Technology management tools: Generalization, integration and configuration

Managers in technology-intensive businesses need to make decisions in complex and dynamic environments. Many tools, frameworks and processes have been developed to support managers in these situations, leading to a proliferation of such approaches, with little consistency in terminology or theoretical foundation, and a lack of understanding of how such tools can be linked together to tackle management challenges in an integrated way. As a step towards addressing these issues, this paper proposes the concept of an integrated 'toolkit', incorporating generalized forms of three core technology management tools that support strategic planning (roadmapping, portfolio analysis and linked analysis grids). © 2006 World Scientific Publishing Company.

On the Relationship Between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions

In this paper, we bound the generalization error of a class of Radial Basis Function networks, for certain well defined function learning tasks, in terms of the number of parameters and number of examples. We show that the total generalization error is partly due to the insufficient representational capacity of the network (because of its finite size) and partly due to insufficient information about the target function (because of finite number of samples). We make several observations about generalization error which are valid irrespective of the approximation scheme. Our result also sheds light on ways to choose an appropriate network architecture for a particular problem.

Justified Generalization: Acquiring Procedures from Examples

This thesis describes an implemented system called NODDY for acquiring procedures from examples presented by a teacher. Acquiring procedures form examples involves several different generalization tasks. Generalization is an underconstrained task, and the main issue of machine learning is how to deal with this underconstraint. The thesis presents two principles for constraining generalization on which NODDY is based. The first principle is to exploit domain based constraints. NODDY demonstrated how such constraints can be used both to reduce the space of possible generalizations to manageable size, and how to generate negative examples out of positive examples to further constrain the generalization. The second principle is to avoid spurious generalizations by requiring justification before adopting a generalization. NODDY demonstrates several different ways of justifying a generalization and proposes a way of ordering and searching a space of candidate generalizations based on how much evidence would be required to justify each generalization. Acquiring procedures also involves three types of constructive generalizations: inferring loops (a kind of group), inferring complex relations and state variables, and inferring predicates. NODDY demonstrates three constructive generalization methods for these kinds of generalization.

Non-anonymous ballot aggregation: an axiomatic generalization of Approval Voting

We study axiomatically situations in which the society agrees to treat voters with different characteristics distinctly. In this setting, we propose a set of intuitive axioms and show that they jointly characterize a new class of voting procedures, called Type-weighted Approval Voting. According to this family, each voter has a strictly positive and finite weight (the weight is necessarily the same for all voters with the same characteristics) and the alternative with the highest number of weighted votes is elected. The implemented voting procedure reduces to Approval Voting in case all voters are identical or the procedure assigns the same weight to all types. Using this idea, we also obtain a new characterization of Approval Voting.

Fear learning circuitry is biased toward generalization of fear associations in posttraumatic stress disorder.

Fear conditioning is an established model for investigating posttraumatic stress disorder (PTSD). However, symptom triggers may vaguely resemble the initial traumatic event, differing on a variety of sensory and affective dimensions. We extended the fear-conditioning model to assess generalization of conditioned fear on fear processing neurocircuitry in PTSD. Military veterans (n=67) consisting of PTSD (n=32) and trauma-exposed comparison (n=35) groups underwent functional magnetic resonance imaging during fear conditioning to a low fear-expressing face while a neutral face was explicitly unreinforced. Stimuli that varied along a neutral-to-fearful continuum were presented before conditioning to assess baseline responses, and after conditioning to assess experience-dependent changes in neural activity. Compared with trauma-exposed controls, PTSD patients exhibited greater post-study memory distortion of the fear-conditioned stimulus toward the stimulus expressing the highest fear intensity. PTSD patients exhibited biased neural activation toward high-intensity stimuli in fusiform gyrus (P<0.02), insula (P<0.001), primary visual cortex (P<0.05), locus coeruleus (P<0.04), thalamus (P<0.01), and at the trend level in inferior frontal gyrus (P=0.07). All regions except fusiform were moderated by childhood trauma. Amygdala-calcarine (P=0.01) and amygdala-thalamus (P=0.06) functional connectivity selectively increased in PTSD patients for high-intensity stimuli after conditioning. In contrast, amygdala-ventromedial prefrontal cortex (P=0.04) connectivity selectively increased in trauma-exposed controls compared with PTSD patients for low-intensity stimuli after conditioning, representing safety learning. In summary, fear generalization in PTSD is biased toward stimuli with higher emotional intensity than the original conditioned-fear stimulus. Functional brain differences provide a putative neurobiological model for fear generalization whereby PTSD symptoms are triggered by threat cues that merely resemble the index trauma.

Layers of generality and types of generalization in pattern activities

Pattern generalization is considered one of the prominent routes for in-troducing students to algebra. However, not all generalizations are al-gebraic. In the use of pattern generalization as a route to algebra, we —teachers and educators— thus have to remain vigilant in order not to confound algebraic generalizations with other forms of dealing with the general. But how to distinguish between algebraic and non-algebraic generalizations? On epistemological and semiotic grounds, in this arti-cle I suggest a characterization of algebraic generalizations. This char-acterization helps to bring about a typology of algebraic and arithmetic generalizations. The typology is illustrated with classroom examples.

Graphical representation and generalization in sequences problems

In this paper we present different ways used by Secondary students to generalize when they try to solve problems involving sequences. 359 Spanish students solved generalization problems in a written test. These problems were posed through particular terms expressed in different representations. We present examples that illustrate different ways of achieving various types of generalization and how students express generalization. We identify graphical representation of generalization as a useful tool of getting other ways of expressing generalization, and we analyze its connection with other ways of expressing it.

A generalization of fiedler's lemma and some applications

In a previous paper [M. Robbiano, E.A. Martins, and I. Gutman, Extending a theorem by Fiedler and applications to graph energy, MATCH Commun. Math. Comput. Chem. 64 (2010), pp. 145-156], a lemma by Fiedler was used to obtain eigenspaces of graphs, and applied to graph energy. In this article Fiedler's lemma is generalized and this generalization is applied to graph spectra and graph energy. © 2011 Taylor & Francis.

A generalization of the Hoffman-Lovász upper bound on the independence number of a regular graph

A family of quadratic programming problems whose optimal values are upper bounds on the independence number of a graph is introduced. Among this family, the quadratic programming problem which gives the best upper bound is identified. Also the proof that the upper bound introduced by Hoffman and Lovász for regular graphs is a particular case of this family is given. In addition, some new results characterizing the class of graphs for which the independence number attains the optimal value of the above best upper bound are given. Finally a polynomial-time algorithm for approximating the size of the maximum independent set of an arbitrary graph is described and the computational experiments carried out on 36 DIMACS clique benchmark instances are reported.

Spectra of graphs obtained by a generalization of the join graph operation

Taking a Fiedler’s result on the spectrum of a matrix formed from two symmetric matrices as a motivation, a more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs (regular in the case of adjacency spectra and arbitrary in the case of Laplacian spectra). Some additional consequences are explored, namely regarding the largest eigenvalue and algebraic connectivity.

Logics of generalization: Derrida, grammatology and transdisciplinarity

This article seeks to explore some issues regarding the different modes of generality at stake in the formation of transdisciplinary concepts within the production of ‘theory’ in the humanities and social sciences. Focused around Jacques Derrida’s seminal account of ‘writing’ in his 1967 book Of Grammatology, the article outlines what it defines as a logic of generalization at stake in Derrida’s elaborations of a quasi-transcendental ‘inscription in general’. Starting out from the questions thereby raised about the relationship between such forms of generality and those historically ascribed to philosophy, the article concludes by contrasting Derrida’s generalized writing with more recent returns to ‘metaphysics’ in the work of Bruno Latour and others. Against the immediately ‘ontological’ orientation of much recent ‘new materialist’ or ‘object-oriented’ thought, the article argues for the necessity of ‘different levels of writing in general’ through a continual folding back of absolute generalization into historically specific disciplinary crossings and exchanges; something suggested by but never really developed in Derrida’s own work.

Fractional generalization of memristor and higher order elements

Fractional calculus generalizes integer order derivatives and integrals. Memristor systems generalize the notion of electrical elements. Both concepts were shown to model important classes of phenomena. This paper goes a step further by embedding both tools in a generalization considering complex-order objects. Two complex operators leading to real-valued results are proposed. The proposed class of models generate a broad universe of elements. Several combinations of values are tested and the corresponding dynamical behavior is analyzed.