As we know, quaternions are very efficient for representing rotations with clear geometric meaning (rotation axis and angle) and only one redundancy. Unfortunately, they do not handle translations, which meanwhile can be made multiplicative along with rotations via the use of homogeneous coordinates. Despite also being 4-tuples, homogeneous coordinates are algebraically incompatible with quater...

All pharmaceutical companies are required to assess pharmacokinetic drug-drug interactions (DDIs) of new chemical entities (NCEs) and mathematical prediction helps to select the best NCE candidate with regard to adverse effects resulting from a DDI before any costly clinical studies. Most current models assume that the liver is a homogeneous organ where the majority of the metabolism occurs. Ho...

With around five million people accessing anti-retroviral treatment, which significantly reduces mortality and extends life, the HIV pandemic now exists in a context of treatment possibility, if not access. This paper discusses ways in which the pandemic is becoming naturalised through medicalisation, normalisation and marketisation, and how these processes undermine themselves internally. The ...

Given a complete nonsingular algebraic variety X and a divisor D with normal crossings, we say that X is log homogeneous with boundary D if the logarithmic tangent bundle TX(− log D) is generated by its global sections. Then the Albanese morphism α turns out to be a fibration with fibers being spherical (in particular, rational) varieties. It follows that all irreducible components of D are non...

We study pushdown systems where control states, stack alphabet, and transition relation, instead of being finite, are first-order definable in a fixed countably-infinite structure. We show that the reachability analysis can be addressed with the well-known saturation technique for the wide class of oligomorphic structures. Moreover, for the more restrictive homogeneous structures, we are able t...

Given a complete nonsingular algebraic variety X and a divisor D with normal crossings, we say that X is log homogeneous with boundary D if the logarithmic tangent bundle T X (− log D) is generated by its global sections. We then show that the Albanese morphism α is a fibration with fibers being spherical (in particular, rational) varieties. It follows that all irreducible components of D are n...

Using the conformally invariant Cotton tensor, we define a geometric flow, the Cotton flow, which is exclusive to three dimensions. This flow tends to evolve the initial metrics into conformally flat ones, and is somewhat orthogonal to the Yamabe flow, the latter being a flow within a conformal class. We define an entropy functional, and study the flow of nine homogeneous spaces both numericall...

The work of Krämer, Luna, Vust, Brion and others [Krä,LV,BLV,BP] established the importance of a very distinguished class of homogeneous varieties G/H, those which are now called spherical. Such varieties are homogeneous for a connected reductive group G and are characterized by many equivalent properties, the most important being (see [BLV]): — Any Borel subgroup B of G has an open orbit in G/...

An adaptive target detector in radar system is used to extract targets from background in noisy environment of unknown statistics. The constant false alarm rate (CFAR) is well known detection algorithm that is being used in almost every modern radar. The cell averaging CFAR is the optimum detector in homogeneous clutter environment when the refence cells have identically independent and exponen...

This work considers small-time local controllability (STLC) of single and multiple-input systems, ẋ = f◦(x) + ∑m i=1 fiu i where f◦(x) contains homogeneous polynomials and f1, . . . , fm are constant vector fields. For single-input systems, it is shown that even-degree homogeneity precludes STLC if the state dimension is larger than one. This, along with the obvious result that for odd-degree h...