On the Complexity of Zero Gap MIP*

The class $\mathsf{MIP}^*$ is the set of languages decidable by multiprover interactive proofs with quantum entangled provers. It was recently shown by Ji, Natarajan, Vidick, Wright and Yuen that $\mathsf{MIP}^*$ is equal to $\mathsf{RE}$, the set of recursively enumerable languages. In particular this shows that the complexity of approximating the quantum value of a non-local game $G$ is equivalent to the complexity of the Halting problem. In this paper we investigate the complexity of deciding whether the quantum value of a non-local game $G$ is exactly $1$. This problem corresponds to a complexity class that we call zero gap $\mathsf{MIP}^*$, denoted by $\mathsf{MIP}^*_0$, where there is no promise gap between the verifier's acceptance probabilities in the YES and NO cases. We prove that $\mathsf{MIP}^*_0$ extends beyond the first level of the arithmetical hierarchy (which includes $\mathsf{RE}$ and its complement $\mathsf{coRE}$), and in fact is equal to $\Pi_2^0$, the class of languages that can be decided by quantified formulas of the form $\forall y \, \exists z \, R(x,y,z)$. Combined with the previously known result that $\mathsf{MIP}^{co}_0$ (the commuting operator variant of $\mathsf{MIP}^*_0$) is equal to $\mathsf{coRE}$, our result further highlights the fascinating connection between various models of quantum multiprover interactive proofs and different classes in computability theory.Comment: Fixed typos and edited protocol to more smoothly follow from reference

Assessing the levels of livability in informal settlements (Case study: Falahat neighborhood, Urmia city)

Objective: Informal settlements face many problems due to lack of proper planning, as they suffer from low service per capita and do not have space to spend their free time. The main purpose of this study is to assess the mental perception of people about the state of living needs and in general the levels of livability in Falahat neighborhood. This neighborhood has poor living conditions due to being marginalized. Methods: The research method is applied in terms of purpose and descriptive-analytical in nature, which has been collected in the form of documents and field surveys. livability criterias in this study include social, economic and physical and environmental. The statistical population of this study is the residents of Falahat neighborhood of Urmia, which according to the health care center statistics in 1397, has a population of 15,000 people. The Cochran's formula was used for sampling and the sample size is 374, which was randomly distributed. Data analysis was performed quantitatively through statistical methods (one-sample t-test and Friedman test). The validity of the questionnaire was confirmed by experts and the reliability of the questionnaire was confirmed by Cronbach's alpha test with a value of 0.732. Results: Findings show that in the social dimension of the three indicators of medical and health considerations and care, personal and social security and participation and solidarity, in the economic dimension of the index of consumer goods and in the physical and environmental dimensions of the facilities and services of infrastructure, pollution and environmental health, Landscape, green space and wasteland have a moderate level of livability. Also, social, economic, physical and environmental dimensions have the same ranking. Conclusion: The results of the research show that the livability of Falahat neighborhood in Urmia is at a moderate level according to the three dimensions of social, economic and physical and environmental, which requires the adoption of empowerment strategies

A generalization of CHSH and the algebraic structure of optimal strategies

Self-testing has been a rich area of study in quantum information theory. It allows an experimenter to interact classically with a black box quantum system and to test that a specific entangled state was present and a specific set of measurements were performed. Recently, self-testing has been central to high-profile results in complexity theory as seen in the work on entangled games PCP of Natarajan and Vidick (FOCS 2018), iterated compression by Fitzsimons et al. (STOC 2019), and NEEXP in MIP* due to Natarajan and Wright (FOCS 2019). In this work, we introduce an algebraic generalization of CHSH by viewing it as a linear constraint system (LCS) game, exhibiting self-testing properties that are qualitatively different. These provide the first example of non-local games that self-test non-Pauli operators resolving an open questions posed by Coladangelo and Stark (QIP 2017). Our games also provide a self-test for states other than the maximally entangled state, and hence resolves the open question posed by Cleve and Mittal (ICALP 2012). Additionally, our games have $1$ bit question and $\log n$ bit answer lengths making them suitable candidates for complexity theoretic application. This work is the first step towards a general theory of self-testing arbitrary groups. In order to obtain our results, we exploit connections between sum of squares proofs, non-commutative ring theory, and the Gowers-Hatami theorem from approximate representation theory. A crucial part of our analysis is to introduce a sum of squares framework that generalizes the \emph{solution group} of Cleve, Liu, and Slofstra (Journal of Mathematical Physics 2017) to the non-pseudo-telepathic regime. Finally, we give the first example of a game that is not a self-test. Our results suggest a richer landscape of self-testing phenomena than previously considered.Comment: Incorporated reviewers comments and fixed typo

Comparison of Forgiveness and Religious Commitment in Couples on the on the Brink of Divorce and Normal Couples

The rising rate of divorce in Iranian society is disconcerting. This study aimed at comparing religious commitment and forgiveness in couples on the rink of divorce and normal couples. The research method is descriptive and causal-comparative. To select the group of couples on the brink of divorce, firstly, the researcher referred to counseling units of the courts and law offices of various cities of the Guilan province. The cases of the couples who were qualified to enter the study were reviewed and of these cases 173 were selected based on availability. Then, 143 normal couples referring to the courts and offices of lawyers which the cause of their resort is nothing but the completions of the divorce case were selected through purposive sampling. They responded to Glock and Stark's Religious Commitment questionnaire, and Ray and et al Forgiveness scale. Obtained data were analyzed by Pearson Chi-squares, independent t-test, multivariate analysis of variance. The results showed that the mean of forgiveness and religious Commitment in couples on the brink of divorce and normal couples significantly different, that is, couples on the brink of divorce have less level of forgiveness than normal couples and in terms of faithfulness and ritual religious commitment, they scored less scores than normal couples. The remarkable difference between the two groups has important marital therapy implications for implementation of forgiveness-oriented intervention and also promotion of religious beliefs and ritual among couples in order to maintain and strengthen the marriage contract

An analysis of the prioritization of indicators of a child-friendly city (Case study: 5 regions of Urmia)

Introduction: The main purpose of this study is an analysis of the prioritization of indicators of a child-friendly city in the five regions of Urmia to review strategies for improving the situation of each region by examining the indicators of a child-friendly city and ranking the regions of this city.Data and Method: The research method of the present study is applied in terms of purpose and descriptive-analytical in nature. The statistical population of this study is the residents of 5 regions of Urmia. To determine the sample size, Cochran's formula was used. The sample size was 384, which was randomly distributed in the range. The criteria studied in this study include physical, access, socio-cultural and environmental criteria. Data analysis has been done quantitatively and qualitatively. One-sample t-test, Kruskal-Wallis, Spearman correlation, and THIESSEN and OPA method were used to analyze the data. The validity of the questionnaire was confirmed by experts and its reliability was confirmed by Cronbach's alpha test with a value of 0.790.Results: The findings of this study indicate that based on field data and the child-friendly city criteria questionnaire, Urmia Region 1 is ranked first and Urmia Region 2 is ranked fifth among other regions. The results of the Spearman correlation test indicate that the physical criterion has the greatest impact on a child-friendly city.Conclusion: The results of this study indicate that the city of Urmia is at a moderate level in terms of the feasibility of the criteria of a child-friendly city and needs the attention of urban management to improve the situation in regions 2 and 3 of Urmia

Predicting Psychological Well-Being of Mothers of Mentally Retarded Children Based on Perceived Social Support, Defense Styles and Self-Compassion

The purpose of this study was to predict the psychological well-being of mothers of mentally retarded children based on perceived social support, defense styles, and self-compassion. The research design was a descriptive-correlational study and the methodology is basic in purpose. The statistical population included mothers of mentally retarded elementary school students in exceptional schools in the northern cities of Khuzestan province (Shoush, Andimeshk and Dezful) in the school year 2020-2021, among whom 120 mothers were selected through purposive sampling. The instruments were: Psychological Well-Being (RSPWB), Multidimensional Perceived Social Support Scale (MSPSS), Defense Styles Questionnaire (DSQ), and Self-Compassion Scale (SCS). Data analysis was performed using Pearson correlation and multiple regression analysis with the method of simultaneous entry in SPSS-24 software. The results showed that there was a positive and significant relationship between psychological well-being and perceived social support, mature defense styles, and self-compassion, and a negative and significant relationship with neurotic and immature defense styles. The results of multiple regression analysis showed that 81% of the changes in psychological well-being were predicted by perceived social support, defense styles, and self-compassion. Based on the knowledge of the main factors affecting psychological well-being, planning and intervention measures can be taken to increase it and reduce problems

Effects of silver nanoparticles added into polyurea coating on sulfate-reducing bacteria activity and electrochemical properties; an environmental nano-biotechnology investigation

In the present work, Ag nanoparticles were added to polyurea coating in order to improve its antibacterial and electrochemical properties in sulfide-reducing bacteria-containing media. To this end, Ag nano-powder was mixed with two component polyuria, and then the antibacterial behavior of the nanocomposite coating was studied in sulfate-reducing bacteria (SRB)-containing medium. The results revealed the inhibitory effects of nanocomposite coating on the formation of SRB biofilms on the samples. Moreover, the SRB population decreased in contact with the Ag nanoparticles-mixed coating over 7 days. Investigation of the growth and activity of the bacteria represented the effective antibacterial properties of Ag nanoparticles in the polyurea matrix. Furthermore, EIS (electrochemical impedance spectroscopy) measurements indicated that the corrosion properties of the nanocomposite coating improved considerably over 7 days. The coating resistance increased 2 times by adding Ag nanoparticles after 1 day and 3.3 times after 7 days. In accordance with the same results, the charge transfer resistance increased 1.5 times and 1.1 times by adding Ag nanoparticles after 1 day and 7 days, respectively. The improvement in the protective properties of the nanocomposite coating are reflected in the increase in both film and charge transfer resistance

Global estimates on the number of people blind or visually impaired by cataract: a meta-analysis from 2000 to 2020

Background: To estimate global and regional trends from 2000 to 2020 of the number of persons visually impaired by cataract and their proportion of the total number of vision-impaired individuals. Methods: A systematic review and meta-analysis of published population studies and gray literature from 2000 to 2020 was carried out to estimate global and regional trends. We developed prevalence estimates based on modeled distance visual impairment and blindness due to cataract, producing location-, year-, age-, and sex-specific estimates of moderate to severe vision impairment (MSVI presenting visual acuity &lt;6/18, ≥3/60) and blindness (presenting visual acuity &lt;3/60). Estimates are age-standardized using the GBD standard population. Results: In 2020, among overall (all ages) 43.3 million blind and 295 million with MSVI, 17.0 million (39.6%) people were blind and 83.5 million (28.3%) had MSVI due to cataract blind 60% female, MSVI 59% female. From 1990 to 2020, the count of persons blind (MSVI) due to cataract increased by 29.7%(93.1%) whereas the age-standardized global prevalence of cataract-related blindness improved by −27.5% and MSVI increased by 7.2%. The contribution of cataract to the age-standardized prevalence of blindness exceeded the global figure only in South Asia (62.9%) and Southeast Asia and Oceania (47.9%). Conclusions: The number of people blind and with MSVI due to cataract has risen over the past 30 years, despite a decrease in the age-standardized prevalence of cataract. This indicates that cataract treatment programs have been beneficial, but population growth and aging have outpaced their impact. Growing numbers of cataract blind indicate that more, better-directed, resources are needed to increase global capacity for cataract surgery.</p