Smoothed Complexity Theory

Smoothed analysis is a new way of analyzing algorithms introduced by Spielman and Teng (J. ACM, 2004). Classical methods like worst-case or average-case analysis have accompanying complexity classes, like P and AvgP, respectively. While worst-case or average-case analysis give us a means to talk about the running time of a particular algorithm, complexity classes allows us to talk about the inherent difficulty of problems. Smoothed analysis is a hybrid of worst-case and average-case analysis and compensates some of their drawbacks. Despite its success for the analysis of single algorithms and problems, there is no embedding of smoothed analysis into computational complexity theory, which is necessary to classify problems according to their intrinsic difficulty. We propose a framework for smoothed complexity theory, define the relevant classes, and prove some first hardness results (of bounded halting and tiling) and tractability results (binary optimization problems, graph coloring, satisfiability). Furthermore, we discuss extensions and shortcomings of our model and relate it to semi-random models.Comment: to be presented at MFCS 201

Magma genesis by rifting of oceanic lithosphere above anomalous mantle: Terceira Rift, Azores

[1] The Terceira Rift formed relatively recently (∼1 Ma ago) by rifting of the old oceanic lithosphere of the Azores Plateau and is currently spreading at a rate of 2–4mm/a. Together with the Mid-Atlantic Ridge, the Terceira Rift forms a triple junction that separates the Eurasian, African, and American Plates. Four volcanic systems (São Miguel, João de Castro, Terceira, Graciosa), three of which are islands, are distinguished along the axis and are separated by deep avolcanic basins similar to other ultraslow spreading centers. The major element, trace element and Sr-Nd-Pb isotope geochemistry of submarine and subaerial lavas display large along-axis variations. Major and trace element modeling suggests melting in the garnet stability field at smaller degrees of partial melting at the easternmost volcanic system (São Miguel) compared to the central and western volcanoes, which appear to be characterized by slightly higher melting degrees in the spinel/garnet transition zone. The degrees of partial melting at the Terceira Rift are slightly lower than at other ultraslow mid-ocean ridge spreading axes (Southwest Indian Ridge, Gakkel Ridge) and occur at greater depths as a result of the melting anomaly beneath the Azores. The combined interaction of a high obliquity, very slow spreading rates, and a thick preexisting lithosphere along the axis probably prevents the formation and eruption of larger amounts of melt along the Terceira Rift. However, the presence of ocean islands requires a relatively stable melting anomaly over relatively long periods of time. The trace element and Sr-Nd-Pb isotopes display individual binary mixing arrays for each volcanic system and thus provide additional evidence for focused magmatism with no (or very limited) melt or source interaction between the volcanic systems. The westernmost mantle sources beneath Graciosa and the most radiogenic lavas from the neighboring Mid-Atlantic Ridge suggest a mantle flow from Graciosa toward the Mid-Atlantic Ridge and hence a flux of mantle material from one spreading axis into the other. The Terceira Rift represents a unique oceanic rift system situated within the thickened, relatively old oceanic lithosphere and thus exhibits both oceanic and continental features

Recoil correction to the bound-electron g factor in H-like atoms to all orders in αZ\alpha Z

The nuclear recoil correction to the bound-electron g factor in H-like atoms is calculated to first order in $m/M$ and to all orders in $\alpha Z$. The calculation is performed in the range Z=1-100. A large contribution of terms of order $(\alpha Z)^5$ and higher is found. Even for hydrogen, the higher-order correction exceeds the $(\alpha Z)^4$ term, while for uranium it is above the leading $(\alpha Z)^2$ correction.Comment: 6 pages, 3 tables, 1 figur

The legacy of 1300 years of land use in Jamaica

Despite decades of archaeological research on Jamaica, little is known about how settlers influenced landscape change on the island over time. Here, we examine the impact of human occupation through a multi-proxy approach using phytolith, charcoal, and stratigraphic analyses. White Marl was a continuously inhabited village settlement (ca. 1050–450 cal yrs BP) with large mounded midden areas, precolonial house structures, and human landscape management practices. We have shown that the local vegetation at White Marl was directly affected by human settlement through the use of agroforestry and burning, and suggest that fire was used to modify vegetation. Manioc phytoliths were found throughout human occupation and are broadly associated with increases in evidence for burning, suggesting fire was used to modify the landscape and clear vegetation for crop cultivation. The phytolith assemblages relate to three distinct temporal vegetation phases: (1) the earliest occupation dominated by arboreal vegetation (pre-ca. 870 cal yrs BP); (2) a transition to palm-dominated vegetation (ca. 870–670 cal yrs BP); and (3) the latest occupation representing European colonization associated with a more open, grass-dominated landscape (after ca. 670 cal yrs BP). These transitions occur independent of changes in paleoclimate records, suggesting humans were the dominant driver of vegetation change.Introduction Archaeological context Archaeobotany in Jamaica The White Marl site Materials and methods - Sampling, stratigraphic analysis, and recording - Phytoliths - Phytolith extraction - Phytolith identification, counting, and quantification - Charcoal extraction and quantification Results - Vegetation phase 1: Arboreal-dominated canopy - Vegetation phase 2: Palm-dominated canopy - Vegetation phase 3: Open grassland-dominated landscape - Crops - Burning indicators - Vegetation changes and climate Discussion Conclusio

Evidence for the absence of regularization corrections to the partial-wave renormalization procedure in one-loop self energy calculations in external fields

The equivalence of the covariant renormalization and the partial-wave renormaliz ation (PWR) approach is proven explicitly for the one-loop self-energy correction (SE) of a bound electron state in the presence of external perturbation potentials. No spurious correctio n terms to the noncovariant PWR scheme are generated for Coulomb-type screening potentia ls and for external magnetic fields. It is shown that in numerical calculations of the SE with Coulombic perturbation potential spurious terms result from an improper treatment of the unphysical high-energy contribution. A method for performing the PWR utilizing the relativistic B-spline approach for the construction of the Dirac spectrum in external magnetic fields is proposed. This method is applied for calculating QED corrections to the bound-electron $g$-factor in H-like ions. Within the level of accuracy of about 0.1% no spurious terms are generated in numerical calculations of the SE in magnetic fields.Comment: 22 pages, LaTeX, 1 figur

Technical Note: Mesocosm approach to quantify dissolved inorganic carbon percolation fluxes

Dissolved inorganic carbon (DIC) fluxes across the vadose zone are influenced by a complex interplay of biological, chemical and physical factors. A novel soil mesocosm system was evaluated as a tool for providing information on the mechanisms behind DIC percolation to the groundwater from unplanted soil. Carbon dioxide partial pressure (<i>p</i>CO₂), alkalinity, soil moisture and temperature were measured with depth and time, and DIC in the percolate was quantified using a sodium hydroxide trap. Results showed good reproducibility between two replicate mesocosms. The <i>p</i>CO₂ varied between 0.2 and 1.1%, and the alkalinity was 0.1–0.6 meq L⁻¹. The measured cumulative effluent DIC flux over the 78-day experimental period was 185–196 mg L⁻¹ m⁻² and in the same range as estimates derived from <i>p</i>CO₂ and alkalinity in samples extracted from the side of the mesocosm column and the drainage flux. Our results indicate that the mesocosm system is a promising tool for studying DIC percolation fluxes and other biogeochemical transport processes in unsaturated environments

Laser spectroscopy of hyperfine structure in highly-charged ions: a test of QED at high fields

An overview is presented of laser spectroscopy experiments with cold, trapped, highly-charged ions, which will be performed at the HITRAP facility at GSI in Darmstadt (Germany). These high-resolution measurements of ground state hyperfine splittings will be three orders of magnitude more precise than previous measurements. Moreover, from a comparison of measurements of the hyperfine splittings in hydrogen- and lithium-like ions of the same isotope, QED effects at high electromagnetic fields can be determined within a few percent. Several candidate ions suited for these laser spectroscopy studies are presented.Comment: 5 pages, 1 figure, 1 table. accepted for Canadian Journal of Physics (2006

The Role of Landscape Connectivity in Planning and Implementing Conservation and Restoration Priorities. Issues in Ecology

Landscape connectivity, the extent to which a landscape facilitates the movements of organisms and their genes, faces critical threats from both fragmentation and habitat loss. Many conservation efforts focus on protecting and enhancing connectivity to offset the impacts of habitat loss and fragmentation on biodiversity conservation, and to increase the resilience of reserve networks to potential threats associated with climate change. Loss of connectivity can reduce the size and quality of available habitat, impede and disrupt movement (including dispersal) to new habitats, and affect seasonal migration patterns. These changes can lead, in turn, to detrimental effects for populations and species, including decreased carrying capacity, population declines, loss of genetic variation, and ultimately species extinction. Measuring and mapping connectivity is facilitated by a growing number of quantitative approaches that can integrate large amounts of information about organisms’ life histories, habitat quality, and other features essential to evaluating connectivity for a given population or species. However, identifying effective approaches for maintaining and restoring connectivity poses several challenges, and our understanding of how connectivity should be designed to mitigate the impacts of climate change is, as yet, in its infancy. Scientists and managers must confront and overcome several challenges inherent in evaluating and planning for connectivity, including: •characterizing the biology of focal species; •understanding the strengths and the limitations of the models used to evaluate connectivity; •considering spatial and temporal extent in connectivity planning; •using caution in extrapolating results outside of observed conditions; •considering non-linear relationships that can complicate assumed or expected ecological responses; •accounting and planning for anthropogenic change in the landscape; •using well-defined goals and objectives to drive the selection of methods used for evaluating and planning for connectivity; •and communicating to the general public in clear and meaningful language the importance of connectivity to improve awareness and strengthen policies for ensuring conservation. Several aspects of connectivity science deserve additional attention in order to improve the effectiveness of design and implementation. Research on species persistence, behavioral ecology, and community structure is needed to reduce the uncertainty associated with connectivity models. Evaluating and testing connectivity responses to climate change will be critical to achieving conservation goals in the face of the rapid changes that will confront many communities and ecosystems. All of these potential areas of advancement will fall short of conservation goals if we do not effectively incorporate human activities into connectivity planning. While this Issue identifies substantial uncertainties in mapping connectivity and evaluating resilience to climate change, it is also clear that integrating human and natural landscape conservation planning to enhance habitat connectivity is essential for biodiversity conservation