Hypotheses testing for a multidimensional parameter of inhomogeneous Poisson processes

We observe a realization of an inhomogeneous Poisson process whose intensity function depends on an unknown multidimensional parameter. We consider the asymptotic behaviour of the Rao score test for a simple null hypothesis against the multilateral alternative. By using the Edgeworth type expansion (under the null hypothesis) for a vector of stochastic integrals with respect to the Poisson process, we refine the (classic) threshold of the test (obtained by the central limit theorem), which improves the first type probability of error. The expansion allows us to describe the power of the test under the local alternative, i.e. a sequence of alternatives, which converge to the null hypothesis with a certain rate. The rates can be different for components of the parameter.     

Power Loss for Inhomogeneous Poisson Processes

In this work, based on a realization of an inhomogeneous Poisson process whose intensity function depends on a real parameter, we consider a simple null hypothesis against the composite one sided alternative. Under certain regularity conditions we will obtain the power loss of the score test which measures its performance with respect to the Neyman-Pearson test. We present the second-order approximation of the power of the score test under the close alternatives by specifying the explicit form of the next term after the Gaussian term.     

Team selection for prediction tasks

Given a random variable \(O \in \mathbb {R}\) and a set of experts \(E\), we describe a method for finding a subset of experts \(S \subseteq E\) whose aggregated opinion best predicts the outcome of \(O\). Therefore, the problem can be regarded as a team formation for performing a prediction task. We show that in case of aggregating experts’ opinions by simple averaging, finding the best team (the team with the lowest total error during past \(k\) rounds) can be modeled with an integer quadratic programming and we prove its NP-hardness whereas its relaxation is solvable in polynomial time. At the end, we do an experimental comparison between different rounding and greedy heuristics on artificial datasets which are generated based on calibration and informativeness of exprets’ information and show that our suggested tabu search works effectively.     

Optimal space coverage with white convex polygons

Assume that we are given a set of points some of which are black and the rest are white. The goal is to find a set of convex polygons with maximum total area that cover all white points and exclude all black points. We study the problem on three different settings (based on overlapping between different convex polygons): (1) In case convex polygons are permitted to have common area, we present a polynomial algorithm. (2) In case convex polygons are not allowed to have common area but are allowed to have common vertices, we prove the NP-hardness of the problem and propose an algorithm whose output is at least \(\left( \frac{OPT}{log(2n/OPT) + 2log(n)}\right) ^{1/4}\). (3) Finally, in case convex polygons are not allowed to have common area or common vertices, also we prove the NP-hardness of the problem and propose an algorithm whose output is at least \(\frac{3\sqrt{3}}{4.\pi }\left( \frac{OPT}{log(2n/OPT) + 2log(n)}\right) ^{1/4}\).     

Euclidean movement minimization

We consider a class of optimization problems called movement minimization on euclidean plane. Given a set of \(m\) nodes on the plane, the aim is to achieve some specific property by minimum movement of the nodes. We consider two specific properties, namely the connectivity (Con) and realization of a given topology (Topol). By minimum movement, we mean either the sum of all movements (Sum) or the maximum movement (Max). We obtain several approximation algorithms and some hardness results for these four problems. We obtain an \(O(m)\)-factor approximation for ConMax and ConSum and extend some known result on graphical grounds and obtain inapproximability results on the geometrical grounds. For the Topol problems (where the final decoration of the nodes must correspond to a given configuration), we find it much simpler and provide FPTAS for both Max and Sum versions.     

Public Sociology and the Democratization of Technology: Drawing on User -led Research to Achieve Mutual Education

In an effort to further advance public sociology and its relationship with technology, this paper looks at a democratic model of collaboration within the technological sciences. We draw on the concept of user- led research to demonstrate how sociologists, scientists and various stakeholders within the public sphere can achieve reciprocal, meaningful and sustained knowledge translation. Furthermore, we argue that by acknowledging participants’ technological needs and reducing unnecessary complexity, the user -led method advances Burawoy’s “dialogue as mutual education” within public sociology.     

Asymptotic deficiency of score test for inhomogeneous Poisson processes

In this work, based on a realization of an inhomogeneous Poisson process whose intensity function depends on an unknown real parameter, we test a simple null hypothesis against a sequence of close (contiguous) one-sided alternatives. The main object is to obtain the asymptotic deficiency of the score test with respect to the Neyman–Pearson test.