On Some Geometric Properties of Slice Regular Functions of a Quaternion Variable

The goal of this paper is to introduce and study some geometric properties of slice regular functions of quaternion variable like univalence, subordination, starlikeness, convexity and spirallikeness in the unit ball. We prove a number of results, among which an Area-type Theorem, Rogosinski inequality, and a Bieberbach-de Branges Theorem for a subclass of slice regular functions. We also discuss some geometric and algebraic interpretations of our results in terms of maps from $\mathbb R^4$ to itself. As a tool for subordination we define a suitable notion of composition of slice regular functions which is of independent interest

Disclosure Style and Its Determinants in Integrated Reports

Integrated Reporting promotes a more cohesive and efficient approach to corporate reporting and aims to improve the quality of information available to providers of financial capital. The purpose of this paper was to investigate the determinants of readability and optimism which build the disclosure style of integrated reports. Our research draws on impression management theory and legitimacy theory, while also taking into consideration the cultural system of Hofstede with its further developments by Gray. Our sample consisted of 30 annual reports, extracted randomly from the Integrated Reporting examples database set up by the International Integrated Reporting Council. For the purposes of our investigation, we have carried out a multivariate regression analysis. Firstly, our results show that the higher the revenues of the reporting company, the more balanced their integrated reports, while younger companies use a more optimistic tone when reporting. Additionally, optimism seems to be inversely correlated with the length of the reports. Secondly, entities based in countries with a stronger tendency towards transparency surprisingly provide less readable integrated reports. It was also revealed that companies operating in non-environmentally sensitive industries, as well as International Financial Reporting Standards adopters deliver foggier and thus less readable integrated reports

Learnability with PAC Semantics for Multi-agent Beliefs

The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence. In an influential paper, Valiant recognised that the challenge of learning should be integrated with deduction. In particular, he proposed a semantics to capture the quality possessed by the output of Probably Approximately Correct (PAC) learning algorithms when formulated in a logic. Although weaker than classical entailment, it allows for a powerful model-theoretic framework for answering queries. In this paper, we provide a new technical foundation to demonstrate PAC learning with multi-agent epistemic logics. To circumvent the negative results in the literature on the difficulty of robust learning with the PAC semantics, we consider so-called implicit learning where we are able to incorporate observations to the background theory in service of deciding the entailment of an epistemic query. We prove correctness of the learning procedure and discuss results on the sample complexity, that is how many observations we will need to provably assert that the query is entailed given a user-specified error bound. Finally, we investigate under what circumstances this algorithm can be made efficient. On the last point, given that reasoning in epistemic logics especially in multi-agent epistemic logics is PSPACE-complete, it might seem like there is no hope for this problem. We leverage some recent results on the so-called Representation Theorem explored for single-agent and multi-agent epistemic logics with the only knowing operator to reduce modal reasoning to propositional reasoning

Predicting battery depletion of neighboring wireless sensor nodes

With a view to prolong the duration of the wireless sensor network, many battery lifetime prediction algorithms run on individual nodes. If not properly designed, this approach may be detrimental and even accelerate battery depletion. Herein, we provide a comparative analysis of various machine-learning algorithms to offload the energy inference task to the most energy-rich nodes, to alleviate the nodes that are entering the critical state. Taken to its extreme, our approach may be used to divert the energy-intensive tasks to a monitoring station, enabling a cloud-based approach to sensor network management. Experiments conducted in a controlled environment with real hardware have shown that RSSI can be used to infer the state of a remote wireless node once it is approaching the cutoff point. The ADWIN algorithm was used for smoothing the input data and for helping a variety of machine learning algorithms particularly to speed up and improve their prediction accuracy