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This celebratory article contains a personal and idiosyncratic selection of a few open problems in discrete probability theory. These include certain well known questions concerning Lorentz scatterers and self-avoiding walks, and also some…

Probability · Mathematics 2022-05-17 Geoffrey R. Grimmett

In this paper, we propose a new method for motion prediction: HSFM-$\Sigma$nn. Our proposed method combines two different approaches: a feedforward network whose layers are model-based transition functions using the HSFM and a Neural…

Computer Vision and Pattern Recognition · Computer Science 2020-09-10 A. Postnikov , A. Gamayunov , G. Ferrer

Predicting the occurrence of links is a fundamental problem in networks. In the link prediction problem we are given a snapshot of a network and would like to infer which interactions among existing members are likely to occur in the near…

Social and Information Networks · Computer Science 2010-11-19 L. Backstrom , J. Leskovec

The non-scientific event of a soccer match is analysed on a strictly scientific level. The analysis is based on the recently introduced concept of a team fitness (Eur. Phys. J. B 67, 445, 2009) and requires the use of finite-size scaling. A…

Data Analysis, Statistics and Probability · Physics 2010-03-03 Andreas Heuer , Christian Mueller , Oliver Rubner

Recent advances in machine learning make it possible to design efficient prediction algorithms for data sets with huge numbers of parameters. This paper describes a new technique for "hedging" the predictions output by many such algorithms,…

Machine Learning · Computer Science 2011-11-22 Alexander Gammerman , Vladimir Vovk

We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness…

Analysis of PDEs · Mathematics 2018-02-16 Mikko Salo

In this paper, we investigate stochastic continuity (with respect to the initial value), irreducibility and non confluence property of the solutions of stochastic differential equations with jumps. The conditions we posed are weaker than…

Probability · Mathematics 2014-07-08 Guangqiang Lan , Jiang-Lun Wu

In this article we determine the implicational fragments of most of the known subintuitionistic logics.

Logic · Mathematics 2025-07-15 Fatemeh Shirmohammadzadeh Maleki , Dick de Jongh

Slope movements (e.g. landslides) are dynamic systems that are complex in time and space and closely linked to both inherited and current preparatory and triggering controls. It is not yet possible to assess in all cases conditions for…

Geophysics · Physics 2007-09-18 Theo Van Asch , Jean-Philippe Malet , Ludovicus Van Beek , David Amitrano

We propose using a discounted version of a convex combination of the log-likelihood with the corresponding expected log-likelihood such that when they are maximized they yield a filter, predictor and smoother for time series. This paper…

Methodology · Statistics 2026-04-29 Simon Donker van Heel , Neil Shephard

We consider how to make probability forecasts of binary labels. Our main mathematical result is that for any continuous gambling strategy used for detecting disagreement between the forecasts and the actual labels, there exists a…

Machine Learning · Computer Science 2007-05-23 Vladimir Vovk , Akimichi Takemura , Glenn Shafer

Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split…

Methodology · Statistics 2026-05-29 Aabesh Bhattacharyya , Boxuan Zhang , Rina Foygel Barber

Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…

Methodology · Statistics 2025-05-23 Sam Allen , Jonathan Koh , Johan Segers , Johanna Ziegel

We study the problem of class distribution estimation under dataset shift. On the training dataset, both features and class labels are observed while on the test dataset only the features can be observed. The task then is the estimation of…

Machine Learning · Computer Science 2023-11-30 Dirk Tasche

Non-geometric mobility hazards such as rover slippage and sinkage posing great challenges to costly planetary missions are closely related to the mechanical properties of terrain. In-situ proprioceptive processes for rovers to estimate…

Robotics · Computer Science 2020-11-04 Ruyi Zhou , Wenhao Feng , Huaiguang Yang , Haibo Gao , Nan Li , Zongquan Deng , Liang Ding

This is an expository article/encyclopedia entry explaining the history, techniques, and central results in the field of smooth ergodic theory.

Dynamical Systems · Mathematics 2008-04-02 Amie Wilkinson

This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach:…

Machine Learning · Statistics 2020-11-09 Juho Piironen , Markus Paasiniemi , Aki Vehtari

We study some properties of the characteristic cycle of a constructible complex on a smooth variety over a perfect field, push-forward and product.

Algebraic Geometry · Mathematics 2016-07-14 Takeshi Saito

Since black holes are `black', methods of their identification must necessarily be indirect. Due to very special boundary condition on the horizon, the advective flow behaves in a particular way, which includes formation of centrifugal…

Astrophysics · Physics 2009-10-31 S. K. Chakrabarti

We study the predictability of large events in self-organizing systems. We focus on a set of models which have been studied as analogs of earthquake faults and fault systems, and apply methods based on techniques which are of current…

Condensed Matter · Physics 2009-10-22 S. L. Pepke , J. M. Carlson