On examples of difference operators for {0,1}\{0,1\}-valued functions over finite sets

Recently V.I.Arnold have formulated a geometrical concept of monads and apply it to the study of difference operators on the sets of $\{0,1\}$-valued sequences of length $n$. In the present note we show particular examples of these monads and indicate one question arising here

Detecting Error-Related Negativity for Interaction Design

This paper examines the ability to detect a characteristic brain potential called the Error-Related Negativity (ERN) using off-the-shelf headsets and explores its applicability to HCI. ERN is triggered when a user either makes a mistake or the application behaves differently from their expectation. We first show that ERN can be seen on signals captured by EEG headsets like Emotiv™ when doing a typical multiple choice reaction time (RT) task – Flanker task. We then present a single-trial online ERN algorithm that works by pre-computing the coefficient matrix of a logistic regression classifier using some data from a multiple choice reaction time task and uses it to classify incoming signals of that task on a single trial of data. We apply it to an interactive selection task that involved users selecting an object under time pressure. Furthermore the study was conducted in a typical office environment with ambient noise. Our results show that online single trial ERN detection is possible using off-the-shelf headsets during tasks that are typical of interactive applications. We then design a Superflick experiment with an integrated module mimicking an ERN detector to evaluate the accuracy of detecting ERN in the context of assisting users in interactive tasks. Based on these results we discuss and present several HCI scenarios for use of ERN.This paper examines the ability to detect a characteristic brain potential called the Error-Related Negativity (ERN) using off-the-shelf headsets and explores its applicability to HCI. ERN is triggered when a user either makes a mistake or the application behaves differently from their expectation. We first show that ERN can be seen on signals captured by EEG headsets like Emotiv™ when doing a typical multiple choice reaction time (RT) task – Flanker task. We then present a single-trial online ERN algorithm that works by pre-computing the coefficient matrix of a logistic regression classifier using some data from a multiple choice reaction time task and uses it to classify incoming signals of that task on a single trial of data. We apply it to an interactive selection task that involved users selecting an object under time pressure. Furthermore the study was conducted in a typical office environment with ambient noise. Our results show that online single trial ERN detection is possible using off-the-shelf headsets during tasks that are typical of interactive applications. We then design a Superflick experiment with an integrated module mimicking an ERN detector to evaluate the accuracy of detecting ERN in the context of assisting users in interactive tasks. Based on these results we discuss and present several HCI scenarios for use of ERN

Optimization of self-similar factor approximants

The problem is analyzed of extrapolating power series, derived for an asymptotically small variable, to the region of finite values of this variable. The consideration is based on the self-similar approximation theory. A new method is suggested for defining the odd self-similar factor approximants by employing an optimization procedure. The method is illustrated by several examples having the mathematical structure typical of the problems in statistical and chemical physics. It is shown that the suggested method provides a good accuracy even when the number of terms in the perturbative power series is small.Comment: Latex file, 16 page