Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation

We present a quantum algorithm to solve systems of linear equations of the form Ax = b , where A is a tridiagonal Toeplitz matrix and b results from discretizing an analytic function, with a circuit complexity of O (1/√ε, poly (log κ, log N )), where N denotes the number of equations, ε is the accuracy, and κ the condition number. The repeat-until-success algorithm has to be run O (κ/(1-ε)) times to succeed, leveraging amplitude amplification, and needs to be sampled O (1/ε 2 ) times. Thus, the algorithm achieves an exponential improvement with respect to N over classical methods. In particular, we present efficient oracles for state preparation, Hamiltonian simulation, and a set of observables together with the corresponding error and complexity analyses. As the main result of this work, we show how to use Richardson extrapolation to enhance Hamiltonian simulation, resulting in an implementation of Quantum Phase Estimation (QPE) within the algorithm with 1/√ε circuits that can be run in parallel each with circuit complexity 1/√ ε instead of 1/ε. Furthermore, we analyze necessary conditions for the overall algorithm to achieve an exponential speedup compared to classical methods. Our approach is not limited to the considered setting and can be applied to more general problems where Hamiltonian simulation is approximated via product formulae, although our theoretical results would need to be extended accordingly. All the procedures presented are implemented with Qiskit and tested for small systems using classical simulation as well as using real quantum devices available through the IBM Quantum Experience.

Survival strategies of SMEs amidst the COVID-19 pandemic: application of SEM and fsQCA

Purpose As a global pandemic, the COVID-19 crisis has profoundly affected the development of local firms, threatening the survival of small and medium enterprises (SMEs). This study aims to present an integrated framework by investigating the impact of strategic tools (i.e. firms’ capability of business agility, marketing operational efficiency, optimisation of innovation capability [OIC], managing employees’ satisfaction and rethinking customers’ experience) on the survival strategies of SMEs amidst the COVID-19 pandemic. Design/methodology/approach The current study used data from managers of SMEs and conducted an asymmetrical analysis (i.e. structural equation modelling [SEM]) to investigate the factors influencing the survival strategies of SMEs amidst the COVID-19 pandemic. This study also applied an asymmetrical approach (i.e. fuzzy sets qualitative comparative analysis-fsQCA) to explore the causal recipes and analysis of the necessary conditions to identify the factors required to achieve the expected outcome. Findings Results from SEM support all hypotheses. Results from fsQCA with the same data set show that firms’ business agility and OIC are necessary conditions for SMEs’ survival strategies. The result from fsQCA also reveals multiple sufficient conditions to succeed SMEs’ survival strategies amidst the COVID-19 pandemic. Practical implications Findings prescribe how SMEs adapt to this vulnerable business condition by applying the strategic tools and recipes suggested for survival. Originality/value This research applied an innovative analysis to reveal necessary and sufficient conditions that conventional methods such as SEM have limited power. This pioneering research in the context of the COVID-19 pandemic is considered novel in terms of the prescriptive strategic recipes offered to SMEs to adapt to and survive in the crisis caused by COVID-19.

Unofficial Media, Government Trust, and System Confidence Evidence From China: An Empirical Exploration of the Attitudes of Netizens Based on the Dual Moderating Effect

Mass media has a significant impact on public support for the government. This manuscript constructs a mixed model with official media use as the moderating variable and government trust as the intermediary variable to explore the mechanism of how unofficial media use affects system confidence, using data from a survey of the political and social attitudes of netizens (2015). The study finds that official media use weakens the negative role of unofficial media use in building system confidence, with the intermediary variable of government trust creating the necessary conditions for weakening the effect of unofficial media use. Moreover, the effect of unofficial media use on system confidence is heterogeneous. These findings remind us that it is necessary to deepen research into the micromechanisms that explain how unofficial media use reduces system confidence, a task for which cognitive theory is well suited.

Boundaries and borders gone! But life goes on

Unlike machines, living systems are distinguished by the continual destruction and regeneration of their boundaries and other components. Stable Markov blankets may be a real feature of the world, or they may be merely a construction of particular models, but they are neither a feature of organisms nor of any model that can capture the necessary conditions of their existence.

The age psychology of minors as a factor determining the features of the preliminary investigation of criminal cases involving them

The age psychology of minors is considered as a factor determining the features of the preliminary investigation of criminal cases involving them. The article deals with issues related to the age psychology of minors, the object of which are the laws, patterns and trends of change in the human psyche, his behavior, life and personality throughout his life. At the same time, it is noted in the legal literature that most crimes committed by minors are due to age-related motivational specifics, committed on the basis of mischief, a misinterpreted sense of camaraderie and romance, the desire for self-affirmation, imitation of both adults and peers who enjoy authority. The behavioral basis of juvenile offenders is formed under the influence of a number of factors, knowledge of which can be important when making tactical and procedural decisions by an investigator during pre-trial proceedings in a criminal case. The behavior of adolescents is largely related to their age characteristics, which largely determine their behavior, which can be observed, including during the preliminary investigation of criminal cases involving them. Thus, knowledge of the peculiarities of age psychology can make it possible to determine the most effective measures of educational work aimed at correcting behavior, correcting and re-educating juvenile offenders. It is these goals that the legislator takes into account, establishing the specifics of the proceedings both in cases of crimes committed by minors and the regulation of investigative actions involving minor victims and witnesses. The peculiarities of the age psychology of minors must also be taken into account when choosing the tactics of investigative actions carried out with their participation, since this is one of the necessary conditions for achieving the goal of the investigative action and the preliminary investigation as a whole.

The Problems Experienced by Employees with Chronic Disease during the COVID-19 Pandemic

Chronic diseases served as a silent global epidemic before the pandemic, and individuals living with chronic disease now form one of the groups most affected by COVID-19. This study aims to determine the problems that employees with chronic disease face during the COVID-19 pandemic. As part of the study, data were collected from 952 individuals who live with chronic disease in Turkey. Of these, 76.6% of respondents worked for the public sector, a large majority of whom (67.7%) have worked full time during the COVID-19 pandemic. It was found that the COVID-19 fear level of employees living with chronic disease was higher than moderate (21.061 ± 7.607). When the variables affecting the COVID-19 fear level are listed in order of relative significance, eating problems, residing in the Mediterranean region, having asthma, and working as a female employee made the greatest impact, respectively. Necessary conditions of work should be provided to those living with chronic disease who could adapt themselves to working flexibly or working from home, so that they would not feel isolated from business life. This group should be provided with essential protective equipment, their working conditions must be reviewed and vaccination priority could be given to them.

Mixed-Norm Amalgam Spaces and Their Predual

In this paper, we introduce mixed-norm amalgam spaces (Lp→,Ls→)α(Rn) and prove the boundedness of maximal function. Then, the dilation argument obtains the necessary and sufficient conditions of fractional integral operators’ boundedness. Furthermore, the strong estimates of linear commutators [b,Iγ] generated by b∈BMO(Rn) and Iγ on mixed-norm amalgam spaces (Lp→,Ls→)α(Rn) are established as well. In order to obtain the necessary conditions of fractional integral commutators’ boundedness, we introduce mixed-norm Wiener amalgam spaces (Lp→,Ls→)(Rn). We obtain the necessary and sufficient conditions of fractional integral commutators’ boundedness by the duality theory. The necessary conditions of fractional integral commutators’ boundedness are a new result even for the classical amalgam spaces. By the equivalent norm and the operators Str(p)(f)(x), we study the duality theory of mixed-norm amalgam spaces, which makes our proof easier. In particular, note that predual of the primal space is not obtained and the predual of the equivalent space does not mean the predual of the primal space.

Regularity of extended conjugate graphs of finite groups

<abstract><p>The extended conjugate graph associated to a finite group $ G $ is defined as an undirected graph with vertex set $ G $ such that two distinct vertices joined by an edge if they are conjugate. In this article, we show that several properties of finite groups can be expressed in terms of properties of their extended conjugate graphs. In particular, we show that there is a strong connection between a graph-theoretic property, namely regularity, and an algebraic property, namely nilpotency. We then give some sufficient conditions and necessary conditions for the non-central part of an extended conjugate graph to be regular. Finally, we study extended conjugate graphs associated to groups of order $ pq $, $ p^3 $, and $ p^4 $, where $ p $ and $ q $ are distinct primes.</p></abstract>