A derivative for complex Lipschitz maps with generalised Cauchy–Riemann equations

AbstractWe introduce the Lipschitz derivative or the L-derivative of a locally Lipschitz complex map: it is a Scott continuous, compact and convex set-valued map that extends the classical derivative to the bigger class of locally Lipschitz maps and allows an extension of the fundamental theorem of calculus and a new generalisation of Cauchy–Riemann equations to these maps, which form a continuous Scott domain. We show that a complex Lipschitz map is analytic in an open set if and only if its L-derivative is a singleton at all points in the open set. The calculus of the L-derivative for sum, product and composition of maps is derived. The notion of contour integration is extended to Scott continuous, non-empty compact, convex valued functions on the complex plane, and by using the L-derivative, the fundamental theorem of contour integration is extended to these functions

Reinforcement Learning for Nash Equilibrium Generation

Copyright © 2015, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.We propose a new conceptual multi-agent framework which, given a game with an undesirable Nash equilibrium, will almost surely generate a new Nash equilibrium at some predetennined, more desirable pure action profile. The agent(s) targeted for reinforcement learn independently according to a standard model-free algorithm, using internally-generated states corresponding to high-level preference rankings over outcomes. We focus in particular on the case in which the additional reward can be considered as resulting from an internal (re-)appraisal, such that the new equilibrium is stable independent of the continued application of the procedure

Power domains and iterated function systems

We introduce the notion of weakly hyperbolic iterated function system (IFS) on a compact metric space, which generalises that of hyperbolic IFS. Based on a domain-theoretic model, which uses the Plotkin power domain and the probabilistic power domain respectively, we prove the existence and uniqueness of the attractor of a weakly hyperbolic IFS and the invariant measure of a weakly hyperbolic IFS with probabilities, extending the classic results of Hutchinson for hyperbolic IFSs in this more general setting. We also present finite algorithms to obtain discrete and digitised approximations to the attractor and the invariant measure, extending the corresponding algorithms for hyperbolic IFSs. We then prove the existence and uniqueness of the invariant distribution of a weakly hyperbolic recurrent IFS and obtain an algorithm to generate the invariant distribution on the digitised screen. The generalised Riemann integral is used to provide a formula for the expected value of almost everywh..

Self-attachment: A self-administrable intervention for chronic anxiety and depression

There has been increasing evidence to suggest that the root cause of much mental illness lies in a sub-optimal capacity for affect regulation. Cognition and emotion are intricately linked and cognitive deficits, which are characteristic of many psychiatric conditions, are often driven by affect dysregulation, which itself can usually be traced back to sub-optimal childhood development as supported by Attachment Theory. Individuals with insecure attachment types in their childhoods are prone to a variety of mental illness, whereas a secure attachment type in childhood provides a secure base in life. We therefore propose a holistic approach to tackle chronic anxiety and depression, typical of Axis II clinical disorders, which is informed by the development of the infant brain in social interaction with its primary care-givers. We formulate, in a self-administrable way, the protocols governing the interaction of a securely attached child with its primary care-givers that produce the capacity for affect regulation in the child. We posit that these protocols construct, by neuroplasticity and long term potentiation, new optimal neural pathways in the brains of adults with insecure childhood attachment that suffer from mental disorder. This procedure is called self-attachment and aims to help the individuals to create their own attachment objects in the form of their adult self looking after their inner child

Cultural management and government role

Culture plays an important role on human lives and it has been in four ancient civilizations of China, Iran, Egypt and Greece. The civilization achievements are normally categorized in two different groups of material and immaterial. Practical experience of the material, social objective is called as a civilization and the mental aspect of spiritual experiences, spiritual and personal is called culture. The purpose of this research is to find a framework for cross-cultural management. First, we define the cultural planning and we review the existing cultural examples in Iranian society and try to provide an overall analysis. The paper also investigates the role of government on creating adaptive culture within the society and explains that government must act as leadership in creating value added culture

Foundation of a computable solid modelling

Solid modelling and computational geometry are based on classical topology and geometry in which the basic predicates and operations, such as membership, subset inclusion, union and intersection, are not continuous and therefore not computable. But a sound computational framework for solids and geometry can only be built in a framework with computable predicates and operations. In practice, correctness of algorithms in computational geometry is usually proved using the unrealistic Real RAM machine model of computation, which allows comparison of real numbers, with the undesirable result that correct algorithms, when implemented, turn into unreliable programs. Here, we use a domaintheoretic approach to recursive analysis to develop the basis of an eective and realistic framework for solid modelling. This framework is equipped with a well-dened and realistic notion of computability which reects the observable properties of real solids. The basic predicates and operations o..