Subexponential Algorithms for Unique Games and Related Problems

2015 ◽  
Vol 62 (5) ◽  
pp. 1-25 ◽  
Author(s):  
Sanjeev Arora ◽  
Boaz Barak ◽  
David Steurer
Keyword(s):  
Subexponential Algorithms ◽  
Unique Games

Psychotherapeutic components of commercially available virtual reality games (Preprint)

2020 ◽  
Author(s):  
Almira Osmanovic Thunström ◽  
Iris Sarajlic Vuković ◽  
Lilas Ali ◽  
Tomas Larson ◽  
Steinn Steingrimsson
Keyword(s):  
Mental Health ◽  
Virtual Reality ◽  
Mental Health Problems ◽  
Treatment Strategies ◽  
Treatment Method ◽  
Health Problems ◽  
E Learning ◽  
The Mean ◽  
Unique Games

BACKGROUND Immersive virtual reality (VR) games are increasingly becoming part of everyday life. Several studies support immersive VR technology as a treatment method for mental health problems. There is however minimal research into the feasibility, prevalence, and quality of commercially available VR games on commercial platforms as tools for treatment or add on to treatment of mental health problems. OBJECTIVE The aim of this study was to explore the prevalence, feasibility and quality of commercially available games related to psychotherapy on a commercially available platform. METHODS We performed a search for keywords related to diagnosis and treatment strategies of mental health problems. The search was performed during March 27th on STEAM (VR content and gaming platform). A usability scale was used as a tool to look at the interaction and usability of the games, the VR-UI-UX-8. The tool contains 8 statements about usability scored 0-10, 0 indicating “Not at all” and 10 indicating “very much so”. The score ranges from 0-80 with a higher score indicating worse usability. RESULTS In total, 516 hits were found, 371 unique games. After the games were reviewed, 83 games passed the inclusion criteria, were purchased and played. Majority of the games which were excluded were either not connected to mental health, contained violence, adult content or were in other ways irrelevant or inappropriate. The mean score for the games on the VR-UI-UX-8 was 16.5 (standard deviation 15.8) with a range from 0-68. Most relevant and feasible games were found in the search words meditation, mindfulness, and LSD. CONCLUSIONS Commercial platforms hold great potential for VR games with psychotherapeutic components. The platforms are only at the beginning of the development towards serious games, e-learning and psychotherapeutic treatments. Currently the quality and usability for clinical and at home applicability are scarce, but hold great potential.

scholarly journals Three candidate plurality is stablest for small correlations

2021 ◽  
Vol 9 ◽  
Author(s):  
Steven Heilman ◽  
Alex Tarter
Keyword(s):  
Structure Theorem ◽  
Semidefinite Program ◽  
Dimensional Euclidean Space ◽  
List Type ◽  
Noise Stability ◽  
Equal Chance ◽  
Unique Games Conjecture ◽  
Fixed Constant ◽  
Correlation Parameters ◽  
Unique Games

Abstract Using the calculus of variations, we prove the following structure theorem for noise-stable partitions: a partition of n-dimensional Euclidean space into m disjoint sets of fixed Gaussian volumes that maximise their noise stability must be $(m-1)$ -dimensional, if $m-1\leq n$ . In particular, the maximum noise stability of a partition of m sets in $\mathbb {R}^{n}$ of fixed Gaussian volumes is constant for all n satisfying $n\geq m-1$ . From this result, we obtain: (i) A proof of the plurality is stablest conjecture for three candidate elections, for all correlation parameters $\rho $ satisfying $0<\rho <\rho _{0}$ , where $\rho _{0}>0$ is a fixed constant (that does not depend on the dimension n), when each candidate has an equal chance of winning. (ii) A variational proof of Borell’s inequality (corresponding to the case $m=2$ ). The structure theorem answers a question of De–Mossel–Neeman and of Ghazi–Kamath–Raghavendra. Item (i) is the first proof of any case of the plurality is stablest conjecture of Khot-Kindler-Mossel-O’Donnell for fixed $\rho $ , with the case $\rho \to L1^{-}$ being solved recently. Item (i) is also the first evidence for the optimality of the Frieze–Jerrum semidefinite program for solving MAX-3-CUT, assuming the unique games conjecture. Without the assumption that each candidate has an equal chance of winning in (i), the plurality is stablest conjecture is known to be false.

scholarly journals Subexponential Algorithms for Class Group and Unit Computations

1997 ◽  
Vol 24 (3-4) ◽  
pp. 433-441 ◽  
Author(s):  
H. COHEN ◽  
F. DIAZ Y DIAZ ◽  
M. OLIVIER
Keyword(s):  
Class Group ◽  
Subexponential Algorithms
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