Named after Scottish neurologist, anatomist, and anatomical artist Sir Charles Bell following his description of the syndrome in 1821, Bell’s palsy is an idiopathic peripheral facial nerve palsy (CN7) producing weakness of the unilateral upper and lower face. Though by definition, Bell’s palsy is idiopathic, recent studies have proposed various viral etiologies such as the herpes simplex virus, Epstein–Barr virus, and varicella-zoster virus. In a minority of cases, the infectious causes are obvious such as in Ramsay–Hunt syndrome and Lyme disease.

Though sarcoidosis commonly involves the nervous system subclinically (~50% found postmortem), clinically evident neurological disease is only present in ~10% of patients with sarcoidosis. Once sarcoidosis involves the nervous system, the so-called neurosarcoidosis can involve any part of the neuroaxis and produce a spectrum of clinical manifestations including cranial neuropathies, intra- and extra-axial granulomatous disease, meningeal disease, and cerebral white matter disease.

While many exact and approximation algorithms work with a linear programming formulation (often a relaxation), the dual LP often plays a key role in the algorithms and their analysis. In this chapter, we analyze the structure of optimum dual solutions for the classical LP relaxations of the TSP, but also for T-joins, and deduce properties like laminarity.

By an efficient uncrossing algorithm and by analyzing extreme point solutions, we obtain optimum primal and dual solutions with linear-size support. Since the primal constraints and dual variables correspond to cuts, enumerating all cuts with a small value is a useful tool in several algorithms.

Russia is one of the main oil and gas producers and one of the biggest emitters of carbon dioxide globally. Its energy policies are still underpinned by the necessity of establishing ‘spheres of influence’ and are not on track to achieve the objectives of the United Nations Framework Convention on Climate Change (UNFCCC) and the Paris Agreement. Politically, war in Ukraine is arguably a consequence of this approach and discloses for the European Union (EU) the possibility of a diversification of its energy sources to achieve security of supply, which unlocks the opportunity of accelerating the green transition envisaged in the European Green Deal. Legally, given that they are not at war with Russia, the EU and its Member States could invoke the energy supply crisis and the political misalignment between the Russian energy policy and the Green Deal, rather than war per se, as a justification to abandon consolidated long-term energy contracts and accelerate the green transition.

Ménière disease (MD) is a relatively rare disorder of the inner ear classically producing the triad of hearing loss, vertigo, and either tinnitus or a sense of ear fullness with most common onset between 50 and 70 years of age and slight female predominance. Also known as idiopathic endolymphatic hydrops, MD is named after French physician Prosper Ménière after his linking of the condition to the inner ear in 1861. Though the exact pathophysiology remains unclear, MD appears to either be caused by or associated with endolymphatic accumulation in organs of the inner ear, namely, the cochlea, semicircular canals, ampulla, and saccule. Dysfunction is thought to be due to the compensatory dilation of the endolymphatic spaces and caused by unequal endolymph secretion and reabsorption.

This chapter explores how identities were forged and developed under the Merovingians, from the creative fiction of ‘Frankishness’ to more personal identities defined by gender and social status. It examines how identities can appear different through stories, laws, dress, and language, highlighting the importance of how people defined and presented themselves according to need and circumstance. It takes seriously the contention that identity formation fed into discourses of power because they structured hierarchies and issues of inclusion and exclusion.

Ataxia-telangiectasia (AT), also called Louis-Bar syndrome, is the most common inherited childhood progressive ataxia in most countries, most often seen during infancy, in ages 1–3. Inherited in an autosomal recessive pattern, AT is caused by mutation of the ATM gene, located on chromosome 11q22–23.

An, Kleinberg, and Shmoys were the first to beat Christofides’ algorithm for Path TSP. Their algorithm, which they called Best-of-Many Christofides, is very natural: Since an LP solution can be written as convex combination of spanning trees, we can do parity correction on each of these trees and output the best of the resulting tours. It turns out that this yields a better guarantee than the 5/3 that Christofides’ algorithm yields.

In this chapter, we analyze this algorithm and study various follow-up works that have yielded better and better approximation ratios; some of them also apply to general T-tours. This includes a structured decomposition into spanning trees (by Gottschalk and Vygen), Best-of-Many Christofides with lonely edge deletion (by Sebő and van Zuylen), and Traub’s T-tour algorithm.

The theme of how life and its environment have coevolved together for about four billion years on Earth is explored in this chapter. The major evolutionary events that unfolded in the Archean eon (4 to 2.5 billion years ago), Proterozoic eon (2.5 to 0.539 billion years ago), and the Phanerozoic eon (0.539 billion years ago to present) are outlined, such as the origin(s) of multicellularity, eukaryotes, complex multicellular organisms, and humans. By drawing on this evolutionary timeline, theoretical paradigms for understanding and grouping the notable evolutionary events are sketched (e.g., major transitions in evolution). The next part of the chapter illustrates the intricate interplay between life and its environment by chronicling the rise in molecular oxygen levels, its possible causes and profound consequences, and its potential connections with key geological changes like the putative Snowball Earth episodes. Lastly, the ‘Big Five’ mass extinctions that transpired in the Phanerozoic, along with their triggers and ramifications, are described.

Geschwind syndrome (GS) was first described in 1975 by American neurologists Norman Geschwind and Stephen Waxman as a behavioral syndrome consisting of hyper-religiosity, hyposexuality, hypergraphia, and irritability. Though GS has classically been described in patients with temporal lobe epilepsy, it has also been reported in cases of frontotemporal dementia, temporal strokes, and hippocampal atrophy. Interestingly, most cases are associated with a nondominant lobe pathology.

Dioecious, more rarely monoecious, evergreen shrubs or small to large trees of very varying individual form, with leaves spreading when young, but adult individuals often with predominantly acicular or cupressoid foliage persisting for many years. The seed-bearing organs are multi-scaled cones whose cone scales become concrescent and fleshy at maturity. Shoots and fruits have a characteristic, often slightly pungent resinous, terpenoid or aromatic smell.

Chronic inflammatory demyelinating polyradiculoneuropathy (CIDP) is a slow, progressive, sensorimotor disease thought to have both a cell-mediated and humoral immune pathogenesis.

First described in 1888 by neurologists Schafer and Brown, and later in 1939 by German American experimental psychologist Heinrick Kluver and American neurosurgeon Paul Clancy Bucy, now named Kluver–Bucy syndrome (KBS), this condition was first described after bilateral temporal lobectomy in monkeys. It was later described in humans in 1955 in the case of a 19-year-old male with epilepsy, again requiring treatment with bilateral temporal lobectomy.