ALBERT

Description: Regional and local patterns in depth to water table, hydrochemistry and peat properties of bogs and their laggs in coastal British Columbia Hydrology and Earth System Sciences, 17, 3421-3435, 2013 Author(s): S. A. Howie and H. J. van Meerveld In restoration planning for damaged raised bogs, the lagg at the bog margin is often not given considerable weight and is sometimes disregarded entirely. However, the lagg is critical for the proper functioning of the bog, as it supports the water mound in the bog. In order to include the lagg in a restoration plan for a raised bog, it is necessary to understand the hydrological characteristics and functions of this rarely studied transition zone. We studied 13 coastal British Columbia (BC) bogs and identified two different gradients in depth to water table, hydrochemistry and peat properties: (1) a local bog expanse–bog margin gradient, and (2) a regional gradient related to climate and proximity to the ocean. Depth to water table generally increased across the transition from bog expanse to bog margin. In the bog expanse, pH was above 4.2 in the Pacific Oceanic wetland region (cooler and wetter climate) and below 4.3 in the Pacific Temperate wetland region (warmer and drier climate). Both pH and pH-corrected electrical conductivity increased significantly across the transition from bog expanse to bog margin, though not in all cases. Na + and Mg 2+ concentrations were generally highest in exposed, oceanic bogs and lower in inland bogs. Ash content in peat samples increased across the bog expanse–bog margin transition, and appears to be a useful abiotic indicator of the location of the bog margin. The observed variation in the hydrological and hydrochemical gradients across the bog expanse–bog margin transition highlights both local and regional diversity of bogs and their associated laggs.

Description: Imperfect scaling in distributions of radar-derived rainfall fields Hydrology and Earth System Sciences Discussions, 10, 11385-11422, 2013 Author(s): M. J. van den Berg, L. Delobbe, and N. E. C. Verhoest Fine scale rainfall observations for modeling exercises are often not available, but rather coarser data derived from a variety of sources are used. Effectively using these data sources in models often requires the probability distribution of the data at the applicable scale. Although numerous models for scaling distributions exist, these are often based on theoretical developments, rather than on data. In this study, we develop a model based on the α-stable distribution of rainfall fields, and tested on 5 min radar data from a Belgian weather radar. We use these data to estimate functions that describe parameters of the distribution over various scales. Moreover, we study how the mean of the distribution and the intermittency change with scale, and validate and design functions to describe the shape parameter of the distribution. This information was combined into an effective model of the distribution. Finally, the model was fitted to data from numerous storms, and the resulting parameters were compared to investigate the change in scaling behavior through time.

Description: Spatially resolved information on karst conduit flow from in-cave dye-tracing Hydrology and Earth System Sciences Discussions, 10, 11311-11335, 2013 Author(s): U. Lauber, W. Ufrecht, and N. Goldscheider Artificial tracers are powerful tools to investigate karst systems. Tracers are commonly injected into sinking streams or dolines, while springs serve as monitoring sites. The obtained flow and transport parameters represent mixed information from the vadose, epiphreatic and phreatic zones, i.e., the aquifer remains a black box. Accessible active caves constitute valuable but underexploited natural laboratories to gain detailed insights into the hydrologic functioning of the aquifer. Two multi-tracer tests in the catchment of a major karst spring (Blautopf, Germany) with injections and monitoring in two associated water caves aimed at obtaining spatially and temporally resolved information on groundwater flow in different compartments of the system. Two tracers were injected in the caves to characterize the hydraulic connections between them and with the spring. Two injections at the land surface, far from the spring, aimed at resolving the aquifer's internal drainage structure. Tracer breakthrough curves were monitored by field fluorimeters in caves and at the spring. Results demonstrate the dendritic drainage structure of the aquifer. It was possible to obtain relevant flow and transport parameters for different sections of this system. The highest mean flow velocities (275 m h −1 ) were observed in the near-spring epiphreatic section (open-channel flow), while velocities in the phreatic zone (pressurized flow) were one order of magnitude lower. Determined conduit water volumes confirm results of water balances and hydrograph analyses. In conclusion, experiments and monitoring in caves can deliver spatially resolved information on karst aquifer heterogeneity and dynamics that cannot be obtained by traditional investigative methods.

Description: On the lack of robustness of hydrologic models regarding water balance simulation – a diagnostic approach on 20 mountainous catchments using three models of increasing complexity Hydrology and Earth System Sciences Discussions, 10, 11337-11383, 2013 Author(s): L. Coron, V. Andréassian, C. Perrin, M. Bourqui, and F. Hendrickx This paper investigates the robustness of rainfall–runoff models when their parameters are transferred in time. More specifically, we studied their ability to simulate water balance on periods with different hydroclimatic characteristics. The testing procedure consisted in a series of parameter transfers between 10-yr periods and the systematic analysis of mean-volume errors. This procedure was applied to three conceptual models of different structural complexity over 20 mountainous catchments in southern France. The results showed that robustness problems are common. Errors on 10-yr-mean flows were significant for all three models and calibration periods, even when the entire record was used for calibration. Various graphical and numerical tools were used to show strong similarities between the shapes of mean flow biases calculated on a 10-yr-long sliding window when various parameter sets are used. Unexpected behavioural similarities were observed between the three models tested, considering their large differences in structural complexity. While the actual causes for robustness problems in these models remain unclear, this work stresses the limited transferability in time of the water balance adjustments made through parameter optimization. Although absolute differences between simulations obtained with different calibrated parameter sets were sometimes substantial, relative differences in simulated mean flows between time periods remained similar regardless of the calibrated parameter sets.

Description: Bayesian networks modelling in support to cross-cutting analysis of water supply and sanitation in developing countries Hydrology and Earth System Sciences, 17, 3397-3419, 2013 Author(s): C. Dondeynaz, J. López Puga, and C. Carmona Moreno Despite the efforts made towards the Millennium Development Goals targets during the last decade, improved access to water supply or basic sanitation still remains unavailable for millions of people across the world. This paper proposes a set of models that use 25 key variables and country profiles from the WatSan4Dev data set involving water supply and sanitation (Dondeynaz et al., 2012). This paper suggests the use of Bayesian network modelling methods because they are more easily adapted to deal with non-normal distributions, and integrate a qualitative approach for data analysis. They also offer the advantage of integrating preliminary knowledge into the probabilistic models. The statistical performance of the proposed models ranges between 20 and 5% error rates, which are very satisfactory taking into account the strong heterogeneity of variables. Probabilistic scenarios run from the models allow an assessment of the relationships between human development, external support, governance aspects, economic activities and water supply and sanitation (WSS) access. According to models proposed in this paper, gaining a strong poverty reduction will require the WSS access to reach 75–76% through: (1) the management of ongoing urbanisation processes to avoid slums development; and (2) the improvement of health care, for instance for children. Improving governance, such as institutional efficiency, capacities to make and apply rules, or control of corruption is positively associated with WSS sustainable development. The first condition for an increment of the HDP (human development and poverty) remains of course an improvement of the economic conditions with higher household incomes. Moreover, a significant country commitment to the environment, associated with civil society freedom of expression constitutes a favourable setting for sustainable WSS services delivery. Intensive agriculture using irrigation practises also appears as a mean for sustainable WSS thanks to multi-uses and complementarities. With a WSS sector organised at national level, irrigation practices can support the structuring and efficiency of the agriculture sector. It may then induce rural development in areas where WSS access often is set back compared to urban areas 1 . External financial support, called Official Development Assistance (ODA CI), plays a role in WSS improvement but comes last in the sensitivity analyses of models. An overall 47% of the Official Development Assistance goes first to poor countries, and is associated to governance aspects: (1) political stability and (2) country commitment to the environment and civil society degree of freedom. These governance aspects constitute a good framework for aid implementation in recipient countries. Modelling is run with the five groups of countries as defined in Dondeynaz et al. (2012). Models for profile 4 (essential external support) and profile 5 (primary material consumption) are specifically detailed and analysed in this paper. For countries in profile 4, fighting against water scarcity and progressing desertification should be the priority. However, for countries in profile 5, efforts should first concentrate on consolidation of political stability while supporting diversification of the economic activities. Nevertheless, for both profiles, reduction of poverty should remain the first priority as previously indicated. 1 JMP statistics, 2004 http://www.wssinfo.org/data-estimates/table/ , last access: 22 July 2013.

Description: Technical Note: A comparison of model and empirical measures of catchment-scale effective energy and mass transfer Hydrology and Earth System Sciences, 17, 3389-3395, 2013 Author(s): C. Rasmussen and E. L. Gallo Recent work suggests that a coupled effective energy and mass transfer (EEMT) term, which includes the energy associated with effective precipitation and primary production, may serve as a robust prediction parameter of critical zone structure and function. However, the models used to estimate EEMT have been solely based on long-term climatological data with little validation using direct empirical measures of energy, water, and carbon balances. Here we compare catchment-scale EEMT estimates generated using two distinct approaches: (1) EEMT modeled using the established methodology based on estimates of monthly effective precipitation and net primary production derived from climatological data, and (2) empirical catchment-scale EEMT estimated using data from 86 catchments of the Model Parameter Estimation Experiment (MOPEX) and MOD17A3 annual net primary production (NPP) product derived from Moderate Resolution Imaging Spectroradiometer (MODIS). Results indicated positive and significant linear correspondence ( R 2 = 0.75; P 〈 0.001) between model and empirical measures with an average root mean square error (RMSE) of 4.86 MJ m −2 yr −1 . Modeled EEMT values were consistently greater than empirical measures of EEMT. Empirical catchment estimates of the energy associated with effective precipitation ( E PPT ) were calculated using a mass balance approach that accounts for water losses to quick surface runoff not accounted for in the climatologically modeled E PPT . Similarly, local controls on primary production such as solar radiation and nutrient limitation were not explicitly included in the climatologically based estimates of energy associated with primary production ( E BIO ), whereas these were captured in the remotely sensed MODIS NPP data. These differences likely explain the greater estimate of modeled EEMT relative to the empirical measures. There was significant positive correlation between catchment aridity and the fraction of EEMT partitioned into E BIO ( F BIO ), with an increase in F BIO as a fraction of the total as aridity increases and percentage of catchment woody plant cover decreases. In summary, the data indicated strong correspondence between model and empirical measures of EEMT with limited bias that agree well with other empirical measures of catchment energy and water partitioning and plant cover.

Description: Review Article: On the relation between the seismic activity and the Hurst exponent of the geomagnetic field at the time of the 2000 Izu swarm Natural Hazards and Earth System Science, 13, 2189-2194, 2013 Author(s): F. Masci and J. N. Thomas Many papers document the observation of earthquake-related precursory signatures in geomagnetic field data. However, the significance of these findings is ambiguous because the authors did not adequately take into account that these signals could have been generated by other sources, and the seismogenic origin of these signals have not been validated by comparison with independent datasets. Thus, they are not reliable examples of magnetic disturbances induced by the seismic activity. Hayakawa et al. (2004) claim that at the time of the 2000 Izu swarm the Hurst exponent of the Ultra-Low-Frequency (ULF: 0.001–10 Hz) band of the geomagnetic field varied in accord with the energy released by the seismicity. The present paper demonstrates that the behaviour of the Hurst exponent was insufficiently investigated and also misinterpreted by the authors. We clearly show that during the Izu swarm the changes of the Hurst exponent were strongly related to the level of global geomagnetic activity and not to the increase of the local seismic activity.

Description: Forest fire danger rating in complex topography – results from a case study in the Bavarian Alps in autumn 2011 Natural Hazards and Earth System Science, 13, 2157-2167, 2013 Author(s): C. Schunk, C. Wastl, M. Leuchner, C. Schuster, and A. Menzel Forest fire danger rating based on sparse meteorological stations is known to be potentially misleading when assigned to larger areas of complex topography. This case study examines several fire danger indices based on data from two meteorological stations at different elevations during a major drought period. This drought was caused by a persistent high pressure system, inducing a pronounced temperature inversion and its associated thermal belt with much warmer, dryer conditions in intermediate elevations. Thus, a massive drying of fuels, leading to higher fire danger levels, and multiple fire occurrences at mid-slope positions were contrasted by moderate fire danger especially in the valleys. The ability of fire danger indices to resolve this situation was studied based on a comparison with the actual fire danger as determined from expert observations, fire occurrences and fuel moisture measurements. The results revealed that, during temperature inversion, differences in daily cycles of meteorological parameters influence fire danger and that these are not resolved by standard meteorological stations and fire danger indices (calculated on a once-a-day basis). Additional stations in higher locations or high-resolution meteorological models combined with fire danger indices accepting at least hourly input data may allow reasonable fire danger calculations under these circumstances.

Description: Preface "Landslide hazard and risk assessment at different scales" Natural Hazards and Earth System Science, 13, 2169-2171, 2013 Author(s): P. Reichenbach, A. Günther, and T. Glade

Description: Antecedent flow conditions and nitrate concentrations in the Mississippi River Basin Hydrology and Earth System Sciences Discussions, 10, 11451-11484, 2013 Author(s): J. C. Murphy, R. M. Hirsch, and L. A. Sprague The influence of antecedent flow conditions on nitrate concentrations was explored at eight sites in the Mississippi River Basin, USA. Antecedent moisture conditions have been shown to influence nutrient export from small, relatively homogenous basins, but this influence has not been observed at a regional or continental scale. Antecedent flow conditions were quantified as the ratio between the mean daily flow of the previous year and the mean daily flow from the period of record ( Q ratio), and the Q ratio was statistically related to nitrate anomalies (the unexplained variability in nitrate concentration after filtering out season, long-term trend, and contemporaneous flow effects) at each site. Nitrate anomaly and Q ratio were negatively related at three of the four major tributary sites and upstream in the Mississippi River, indicating that when the previous year was drier than average, at these sites, nitrate concentrations were higher than expected. The strength of these relationships increased when data were subdivided by contemporaneous flow conditions. Five of the eight sites had significant negative relationships ( p ≤ 0.05) at high or moderately high contemporaneous flows, suggesting nitrate that accumulates in these basins during a drought is flushed during subsequent storm events. At half of the sites, when flow during the previous year was 50% drier than average, nitrate concentration can be from 9 and 27% higher than nitrate concentrations that follow a year with average daily flow. Conversely, nitrate concentration can be from 8 and 21% lower than expected when the previous year was 50% wetter than average. These relationships between nitrate concentration and Q ratio serve as the basis for future studies that can better define specific hydrologic processes occurring during and after a drought, which influence nitrate concentration, such as the duration or magnitude of low flows, and the timing of low and high flows.

Description: Tidally induced velocity variations of the Beardmore Glacier, Antarctica, and their representation in satellite measurements of ice velocity The Cryosphere, 7, 1375-1384, 2013 Author(s): O. J. Marsh, W. Rack, D. Floricioiu, N. R. Golledge, and W. Lawson Ocean tides close to the grounding line of outlet glaciers around Antarctica have been shown to directly influence ice velocity, both linearly and non-linearly. These fluctuations can be significant and have the potential to affect satellite measurements of ice discharge, which assume displacement between satellite passes to be consistent and representative of annual means. Satellite observations of horizontal velocity variation in the grounding zone are also contaminated by vertical tidal effects, the importance of which is highlighted here in speckle tracking measurements. Eight TerraSAR-X scenes from the grounding zone of the Beardmore Glacier are analysed in conjunction with GPS measurements to determine short-term and decadal trends in ice velocity. Diurnal tides produce horizontal velocity fluctuations of 〉50% on the ice shelf, recorded in the GPS data 4 km downstream of the grounding line. This variability decreases rapidly to 〈5% only 15 km upstream of the grounding line. Daily fluctuations are smoothed to 〈1% in the 11-day repeat pass TerraSAR-X imagery, but fortnightly variations over this period are still visible and show that satellite-velocity measurements can be affected by tides over longer periods. The measured tidal displacement observed in radar look direction over floating ice also allows the grounding line to be identified, using differential speckle tracking where phase information cannot be easily unwrapped.

Description: Contribution of snow and glacier melt to discharge for highly glacierised catchments in Norway Hydrology and Earth System Sciences Discussions, 10, 11485-11517, 2013 Author(s): M. Engelhardt, T. V. Schuler, and L. M. Andreassen Glacierised catchments significantly alter the streamflow regime due to snow and glacier meltwater contribution to discharge. In this study, we modelled the mass balance and discharge rates for three highly glacierised catchments (〉50% glacier cover) in western Norway over the period 1961–2012. The spatial pattern of the catchments follows a gradient in climate continentality from west to east. The model uses gridded temperature and precipitation values from seNorge ( http://senorge.no ) as input which are available at a daily resolution. It accounts for accumulation of snow, transformation of snow to firn and ice, evaporation and melt. The model was calibrated for each catchment based on measurements of seasonal glacier mass-balances and daily discharge rates. For validation, daily melt rates were compared with measurements from sonic rangers located in the ablation zones of two of the glaciers and an uncertainty analysis was performed for the third catchment. The discharge contributions from snowmelt, glacier melt and rain were analysed with respect to spatial variations and temporal evolution. The model simulations reveal an increase of the relative contribution from glacier melt for the three catchments from less than 10% in the early 1990s to 15–30% in the late 2000s. The decline in precipitation by 10–20% in the same period was therefore overcompensated resulting in an increase of the annual discharge by 5–20%. Annual discharge sums and annual glacier melt are strongest correlated with annual and winter precipitation at the most maritime glacier and, with increased climate continentality, variations in both glacier melt contribution and annual discharge are becoming stronger correlated with variations in summer temperatures.

Description: The tension between the meaning of causality in science and law or public policy is well-known; however, defendants in product liability cases or industries that might be affected by a government regulation may try to convince the factfinder to require evidence of a causal relationship that meets the standards of science. From the perspective of public health, however, people may be exposed unnecessarily to a health risk during the time period between the establishment of reasonably strong evidence of a causal relationship and the overwhelming evidence required for scientific causality. The Bayesian paradigm enables one to update information from epidemiologic studies as they accumulate, providing estimates of the probability that the relative risk of a particular harm from exposure exceeds a threshold value, e.g. 2.0 or 4.0 that is sufficient to meet the preponderance of the evidence standard or to support a health initiative. In order to diminish the role of the initial prior distribution, which may be quite subjective, the first case-control study or an analysis of adverse event and case reports is used to determine two prior distributions. One is the most favourable to the defendant, or industry that might be regulated, which is consistent with the previous data. The other is centred on or near the estimated relative risk from the first study. The method is applied to the studies that linked aspirin use to Reye syndrome and demonstrates that the evidence of a causal association was sufficiently strong in 1982, when the Food and Drug Administration first proposed that the public be warned of the risk, to support the regulation. Thus, lives would have been saved had the warning been given at the end of 1982 rather than in early 1985.

Description: In law, inferences of causation are sometimes made through a structured process in which multiple participants play various roles, and make decisions concerning various logical components of the overall inference (such as legal rules, policy objectives, presumptions, evidence, burdens of proof and findings of fact). This article illustrates such a process using empirical research into compensation decisions in the USA for injuries allegedly caused by vaccinations. Empirical research into actual legal processes is essential, in order to discover how various players approach their sub-tasks of decision-making. It also provides insights for areas outside of law, such as non-monotonic logic, cognitive science, sociology and artificial intelligence.

Description: Situations of causal factual uncertainty are relatively common in law. The problems and difficulties regarding ‘factual causation’ in law point to the need of ‘evidence’ and ‘proof’ models that are adequate and capable to accommodate the tests and methodologies used to explain and demonstrate it in a legal context. Given the configuration of the situations of causal factual uncertainty and the available ‘evidence’ and ‘proof’ models, I argue that it is justified to use an ‘argumentative-narrative’ model for ‘proving causation’ in law. However, considering that each model of ‘evidence’ and ‘proof’ reveals a different kind of ‘rationality’ that can still be viewed in different ways, I also argue that we must try to match the perspective we have on the ‘rationality’ behind the chosen model of ‘evidence’ and ‘proof’ with the ‘rationality’ underlying ‘causation’ in law.

Description: At least in some cases, the values confronted in legal decision-making appear to be incommensurable. Some legal theorists resist incommensurability because they fear that this presents an overwhelming obstacle to rational decision-making. By offering a close analysis of proportionality and, more particularly, measures of proportional value satisfaction, I show that this fear is unfounded. Comparative measures of proportional value satisfaction do not require the values to be commensurable. However, assuming incommensurability presents us with the problem of public significance in the proportional satisfaction of values. When two values are commensurable, this public significance is provided by the mediating effects of the overarching third value that provides the common measure of the values. However, when this common measure is removed, then the public significance of value satisfaction must be otherwise achieved. This is why I propose an equal proportional value satisfaction as the most appropriate proportionality maximand. Under equal proportional value satisfaction, the proportional satisfaction of any one value has significance for each and every other value. This kind of public significance is interpersonal rather than impersonal (or second-personal rather than third-personal). The article then shows that the legal process that is most appropriate to equal proportionality is a process that implements defeasible legal rules.

Description: In order to allocate the risk between parties in legal adjudication, we use evidentiary techniques with the main device among them being the standard of proof (SoP). The traditional view holds the grade of probability to be the parameter that shifts when moving to different standards. However, as soon as we dig slightly deeper, an incoherent picture is being revealed. In this article, I challenge the accepted view and try to show that it faces insurmountable problems concerning the rationality, the grammatical consistency and the impact of the SoP for the acceptability of verdicts. At the end of the article, I shortly discuss the theory of epistemological contextualism and propose a framework that allows rational distinctions to be drawn between different standards of proof. In the second part of this project (forthcoming), I will defend a contextualist view according to which shifting parameter is not the grade of (aleatory) probability, but instead the Set of Epistemic Defeaters in play.

Description: Decadal trends in the Antarctic sea ice extent ultimately controlled by ice-ocean feedback The Cryosphere Discussions, 7, 4585-4632, 2013 Author(s): H. Goosse and V. Zunz The large natural variability of the Antarctic sea ice is a key characteristic of the system that might be responsible for the small positive trend in sea ice extent observed since 1979. In order to gain insight in the processes responsible for this variability, we have analysed in a control simulation performed with a coupled climate model a strong positive ice-ocean feedback that amplifies sea ice variations. When sea ice concentration increases in a region, in particular close to the ice edge, the mixed layer depth tends to decrease. This can be caused by a net inflow of ice and thus of freshwater that stabilizes the water column. Another stabilizing mechanism at interannual time scales that appears more widespread in our simulation is associated with the downward salt transport due to the seasonal cycle of ice formation: brine is released in winter when ice is formed and mixed over a deep layer while the freshwater flux caused by ice melting is included in a shallow layer, resulting in a net vertical transport of salt. Because of this stronger stratification due to the presence of sea ice, more heat is stored at depth in the ocean and the vertical oceanic heat flux is reduced, which contributes to maintain a higher ice extent. This positive feedback is not associated with a particular spatial pattern. Consequently, the spatial distribution of the trend in ice concentration is largely imposed by the wind changes that can provide the initial perturbation. A positive freshwater flux could alternatively be the initial trigger but the amplitude of the final response of the sea ice extent is finally set up by the amplification related to ice-ocean feedback. Initial conditions have also an influence as the chance to have a large increase in ice extent is higher if starting from a state characterized by a low value.

Description: The aim of this paper is to study the relations between the Hausdorff dimensions of k -quasilines and the theory of extremal quasiconformal mappings. We show that there is an open and dense subset (Strebel points) of the universal Teichmüller space T (H) such that, for every [ f ] in the set, the Hausdorff dimension of the k -quasiline determined by [ f ] is strictly less than 1 + k 2 . We also show that there are some points [ f ] != [id] outside the open and dense set in the universal Teichmüller space such that the Hausdorff dimension of the quasiline determined by [ f ] is 1. Moreover, some results on the Hausdorff dimensions of the quasilines varying in the asymptotic Teichmüller space are also obtained.

Description: A new uniqueness result for a general n th order differential equation is obtained. We show that some previous results follow immediately from our theorem.

Description: Consider a discrete uniformly elliptic divergence form equation on the d ≥3 dimensional lattice Z d with random coefficients. In Conlon and Spencer [ Trans. Amer. Math. Soc. , http://www.math.lsa.umich.edu/~conlon/paper/hom10.pdf ], rate of convergence results in homogenization and estimates on the difference between the averaged Green's function and the homogenized Green's function for random environments which satisfy a Poincaré inequality were obtained. Here, these results are extended to certain environments in which correlations can have arbitrarily small power law decay. These environments are simply related via a convolution to environments which do satisfy a Poincaré inequality.

Description: In this paper, we prove that, for any a , M N with ( a , M ) = 1, there are infinitely many Carmichael numbers m such that m a mod M .

Description: We give a topological analogue for openness of a criterion for flatness that originates with Auslander. Over a normal base of dimension n , failure of openness is detected by a vertical component in the n th fibred power of the morphism.

Description: Investigated are regular maps from real algebraic varieties into real Fermat varieties. It is proved that under some natural assumptions, all such maps are null homotopic.

Description: Let ( M , g ) be a complete non-compact Riemannian manifold. We consider operators of the form g + V , where g is the non-negative Laplacian associated with the metric g , and V a locally integrable function. Let be a Riemannian covering, with Laplacian g and potential . If the operator + V is non-negative on ( M , g ), then the operator is non-negative on . In this note, we show that the converse statement is true provided that is a co-amenable subgroup of 1 ( M ).

Description: Peak interpolation is concerned with a foundational kind of mathematical task: building functions in a fixed algebra A , which have prescribed values or behaviour on a fixed closed subset (or on several disjoint subsets). In this paper, we do the same but now A is an algebra of operators on a Hilbert space. We briefly survey this noncommutative peak interpolation , which we have studied with coauthors in a long series of papers, and whose basic theory now appears to be approaching its culmination. This programme developed from, and is based partly on, theorems of Hay and Read whose proofs were spectacular, but therefore inaccessible to an uncommitted reader. We give short proofs of these results, using recent progress in noncommutative peak interpolation, and conversely give examples of the use of these theorems in peak interpolation. For example, we prove a useful new noncommutative peak interpolation theorem.

Description: We show how a parameterized family of maps of the spine of a manifold can be used to construct a family of homeomorphisms of the ambient manifold which have the inverse limits of the spine maps as global attractors. We describe applications to unimodal families of interval maps, to rotation sets, and to the standard family of circle maps.

Description: For every prime p , we give infinitely many examples of torsors under abelian varieties over Q that are locally trivial but not divisible by p in the Weil–Châtelet group. We also give an example of a locally trivial torsor under an elliptic curve over Q that is not divisible by 4 in the Weil–Châtelet group. This gives a negative answer to a question of Cassels.

Description: We show that at least of the zeros of the Riemann zeta-function are simple, assuming the Riemann hypothesis. This was previously established by Conrey, Ghosh and Gonek [ Proc. London Math. Soc. 76 (1998) 497–522] under the additional assumption of the generalized Lindelöf hypothesis. We are able to remove this hypothesis by careful use of the generalized Vaughan identity.

Description: We construct an infinite family of hyperbolic, homologically thin knots that are not quasi-alternating. To establish the latter, we argue that the branched double-cover of each knot in the family does not bound a negative-definite 4-manifold with trivial first homology and bounded second Betti number. This fact depends in turn on information from the correction terms in Heegaard Floer homology, which we establish by way of a relationship to, and calculation of, the Turaev torsion.

Description: We observe that E -resultant of a very ample rank 2 vector bundle E on a real projective curve (with no real points) is nonnegative when restricted to the space of real sections. Moreover, we show that if E has a section vanishing at exactly two points and the degree d of E satisfies d ( d – 6) ≥ 4( g – 1), then this polynomial cannot be written as a sum of squares.

Description: Let G be one of the Ricci-flat holonomy groups SU( n ), Sp( n ), Spin(7) or G 2 , and M a compact manifold of dimension 2 n , 4 n , 8 or 7, respectively. We prove that the natural map from the moduli space of torsion-free G -structures on M to the moduli space of Ricci-flat metrics is open, and that the image is a smooth manifold. For the exceptional cases G = Spin(7) and G 2 , we extend the result to asymptotically cylindrical manifolds.

Description: We improve the results of Booker and Krishnamurthy ( Compos. Math. 147 (2011) 669–715) by allowing restricted sets of poles among the unramified twists. This allows for a clean statement of the GL(2) converse theorem which includes all cases of Eisenstein series.

Description: Contribution of directly connected and isolated impervious areas to urban drainage network hydrographs Hydrology and Earth System Sciences, 17, 3473-3483, 2013 Author(s): Y. Seo, N.-J. Choi, and A. R. Schmidt This paper addresses the mass balance error observed in runoff hydrographs in urban watersheds by introducing assumptions regarding the contribution of infiltrated rainfall from pervious areas and isolated impervious area (IIA) to the runoff hydrograph. Rainfall infiltrating into pervious areas has been assumed not to contribute to the runoff hydrograph until Hortonian excess rainfall occurs. However, mass balance analysis in an urban watershed indicates that rainfall infiltrated to pervious areas can contribute directly to the runoff hydrograph, thereby offering an explanation for the long hydrograph tail commonly observed in runoff from urban storm sewers. In this study, a hydrologic analysis based on the width function is introduced, with two types of width functions obtained from both pervious and impervious areas, respectively. The width function can be regarded as the direct interpretation of the network response. These two width functions are derived to obtain distinct response functions for directly connected impervious areas (DCIA), IIA, and pervious areas. The results show significant improvement in the estimation of runoff hydrographs and suggest the need to consider the flow contribution from pervious areas to the runoff hydrograph. It also implies that additional contribution from flow paths through joints and cracks in sewer pipes needs to be taken into account to improve the estimation of runoff hydrographs in urban catchments.

Description: Let G be a solvable subgroup of the automorphism group Aut( X ) of a compact Kähler manifold X of complex dimension n , and let N ( G ) be the normal subgroup of G consisting of elements with null entropy. Let us denote by G * the image of G under the natural map from Aut( X ) to GL( V , R ), where V is the Dolbeault cohomology group H 1, 1 ( X , R ). Assume that the Zariski closure of G * in GL( V C ) is connected. The main aim of this paper is to show that, when the rank r ( G ) of the quotient group G / N ( G ) is equal to n – 1 and the identity component of Aut( X ) is trivial, then the normal subgroup N ( G ) of G is finite. This affirmatively answers a question in Invent. Math. posed by D.-Q. Zhang.

Description: Bias correction can modify climate model-simulated precipitation changes without adverse affect on the ensemble mean Hydrology and Earth System Sciences Discussions, 10, 11585-11611, 2013 Author(s): E. P. Maurer and D. W. Pierce When applied to remove climate model biases in precipitation, quantile mapping can in some settings modify the simulated trends. This has important implications when the precipitation will be used to drive an impacts model that is sensitive to changes in precipitation. We use daily precipitation output from 12 general circulation models (GCMs) over the conterminous United States interpolated to a common 1° grid, and gridded observations aggregated to the same scale, to compare precipitation differences before and after quantile mapping bias correction. The change in seasonal mean (winter, DJF, and summer, JJA) precipitation between different 30-yr historical periods is compared to examine (1) the consensus among GCMs as to whether the bias correction tends to amplify or diminish their simulated precipitation trends, and (2) whether the modification of the change in precipitation tends to improve or degrade the correspondence to observed changes in precipitation for the same periods. In some cases, for a particular GCM, the trend modification can be as large as the original simulated change, though the areas where this occurs varies among GCMs so the ensemble median shows smaller trend modification. In specific locations and seasons the trend modification by quantile mapping improves correspondence with observed trends, and in others it degrades it. In the majority of the domain the ensemble median is for little effect on the correspondence of simulated precipitation trends with observed. This highlights the need to use an ensemble of GCMs rather than relying on a small number of models to estimate impacts.

Description: Linking ICT and society in early warning and adaptation to hydrological extremes in mountains Natural Hazards and Earth System Science, 13, 2253-2270, 2013 Author(s): C. de Jong The assessment of the societal impact of hydrological extremes is particularly important in mountain regions, since mountains can be considered both as the generators and victims of extreme events. ICT can provide a powerful tool for transmitting hydro-meteorological information to predict, prepare and adapt to such events. However, in remote regions, such as mountains, the poles, deserts and islands, preventive and adaptive measures are often restricted by data availability and lack and/or incoherence of data networks. This paper distinguishes between early warning of floods and droughts, emphasising the latter in particular in mountains and explores the possibilities of enhancing the role of society in data collection, the identification, activation and application of stakeholder knowledge and transferral of data from gauged to ungauged catchments.

Description: This paper deals with the boundary control problems for the system described by first-order hyperbolic partial integro-differential equations with nonlocal boundary conditions by means of the deformation formulas. It is shown that the associated operator with nonlocal terms generates a C 0 -semigroup and the system defines an abstract boundary control system in L 2 -space. On the basis of the construction of integral kernel function, the ordinal and evolutional deformation formulas are established for a general class of Volterra integro-differential equations with nonlocal terms. By applying a special form of the formulas, a design of feedback boundary control law is given, which makes the scalar boundary control system null controllable in finite time. Furthermore, the null controllability result is extended to coupled nonsymmetric first-order hyperbolic systems by using appropriate linear transformations. Applications to physically important coupled systems are also given.

Description: Snow on the Ross Ice Shelf: comparison of reanalyses and observations from automatic weather stations The Cryosphere, 7, 1399-1410, 2013 Author(s): L. Cohen and S. Dean Snow accumulation measurements from automatic weather stations (AWS) around the Ross Ice Shelf (RIS), Antarctica, are used to provide a new set of ground-based observations which are compared to precipitation from the ECMWF ERA-Interim and NCEP/NCAR Reanalysis-2 datasets. The high temporal resolution of the AWS snow accumulation measurements allow for an event-based comparison of reanalyses precipitation to the in situ observations. Snow accumulation records from nine AWS provide multiple years of accumulation data between 2008 and 2012 over a relatively large, homogeneous region of Antarctica, and also provide the basis for a statistical evaluation of accumulation and precipitation events. The complex effects of wind on snow accumulation (which can both limit and enhance accumulation) complicate the use of the accumulation measurements, but this analysis shows that they can provide a valuable source of ground-based observations for comparisons to modelled precipitation on synoptic timescales. The analysis shows that ERA-Interim reproduces more precipitation events than NCEP-2, and these events correspond to an average 8.2% more precipitation. Significant correlations between reanalyses and AWS event sizes are seen at several stations and show that ERA-Interim consistently produces larger precipitation events than NCEP-2.

Description: The environmental impact of the Puyehue–Cordon Caulle 2011 volcanic eruption on Buenos Aires Natural Hazards and Earth System Science, 13, 2319-2330, 2013 Author(s): G. B. Raga, D. Baumgardner, A. G. Ulke, M. Torres Brizuela, and B. Kucienska On 4 June 2011, the volcanic complex Puyehue–Cordon Caulle located in the Chilean Andes erupted, producing a plume of gases and particles that eventually circled the Southern Hemisphere, disrupting air travel and depositing ash in large quantities. On eight occasions, the plume passed over the city of Buenos Aires, Argentina, leading local authorities to close the two international airports. The eruption occurred during an on-going field campaign when measurements of the properties of atmospheric aerosol particles were being made in Buenos Aires as part of a year-long study of the concentration and optical properties of aerosol at one site in the city. The suite of instruments deployed in Buenos Aires were not tailored to measurements of volcanic ash, but were designed to characterize urban conditions. Nevertheless, these measurements were analysed for periods when vertical profiles of aerosol backscatter, made with a ceilometer, clearly showed the presence of the volcano plume over the research site and resulted in airport closure. Aerosol optical thickness derived from AERONET, MODIS and a ceilometer at our research site, all show enhanced values clearly indicating that the three platforms identified the volcanic plume simultaneously. However, a quantitative comparison of the different estimates proves difficult, suggesting large spatial and temporal variability of the plume. Our results indicate that the number concentration of condensation nuclei (CN), the mass concentration of particle-bound polycyclic aromatic hydrocarbons (PPAH) and the light absorption coefficient exceeded the average background values by more than one standard deviation during the events of volcanic plume. The anomalous concentrations of CN suggest new particle formation, presumably from the conversion of SO 2 , while the anomalous concentrations of PPAH may come from the uptake of PAHs on the plume particles or from chemical reactions on the surface of plume particles. The anomalous absorption coefficients indicate that plume particles may contain certain compounds that can absorb radiation at 550 nm. Another possible explanation consistent with the observations is the scavenging of black carbon from urban sources as the plume descends through the boundary layer to the surface. In addition, the volcanic plume influenced the local meteorology resulting in a decrease of the temperature when compared to the average temperature during days with no plume present.

Description: Contribution of land use changes to future flood damage along the river Meuse in the Walloon region Natural Hazards and Earth System Science, 13, 2301-2318, 2013 Author(s): A. Beckers, B. Dewals, S. Erpicum, S. Dujardin, S. Detrembleur, J. Teller, M. Pirotton, and P. Archambeau Managing flood risk in Europe is a critical issue because climate change is expected to increase flood hazard in many european countries. Beside climate change, land use evolution is also a key factor influencing future flood risk. The core contribution of this paper is a new methodology to model residential land use evolution. Based on two climate scenarios ("dry" and "wet"), the method is applied to study the evolution of flood damage by 2100 along the river Meuse. Nine urbanization scenarios were developed: three of them assume a "current trend" land use evolution, leading to a significant urban sprawl, while six others assume a dense urban development, characterized by a higher density and a higher diversity of urban functions in the urbanized areas. Using damage curves, the damage estimation was performed by combining inundation maps for the present and future 100 yr flood with present and future land use maps and specific prices. According to the dry scenario, the flood discharge is expected not to increase. In this case, land use changes increase flood damages by 1–40%, to €334–462 million in 2100. In the wet scenario, the relative increase in flood damage is 540–630%, corresponding to total damages of €2.1–2.4 billion. In this extreme scenario, the influence of climate on the overall damage is 3–8 times higher than the effect of land use change. However, for seven municipalities along the river Meuse, these two factors have a comparable influence. Consequently, in the "wet" scenario and at the level of the whole Meuse valley in the Walloon region, careful spatial planning would reduce the increase in flood damage by no more than 11–23%; but, at the level of several municipalities, more sustainable spatial planning would reduce future flood damage to a much greater degree.

Description: A general treatment of snow microstructure exemplified by an improved relation for thermal conductivity The Cryosphere, 7, 1473-1480, 2013 Author(s): H. Löwe, F. Riche, and M. Schneebeli Finding relevant microstructural parameters beyond density is a longstanding problem which hinders the formulation of accurate parameterizations of physical properties of snow. Towards a remedy, we address the effective thermal conductivity tensor of snow via anisotropic, second-order bounds. The bound provides an explicit expression for the thermal conductivity and predicts the relevance of a microstructural anisotropy parameter Q , which is given by an integral over the two-point correlation function and unambiguously defined for arbitrary snow structures. For validation we compiled a comprehensive data set of 167 snow samples. The set comprises individual samples of various snow types and entire time series of metamorphism experiments under isothermal and temperature gradient conditions. All samples were digitally reconstructed by micro-computed tomography to perform microstructure-based simulations of heat transport. The incorporation of anisotropy via Q considerably reduces the root mean square error over the usual density-based parameterization. The systematic quantification of anisotropy via the two-point correlation function suggests a generalizable route to incorporate microstructure into snowpack models. We indicate the inter-relation of the conductivity to other properties and outline a potential impact of Q on dielectric constant, permeability and adsorption rate of diffusing species in the pore space.

Description: Arguments need to be judged against other arguments. The decision to accept or reject an argument is generally a global decision that involves examining the same question for other arguments that oppose or can defend the argument in question. This article presents the acceptability semantics for abstract argumentation that through a recursive definition gives a global assignment of the acceptable and non-acceptable subsets of arguments. This semantics stems from the aim to formalize directly the generally accepted intuition that: ‘An argument can be accepted if and only if all its challenging arguments can be rejected.’ The acceptability semantics tightly integrates the notion of defending against a challenging argument by counter-attacking it with the notion of self-defeating (or self-rejecting) arguments that (help to) bring about their own non-acceptability. The proposal is motivated by earlier studies of the semantics of Logic Programming (LP) in terms of argumentation, where the basic well founded and stable model semantics of LP can be uniformly captured using a recursively defined argumentation semantics for Negation as Failure and where these standard semantics of LP can be further extended through argumentation.

Description: This article is concerned with the design and analysis of polynomial time algorithms for determining whether a Planar Quantified Integer Program (PQIP) is feasible. A PQIP can be described briefly as an integer program involving two variables, in which each variable can be either universally or existentially quantified. There are four types of PQIPs, depending on how the variables are quantified (existentially or universally). In this article, we present two new, simple, and efficient algorithms for the case as well as a detailed account of the complexity of the other cases. Moreover, we discuss certification with respect to the provided algorithms.

Description: In the present article, the quantifiers over propositions are first introduced into the language for reasoning about probability, then the complexity issues for validity problems dealing with the corresponding hierarchy of probabilistic sentences are investigated. We prove, among other things, the $${\Pi }_{1}^{1}$$ -completeness for the general validity and also indicate the least level in the hierarchy for which the validity problem is undecidable.

Description: We use mosaics to provide a simple, sound, complete and terminating tableau reasoning procedure for the temporal logic of until and since over general linear time.

Description: The aim of what semantic science is to have scientific ontologies, data and hypotheses represented and published in machine understandable forms that enable predictions on new cases. There is much work on developing scientific ontologies and representing scientific data in terms of these ontologies. The next step is to publish hypotheses that can make (probabilistic) predictions on the published data and can be used for prediction on new cases. The published data can be used to evaluate hypotheses. To make a prediction in a particular case, hypotheses are combined to form models. This article considers feature-based semantic science where the data and new cases are described in terms of features. A prediction for a new case is made by building a model made up of hypotheses that fit together, are consistent with the ontologies used, and are adequate for the case. We give some desiderata for such models, and show how the construction of such models is a form of abduction. We provide a definition for models that satisfies these criteria and prove that it produces a coherent probability distribution over the values of interest.

Description: In this article we present methods of transition from one perspective on logic to others, and apply this in particular to obtain a coalgebraic presentation of logic. The central ingredient in this process is to view consequence relations as morphisms in a category.

Description: We consider the expressive power of the first-order structure 〈, C 〉 where is either of two of different domains of extended regions in Euclidean space, and C(x,y) is the topological relation ‘Region x is in contact with region y .’ We prove two main theorems: Let $$\mathcal{P}$$ [Q] be the domain of bounded, non-empty, rational polyhedra in two- or three-dimensional Euclidean space. A relation over $$\mathcal{P}$$ [Q] is definable in the structure 〈 $$\mathcal{P}$$ [Q], C 〉 if and only if is arithmetic and invariant under rational PL-homeomorphisms of the space to itself. We also extend this result to a number of other domains, including the domain of all polyhedra and the domain of semi-algebraic regions. Let $$\mathcal{R}$$ be the space of bounded, non-empty, closed regular regions in n -dimensional Euclidean space. Any analytical relation over lower dimensional (i.e. empty interior) compact point sets that is invariant under homeomorphism is implicitly definable in the structure 〈 $$\mathcal{R}$$ , C 〉.

Description: We give explicit atomic bases of arbitrary coefficient-free cluster algebras of types A and à . This entails showing that the minimal elements of the positive semiring of these cluster algebras form a linear basis over the integers for the cluster algebra.

Description: We prove that strongly F -regular and F -pure singularities satisfy Bertini-type theorems (including in the context of pairs) by building upon a framework of Cumino, Greco and Manaresi (compare with the work of Jouanolou and Spreafico). We also prove that F -injective singularities fail to satisfy even the most basic Bertini-type results.

Description: This is the second of a pair of papers on the Delta-group structure on the braid and mapping class groups of a surface. We obtain a description of the homotopy groups of these Delta-groups and generalize to an arbitrary surface the Berrick–Cohen–Wong–Wu exact sequence relating the Brunnian braid groups of the 2-sphere to its homotopy groups. We prove a similar result for Brunnian mapping class groups.

Description: We construct a geometric realization of the Khovanov–Lauda–Rouquier algebra R associated with a symmetric Borcherds–Cartan matrix A = ( a ij ) i , j I via quiver varieties. As an application, if a ii != 0 for any i I , we prove that there exists a one-to-one correspondence between Kashiwara's lower global basis (or Lusztig's canonical basis) of U A – (g) (respectively, V A ( )) and the set of isomorphism classes of indecomposable projective graded modules over R (respectively, R ).

Description: The purpose of this paper is to study the nature of quasi-invariant measures for finitely generated non-discrete subgroups of Diff ( S 1 ). For this, we apply ideas involving the closure of these groups to find out that the regularity of the measure depends on a ‘measurable version’ of well-known problems concerning stable self-intersection of Cantor sets. As applications, we prove that every d -quasiconformal probability measure for a non-solvable and non-discrete group must be absolutely continuous. Concerning singular quasi-invariant measures, it is also proved that their associated Hausdorff measures must either be zero or of infinite mass, a result contrasting with the case of dynamically defined Cantor sets and also applicable to the examples of singular stationary measures constructed by Kaimanovich and Le Prince. As a further application of our methods, a theorem of rigidity for measurable conjugations between groups as above is obtained.

Description: We study the space of period polynomials associated with modular forms of integral weight for finite-index subgroups of the modular group. For the modular group, this space is endowed with a pairing, corresponding to the Petersson inner product on modular forms via a formula of Haberland, and with an action of Hecke operators, defined algebraically by Zagier. We generalize Haberland's formula to (not necessarily cuspidal) modular forms for finite-index subgroups, and we show that it conceals two stronger formulas. We extend the action of Hecke operators to period polynomials of modular forms, we show that the pairing on period polynomials appearing in Haberland's formula is nondegenerate, and we determine the adjoints of Hecke operators with respect to it. We give a few applications for 1 ( N ): an extension of the Eichler–Shimura isomorphism to the entire space of modular forms; the determination of the relations satisfied by the even and odd parts of period polynomials associated with cusp forms, which are independent of the period relations; and an explicit formula for Fourier coefficients of Hecke eigenforms in terms of their period polynomials, generalizing the Coefficient theorem of Manin.

Description: Influence of high-order mechanics on simulation of glacier response to climate change: insights from Haig Glacier, Canadian Rocky Mountains The Cryosphere, 7, 1527-1541, 2013 Author(s): S. Adhikari and S. J. Marshall Evolution of glaciers in response to climate change has mostly been simulated using simplified dynamical models. Because these models do not account for the influence of high-order physics, corresponding results may exhibit some biases. For Haig Glacier in the Canadian Rocky Mountains, we test this hypothesis by comparing simulation results obtained from 3-D numerical models that deal with different assumptions concerning physics, ranging from simple shear deformation to comprehensive Stokes flow. In glacier retreat scenarios, we find a minimal role of high-order mechanics in glacier evolution, as geometric effects at our site (the presence of an overdeepened bed) result in limited horizontal movement of ice (flow speed on the order of a few meters per year). Consequently, high-order and reduced models all predict that Haig Glacier ceases to exist by ca. 2080 under ongoing climate warming. The influence of high-order mechanics is evident, however, in glacier advance scenarios, where ice speeds are greater and ice dynamical effects become more important. Although similar studies on other glaciers are essential to generalize such findings, we advise that high-order mechanics are important and therefore should be considered while modeling the evolution of active glaciers. Reduced model predictions may be adequate for other glaciologic and topographic settings, particularly where flow speeds are low and where mass balance changes dominate over ice dynamics in determining glacier geometry.

Description: Meteorological drivers of ablation processes on a cold glacier in the semi-arid Andes of Chile The Cryosphere, 7, 1513-1526, 2013 Author(s): S. MacDonell, C. Kinnard, T. Mölg, L. Nicholson, and J. Abermann Meteorological and surface change measurements collected during a 2.5 yr period are used to calculate surface mass and energy balances at 5324 m a.s.l. on Guanaco Glacier, a cold-based glacier in the semi-arid Andes of Chile. Meteorological conditions are marked by extremely low vapour pressures (annual mean of 1.1 hPa), strong winds (annual mean of 10 m s −1 ), shortwave radiation receipt persistently close to the theoretical site maximum during cloud-free days (mean annual 295 W m −2 ; summer hourly maximum 1354 W m −2 ) and low precipitation rates (mean annual 45 mm w.e.). Snowfall occurs sporadically throughout the year and is related to frontal events in the winter and convective storms during the summer months. Net shortwave radiation provides the greatest source of energy to the glacier surface, and net longwave radiation dominates energy losses. The turbulent latent heat flux is always negative, which means that the surface is always losing mass via sublimation, which is the main form of ablation at the site. Sublimation rates are most strongly correlated with net shortwave radiation, incoming shortwave radiation, albedo and vapour pressure. Low glacier surface temperatures restrict melting for much of the period, however episodic melting occurs during the austral summer, when warm, humid, calm and high pressure conditions restrict sublimation and make more energy available for melting. Low accumulation (131 mm w.e. over the period) and relatively high ablation (1435 mm w.e.) means that mass change over the period was negative (−1304 mm w.e.), which continued the negative trend recorded in the region over the last few decades.

Description: Antarctic ice-mass balance 2003 to 2012: regional reanalysis of GRACE satellite gravimetry measurements with improved estimate of glacial-isostatic adjustment based on GPS uplift rates The Cryosphere, 7, 1499-1512, 2013 Author(s): I. Sasgen, H. Konrad, E. R. Ivins, M. R. Van den Broeke, J. L. Bamber, Z. Martinec, and V. Klemann We present regional-scale mass balances for 25 drainage basins of the Antarctic Ice Sheet (AIS) from satellite observations of the Gravity and Climate Experiment (GRACE) for time period January 2003 to September 2012. Satellite gravimetry estimates of the AIS mass balance are strongly influenced by mass movement in the Earth interior caused by ice advance and retreat during the last glacial cycle. Here, we develop an improved glacial-isostatic adjustment (GIA) estimate for Antarctica using newly available GPS uplift rates, allowing us to more accurately separate GIA-induced trends in the GRACE gravity fields from those caused by current imbalances of the AIS. Our revised GIA estimate is considerably lower than previous predictions, yielding an estimate of apparent mass change of 53 ± 18 Gt yr −1 . Therefore, our AIS mass balance of −114 ± 23 Gt yr −1 is less negative than previous GRACE estimates. The northern Antarctic Peninsula and the Amundsen Sea sector exhibit the largest mass loss (−26 ± 3 Gt yr −1 and −127 ± 7 Gt yr −1 , respectively). In contrast, East Antarctica exhibits a slightly positive mass balance (26 ± 13 Gt yr −1 ), which is, however, mostly the consequence of compensating mass anomalies in Dronning Maud and Enderby Land (positive) and Wilkes and George V Land (negative) due to interannual accumulation variations. In total, 6% of the area constitutes about half the AIS imbalance, contributing 151 ± 7 Gt yr −1 (ca. 0.4 mm yr −1 ) to global mean sea-level change. Most of this imbalance is caused by ice-dynamic speed-up expected to prevail in the near future.

Description: This study develops a spectral theory of the interior transmission problem (ITP) for heterogeneous and anisotropic elastic solids. The subject is central to the so-called qualitative methods for inverse scattering involving penetrable obstacles. Although simply stated as a coupled pair of elastodynamic wave equations, the ITP for elastic bodies is neither self-adjoint nor elliptic. To help deal with such impediments, earlier studies have established the well-posedness of an elastodynamic ITP under notably restrictive assumptions on the contrast in elastic and mass density parameters between the scatterer and the background solid. Due to lack of self-adjointness of the problem, these analyses were further successful in substantiating the discreteness of the relevant eigenvalue spectrum but not its existence. The aim of this work is to provide a systematic treatment of the ITP for elastic bodies that transcends the limitations of earlier analyses. Considering a broad range of material-contrast configurations, this paper investigates the questions of the solvability of the ITP, the discreteness of its eigenvalues and, for the first time, of the existence of such eigenvalue spectrum. Necessitated by the breadth of material configurations studied, the relevant claims are established via a suite of variational formulations, each customized to meet the needs of a particular subclass of eigenvalue problems.

Description: Rayleigh–Stokes problems have in recent years received much attention due to their importance in physics. In this article, we focus on the variable-order Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative. Implicit and explicit numerical methods are developed to solve the problem. The convergence, stability of the numerical methods and solvability of the implicit numerical method are discussed via Fourier analysis. Moreover, a numerical example is given and the results support the effectiveness of the theoretical analysis.

Description: The effect of training image and secondary data integration with multiple-point geostatistics in groundwater modeling Hydrology and Earth System Sciences Discussions, 10, 11829-11860, 2013 Author(s): X. He, T. O. Sonnenborg, F. Jørgensen, and K. H. Jensen Multiple-point geostatistic simulation (MPS) has recently become popular in stochastic hydrogeology, primarily because of its capability to derive multivariate distributions from the training image (TI). However, its application in three dimensional simulations has been constrained by the difficulty of constructing 3-D TI. The object-based TiGenerator may be a useful tool in this regard; yet the sensitivity of model predictions to the training image has not been documented. Another issue in MPS is the integration of multiple geophysical data. The best way to retrieve and incorporate information from high resolution geophysical data is still under discussion. This work shows that TI from TiGenerator delivers acceptable results when used for groundwater modeling, although the TI directly converted from high resolution geophysical data leads to better simulation. The model results also indicate that soft conditioning in MPS is a convenient and efficient way of integrating secondary data such as 3-D airborne electromagnetic data, but over conditioning has to be avoided.

Description: Multi-decadal river flows variations in France Hydrology and Earth System Sciences Discussions, 10, 11861-11900, 2013 Author(s): J. Boé and F. Habets In this article, multi-decadal variations in French hydroclimate are investigated, with a specific focus on river flows. Based on long observed series, it is shown that river flows in France generally exhibit large multi-decadal variations on the historical period, especially in spring. Differences of means between two 21 yr periods of the 20th century as large as 40% are indeed found for many gauging stations. Multi-decadal spring river flows variations are associated with variations in spring precipitation and temperature. These multi-decadal variations in precipitation are themselves found to be driven by large-scale atmospheric circulation, more precisely by a multi-decadal oscillation in a sea level pressure dipole between western Europe and the East Atlantic. It is suggested that the Atlantic Multidecadal Variability, the main mode of decadal variability in the North Atlantic/Europe sector, controls those variations in large-scale circulation and is therefore the main ultimate driver of multi-decadal variations in spring river flows. Multi-decadal variations in river flows in other seasons, and in particular summer, are also noted. As they are not associated with significant surface climate anomalies (i.e. temperature, precipitation) in summer, other mechanisms are investigated based on hydrological simulations. The impact of climate variations in spring on summer soil moisture, and the impact of soil moisture in summer on the runoff to precipitation ratio, could potentially play a role in multi-decadal summer river flows variations. The large amplitude of the multi-decadal variations in French river flows suggests that internal variability may play a very important role in the evolution of river flows during the next decades, potentially temporarily limiting, reversing or seriously aggravating the long-term impacts of anthropogenic climate change.

Description: In this paper, the rigorous linking of exact stochastic models to mean-field approximations is studied. Using a continuous-time Markov chain, we start from the exact formulation of a simple epidemic model on a certain class of networks, including completely connected and regular random graphs, and rigorously derive the well-known mean-field approximation that is usually justified based on biological hypotheses. We propose a unifying framework that incorporates and discusses the details of two existing proofs and we put forward a new ordinary differential equation (ODE)-based proof. The more well-known proof is based on a first-order partial differential equation approximation, while the other, more technical one, uses Martingale and Semigroup theory. We present the main steps of both proofs to investigate their applicability in different modelling contexts and to make these ideas more accessible to a broader group of applied researchers. The main result of the paper is a new ODE-based proof that may serve as a building block to prove similar convergence results for more complex networks. The new proof is based on deriving a countable system of ODEs for the moments of a distribution of interest and proving a perturbation theorem for this infinite system.

Description: In this paper, we extend certain key results from the classical theory of isotropic elasticity to the generalized theory of elasticity for decagonal quasicrystaline composites. These results include: (i) the dependence of the solution on the number of elastic constants, (ii) Green's functions for bimaterials consisting of two bonded half-planes, (iii) Green's functions for a circular elastic inclusion, (iv) the oscillatory singular stress field in the vicinity of an interface crack tip and (v) the inverse problem corresponding to the design of harmonic shapes.

Description: The note develops an approximate approach to mixed boundary value problems in linear elasticity starting from an explicit asymptotic model for the Rayleigh surface wave. It is demonstrated that the original vector mixed problem may be reduced to a scalar problem for the Laplace equation. As an illustration, the steady-state motion of a rigid stamp is analysed. Comparison of asymptotic and exact results is presented.

Description: Estimating soil suction from electrical resistivity Natural Hazards and Earth System Science, 13, 2369-2379, 2013 Author(s): E. Piegari and R. Di Maio Soil suction and resistivity strongly depend on the degree of soil saturation and, therefore, both are used for estimating water content variations. The main difference between them is that soil suction is measured using tensiometers, which give point information, while resistivity is obtained by tomography surveys, which provide distributions of resistivity values in large volumes, although with less accuracy. In this paper, we have related soil suction to electrical resistivity with the aim of obtaining information about soil suction changes in large volumes, and not only for small areas around soil suction probes. We derived analytical relationships between soil matric suction and electrical resistivity by combining the empirical laws of van Genuchten and Archie. The obtained relationships were used to evaluate maps of soil suction values in different ashy layers originating in the explosive activity of the Mt Somma-Vesuvius volcano (southern Italy). Our findings provided a further example of the high potential of geophysical methods in contributing to more effective monitoring of soil stress conditions; this is of primary importance in areas where rainfall-induced landslides occur periodically.

Description: A data set of world-wide glacier length fluctuations The Cryosphere Discussions, 7, 4775-4811, 2013 Author(s): P. W. Leclercq, J. Oerlemans, H. J. Basagic, I. Bushueva, A. J. Cook, and R. Le Bris Glacier fluctuations contribute to variations in sea level and historical glacier length fluctuations are natural indicators of climate change. To study these subjects, long-term information of glacier change is needed. In this paper we present a~data set of global long-term glacier length fluctuations. The data set is a compilation of available information on changes in glacier length world-wide, including both measured and reconstructed glacier length fluctuations. All 471 length series start before 1950 and cover at least four decades. The longest record starts in 1534, but the majority of time series start after 1850. The number of available records decreases again after 1962. The data set has global coverage including records from all continents. However, the Canadian Arctic is not represented in the data set. The glacier length series show relatively small fluctuations until the mid-19th century followed by a global retreat that was strongest in the first half of the 20th century, although large variability in the length change of the different glaciers is observed. During the 20th century, calving glaciers retreated more than land terminating glaciers, but their relative length change was approximately equal. Besides calving, the glacier slope is the most important glacier property determining length change: steep glaciers have retreated less than glaciers with a gentle slope.

Description: An original interpretation of the wet edge of the surface temperature–albedo space to estimate crop evapotranspiration (SEB-1S), and its validation over an irrigated area in northwestern Mexico Hydrology and Earth System Sciences, 17, 3623-3637, 2013 Author(s): O. Merlin The space defined by the pair surface temperature ( T ) and surface albedo (α), and the space defined by the pair T and fractional green vegetation cover ( f vg ) have been extensively used to estimate evaporative fraction (EF) from solar/thermal remote sensing data. In both space-based approaches, evapotranspiration (ET) is estimated as remotely sensed EF times the available energy. For a given data point in the T -α space or in the T - f vg space, EF is derived as the ratio of the distance separating the point from the line identified as the dry edge to the distance separating the dry edge and the line identified as the wet edge. The dry and wet edges are classically defined as the upper and lower limit of the spaces, respectively. When investigating side by side the T -α and the T - f vg spaces, one observes that the range covered by T values on the (classically determined) wet edge is different for both spaces. In addition, when extending the wet and dry lines of the T -α space, both lines cross at α ≈ 0.4 although the wet and dry edges of the T - f vg space never cross for 0 ≤ f vg 〈 1. In this paper, a new ET (EF) model (SEB-1S) is derived by revisiting the classical physical interpretation of the T -α space to make its wet edge consistent with that of the T - f vg space. SEB-1S is tested over a 16 km by 10 km irrigated area in northwestern Mexico during the 2007–2008 agricultural season. The classical T -α space-based model is implemented as benchmark to evaluate the performance of SEB-1S. Input data are composed of ASTER (Advanced Spaceborne Thermal Emission and Reflection radiometer) thermal infrared, Formosat-2 shortwave, and station-based meteorological data. The fluxes simulated by SEB-1S and the classical T -α space-based model are compared on seven ASTER overpass dates with the in situ measurements collected at six locations within the study domain. The ET simulated by SEB-1S is significantly more accurate and robust than that predicted by the classical T -α space-based model. The correlation coefficient and slope of the linear regression between simulated and observed ET is improved from 0.82 to 0.93, and from 0.63 to 0.90, respectively. Moreover, constraining the wet edge using air temperature data improves the slope of the linear regression between simulated and observed ET.

Description: Teleconnection analysis of runoff and soil moisture over the Pearl River basin in South China Hydrology and Earth System Sciences Discussions, 10, 11943-11982, 2013 Author(s): J. Niu, J. Chen, and B. Sivakumar This study explores the teleconnection of two climatic patterns, namely the El Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD), with hydrological processes over the Pearl River basin in South China. The Variable Infiltration Capacity (VIC) model is used to simulate the daily hydrological processes over the basin for the study period 1952–2000, and then, using the simulation results, the time series of the monthly runoff and soil moisture anomalies for its ten sub-basins are aggregated. Wavelet analysis is performed to explore the variability properties of these time series at 49 timescales ranging from 2 months to 9 yr. Use of wavelet coherence and rank correlation method reveals that the dominant variabilities of the time series of runoff and soil moisture are basically correlated with IOD. The influences of ENSO on the terrestrial hydrological processes are mainly found in the eastern sub-basins. The teleconnections between climatic patterns and hydrological variability also serve as a reference basis for inferences on the occurrence of extreme hydrological events (e.g. floods and droughts).

Description: On an improved sub-regional water resources management representation for integration into earth system models Hydrology and Earth System Sciences, 17, 3605-3622, 2013 Author(s): N. Voisin, H. Li, D. Ward, M. Huang, M. Wigmosta, and L. R. Leung Human influence on the hydrologic cycle includes regulation and storage, consumptive use and overall redistribution of water resources in space and time. Representing these processes is essential for applications of earth system models in hydrologic and climate predictions, as well as impact studies at regional to global scales. Emerging large-scale research reservoir models use generic operating rules that are flexible for coupling with earth system models. Those generic operating rules have been successful in reproducing the overall regulated flow at large basin scales. This study investigates the uncertainties of the reservoir models from different implementations of the generic operating rules using the complex multi-objective Columbia River Regulation System in northwestern United States as an example to understand their effects on not only regulated flow but also reservoir storage and fraction of the demand that is met. Numerical experiments are designed to test new generic operating rules that combine storage and releases targets for multi-purpose reservoirs and to compare the use of reservoir usage priorities and predictors (withdrawals vs. consumptive demands, as well as natural vs. regulated mean flow) for configuring operating rules. Overall the best performing implementation is with combined priorities rules (flood control storage targets and irrigation release targets) set up with mean annual natural flow and mean monthly withdrawals. The options of not accounting for groundwater withdrawals, or on the contrary, of assuming that all remaining demand is met through groundwater extractions, are discussed.

Description: We show the existence and uniqueness of a solution for the nonlocal vector-valued Allen–Cahn variational inequality in a formulation involving Lagrange multipliers for local and nonlocal constraints. Furthermore, we propose and analyse a primal–dual active set (PDAS) method for local and nonlocal vector-valued Allen–Cahn variational inequalities. The local convergence behaviour of the PDAS algorithm is studied by interpreting the approach as a semismooth Newton method and numerical simulations are presented demonstrating its efficiency.

Description: In this paper, we will present a generalized convolution quadrature for solving linear parabolic and hyperbolic evolution equations. The original convolution quadrature method by Lubich works very nicely for equidistant time steps while the generalization of the method and its analysis to nonuniform time stepping is by no means obvious. We will introduce the generalized convolution quadrature allowing for variable time steps and develop a theory for its error analysis. This method opens the door for further development towards adaptive time stepping for evolution equations. As the main application of our new theory, we will consider the wave equation in exterior domains which is formulated as a retarded boundary integral equation.

Description: On selection of the optimal data time interval for real-time hydrological forecasting Hydrology and Earth System Sciences, 17, 3639-3659, 2013 Author(s): J. Liu and D. Han With the advancement in modern telemetry and communication technologies, hydrological data can be collected with an increasingly higher sampling rate. An important issue deserving attention from the hydrological community is which suitable time interval of the model input data should be chosen in hydrological forecasting. Such a problem has long been recognised in the control engineering community but is a largely ignored topic in operational applications of hydrological forecasting. In this study, the intrinsic properties of rainfall–runoff data with different time intervals are first investigated from the perspectives of the sampling theorem and the information loss using the discrete wavelet transform tool. It is found that rainfall signals with very high sampling rates may not always improve the accuracy of rainfall–runoff modelling due to the catchment low-pass-filtering effect. To further investigate the impact of a data time interval in real-time forecasting, a real-time forecasting system is constructed by incorporating the probability distributed model (PDM) with a real-time updating scheme, the autoregressive moving-average (ARMA) model. Case studies are then carried out on four UK catchments with different concentration times for real-time flow forecasting using data with different time intervals of 15, 30, 45, 60, 90 and 120 min. A positive relation is found between the forecast lead time and the optimal choice of the data time interval, which is also highly dependent on the catchment concentration time. Finally, based on the conclusions from the case studies, a hypothetical pattern is proposed in three-dimensional coordinates to describe the general impact of the data time interval and to provide implications of the selection of the optimal time interval in real-time hydrological forecasting. Although nowadays most operational hydrological systems still have low data sampling rates (daily or hourly), the future is that higher sampling rates will become more widespread, and there is an urgent need for hydrologists both in academia and in the field to realise the significance of the data time interval issue. It is important that more case studies in different catchments with various hydrological forecasting systems are explored in the future to further verify and improve the proposed hypothetical pattern.

Description: We address the error control of Galerkin discretization (in space) of linear second-order hyperbolic problems. More specifically, we derive a posteriori error bounds in the L ( L 2 ) norm for finite element methods for the linear wave equation, under minimal regularity assumptions. The theory is developed for both the space-discrete case and for an implicit fully discrete scheme. The derivation of these bounds relies crucially on carefully constructed space and time reconstructions of the discrete numerical solutions, in conjunction with a technique introduced by Baker (1976, Error estimates for finite element methods for second-order hyperbolic equations. SIAM J. Numer. Anal. , 13 , 564–576) in the context of a priori error analysis of Galerkin discretization of the wave problem in weaker-than-energy spatial norms.

Description: The surface finite element method can be used to approximate curvatures on embedded hypersurfaces and to discretize geometric partial differential equations. In this paper, we present a definition of discrete Ricci curvature on polyhedral hypersurfaces of arbitrary dimension based on the discretization of a weak formulation with isoparametric finite elements. We prove that for a piecewise quadratic approximation of a two- or three-dimensional hypersurface R n +1 , this definition approximates the Ricci curvature of with a linear order of convergence in the L 2 ( ) norm. By using a smoothing scheme in the case of a piecewise linear approximation of , we still get a convergence of order 2/3 in the L 2 ( ) norm and of order 1/3 in the W 1, 2 ( ) norm.

Description: We give general conditions which guarantee that the sequence generated by a descent algorithm converges to an equilibrium point. The convergence result is based on the Lojasiewicz gradient inequality; optimal convergence rates are also derived, as well as a stability result. We show how our results apply to a large variety of standard time discretizations of gradient-like flows. Schemes with variable time step are considered and optimal conditions on the maximal step size are derived. Applications to time and space discretizations of the Allen–Cahn equation, the sine–Gordon equation and a damped wave equation are given.

Description: This paper presents quadratic finite-volume methods for elliptic and parabolic problems on quadrilateral meshes that use Barlow points (optimal stress points) for dual partitions. Introducing Barlow points into the finite-volume formulations results in better approximation properties at the cost of loss of symmetry. The novel ‘symmetrization’ technique adopted in this paper allows us to derive optimal-order error estimates in the H 1 - and L 2 -norms for elliptic problems and in the L ( H 1 )- and L ( L 2 )-norms for parabolic problems. Superconvergence of the difference between the gradients of the finite-volume solution and the interpolant can also be derived. Numerical results confirm the proved error estimates.

Description: A linear parabolic differential equation on a moving surface is discretized in space by evolving-surface finite elements and in time by backward difference formulas (BDFs). Using results from Dahlquist's G-stability theory and Nevanlinna & Odeh's multiplier technique together with properties of the spatial semidiscretization, stability of the full discretization is proved for BDF methods up to order 5 and optimal-order convergence is shown. Numerical experiments illustrate the behaviour of the fully discrete method.

Description: In this article, we develop the a priori and a posteriori error analysis of hp -version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain R d , d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp -adaptive refinement algorithm.

Description: In recent years, it has become increasingly clear that the critical issue in gradient methods is the choice of the step length, whereas using gradient as the search direction may lead to very effective algorithms, whose surprising behaviour has only been partially explained, mostly in terms of the spectrum of the Hessian matrix. On the other hand, the convergence of the classical Cauchy steepest descent (SD) method has been analysed extensively and related to the spectral properties of the Hessian matrix, but the connection with the spectrum of the Hessian has not been exploited much to modify the method in order to improve its behaviour. In this work, we show how, for convex quadratic problems, moving from some theoretical properties of the SD method, second-order information provided by the step length can be exploited to dramatically improve the usually poor practical behaviour of this method. This allows us to achieve computational results comparable with those of the Barzilai and Borwein algorithm, with the further advantage of monotonic behaviour.

Description: Benchmark products for land evapotranspiration: LandFlux-EVAL multi-data set synthesis Hydrology and Earth System Sciences, 17, 3707-3720, 2013 Author(s): B. Mueller, M. Hirschi, C. Jimenez, P. Ciais, P. A. Dirmeyer, A. J. Dolman, J. B. Fisher, M. Jung, F. Ludwig, F. Maignan, D. G. Miralles, M. F. McCabe, M. Reichstein, J. Sheffield, K. Wang, E. F. Wood, Y. Zhang, and S. I. Seneviratne Land evapotranspiration (ET) estimates are available from several global data sets. Here, monthly global land ET synthesis products, merged from these individual data sets over the time periods 1989–1995 (7 yr) and 1989–2005 (17 yr), are presented. The merged synthesis products over the shorter period are based on a total of 40 distinct data sets while those over the longer period are based on a total of 14 data sets. In the individual data sets, ET is derived from satellite and/or in situ observations (diagnostic data sets) or calculated via land-surface models (LSMs) driven with observations-based forcing or output from atmospheric reanalyses. Statistics for four merged synthesis products are provided, one including all data sets and three including only data sets from one category each (diagnostic, LSMs, and reanalyses). The multi-annual variations of ET in the merged synthesis products display realistic responses. They are also consistent with previous findings of a global increase in ET between 1989 and 1997 (0.13 mm yr −2 in our merged product) followed by a significant decrease in this trend (−0.18 mm yr −2 ), although these trends are relatively small compared to the uncertainty of absolute ET values. The global mean ET from the merged synthesis products (based on all data sets) is 493 mm yr −1 (1.35 mm d −1 ) for both the 1989–1995 and 1989–2005 products, which is relatively low compared to previously published estimates. We estimate global runoff (precipitation minus ET) to 263 mm yr −1 (34 406 km 3 yr −1 ) for a total land area of 130 922 000 km 2 . Precipitation, being an important driving factor and input to most simulated ET data sets, presents uncertainties between single data sets as large as those in the ET estimates. In order to reduce uncertainties in current ET products, improving the accuracy of the input variables, especially precipitation, as well as the parameterizations of ET, are crucial.

Description: Spatial patterns in timing of the diurnal temperature cycle Hydrology and Earth System Sciences, 17, 3695-3706, 2013 Author(s): T. R. H. Holmes, W. T. Crow, and C. Hain This paper investigates the structural difference in timing of the diurnal temperature cycle (DTC) over land resulting from choice of measuring device or model framework. It is shown that the timing can be reliably estimated from temporally sparse observations acquired from a constellation of low Earth-orbiting satellites given record lengths of at least three months. Based on a year of data, the spatial patterns of mean DTC timing are compared between temperature estimates from microwave Ka-band, geostationary thermal infrared (TIR), and numerical weather prediction model output from the Global Modeling and Assimilation Office (GMAO). It is found that the spatial patterns can be explained by vegetation effects, sensing depth differences and more speculatively the orientation of orographic relief features. In absolute terms, the GMAO model puts the peak of the DTC on average at 12:50 local solar time, 23 min before TIR with a peak temperature at 13:13 (both averaged over Africa and Europe). Since TIR is the shallowest observation of the land surface, this small difference represents a structural error that possibly affects the model's ability to assimilate observations that are closely tied to the DTC. The equivalent average timing for Ka-band is 13:44, which is influenced by the effect of increased sensing depth in desert areas. For non-desert areas, the Ka-band observations lag the TIR observations by only 15 min, which is in agreement with their respective theoretical sensing depth. The results of this comparison provide insights into the structural differences between temperature measurements and models, and can be used as a first step to account for these differences in a coherent way.

Description: I begin by drawing a parallel between the intuitionistic understanding of quantification over all natural numbers and the generality relativist understanding of quantification over absolutely everything. I then argue that adoption of an intuitionistic reading of relativism not only provides an immediate reply to the absolutist's charge of incoherence but it also throws a new light on the debates surrounding absolute generality.

Description: In Plato's Phaedrus , Socrates offers two speeches, the first portraying madness as mere disease, the second celebrating madness as divine inspiration. Each speech is correct, says Socrates, though neither is complete. The two kinds of madness are like the left and right sides of a living body: no account that focuses on just one half can be adequate. In a recent paper, Hugh Benson gives a left-handed speech about a psychic condition endemic among mathematicians: dianoia . Benson acknowledges that his account is one-sided, but only hints at the virtues of right-handed dianoia . This note sketches a somewhat fuller picture.

Description: In a recent paper, Aidan Lyon and Mark Colyvan have proposed an explanation of the structure of the bee's honeycomb based on the mathematical Honeycomb Conjecture. This explanation has instantly become one of the standard examples in the philosophical debate on mathematical explanations of physical phenomena. In this critical note, I argue that the explanation is not scientifically adequate. The reason for this is that the explanation fails to do justice to the essentially three-dimensional structure of the bee's honeycomb.

Description: Hilary Putnam first published the consistency objection against Ludwig Wittgenstein’s account of mathematics in 1979. In 1983, Putnam and Benacerraf raised this objection against all conventionalist accounts of mathematics. I discuss the 1979 version and the scenario argument, which supports the key premise of the objection. The wide applicability of this objection is not apparent; I thus raise it against an imaginary axiomatic theory T similar to Peano arithmetic in all relevant aspects. I argue that a conventionalist can explain the consistency of T and suggest that an analogous explanation can be provided for the consistency of Peano arithmetic.

Description: In this paper I examine some difficulties with the argument presented as a topological sorites in Z. Weber and M. Colyvan, ‘A topological sorites’, Journal of Philosophy 107, 311–325. In particular, I suggest that the argument may be used to support the claim that sorites-type paradoxes cannot arise in a cohesive environment.

Description: Mistaken reasons for thinking diagrammatic proofs aren't rigorous are explored. The main result is that a confusion between the contents of a proof procedure (what's expressed by the referential elements in a proof procedure) and the unarticulated mathematical aspects of a proof procedure (how that proof procedure is enabled) gives the impression that diagrammatic proofs are less rigorous than language proofs. An additional (and independent) factor is treating the impossibility of naturally generalizing a diagrammatic proof procedure as an indication of lack of rigor.

Description: This paper examines the ontological commitments of the second-order language of arithmetic and argues that they do not extend beyond the first-order language. Then, building on an argument by George Boolos, we develop a Tarski-style definition of a truth predicate for the second-order language of arithmetic that does not involve the assignment of sets to second-order variables but rather uses the same class of assignments standardly used in a definition for the first-order language.

Description: This note has three goals. First, we discuss a presentation of Bertrand's paradox in a recent issue of Philosophia Mathematica , which we believe to be a subtle but important misinterpretation of the problem. We compare claims made about Bertrand with his 1889 Calcul des Probabilités . Second, we use this source to understand Bertrand's true intention in describing what we now call his paradox, comparing it both to another problem he describes in the same section and to a modern treatment. Finally, we briefly consider the importance of knowing when a specific example represents a general case.