9,084 research outputs found
Axiomatic structure of k-additive capacities
In this paper we deal with the problem of axiomatizing the preference relations modelled through Choquet integral with respect to a -additive capacity, i.e. whose Möbius transform vanishes for subsets of more than elements. Thus, -additive capacities range from probability measures () to general capacities (). The axiomatization is done in several steps, starting from symmetric 2-additive capacities, a case related to the Gini index, and finishing with general -additive capacities. We put an emphasis on 2-additive capacities. Our axiomatization is done in the framework of social welfare, and complete previous results of Weymark, Gilboa and Ben Porath, and Gajdos.Axiomatic; Capacities; k-Additivity
Self-intersecting fuzzy extra dimensions from squashed coadjoint orbits in SYM and matrix models
We find new vacuum solutions of super-Yang-Mills with totally
anti-symmetric cubic soft SUSY breaking terms, or equivalently solutions of the
IKKT matrix model of type with flux
terms. The solutions can be understood in terms of 4- and 6- dimensional fuzzy
branes in extra dimensions, describing self-intersecting
projections of compact flag manifolds of . The 6-dimensional solutions
provide a 6-fold covering of the internal space near the origin, while the
4-dimensional branes have a triple self-intersections spanning all 6 internal
directions. The solutions have lower energy than the trivial vacuum, and we
prove that there are no negative modes. The massless modes are identified
explicitly. In particular there are chiral fermionic zero modes, linking the
coincident sheets with opposite flux at the origin. They have a
family symmetry, originating from the Weyl group rotations.Comment: 28+8 pages, 2 figures. V2: improved discussion, published versio
Maximin Safety: When Failing to Lose is Preferable to Trying to Win
We present a new decision rule, \emph{maximin safety}, that seeks to maintain
a large margin from the worst outcome, in much the same way minimax regret
seeks to minimize distance from the best. We argue that maximin safety is
valuable both descriptively and normatively. Descriptively, maximin safety
explains the well-known \emph{decoy effect}, in which the introduction of a
dominated option changes preferences among the other options. Normatively, we
provide an axiomatization that characterizes preferences induced by maximin
safety, and show that maximin safety shares much of the same behavioral basis
with minimax regret.Comment: 14 page
Modelling microgels with controlled structure across the volume phase transition
Thermoresponsive microgels are soft colloids that find widespread use as
model systems for soft matter physics. Their complex internal architecture,
made of a disordered and heterogeneous polymer network, has been so far a major
challenge for computer simulations. In this work we put forward a
coarse-grained model of microgels whose structural properties are in
quantitative agreement with results obtained with small-angle X-ray scattering
experiments across a wide range of temperatures, encompassing the volume phase
transition. These results bridge the gap between experiments and simulations of
individual microgel particles, paving the way to theoretically address open
questions about their bulk properties with unprecedented nano and microscale
resolution
Complexity, BioComplexity, the Connectionist Conjecture and Ontology of Complexity\ud
This paper develops and integrates major ideas and concepts on complexity and biocomplexity - the connectionist conjecture, universal ontology of complexity, irreducible complexity of totality & inherent randomness, perpetual evolution of information, emergence of criticality and equivalence of symmetry & complexity. This paper introduces the Connectionist Conjecture which states that the one and only representation of Totality is the connectionist one i.e. in terms of nodes and edges. This paper also introduces an idea of Universal Ontology of Complexity and develops concepts in that direction. The paper also develops ideas and concepts on the perpetual evolution of information, irreducibility and computability of totality, all in the context of the Connectionist Conjecture. The paper indicates that the control and communication are the prime functionals that are responsible for the symmetry and complexity of complex phenomenon. The paper takes the stand that the phenomenon of life (including its evolution) is probably the nearest to what we can describe with the term “complexity”. The paper also assumes that signaling and communication within the living world and of the living world with the environment creates the connectionist structure of the biocomplexity. With life and its evolution as the substrate, the paper develops ideas towards the ontology of complexity. The paper introduces new complexity theoretic interpretations of fundamental biomolecular parameters. The paper also develops ideas on the methodology to determine the complexity of “true” complex phenomena.\u
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