Partial theta functions and mock modular forms as q-hypergeometric series

Ramanujan studied the analytic properties of many $q$-hypergeometric series. Of those, mock theta functions have been particularly intriguing, and by work of Zwegers, we now know how these curious $q$-series fit into the theory of automorphic forms. The analytic theory of partial theta functions however, which have $q$-expansions resembling modular theta functions, is not well understood. Here we consider families of $q$-hypergeometric series which converge in two disjoint domains. In one domain, we show that these series are often equal to one another, and define mock theta functions, including the classical mock theta functions of Ramanujan, as well as certain combinatorial generating functions, as special cases. In the other domain, we prove that these series are typically not equal to one another, but instead are related by partial theta functions.Comment: 13 page

Truth In Intellectual Property Revisited: Embracing eBay at the Edge

In addition to whatever else it might do to serve the public interest, intellectual property diminishes the commons. To that extent, any particular intellectual property claim intersects the public interest and affects more than just the immediate parties. Not only does intellectual property diminish the commons, but also each of its disciplines contains an almost casually incoherent metaphysic. There is incoherence, if not at the core, at least at the critical edges of intellectual property law that is systemic and fundamental. Notwithstanding over 200 years of practice in the United States, the goal of establishing a sufficiently principled, practical and predictable set of intellectual property rules is still not satisfied. In this context the otherwise peculiar result of eBay is not only tolerable, but welcome. At the critical edge of intellectual property law where the rules seem especially odd and the distinctions particularly refined and subtle a limited remedy can limit the damage that an unmanageable intellectual property law regime can inflict on the commons against the public interest. A qualified embrace of eBay supports the public interest and provides a way out of the hall of mirrors that is modem intellectual property law, short of breaking all the mirrors and starting over

New England\u27s agricultural position

New England\u27s agriculture has been denounced repeatedly as backward and a failure, and some of the critics have been decidedly caustic and pessimistic In their outspokenness. One writer (l )• stated: New England\u27s agriculture is a thing apart from Heir England. That group of states re ante the ultimate in industrial supremacy; broadly visualised, the agriculture therein stands for all that is retrogressive. •Once the agricultural colossus of the nation, New England farming today is the Inspiration of gloom. For more than half a century the product has declined. The rural population, unable to endure, has migrated to the cities or to the fields of the west, leaving a serried rear-guard to keep up the fight. New England\u27s Colonial and Revolutionary history and her wealth of manufacturing industry must be her boast. Her agriculture is a broken reed. * Elsewhere (3) he continued: Outside the boundaries of Hew England, the belief prevails that these states are composed of series of abandoned farms with cultivated areas thrown in to break the monotony; that anybody can go in there and pick up a farm for a little more than a song. He interviewed the secretary of the Connecticut Board of Agriculture who denied that such charges applied to his state; but official assurances from Washington Informed him that the state had some 300,000 acres of cut-over land and many neglected farms. Very frequently there appear in print statements to the effect that crops once raised extensively are seldom grown now in New England and yields are shrinking; that farm animal and their products are diminishing in number and amount; that farm products generally are inferior in quality and smaller in quantity than they should be; that the agricultural industry is becoming steadily less capable of sustaining Hew England\u27s population; that rural population is declining in what were once prosperous agricultural sections; that the numbers of farmers and of farms are dwindling and that farm property is lessening in value

Toward Non-Neutral First Principles of Private Law: Designing Secondary Liability Rules for New Technological Uses

A series of recent cases revisits secondary liability in intellectual property law, solving some particular problems but without providing completely specified rules that are predictable and principled. Prior law already includes several varieties of secondary liability with a rationale for each. Together, these old and new sources point the way towards a synthesis, which may allow for a designed solution that is more fully specified, at least in respect of new technological uses. When all is said, secondary liability in intellectual property law still turns on two essential questions: (1) is there someone who is liable for direct infringement, and if so (2) is it just to hold someone else accountable? Both of these inquiries contain embedded variables, which are to a surprising degree free and indeterminate with respect to users of new technologies in places created by code. These places created by code include the metaverse, virtual worlds, cypherspace, and cyberspace proper (the code world ). The code world and the new machines that enable it constitute new technological uses (NTUs) that have great economic and practical consequence. I propose legal rules purposely chosen to encourage a designed architecture for NTUs that will prefer hitchhikers, guides and ordinary users to predators, pirates and spoilers of the new machines and the code world. I propose both a short-term solution centered on interim safe harbors and a longer-term project to disintegrate liability-style rules from property-style rules. The solutions depend upon intentional design of liability rules (is there someone liable for direct infringement?), and of limited remedies intentionally fitted to the new technological uses for which they are designed (is it just to hold someone else accountable?)

An Invitation to a New Transportation Mode

The trends of Personal Rapid Transit (PRT) and Automated Highways are converging. The result may be a new transportation mode built around robotic vehicles. This paper outlines how technology can transform transportation, making it more convenient, safer, more sustainable and less subject to congestion. Such a system could utilize existing infrastructure, but split highway lanes in half with vehicles less than a meter wide. This paper presents lessons from several relevant vehicles that the author's research teams have worked on. It describes open source work in progress and invites participation from other researchers

Designing Food, Owning the Cornucopia: What the Patented Peanut Butter & Jelly Sandwich Might Teach About GMOs, Modified Foods, the Replicator, and Non-Scarcity Economics

Imagine for purposes of discussion that the technology for designing and building an actual cornucopia—something that embodies code, genetically modified organisms, or other techniques for producing, modifying, creating, or duplicating food (call it neo-tech food design)— exists, works, and is safe. To frame the problems of neo-tech food design, I start with what ought to be an easy case of low-tech food design, the peanut butter and jelly sandwich. Since it is a prime example of an incremental improvement invention, and hence like very many other inventions that are routinely patented, it must be asked: was there a problem? And if so, what exactly was the problem with the issuance, or cancelation of a patent on a sandwich comprising a doubly sealed, doubly encapsulated jelly filling with spaced apart seals, one of which capsules is peanut butter? Based on lessons learned from the once-patented sandwich, I present two proposals, in the alternative. First, and as what might seem an unlikely solution, I endorse the creation of a Public Domain Protection Agency (PDPA) with resources to help resolve the problems that will predictably arise out of a cornucopia. The PDPA might also serve as a counterweight to the tendency, exemplified by the agreement on Trade-Related Aspects of Intellectual Property Rights (TRIPS), to lock-in some of the current developed nations’ standards for patentability, world-wide. Second, I present an alternate proposal that is more attainable: (1) virtual field of use limitations, and (2) virtual ratemaking proceedings. This last proposal can be practically implemented by a revitalization of the beneficial utility (or ordre public) doctrine or by a purposive reconsideration, and discretionary implementation of existing remedies under current patent law. Preparing in advance for the problems of neo-tech food design has the advantage of preserving the system of patent law, rebalancing it in the interest of justice to ensure an economic return to inventors in global markets while avoiding the charge of profiteering on hunger in certain less fortunate markets. This is a particular instance of a larger problem. The problem is that some of the new technologies extend the unexplored limits of non-scarcity economics to a degree not previously seen in patent law. This, in turn, challenges the “justice” of the conventional patent system

Minority Report: Real Patent Reform, Maybe Later - the America Invents Act and the Quasi-Recodification Solution

This Article has three parts. In Part One, I describe what Congress claims to have done, then what the Act actually has done, and therefore what is the most that can be hoped to come from it. In considering what Congress has done, I briefly outline the theoretical basis of the new hybrid system, neither first-to-invent nor first-to-file, but rather a first to declare system with a one-year grace period that is both a shield and a sword to the declarant. More importantly, Congress has indicated it believes the new system is compatible with the Constitutional grant, and I suggest that Congress\u27 new perspective may lead to a new understanding of what the Constitution minimally requires, thereby opening the way for a more flexible, efficient, and streamlined patent regime despite the ALA. In Part Two, I describe the nature of the underlying problems in patent law. What, exactly, makes a bad patent worse than any other patent? If there were a serious problem with bad patents prior to the AIA, there still is. The reason for asking the question is stunningly simple: if so many routinely issued patents are bad, then it must be said that bad patents are not an abuse of the current system, they are the system. In this section, I describe what the AIA has failed to do, propose a working definition of bad patents, and provide some hypotheticals aimed at the non-specialist. I claim the problem of bad patents is endemic to the existing system, is not nearly cured by or even defined in the AIA, and yet is possible of cure according to a new way of framing that might be embedded in the AIA. How, then, ever to attain real and fundamental patent reform post-AIA

Social Ramifications of Autonomous Urban Land

Abstract—Autonomous vehicle technology may arrive much sooner than most people expect and it has profound implications for transportation. The technology facilitates a rail-less personal rapid transit (PRT) system using both public and private vehicles. Road traffic fatalities and injuries may decline by one to two orders of magnitude. A PRT system can provide mobility to the blind, elders suffering from dementia, children and the intoxicated. The system can make use of existing infrastructure, reduces urban sprawl and eases congestion. Autonomous vehicle based systems can improve fuel efficiency. The technology presents a window of opportunity for a new mode of transportation that obtains efficiencies of up to 0.25 l/100 km (1000 mpg equivalent), reducing U.S. petroleum consumption by up to 16%. The U.S. carbon savings could reach the equivalent of 12 trains of 100 coal cars daily. Keywords-Autonomous vehicles, personal rapid transit, traffic safety, fuel efficiency, mobility, global warming, people mover, pod car. I