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In this paper we consider two natural notions of connectivity for hypergraphs: weak and strong. We prove that the strong vertex connectivity of a connected hypergraph is bounded by its weak edge connectivity, thereby extending a theorem of Whitney from graphs to hypergraphs. We find that, while determining a minimum weak vertex cut can be done in polynomial time and is equivalent to finding a minimum vertex cut in the 2-section of the hypergraph in question, determining a minimum strong vertex cut is NP-hard for general hypergraphs. Moreover, the problem of finding minimum strong vertex cuts remains NP-hard when restricted to hypergraphs with maximum edge size at most 3. We also discuss the relationship between strong vertex connectivity and the minimum transversal problem for hypergraphs, showing that there are classes of hypergraphs for which one of the problems is NP-hard, while the other can be solved in polynomial time.
Transient Ischaemic Attack (TIA) is a neurologic event with symptom resolution within 24 hours. Early specialist assessment of TIA reduces risk of stroke and death. National United Kingdom (UK) guidelines recommend patients with TIA are seen in specialist clinics within 24 hours (high risk) or seven days (low risk).
We aimed to develop a complex intervention for patients with low risk TIA presenting to the emergency ambulance service. The intervention is being tested in the TIER feasibility trial, in line with Medical Research Council (MRC) guidance on staged development and evaluation of complex interventions.
We conducted three interrelated activities to produce the TIER intervention:
•Survey of UK Ambulance Services (n = 13) to gather information about TIA pathways already in use
•Scoping review of literature describing prehospital care of patients with TIA
•Synthesis of data and definition of intervention by specialist panel of: paramedics; Emergency Department (ED) and stroke consultants; service users; ambulance service managers.
The panel used results to define the TIER intervention, to include:
1.Protocol for paramedics to assess patients presenting with TIA and identify and refer low risk patients for prompt (< 7day) specialist review at TIA clinic
2.Patient Group Directive and information pack to allow paramedic administration of aspirin to patients left at home with referral to TIA clinic
3.Referral process via ambulance control room
4.Training package for paramedics
5.Agreement with TIA clinic service provider including rapid review of referred patients
We followed MRC guidance to develop a clinical intervention for assessment and referral of low risk TIA patients attended by emergency ambulance paramedic. We are testing feasibility of implementing and evaluating this intervention in the TIER feasibility trial which may lead to fully powered multicentre randomized controlled trial (RCT) if predefined progression criteria are met.
The long-term outcome of persons with impaired consciousness after brain injury remains relatively unclear. The first 12 months post ictus are widely reported as the period of greatest change, with an estimated 20% of persons with traumatic brain injury recovering consciousness. However, beyond 12 months post traumatic and 6 months post-nontraumatic injury the chances of further recovery are thought to diminish significantly. The aim of this study was to investigate the behavioural and psychosocial outcome of 12 patients with impaired consciousness 2 years post ictus. At the time of recruitment five of these patients met the diagnostic criteria defining the vegetative state and seven of these patients met the diagnostic criteria defining the minimally conscious state. Patients were assessed using the Wessex Head Injury Matrix at recruitment and again at least 2 years after initial contact. Functional and psychosocial outcome were also explored. Most patients showed some improvements to their behavioural portfolio, but all were still very dependent physically and all required a high level of support in their activities of daily living. None of the patients had emerged from their original condition, despite exhibiting larger behavioural portfolios. The implications of these findings for the management of patients in low awareness states are discussed.
When deciding how to give away property the owner of assets has a choice between outright gift or a gift in trust. Stripped to its essence the private trust, to reiterate a point made earlier, is a gift projected on the plane of time. However, the limited functional similarity of these two forms of gift, the absolute gift and the gift in trust, must not disguise the fact that they are conceptually distinct.
Thus there are gifts, which are Legal, and, then again, there are trusts, which are Equitable. These are two distinct arrangements, not simply two types of benefaction, although it is not clear whether we treat them as distinct because we sharply distinguish wanting to make a gift to another, on the one hand, from wanting to make a trust for another, on the other hand, or because we pay attention to the historical distinction that gifts were creatures of Law, and trusts, creatures of Equity. But distinct they are, and so we think that there are separate requirements peculiar to each …
(M Pickard ‘The Goodness of Giving, The Justice of Gifts and Trusts’ (1983) 33 U Toronto LJ 381)
In practice also there will usually be no difficulty in distinguishing the two forms since trusts are commonly created in writing, usually by deed, wherein the donor designates another person or group of persons as trustee(s). But neither writing nor the appointment of others as trustees is essential.
With its unique contextual emphasis and authoritative commentary, Trusts Law: Text and Materials is a book that no serious undergraduate on trust law courses can afford to be without. The book is divided into four main parts: trusts and the preservation of family wealth; trusts and family breakdown; trusts and commerce; and trusts and non-profit activity. Within each of these parts, leading cases, statutes, and historical and research materials are placed alongside the narrative of the author's text to give emphasis both to general theories of trust concepts and to the practical operation of trusts. Attention is also given to important themes such as the developing relationship between trusts law and other areas of private law such as the Law of Restitution. This new edition takes account of all relevant judicial and legislative developments since the third edition, and expands discussion of key themes in current developments of the law.
This chapter is concerned with the role played by imputed trusts in resolving disputes over the ownership of family property. By ‘family property’, we mean property acquired by spouses or unmarried cohabiting partners during the course of their relationship, usually (but not always) for their joint use. The disputes with which we are concerned often arise between unmarried partners rather than spouses because, for reasons we shall explore, questions of ownership by married couples are dealt with in other ways. Also, because of the costs involved, these disputes are litigated only when there is property of significant value at stake; and for many couples, the most significant asset will be the owner-occupied family home. Hence, most disputes are over the parties' respective entitlements, on the breakdown of a non-marital cohabiting relationship, to the money value (ie sale proceeds minus any outstanding mortgage) of the family home. There may also be cases where issues of ownership arise in disputes between family members and a third party (such as a mortgage lender): here, the question of ownership is just as important for spouses as for unmarried couples.
The origins of the imputed trust (in the shape of the ‘resulting use’) can be traced back to the latter half of the fifteenth century (see Baker An Introduction to English Legal History (4th edn, 2002) p 251). This chapter, therefore, provides a further illustration of the theme, pursued elsewhere in this book, of the adaptability of ancient trust-forms to new functions.
Management is a convenient umbrella term under which cluster a diversity of trustee tasks. In the case of those trusts not confined simply to the holding and retaining of legal title to designated property, the task dominating all others is that of protecting and indeed enhancing the value of the trust fund through effective investment. But trustees cannot just behave as individuals might with their own funds to invest. The courts of equity, in refining the obligations of trusteeship, have imposed a range of duties upon trustees, some of which impinge directly on the management of the trust fund. In this chapter we therefore consider, in addition to the duty of investment, the duties to act impartially between beneficiaries and not to delegate the trust. There is a complex interaction between these three topics. For example, on the one hand the variety of investments available to trustees suggests a need for expert help, and the process of investment-reinvestment itself necessarily involves some delegation of functions to intermediaries such as real estate valuers, stockbrokers, bankers and solicitors. On the other hand, in principle trustees have until recently been required to reserve to themselves the exercise of their discretions over investment decisions, especially with regard to the duty of impartiality. This long-held principle of non-delegation of discretions seemed increasingly to be at odds with a changing economic and social environment.
One of the first decisions to be taken by a settlor or testator creating a trust concerns the selection of the trustees. Who should be appointed: the settlor himself or herself, a family friend, a professional person – probably an accountant or solicitor – or a corporate trustee such as a trust department or trust subsidiary of a bank, or indeed some combination of these? The decision is of the greatest importance. Not only may the trustees be empowered to decide beneficial entitlement but also they will be responsible for trust administration including preserving the value of the trust fund through effective investment. Decisions about whom to appoint assume the existence of people or organisations willing to serve as trustees. After all, people cannot be forced to become trustees of express trusts, and if appointed may immediately disclaim or subsequently retire (see Chapter 11). It may therefore be important that the law, in seeking to oversee the exercise of trusteeship, does not unduly discourage potential trustees.
This chapter and the next two are concerned predominantly with the benefits and burdens of trusteeship. First, this chapter focuses on the nature of trusteeship with particular reference to a possible source of tension created between, on the one hand, a concept of trusteeship rooted in moral obligation and, on the other, one which perceives trusteeship as a managerial function to be financially rewarded.
In Chapter 18 we noted that the Charitable Trusts Acts 1853–1860 established, for the first time, a central permanent Charity Commission empowered to supervise the management of charitable trusts and to remodel their purposes when they proved impracticable or impossible. But its role was severely constrained in three particular respects: (1) its jurisdiction, which extended to certain charitable endowments only and not to ‘collecting’ charities; (2) its freedom to act of its own motion, which was limited by the degree of autonomy preserved for trustees; and (3) the circumstances in which the Charity Commissioners (or the court) could make cy-près schemes.
Since then two trends in the legal and administrative framework regulating charity have become apparent. On the one hand, charities have been favoured more, notably in financial respects. On the other hand, an attempt has been made to extract a higher price from charities in return for these favours by extending and strengthening the supervisory framework, initially via the Charities Act 1960. This statute enacted most of the recommendations for reform contained in the Nathan Report (Committee on the Law and Practice Relating to Charitable Trusts (Cmd 8710, 1952)). Notwithstanding these changes, concern about the efficiency of charities and the effectiveness of supervision over them grew apace, culminating in a series of critical reports in the late 1980s (see An Efficiency Scrutiny of the Supervision of Charities (Woodfield Report) (1987); National Audit Office (NAO) Monitoring and Control of Charities in England and Wales (HC Paper no 380 (1986–87) and HC Paper no 13 (1990–91)); Public Accounts Committee (HC Paper no 116 (1987–88) and HC Paper no 85 (1991)).
The focus in this book has so far been on the use or imposition of the trust in various family contexts. It was often in response to problems posed in these contexts in particular that many of the basic rules of trusts law evolved. Some rules, for example, those relating to duties concerning investment and delegation, indirectly provide guidelines for commercial decisions to be taken during administration of a trust. But the trust concept has today also penetrated more directly into many and varied areas of commercial and financial activity (see Chapter 1 at p 9). In this chapter our focus shifts to one of those areas where the trust retains a significant role, namely collective saving for retirement via occupational pension provision. This is not to say that the trust does not feature significantly in other areas of commerce and finance. In the form of the ‘unit trust’, a hybrid creation comprising a complex amalgam of the concepts of common law contract and equitable trust, it provides a medium of collective investment for investors who wish to spread their risks over a wide range of securities (see Chapter 1). Recent estimates put the total number of unit trusts at closer to 1,800 with a market value in the region of £275 billion (thousand million) (Financial Statistics no 517, May 2005).
Charity is a deep-rooted element in human behaviour. To provide emotional, spiritual or material comfort to those in need is an instinctive aspect of social behaviour, and is reinforced by religious and ethical precepts extolling it as one of the most ennobling forms of conduct (see generally Chesterman Charities, Trusts and Social Welfare (1979) ch 1). In the words of a standard legal text (Tudor on Charities (9th edn, 2003) p 1) elaborating on the words of Sir William Grant MR in Morice v Bishop of Durham (1805)): ‘in its widest sense, the word “charity” denotes “all the good affections that men ought to bear towards each other”.’ And at its best, charity invokes a warm response. There is a touching depth of pity and sympathy shown by the following message sent with a donation in 1966 to the Aberfan Disaster Trust Fund: ‘Please use this small amount in any way you wish. I was saving it up for a new coat, O God, I wish I had save [sic] more. Yours sincerely, A Mother’ (Nightingale Charities (1973) p 178). The Bob Geldof-inspired Band Aid Trust appeared to strike a similar chord when remarkably raising £69m in 1985 in aid of famine relief. And the fund-raising antics displayed on ‘Red Nose Day’ commonly raise in the region of £50m for Comic Relief to be used on a wide range of charitable purposes.
As indicated at the end of Chapter 1, the trust concept originated in English law in medieval times, chiefly as a result of the efforts of conveyancers to preserve the landholdings of their clients from certain forms of feudal taxation and to increase the range of dispositions of land which their clients could legally make on death. The emergence of the trust concept at this time is intimately bound up with the assumption of jurisdiction in legal matters by the Lord Chancellor, on grounds of ‘equity’. In time, as we will see, that jurisdiction became sufficiently pervasive and ordered so as to justify substituting an upper case ‘E’ in place of the lower case ‘e’. The development of Equity in that manner involves matters that range far beyond those concerning the trust. Since it is the latter that is our prime concern, the roles are reversed here and Equity therefore appears in our story mostly as a member of the supporting cast only.
This chapter seeks to explain the development of major segments of trusts law – specifically, the law governing private express trusts – from these early beginnings until, approximately, the beginning of the twentieth century. It does so with particular reference to the trust transactions which served, in various ways, to aggregate and safeguard privately held wealth for the benefit of members of a family and to ensure the smooth transmission of wealth from one generation of a family to the next.
It will be seen in Chapters 18–20 that the trust has come to play an important part in the context of not-for-profit activity that the law regards as charitable. But the trust also has an important role to play, alongside other legal concepts such as contract, in non-charitable not-for-profit activity. Numerous not-for-profit organisations are formed not as companies or any other kind of corporate body, but as unincorporated associations. In Conservative and Unionist Central Office v Burrell  1 WLR 522 Lawton LJ suggested that an unincorporated association will have the following features:
(i) two or more persons bound together for one or more common purposes (not being business purposes);
(ii) having mutual rights and duties arising from a contract between them;
(iii) in an organisation with rules to determine who controls it and its funds and on what terms; and
(iv) which members must be able to join or leave at will.
This last named requirement is contentious unless it means that membership is voluntary, since many unincorporated associations are likely to have rules which impose some restrictions on membership (see also Underhill and Hayton p 123 for a similar criticism).
The trust concept is invoked when the rules make provision – as they do commonly, but not in every case – for the property collectively owned by the association's members to be vested in the names of trustees.
A ‘trust’ in English law is in some measure the translation into legal terms of the word ‘trust’ as used in ordinary speech. Its conceptual starting-point is ‘a confidence reposed in some other’ (this phrase is from the sixteenth-century legal commentaries of Lord Chief Justice Coke). The ‘confidence’ so reposed gives rise to moral obligations to which the courts, aided by the legislature, have purported to develop legal parallels. Inevitably, the moral weight given to trust and trusteeship in ordinary usage – to be ‘in breach’ of a ‘sacred trust’ is a serious matter, with repercussions possibly in the next world as well as this one – has had a significant impact on both the scope and the content of trusts law principles. There are still some contexts in which it may be difficult to say whether the word ‘trust’ is used in a legal or purely moral sense.
Yet this is by no means the whole story of trusts law. In the early twentieth century the historian and jurist F W Maitland praised the trust (see Equity (2nd edn, 1936) p 23 and Selected Historical Essays(1936) p 129); he regarded ‘the development from century to century of the trust idea’ as ‘the greatest and most distinctive achievement performed by Englishmen in the field of jurisprudence’. But this was not because the trust embodied basic ethical principles but rather because of its versatility.