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Beyond identifying genetic variants, we introduce a set of Boolean relations that allows for a comprehensive classification of the relations for every pair of variants by taking all minimal alignments into account. We present an efficient algorithm to compute these relations, including a novel way of efficiently computing all minimal alignments within the best theoretical complexity bounds. We show that for variants of the CFTR gene in dbSNP these relations are common and many non-trivial. Ultimately, we present an approach for the storing and indexing of variants in the context of a database that enables efficient querying for all these relations., Comment: 20 pages, 6 figures

Deep reinforcement learning has shown remarkable success in the past few years. Highly complex sequential decision making problems from game playing and robotics have been solved with deep model-free methods. Unfortunately, the sample complexity of model-free methods is often high. To reduce the number of environment samples, model-based reinforcement learning creates an explicit model of the environment dynamics. Achieving high model accuracy is a challenge in high-dimensional problems. In recent years, a diverse landscape of model-based methods has been introduced to improve model accuracy, using methods such as uncertainty modeling, model-predictive control, latent models, and end-to-end learning and planning. Some of these methods succeed in achieving high accuracy at low sample complexity, most do so either in a robotics or in a games context. In this paper, we survey these methods; we explain in detail how they work and what their strengths and weaknesses are. We conclude with a research agenda for future work to make the methods more robust and more widely applicable to other applications., Comment: arXiv admin note: text overlap with arXiv:2008.05598

Deep reinforcement learning has shown remarkable success in the past few years. Highly complex sequential decision making problems have been solved in tasks such as game playing and robotics. Unfortunately, the sample complexity of most deep reinforcement learning methods is high, precluding their use in some important applications. Model-based reinforcement learning creates an explicit model of the environment dynamics to reduce the need for environment samples. Current deep learning methods use high-capacity networks to solve high-dimensional problems. Unfortunately, high-capacity models typically require many samples, negating the potential benefit of lower sample complexity in model-based methods. A challenge for deep model-based methods is therefore to achieve high predictive power while maintaining low sample complexity. In recent years, many model-based methods have been introduced to address this challenge. In this paper, we survey the contemporary model-based landscape. First we discuss definitions and relations to other fields. We propose a taxonomy based on three approaches: using explicit planning on given transitions, using explicit planning on learned transitions, and end-to-end learning of both planning and transitions. We use these approaches to organize a comprehensive overview of important recent developments such as latent models. We describe methods and benchmarks, and we suggest directions for future work for each of the approaches. Among promising research directions are curriculum learning, uncertainty modeling, and use of latent models for transfer learning.

In this paper we describe several player preferences in games with $N \geq 2$ players, in particular the case $N = 3$, and use them to simplify game trees, using the game of Clobber as our example. We show that, using a fixed starting player and a certain ruleset, any short game can be simplified to a value in a very concise set. Omitting the fixed starting player and generalising the theory to more than 3 players remains a challenge., Comment: 15 pages. Master research project at the Leiden Institute of Advanced Computer Science (LIACS)

Let $p$ be a prime and let $K$ be a finite extension of $\mathbb{Q}_p$. Let $E/K$ be an elliptic curve with additive reduction. In this paper, we study the topological group structure of the set of points of good reduction of $E(K)$. In particular, if $K/\mathbb{Q}_p$ is unramified, we show how one can read off the topological group structure from the Weierstrass coefficients defining $E$., Comment: 12 pages, this is an extended version of arXiv:1211.5833 and contains some overlap

Let $K$ be a function field over a finite field $k$ of characteristic $p$ and let $K_{\infty}/K$ be a geometric extension with Galois group $\mathbb{Z}_p$. Let $K_n$ be the corresponding subextension with Galois group $\mathbb{Z}/p^n\mathbb{Z}$ and genus $g_n$. In this paper, we give a simple explicit formula $g_n$ in terms of an explicit Witt vector construction of the $\mathbb{Z}_p$-tower. This formula leads to a tight lower bound on $g_n$ which is quadratic in $p^n$. Furthermore, we determine all $\mathbb{Z}_p$-towers for which the genus sequence is stable, in the sense that there are $a,b,c \in \mathbb{Q}$ such that $g_n=a p^{2n}+b p^n +c$ for $n$ large enough. Such genus stable towers are expected to have strong stable arithmetic properties for their zeta functions. A key technical contribution of this work is a new simplified formula for the Schmid-Witt symbol coming from local class field theory., Comment: 13 pages, this is a short version of arXiv:1607.00523