Linking Parametric CAD with Adjoint Surface Sensitivities

The goal of this work is to present an efficient CAD-based adjoint process chain for calculating parametric sensitivities (derivatives of the objective function with respect to the CAD parameters) in timescales acceptable for industrial design processes. The idea is based on linking parametric design velocities (geometric sensitivities computed from the CAD model) with adjoint surface sensitivities. A CAD-based design velocity computation method has been implemented based on distances between discrete representations of perturbed geometries. This approach differs from other methods due to the fact that it works with existing commercial CAD packages (unlike most analytical approaches) and it can cope with the changes in CAD model topology and face labeling. Use of the proposed method allows computation of parametric sensitivities using adjoint data at a computational cost which scales with the number of objective functions being considered, while it is essentially independent of the number of design variables. The gradient computation is demonstrated on test cases for a Nozzle Guide Vane (NGV) model and a Turbine Rotor Blade model. The results are validated against finite difference values and good agreement is shown. This gradient information can be passed to an optimization algorithm, which will use it to update the CAD model parameters.

Three dimensional Sklyanin algebras and Gröbner bases

We consider Sklyanin algebras $S$ with 3 generators, which are quadratic algebras over a field $\K$ with $3$ generators $x,y,z$ given by $3$ relations $pxy+qyx+rzz=0$, $pyz+qzy+rxx=0$ and $pzx+qxz+ryy=0$, where $p,q,r\in\K$. this class of algebras has enjoyed much attention. In particular, using tools from algebraic geometry, Feigin, Odesskii \cite{odf}, and Artin, Tate and Van Den Bergh, showed that if at least two of the parameters $p$, $q$ and $r$ are non-zero and at least two of three numbers $p^3$, $q^3$ and $r^3$ are distinct, then $S$ is Artin--Schelter regular. More specifically, $S$ is Koszul and has the same Hilbert series as the algebra of commutative polynomials in 3 indeterminates (PHS). It has became commonly accepted that it is impossible to achieve the same objective by purely algebraic and combinatorial means like the Groebner basis technique. The main purpose of this paper is to trace the combinatorial meaning of the properties of Sklyanin algebras, such as Koszulity, PBW, PHS, Calabi-Yau, and to give a new constructive proof of the above facts due to Artin, Tate and Van Den Bergh. Further, we study a wider class of Sklyanin algebras, namely
the situation when all parameters of relations could be different. We call them generalized Sklyanin algebras. We classify up to isomorphism all generalized Sklyanin algebras with the same Hilbert series as commutative polynomials on
3 variables. We show that generalized Sklyanin algebras in general position have a Golod–Shafarevich Hilbert series (with exception of the case of field with two elements).

Calcium-rich gap transients: Tidal detonations of white dwarfs?

We hypothesize that at least some of the recently discovered class of calcium-rich gap transients are tidal detonation events of white dwarfs (WDs) by black holes (BHs) or possibly neutron stars. We show that the properties of the calcium-rich gap transients agree well with the predictions of the tidal detonation model. Under the predictions of this model, we use a follow-up X-ray observation of one of these transients, SN 2012hn, to place weak upper limits on the detonator mass of this system that include all intermediate-mass BHs (IMBHs). As these transients are preferentially in the stellar haloes of galaxies, we discuss the possibility that these transients are tidal detonations of WDs caused by random flyby encounters with IMBHs in dwarf galaxies or globular clusters. This possibility has been already suggested in the literature but without connection to the calcium-rich gap transients. In order for the random flyby cross-section to be high enough, these events would have to be occurring inside these dense stellar associations. However, there is a lack of evidence for IMBHs in these systems, and recent observations have ruled out all but the very faintest dwarf galaxies and globular clusters for a few of these transients. Another possibility is that these are tidal detonations caused by three-body interactions, where a WD is perturbed towards the detonator in isolated multiple star systems. We highlight a number of ways this could occur, even in lower mass systems with stellar-mass BHs or neutron stars. Finally, we outline several new observational tests of this scenario, which are feasible with current instrumentation.

Metabolic signatures of Huntington's disease (HD): 1H NMR analysis of the polar metabolome in post mortem human brain

Huntington’s disease (HD) is an autosomal neurodegenerative disorder affecting approximately 5-10 persons per 100,000 worldwide. The pathophysiology of HD is not fully understood but the age of onset is known to be highly dependent on the number of CAG triplet repeats in the huntingtin gene. Using 1H NMR spectroscopy this study biochemically profiled 39 brain metabolites in post-mortem striatum (n=14) and frontal lobe (n=14) from HD sufferers and controls (n=28). Striatum metabolites were more perturbed with 15 significantly affected in HD cases, compared with only 4 in frontal lobe (P<0.05; q<0.3). The metabolite which changed most overall was urea which decreased 3.25-fold in striatum (P<0.01). Four metabolites were consistently affected in both brain regions. These included the neurotransmitter precursors tyrosine and L-phenylalanine which were significantly depleted by 1.55-1.58-fold and 1.48-1.54-fold in striatum and frontal lobe, respectively (P=0.02-0.03). They also included L-leucine which was reduced 1.54-1.69-fold (P=0.04-0.09) and myo-inositol which was increased 1.26-1.37-fold (P<0.01). Logistic regression analyses performed with MetaboAnalyst demonstrated that data obtained from striatum produced models which were profoundly more sensitive and specific than those produced from frontal lobe. The brain metabolite changes uncovered in this first 1H NMR investigation of human HD offer new insights into the disease pathophysiology. Further investigations of striatal metabolite disturbances are clearly warranted.