This systematic review summarizes the existing data on headache and pregnancy with a scope on clinical headache phenotypes, treatment of headaches in pregnancy and effects of headache medications on the child during pregnancy and breastfeeding, headache related complications, and diagnostics of headache in pregnancy. Headache during pregnancy can be both primary and secondary, and in the last case can be a symptom of a life-threatening condition. The most common secondary headaches are stroke, cerebral venous thrombosis, subarachnoid hemorrhage, pituitary tumor, choriocarcinoma, eclampsia, preeclampsia, idiopathic intracranial hypertension, and reversible cerebral vasoconstriction syndrome. Migraine is a risk factor for pregnancy complications, particularly vascular events. Data regarding other primary headache conditions are still scarce. Early diagnostics of the disease manifested by headache is important for mother and fetus life. It is especially important to identify “red flag symptoms” suggesting that headache is a symptom of a serious disease. In order to exclude a secondary headache additional studies can be necessary: electroencephalography, ultrasound of the vessels of the head and neck, brain MRI and MR angiography with contrast ophthalmoscopy and lumbar puncture. During pregnancy and breastfeeding the preferred therapeutic strategy for the treatment of primary headaches should always be a non-pharmacological one. Treatment should not be postponed as an undermanaged headache can lead to stress, sleep deprivation, depression and poor nutritional intake that in turn can have negative consequences for both mother and baby. Therefore, if non-pharmacological interventions seem inadequate, a well-considered choice should be made concerning the use of medication, taking into account all the benefits and possible risks.

BackgroundThe three primary headaches, tension-type headache, migraine and cluster headache, occur in both genders, but all seem to have a sex-specific prevalence. These gender differences suggest that both male and female sex hormones could have an influence on the course of primary headaches. This review aims to summarise the most relevant and recent literature on this topic.MethodsTwo independent reviewers searched PUBMED in a systematic manner. Search strings were composed using the terms LH, FSH, progesteron*, estrogen*, DHEA*, prolactin, testosterone, androgen*, headach*, migrain*, “tension type” or cluster. A timeframe was set limiting the search to articles published in the last 20 years, after January 1st 1997.ResultsMigraine tends to follow a classic temporal pattern throughout a woman’s life corresponding to the fluctuation of estrogen in the different reproductive stages. The estrogen withdrawal hypothesis forms the basis for most of the assumptions made on this behalf. The role of other hormones as well as the importance of sex hormones in other primary headaches is far less studied.ConclusionThe available literature mainly covers the role of sex hormones in migraine in women. Detailed studies especially in the elderly of both sexes and in cluster headache and tension-type headache are warranted to fully elucidate the role of these hormones in all primary headaches.

We consider Lie(G)-valued G-invariant connections on bundles over spaces G/H, R×G/H and R 2 ×G/H, where G/H is a compact nearly Kähler six-dimensional homogeneous space, and the manifolds R×G/H and R 2 ×G/H carry G 2 -and Spin(7)-structures, respectively. By making a G-invariant ansatz, Yang-Mills theory with torsion on R×G/H is reduced to Newtonian mechanics of a particle moving in a plane with a quartic potential. For particular values of the torsion, we find explicit particle trajectories, which obey first-order gradient or hamiltonian flow equations. In two cases, these solutions correspond to anti-self-dual instantons associated with one of two G 2 -structures on R×G/H. It is shown that both G 2 -instanton equations can be obtained from a single Spin(7)-instanton equation on R 2 ×G/H.

We consider LieG-valued Yang-Mills fields on the space R×G/H, where G/H is a compact nearly Kähler six-dimensional homogeneous space, and the manifold R×G/H carries a G 2 -structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on R×G/H is reduced to Newtonian mechanics of a particle moving in R 6 , R 4 or R 2 under the influence of an inverted double-well-type potential for the cases G/H = SU(3)/U(1)×U(1), Sp(2)/Sp(1)×U (1) or G 2 /SU (3), respectively. We analyze all critical points and present analytical and numerical kink-and bounce-type solutions, which yield G-invariant instanton configurations on those cosets. Periodic solutions on S 1 ×G/H and dyons on iR×G/H are also given.

We consider the Yang-Mills flow equations on a reductive coset space G/H and the Yang-Mills equations on the manifold R×G/H. On nonsymmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang-Mills equations to φ 4 -kink equations on R. Depending on the boundary conditions and torsion, we obtain solutions to the Yang-Mills equations describing instantons, chains of instanton-anti-instanton pairs or modifications of gauge bundles. For Lorentzian signature on R × G/H, dyon-type configurations are constructed as well. We also present explicit solutions to the Yang-Mills flow equations and compare them with the Yang-Mills solutions on R × G/H.

There exists a recursive algorithm for constructing BPST-type multi-instantons on commutative R 4 . When deformed noncommutatively, however, it becomes difficult to write down nonsingular instanton configurations with topological charge greater than one in explicit form. We circumvent this difficulty by allowing for the translational instanton moduli to become noncommutative as well. Such a scenario is natural in the self-dual Yang-Mills hierarchy of integrable equations where the moduli of solutions are seen as extended space-time coordinates associated with higher flows. By judicious adjustment of the moduli-noncommutativity we achieve the ADHM construction of generalized 't Hooft multi-instanton solutions with everywhere self-dual field strengths on noncommutative R 4 .

We consider cones over manifolds admitting real Killing spinors and instanton equations on connections on vector bundles over these manifolds. Such cones are manifolds with special (reduced) holonomy. We generalize the scalar ansatz for a connection proposed by Harland and Nölle [D. Harland and C. Nölle, J. High Energy Phys. 03 (2012) 082.] in such a way that instantons are parametrized by constrained matrixvalued functions. Our ansatz reduces instanton equations to matrix model equations which can be further reduced to Newtonian mechanics with particle trajectories obeying first-order gradient flow equations. Generalizations to Kähler-Einstein manifolds and resolved Calabi-Yau cones are briefly discussed. Our construction allows one to associate quiver gauge theories with special holonomy manifolds via dimensional reduction. 1 A Killing spinor on a Riemannian manifold N is a spinor field which satisfies r L ¼ iL Á for all tangent vectors L, where r is the spinor covariant derivative, Á is Clifford multiplication, and is a constant. If ¼ 0 then the spinor is called parallel, and N is a manifold with special (reduced) holonomy.

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