Incorporating Constraints into Matrix Factorization for Clothes Package Recommendation

Recommender systems have been widely applied in the literature to suggest individual items to users. In this paper, we consider the harder problem of package recommendation, where items are recommended together as a package. We focus on the clothing domain, where a package recommendation involves a combination of a "top'' (e.g. a shirt) and a "bottom'' (e.g. a pair of trousers). The novelty in this work is that we combined matrix factorisation methods for collaborative filtering with hand-crafted and learnt fashion constraints on combining item features such as colour, formality and patterns. Finally, to better understand where the algorithms are underperforming, we conducted focus groups, which lead to deeper insights into how to use constraints to improve package recommendation in this domain

Break Up Variations: An Annotated Score

Break Up Variations is an annotated score by means of which we consider the document as a break-up from — and with — the thinking of performance. We explore the formal categories of page-based and stage-based scores and documentations of performance, asserting the simultaneity of the document and its performance in their mutual departures, theorising the break-up as a form of relation, not as its absence. As a committee of interdisciplinary researchers and practitioners, we consider annotation in terms of affective and theoretical responses to each other’s subject positions. Break Up Variations relates to the problems particular to working in groups: the challenges of collaboration, the disagreements and community-led conflict resolutions, the difficulties with acting professionally, and the desires to keep working together, despite it all. We ask the following questions of each other and ourselves: What are the strategies that art, science, politics and theory might offer each other for navigating — possibly circumventing — the demise of relationships? If the working relationship breaks down, could the end of the group be considered a constitutive aspect of that group? We consider these questions to be about institutions as much as they are about interdependence on personal and planetary scales. Riffing on ideas about romantic break-ups, political dissolutions and ecological collapse, Break Up Variations considers the possibility that an end to a dream of symbiotic life is exactly what makes that dream possible and important

Credit Constraints in Education

We review studies of the impact of credit constraints on the accumulation of human capital. Evidence suggests that credit constraints are increasingly important for schooling and other aspects of households' behavior. We highlight the importance of early childhood investments, since their response largely determines the impact of credit constraints on the overall lifetime acquisition of human capital. We also review the intergenerational literature and examine the macroeconomic impacts of credit constraints on social mobility and the income distribution. A common limitation across all areas of the human capital literature is the imposition of ad hoc constraints on credit. We propose a more careful treatment of the structure of government student loan programs as well as the incentive problems underlying private credit. We show that endogenizing constraints on credit for human capital helps explain observed borrowing, schooling, and default patterns and offers new insights about the design of government policy.Human Capital, Incentive Problems, Government Loans, Early Investments, Social Mobility

Linear constraints from generally covariant systems with quadratic constraints

How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with previous works which use infinitesimal ones. Two kinds of variational principles are taken into account; the first one features non-gauge-invariant actions whereas the second includes fully gauge-invariant actions. Furthermore, it is shown that it is possible to rewrite fully gauge-invariant actions featuring first class constraints quadratic in the momenta into first class constraints linear in the momenta (and homogeneous in some cases) due to the full gauge invariance of their actions. This shows that the gauge symmetry present in generally covariant theories having first class constraints quadratic in the momenta is not of a different kind with respect to the one of theories with first class constraints linear in the momenta if fully gauge-invariant actions are taken into account for the former theories. These ideas are implemented for the parametrized relativistic free particle, parametrized harmonic oscillator, and the SL(2,R) model.Comment: Latex file, revtex4, 18 pages, no figures. This version includes the corrections to many misprints of v1 and also the ones of the published version. The conceptual and technical parts of the paper are not altere

Local Quantum Constraints

We analyze the situation of a local quantum field theory with constraints, both indexed by the same set of space-time regions. In particular we find ``weak'' Haag-Kastler axioms which will ensure that the final constrained theory satisfies the usual Haag-Kastler axioms. Gupta-Bleuler electromagnetism is developed in detail as an example of a theory which satisfies the ``weak'' Haag-Kastler axioms but not the usual ones. This analysis is done by pure C*-algebraic means without employing any indefinite metric representations, and we obtain the same physical algebra and positive energy representation for it than by the usual means. The price for avoiding the indefinite metric, is the use of nonregular representations and complex valued test functions. We also exhibit the precise connection with the usual indefinite metric representation. We conclude the analysis by comparing the final physical algebra produced by a system of local constrainings with the one obtained from a single global constraining and also consider the issue of reduction by stages. For the usual spectral condition on the generators of the translation group, we also find a ``weak'' version, and show that the Gupta-Bleuler example satisfies it.Comment: 52 pages, Latex2e, to appear in Rev. Math. Phys. Corrected a mistake in Sect 5.2,- needed to include additional nonlocal elements in the field algebra which will be eliminated by the constraints. Added Theorem 5.16, proving that the local physical algebras are simple. Added Subsect. 5.6, making explicit the connections between the indefinite metric representation of Gupta-Bleuler electromagnetism, and the C*-algebraic version of it constructed here. Added reference