We investigate online group formation where members seek to increase their learning potential via collaboration. We capture two common learning models: LpA where each member learns from all higher skilled ones, and LpD where the least skilled member learns from the most skilled one. We formulate the problem of forming groups with the purpose of optimizing peer learning under different affinity structures: AffD where group affinity is the smallest between all members, and AffC where group affinity is the smallest between a designated member (e.g., the least skilled or the most skilled) and all others. This gives rise to multiple variants of a multiobjective optimization problem. We propose principled modeling of these problems and investigate theoretical and algorithmic challenges. We first present hardness results, and then develop computationally efficient algorithms with constant approximation factors. Our real-data experiments demonstrate with statistical significance that forming groups considering affinity improves learning. Our extensive synthetic experiments demonstrate the qualitative and scalability aspects of our solutions.

In this paper, we study some important means of Jordan's totient function, especially, we obtain asymptotic formula for geometric mean and harmonic mean. We also study alternating sums of Jordan's totient function and Carleman's inequality for this function.

Current crowdsourcing platforms provide little support for worker feedback. Workers are sometimes invited to post free text describing their experience and preferences in completing tasks. They can also use forums such as Turker Nation 1 to exchange preferences on tasks and requesters. In fact, crowdsourcing platforms rely heavily on observing workers and inferring their preferences implicitly. In this work, we believe that asking workers to indicate their preferences explicitly improve their experience in task completion and hence, the quality of their contributions. Explicit elicitation can indeed help to build more accurate worker models for task completion that captures the evolving nature of worker preferences. We design a worker model whose accuracy is improved iteratively by requesting preferences for task factors such as required skills, task payment, and task relevance. We propose a generic framework, develop efficient solutions in realistic scenarios, and run extensive experiments that show the benefit of explicit preference elicitation over implicit ones with statistical significance.

BackgroundDetermining interacting SNPs in genome-wide association studies is computationally expensive yet of considerable interest in genomics. Findings We present a program Chi8 that calculates the Chi-square 8 degree of freedom test between all pairs of SNPs in a brute force manner on a Graphics Processing Unit. We analyze each of the seven WTCCC genome-wide association studies that have about 5000 total case and controls and 400,000 SNPs in an average of 9.6 h on a single GPU. We also study the power, false positives, and area under curve of our program on simulated data and provide a comparison to the GBOOST program. Our program source code is freely available from http://www.cs.njit.edu/usman/Chi8.Electronic supplementary materialThe online version of this article (doi:10.1186/s13104-015-1392-5) contains supplementary material, which is available to authorized users.

Diversifying recommendations on a sequence of sets (or sessions) of items captures a variety of applications. Notable examples include recommending online music playlists, where a session is a channel and multiple channels are listened to in sequence, or recommending tasks in crowdsourcing, where a session is a set of tasks and multiple task sessions are completed in sequence. Item diversity can be defined in more than one way, e.g., as a genre diversity for music, or as a function of reward in crowdsourcing. A user who engages in multiple sessions may intend to experience diversity within and/or across sessions. Intra session diversity is set-based, whereas, Inter session diversity is naturally sequence-based. This novel formulation gives rise to four bi-objective problems with the goal of minimizing or maximizing Inter and Intra diversities. We prove hardness and develop efficient algorithms with theoretical guarantees. Our experiments with human subjects