On satellites in semi-abelian categories: Homology without projectives

Working in a semi-abelian context, we use Janelidze's theory of generalised satellites to study universal properties of the Everaert long exact homology sequence. This results in a new definition of homology which does not depend on the existence of projective objects. We explore the relations with other notions of homology, and thus prove a version of the higher Hopf formulae. We also work out some examples.Comment: 29 pages; major changes in Example 4.15, minor changes throughout the tex

Short communication: a hierarchy of items within Eysenck’s EPI

Based on the recent finding of a hierarchical scale for Neuroticism in the NEO-Five Factor Inventory, two further personality inventories: the Eysenck Personality Inventory and Goldberg’s International Personality Item Pool were analysed using the Mokken Scaling Procedure for hierarchical scales. Items from two dimensions of the Eysenck Personality Inventory: Neuroticism and Extraversion produced hierarchical scales of 12 and five items, respectively. The Neuroticism items ran from items expressing mild to more extreme worry and the Extraversion items ran from mild sociability to more extreme ‘showing off’. The utility of hierarchical scales in personality measurement is discussed in terms of furthering theoretical understanding of personality and also practical application. In addition, the reasons why only one of these scales should produce hierarchical sets of items is discussed

Equations resolving a conjecture of Rado on partition regularity

A linear equation L is called k-regular if every k-coloring of the positive integers contains a monochromatic solution to L. Richard Rado conjectured that for every positive integer k, there exists a linear equation that is (k-1)-regular but not k-regular. We prove this conjecture by showing that the equation $\sum_{i=1}^{k-1} \frac{2^i}{2^i-1} x_i = (-1 + \sum_{i=1}^{k-1} \frac{2^i}{2^i-1}) x_0$ has this property. This conjecture is part of problem E14 in Richard K. Guy's book "Unsolved problems in number theory", where it is attributed to Rado's 1933 thesis, "Studien zur Kombinatorik".Comment: 2 pages, no figures. The replaced version (v2) differs from the original (v1) only in expositio

A non-symmetric Yang-Baxter Algebra for the Quantum Nonlinear Schr\"odinger Model

We study certain non-symmetric wavefunctions associated to the quantum nonlinear Schr\"odinger model, introduced by Komori and Hikami using Gutkin's propagation operator, which involves representations of the degenerate affine Hecke algebra. We highlight how these functions can be generated using a vertex-type operator formalism similar to the recursion defining the symmetric (Bethe) wavefunction in the quantum inverse scattering method. Furthermore, some of the commutation relations encoded in the Yang-Baxter equation for the relevant monodromy matrix are generalized to the non-symmetric case.Comment: 31 pages; added some references; minor corrections throughou

Pivots, Determinants, and Perfect Matchings of Graphs

We give a characterization of the effect of sequences of pivot operations on a graph by relating it to determinants of adjacency matrices. This allows us to deduce that two sequences of pivot operations are equivalent iff they contain the same set S of vertices (modulo two). Moreover, given a set of vertices S, we characterize whether or not such a sequence using precisely the vertices of S exists. We also relate pivots to perfect matchings to obtain a graph-theoretical characterization. Finally, we consider graphs with self-loops to carry over the results to sequences containing both pivots and local complementation operations.Comment: 16 page

Superfilters, Ramsey theory, and van der Waerden's Theorem

Superfilters are generalized ultrafilters, which capture the underlying concept in Ramsey theoretic theorems such as van der Waerden's Theorem. We establish several properties of superfilters, which generalize both Ramsey's Theorem and its variant for ultrafilters on the natural numbers. We use them to confirm a conjecture of Ko\v{c}inac and Di Maio, which is a generalization of a Ramsey theoretic result of Scheepers, concerning selections from open covers. Following Bergelson and Hindman's 1989 Theorem, we present a new simultaneous generalization of the theorems of Ramsey, van der Waerden, Schur, Folkman-Rado-Sanders, Rado, and others, where the colored sets can be much smaller than the full set of natural numbers.Comment: Among other things, the results of this paper imply (using its one-dimensional version) a higher-dimensional version of the Green-Tao Theorem on arithmetic progressions in the primes. The bibliography is now update

Obstructing extensions of the functor Spec to noncommutative rings

In this paper we study contravariant functors from the category of rings to the category of sets whose restriction to the full subcategory of commutative rings is isomorphic to the prime spectrum functor Spec. The main result reveals a common characteristic of these functors: every such functor assigns the empty set to M_n(C) for n >= 3. The proof relies, in part, on the Kochen-Specker Theorem of quantum mechanics. The analogous result for noncommutative extensions of the Gelfand spectrum functor for C*-algebras is also proved.Comment: 23 pages. To appear in Israel J. Math. Title was changed; introduction was rewritten; old Section 2 was removed to streamline the exposition; final section was rewritten to omit an error in the earlier proof of Theorem 1.

Which activities threaten independent living of elderly when becoming problematic : inspiration for meaningful service robot functionality

Purpose: In light of the increasing elderly population and the growing demand for home care, the potential of robot support is given increasing attention. In this paper, an inventory of activities was made that threaten independent living of elderly when becoming problematic. Results will guide the further development of an existing service robot, the Care-O-bot®. Method: A systematic literature search of PubMed was performed, focused on the risk factors for institutionalization. Additionally, focus group sessions were conducted in the Netherlands, United Kingdom and France. In these focus group sessions, problematic activities threatening the independence of elderly people were discussed. Three separate target groups were included in the focus group sessions: (1) elderly persons (n = 41), (2) formal caregivers (n = 40) and (3) informal caregivers (n = 32). Results: Activities within the International Classification of Functioning domains mobility, self-care, and interpersonal interaction and relationships were found to be the most problematic. Conclusions: A distinct set of daily activities was identified that may threaten independent living, but no single activity could be selected as the main activity causing a loss of independence as it is often a combination of problematic activities that is person-specific. Supporting the problematic activities need not involve a robotic solution Read More: http://informahealthcare.com/doi/abs/10.3109/17483107.2013.840861Peer reviewe

Automatically generating streamlined constraint models with ESSENCE and CONJURE

Streamlined constraint reasoning is the addition of uninferred constraints to a constraint model to reduce the search space, while retaining at least one solution. Previously, effective streamlined models have been constructed by hand, requiring an expert to examine closely solutions to small instances of a problem class and identify regularities. We present a system that automatically generates many conjectured regularities for a given Essence specification of a problem class by examining the domains of decision variables present in the problem specification. These conjectures are evaluated independently and in conjunction with one another on a set of instances from the specified class via an automated modelling tool-chain comprising of Conjure, Savile Row and Minion. Once the system has identified effective conjectures they are used to generate streamlined models that allow instances of much larger scale to be solved. Our results demonstrate good models can be identified for problems in combinatorial design, Ramsey theory, graph theory and group theory - often resulting in order of magnitude speed-ups.Postprin

A hierarchy of happiness? Mokken scaling analysis of the Oxford Happiness Inventory

The items of the Oxford Happiness Inventory (OHI, a self-report assessment of happiness, are subjected to an analysis for hierarchy among its items. By using Mokken scaling analyses we can assess whether items can reliably be ordered between persons as severity indicators on a latent trait; in this case, a latent trait of Happiness. OHI item-level data from 1024 participants were entered into the Mokken Scaling Procedure (MSP) seeking reliable scales with H > 0.30. 12 OHI items formed a reliable and statistically significant hierarchy. However, the MSP values indicate a 'weak' scale. The 'most difficult' (happiest) item on the scale is 'feeling energetic' and the 'least difficult' (least happy) is 'I have fun'. Items in the scale are consistent with what is already known about both happiness and low mood. The reduction in the OHI's items from 29 to 12 in the Mokken scale may have utility making it more accessible to participants as well as identifying items with reliably different levels of 'difficulty'. (C) 2010 Elsevier Ltd. All rights reserved