Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size

This paper analyzes whether standard covariance matrix tests work whendimensionality is large, and in particular larger than sample size. Inthe latter case, the singularity of the sample covariance matrix makeslikelihood ratio tests degenerate, but other tests based on quadraticforms of sample covariance matrix eigenvalues remain well-defined. Westudy the consistency property and limiting distribution of these testsas dimensionality and sample size go to infinity together, with theirratio converging to a finite non-zero limit. We find that the existingtest for sphericity is robust against high dimensionality, but not thetest for equality of the covariance matrix to a given matrix. For thelatter test, we develop a new correction to the existing test statisticthat makes it robust against high dimensionality.

Detection of recurrence of large-bowel carcinoma by radioimmunoassay of circulating carcinoembryonic antigen (C.E.A.).

The usefulness and limitations of the carcinoembryonic antigen (C.E.A.) radioimmunoassay for the evaluation of tumour resection and for the detection of tumour relapse were studied in patients with large-bowel carcinoma. The level of plasma-C.E.A. was determined before any treatment in a group of 101 patients with histologically proven adenocarcinoma of the colon and rectum. 71% of all patients and 63% of cases with localised tumour (Dukes A and B) had a preoperative C.E.A. value of 5 ng. per ml. or higher. This limit was reached by only 1 of 90 apparently healthy, non-smoking blood-donors. Among 45 patients for whom a complete tumour resection was reported, all patients except 5 showed a drop of C.E.A. to normal values after surgery. The 5 patients whose C.E.A. did not fall to below 5 ng. per ml. showed a subsequent rise in C.E.A. level and were all found later to have a tumour relapse. The results indicate that an incomplete drop of circulating C.E.A. level one month after surgery has a bad prognostic significance. 22 of these patients were followed up by repeated C.E.A. radioimmunoassay for several months after surgery. 8 showed a progressive increase in C.E.A. levels preceding clinical diagnosis of tumour relapse by two to ten months. 6 other patients showed a moderate increase in C.E.A. levels, suggesting a tumour relapse not yet clinically detectable. The remaining 8 patients showed no increase in C.E.A. level above 5 ng. per ml. and no clinical symptoms of relapse. The results demonstrate that relapses of colon and rectum carcinoma can be detected by increased C.E.A. levels months before the appearance of any clinical evidence.

Cosmic rays as probes of large extra dimensions and TeV gravity

If there are large extra dimensions and the fundamental Planck scale is at the TeV scale, then the question arises of whether ultrahigh energy cosmic rays might probe them. We study the neutrino-nucleon cross section in these models. The elastic forward scattering is analyzed in some detail, hoping to clarify earlier discussions. We also estimate the black hole production rate. We study energy loss from graviton mediated interactions and conclude that they cannot explain the cosmic ray events above the GZK energy limit. However, these interactions could start horizontal air showers with characteristic profile and at a rate higher than in the standard model.

Large deviations for stochastic Volterra equations

This paper is devoted to prove a large-deviation principle for solutions to multidimensional stochastic Volterra equations.

Spectral analysis and limit behaviours in a spring-mass system

We consider a model for a damped spring-mass system that is a strongly damped wave equation with dynamic boundary conditions. In a previous paper we showed that for some values of the parameters of the model, the large time behaviour of the solutions is the same as for a classical spring-mass damper ODE. Here we use spectral analysis to show that for other values of the parameters, still of physical relevance and related to the effect of the spring inner viscosity, the limit behaviours are very different from that classical ODE

Importance of abiotic stress as a range-limit determinant for European plants: insights from species' responses to climatic gradients

Aim We examined whether species occurrences are primarily limited by physiological tolerance in the abiotically more stressful end of climatic gradients (the asymmetric abiotic stress limitation (AASL) hypothesis) and the geographical predictions of this hypothesis: abiotic stress mainly determines upper-latitudinal and upper-altitudinal species range limits, and the importance of abiotic stress for these range limits increases the further northwards and upwards a species occurs. Location Europe and the Swiss Alps. Methods The AASL hypothesis predicts that species have skewed responses to climatic gradients, with a steep decline towards the more stressful conditions. Based on presence-absence data we examined the shape of plant species responses (measured as probability of occurrence) along three climatic gradients across latitudes in Europe (1577 species) and altitudes in the Swiss Alps (284 species) using Huisman-Olff-Fresco, generalized linear and generalized additive models. Results We found that almost half of the species from Europe and one-third from the Swiss Alps showed responses consistent with the predictions of the AASL hypothesis. Cold temperatures and a short growing season seemed to determine the upper-latitudinal and upper-altitudinal range limits of up to one-third of the species, while drought provided an important constraint at lower-latitudinal range limits for up to one-fifth of the species. We found a biome-dependent influence of abiotic stress and no clear support for abiotic stress as a stronger upper range-limit determinant for species with higher latitudinal and altitudinal distributions. However, the overall influence of climate as a range-limit determinant increased with latitude. Main conclusions Our results support the AASL hypothesis for almost half of the studied species, and suggest that temperature-related stress controls the upper-latitudinal and upper-altitudinal range limits of a large proportion of these species, while other factors including drought stress may be important at the lower range limits.

Heuristics for the Critical Node Detection Problem in Large Complex Networks

Complex networks have recently attracted a significant amount of research attention due to their ability to model real world phenomena. One important problem often encountered is to limit diffusive processes spread over the network, for example mitigating pandemic disease or computer virus spread. A number of problem formulations have been proposed that aim to solve such problems based on desired network characteristics, such as maintaining the largest network component after node removal. The recently formulated critical node detection problem aims to remove a small subset of vertices from the network such that the residual network has minimum pairwise connectivity. Unfortunately, the problem is NP-hard and also the number of constraints is cubic in number of vertices, making very large scale problems impossible to solve with traditional mathematical programming techniques. Even many approximation algorithm strategies such as dynamic programming, evolutionary algorithms, etc. all are unusable for networks that contain thousands to millions of vertices. A computationally efficient and simple approach is required in such circumstances, but none currently exist. In this thesis, such an algorithm is proposed. The methodology is based on a depth-first search traversal of the network, and a specially designed ranking function that considers information local to each vertex. Due to the variety of network structures, a number of characteristics must be taken into consideration and combined into a single rank that measures the utility of removing each vertex. Since removing a vertex in sequential fashion impacts the network structure, an efficient post-processing algorithm is also proposed to quickly re-rank vertices. Experiments on a range of common complex network models with varying number of vertices are considered, in addition to real world networks. The proposed algorithm, DFSH, is shown to be highly competitive and often outperforms existing strategies such as Google PageRank for minimizing pairwise connectivity.

Large-scale surface mass balance of ice sheets from a comprehensive atmospheric model

The surface mass balance for Greenland and Antarctica has been calculated using model data from an AMIP-type experiment for the period 1979–2001 using the ECHAM5 spectral transform model at different triangular truncations. There is a significant reduction in the calculated ablation for the highest model resolution, T319 with an equivalent grid distance of ca 40 km. As a consequence the T319 model has a positive surface mass balance for both ice sheets during the period. For Greenland, the models at lower resolution, T106 and T63, on the other hand, have a much stronger ablation leading to a negative surface mass balance. Calculations have also been undertaken for a climate change experiment using the IPCC scenario A1B, with a T213 resolution (corresponding to a grid distance of some 60 km) and comparing two 30-year periods from the end of the twentieth century and the end of the twenty-first century, respectively. For Greenland there is change of 495 km3/year, going from a positive to a negative surface mass balance corresponding to a sea level rise of 1.4 mm/year. For Antarctica there is an increase in the positive surface mass balance of 285 km3/year corresponding to a sea level fall by 0.8 mm/year. The surface mass balance changes of the two ice sheets lead to a sea level rise of 7 cm at the end of this century compared to end of the twentieth century. Other possible mass losses such as due to changes in the calving of icebergs are not considered. It appears that such changes must increase significantly, and several times more than the surface mass balance changes, if the ice sheets are to make a major contribution to sea level rise this century. The model calculations indicate large inter-annual variations in all relevant parameters making it impossible to identify robust trends from the examined periods at the end of the twentieth century. The calculated inter-annual variations are similar in magnitude to observations. The 30-year trend in SMB at the end of the twenty-first century is significant. The increase in precipitation on the ice sheets follows closely the Clausius-Clapeyron relation and is the main reason for the increase in the surface mass balance of Antarctica. On Greenland precipitation in the form of snow is gradually starting to decrease and cannot compensate for the increase in ablation. Another factor is the proportionally higher temperature increase on Greenland leading to a larger ablation. It follows that a modest increase in temperature will not be sufficient to compensate for the increase in accumulation, but this will change when temperature increases go beyond any critical limit. Calculations show that such a limit for Greenland might well be passed during this century. For Antarctica this will take much longer and probably well into following centuries.

Nationalised large-scale mining, trade unions and community representation: perspectives from Northern Madagascar

This article critically explores the nature and purpose of relationships and inter-dependencies between stakeholders in the context of a parastatal chromite mining company in the Betsiboka Region of Northern Madagascar. An examination of the institutional arrangements at the interface between the mining company and local communities identified power hierarchies and dependencies in the context of a dominant paternalistic environment. The interactions, inter alia, limited social cohesion and intensified the fragility and weakness of community representation, which was further influenced by ethnic hierarchies between the varied community groups; namely, indigenous communities and migrants to the area from different ethnic groups. Moreover, dependencies and nepotism, which may exist at all institutional levels, can create civil society stakeholder representatives who are unrepresentative of the society they are intended to represent. Similarly, a lack of horizontal and vertical trust and reciprocity inherent in Malagasy society engenders a culture of low expectations regarding transparency and accountability, which further catalyses a cycle of nepotism and elite rent-seeking behaviour. On the other hand, leaders retain power with minimal vertical delegation or decentralisation of authority among levels of government and limit opportunities to benefit the elite, perpetuating rent-seeking behaviour within the privileged minority. Within the union movement, pluralism and the associated politicisation of individual unions restricts solidarity, which impacts on the movement’s capacity to act as a cohesive body of opinion and opposition. Nevertheless, the unions’ drive to improve their social capital has increased expectations of transparency and accountability, resulting in demands for greater engagement in decision-making processes.

Improving a global model from the boundary layer: total turbulent energy and the neutral limit Prandtl number

Model intercomparisons have identified important deficits in the representation of the stable boundary layer by turbulence parametrizations used in current weather and climate models. However, detrimental impacts of more realistic schemes on the large-scale flow have hindered progress in this area. Here we implement a total turbulent energy scheme into the climate model ECHAM6. The total turbulent energy scheme considers the effects of Earth’s rotation and static stability on the turbulence length scale. In contrast to the previously used turbulence scheme, the TTE scheme also implicitly represents entrainment flux in a dry convective boundary layer. Reducing the previously exaggerated surface drag in stable boundary layers indeed causes an increase in southern hemispheric zonal winds and large-scale pressure gradients beyond observed values. These biases can be largely removed by increasing the parametrized orographic drag. Reducing the neutral limit turbulent Prandtl number warms and moistens low-latitude boundary layers and acts to reduce longstanding radiation biases in the stratocumulus regions, the Southern Ocean and the equatorial cold tongue that are common to many climate models.

Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities

We construct a quasi-sure version (in the sense of Malliavin) of geometric rough paths associated with a Gaussian process with long-time memory. As an application we establish a large deviation principle (LDP) for capacities for such Gaussian rough paths. Together with Lyons' universal limit theorem, our results yield immediately the corresponding results for pathwise solutions to stochastic differential equations driven by such Gaussian process in the sense of rough paths. Moreover, our LDP result implies the result of Yoshida on the LDP for capacities over the abstract Wiener space associated with such Gaussian process.

Large deviations of Rouse polymer chain: first passage problem

The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations, and measure the mean first-passage time $\tau(z)$ for the free end to reach a certain distance $z$ away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of $\tau(z)$ are observed, with transition between them varying as a function of chain length. We use these simulations results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations lead us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more.

On translational superfluidity and the Landau criterion for Bose gases in the Gross-Pitaevski limit

The two-fluid and Landau criteria for superfluidity are compared for trapped Bose gases. While the two-fluid criterion predicts translational superfluidity, it is suggested, on the basis of the homogeneous Gross-Pitaevski limit, that a necessary part of Landau`s criterion, adequate for non-translationally invariant systems, does not hold for trapped Bose gases in the GP limit. As a consequence, if the compressibility is detected to be very large (infinite by experimental standards), the two-fluid criterion is seen to be the relevant one in case the system is a translational superfluid, while the Landau criterion is the relevant one if translational superfluidity is absent.

Limit theorems for sequences of random trees

We consider a random tree and introduce a metric in the space of trees to define the ""mean tree"" as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.

Phytoplankton assemblages in a reservoir cascade of a large tropical - subtropical river (SE, Brazil)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)