Modelling the Fluid Mechanics of Cilia and Flagella in Reproduction and Development

Cilia and flagella are actively bending slender organelles, performing functions such as motility, feeding and embryonic symmetry breaking. We review the mechanics of viscous-dominated microscale flow, including time-reversal symmetry, drag anisotropy of slender bodies, and wall effects. We focus on the fundamental force singularity, higher order multipoles, and the method of images, providing physical insight and forming a basis for computational approaches. Two biological problems are then considered in more detail: (1) left-right symmetry breaking flow in the node, a microscopic structure in developing vertebrate embryos, and (2) motility of microswimmers through non-Newtonian fluids. Our model of the embryonic node reveals how particle transport associated with morphogenesis is modulated by the gradual emergence of cilium posterior tilt. Our model of swimming makes use of force distributions within a body-conforming finite element framework, allowing the solution of nonlinear inertialess Carreau flow. We find that a three-sphere model swimmer and a model sperm are similarly affected by shear-thinning; in both cases swimming due to a prescribed beat is enhanced by shear-thinning, with optimal Deborah number around 0.8. The sperm exhibits an almost perfect linear relationship between velocity and the logarithm of the ratio of zero to infinite shear viscosity, with shear-thickening hindering cell progress.Comment: 20 pages, 24 figure

The Changing Financial Structure of the U.S. Farm Sector

Agricultural Finance,

Real-world Quantum Sensors: Evaluating Resources for Precision Measurement

Quantum physics holds the promise of enabling certain tasks with better performance than possible when only classical resources are employed. The quantum phenomena present in many experiments signify nonclassical behavior, but do not always imply superior performance. Quantifying the enhancement achieved from quantum behavior requires careful analysis of the resources involved. We analyze the specific case of parameter estimation using an optical interferometer, where increased precision can be achieved using quantum probe states. Common performance measures are examined and it is shown that some overestimate the improvement. For the simplest experimental case we compare the different measures and show this overestimate explicitly. We give the preferred analysis of real-world experiments and calculate benchmark values for experimental parameters necessary to realize a precision enhancement.Comment: 8 pages, 3 figure

The Web of Law

Scientists and mathematicians in recent years have become intensely interested in the structure of networks. Networks turn out to be crucial to understanding everything from physics and biology, to economics and sociology. This Article proposes that the science of networks has important contributions to make to the study of law as well. The network of American case law closely resembles the Web in structure and can be studied using techniques that are now being used to describe many other networks, some found in nature, and others created by human action. Studying the legal network can shed light on how the legal system evolves, and many other questions. I present in this Article the preliminary results of a significant citation study of nearly four million American legal precedents, which was undertaken at my request by the LexisNexis corporation using the Shepard\u27s citation service. This study demonstrates that the American case law network has the overall structure that network theory predicts it would. It is a highly skewed, scale-free, or similar network. The remarkably great degree of skew is significant. Precendential authority is concentrated in a small number of cases. The vast majority of cases are rarely or never cited. In that it consists largely of dead cases, the Web of Law closely resembles scientific paper citation networks, which consist mostly of dead papers. This Article has three parts. First, I introduce some basic concepts of network science, including such important ideas as nodes, links, random graphs, evolving networks, scale-free networks, small worlds, the rich get richer dynamic, node fitness, and clusters. In Part II, I show that both over all and by particular jurisdiction, the Web of Law is a scale-free or similarly highly skewed network. In Part III, I describe some insights that appear from this application and suggest areas for future research. The Web of Law has a structure very similar to that of other real networks, such as the Web and the network of scientific papers. Indeed, preliminary analysis suggests the citation network of U.S. Supreme Court cases is nearly identical to the network of high-energy physics papers, and is well described by a two-power-law model. The Web of Law is organized with hub cases that have many citations and the vast majority of cases, which have very few. The distribution of citation frequency appears to be well described by a two power-law distribution, very similar to scientific paper citation networks. Many promising hypotheses can be generated by considering the law as a scale-free network. State and federal systems can be examined empirically to measure how well integrated each is with itself, and with each other, and how this is changing over time. Legal authorities can be measured to determine whether their authority is emerging or declining. Institutional bodies, such as courts, can be examined in the same way. Clusters of cases, which will reveal the semantic topology of law, can be mapped to determine whether traditional legal categories are accurate or require reform. These methods can be used to develop computer programs to improve the efficiency of searching electronic legal databases. Network theory hints at complex, but analyzable, interactions between the legal doctrines of precedent, and the systems of common law and multiple sovereignties. Because law grows and because it has doctrines of authority, it creates a network of a certain shape, which spontaneously organizes itself. Legal databases, which are huge, precisely documented, and readily accessible, present a perfect opportunity for the application of network science. This research would produce new knowledge of general jurisprudence that has simply been impossible until now, when we have the necessary advances in network science, the fast computers, and the existence of a complete record of the legal network in electronic form, waiting to be explored

The Web of Law

Scientists and mathematicians in recent years have become intensely interested in the structure of networks. Networks turn out to be crucial to understanding everything from physics and biology, to economics and sociology. This article proposes that the science of networks has important contributions to make to the study of law as well. Legal scholars have yet to study, or even recognize as such, one of the largest, most accessible, and best documented human-created networks in existence. This is the centuries-old network of case law and other legal authorities into which lawyers, judges, and legal scholars routinely delve in order to discover what the law is on any given topic. The network of American case law closely resembles the Web in structure. It has the peculiar mathematical and statistical properties that networks have. It can be studied using techniques that are now being used to describe many other networks, some found in nature, and others created by human action. Studying the legal network can shed light on how the legal system evolves, and many other questions. To initiate what I hope will become a fruitful new type of legal scholarship, I present in this article the preliminary results of a significant citation study of nearly four million American legal precedents, which was undertaken at my request by the LexisNexis corporation using their well-known Shepard\u27s citation service. This study demonstrates that the American case law network has the overall structure that network theory predicts it would. This article has three parts. First, I introduce some basic concepts of network science, including such important ideas as nodes, links, random graphs, evolving networks, scale-free networks, small worlds, the rich get richer dynamic, node fitness, and clusters. Oddly enough, the mathematical tools that have proven most useful for studying networks (or at least scale-free networks) come from statistical mechanics, a branch of physics. Having introduced network theory in Part I, and having presented evidence that American case law is a scale-free network in Part II, I argue for the significance of this discovery in Part III. I hope that by the time they reach Part III, readers will already be realizing the potential richness of applying network theory to legal systems. In Part III, I describe some insights that appear from this application and suggest areas for future research. The most famous hypothesis about the structure of law is that it is a seamless web. This old phrase, however, is just a metaphor we have used to grope for a reality we have not been in a position to express more precisely. Network science changes that. The Web of Law can be considered as a mathematical object whose topology can be analyzed using the tools pioneered by physicists and others who wanted to explore the structure of the Web and other real networks. The Web of Law has a structure very similar to that of other real networks, such as the Web and the network of scientific papers. The Web of Law is in substantial part a scale-free network, organized with hub cases that have many citations and the vast majority of cases, which have very few. The distribution of citation frequency approximates a power-law distribution, as is common with real scale-free networks, with truncations at either extreme of its distribution, which is also common. Many promising hypotheses can be generated by considering the law as a scale-free network. State and federal systems can be examined empirically to measure how well integrated each is with itself, and with each other, and how this is changing over time. Legal authorities can be measured to determine whether their authority is emerging or declining. Institutional bodies, such as courts, can be examined in the same way. Clusters of cases, which will reveal the semantic topology of law, can be mapped to determine whether traditional legal categories are accurate or require reform. These methods can be used to develop computer programs to improve the efficiency of searching electronic legal databases. The topology of American law can be compared to that of other legal systems to determine whether legal systems share universal architectural features, and in what respects different systems are unique. Changing dynamics of the citation frequency and the fitness of particular cases can be studied over historical periods to test historiographical hypotheses. So, for example, Farber\u27s hypothesis that changes in constitutional interpretation occur suddenly, and many others, may be tested rigorously. The dynamics of authority in law generally can be studied much more rigorously. The mere fact that law is a scale free, not a random network, suggests a high degree of intellectual coherence, contrary to what some critics have suggested. The shape of the degree distribution graph of the Web of Law, in its similarity to the scientific citation network, also suggests that cases age, in the sense of losing the ability to attract citations, over time, just as scientific papers do. Yet Supreme Court cases seem to age more slowly. How nodes age profoundly affects overall network structure and therefore affects the shape of the Web of Law. Network theory hints at complex, but analyzable, interactions between the legal doctrines of precedent, and the systems of common law and multiple sovereignties. Because law grows and because it has doctrines of authority, it creates a network of a certain shape, which spontaneously organizes itself. This is the product of laws that govern networks of computers as inexorably as they govern networks of cases, laws arising from the underlying mathematics of networks. Legal databases, which are huge, precisely documented, and readily accessible, present a perfect opportunity for the application of network science. This research would produce new knowledge of general jurisprudence that has simply been impossible until now, when we have the necessary advances in network science, the fast computers, and the existence of a complete record of the legal network in electronic form, waiting to be explored

The Efficient Norm for Corporate Law: A Neotraditional Interpretation of Fiduciary Duty

To economically oriented corporate law professors, distinguishing between directors\u27 fiduciary duty to shareholders and a duty to the corporation1 itself smacks of reification - treating the fictional corporate entity as if it were a real thing. Now the orthodox view among corporate law scholars is that the corporate fiduciary duty is a norm that requires firm managers to maximize shareholder value. Giving the corporation itself any serious role in the analysis of fiduciary duty, the thinking goes, obscures scientific insight with bad legal metaphysics. Some recent scholarship and legislation, such as constituency statutes, have challenged this shareholder primacy view. Contestants on both sides of the debate over corporate fiduciary duty assume, however, that economic analysis inevitably favors shareholder primacy. Critics of shareholder value maximization encourage this assumption by making their case turn, in part, on criticisms of economic methodology itself and on invocations of moral and political values most economists would find controversial at best. Nevertheless, the economic approach to corporate law does not foreordain the maximization of shareholder value as the primary norm of corporate law. The economic case for shareholder value maximization is, in fact, initially puzzling and ultimately unconvincing. If economic efficiency is the normative guidepost for substantive law, the principal norm of corporate law cannot be the maximization of shareholder value