Approximate kernel clustering

In the kernel clustering problem we are given a large $n\times n$ positive semi-definite matrix $A=(a_{ij})$ with $\sum_{i,j=1}^na_{ij}=0$ and a small $k\times k$ positive semi-definite matrix $B=(b_{ij})$. The goal is to find a partition $S_1,...,S_k$ of $\{1,... n\}$ which maximizes the quantity $$\sum_{i,j=1}^k (\sum_{(i,j)\in S_i\times S_j}a_{ij})b_{ij}.$$ We study the computational complexity of this generic clustering problem which originates in the theory of machine learning. We design a constant factor polynomial time approximation algorithm for this problem, answering a question posed by Song, Smola, Gretton and Borgwardt. In some cases we manage to compute the sharp approximation threshold for this problem assuming the Unique Games Conjecture (UGC). In particular, when $B$ is the $3\times 3$ identity matrix the UGC hardness threshold of this problem is exactly $\frac{16\pi}{27}$. We present and study a geometric conjecture of independent interest which we show would imply that the UGC threshold when $B$ is the $k\times k$ identity matrix is $\frac{8\pi}{9}(1-\frac{1}{k})$ for every $k\ge 3$

A Characterization of Approximation Resistance for Even kk-Partite CSPs

A constraint satisfaction problem (CSP) is said to be \emph{approximation resistant} if it is hard to approximate better than the trivial algorithm which picks a uniformly random assignment. Assuming the Unique Games Conjecture, we give a characterization of approximation resistance for $k$-partite CSPs defined by an even predicate

The use of botanical synergists to increase the efficacy of natural pyrethrins

Insecticide resistance is an important aspect of pest control on both crop pests and vectors of animal diseases. Resistance can be caused by a number of mechanisms, one of which is enhanced detoxification of the insecticide by metabolic enzymes. Synergists may be used in insecticide formulations to inhibit metabolic defences in the insect, allowing the insecticide to reach its target site and kill the insect, thus enhancing the effect of the insecticide. This PhD project investigated the use of the synergist piperonyl butoxide (PBO) in combination with natural pyrethrins (tank mix) and as a pre-treatment prior to application of pyrethrins, as methods of enhancing the efficacy of the insecticide. The insects studied were Myzus persicae, Bemisia tabaci and Musca domestica. Results showed that the combination treatment (tank mix) was at least as good as, and sometimes better than, the pre-treatment. This is unlike the situation for synthetic pyrethroids where pre-treatments have been shown to be more effective than tank mixes. It is proposed that for natural pyrethrins, PBO aids the penetration of the pyrethrins into the insect, and this enhancement effect is greater than full inhibition of the metabolic enzymes. In some cases, the tank mix enabled less insecticide to be used to achieve 50% mortality in resistant insects, compared to a susceptible population treated with pyrethrins alone. A novel laboratory assay was developed to enable the screening of botanical extracts for their ability to inhibit esterase enzymes. This was used to test a range of compounds and those showing esterase inhibition were also screened for their ability to inhibit cytochrome P450 activity. The competency of some of these compounds as synergists was also tested in vivo with some showing potential activity both in vitro and in vivo

Answering Complex Questions Using Open Information Extraction

While there has been substantial progress in factoid question-answering (QA), answering complex questions remains challenging, typically requiring both a large body of knowledge and inference techniques. Open Information Extraction (Open IE) provides a way to generate semi-structured knowledge for QA, but to date such knowledge has only been used to answer simple questions with retrieval-based methods. We overcome this limitation by presenting a method for reasoning with Open IE knowledge, allowing more complex questions to be handled. Using a recently proposed support graph optimization framework for QA, we develop a new inference model for Open IE, in particular one that can work effectively with multiple short facts, noise, and the relational structure of tuples. Our model significantly outperforms a state-of-the-art structured solver on complex questions of varying difficulty, while also removing the reliance on manually curated knowledge.Comment: Accepted as short paper at ACL 201

Optimization for efficient structure-control systems

The efficiency of a structure-control system is a nondimensional parameter which indicates the fraction of the total control power expended usefully in controlling a finite-dimensional system. The balance of control power is wasted on the truncated dynamics serving no useful purpose towards the control objectives. Recently, it has been demonstrated that the concept of efficiency can be used to address a number of control issues encountered in the control of dynamic systems such as the spillover effects, selection of a good input configuration and obtaining reduced order control models. Reference (1) introduced the concept and presented analyses of several Linear Quadratic Regulator designs on the basis of their efficiencies. Encouraged by the results of Ref. (1), Ref. (2) introduces an efficiency modal analysis of a structure-control system which gives an internal characterization of the controller design and establishes the link between the control design and the initial disturbances to affect efficient structure-control system designs. The efficiency modal analysis leads to identification of principal controller directions (or controller modes) distinct from the structural natural modes. Thus ultimately, many issues of the structure-control system revolve around the idea of insuring compatibility of the structural modes and the controller modes with each other, the better the match the higher the efficiency. A key feature in controlling a reduced order model of a high dimensional (or infinity-dimensional distributed parameter system) structural dynamic system must be to achieve high efficiency of the control system while satisfying the control objectives and/or constraints. Formally, this can be achieved by designing the control system and structural parameters simultaneously within an optimization framework. The subject of this paper is to present such a design procedure