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We obtain stochastic duality functions for specific Markov processes using representation theory of Lie algebras. The duality functions come from the kernel of a unitary intertwiner between $*$-representations, which provides (generalized) orthogonality relations for the duality functions. In particular, we consider representations of the Heisenberg algebra and $\mathfrak{su}(1,1)$. Both cases lead to orthogonal (self-)duality functions in terms of hypergeometric functions for specific interacting particle processes and interacting diffusion processes., 23 pages

In this paper I classify situations of interdependent decision-making, or games based on the type of decision-makers, or players involved. The classification builds on a distinction between three basic types of decision-making agents: individuals, cooperative or unitary groups -- groups whose members can reach a binding (and costless) agreement on a joint strategy -- and non-cooperative groups -- groups whose members act independently without being able to make a binding agreement. Pitting individuals, unitary groups, and non-cooperative groups against one another, and adding Nature as a potential “opponent”, generates a 3 (type of agent) X 4 (type of opponent) matrix of social situations. This framework is used to review the experimental decision-making literature and point out the gaps that still exist in it.

This study advances an attention-based view of corporate strategy and explores its implications for organizational design. We examine the governance of resource allocation in a multi-business organization through the firm’s network of decision-making and communication channels. Using both primary and secondary sources, we analyze the changes in the decision-making channels at General Electric (GE) over a 51-year period across four CEO regimes: Ralph J. Cordiner, Fred J. Borch, Reginald H. Jones and John F. Welch. We identify four distinct channel functions: reporting, staff, control and agenda management. Through our analysis, we find that strategy does not emerge from any unitary, bounded process but from the pattern that emerges from a network of tightly and loosely coupled channels operating simultaneously.

Autopoietic theory is more than a mere characterization of the living, as it can be applied to a wider class of systems and involves both organizational and epistemological aspects. In this paper we assert the necessity of considering the relation between autopoiesis and emergence, focusing on the crucial importance of the observer’s activity and demonstrating that autopoietic systems can be considered intrinsically emergent processes. From the attempts to conceptualize emergence, especially Rosen’s, autopoiesis stands out for its attention to the unitary character of systems and to emergent levels, both inseparable from the observer’s operations. These aspects are the basis of Varela’s approach to multiple level relationships, considered as descriptive complementarities.

Nowadays, dynamic S-P-R models, developed within personality research, seem to offer the chance for the development of a unitary research framework, one including individual and environmental factors, from both structural and dynamic levels of personality. Complexity concept is a fundamental element of convergence of the different existing theoretical and methodological approaches. From this expanded view, personality appears as an “hyper-complex” system of intra-individual circular interactions, and of recursive relations between internal and external factors, that develops and grows self-organizing. This approach takes into account, within a wide interpretative framework, the contributions from various humanistic and scientific disciplines.

The vertical structure of government in all OECD countries is characterized by a hierarchy of two or three layers of governments, with the national government at the top and local government at the bottom. Typically, unitary states like Sweden have two layers, while federal states like Germany have three layers of more. This structure serves as a basis for assigning specific tasks to local governments, which, due to their closer proximity to the citizen and their better knowledge of local economic conditions, they can fulfil better than the central government.1 Decentralization of the public sector also serves to create competition for taxpayers among local governments. Such competition is regarded as a check on rent-seeking behavior of selfish politicians and on excessive growth of government.2

Preface.- 1. Introduction - Problems of Multi-level Democracies.- 2. Division of Powers.- 3. Swedish Local Government: Is There a Bailout Problem?- 4. Fiscal Equalisation between Swedish Municipalities.- 5. Constraining Misuse of Funds from Intergovernmental Grants: A Legal Analysis.- 6. Democratic Governance and Local Autonomy.- 7. Why Federalism?- 8. Strengthening Federalism in Sweden.- 9. A Summary, and Four Theses on State-local Relationships.- Index.

In their text, Client-led Design, Stowell and West (1994) suggested that Vickers’ concept of relationship-maintaining might provide a basis of a concept of organisation that was more appropriate to interpretive IS work than the ‘traditional’ goal-seeking view of organisation. Whilst they may have gone one step further than Walsham (1993) in trying to make explicit the model of organisation their work implied, they failed to develop the model beyond a description of the nature of appreciation and its application in IS work. More recently, Checkland and Holwell (1998) have set down what they refer to as the “conventional wisdom model of ‘an organisation’ in much of the IS literature” (p82), which is based upon the pursuit of organisational goals, and compare this with what they propose as “a richer model of the concept of ‘an organisation’ than the ‘conventional wisdom’ [model]” (ibid., p83). Their ‘conventional wisdom’ model is based upon the premise that organizations are taken to exist as entities in the ‘real world’; that is, they are treated as “a conscious, person-like entity capable of unitary purposeful action” (ibid., p82). In this model, organizational members are considered to understand and share the organization’s aims and objectives, and consequently, work within the organization to attain these objectives. Objective attainment is commonly expressed through the concepts and language of ‘goal-seeking’. Checkland and Holwell state that “Philosophically, this is a positivistic model, sociologically, a functionalist one” (ibid., p82).

The Economic Theory of Federalism yields one clear and overriding result: a federal (i.e. decentralized) state is superior to a centralized one in the sense that it fulfils the demands of the citizens more effectively. A federal constitution that endowes the federal units (provinces, Lander, states, cantons or communes) with sufficient decision-making rights and taxing power has three major advantages over a unitary state: Advantage 1: More flexible politics. In all societies, citizens differ widely in their demand for services provided by the state. These differences in demand are not only the result of heterogeneous tastes due to differences in tradition, culture, language etc, but also of unequal economic conditions. The latter are caused by, for example, leads or lags in the general business cycle and, of course, special structural conditions such as differences in infrastructure, unemployment, the concentration of particular industries etc. These differences in the demand for public services must be met by differentiated supply policies if citizens’ preferences are to be fulfilled. Federal subunits are best able to meet this challenge. The politicians in charge are better endowed with information about the local requirements. They have the incentives to provide these services according to the preferences of the citizens because they are directly accountable for the local policy and their reelection depends on the satisfaction of the voters they represent1.

As mentioned in Chapter 5, it may not be possible to experiment with all the combinations of alternatives required by a factorial design under homogeneous conditions. This situation is managed using blocks. As discussed in preceding chapters, blocks can refer to the subjects running the experiment, the times at which they are run, variations in the projects used as experimental units or any other undesired variation that occurs from one unitary experiment to another.

Exchange does not seem to be a problem for Levi-Strauss. It is an “unconscious necessity,” “a structure of the mind,” “the primitive phenomenon”1. Mauss, said Levi-Strauss, has raised unnecessary problems by breaking up the essentially unitary act of exchange into three different actions: giving, receiving and returning. Above all, “the source of energy that realises the synthesis” (p. XXXVIII) has to be located. For Levi-Strauss on the other hand, there is no question of synthesis where there is no antithesis; there is only a given in symbolic thinking.

Existence results for vaxiational-hemivariational inequalities are presented as consequences of a unitary proving method based on a regularization method and on a F.E.Вrowder technique.

Having designed the experimentation, each unitary experiment is run as prescribed by the design. Measurements of the response variable are taken during the experiments. So, after completing the unitary experiments, experimenters have a collection of data, called the results of the experimentation. By examining or analysing these data, experimenters will arrive at conclusions about the relationships between factors, the influence of factors on the response variables and the alternatives that improve the values of the response variables. The data analysis branch of statistics provides the techniques for examining the experimental results. These are statistical methods that are used to analyse the data output by experiments and are explained in this, the third part of the book.

When World War II ended and Western Europeans began to rebuild, a few visionaries promoted European federation as the path to prosperity and peace (Burgess 1: Newman 15–16). But their early visions crumbled on the old, inert nation-states. International organizations such as the European Coal and Steel Community were intergovernmental rather than federal, which would have required limits on national sovereignty. Federalism was almost non-existent within Western European countries as well. West Germany and Switzerland were the only federations; the others were either unitary democracies or dictatorships.

Models of economic growth attempt to explain broad trends in economic development by the interaction and accumulation of inputs, subject to such basic principles as diminishing returns. In practice, a very large proportion of this literature, from Solow’s epochal paper (1956) to the 1990’s, has relied on the Cobb-Douglas production function, and the studies reported in the previous chapters have followed this tradition. The Cobb-Douglas schema combines power and simplicity in expressing the assumptions of input substitutability subject to diminishing returns, but its simplicity is also a limit. Because the Cobb-Douglas production function entails that the elasticities of substitution among inputs are unitary, there are certain hypotheses it excludes from the first. For example, Stokey argues (1996 p. 422-23) that capital and unskilled labor are highly substitutable, while skilled labor (or, we shall say, human capital) is less substitutable for both1. In a slightly different framework Johnson, following Griliches and Goldin and Katz, proposes a model in which skilled labor and capital are less substitutable than either is for unskilled labor. This sort of reasoning, too, is excluded by the assumption of a unitary elasticity of demand. Finally, Duffy and Papageorgiou observe that, with an elasticity of substitution greater than one, endogenous growth becomes a possibility in a two-factor growth model, and they provide some evidence from a cross-country study that the elasticity of substitution of capital for labor (with or without adjustment for human capital) is indeed greater than one.

A new method for designing sequences which lead to a constant envelope in Wavelet-based Multicarrier spread spectrum systems is presented. It is shown that this method is valid for any unitary or orthogonal matrix and can generate sequences with quantized coefficients, which are suitable for fixed-point DSP implementations.

Much of the interest in bilingual first language acquisition has focused on the question whether or not very young bilingual children are able to differentiate between their two languages. Many researchers argue that bilingual children start with a unitary system in the acquisition of phonology. However, most studies in this area are restricted to the segmental level where cross-linguistic similarities in early inventories provide ambiguous results. Thus, investigations on a suprasegmental level such as the system of pitch might offer new evidence. It has been proposed that the use of pitch is acquired very early by children. Experimental studies in this area, however, have produced contradictory results. This study investigates the acquisition of the systematic use of pitch by German/English bilingual children. The longitudinal data show that the linguistic use of pitch patterns is far from completed by age 2;5. By investigating the acquisition of the intonational marking of questions from 2;5 to 4;3 for one of the children, it was possible to gather evidence for two separate phonological systems.

Despite an emerging consensus on the importance of corporate social capital, little work has been done on the analytical problem of which aspects, precisely, of a corporate network might be identified as manifesting the concept. Where in a specific configuration of network ties is the corporate social capital located? Is network capital a unitary phenomenon or are there various ways to conceptualize it? In addressing these questions, we formulate models for corporate networks that produce counts for the expected number of ties between each pair of actors on the basis of sets of parameters which are themselves measures of network capital. The model we prefer decomposes a network into separable dimensions comprising status, volume, and proximity. We apply the models to a network of ‘doing deals’ in which billions of dollars of finance capital was raised by syndicates of major U.S. investment banks, data of Eccles and Crane (1988). We show that the model performs well with respect to empirical validity. The modeling framework can be applied and extended to other corporate network settings, and provides measures appropriate for theoretical analyses of markets and corporate relations conceptualized as embedded within social fields.

The division of tasks between management and Board of Directors takes various forms. Nonetheless, it is possible to identify the following typology: the 1-tier or unitary Board of Directors which includes both inside or active directors, who also fulfil management functions within the company, and external non-active directors; the 2-tier or dual governance system, which has two individual boards, one responsible for day-to-day policy and composed exclusively of executives and a second type of Supervisory Board which is made up exclusively of non-active directors; occasionally, an optional system exists (basic system is either 1-tier or 2-tier with option of other version).

J-unitary operators and their siblings, symplectic operators, play an important role in physics and mathematics. Aside from the fact that they describe a physically interesting situation, they are instrumental in interpolation and approximation theory as well. The physical motivation is found in lossless scattering theory, which gives an operator description of wave propagation and reflection. An introduction to this is given in section 8.1. We saw in the previous chapters that reachability and observability spaces are instrumental in the realization theory of operators in general. In the case of J-unitary operators these spaces turn out to be rather special, with interesting geometrical properties (sections 8.2 and 8.4).

It will be shown that the minimum error bound in binary decision of linearly-independent pure-state signals can be achieved for any given measurement process by installing an appropriate unitary transformation for the signal states in front of the measurement. The optimum decision problem can be viewed as how to find this transformation which modifies the received signals so as to cause the quantum interference optimally at the measurement. It will be discussed how the origin of the error reduction can be identified and how the required unitary control process can be constructed.

Necessary and sufficient conditions of an optimum pair of signals for given decision operators are given. These conditions show what kind of signals are desired for the output of the unitary transformation in a received quantum state control system by unitary process in order to achieve the Helstrom’s bound. We show pictures of optimum signals which the conditions imply. Then we consider as examples two of received quantum state control systems by unitary process.

We have developed a theory of sharing which captures the behaviour of programs with respect to shared data into the framework of process algebra. The core theory can describe programs performing read and write access to unitary pieces of shared data. Extensions allow shared data to be decomposed and atomic copies to be made, reflecting the common operations of parallel programs. We describe the theory and give an example of its use in analysing and transforming a sample mathematical application.

Applications of quantum algebras (of su q (2) as most widespread example) to phenomenological description of rotational spectra of deformed heavy nuclei and diatomic molecules, have appeared a couple of years ago and seem to be encouraging [1–3] (concerning physical applications of quantum groups/algebras in a wider context see ref. [4] and references therein).

Integrated Catchment Management (ICM) has all the characteristics of a ‘messy’ problem. It involves numerous interests all with a different perception as to what ICM actually means. It involves technical, social, economic and environmental aspects as well as numerous government, industrial, agricultural and civic groups. Water itself is a multipurpose resource and has time, place and quality characteristics (Watson & Johnson, 1993). ICM is a ‘complex’ problem situation as classified by Flood & Jackson (1991). The other axis to their classification regards the problem situation as either unitary, pluralist, or, coercive. The sheer number of interests in ICM tends to make some aspects of power play appear, so it is legitimate to call the situation coercive. Whatever classification is used for management purposes, the problem is definitely a systemic one. It is surprising to find, however, that explicit systems techniques are rarely used when designing ICM systems and organisational structures although some attempts have been made on the periphery by academics, e.g. Levy & Synnott (1993).

Whenever the human central nervous system is compromised, whether as the result of disease, trauma, fatigue, or intoxication, the higher cognitive functions suffer. This cognitive machinery is typically described and conceptually divided by hypothetical constructs such as memory, language, and attention. These constructs are not unitary entities but, rather, constitute integrated medleys of more elemental processes.

Our experience in evaluation has been that we need to find ways of working in situations which have a high degree of variety and in which acceptance and respect for difference is important. Such situations display a high degree of heterogeneity, in a number of different senses: the differences between the people involved in the situation; differences between groups; and lack of stability in the environment. In contrast, most well-established evaluation strategies expect a stable hypothesis to be under test, do not recognise more than one perception of a situation, and are based on the implicit assumption that a unitary description of reality can be offered. The starting point for the paper will be a critical analysis of a particular strategy for evaluation arising from within the systems tradition. The concept of heterogeneity will be explored and the paper will present an alternative way of approaching evaluation, which we have found particularly valuable for use where a high degree of variety exists. The pluralist strategy described is based on the acknowledgement and respect of difference, rather than its rationalisation. Elements of this strategy for evaluation will be illustrated with examples from recent work in the social policy arena.

This paper provides a brief introduction to how unitary representations of diffeomorphism groups can describe certain quantum systems having infinitely many degrees of freedom. It is a partial report of our joint work [1], based on the August 1994 talk by the first author at the Symmetries in Science VIII conference in Bregenz, Austria. We would like to express appreciation to the conference organizers, especially Professor Bruno Gruber, for the opportunity to present our results.

The reasons for the absence of consistent correlations between systematic systems for ascomycetes and deuteromycetes are discussed, especially in relation to the inadequate descriptive terminology for conidiogenous events. Twenty unitary parameters in conidiogenesis are defined and diagrammatically illustrated. Their application to anamorphic genera is viewed as a necessary precursor to the future reassessments of correlations with ascomycetes.

It gives me great pleasure to present this talk at this Symposium held in honor of Professor Larry Biedenharn on the occasion of his 70th birthday. Among his many contributions to mathematical physics, Professor Biedenharn has shown us how to construct unitary quantum Lie algebras in terms of q-oscillators.1 In this talk, I would like to take the dual course and discuss the direct relationship between q-oscillators and quantum groups. I will also talk about their physical interpretation as relativistic oscillators. My discussion will mainly focus on our contribution to the subject.2−7 However I will try to present a unified overview.

The study of unitarization of representations for non compact real forms of simple Lie Algebras has been achieved in the past decade by Jakobsen (JA81, JA83) and by Enright, Howe and Wallach (EH83) following different paths but arriving at the same final results.

After the excellent discussion of the subject presented at this conference by E. Corrigan, it would be redundant to repeat in detail the different steps that make it possible to simplify the difficult problem of the determination of the S matrices in certain integrable off-critical systems. Instead, I will only briefly review the different tools, those developed by Zamolod-chikov [1], and the arguments that connect the subject to Toda field theories [2, 3, 4], in an effort to add new comments about each of them. The Tricritical Ising Model (TIM), that will be the standard example, is discussed in more detail in ref.[5], written with G. Mussardo. The interesting examples of the D n Toda systems are discussed in [6] and in the talk of E. Corrigan at this conference. In a second part, I will discuss in more detail certain selected features of Toda systems. The rich multipole structure and the connection of the exact solution for the S functions to the perturbative expansion is discussed. Finally I will comment on the relation between unitary and non-unitary off-critical integrable models that seems very closely related. The content of this talk represents the results obtained in collaboration with Giuseppe Mussardo.

Electroweak radiative corrections to the Z peak are determined in the unitary gauge. Peculiarities of this gauge are discussed. A gauge-invariant expression for the weak loop corrections is presented. An approximate cross section formula based on partial Z widths may be derived from the exact one loop calculations.

The aim of the present theoretical contribution is twofold. First, I shall attempt to show that all optical quantum systems are inherently related to unitary symmetries of SU(N). Hence, the coherence in multilevel quantum systems can be most elegantly treated by recurrence to the well established methods of the theory of unitary groups. Secondly, I wish to extend the study of nonlinear coherence phenomena to coupled systems.

The aim of this paper is to present a unitary model of some of the mental processes involved in speaking and listening. The model is cast in the form of a computer program, but the program is not intended as a contribution to either Artificial Intelligence or Computer Simulation. We regard it as an exercise in programmatic psychology, and perhaps a few words are necessary in order to explain the nature of this claim. On the one hand, proponents of Artificial Intelligence (AI) aim to develop machines capable of intelligent behaviour and, in particular, to devise computer programs capable of such tasks as interpreting visual scenes, providing theorems, and understanding natural language. Although the methods implemented in these programs are likely to interest a psychologist, any resemblance to human performance may be entirely coincidental. AI is concerned with intelligence in general, not merely its embodiment in living organisms. On the other hand, proponents of Computer Simulation aim to understand human behaviour by simulating it.

It is shown that for each unitary irreducible representation (UIR) of the u(p, 1) algebra there is a unique extremal vector determining the structure of corresponding UIR. The classification of UIRs belonging to discrete and continuous series is given.

The theme of this book is the complementary relationship between privacy and communality. Entities which are complementary, like the two sides of a coin, are merely different manifestations of the same thing: together they constitute an essential unity. To speak of privacy and communality as complements, however, involves more sophistication than simply acknowledging that both are important for the individual or the group. Complements are not opposites, although too often they are treated that way. Complements are mutual contributors to an underlying cause, or to an overall picture, much like the pieces of a jigsaw puzzle each of which uniquely contributes to the unitary integrity of the puzzle.

In any model-based controller design procedure the engineer is commonly confronted with some significant model uncertainties, consideration of which is relevant to the design result. Frequently, the plant is not completely known, since the only information is based on measured step responses, either a simplified model is used to deal with a complex decentralized control problem, or some plants cannot be described by a linear model at all.

Despite evidence to the contrary, “real intelligence” historically has been considered to be a relatively unitary trait, constant over age, and pervasive in its governance of nearly all mental behaviors (Hunt, 1961). Although it is currently fashionable to denigrate such a view, it is still prevalent to some extent. For example, the excitement in certain quarters about brain-wave tests of intelligence because scores reflect a unitary characteristic, are apparently constant over age, and are equally distributed among different cultural groups stands as testimony to the lingering vestiges of a unitary, developmentally constant “intelligence.”

Historically, face-to-face meetings have played an important role in the social, and especially the political, life of Western and non-Western societies. Jane Mansbridge (1983) argues that the concept of unitary democracy is the oldest and longest-lived form of human organization and face-to-face meetings and unitary democracy go hand in hand because it is this context that makes it possible to formalize and extend to the level of a polity the relations of friendship (p. 8): The Greeks were aware of this connection. With the phrase, “Friendship [philia] appears to hold city-states together” Aristotle illuminates the bond between citizens in a unitary polity.... Drawing from the experience of friendship, a democrat could easily believe that relations between citizens ought to be like relations between friends. Friends are equals. They choose to spend time together. They share common values. They expand in each other’s company. So, too, in a democracy based on friendship, participants are equal in status; the costs of participation, of which some make so much, do not feel heavy. Citizens “fly to the assemblies” as if to meet their friends. They value the time they spend on their common affairs. They share a common good, and are able, as a consequence, to make their decisions unanimously. The characteristics of unitary democracy—equal respect, face-to-face contact, common interest, and consensus—are from this perspective nothing but the natural conditions that prevail among friends. (pp. 8–9)

In nuclear spectroscopy an N-dimensional orbital space underlies the whole discussion. It seems natural therefore to begin the application of group theory in nuclear spectroscopy by considering unitary transformations among these N single-particle states. In fact the very idea of introducing the N orbital states can be looked upon as introducing a symmetry that is defined by the group U(N). This is because, on the one hand, the nuclear states in this “model” space have a definite U(N) symmetry, and, on the other hand, the “goodness” of our truncation scheme is directly related to the “goodness” of U(N) symmetry, i.e., whether the model space constructed from N single-particle states is adequate to describe the nuclear states. It is clear therefore that the group U(N) enters quite naturally into almost any discussion of group symmetries in nuclear structure, and hence, in most applications of group theory to nuclear physics, we will deal with the group U(N) and its subgroups.

This paper addresses two complementary questions: What is the appropriate set of tools for the study of the networks of animal and human brains, and what are the strategies for building computers with “intelligence”? We argue that there are overall architectural principles which unite both sides of this study, namely, that a computer no longer be thought of as a unitary system but rather as a network of more specialized devices, and that many of these devices be structured as highly parallel arrays of interacting neuron-like components. We illustrate this with a discussion of the architecture of the frog’s brain as revealed in studies of the mechanisms of visuomotor coordination, and of the design of vision and motor conrol systems for robots. The following topics are treated: (1) What is a schema? (2) Schemas for Rana computatrix. (3) Tectal columns (4) Depth perception. (5) Pathplanning and detours. (6) Schemas for hand control. (7) Schemas for vision. (8) Challenges for cooperation.

In recent years, two authors (Gartlan, 1968; Rowell, 1974) have examined and found wanting the application of concepts of social dominance to the behavior of, primarily, nonhuman primates. These criticisms, I believe, fulfill the purpose of ridding us of an outmoded unitary concept, but they also suffer from a degree of unclarity and excessive zeal, brushing aside many well-established, puzzling, and interesting findings. While preparing a reply to these criticisms, I found two ideas to be of underlying importance. One of these is that discussions of social dominance must guard against muddling of conceptual levels. The other is that certain time-honored approaches to the study of dominance attempt to dispense with variability when that variability is itself likely to be our clue to any further understanding. These and other, minor, novelties I hope will make this paper more than just a reply to a critique.

Scholten et al.1 showed that the interacting boson model gives a satisfactory and unitary description of the even-even Sm isotopes, whose spectra change character with increasing mass number, going from the vibrational to the rotational limit. The neighbouring odd-A Eu isotopes, which also show such a transition, are therefore a suitable test of the Interacting Boson-Fermion Model (IBFM).

Boson expansion theories have recently generated a great deal of interest1-5) as a convenient means for describing collective nuclear properties. Both unitary and nonunitary mappings have been used. The latter, referred to as the Dyson boson theory, has two advantages. It is exact and provides a finite boson expansion whereas the Hermitian theories are characterized by infinite boson expansions. However, some problems also arise. Due to the nonunitary nature of the Dyson mapping the normalization condition is not sufficient to normalize bra and ket vectors separately5-7).

The grammar of the linguist describes, as we have already said, the structure of sentences in the form of a system of rules. The linguist looks at language as such, that is to say, neither under the aspect of producing or speaking nor under the aspect of understanding the particular sentence. Grammar and lexicon are valid for the linguist in the same way for both production and for reception. Therefore, psycholinguistics has also tried for a long time to describe speaking and understanding in one unitary model.