Lattice rules of minimal and maximal rank with good figures of merit

For periodic integrands with unit period in each variable, certain error bounds for lattice rules are conveniently characterised by the figure of merit ρ, which was originally introduced in the context of number theoretic rules. The problem of finding good rules of order N (that is, having N distinct nodes) then becomes that of finding rules with large values of ρ. This paper presents efficient search methods for the discovery of rank 1 rules, and of maximal rank rules of high order, which possess good figures of merit. © 1999 Elsevier Science B.V

Modernizing Language in the California Government Claims Act to Enable Consistent Enforcement of Statutory Sovereign Immunity

Ideally, sovereign immunity provisions should (1) protect public officials from undue interference with discharge of their duties and (2) hold accountable public officials who act unlawfully. Analytical frameworks and statutes at both the federal and state levels often fail to fulfill these objectives. Federal courts are guided by statutes and objectives that are indirectly relevant to state courts. As a result, states are left to address independently how to address clams of sovereign immunity when plaintiffs file suits alleging torts by public entities and employees. In California, when plaintiffs sue public employees or entities in civil court, the California Government Claims Act (GCA) determines whether defenses of sovereign immunity may preclude liability. However, the statutory language of the GCA mirrors the common law language in force at the time the GCA was enacted. This language has led to inconsistent interpretations of California’s sovereign immunity statutes. This Comment argues (1) that the GCA\u27s use of common law language can frustrate the ability of courts to establish a consistent understanding of which tortious actions may be protected by immunity from charges of either intentional or negligent misconduct; and (2) that a lack of legislative guidance frustrates the ability of courts to determine whether certain state actions are either discretionary acts protected by absolute immunity or mandatory duties protected by qualified immunity. Further, modernizing language throughout the GCA would ensure more consistent enforcement of statutory sovereign immunity. Part I of this Comment outlines the history of the doctrine of sovereign immunity and summarizes the public policy arguments for and against its continuation. Part II provides an overview of the GCA\u27s architecture and how judicial interpretations have shaped its implementation. Part III analyzes statutory language and recommends amendments

The determination of canonical forms for lattice quadrature rules

AbstractLattice rules are equal weight numerical quadrature rules for the integration of periodic functions over the s-dimensional unit hypercube Us = [0, 1)s. For a given lattice rule, say QL, a set of points L (the integration lattice), regularly spaced in all of Rs, is generated by a finite number of rational vectors. The abscissa set for QL is then P(QL)= L ∩ Us. It is known that P(QL) is a finite Abelian group under addition modulo the integer lattice Zs, and that QL(f) may be written in the form of a nonrepetitive multiple sum, QL(f)=1n1⋯nm∑j1=1n1⋯∑jm=1nmfj1n1z1+⋯+jmnmzm, known as a canonical form, in which + denotes addition modulo Zs. In this form, zi ∈ Zs, m is called the rank and n1, n2,…, nm are called the invariants of QL, and ni+1¦ni for i = 1,2,…, m − 1. The rank and invariants are uniquely determined for a given lattice rule. In this paper we provide a construction of a canonical form for a lattice rule QL, given a generator set for the lattice L. We then show how the rank and invariants of QL may be determined directly from the generators of the dual lattice L⊥

Inside the West Wing: Lobbying as a contest

When a government makes many different policy decisions, lobbying can be viewed as a contest between the government and many different special interest groups. The government fights lobbying by interest groups with its own political capital. In this world, we find that a government wants to `sell protection' -- give favourable treatment in exchange for contributions -- to certain interest groups. It does this in order to build its own `war chest' of political capital, which improves its position in fights with other interest groups. And it does so until it wins all remaining contests with certainty. This stands in contrast to existing models that often view lobbying as driven by information or agency problems

The Classical and Maximin Versions of the Two-Envelope Paradox

The Two-Envelope Paradox is classically presented as a problem in decision theory that turns on the use of probabilities in calculating expected utilities. I formulate a Maximin Version of the paradox, one that is decision-theoretic but omits considerations of probability. I investigate the source of the error in this new argument, and apply the insights thereby gained to the analysis of the classical version

Aspects of leadership in a modern army

The author discusses some physiological and psychological aspects of leadership training in the Australian army. He argues that human performance is the crux of a military leader's profession and that it should be studied formally within the profession

Biometric Data Collection: Market Necessity or Unconstitutional Overkill?

Congress should pass, and the President should sign into law, the National Biometric Information Privacy Act of 2020 (National BIPA). Introduced by Senators Jeff Merkley (D-OR) and Bernie Sanders (I-VT), this bill limits the ability of private entities to collect biometric data and requires them to ensure the privacy and security of data they do collect. Unlike most federal regulatory legislation, it also provides for a private right of action through which individuals can seek meaningful remedies. Critics argue that the bill will deprive consumers of online shopping services and convenient digital security, and that employers and retailers may retaliate by requiring consent for biometric data collection as a condition of service or employment. Supporters argue that the status quo has already defaulted to mandatory consent, and that without legislation, citizens who value their privacy are left without a remedy. Biometric data collection provides relatively negligible benefits in commercial and employment contexts. Conversely, unregulated collection erodes civil liberties and violates the fundamental right to privacy. On balance, the risks far outweigh the benefits