Noise-Resilient Group Testing: Limitations and Constructions

We study combinatorial group testing schemes for learning $d$-sparse Boolean vectors using highly unreliable disjunctive measurements. We consider an adversarial noise model that only limits the number of false observations, and show that any noise-resilient scheme in this model can only approximately reconstruct the sparse vector. On the positive side, we take this barrier to our advantage and show that approximate reconstruction (within a satisfactory degree of approximation) allows us to break the information theoretic lower bound of $\tilde{\Omega}(d^2 \log n)$ that is known for exact reconstruction of $d$-sparse vectors of length $n$ via non-adaptive measurements, by a multiplicative factor $\tilde{\Omega}(d)$. Specifically, we give simple randomized constructions of non-adaptive measurement schemes, with $m=O(d \log n)$ measurements, that allow efficient reconstruction of $d$-sparse vectors up to $O(d)$ false positives even in the presence of $\delta m$ false positives and $O(m/d)$ false negatives within the measurement outcomes, for any constant $\delta < 1$. We show that, information theoretically, none of these parameters can be substantially improved without dramatically affecting the others. Furthermore, we obtain several explicit constructions, in particular one matching the randomized trade-off but using $m = O(d^{1+o(1)} \log n)$ measurements. We also obtain explicit constructions that allow fast reconstruction in time \poly(m), which would be sublinear in $n$ for sufficiently sparse vectors. The main tool used in our construction is the list-decoding view of randomness condensers and extractors.Comment: Full version. A preliminary summary of this work appears (under the same title) in proceedings of the 17th International Symposium on Fundamentals of Computation Theory (FCT 2009

The Length of a Minimal Tree With a Given Topology: generalization of Maxwell Formula

The classic Maxwell formula calculates the length of a planar locally minimal binary tree in terms of coordinates of its boundary vertices and directions of incoming edges. However, if an extreme tree with a given topology and a boundary has degenerate edges, then the classic Maxwell formula cannot be applied directly, to calculate the length of the extreme tree in this case it is necessary to know which edges are degenerate. In this paper we generalize the Maxwell formula to arbitrary extreme trees in a Euclidean space of arbitrary dimension. Now to calculate the length of such a tree, there is no need to know either what edges are degenerate, or the directions of nondegenerate boundary edges. The answer is the maximum of some special linear function on the corresponding compact convex subset of the Euclidean space coinciding with the intersection of some cylinders.Comment: 6 ref

A Partition-Based Random Search Method for Multimodal Optimization

Practical optimization problems are often too complex to be formulated exactly. Knowing multiple good alternatives can help decision-makers easily switch solutions when needed, such as when faced with unforeseen constraints. A multimodal optimization task aims to find multiple global optima as well as high-quality local optima of an optimization problem. Evolutionary algorithms with niching techniques are commonly used for such problems, where a rough estimate of the optima number is required to determine the population size. In this paper, a partition-based random search method is proposed, in which the entire feasible domain is partitioned into smaller and smaller subregions iteratively. Promising regions are partitioned faster than unpromising regions, thus, promising areas will be exploited earlier than unpromising areas. All promising areas are exploited in parallel, which allows multiple good solutions to be found in a single run. The proposed method does not require prior knowledge about the optima number and it is not sensitive to the distance parameter. By cooperating with local search to refine the obtained solutions, the proposed method demonstrates good performance in many benchmark functions with multiple global optima. In addition, in problems with numerous local optima, high-quality local optima are captured earlier than low-quality local optima

You can't see what you can't see: Experimental evidence for how much relevant information may be missed due to Google's Web search personalisation

The influence of Web search personalisation on professional knowledge work is an understudied area. Here we investigate how public sector officials self-assess their dependency on the Google Web search engine, whether they are aware of the potential impact of algorithmic biases on their ability to retrieve all relevant information, and how much relevant information may actually be missed due to Web search personalisation. We find that the majority of participants in our experimental study are neither aware that there is a potential problem nor do they have a strategy to mitigate the risk of missing relevant information when performing online searches. Most significantly, we provide empirical evidence that up to 20% of relevant information may be missed due to Web search personalisation. This work has significant implications for Web research by public sector professionals, who should be provided with training about the potential algorithmic biases that may affect their judgments and decision making, as well as clear guidelines how to minimise the risk of missing relevant information.Comment: paper submitted to the 11th Intl. Conf. on Social Informatics; revision corrects error in interpretation of parameter Psi/p in RBO resulting from discrepancy between the documentation of the implementation in R (https://rdrr.io/bioc/gespeR/man/rbo.html) and the original definition (https://dl.acm.org/citation.cfm?id=1852106) as per 20/05/201

Complete moduli of cubic threefolds and their intermediate Jacobians

The intermediate Jacobian map, which associates to a smooth cubic threefold its intermediate Jacobian, does not extend to the GIT compactification of the space of cubic threefolds, not even as a map to the Satake compactification of the moduli space of principally polarized abelian fivefolds. A much better "wonderful" compactification of the space of cubic threefolds was constructed by the first and fourth authors --- it has a modular interpretation, and divisorial normal crossing boundary. We prove that the intermediate Jacobian map extends to a morphism from the wonderful compactification to the second Voronoi toroidal compactification of the moduli of principally polarized abelian fivefolds --- the first and fourth author previously showed that it extends to the Satake compactification. Since the second Voronoi compactification has a modular interpretation, our extended intermediate Jacobian map encodes all of the geometric information about the degenerations of intermediate Jacobians, and allows for the study of the geometry of cubic threefolds via degeneration techniques. As one application we give a complete classification of all degenerations of intermediate Jacobians of cubic threefolds of torus rank 1 and 2.Comment: 56 pages; v2: multiple updates and clarification in response to detailed referee's comment

1/m_Q Corrections to the Heavy-to-Light-Vector Transitions in the HQET

Within the HQET, the heavy to light vector meson transitions are systematically analyzed to the order of 1/m_Q. Besides the four universal functions at the leading order, there are twenty-two independent universal form factors at the order of 1/m_Q. Both the semileptonic decay B->\rho which is relevant to the |V_{ub}| extraction, and the penguin induced decay B -> K^* which is important to new physics discovering, depend on these form factors. Phenomenological implications are discussed.Comment: RevTeX, 9 pages, no figure

Predicting the solar maximum with the rising rate

The growth rate of solar activity in the early phase of a solar cycle has been known to be well correlated with the subsequent amplitude (solar maximum). It provides very useful information for a new solar cycle as its variation reflects the temporal evolution of the dynamic process of solar magnetic activities from the initial phase to the peak phase of the cycle. The correlation coefficient between the solar maximum (Rmax) and the rising rate ({\beta}a) at {\Delta}m months after the solar minimum (Rmin) is studied and shown to increase as the cycle progresses with an inflection point (r = 0.83) at about {\Delta}m = 20 months. The prediction error of Rmax based on {\beta}a is found within estimation at the 90% level of confidence and the relative prediction error will be less than 20% when {\Delta}m \geq 20. From the above relationship, the current cycle (24) is preliminarily predicted to peak around October 2013 with a size of Rmax =84 \pm 33 at the 90% level of confidence.Comment: 7 pages, 3 figures, accepted for publication in SCIENCE CHINA Physics,Mechanics & Astronom

Total-Factor Energy Efficiency in China’s Agricultural Sector: Trends, Disparities and Potentials

This paper investigates total-factor energy efficiency and analyses the trends of the efficiency changes in China’s agricultural production across 30 provinces and three regions from 2001 to 2011, based on data envelopment analysis (DEA) approach. The potential amount of energy savings and five potential factors for energy efficiency improvement are also empirically studied by Tobit regression model. The findings show that (1) total-factor energy efficiency in China’s agricultural sector is increasing over years but performs heterogeneously across regions; (2) agriculture intensive regions and energy abundant provinces tend to be relatively energy inefficient in agricultural production; and (3) economic structure, agricultural production structure, technological progress and income effect are major potentials for improving energy efficiency, whereas energy price is not a significant factor. This phenomenon results from the divergence of economic development, endowment effects as well as the scale of agricultural production. Policy implications drawn from this research are to upgrade industrial structure and promote agricultural transformation to enhance farmers’ income as well as to establish a land market with entitling land property rights to farmers. This conclusion can assist to form more scientific rural energy policy decision-making in China and also can be extended to other developing economies for sustainable agriculture

Clean heating and heating poverty: A perspective based on cost-benefit analysis

To improve the air quality in winter, clean heating policy was implemented in “2 + 26” cities of China in 2016, which mainly included replacing coal with gas or electricity. Tremendous financial subsidies have been provided by city and central governments. This new heating mode changed the heating fee-cost to residents. This paper estimates the economic costs to both governments and residents, and evaluates the environmental and public health benefits by combining a difference-in-differences model with an exposure-response function. Results show that the total costs of clean heating were up to 43.1 billion yuan. Governments and residents account for 44% and 56% of the total costs, respectively. In terms of benefits, the clean heating project is effective for air pollution control and brings health economic benefits of about 109.85 billion yuan (95% CI: 22.40–159.83). The clean heating policy was identified as a net-positive benefit program with environmental and public health improvements. However, the inequality in subsidies from different cities governments increases the heating burden on low-income households and leads to heating poverty for households in the less developed regions. We provide suggestions for implementation in future clean heating campaigns and in subsidy mechanism design in China and for other developing countries