Search results for: non-canonical scalar multiplication

Authors: Jeremie Coullon, Robert J. Webber

Abstract:

We introduce a Markov chain Monte Carlo (MCMC) sam-pler for infinite-dimensional inverse problems. Our sam-pler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensem-ble sampler for the first time to infinite-dimensional func-tion spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable. In many Bayes-ian inverse problems, Markov chain Monte Carlo (MCMC) meth-ods are needed to approximate distributions on infinite-dimensional function spaces, for example, in groundwater flow, medical imaging, and traffic flow. Yet designing efficient MCMC methods for function spaces has proved challenging. Recent gradi-ent-based MCMC methods preconditioned MCMC methods, and SMC methods have improved the computational efficiency of functional random walk. However, these samplers require gradi-ents or posterior covariance estimates that may be challenging to obtain. Calculating gradients is difficult or impossible in many high-dimensional inverse problems involving a numerical integra-tor with a black-box code base. Additionally, accurately estimating posterior covariances can require a lengthy pilot run or adaptation period. These concerns raise the question: is there a functional sampler that outperforms functional random walk without requir-ing gradients or posterior covariance estimates? To address this question, we consider a gradient-free sampler that avoids explicit covariance estimation yet adapts naturally to the covariance struc-ture of the sampled distribution. This sampler works by consider-ing an ensemble of walkers and interpolating and extrapolating between walkers to make a proposal. This is called the affine in-variant ensemble sampler (AIES), which is easy to tune, easy to parallelize, and efficient at sampling spaces of moderate dimen-sionality (less than 20). The main contribution of this work is to propose a functional ensemble sampler (FES) that combines func-tional random walk and AIES. To apply this sampler, we first cal-culate the Karhunen–Loeve (KL) expansion for the Bayesian prior distribution, assumed to be Gaussian and trace-class. Then, we use AIES to sample the posterior distribution on the low-wavenumber KL components and use the functional random walk to sample the posterior distribution on the high-wavenumber KL components. Alternating between AIES and functional random walk updates, we obtain our functional ensemble sampler that is efficient and easy to use without requiring detailed knowledge of the target dis-tribution. In past work, several authors have proposed splitting the Bayesian posterior into low-wavenumber and high-wavenumber components and then applying enhanced sampling to the low-wavenumber components. Yet compared to these other samplers, FES is unique in its simplicity and broad applicability. FES does not require any derivatives, and the need for derivative-free sam-plers has previously been emphasized. FES also eliminates the requirement for posterior covariance estimates. Lastly, FES is more efficient than other gradient-free samplers in our tests. In two nu-merical examples, we apply FES to challenging inverse problems that involve estimating a functional parameter and one or more scalar parameters. We compare the performance of functional random walk, FES, and an alternative derivative-free sampler that explicitly estimates the posterior covariance matrix. We conclude that FES is the fastest available gradient-free sampler for these challenging and multimodal test problems.

Keywords: Bayesian inverse problems, Markov chain Monte Carlo, infinite-dimensional inverse problems, dimensionality reduction

Procedia PDF Downloads 128

Authors: Dionyssia Lyra, Shoaib Ismail

Abstract:

Salinization of natural resources constitutes a significant component of the degradation force that leads to depletion of productive lands and fresh water reserves. The global extent of salt-affected soils is approximately 7% of the earth’s land surface and is expanding. The problems of excessive salt accumulation are most widespread in coastal, arid and semi-arid regions, where agricultural production is substantially hindered. The use of crops that can withstand high saline conditions is extremely interesting in such a context. Salt-loving plants or else ‘halophytes’ thrive when grown in hostile saline conditions, where traditional crops cannot survive. Salicornia bigelovii, a halophytic crop with multiple uses (vegetable, forage, biofuel), has demonstrated remarkable adaptability to harsh climatic conditions prevailing in dry areas with great potential for its expansion. Since 2011, the International Center for Biosaline Agriculture (ICBA) with Masdar Institute (MI) and King Abdul Aziz University of Science & Technology (KAUST) to look into the potential for growing S. bigelovii under hot and dry conditions. Through the projects undertaken, 50 different S. bigelovii genotypes were assessed under high saline conditions. The overall goal was to select the best performing S. bigelovii populations in terms of seed and biomass production for future breeding. Specific objectives included: 1) evaluation of selected S. bigelovii genotypes for various agronomic and growth parameters under field conditions, 2) seed multiplication of S. bigelovii using saline groundwater and 3) acquisition of inbred lines for further breeding. Field trials were conducted for four consecutive years at ICBA headquarters. During the first year, one Salicornia population was evaluated for seed and biomass production at different salinity levels, fertilizer treatments and planting methods. All growth parameters and biomass productivity for the salicornia population showed better performance with optimal biomass production in terms of both salinity level and fertilizer application. During the second year, 46 Salicornia populations (obtained from KAUST and Masdar Institute) were evaluated for 24 growth parameters and treated with groundwater through drip irrigation. The plant material originated from wild collections. Six populations were also assessed for their growth performance under full-strength seawater. Salicornia populations were highly variable for all characteristics under study for both irrigation treatments, indicating that there is a large pool of genetic information available for breeding. Irrigation with the highest level of salinity had a negative impact on the agronomic performance. The maximum seed yield obtained was 2 t/ha at 20 dS/m (groundwater treatment) at 25 cm x 25 cm planting distance. The best performing Salicornia populations for fresh biomass and seed yield were selected for the following season. After continuous selection, the best performing salicornia will be adopted for scaling-up options. Taking into account the results of the production field trials, salicornia expansion will be targeted in coastal areas of the Arabian Peninsula. As a crop with high biofuel and forage potential, its cultivation can improve the livelihood of local farmers.

Keywords: biosaline agriculture, genotypes selection, halophytes, Salicornia bigelovii

Procedia PDF Downloads 383

Authors: Chiu-Yin Leung

Abstract:

This research investigates a complex assemblage among indigenous identities, socio-political organization and national apparatus in the border landscape of post-colonial Hong Kong. This former British colony had designated a transient mode of governance in its New Territories and particularly the northernmost borderland in 1951-2012. With a discriminated system of land provisions for the indigenous villagers, the place has been inherited with distinctive village-based culture, historic monuments and agrarian practices until its sovereignty return into the People’s Republic of China. In its latest development imperatives by the national strategic planning, the frontier area of Hong Kong has been identified as a strategy site for regional economic integration in South China, with cross-border projects of innovation and technology zones, mega-transport infrastructure and inter-jurisdictional arrangement. Contemporary literature theorizes borders as the material and discursive production of territoriality, which manifest in state apparatus and the daily lives of its citizens and condense in the contested articulations of power, security and citizenship. Drawing on the concept of assemblage, this paper attempts to tract how the border regime and infrastructure in Hong Kong as a city are deeply ingrained in the everyday lived spaces of the local communities but also the changing urban and regional strategies across different longitudinal moments. Through an intensive ethnographic fieldwork among the borderland villages since 2008 and the extensive analysis of colonial archives, new development plans and spatial planning frameworks, the author navigates the genealogy of the border landscape in Ta Kwu Ling frontier area and its implications as the milieu for new state space, covering heterogeneous fields particularly in indigenous rights, heritage preservation, rural sustainability and regional economy. Empirical evidence suggests an apparent bias towards indigenous power and colonial representation in classifying landscape values and conserving historical monuments. Squatter and farm tenants are often deprived of property rights, statutory participation and livelihood option in the planning process. The postcolonial bureaucracies have great difficulties in mobilizing resources to catch up with the swift, political-first approach of the mainland counterparts. Meanwhile, the cultural heritage, lineage network and memory landscape are not protected altogether with any holistic view or collaborative effort across the border. The enactment of land resumption and compensation scheme is furthermore disturbed by lineage-based customary law, technocratic bureaucracy, intra-community conflicts and multi-scalar political mobilization. As many traces of colonial misfortune and tyranny have been whitewashed without proper management, the author argues that postcolonial justice is yet reconciled in this fragmented border landscape. The assemblage of border in mainstream representation has tended to oversimplify local struggles as a collective mist and setup a wider production of schizophrenia experiences in the discussion of further economic integration among Hong Kong and other mainland cities in the Pearl River Delta Region. The research is expected to shed new light on the theorizing of border regions and postcolonialism beyond Eurocentric perspectives. In reassembling the borderland experiences with other arrays in state governance, village organization and indigenous identities, the author also suggests an alternative epistemology in reconciling socio-spatial differences and opening up imaginaries for positive interventions.

Keywords: heritage conservation, indigenous communities, post-colonial borderland, regional development, rural sustainability

Procedia PDF Downloads 182