Algebraic and logistic investigations on free lattices

Lorenzen's "Algebraische und logistische Untersuchungen \"uber freie Verb\"ande" appeared in 1951 in The journal of symbolic logic. These "Investigations" have immediately been recognised as a landmark in the history of infinitary proof theory, but their approach and method of proof have not been incorporated into the corpus of proof theory. More precisely, Lorenzen proves the admissibility of cut by double induction, on the cut formula and on the complexity of the derivations, without using any ordinal assignment, contrary to the presentation of cut elimination in most standard texts on proof theory. This translation has the intent of giving a new impetus to their reception. The "Investigations" are best known for providing a constructive proof of consistency for ramified type theory without axiom of reducibility. They do so by showing that it is a part of a trivially consistent "inductive calculus" that describes our knowledge of arithmetic without detour. The proof resorts only to the inductive definition of formulas and theorems. They propose furthermore a definition of a semilattice, of a distributive lattice, of a pseudocomplemented semilattice, and of a countably complete boolean lattice as deductive calculuses, and show how to present them for constructing the respective free object over a given preordered set. This translation is published with the kind permission of Lorenzen's daughter, Jutta Reinhardt.Comment: Translation of "Algebraische und logistische Untersuchungen \"uber freie Verb\"ande", J. Symb. Log., 16(2), 81--106, 1951, http://www.jstor.org/stable/226668

Chemical milling solution produces smooth surface finish on aluminum

Elementary sulfur mixed into a solution of caustic soda and salts produces an etchant which will chemically mill end-grain surfaces on aluminum plate. This composition results in the least amount of thickness variation and pitting

Information Cost, Learning, and Trust Lessons from Co-operation and Higher-order Capabilities Amongst Geographically Proximate Firms

In this short paper, I put forward an argument about trust based upon an information cost perspective. I argue that, in different contexts, different origins of trust come to dominate. This is so, because different possible origins of trust have a different information cost, and different contexts have different information availability. Agents learn about this, and place their trust accordingly. I provide an empirical example, and list some traits of information availability between geographically proximate firms. The information cost argument explains why a particular way of trusting is prevalent in some proximate ‘communities’ of agents.Trust; governance; information cost; organisational learning; industrial districts

On the convergence of stochastic MPC to terminal modes of operation

The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that guarantee closed-loop performance bounds and boundedness of the state, but convergence to a terminal control law is typically not shown. In this work we use results on general state space Markov chains to find conditions that guarantee convergence of disturbed nonlinear systems to terminal modes of operation, so that they converge in probability to a priori known terminal linear feedback laws and achieve time-average performance equal to that of the terminal control law. We discuss implications for the convergence of control laws in stochastic MPC formulations, in particular we prove convergence for two formulations of stochastic MPC

Localized Learning and Social Capital The Geography Effect in Technological and Institutional Dynamics

Providing a concise working definition of social capital, this conceptual paper analyses why social capital is important for learning and economic development, why it has a regional dimension, and how it is created. It argues that with the rise of the Knowledge Economy, social capital is becoming valuable because it organizes markets, lowering business firms’ costs of coordinating and allowing them to flexibly connect and reconnect. Thus, it serves as a social framework for localized learning in both breadth and depth. The paper suggests that a range of social phenomena such as altruism, trust, participation, and inclusion, are created when a matrix of various social relations is combined with particular normative and cognitive social institutions that facilitate cooperation and reciprocity. Such a matrix of social relations, plus facilitating institutions, is what the paper defines as “social capital”. The paper further suggests that social capital is formed at the regional (rather than national or international) level, because it is at this level we find the densest matrices of social relations. The paper also offers a discussion of how regional policies may be suited for promoting social capital.Social capital, knowledge economy, regional dimension

The Cluster as Market Organization

The many competing schools of thought concerning themselves with industrial clusters have at least one thing in common: they all agree that clusters are real life phenomena characterized by the co-localization of separate economic entities, which are in some sense related, but not joined together by any common ownership or management. So hierarchies they are certainly not. Yet, it is usually taken for granted that clusters, almost regardless of how they are defined, all expatriate the 'swollen middle' of various hybrid 'forms of long-term contracting, reciprocal trading, regulation, franchising and the like' residing somewhere between hierarchies and markets. This fundamental (but usually implicit) assumption would, perhaps, be justified if markets could be reduced to events of exchange of property rights, between large numbers of price-taking anonymous buyers and sellers supplied with perfect information as they are commonly conceived in mainstream economics. One of the original attractions of Neoclassical price theory was precisely that it promised a way of analysing the economy in general and market exchange in particular independently of specific institutional settings. However, introducing transaction costs as more than fees paid to intermediaries leads inevitably to comparative institutional analysis and, not to be forgotten, to the perception of markets as institutions with specific characteristics of their own. Some sets of characteristics are so common that they represent a specific market organization or market form. The cluster is one such specific market organization that is structured along territorial lines because this enables the building of a set of institutions that are helpful in conducting certain kinds of economic activities. Supported by empirical illustrations the paper argues that clusters are markets where commodities, services and knowledge are traded in a notably efficient way among the insiders without restricting their abilities to build pipelines and to interact with suppliers and customers residing elsewhere. The institutions characterizing this market form help creating an environment among insiders that reduces the barriers to acquiring and utilising knowledge produced or used locally.Clusters, organisation, knowledge transfer, transaction costs

On the Economics of Innovation Projects Product Experimentation in the Music Industry

The paper is conceptual, combining project and economic organization literatures in order to explain the organization and management of market-based projects. It dedicates particular focus to projects set up in order to facilitate product innovation through experimentation. It investigates the internal vs. market economies of scale and scope related to projects, as well as the issues of governance, planning and coordination related to reaping such economies. Incorporating transaction cost perspectives as well as considerations of labour markets, the paper explains the management of market-organized innovation projects by virtue of localized project ecologies and local labour markets of leaders and boundary spanners. It illustrates its arguments with a case study of the Recorded Music industry.Project management, product innovation

Propositional computability logic I

In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a machine against the environment, their computability as existence of a machine that always wins the game, logical operators as operations on computational problems, and validity of a logical formula as being a scheme of "always computable" problems. The present contribution gives a detailed exposition of a soundness and completeness proof for an axiomatization of one of the most basic fragments of computability logic. The logical vocabulary of this fragment contains operators for the so called parallel and choice operations, and its atoms represent elementary problems, i.e. predicates in the standard sense. This article is self-contained as it explains all relevant concepts. While not technically necessary, however, familiarity with the foundational paper "Introduction to computability logic" [Annals of Pure and Applied Logic 123 (2003), pp.1-99] would greatly help the reader in understanding the philosophy, underlying motivations, potential and utility of computability logic, -- the context that determines the value of the present results. Online introduction to the subject is available at http://www.cis.upenn.edu/~giorgi/cl.html and http://www.csc.villanova.edu/~japaridz/CL/gsoll.html .Comment: To appear in ACM Transactions on Computational Logi

Stochastic Model Predictive Control with Discounted Probabilistic Constraints

This paper considers linear discrete-time systems with additive disturbances, and designs a Model Predictive Control (MPC) law to minimise a quadratic cost function subject to a chance constraint. The chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon. By penalising violation probabilities close to the initial time and ignoring violation probabilities in the far future, this form of constraint enables the feasibility of the online optimisation to be guaranteed without an assumption of boundedness of the disturbance. A computationally convenient MPC optimisation problem is formulated using Chebyshev's inequality and we introduce an online constraint-tightening technique to ensure recursive feasibility based on knowledge of a suboptimal solution. The closed loop system is guaranteed to satisfy the chance constraint and a quadratic stability condition.Comment: 6 pages, Conference Proceeding

Global Strategy and the Acquisition of Local Knowledge How MNCs Enter Regional Knowledge Clusters

The paper addresses two recent interrelated phenomena: High- tech regional knowledge clusters, and globalization of R&D activities by multinational corporations (MNCs). Combining MNC literature; regional development literature; and literature on social networks, the paper discusses determinants of entry modes used by MNCs that localize R&D units in regional knowledge clusters. The paper states that the entry mode used by a MNC depends upon the type of agglomeration economies the latter seeks to appropriate: Those related to network relations; to local labor market specialization; or to institutional specialization. The paper adds theoretical insight into advantages and disadvantages of different entry modes with respect to appropriation of agglomeration economies, and special attention is dedicated to discussing acquisition. Through the use of an empirical case ¾ the entry of five MNCs into the Danish telecommunications cluster in Aalborg, the paper exemplifies its theoretical observations, but also points to how the evolution of a knowledge cluster may be severely affected by MNCs that enter through acquisition.MNCs; entry mode; acquisition; explorative R&D; regional clusters; localized learning; networks; telecommunications industry; North Jutland; Denmark.