Hamilton’s Principle with Variable Order Fractional Derivatives

MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

Effect of second order signal-noise interactions in nonlinearity compensated optical transmission systems

In this Letter, we theoretically and numerically analyze the performance of coherent optical transmission systems that deploy inline or transceiver based nonlinearity compensation techniques. For systems where signal-signal nonlinear interactions are fully compensated, we find that beyond the performance peak the signal-to-noise ratio degradation has a slope of 3 dBSNR/dBPower suggesting a quartic rather than quadratic dependence on signal power. This is directly related to the fact that signals in a given span will interact not only with linear amplified spontaneous emission noise, but also with the nonlinear four-wave mixing products generated from signal-noise interaction in previous (hitherto) uncompensated spans. The performance of optical systems employing different nonlinearity compensation schemes were numerically simulated and compared against analytical predictions, showing a good agreement within a 0.4 dB margin of error.

Capital 2.0 capital formation and legal risk in a new global economic order from fiat to exit: including case studies of the proposed transatlantic trade and investment partnership between the United States and the European Union and the financing relation between the United States and the People’s Republic of China

Following the intrinsically linked balance sheets in his Capital Formation Life Cycle, Lukas M. Stahl explains with his Triple A Model of Accounting, Allocation and Accountability the stages of the Capital Formation process from FIAT to EXIT. Based on the theoretical foundations of legal risk laid by the International Bar Association with the help of Roger McCormick and legal scholars such as Joanna Benjamin, Matthew Whalley and Tobias Mahler, and founded on the basis of Wesley Hohfeld’s category theory of jural relations, Stahl develops his mutually exclusive Four Determinants of Legal Risk of Law, Lack of Right, Liability and Limitation. Those Four Determinants of Legal Risk allow us to apply, assess, and precisely describe the respective legal risk at all stages of the Capital Formation Life Cycle as demonstrated in case studies of nine industry verticals of the proposed and currently negotiated Transatlantic Trade and Investment Partnership between the United States of America and the European Union, TTIP, as well as in the case of the often cited financing relation between the United States and the People’s Republic of China. Having established the Four Determinants of Legal Risk and its application to the Capital Formation Life Cycle, Stahl then explores the theoretical foundations of capital formation, their historical basis in classical and neo-classical economics and its forefathers such as The Austrians around Eugen von Boehm-Bawerk, Ludwig von Mises and Friedrich von Hayek and most notably and controversial, Karl Marx, and their impact on today’s exponential expansion of capital formation. Starting off with the first pillar of his Triple A Model, Accounting, Stahl then moves on to explain the Three Factors of Capital Formation, Man, Machines and Money and shows how “value-added” is created with respect to the non-monetary capital factors of human resources and industrial production. Followed by a detailed analysis discussing the roles of the Three Actors of Monetary Capital Formation, Central Banks, Commercial Banks and Citizens Stahl readily dismisses a number of myths regarding the creation of money providing in-depth insight into the workings of monetary policy makers, their institutions and ultimate beneficiaries, the corporate and consumer citizens. In his second pillar, Allocation, Stahl continues his analysis of the balance sheets of the Capital Formation Life Cycle by discussing the role of The Five Key Accounts of Monetary Capital Formation, the Sovereign, Financial, Corporate, Private and International account of Monetary Capital Formation and the associated legal risks in the allocation of capital pursuant to his Four Determinants of Legal Risk. In his third pillar, Accountability, Stahl discusses the ever recurring Crisis-Reaction-Acceleration-Sequence-History, in short: CRASH, since the beginning of the millennium starting with the dot-com crash at the turn of the millennium, followed seven years later by the financial crisis of 2008 and the dislocations in the global economy we are facing another seven years later today in 2015 with several sordid debt restructurings under way and hundred thousands of refugees on the way caused by war and increasing inequality. Together with the regulatory reactions they have caused in the form of so-called landmark legislation such as the Sarbanes-Oxley Act of 2002, the Dodd-Frank Act of 2010, the JOBS Act of 2012 or the introduction of the Basel Accords, Basel II in 2004 and III in 2010, the European Financial Stability Facility of 2010, the European Stability Mechanism of 2012 and the European Banking Union of 2013, Stahl analyses the acceleration in size and scope of crises that appears to find often seemingly helpless bureaucratic responses, the inherent legal risks and the complete lack of accountability on part of those responsible. Stahl argues that the order of the day requires to address the root cause of the problems in the form of two fundamental design defects of our Global Economic Order, namely our monetary and judicial order. Inspired by a 1933 plan of nine University of Chicago economists abolishing the fractional reserve system, he proposes the introduction of Sovereign Money as a prerequisite to void misallocations by way of judicial order in the course of domestic and transnational insolvency proceedings including the restructuring of sovereign debt throughout the entire monetary system back to its origin without causing domino effects of banking collapses and failed financial institutions. In recognizing Austrian-American economist Schumpeter’s Concept of Creative Destruction, as a process of industrial mutation that incessantly revolutionizes the economic structure from within, incessantly destroying the old one, incessantly creating a new one, Stahl responds to Schumpeter’s economic chemotherapy with his Concept of Equitable Default mimicking an immunotherapy that strengthens the corpus economicus own immune system by providing for the judicial authority to terminate precisely those misallocations that have proven malignant causing default perusing the century old common law concept of equity that allows for the equitable reformation, rescission or restitution of contract by way of judicial order. Following a review of the proposed mechanisms of transnational dispute resolution and current court systems with transnational jurisdiction, Stahl advocates as a first step in order to complete the Capital Formation Life Cycle from FIAT, the creation of money by way of credit, to EXIT, the termination of money by way of judicial order, the institution of a Transatlantic Trade and Investment Court constituted by a panel of judges from the U.S. Court of International Trade and the European Court of Justice by following the model of the EFTA Court of the European Free Trade Association. Since the first time his proposal has been made public in June of 2014 after being discussed in academic circles since 2011, his or similar proposals have found numerous public supporters. Most notably, the former Vice President of the European Parliament, David Martin, has tabled an amendment in June 2015 in the course of the negotiations on TTIP calling for an independent judicial body and the Member of the European Commission, Cecilia Malmström, has presented her proposal of an International Investment Court on September 16, 2015. Stahl concludes, that for the first time in the history of our generation it appears that there is a real opportunity for reform of our Global Economic Order by curing the two fundamental design defects of our monetary order and judicial order with the abolition of the fractional reserve system and the introduction of Sovereign Money and the institution of a democratically elected Transatlantic Trade and Investment Court that commensurate with its jurisdiction extending to cases concerning the Transatlantic Trade and Investment Partnership may complete the Capital Formation Life Cycle resolving cases of default with the transnational judicial authority for terminal resolution of misallocations in a New Global Economic Order without the ensuing dangers of systemic collapse from FIAT to EXIT.

A numerical method to solve higher-order fractional differential equations

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method.

A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).

Maintaining human agency in the design on context-aware systems : Design games in a dental surgery

This paper describes a series of design games, specifically aimed at exploring shifts in human agency in order to inform the design of context-aware applications. The games focused on understanding information handling issues in dental practice with participants from a university dental school playing an active role in the activities. Participatory design activities help participants to reveal potential implicit technical resources that can be presented explicitly in technologies in order to assist humans in managing their interactions with and amidst technical systems gracefully.

Managing infrastructure transitions : a complex adaptive systems perspective

Engineering assets such as roads, rail, bridges and other forms of public works are vital to the effective functioning of societies {Herder, 2006 #128}. Proficient provision of this physical infrastructure is therefore one of the key activities of government {Lædre, 2006 #123}. In order to ensure engineering assets are procured and maintained on behalf of citizens, government needs to devise the appropriate policy and institutional architecture for this purpose. The changing institutional arrangements around the procurement of engineering assets are the focus of this paper. The paper describes and analyses the transition to new, more collaborative forms of procurement arrangements which are becoming increasingly prevalent in Australia and other OECD countries. Such fundamental shifts from competitive to more collaborative approaches to project governance can be viewed as a major transition in procurement system arrangements. In many ways such changes mirror the shift from New Public Management, with its emphasis on the use of market mechanisms to achieve efficiencies {Hood, 1991 #166}, towards more collaborative approaches to service delivery, such as those under network governance arrangements {Keast, 2007 #925}. However, just as traditional forms of procurement in a market context resulted in unexpected outcomes for industry, such as a fragmented industry afflicted by chronic litigation {Dubois, 2002 #9}, the change to more collaborative forms of procurement is unlikely to be a panacea to the problems of procurement, and may well also have unintended consequences. This paper argues that perspectives from complex adaptive systems (CAS) theory can contribute to the theory and practice of managing system transitions. In particular the concept of emergence provides a key theoretical construct to understand the aggregate effect that individual project governance arrangements can have upon the structure of specific industries, which in turn impact individual projects. Emergence is understood here as the macro structure that emerges out of the interaction of agents in the system {Holland, 1998 #100; Tang, 2006 #51}.

The Order Fulfillment Process Model

This appendix describes the Order Fulfillment process followed by a fictitious company named Genko Oil. The process is freely inspired by the VICS (Voluntary Inter-industry Commerce Solutions) reference model1 and provides a demonstration of YAWL’s capabilities in modelling complex control-flow, data and resourcing requirements.

Information enrichment for quality recommender systems

The explosive growth of the World-Wide-Web and the emergence of ecommerce are the major two factors that have led to the development of recommender systems (Resnick and Varian, 1997). The main task of recommender systems is to learn from users and recommend items (e.g. information, products or books) that match the users’ personal preferences. Recommender systems have been an active research area for more than a decade. Many different techniques and systems with distinct strengths have been developed to generate better quality recommendations. One of the main factors that affect recommenders’ recommendation quality is the amount of information resources that are available to the recommenders. The main feature of the recommender systems is their ability to make personalised recommendations for different individuals. However, for many ecommerce sites, it is difficult for them to obtain sufficient knowledge about their users. Hence, the recommendations they provided to their users are often poor and not personalised. This information insufficiency problem is commonly referred to as the cold-start problem. Most existing research on recommender systems focus on developing techniques to better utilise the available information resources to achieve better recommendation quality. However, while the amount of available data and information remains insufficient, these techniques can only provide limited improvements to the overall recommendation quality. In this thesis, a novel and intuitive approach towards improving recommendation quality and alleviating the cold-start problem is attempted. This approach is enriching the information resources. It can be easily observed that when there is sufficient information and knowledge base to support recommendation making, even the simplest recommender systems can outperform the sophisticated ones with limited information resources. Two possible strategies are suggested in this thesis to achieve the proposed information enrichment for recommenders: • The first strategy suggests that information resources can be enriched by considering other information or data facets. Specifically, a taxonomy-based recommender, Hybrid Taxonomy Recommender (HTR), is presented in this thesis. HTR exploits the relationship between users’ taxonomic preferences and item preferences from the combination of the widely available product taxonomic information and the existing user rating data, and it then utilises this taxonomic preference to item preference relation to generate high quality recommendations. • The second strategy suggests that information resources can be enriched simply by obtaining information resources from other parties. In this thesis, a distributed recommender framework, Ecommerce-oriented Distributed Recommender System (EDRS), is proposed. The proposed EDRS allows multiple recommenders from different parties (i.e. organisations or ecommerce sites) to share recommendations and information resources with each other in order to improve their recommendation quality. Based on the results obtained from the experiments conducted in this thesis, the proposed systems and techniques have achieved great improvement in both making quality recommendations and alleviating the cold-start problem.

Augmenting competitiveness of cities through tourism planning : the role of collaborative decision support systems

Many cities around the globe are now considering tourism facilities and their remarkable revenues in order to become competitive in the global economy. In many of these cities a great emphasis is given to the cultural tourism as it plays an important role in the establishment of creative and knowledge-base of cities. The literature points out the importance of local community support in cultural tourism. In such context, the use of new approach and technologies in tourism planning in order to increase the community participation and competitiveness of cities’ cultural assets gains a great significance. This paper advocates a new planning approach for tourism planning, particularly for cultural tourism, to increase the competitiveness of cities. As part of this new approach, the paper introduces the joined up planning approach integrated with a collaborative decision support system: ‘the community-oriented decision support system’. This collaborative planning support system is an effective and efficient tool for cultural tourism planning, which provides a platform for local communities’ participation in the development decision process.

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.