Related papers: Individual choice sequences -- History, developmen…
We present a solution of Exercise 1.2.1 of [2] which yields a short new proof of a key step in one of proofs of Brouwer's fixed point theorem, 1910. A few people asked the author about the details of the solution and they might be…
Step by step a substitution of the well known Brouwer choice sequence will be constructed. It begins with an establishing of quasi alternating prime number series followed by a construction of a virtual sequence in sense of the virtual set…
Modeling user preferences (long-term history) and user dynamics (short-term history) is of greatest importance to build efficient sequential recommender systems. The challenge lies in the successful combination of the whole user's history…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
Modeling user sequential behaviors has recently attracted increasing attention in the recommendation domain. Existing methods mostly assume coherent preference in the same sequence. However, user personalities are volatile and easily…
Is it a good idea to use the frequency of events in the past, as a guide to their frequency in the future (as we all do anyway)? In this paper the question is attacked from the perspective of universal prediction of individual sequences. It…
The notion of an individual random sequence goes back to von Mises. We describe the evolution of this notion, especially the use of martingales (suggested by Ville), and the development of algorithmic information theory in 1960s and 1970s…
Analogously to de Bruijn sequences, Orientable sequences have application in automatic position-location applications and, until recently, studies of these sequences focused on the binary case. In recent work by Alhakim et al., recursive…
Modeling the sequential correlation of users' historical interactions is essential in sequential recommendation. However, the majority of the approaches mainly focus on modeling the \emph{intra-sequence} item correlation within each…
Bayesian persuasion and its derived information design problem has been one of the main research agendas in the economics and computation literature over the past decade. However, when attempting to apply its model and theory, one is often…
Recommender systems are ubiquitous in on-line services to drive businesses. And many sequential recommender models were deployed in these systems to enhance personalization. The approach of using the transformer decoder as the sequential…
To make decisions organisms often accumulate information across multiple timescales. However, most experimental and modeling studies of decision-making focus on sequences of independent trials. On the other hand, natural environments are…
Brouwer's fixed point theorem from 1911 is a basic result in topology - with a wealth of combinatorial and geometric consequences. In these lecture notes we present some of them, related to the game of HEX and to the piercing of multiple…
The first seeds of mathematical intuitionism germinated in Europe over a century ago in the constructive tendencies of Borel, Baire, Lebesque, Poincar\'e, Kronecker and others. The flowering was the work of one man, Luitzen Egbertus Jan…
We examine a recursive sequence in which $s_n$ is a literal description of what the binary expansion of the previous term $s_{n-1}$ is not. By adapting a technique of Conway, we determine limiting behaviour of $\{s_n\}$ and dynamics of a…
We study how to infer new choices from previous choices in a conservative manner. To make such inferences, we use the theory of choice functions: a unifying mathematical framework for conservative decision making that allows one to impose…
Though the relationship between the theoretical statistical physics and machine learning techniques has been a well-discussed topic, the studies on the mechanism of learning inspired by the biological system are still developing. In this…
This paper describes new, simple, recursive methods of construction for orientable sequences, i.e. periodic binary sequences in which any n-tuple occurs at most once in a period in either direction. As has been previously described, such…
It can be important in Bayesian analyses of complex models to construct informative prior distributions which reflect knowledge external to the data at hand. Nevertheless, how much prior information an analyst can elicit from an expert will…
A case is made that researchers are interested in studying processes. Often the inferences they are interested in making are about the process and its associated population. On other occasions, a researcher may be interested in making an…