartphones, capable of recording tri-axial acceleration. Using these smartphones, patients conducted self-administered, short (less than 5 minute) controlled gait and postural sway tests. We analyzed a wide range of summary measures of gait and postural sway from the accelerometry data. Using statistical machine learning techniques, we identified discriminating patterns in the summary measures in order to distinguish PD subjects from controls. Results: Compliance was high all 20 participants performed an average of 3.1 tests per day for the duration of the study. Using this test data, we demonstrated cross-validated sensitivity of 98% and specificity of 98% in discriminating PD subjects from healthy controls. Conclusions: Using consumer-grade smartphone accelerometers, it is possible to distinguish PD from healthy controls with high accuracy. Since these smartphones are inexpensive (around $30 each) and easily available, and the tests are highly non-invasive and objective, we envisage that this kind of smartphone-based testing could radically increase the reach and effectiveness of experts in diagnosing PD.

Activity-regulated cytoskeleton-associated protein controls AMPAR endocytosis through a direct interaction with clathrin-adaptor protein 2

The activity-regulated cytoskeleton-associated (Arc) protein controls synaptic strength by facilitating AMPA receptor (AMPAR) endocytosis. Here we demonstrate that Arc targets AMPAR to be internalized through a direct interaction with the clathrin-adaptor protein 2 (AP-2). We show that Arc overexpression in dissociated hippocampal neurons obtained from C57BL/6 mouse reduces the density of AMPAR GluA1 subunits at the cell surface and reduces the amplitude and rectification of AMPAR-mediated miniature-EPSCs (mEPSCs). Mutations of Arc, that prevent the AP-2 interaction reduce Arc-mediated endocytosis of GluA1 and abolish the reduction in AMPAR-mediated mEPSC amplitude and rectification. Depletion of the AP-2 subunit µ2 blocks the Arc-mediated reduction in mEPSC amplitude, an effect that is restored by reintroducing µ2. The Arc-AP-2 interaction plays an important role in homeostatic synaptic scaling as the Arc-dependent decrease in mEPSC amplitude, induced by a chronic increase in neuronal activity, is inhibited by AP-2 depletion. These data provide a mechanism to explain how activity-dependent expression of Arc decisively controls the fate of AMPAR at the cell surface and modulates synaptic strength, via the direct interaction with the endocytic clathrin adaptor AP-2.

The costs and controls of flowering and fruiting in {\it Spondias purpurea\/}

Small potted trees of Spondias purpurea were monitored to determine the costs and controls of flowering and fruiting. The effect of photoperiod, extremes in moisture and temperature, and defoliation were examined. The carbon exchange rates of the leaves, shoots and fruits were determined. Light response curves and diurnal levels were also investigated. $\sp{13}$Carbon labeling was used to determine which plant parts are carbon sinks. Photoperiod induces dormancy and bud activity. Extremes in soil moisture and temperature induce leaf fall. Flowers, fruits, and roots are carbon sinks. The results were used to develop a phenological model with latitude, soil moisture, and air temperature as variables. ^

Controls on fish distribution and abundance in temporary wetlands

Our main goal was to determine if fish distribution and adundance in temporary wetlands were shaped primarily by large-scale (landscape) or small-scale (local) characteristics and to investigate the influence of cattle ranching on fish assemblages. A total of 24 temporary ponds were selected at the Kissimmee Prairie Sanctuary and the Mac- Arthur Agro-Ecology Research Center. Each wetland was sampled for fish using throw traps and dip nets during 1999. Landscape processes (connectivity to permanent water bodies) predominately influenced fish assemblages, although local processes (depth–hydroperiod) were also important. Furthermore, no colonizing species went locally extinct before wetlands began to dry. Our findings suggest that large-scale processes that influence colonization dynamics are of more importance than small-scale processes that influence extinction dynamics. Finally, hydrological changes (ditching) associated with agriculture (cattle ranching) have adversely affected temporary wetland fish assemblages by reducing wetland hydroperiods and connectivity.

Controls on mangrove forest-atmosphere carbon dioxide exchanges in western Everglades National Park

We report on net ecosystem production (NEP) and key environmental controls on net ecosystem exchange (NEE) of carbon dioxide (CO2) between a mangrove forest and the atmosphere in the coastal Florida Everglades. An eddy covariance system deployed above the canopy was used to determine NEE during January 2004 through August 2005. Maximum daytime NEE ranged from −20 to −25 mmol (CO2) m−2 s−1 between March and May. Respiration (Rd) was highly variable (2.81 ± 2.41 mmol (CO2) m−2 s−1), reaching peak values during the summer wet season. During the winter dry season, forest CO2 assimilation increased with the proportion of diffuse solar irradiance in response to greater radiative transfer in the forest canopy. Surface water salinity and tidal activity were also important controls on NEE. Daily light use efficiency was reduced at high (>34 parts per thousand (ppt)) compared to low (ppt) salinity by 46%. Tidal inundation lowered daytime Rd by ∼0.9 mmol (CO2) m−2 s−1 and nighttime Rd by ∼0.5 mmol (CO2) m−2 s−1. The forest was a sink for atmospheric CO2, with an annual NEP of 1170 ± 127 g C m−2 during 2004. This unusually high NEP was attributed to year‐round productivity and low ecosystem respiration which reached a maximum of only 3 g C m−2 d−1. Tidal export of dissolved inorganic carbon derived from belowground respiration likely lowered the estimates of mangrove forest respiration. These results suggest that carbon balance in mangrove coastal systems will change in response to variable salinity and inundation patterns, possibly resulting from secular sea level rise and climate change. Citation: Barr, J. G., V. Engel, J. D. Fuentes,

Climatic Controls on Phytoplankton Biomass in a Sub-tropical Estuary, Florida Bay, USA

The extraction of climatic signals from time series of biogeochemical data is further complicated in estuarine regions because of the dynamic interaction of land, ocean, and atmosphere. We explored the behavior of potential global and regional climatic stressors to isolate specific shifts or trends, which could have a forcing role on the behavior of biogeochemical descriptors of water quality and phytoplankton biomass from Florida Bay, as an example of a sub-tropical estuary. We performed statistical analysis and subdivided the bay into six zones having unique biogeochemical characteristics. Significant shifts in the drivers were identified in all the chlorophyll a time series. Chlorophyll a concentrations closely follow global forcing and display a generalized declining trend on which seasonal oscillations are superimposed, and it is only interrupted by events of sudden increase triggered by storms which are followed by a relatively rapid return to pre-event conditions trailing again the long-term trend.

Application of excitation emission matrix fluorescence monitoring in the assessment of spatial and seasonal drivers of dissolved organic matter composition: Sources and physical disturbance controls

The environmental dynamics of dissolved organic matter (DOM) were characterized for a shallow, subtropical, seagrass-dominated estuarine bay, namely Florida Bay, USA. Large spatial and seasonal variations in DOM quantity and quality were assessed using dissolved organic C (DOC) measurements and spectrophotometric properties including excitation emission matrix (EEM) fluorescence with parallel factor analysis (PARAFAC). Surface water samples were collected monthly for 2 years across the bay. DOM characteristics were statistically different across the bay, and the bay was spatially characterized into four basins based on chemical characteristics of DOM as determined by EEM-PARAFAC. Differences between zones were explained based on hydrology, geomorphology, and primary productivity of the local seagrass community. In addition, potential disturbance effects from a very active hurricane season were identified. Although the overall seasonal patterns of DOM variations were not significantly affected on a bay-wide scale by this disturbance, enhanced freshwater delivery and associated P and DOM inputs (both quantity and quality) were suggested as potential drivers for the appearance of algal blooms in high impact areas. The application of EEM-PARAFAC proved to be ideally suited for studies requiring high sample throughput methods to assess spatial and temporal ecological drivers and to determine disturbance-induced impacts in aquatic ecosystems.

Controls on herbaceous litter decomposition in the estuarine ecotones of the Florida Everglades

The effects of nutrient availability and litter quality on litter decomposition were measured in two oligotrophic phosphorus (P)-limited Florida Everglades esturies, United States. The two estuaries differ, in that one (Shark River estuary) is directly connected to the Gulf of Mexico and receives marine P, while the other (Taylor Slough estuary) does not receive marine P because Florida Bay separates it from the Gulf of Mexico. Decomposition of three macrophytes.Cladium jamaicense, Eleochaaris spp., andJuncus roemerianus, was studied using a litter bag technique over 18 mo. Litter was exposed to three treatments: soil surface+macroinvertebrates (=macro), soil surface without macroinvertebrates (=wet), and above the soil and water (=aerial). The third treatment replicated the decomposition of standing dead leaves. Decomposition rates showed that litter exposed to the wet and macro treatments decomposed significantly faster than the aerial treatment, where atmospheric deposition was the only source of nutrients. Macroinvertebrates had no influence on litter decompostion rates.C. jamaicense decomposed faster at sites, with higher P, andEleocharis spp. decomposed significantly faster at sites with higher nitrogen (N). Initial tissue C:N and C:P molar ratios revealed that the nutrient quality of litter of bothEleocharis spp. andJ. roemerianus was higher thanC. jamaicense, but onlyEleocharis spp. decomposed faster thanC. jamaicense. C. jamaicense litter tended to immobilize P, whileEleocharis spp. litter showed net remineralization of N and P. A comparison with other estuarine and wetland systems revealed the dependence of litter decomposition on nutrient availability and litter quality. The results from this experiment suggest that Everglades restoration may have an important effect on key ecosystem processes in the estuarine ecotone of this landscape.