A new Lenstra-type Algorithm for Quasiconvex Polynomial Integer Minimization with Complexity 2^O(n log n)

We study the integer minimization of a quasiconvex polynomial with quasiconvex polynomial constraints. We propose a new algorithm that is an improvement upon the best known algorithm due to Heinz (Journal of Complexity, 2005). This improvement is achieved by applying a new modern Lenstra-type algorithm, finding optimal ellipsoid roundings, and considering sparse encodings of polynomials. For the bounded case, our algorithm attains a time-complexity of s (r l M d)^{O(1)} 2^{2n log_2(n) + O(n)} when M is a bound on the number of monomials in each polynomial and r is the binary encoding length of a bound on the feasible region. In the general case, s l^{O(1)} d^{O(n)} 2^{2n log_2(n) +O(n)}. In each we assume d>= 2 is a bound on the total degree of the polynomials and l bounds the maximum binary encoding size of the input.Comment: 28 pages, 10 figure

Event-triggered joint connectivity topology containment control for unmanned surface ship systems under time delay

For the containment control problem of unmanned surface ship systems (USSs) with time delay and limited communication bandwidth, this paper proposes a distributed event-triggered control strategy using a joint connection switching topology. The communication of unmanned surface ship systems inevitably has delay and the topology is time-varying. Firstly, a joint connectivity switching topology model and the state control method of USSs with delay are designed. Secondly, an event-triggered control mechanism is established, and a new trigger condition of USSs communication is designed. In case of time delay, the USS updates its information and sends it to its neighboring USSs under time delay, minimizes communication consumption and saves energy, and rapidly converges to the steady state. Based on the Lyapunov method, the stability of the system is analyzed, and the Zeno behavior when event-triggered is excluded. It is proved that under the designed control strategy, if the communication topology is jointly connected in a certain time, the follower USS can converge to the convex hull formed by multiple leader USS within a certain delay range. Finally, the correctness and validity of the conclusions are verified by simulation

Spatio-temporal models for air pollution

Air pollution is the biggest environmental risk to global health and it is estimated that, globally, 7 million deaths can be attributed to air pollution each year \citep{WHO2018}. The World Bank estimates that, in 2016, the overall cost of ambient air pollution to the global economy was an estimated US \5.7 trillion or 4.4 per cent of global GDP \citep{worldbank}. A number of different air pollutants have been associated with adverse health effects, including fine particulate matter (PM_{2.5}$), nitrogen dioxide and ozone. In studies of the effects of air pollution, exposure information is often obtained from a fixed number of monitoring sites within the region of interest. However, an increasing number of models of air pollution are being used that provide estimates of concentrations. These are used to represent exposures at every location in a health study area, rather than just at a number of fixed measurement locations. Another use of modelling of air pollution is to provide short-term forecasts that can be used to inform the behaviour of vulnerable people. In this thesis, we develop statistical approaches to modelling, and forecasting, daily concentrations of$\mbox{PM}_{2.5}$in urban areas. We consider two different approaches, both in terms of model formulation and performing inference. The first approach is Dynamic Space-Time Models (DSTM). Under this framework, a \textit{data} model relates observations (measurements) to a \textit{process} model that specifies the dynamic evolution of the "true" underlying process. This approach is implemented using two different methods for estimation: methods of moments and expectation-maximisation. We also develop an approach using Bayesian Hierarchical Spatio-Temporal modelling (BHSTM). The inference is done using computational efficient methods for Bayesian inference (integrated nested Laplace approximations). This model allows predictions of daily PM$_{2.5}$over both space and time, which can be used to interpolate both past measurements and future predictions. Both approaches were implemented using data from Greater London, with their performance evaluated in terms of their ability to predict daily concentrations of PM$_{2.5}$over time at different measuring sites. Both methods were able to accurately predict future values of daily PM$_{2.5}$ at different locations, with one-day ahead predictions being more accurate than those used for longer periods, as might be expected. One of the major advantages of the BHSTM approach is that it provides a straightforward method for producing estimates of the uncertainty that is associated with predictions

Theory of elementary particles

Imperial Users onl

Rational Krylov subspace methods for phi-functions in exponential integrators

Exponential integrators are a class of numerical methods for stiff systems of differential equations which require the computation of products of so-called matrix phi-functions and vectors. In this thesis, we consider the approximation of these matrix functions times some vector by rational and extended Krylov subspace methods. For arbitrary matrices with a field of values in the left complex half-plane, a uniform approximation is obtained that predicts a sublinear convergence

Application of variations of non-linear CCA for feature selection in drug sensitivity prediction

Cancer arises due to the genetic alteration in patient DNA. Many studies indicate the fact that these alterations vary among patients and can affect the therapeutic effect of cancer treatment dramatically. Therefore, extensive studies focus on understanding these alterations and their effects. Pre-clinical models play an important role in cancer drug discovery and cancer cell lines are one of the main ingredients of these pre-clinical studies which can capture many different aspects of multi-omics properties of cancer cells. However, the assessment of cancer cell line responses to different drugs is faulty and laborious. Therefore, in-silico models, which perform accurate prediction of drug sensitivity values, enhance cancer drug discovery. In the past decade, many computational methods achieved high performances by studying similarity between cancer cell lines and drug compounds and used them to obtain an accurate predictive model for unknown instances. In this thesis, we study the effect of non-linear feature selection through two variations of canonical correlation analysis, KCCA, and HSIC-SCCA, on the prediction of drug sensitivity. To estimate the performance of these features we use pairwise kernel ridge regression to predict the drug sensitivity, measured as IC50 values. The data set under study is a subset of Genomics of Drug Sensitivity in Cancer comprise of 124 cell lines and 124 drug compounds. The high diversity between cell lines and drug compound samples and the high dimension of data matrices reduce the accuracy of the model obtained by pairwise kernel ridge regression. This accuracy reduced by employing HSIC-SCCA method as a dimension reduction step since the HSIC-SCCA method increased the differences among the samples by employing different projection vectors for samples in different folds of cross-validation. Therefore, the obtained variables are rotated to provide more homogeneous samples. This step slightly improved the accuracy of the model