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## A formal proof of the ε-optimality of absorbing continuous pursuit algorithms using the theory of regular functions

### Applied Intelligence (2014-10-01) 41: 974-985 , October 01, 2014

The most difficult part in the design and analysis of Learning Automata (LA) consists of the formal proofs of their convergence accuracies. The mathematical techniques used for the different families (Fixed Structure, Variable Structure, Discretized etc.) are quite distinct. Among the families of LA, Estimator Algorithms (EAs) are certainly the fastest, and within this family, the set of Pursuit algorithms have been considered to be the pioneering schemes. Informally, if the environment is stationary, their *ε*-optimality is defined as their ability to converge to the optimal action with an arbitrarily large probability, if the learning parameter is sufficiently small/large. The existing proofs of all the reported EAs follow the same fundamental principles, and to clarify this, in the interest of simplicity, we shall concentrate on the family of Pursuit algorithms. Recently, it has been reported Ryan and Omkar (J Appl Probab 49(3):795–805, ) that the previous proofs for *ε*-optimality of all the reported EAs have a common flaw. The flaw lies in the condition which apparently supports the so-called “monotonicity” property of the probability of selecting the optimal action, which states that after some time instant *t*_{0}, the reward probability estimates will be ordered correctly *forever*. The authors of the various proofs have rather offered a proof for the fact that the reward probability estimates are ordered correctly *at a single point of time* after *t*_{0}, which, in turn, does not guarantee the ordering *forever*, rendering the previous proofs incorrect. While in Ryan and Omkar (J Appl Probab 49(3):795–805, ), a rectified proof was presented to prove the *ε*-optimality of the Continuous Pursuit Algorithm (CPA), which was the pioneering EA, in this paper, a new proof is provided for the Absorbing CPA (ACPA), i.e., an algorithm which follows the CPA paradigm but which artificially has absorbing states whenever any action probability is arbitrarily close to unity. Unlike the previous flawed proofs, instead of examining the monotonicity property of the action probabilities, it rather examines their submartingale property, and then, unlike the traditional approach, invokes the theory of Regular functions to prove that the probability of converging to the optimal action can be made arbitrarily close to unity. We believe that the proof is both unique and pioneering, and adds insights into the convergence of different EAs. It can also form the basis for formally demonstrating the *ε*-optimality of other Estimator algorithms which are artificially rendered absorbing.

## Synthesizing trees by plantons

### The Visual Computer (2006-03-31) 22: 238-248 , March 31, 2006

In this paper, we present a two-level statistical model for characterizing the stochastic and specific nature of trees. At the low level, we define *plantons*, which are a group of similar organs, to depict tree organ details statistically. At the high level, a set of transitions between plantons is provided to describe the stochastic distribution of organs.

Based on such a tree model, we propose a novel tree modeling approach, synthesizing trees by plantons, which are extracted from tree samples. All tree samples are captured from the real world. We have designed a maximum likelihood estimation algorithm to acquire the two-level statistical tree model from single samples or multi- samples. Experimental results show that our new model is capable of synthesizing new trees with similar, yet visually different shapes.

## Refining the Undecidability Frontier of Hybrid Automata

### FSTTCS 2005: Foundations of Software Technology and Theoretical Computer Science (2005-01-01) 3821: 261-272 , January 01, 2005

Reachability becomes undecidable in hybrid automata (HA) that can simulate a Turing (TM) or Minsky (MM) machine. Asarin and Schneider have shown that, between the decidable 2-dim Piecewise Constant Derivative (PCD) class and the undecidable 3-dim PCD class, there lies the “open” class 2-dim Hierarchical PCD (HPCD). This class was shown to be equivalent to the class of 1-dim Piecewise Affine Maps (PAM). In this paper, we first explore 2-dim HPCD’s proximity to decidability, by showing that they are equivalent to 2-dim PCDs with translational resets, and to HPCDs without resets. A hierarchy of intermediates also equivalent to the HPCD class is presented, revealing semblance to timed and initialized rectangular automata. We then explore the proximity to the undecidability frontier. We show that 2-dim HPCDs with zeno executions or integer-checks can simulate the 2-counter MM. We conclude by retreating HPCDs as PAMs, to derive a simple over-approximating algorithm for reachability. This also defines a decidable subclass 1-dim Onto PAM (oPAM). The novel non-trivial transformation of 2-dim HPCDs into “almost decidable” systems, is likely to pave the way for approximate reachability algorithms, and the characterization of decidable subclasses. It is hoped that these ideas eventually coalesce into a complete understanding of the reachability problem for the class 2-dim HPCD (1-dim PAM).

## Back Matter - Supervised and Unsupervised Ensemble Methods and their Applications

### Supervised and Unsupervised Ensemble Methods and their Applications (2008-01-01): 126 , January 01, 2008

## Genetic Algorithms — A Survey of Models and Methods

### Handbook of Natural Computing (2012-01-01): 637-671 , January 01, 2012

This chapter first reviews the simple genetic algorithm. Mathematical models of the genetic algorithm are also reviewed, including the schema theorem, exact infinite population models, and exact Markov models for finite populations. The use of bit representations, including Gray encodings and binary encodings, is discussed. Selection, including roulette wheel selection, rank-based selection, and tournament selection, is also described. This chapter then reviews other forms of genetic algorithms, including the steady-state Genitor algorithm and the CHC (cross-generational elitist selection, heterogenous recombination, and cataclysmic mutation) algorithm. Finally, landscape structures that can cause genetic algorithms to fail are looked at, and an application of genetic algorithms in the domain of resource scheduling, where genetic algorithms have been highly successful, is also presented.

## Challenges of Government Enterprise Architecture Work – Stakeholders’ Views

### Electronic Government (2008-01-01) 5184: 364-374 , January 01, 2008

At present, a vast transformation within government systems is executed towards electronic government. In some countries, this change is initiated as enterprise architecture work. This paper introduces results from an empirical study on different stakeholders’ views on enterprise architecture development within Finnish state government. The data is gathered from 21 interviews accomplished during spring 2007 among participants of the Interoperability Programme of Finnish state administration. The interviewees represent different sectors and levels of Finnish government and IT companies. On the basis of qualitative data analysis we discuss challenges of enterprise architecture work in the context of state government. The key conclusion is that the governance level of enterprise architecture needs to be adequately adjusted and enforced as a tool for the development of business operations.

## Fair E-Payment Protocol Based on Certificateless Signature and Authenticated Key Exchange

### Information Computing and Applications (2010-01-01) 6377: 103-110 , January 01, 2010

E-payment protocol allows two or more users to securely exchange e-cash and digital product among them over an open network. There are some problems in the E-payment applications of cross-domain and cross-organization scenarios because of certificate-based authentication and digital signature, like inconsistent public key certificates and a heavy certificate management burden. ID-based cryptography is adopted to solve those problems, but it suffers the key escrow issue. Certificateless cryptography has been introduced to mitigate those limitations. A certificateless signature and authenticated key exchange scheme (CL-SAKE for short) is proposed, and its security is proved in the extended random oracle model. As an application, an E-payment protocol based on the new CL-SAKE is then proposed, which achieves unforgeability and un-reusability of e-cash, customer anonymity and fair exchange.

## Front Matter - Learn Android App Development

### Learn Android App Development (2013-01-01) , January 01, 2013

## Towards evolvable Internet architecture-design constraints and models analysis

### Science China Information Sciences (2014-11-01) 57: 1-24 , November 01, 2014

There is a general consensus about the success of Internet architecture in academia and industry. However, with the development of diversified application, the existing Internet architecture is facing more and more challenges in scalability, security, mobility and performance. A novel evolvable Internet architecture framework is proposed in this paper to meet the continuous changing application requirements. The basic idea of evolvability is relaxing the constraints that limit the development of the architecture while adhering to the core design principles of the Internet. Three important design constraints used to ensure the construction of the evolvable architecture, including the evolvability constraint, the economic adaptability constraint and the manageability constraint, are comprehensively described. We consider that the evolvable architecture can be developed from the network layer under these design constraints. What’s more, we believe that the address system is the foundation of the Internet. Therefore, we propose a general address platform which provides a more open and efficient network environment for the research and development of the evolvable architecture.

## Inequalities from Two Rows of a Simplex Tableau

### Integer Programming and Combinatorial Optimization (2007-01-01) 4513: 1-15 , January 01, 2007

In this paper we explore the geometry of the integer points in a cone rooted at a rational point. This basic geometric object allows us to establish some links between lattice point free bodies and the derivation of inequalities for mixed integer linear programs by considering two rows of a simplex tableau simultaneously.