The container methods are powerful tools to bound the number of independent sets of graphs and hypergraphs, and they have been extremely inuential in the area of extremal and probabilistic combinatorics. We will focus on more specialized graph container methods due to Sapozhenko (1987) that deal with sets in expander graphs. Entropy, first introduced by Shannon (1948) in the area of information theory, is a measure of the expected amount of information contained in a random variable. Entropy has seen lots of fascinating applications in a wide range of enumeration problems. In this survey article, we will discuss recent developments that exploit a combination of the two methods on enumerating graph homomorphisms.

This chapter examines the people who lived in the countryside and how they might have experienced their everyday lives. Using archaeological, textual and iconographic evidence, it explores the examples of a shepherd boy, a female villa supervisor and a small landowner through a creative nonfiction approach.

Recent years brought their share of losses, among them the loss of close musician friends, including composers David Macbride and Stephen Siegel, my dear friends Maxine Neuman and Reinhard Humburg, my close childhood companion, Jay Hamburger. These losses have struck home in an entirely different way than the deaths from an earlier time, and they have magnified my sense of gratitude for having been allowed to live this long, and until recently with only minor health problems.

My migraines vanished as mysteriously as they had begun. Up until recently I escaped serious health issues, apart from two sobering reminders of life's finitude that had an impact on musical work: moderate hearing loss, limiting perception of upper frequencies and requiring hearing aids; and surgery on my left hand, contracting it, diminishing its mobility, and making it impossible to play many of the pieces that I used to navigate easily.

I have never tired of teaching composition, and I remain eager to see the students’ work in progress, amazed by their inventiveness and imagination. I try to observe the Hippocratic Oath and “do no harm”; sometimes I can be helpful. I flatter myself that I may have absorbed some aspects of my father's editing skills.

I particularly enjoy exploring with students the old forms that Norwood taught us about, and I regularly offer a course with the electronic music faculty in composing music for acoustic instruments with electronics, despite having never worked this way myself.

Throughout this study I have argued that, for Scottish writers creatively recollecting the Wars of Independence, the past is crucial in shaping responses to the present situation; that is, rather than these historiographical and literary works being concerned solely with detailing the wars as historical record they recollect the past precisely to affect the present and the future. For example, in Chapter 4 I argued that Hary's Wallace creatively reimagines English violence as moments of punctual trauma, revealing a vehement conviction of the dangers posed to Scottish sovereignty and identity by rapprochement with the English. Hary's assessment provides one way of reading, but it is misleading. James III's policies, and his overall approach to governance, were met with opposition that resulted in open rebellion and his death at Sauchieburn in 1488; nevertheless, Alasdair MacDonald tempers the view that he alienated all of his nobility to note that James ‘retained the loyalty of important intellectuals and counsellors, such as John Ireland and William Elphinstone’. MacDonald points out that James III's reputation inevitably suffered because he ‘had the ironic misfortune to be the father of a son whose reign is generally … upheld as marking the Golden Age of late medieval Scotland’.

Why, in spite of much research, are psychiatrists unable to predict or prevent suicide?

This chapter examines Paul Cullen’s growing mastery of the Roman curia, first through his navigation of the attempt by Archbishop John MacHale to secure papal condemnation of the Irish system of national education, and then through his role as a consultor at the Congregation of the Index.

Hollywood’s overseas expansion during the 1920s–1930s resulted from interwoven economic, political, and industrial changes. Although European agents rented Hollywood movies prior to 1914, World War I destroyed European film industry infrastructures, thus allowing American companies to flood markets with their products. Simultaneously, US domestic growth resulted in vertically integrated companies whose international revenues facilitated greater quality and quantity of production. This achievement fostered by Jewish immigrant studio moguls repackaged the very utopian promise that had brought them to the United States. They accomplished what the US government could not – global advertisement for an American way of life and consumerism. Even though some nations attempted building robust film industries, boycotting American theatres and products, or legislating restrictions, the rise of Nazism and World War II prevented effective national cinemas. Hollywood’s global ascendancy is not simply about American domination but about how a national cinema became a global one.

Classical mythology, Hellenistic odeporic and teratological literature, and medieval Christian bestiaries all teemed with human-animal hybrids. This paper will focus on two such therianthropic beings, the (hippo) centaurs, half-human and half-equine, and the onocentaurs, half-human and half-asinine, as described in the Liber monstrorum de diversis generibus (henceforth LM), a teratological compendium from early eighth-century England. While the origin of centaurs and onocentaurs can be traced to times and places very distant from pre-Conquest England, they form two perfect case studies of a distinct category of monsters, namely those creatures whose monstrosity originates from a degradation of humanity or from the aberrant conjunction of the human and the bestial, which seems to have especially resonated with early English sensibility. The porosity of the boundaries between the human and the monstrous is precisely one of the most distinctive, if disturbing, traits of the LM, as well as of texts which have been closely associated with it, such as Beowulf

or Aldhelm's Aenigmata. While the immediate sources of the two LM entries on (hippo) centaurs and onocentaurs have been identified as Jerome's Vita S. Pauli eremitae and Isidore of Seville's Etymologiae, XI.iii.39, respectively, they in fact rely on a blend of ultimate sources. These multiple layers of sources will be explored and disentangled by also looking at Aldhelm, who has long been attributed with the authorship of the LM and dealt himself with hybrid monsters, such as the Minotaur and the centaur.

This premiere took place on 30 December 1846 with Paul Barroilhet as Robert and Rosine Stoltz as Marie. The plot was concocted by two librettists, the Belgian Gustave Vaez (1812–62) and the Frenchman Alphonse Royer (1803–75).

The situation at the Opéra is extremely serious. I shan't deal with the question of money, about which I’m ignorant and which anyway I’m not competent to write about; as I understand it, it's a question over which the government has the right to intervene, rather than any individual. Instead, I’ll concentrate on the musical resources still available to this unfortunate theatre, and on the influence of the disastrous condition to which it finds itself reduced upon the state of the art throughout France, to the astonishment of those who visit our country. This ruin of an institution which was, and maybe still is, so beautiful, so much loved by our country in every way – for which it makes so many sacrifices each year, and which it's in the habit of regarding as the focal point of its pretentions to artistic splendour –this ruin is due to causes we can't help wondering about, the reality of which continues to strike everyone who can see clearly and is without prejudice.

Having failed to acquire a new work from any of the major composers of Germany, Italy or France, the Opéra has found itself constrained to beg Rossini to do them the insulting favour of rummaging around in his paperwork to extract from it fragments of old scores made popular throughout Europe by the best Italian singers – admirable fragments, no doubt, but which, put together more or less competently by someone else, could not by any means, at any time or in any country however barbarous, constitute a true, serious work of art or, whatever the posters might tell us, justify the title of ‘a new opera’.

The Encyclopaedia of Music in Ireland represents the first comprehensive survey of Irish musical experience across recorded history, although its principal span extends from the early Middle Ages to the present day. EMIR (to use the abbreviation by which it is now known) addresses several distinct areas of musical practice, including traditional music, art music, church music, popular music and the music trade (printing and publishing; instrument manufacture), as well as the relationship between music, literature and political culture in Ireland. It also documents Irish musical practice elsewhere, notably in North America (the United States and Canada) and the United Kingdom.

Perhaps the most important aspect of EMIR from the general perspective of musical lexicography is its attempt to broaden the base of musical practice as this is conceived in older works of musical reference. In particular, EMIR reflects a sequence of editorial principles sufficiently pliant to address the topography of Irish musical practice, in which there has long been a pronounced tension between the claims of the composer and the musical work on one side, and the claims of oral and popular culture on the other. Although EMIR represents the apparatus of Irish art music (as in biographical and critical entries on composers, complete with worklists, sources and bibliographies), it also engages closely with the transmission and dissemination of traditional and popular music. But however comprehensive its address, EMIR implicitly draws attention to the fundamental challenge of musical lexicography (in Ireland as well as elsewhere), which is to reconcile an apparently insatiable quest for information with the imperative of critical and historical interpretation.

The Five Axes

In the poetry of many cultures, there is an enduring image: of a shore that recedes even as you move towards it. If transformative constitutionalism's metaphor of the bridge expresses confidence that the chasm between the past and the future will be bridged, then the language of poetry warns us about the ‘essential cruelty of hope’. Transformative constitutionalism may be a bridge, but a bridge to a horizon that is always receding.

The chapters in this book trace the journey of transformative constitutionalism under Kenya's 2010 Constitution, between the bridge and the horizon. These chapters – each dedicated to a constitutional dispute that was brought before the Kenyan courts between 2010 and 2025 – correspond to five axes of transformation.

The first axis is that of constraining the executive and empowering the People. This was at issue in the BBI Case, where an executive-driven attempt to make large-scale changes to the 2010 Constitution was rebuffed by the courts. The ball was set rolling by the High Court, which reached into history to hold that sweeping constitutional change could not be done without a correspondingly deep participation of the People. In doing so, the High Court offered to the world a new – and distinctively Kenyan – articulation of the famous basic structure doctrine. While the Supreme Court disagreed with the High Court on the applicability of the doctrine to the Kenyan context, its own interpretation of the Constitution affirmed – in substance – the document's commitment to public participation in constitutional change.

On January 11, 1896, Johannes Brahms spent several memorable hours in the company of Adolph Menzel, the dean of German artists in the second half of the nineteenth century. Menzel had recently marked his eightieth birthday, and Brahms, who enjoyed a warm friendship with the artist in his autumn years, had come to join him in a belated private celebration at his Berlin atelier. After ascending four flights of stairs, the composer was greeted by his host in the corridor and escorted into the studio. Upon entering he would have immediately caught sight of the large unfinished oil painting “Frederick the Great Addressing His Generals before the Battle of Leuthen” (1859–61), which was prominently displayed on one of the studio walls. The two men soon sat down to a deluxe meal of oysters served with fine wine. The drinking was heavy, the examination of the artist's work so engrossing, that Brahms lost all track of time and barely made it to a dinner that had been arranged in his honor by the Prussian Academy of Arts. Max Kalbeck, the author of the first substantial biography of the composer, described the visit in characteristically flowery prose:

The tiny hoary [Menzel], in whom a sorcerous necromancer was hiding, had held [Brahms] spellbound. One glass after another was emptied as libation for the spirits that emerged from the books and folders all around and took on flesh and blood when the conjurer, to the boundless astonishment of his guest, called them all by name.