Stochastic control liaisons: Richard Sinkhorn meets gaspard monge on a schr\uf6dinger bridge

In 1931-1932, Erwin Schr\uf6dinger studied a hot gas Gedankenexperiment (an instance of large deviations of the empirical distribution). Schr\uf6dinger's problem represents an early example of a fundamental inference method, the so-called maximum entropy method, having roots in Boltzmann's work and being developed in subsequent years by Jaynes, Burg, Dempster, and Csisz\ue1r. The problem, known as the Schr\uf6dinger bridge problem (SBP) with "uniform"prior, was more recently recognized as a regularization of the Monge-Kantorovich optimal mass transport (OMT) problem, leading to effective computational schemes for the latter. Specifically, OMT with quadratic cost may be viewed as a zerotemperature limit of the problem posed by Schr\uf6dinger in the early 1930s. The latter amounts to minimization of Helmholtz's free energy over probability distributions that are constrained to possess two given marginals. The problem features a delicate compromise, mediated by a temperature parameter, between minimizing the internal energy and maximizing the entropy. These concepts are central to a rapidly expanding area of modern science dealing with the so-called Sinkhorn algorithm, which appears as a special case of an algorithm first studied in the more challenging continuous space setting by the French analyst Robert Fortet in 1938-1940 specifically for Schr\uf6dinger bridges. Due to the constraint on end-point distributions, dynamic programming is not a suitable tool to attack these problems. Instead, Fortet's iterative algorithm and its discrete counterpart, the Sinkhorn iteration, permit computation of the optimal solution by iteratively solving the so-called Schr\uf6dinger system. Convergence of the iteration is guaranteed by contraction along the steps in suitable metrics, such as Hilbert's projective metric. In both the continuous as well as the discrete time and space settings, stochastic control provides a reformulation of and a context for the dynamic versions of general Schr\uf6dinger bridge problems and of their zero-temperature limit, the OMT problem. These problems, in turn, naturally lead to steering problems for flows of one-time marginals which represent a new paradigm for controlling uncertainty. The zero-temperature problem in the continuous-time and space setting turns out to be the celebrated Benamou-Brenier characterization of the McCann displacement interpolation flow in OMT. The formalism and techniques behind these control problems on flows of probability distributions have attracted significant attention in recent years as they lead to a variety of new applications in spacecraft guidance, control of robot or biological swarms, sensing, active cooling, and network routing as well as in computer and data science. This multifaceted and versatile framework, intertwining SBP and OMT, provides the substrate for the historical and technical overview of the field given in this paper. A key motivation has been to highlight links between the classical early work in both topics and the more recent stochastic control viewpoint, which naturally lends itself to efficient computational schemes and interesting generalizations

The effect of Visual Design Quality on Player Experience Components in Tablet Games

Research in the field of Human Computer Interaction Design indicates that there is a need to develop further methods, tools, and frameworks for the design and evaluation of digital game interfaces. This thesis aims to design, develop, and evaluate two different types of tablet games with varying visual design quality interfaces to examine users’ perceptions of hedonic quality, visual design, emotions, and game enjoyment in different channels of experience. The design-oriented approach was adopted to combine both creative practice and scientific inquiry in the game design process and empirical evaluation. Hypotheses were formulated to explore the significance of visual design quality in relation to the components of player experience. The study entailed two phases. In the first phase, participatory design methods were employed to design and develop the tablet games encompassing mind-mapping techniques, focus groups, iterative prototyping with multiple cycles of usability testing of user interfaces. In the second phase, survey instruments were applied to collect and analyze data from 111 participants using tablet games as stimuli in a controlled experimental condition. The main contribution of this research is creation of a player experience model, validated in the domain of tablet gaming, to serve as a new theory. This research will allow for game researchers and practitioners to obtain a deeper understanding of the significance of the player experience framework components to create optimal player experience in tablet games. The finding shows that highly attractive game user interfaces were perceived to have higher utility and ease of use. Participants exhibited higher levels of arousal and valence in the high visual design quality interfaces mediated by hedonic quality. Participants who were highly sensitive to visual design did not necessarily derive the highest level of game enjoyment. Participants derived a heightened level of engagement in the arousal channel of experience and the highest level of enjoyment in the flow state. The use of 2.5D graphics and analogous color schemes created a spatial illusion that captivated users' attention. Practitioners are encouraged to design game artifacts with feature sets and mechanics capable of transporting players into the state of flow, as this is the stage where they experience game control, excitement and relaxation in addition to game immersion in the state of arousal

MountainRise, Volume 3, Number 1

Volume 3, Number 1 (2006). MountainRise, an open, peer-reviewed, international electronic journal, was published by the Coulter Faculty Commons for Excellence in Teaching & Learning at Western Carolina University. Originating in the ancient mountains of western North Carolina, MountainRise served as an international vehicle for the Scholarship of Teaching & Learning (SoTL). MountainRise applied insightful scholarly methodologies to the processes of teaching and learning. The aim of the journal was to foster a higher education culture that embraced innovation in teaching and learning

The Use of digital games to enhance the physical exercise activity of the elderly : a case of Finland

According to the World Health Organization (WHO), population ageing is a global phenomenon, which brings both challenges and opportunities for society. The current longer expected lifespan can create opportunities for the elderly to contribute in many ways to their families and communities. However, it greatly depends on their quality of life, which is affected by many factors, including physical and functional health, social well-being, and cognitive abilities. The WHO (2012) states that physical health is one of the indicators for the elderly’s quality of life, and it declines with increasing age. Participation in regular physical exercises can help the elderly improve their physical and mental health, and this has been aided by the use of modern technologies to promote the elderly’s physical and functional health. Of these latest technologies, digital games have shown promise to improve and enhance the elderly’s physical activities through fun and engaging gameplay. The literature highlights that some commercial games in the market (e.g. Microsoft Kinect- Sports and Nintendo Wii Sports games) have the potential to improve the elderly’s physical health such as gait, balance, and fall prevention. However, researchers argue that these commercial games are not designed specifically for the elderly and their physical exercise activities. They state that most commercial games are not user-friendly for the elderly whose functional and physical abilities are limited due to their advanced years. The literature points out that more studies need to be undertaken to understand the usability and usefulness of digital games for physical exercise activities so that game designers can create elderly-friendly digital games in the future. In Finland, the government has been focusing on promoting healthy ageing and increasing home care services for the elderly. In recent years, Finnish researchers have used digital games to promote older Finns’ healthy and active ageing. The existing literature, whilst showing the potential of digital games for elderly Finns’ physical health, also acknowledges further research is needed particularly in the context of Finland. Thus, in this study, we aimed at investigating digital games to specifically assess their applications for older Finns’ physical activities, focusing on the quality of users’ experiences, and their reported ease of use and perceived usefulness. We used the mixed methods approach, which applies both qualitative and quantitative research methods. The study design included four stages: requirements gathering, analysis and design, prototyping, and evaluation. Firstly, we conducted pre-studies to elicit users’ requirements. This was followed by the analysis of the resulting data to identify trends and patterns, which fuelled ideas in the brainstorming game design and development phases. The final product was a digital game-based physical exercise called the Skiing Game. We then evaluated the Skiing Game in Finland with 21 elderly Finns (M=7, F=14, Average Age =76). By using questionnaires, observation, and interviews, we investigated user experiences, focusing on the game’s usability, and usefulness for enhancing the physical activity and wellbeing of the elderly. We also conducted a comparative test of the Skiing Game in Japan with 24 elderly Japanese participants (M=12, F=12, Average Age = 72) to further understand non-Finnish elderly users’ experiences. The findings from the usability study of the Skiing Game in Finland demonstrated that elderly Finns had a positive experience in the gameplay, and their motivation was noticeably high. It also confirmed that elderly Finns have a genuine interest in digital game-based exercises and strong intentions to play digital games as a form of physical exercise in the future. Although prior to the study most of them had negative views and misconceptions about digital games, after the gameplay their attitudes were decidedly positive. They acknowledged that whilst playing digital games could be an alternative way of exercising for them their use would primarily be when they don’t have access to their usual non-digital physical exercise. The Japanese usability of the Skiing Game showed that the elderly Japanese people also had positive user experiences in playing digital games, and also intend to use them in the future. Similarly, after playing the game they reported that their attitudes towards digital games become positive, and indicated playing digital games could be an alternative way of exercising. Although the comparison of the two studies suggests that the elderly Finns had relatively more positive experiences whilst playing the Skiing Game, compared to their Japanese counterparts, in general, both groups had a positive experience in the gameplay and showed interest in digital games as an alternative exercise. Based on the usability lessons learned from these two studies, recommendations for practitioners and designers regarding improvements in game design and development are made in this report. Implementing these modifications into future designs and further development of digital games for the elderly will improve their commercial viability and user uptake. The findings from this study can provide valuable insights, particularly for Finnish policymakers and healthcare practitioners who are keen to introduce digital games into the aged-care sector in Finland. The studies have also provided valuable insights into the optimal methods for introducing Finnish digital games to international markets, in particular, digital games tailored specifically for the physical exercise needs and motivations of the elderly. By taking into consideration the limitations of the study, we provide our future studies and further improvements of the game to be conducted

Global Constraint Catalog, 2nd Edition

This report presents a catalogue of global constraints where each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing filtering algorithms

Global Constraint Catalog, 2nd Edition (revision a)

This report presents a catalogue of global constraints where each constraint is explicitly described in terms of graph properties and/or automata and/or first order logical formulae with arithmetic. When available, it also presents some typical usage as well as some pointers to existing filtering algorithms