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Flocks, Herds, And Schools Alternative Currency, Participatory Sensing, Complexity Theory

This study explored participation by Japanese university English as a Foreign Language (EFL) learners in Computer Assisted Language Learning/Mobile Assisted Language Learning (CALL/MALL) vocabulary tasks through the lens of Complexity Theory (CT). CT, which studies how complex systems are influenced by changes in interconnected variables (Larsen-Freeman & Cameron, 2008), has been advocated as an approach that aligns well with Second Language Acquisition (SLA) and CALL research (Godwin-Jones, 2019). In this study, CT was applied to action research involving learners using smartphones to create game-based vocabulary quizzes. It aimed to understand how the context, personal attributes, and in-class interactions affected participation and learning outcomes. The results show the variability and nonlinearity of learners' language development, the importance of initial conditions, and the vital role of teacher input. It also demonstrated that there are various ways to successfully complete a task, so viewing tasks as dynamic systems may be a fruitful approach. [For the complete volume, "CALL for Widening Participation: Short Papers from EUROCALL 2020 (28th, Online, August 20-21, 2020)," see ED610330.]

Complexity theory is an interdisciplinary set of concepts and tools that has proved useful for many fields and there is potential benefit for the military as well. Six concepts from complex adaptive systems theory-fitness landscape, agent fitness, agent response profiles, building blocks, identity tags, and emergent phenomena-can improve social systems analysis in doctrinal operations processes. These in turn support four of the six commander activities-understand, visualize, describe, and assess-within U.S. Joint Force operations. The six concepts from complex adaptive system theory should be included with the existing general systems analytic methodology described in Joint Publication 2-01.3: Joint Intelligence Preparation of the Operational Environment, Chapter II, Section B, Part 12. This action is simply a start to updating Joint doctrine to account for complexity and this monograph recommends further research to identify and incorporate other tools from complexity theory for the U.S. Joint Force.

In this lecture we will talk about di_erent kinds of Non-deterministic Turing Machines (NTM) and then how to construct Alternating Turing Machines from them. We�ll also examine the relation of ATMs to deterministic classes, then we will prove a few di_erent relations between alternating and deterministic time and space

This booklet contains a variety or comments regarding J. Glenn Brookshear's text "Theory of Computation: Formal Languages, Automata, and Complexity" (ISBN 0-8053-0143-7) along with some ideas and transparency masters that a teacher or a course based on that text may want to use. The booklet contains a chapter corresponding to each chapter in the parent text and concludes with a section of transparency masters. Within each chapter are sections entitled General Comments, Comments Regarding Chapter Review Problems, and Additional Problems. ISBN 0-8053-0144-5

We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This semantic-based approach should apply uniformly to various computational paradigms, and enable the use of new mathematical methods and tools to attack problem in computational complexity. This paper provides the background, motivations and perspectives of this complexity-through-realisability theory to be developed, and illustrates it with recent results.

We show that the Bergman, Szego, and Poisson kernels associated to a finitely connected domain in the plane are all composed of finitely many easily computed functions of one variable. The new formulas give rise to new methods for computing the Bergman and Szeg\H o kernels in which all integrals used in the computations are line integrals; at no point is an integral with respect to area measure required. The results mentioned so far can be interpreted as saying that the kernel functions are simpler than one might expect. However, we also prove that the kernels cannot be too simple by showing that the only finitely connected domains in the plane whose Bergman or Szeg\H o kernels are rational functions are the obvious ones. This leads to a proof that the classical Green's function associated to a finitely connected domain in the plane is the logarithm of a rational function if and only if the domain is simply connected and rationally equivalent to the unit disc.

We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on ``generic-case complexity'' we show that if a finitely generated group $G$ has the word problem solvable in subexponential time and has a subgroup of finite index which possesses a non-elementary word-hyperbolic quotient group, then the average-case complexity of the word problem for $G$ is linear time, uniformly with respect to the collection of all length-invariant measures on $G$. For example, the result applies to all braid groups $B_n$.

We develop a theory of complexity for numerical computations that takes into account the condition of the input data and allows for roundoff in the computations. We follow the lines of the theory developed by Blum, Shub, and Smale for computations over R (which in turn followed those of the classical, discrete, complexity theory as laid down by Cook, Karp, and Levin among others). In particular, we focus on complexity classes of decision problems and paramount among them, on appropriate versions of the classes P, NP and EXP of polynomial, nondeterministic polynomial, and exponential time, respectively. We prove some basic relationships between these complexity classes and exhibit natural NP-complete problems.

Since October 1, 1979, research in Complexity Theory and Combinatorial Algorithms at the Department of Computer Science at the University of Illinois was supported by the Office of Naval Research. During this period of time, research work was carried out in the areas of Computational Complexity Theory, Scheduling Algorithms, Graph Algorithms, Dynamic Programming, and Fault- Tolerance Computing. We summarize here our accomplishments and our future plans, and we wish to request continued support for the period of October 1, 1980 - September 30, 1982 from ONR for research in these areas. Scheduling to meet deadlines -- The problem of scheduling jobs to meet their deadlines was studied. Given a set of jobs each of which is specified by three parameters, ready time, deadline, and computation time, we want to schedule them on a computer system so that, if possible, all deadlines will be met. Furthermore, if indeed all deadlines can be met, we want to know the possibility of completing the executing of each job so that there will be a 'slack time' between the time of completion and the deadline. In particular, the following model is used: There is a single processor in the computing system. Each job consists of an infinite stream of periodic and identical requests. A request is ready when it arrives and should be completed prior to the arrival of the next request of the same job. The execution of a job can be interrupted and be resumed later on.

Since October 1, 1979, research in Complexity Theory and Combinatorial Algorithms at the Department of Computer Science at the University of Illinois was supported by the Office of Naval Research. During this period of time, research work was carried out in the areas of Computational Complexity Theory, Scheduling Algorithms, Graph Algorithms, Dynamic Programming, and Fault- Tolerance Computing. We summarize here our accomplishments and our future plans, and we wish to request continued support for the period of October 1, 1980 - September 30, 1982 from ONR for research in these areas. Scheduling to meet deadlines -- The problem of scheduling jobs to meet their deadlines was studied. Given a set of jobs each of which is specified by three parameters, ready time, deadline, and computation time, we want to schedule them on a computer system so that, if possible, all deadlines will be met. Furthermore, if indeed all deadlines can be met, we want to know the possibility of completing the executing of each job so that there will be a 'slack time' between the time of completion and the deadline. In particular, the following model is used: There is a single processor in the computing system. Each job consists of an infinite stream of periodic and identical requests. A request is ready when it arrives and should be completed prior to the arrival of the next request of the same job. The execution of a job can be interrupted and be resumed later on.

In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have the following features and motivations: -we give a new computable definition of information and complexity which allows to give a computable characterization of the K-S entropy; -these definitions make sense even for a single orbit and can be measured by suitable data compression algorithms; hence they can be used in simulations and in the analysis of experimental data; -the asymptotic behavior of these quantities allows to compute not only the Kolmogorov-Sinai entropy but also other quantities which give a measure of the chaotic behavior of a dynamical system even in the case of null entropy.

We provide a list of new natural $\mathsf{VNP}$-intermediate polynomial families, based on basic (combinatorial) $\mathsf{NP}$-complete problems that are complete under parsimonious reductions. Over finite fields, these families are in $\mathsf{VNP}$, and under the plausible hypothesis $\mathsf{Mod}_p\mathsf{P} \not\subseteq \mathsf{P/poly}$, are neither $\mathsf{VNP}$-hard (even under oracle-circuit reductions) nor in $\mathsf{VP}$. Prior to this, only the Cut Enumerator polynomial was known to be $\mathsf{VNP}$-intermediate, as shown by B\"{u}rgisser in 2000. We next show that over rationals and reals, two of our intermediate polynomials, based on satisfiability and Hamiltonian cycle, are not monotone affine polynomial-size projections of the permanent. This augments recent results along this line due to Grochow. Finally, we describe a (somewhat natural) polynomial defined independent of a computation model, and show that it is $\mathsf{VP}$-complete under polynomial-size projections. This complements a recent result of Durand et al. (2014) which established $\mathsf{VP}$-completeness of a related polynomial but under constant-depth oracle circuit reductions. Both polynomials are based on graph homomorphisms. A simple restriction yields a family similarly complete for $\mathsf{VBP}$.

An important goal of computational linguistics has been to use linguistic theory to guide the construction of computationally efficient real-world natural language processing systems. At first glance, generalized phrase structure grammar (GPSG) appears to be a blessing on two counts. First, the precise formalisms of GPSG might be a direct and transparent guide for parser design and implementation. Second, since GPSG has weak context-free generative power and context-free languages can be parsed in by a wide range of algorithms, GPSG parsers would appear to run in polynomial time. This widely-assumed GPSG efficient parsability result is misleading: here we prove that the universal recognition problem of current GPSG theory is exponential-polynomial time hard, and assuredly intractable. The paper pinpoints sources of complexity (e.g. metarules and the theory of syntactic features) in the current GPSG theory and concludes with some linguistically and computationally motivated restrictions on GPSG.

The scientific revolution, ushered in by Newtonian laws, had a major impact on Western military thinking. By believing in the power of reductionism, planners were taught to decompose problems into their constituent parts and solve them, almost in isolation. This analysis was followed by a synthesis of the constituent parts in order to solve the problem. The use of systems theory in war offers another approach to Newtonian science. Armies mimic complex adaptive systems by exhibiting a self-organizing capability that prevents them from slipping into chaos. A complex system adapts to its surroundings and learns from its interactions. This learning enables the system to maximize its position vis-a- -vis its environment and can lead to an emergence of a new and unexpected system that cannot be predicted from the original elements. These new sciences stress non-linearity and the need to view problems holistically. Despite recognizing the change in the environment and the enemy, US Army doctrine is still rooted in the symmetrical battle concept and many current theoretical models do not adequately deal with the increasing complexity of war. This monograph suggests that the analysis of complexity and chaos can provide a more framework for operational shock.

The conjugate gradient algorithm (called CG hereafter) is a popular way to solve large sparse positive definite systems of equations. The minimum residual algorithm (called MR) is closely related to CG and can be applied to any nonsingular system. In this summary we describe, our result and, of more importance, comment on their significance. The discussion is confined to exact arithmetic because this enquiry concerns only the theory of MR, CG and related algorithms, not their implementation.

The existence of lower bounds for problems in NP intersection coNP is equivalent to the existence of nonstandard, noneffective models of a fragment, PT, of complete arthmetic. A typical corrollary is that factoring integers is intractable if there is a model of arithmetic in which primes fail to have primitive roots. Following from the proof of the main result is an existential proof procedure for polynomial time algorithms. (Author)

The concept of relational complexity is applied to explain the persistent difficulties of young children with theory of mind. Relational complexity has been found useful as a general cognitive complexity metric. Children must understand that the relation between an object and a person's percept is conditional on a third variable, such as a filter or other condition that affects a person's knowledge state. Processing three interacting variables is equivalent to a ternary relation, and this level of complexity is often difficult for young children. It was hypothesized that if relational complexity is a factor in concept of mind, it should be related to tasks at the same level of complexity in other domains. Forty-eight 3- to 5-year-olds were tested on four false belief tasks and on four appearance-reality tasks. They were also assessed on transitivity, hierarchical classification, and cardinality tasks that had previously been shown to require the same level of relational complexity. Results indicate that the performance of 3-year-olds was significantly lower than the older age groups on both the theory-of-mind and relational complexity tasks. The findings support the relational complexity interpretation of concept of mind. (Author/EMK)

The concept of relational complexity is applied to explain the persistent difficulties of young children with theory of mind. Relational complexity has been found useful as a general cognitive complexity metric. Children must understand that the relation between an object and a person's percept is conditional on a third variable, such as a filter or other condition that affects a person's knowledge state. Processing three interacting variables is equivalent to a ternary relation, and this level of complexity is often difficult for young children. It was hypothesized that if relational complexity is a factor in concept of mind, it should be related to tasks at the same level of complexity in other domains. Forty-eight 3- to 5-year-olds were tested on four false belief tasks and on four appearance-reality tasks. They were also assessed on transitivity, hierarchical classification, and cardinality tasks that had previously been shown to require the same level of relational complexity. Results indicate that the performance of 3-year-olds was significantly lower than the older age groups on both the theory-of-mind and relational complexity tasks. The findings support the relational complexity interpretation of concept of mind. (Author/EMK)

This article describes a {\em nonstandard} quantum group that may be used to derive a positive formula for the plethysm problem, just as the standard (Drinfeld-Jimbo) quantum group can be used to derive the positive Littlewood-Richardson rule for arbitrary complex semisimple Lie groups. The sequel \cite{GCT8} gives conjecturally correct algorithms to construct canonical bases of the coordinate rings of these nonstandard quantum groups and canonical bases of the dually paired nonstandard deformations of the symmetric group algebra. A positive $#P$-formula for the plethysm constant follows from the conjectural properties of these canonical bases and the duality and reciprocity conjectures herein.

This article gives conjecturally correct algorithms to construct canonical bases of the irreducible polynomial representations and the matrix coordinate rings of the nonstandard quantum groups in GCT4 and GCT7, and canonical bases of the dually paired nonstandard deformations of the symmetric group algebra therein. These are generalizations of the canonical bases of the irreducible polynomial representations and the matrix coordinate ring of the standard quantum group, as constructed by Kashiwara and Lusztig, and the Kazhdan-Lusztig basis of the Hecke algebra. A positive ($#P$-) formula for the well-known plethysm constants follows from their conjectural properties and the duality and reciprocity conjectures in \cite{GCT7}.

We show that there are simplex pivoting rules for which it is PSPACE-complete to tell if a particular basis will appear on the algorithm's path. Such rules cannot be the basis of a strongly polynomial algorithm, unless P = PSPACE. We conjecture that the same can be shown for most known variants of the simplex method. However, we also point out that Dantzig's shadow vertex algorithm has a polynomial path problem. Finally, we discuss in the same context randomized pivoting rules.

The conjugate gradient algorithm (called CG hereafter) is a popular way to solve large sparse positive definite systems of equations. The minimum residual algorithm (called MR) is closely related to CG and can be applied to any nonsingular system. In this summary we describe, our result and, of more importance, comment on their significance. The discussion is confined to exact arithmetic because this enquiry concerns only the theory of MR, CG and related algorithms, not their implementation.

The conjugate gradient algorithm (called CG hereafter) is a popular way to solve large sparse positive definite systems of equations. The minimum residual algorithm (called MR) is closely related to CG and can be applied to any nonsingular system. In this summary we describe, our result and, of more importance, comment on their significance. The discussion is confined to exact arithmetic because this enquiry concerns only the theory of MR, CG and related algorithms, not their implementation.

The conjugate gradient algorithm (called CG hereafter) is a popular way to solve large sparse positive definite systems of equations. The minimum residual algorithm (called MR) is closely related to CG and can be applied to any nonsingular system. In this summary we describe, our result and, of more importance, comment on their significance. The discussion is confined to exact arithmetic because this enquiry concerns only the theory of MR, CG and related algorithms, not their implementation.

The conjugate gradient algorithm (called CG hereafter) is a popular way to solve large sparse positive definite systems of equations. The minimum residual algorithm (called MR) is closely related to CG and can be applied to any nonsingular system. In this summary we describe, our result and, of more importance, comment on their significance. The discussion is confined to exact arithmetic because this enquiry concerns only the theory of MR, CG and related algorithms, not their implementation.

The conjugate gradient algorithm (called CG hereafter) is a popular way to solve large sparse positive definite systems of equations. The minimum residual algorithm (called MR) is closely related to CG and can be applied to any nonsingular system. In this summary we describe, our result and, of more importance, comment on their significance. The discussion is confined to exact arithmetic because this enquiry concerns only the theory of MR, CG and related algorithms, not their implementation.

The conjugate gradient algorithm (called CG hereafter) is a popular way to solve large sparse positive definite systems of equations. The minimum residual algorithm (called MR) is closely related to CG and can be applied to any nonsingular system. In this summary we describe, our result and, of more importance, comment on their significance. The discussion is confined to exact arithmetic because this enquiry concerns only the theory of MR, CG and related algorithms, not their implementation.

This paper explicates how statutes and case law (court cases) can be used as sources for discourse analysis when researching South African education reform through a complexity theory lens. Firstly, the law-making process is built on discourses at different levels. Secondly, discourses are manifested in case law because in order to resolve disputes arguments are presented on which the court is then required to rule. Discourse analysis explores how meaning, identities, activities and relationships are negotiated and constructed and these sources of discourse are useful when the focus is on the study of actions and interactions within the education system. [For the complete Volume 20 proceedings, see ED622631.]

We prove the lower bound R(M_m) \geq 3/2 m^2 - 2 on the border rank of m x m matrix multiplication by exhibiting explicit representation theoretic (occurence) obstructions in the sense of the geometric complexity theory (GCT) program. While this bound is weaker than the one recently obtained by Landsberg and Ottaviani, these are the first significant lower bounds obtained within the GCT program. Behind the proof is the new combinatorial concept of obstruction designs, which encode highest weight vectors in Sym^d\otimes^3(C^n)^* and provide new insights into Kronecker coefficients.

We study probabilistic complexity classes and questions of derandomisation from a logical point of view. For each logic L we introduce a new logic BPL, bounded error probabilistic L, which is defined from L in a similar way as the complexity class BPP, bounded error probabilistic polynomial time, is defined from PTIME. Our main focus lies on questions of derandomisation, and we prove that there is a query which is definable in BPFO, the probabilistic version of first-order logic, but not in Cinf, finite variable infinitary logic with counting. This implies that many of the standard logics of finite model theory, like transitive closure logic and fixed-point logic, both with and without counting, cannot be derandomised. Similarly, we present a query on ordered structures which is definable in BPFO but not in monadic second-order logic, and a query on additive structures which is definable in BPFO but not in FO. The latter of these queries shows that certain uniform variants of AC0 (bounded-depth polynomial sized circuits) cannot be derandomised. These results are in contrast to the general belief that most standard complexity classes can be derandomised. Finally, we note that BPIFP+C, the probabilistic version of fixed-point logic with counting, captures the complexity class BPP, even on unordered structures.

where will you go morons if it strikes the building?

Following more than a decade of counterinsurgency operations (COIN), the US military is transitioning to new force structure, operating concepts, organization, resourcing, and threat forecasting. During such transitions, much discussion centers around each service's ability to innovate across the gap between organizational resources and an uncertain and complex future operating environment. As the USMC resets the force and forges a path forward, the service must comprehensively leverage its best ideas from across the organization to effectively visualize, adapt, and act in the future operational environment. However, increasing globalization and interconnectedness make leading innovation in today's organizations progressively more complex and dynamic. Complexity Leadership Theory (CLT) attempts to reconcile traditional bureaucratic and hierarchal leadership with approaches that incorporate the complex, adaptive, and systems characteristics found in information age organizations. This monograph overlays CLT on two periods of significant warfare innovation in the Marine Corps to evaluate the role of senior leadership in each event. The emergence of amphibious warfare in the 1920s and 1930s and helicopter warfare in the 1940s and 1950s not only transformed the Marine Corps, but changed broader warfare. In each case, the US and allied militaries relied on the innovation for the operating environment that immediately followed. The case studies indicate a legacy of Marine Corps' senior leadership fostering a culture with the capacity to circumvent bureaucracy, and effectively solicit and implement innovation from all levels of the organization. The nature of such senior leadership exhibits many of the characteristics of CLT that remain applicable for current, military leadership.

This paper is a survey dedicated to the analogy between the notions of {\it complexity} in theoretical computer science and {\it energy} in physics. This analogy is not metaphorical: I describe three precise mathematical contexts, suggested recently, in which mathematics related to (un)computability is inspired by and to a degree reproduces formalisms of statistical physics and quantum field theory.

Let $\mathscr{N}(b)$ be the set of real numbers which are normal to base $b$. A well-known result of H. Ki and T. Linton is that $\mathscr{N}(b)$ is $\boldsymbol{\Pi}^0_3$-complete. We show that the set $\mathscr{N}(b)$ of reals which preserve $\mathscr{N}(b)$ under addition is also $\boldsymbol{\Pi}^0_3$-complete. We use the characteriztion of $\mathscr{N}(b)$ given by G. Rauzy in terms of an entropy-like quantity called the noise. It follows from our results that no further characteriztion theorems could result in a still better bound on the complexity of $\mathscr{N}(b)$. We compute the exact descriptive complexity of other naturally occurring sets associated with noise. One of these is complete at the $\boldsymbol{\Pi}^0_4$ level. Finally, we get upper and lower bounds on the Hausdorff dimension of the level sets associated with the noise.

Geometric complexity theory (GCT) is an approach to the P vs. NP and related problems. This article gives its complexity theoretic overview without assuming any background in algebraic geometry or representation theory.

Geometric complexity theory (GCT) is an approach to the P vs. NP and related problems. This article gives its complexity theoretic overview without assuming any background in algebraic geometry or representation theory.

We prove that the Bergman kernel function associated to a finitely connected domain in the plane is given as a rational combination of only three basic functions of one complex variable: an Alhfors map, its derivative, and one other function whose existence is deduced by means of the field of meromorphic functions on the double of the domain. Because many other functions of conformal mapping and potential theory can be expressed in terms of the Bergman kernel, our results shed light on the complexity of these objects. We also prove that the Bergman kernel is an algebraic function of a single Ahlfors map and its derivative. It follows that many objects of potential theory associated to a multiply connected domain are algebraic if and only if the domain is a finite branched cover of the unit disc via an algebraic holomorphic mapping.

A category used by de Paiva to model linear logic also occurs in Vojtas's analysis of cardinal characteristics of the continuum. Its morphisms have been used in describing reductions between search problems in complexity theory. We describe this category and how it arises in these various contexts. We also show how these contexts suggest certain new multiplicative connectives for linear logic. Perhaps the most interesting of these is a sequential composition suggested by the set-theoretic application.

We introduce the Hermitian-invariant group $\Gamma_f$ of a proper rational map $f$ between the unit ball in complex Euclidean space and a generalized ball in a space of typically higher dimension. We use properties of the groups to define the crucial new concepts of essential map and the source rank of a map. We prove that every finite subgroup of the source automorphism group is the Hermitian-invariant group of some rational proper map between balls. We prove that $\Gamma_f$ is non-compact if and only if $f$ is a totally geodesic embedding. We show that $\Gamma_f$ contains an $n$-torus if and only if $f$ is equivalent to a monomial map. We show that $\Gamma_f$ contains a maximal compact subgroup if and only if $f$ is equivalent to the juxtaposition of tensor powers. We also establish a monotonicity result; the group, after intersecting with the unitary group, does not decrease when a tensor product operation is applied to a polynomial proper map. We give a necessary condition for $\Gamma_f$ (when the target is a generalized ball) to contain automorphisms that move the origin.

We introduce the Hermitian-invariant group $\Gamma_f$ of a proper rational map $f$ between the unit ball in complex Euclidean space and a generalized ball in a space of typically higher dimension. We use properties of the groups to define the crucial new concepts of essential map and the source rank of a map. We prove that every finite subgroup of the source automorphism group is the Hermitian-invariant group of some rational proper map between balls. We prove that $\Gamma_f$ is non-compact if and only if $f$ is a totally geodesic embedding. We show that $\Gamma_f$ contains an $n$-torus if and only if $f$ is equivalent to a monomial map. We show that $\Gamma_f$ contains a maximal compact subgroup if and only if $f$ is equivalent to the juxtaposition of tensor powers. We also establish a monotonicity result; the group, after intersecting with the unitary group, does not decrease when a tensor product operation is applied to a polynomial proper map. We give a necessary condition for $\Gamma_f$ (when the target is a generalized ball) to contain automorphisms that move the origin.

Focusing upon the central problems of effective community practice in town and country areas, the four speeches in this collection emphasize some key analytical notions in what has been termed an interactional or activity field conception of community. Among the ideas emphasized are the complexity/integration and the coordination/integration of community structure and the coordinating association and the service agency as key organizations in community development. The four papers are titled and sub-titled as follows: (1) "Community Development: Dialectics in Practice and Theory" (Technology and Community Structure; Community Structures and Processes; Multiple Fields and Goal-Structure Interaction; Community Coordination and Development Models); (2) "Two Basic Structures in the Development of the Modern Community" (Community Coordinating Structures; The Service Agency; Basic Structures, Development Models, and Goal Attainment); (3) "The Multi-County Area as a Community" (The Social Field Perspective; The Emerging Rural-Urban Locality; Two or More Fields in a Multicounty Area; Type of Field and Nature of Integration; Integration of the Multicounty Area); (4) "The Community Association and Comprehensive Development" (Structural Dimensions; New Structures and Projects; The Coordination of Organization; Use of External Resources; Local Development and Community Theory). (JC)

Focusing upon the central problems of effective community practice in town and country areas, the four speeches in this collection emphasize some key analytical notions in what has been termed an interactional or activity field conception of community. Among the ideas emphasized are the complexity/integration and the coordination/integration of community structure and the coordinating association and the service agency as key organizations in community development. The four papers are titled and sub-titled as follows: (1) "Community Development: Dialectics in Practice and Theory" (Technology and Community Structure; Community Structures and Processes; Multiple Fields and Goal-Structure Interaction; Community Coordination and Development Models); (2) "Two Basic Structures in the Development of the Modern Community" (Community Coordinating Structures; The Service Agency; Basic Structures, Development Models, and Goal Attainment); (3) "The Multi-County Area as a Community" (The Social Field Perspective; The Emerging Rural-Urban Locality; Two or More Fields in a Multicounty Area; Type of Field and Nature of Integration; Integration of the Multicounty Area); (4) "The Community Association and Comprehensive Development" (Structural Dimensions; New Structures and Projects; The Coordination of Organization; Use of External Resources; Local Development and Community Theory). (JC)

The authors discuss the role of controversy in mathematics as a preface to two opposing articles on computational complexity theory: "Some basic information on information-based complexity theory" by Beresford Parlett [math.NA/9201266] and "Perspectives on information-based complexity" by J. F. Traub and Henryk Wo\'zniakowski [math.NA/9201269].

One of the central problems in quantum mechanics is to determine the ground state properties of a system of electrons interacting via the Coulomb potential. Since its introduction by Hohenberg, Kohn, and Sham, Density Functional Theory (DFT) has become the most widely used and successful method for simulating systems of interacting electrons, making their original work one of the most cited in physics. In this letter, we show that the field of computational complexity imposes fundamental limitations on DFT, as an efficient description of the associated universal functional would allow to solve any problem in the class QMA (the quantum version of NP) and thus particularly any problem in NP in polynomial time. This follows from the fact that finding the ground state energy of the Hubbard model in an external magnetic field is a hard problem even for a quantum computer, while given the universal functional it can be computed efficiently using DFT. This provides a clear illustration how the field of quantum computing is useful even if quantum computers would never be built.

A general theory of innovation and progress in human society is outlined, based on the combat between two opposite forces (conservatism/inertia and speculative herding "bubble" behavior). We contend that human affairs are characterized by ubiquitous ``bubbles'', which involve huge risks which would not otherwise be taken using standard cost/benefit analysis. Bubbles result from self-reinforcing positive feedbacks. This leads to explore uncharted territories and niches whose rare successes lead to extraordinary discoveries and provide the base for the observed accelerating development of technology and of the economy. But the returns are very heterogeneous, very risky and may not occur. In other words, bubbles, which are characteristic definitions of human activity, allow huge risks to get huge returns over large scales. We outline some underlying mathematical structure and a few results involving positive feedbacks, emergence, heavy-tailed power laws, outliers/kings/black swans, the problem of predictability and the illusion of control, as well as some policy implications.

Book Source: Digital Library of India Item 2015.193376 dc.contributor.author: Ajitbhai M.suthar dc.date.accessioned: 2015-07-08T02:37:08Z dc.date.available: 2015-07-08T02:37:08Z dc.date.digitalpublicationdate: 2005-09-27 dc.identifier.barcode: 1990010091714 dc.identifier.origpath: /rawdataupload/upload/0091/714 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/193376 dc.description.scannerno: 14 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 47 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Technology dc.subject.classification: Engineering. Technology In General dc.subject.classification: Computer Science & Engineering dc.title: An Application Of The Fixpoint Theory To Complexity Of Programs

Book Source: Digital Library of India Item 2015.193376 dc.contributor.author: Ajitbhai M.suthar dc.date.accessioned: 2015-07-08T02:37:08Z dc.date.available: 2015-07-08T02:37:08Z dc.date.digitalpublicationdate: 2005-09-27 dc.identifier.barcode: 1990010091714 dc.identifier.origpath: /rawdataupload/upload/0091/714 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/193376 dc.description.scannerno: 14 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 47 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Technology dc.subject.classification: Engineering. Technology In General dc.subject.classification: Computer Science & Engineering dc.title: An Application Of The Fixpoint Theory To Complexity Of Programs