Reconstruction of Integers from Pairwise Distances

Given a set of integers, one can easily construct the set of their pairwise distances. We consider the inverse problem: given a set of pairwise distances, find the integer set which realizes the pairwise distance set. This problem arises in a lot of fields in engineering and applied physics, and has confounded researchers for over 60 years. It is one of the few fundamental problems that are neither known to be NP-hard nor solvable by polynomial-time algorithms. Whether unique recovery is possible also remains an open question. In many practical applications where this problem occurs, the integer set is naturally sparse (i.e., the integers are sufficiently spaced), a property which has not been explored. In this work, we exploit the sparse nature of the integer set and develop a polynomial-time algorithm which provably recovers the set of integers (up to linear shift and reversal) from the set of their pairwise distances with arbitrarily high probability if the sparsity is O(n^{1/2-\eps}). Numerical simulations verify the effectiveness of the proposed algorithm.Comment: 14 pages, 4 figures, submitted to ICASSP 201

Agroforestry for a Changing Climate

The brief tackles the role of agroforestry in achieving food and nutritional security, climate change mitigation and environmental resilience. The publication is based on the small agroforestry project in Guinayangan Climate-Smart Village in Quezon Province, Philippines implemented by the International Institute of Rural Reconstruction and CCAFS Southeast Asia

Building Community-Based Models for Climate Resilient Agriculture and Fisheries Across Landscapes within the Municipality of Ivisan, Capiz

A recent Inter-governmental Panel on Climate Change (IPCC) report states that climate change is unequivocal and its immediate impact is the modification of the worlds’ biophysical and natural systems resulting to changes in interspecies dynamics, movement of range, altered abundance, and shift in seasonal activities in various ecosystems. Agriculture will be the hardest hit sector globally as its productivity is primarily based on the integrity of agro-ecosystems. Adverse impacts to agriculture will have direct impacts on livelihoods, food security, and nutrition in rural areas. Climate resilient or smart agriculture (CRA/CSA), as a climate change response, provides an option for resource poor farmers in rural areas through its three- tiered objectives, which are: (a) increasing agriculture productivity and income in a sustainable, environmentally sound manner; (b) building capacity of households and food systems to adapt to climate change; and (c) reducing emissions of Greenhouse Gases (GHG’s) while increasing carbon sequestration of agro-ecosystems. Healthy landscapes support food security, livelihoods, and ecosystem functions (helping build resilience). Global knowledge and experience on CRA/CSA is already vast. IIRR believes that its greater adoption by small-holder farmers, especially in the Philippine context, could be facilitated and accelerated, if and when, interventions are coordinated and done through community-based approaches. Communitybased participatory adaptation will be facilitated if interventions are undertaken through multiscalar and multisectoral approaches, with public and private actors converging their services at community and sub-national levels

Bayesian Reconstruction of Missing Observations

We focus on an interpolation method referred to Bayesian reconstruction in this paper. Whereas in standard interpolation methods missing data are interpolated deterministically, in Bayesian reconstruction, missing data are interpolated probabilistically using a Bayesian treatment. In this paper, we address the framework of Bayesian reconstruction and its application to the traffic data reconstruction problem in the field of traffic engineering. In the latter part of this paper, we describe the evaluation of the statistical performance of our Bayesian traffic reconstruction model using a statistical mechanical approach and clarify its statistical behavior

Optimal signal reconstruction from a series of recurring delayed measurements

The modern sampled-data approach provides a general methodology for signal reconstruction. This paper discusses some implications for optimal signal reconstruction when a series of recurring measurements, some delayed, are available for the reconstruction.\ud \u

Reconstruction of Random Colourings

Reconstruction problems have been studied in a number of contexts including biology, information theory and and statistical physics. We consider the reconstruction problem for random $k$-colourings on the $\Delta$-ary tree for large $k$. Bhatnagar et. al. showed non-reconstruction when $\Delta \leq \frac12 k\log k - o(k\log k)$ and reconstruction when $\Delta \geq k\log k + o(k\log k)$. We tighten this result and show non-reconstruction when $\Delta \leq k[\log k + \log \log k + 1 - \ln 2 -o(1)]$ and reconstruction when $\Delta \geq k[\log k + \log \log k + 1+o(1)]$.Comment: Added references, updated notatio