Particle algorithms for optimization on binary spaces

We discuss a unified approach to stochastic optimization of pseudo-Boolean objective functions based on particle methods, including the cross-entropy method and simulated annealing as special cases. We point out the need for auxiliary sampling distributions, that is parametric families on binary spaces, which are able to reproduce complex dependency structures, and illustrate their usefulness in our numerical experiments. We provide numerical evidence that particle-driven optimization algorithms based on parametric families yield superior results on strongly multi-modal optimization problems while local search heuristics outperform them on easier problems

Matter in Plotinus's Normative Ontology.

To most interpreters, the case seems to be clear: Plotinus identifies matter and evil, as he bluntly states in Enn. I.8[51] that ‘last matter’ is ‘evil’, and even ‘evil itself’. In this paper, I challenge this view: how and why should Plotinus have thought of matter, the sense-making έσχατον of his derivational ontology from the One and Good, evil? A rational reconstruction of Plotinus’s tenets should neither accept the paradox that evil comes from Good, nor shirk the arduous task of interpreting Plotinus’s texts on evil as a fitting part of his philosophy on the whole. Therefore, I suggest a reading of evil in Plotinus as the outcome of an incongruent interaction of matter and soul, maintaining simultaneously that neither soul nor matter are to be considered as bad or evil. When Plotinus calls matter evil, he does so metonymically denoting matter’s totally passive potentiality as perceived by the toiling soul trying to act upon it as a form-bringer. As so often, Plotinus is speaking quoad nos here rather than referring to ‘matter per se’ (for Plotinus, somewhat of an oxymoron) which, as mere potentiality (and nothing else) is not nor can be evil. In short: matter is no more evil than the melancholy evening sky is melancholy – not in itself (for it isn’t), but as to its impression on us who contemplate it. As I buttress this view, it will also become clear that matter cannot tritely be considered to be the αυτό κακόν as a prima facie-reading of Enn. I.8[51] might powerfully suggest, but that the αυτό κακόν, far from being a principle of its own, has to be interpreted within the dynamics of Plotinus’s philosophical thinking as a unique, though numerously applicable flaw-pattern for all the single kakã (hence the Platonic αύτό). To conclude, I shall offer a short outlook on the consistency of this interpretation with Plotinus’s teaching on the soul and with the further Neoplatonic development of the doctrine of evil

Fungicidal activity plus reservoir effect allow short treatment courses with terbinafine in tinea pedis

Terbinafine, a synthetic allylamine, exerts fungicidal activity against dermatophytes, the causative pathogens of tinea pedis. As proven in numerous clinical trials, tinea pedis can be effectively and safely treated by topical terbinafine. In fact, a 1-week application of terbinafine 1% cream eradicated fungal pathogens at least as effectively as 4-week treatment courses with topical azole derivative antifungals and showed lower relapse rates. A new innovative single-application formulation of terbinafine 1% in a film-forming solution produces a high concentration gradient on the skin surface and enables a prolonged (up to 13 days) exposure of the skin to terbinafine. High drug penetration into the skin results in an otherwise not obtained drug reservoir in the horny layer, the location of dermatophytes in tinea pedis. Although azole antimycotics can also effectively penetrate into the horny layer of the skin, short-term therapy might not be feasible due to its primarily fungistatic activity against dermatophytes. Thus, we conclude that the high efficacy of short-term treatment with terbinafine in patients with tinea pedis is possible due to its fungicidal activity coupled with a distinct reservoir formation in the upper layers of the epidermis. Copyright (C) 2008 S. Karger AG, Basel

Parametric families on large binary spaces

In the context of adaptive Monte Carlo algorithms, we cannot directly generate independent samples from the distribution of interest but use a proxy which we need to be close to the target. Generally, such a proxy distribution is a parametric family on the sampling spaces of the target distribution. For continuous sampling problems in high dimensions, we often use the multivariate normal distribution as a proxy for we can easily parametrise it by its moments and quickly sample from it. Our objective is to construct similarly flexible parametric families on binary sampling spaces too large for exhaustive enumeration. The binary sampling problem is more difficult than its continuous counterpart since the choice of a suitable proxy distribution is not obvious