The Maximum Traveling Salesman Problem with Submodular Rewards

In this paper, we look at the problem of finding the tour of maximum reward on an undirected graph where the reward is a submodular function, that has a curvature of $\kappa$, of the edges in the tour. This problem is known to be NP-hard. We analyze two simple algorithms for finding an approximate solution. Both algorithms require $O(|V|^3)$ oracle calls to the submodular function. The approximation factors are shown to be $\frac{1}{2+\kappa}$ and $\max\set{\frac{2}{3(2+\kappa)},2/3(1-\kappa)}$, respectively; so the second method has better bounds for low values of $\kappa$. We also look at how these algorithms perform for a directed graph and investigate a method to consider edge costs in addition to rewards. The problem has direct applications in monitoring an environment using autonomous mobile sensors where the sensing reward depends on the path taken. We provide simulation results to empirically evaluate the performance of the algorithms.Comment: Extended version of ACC 2013 submission (including p-system greedy bound with curvature

Reconstructing Patent Eligibility

Patent law’s doctrine of ineligible subject matter is widely agreed to be in a bad state of repair. Even those welcoming the Supreme Court’s return to express subject-matter bars have been left disoriented by the Court’s pronouncements in this area. Which subject matter is ineligible, why it is ineligible, and how it might become eligible have all remained enshrouded in mystery. The nub of the problem, this Article contends, is two-fold. First, from its nineteenth-century origins to the present, courts grappling with ineligibility doctrine have remained in the grip of a series of “physicalist” misconceptions of the object of patent rights, and hence of the subject matter claimed in the patents at issue. In a nutshell, courts have not fully internalized that the object of patent rights is always and only an intangible space of “knowledge of” something, and never some “thing” itself. As a result, they have failed to characterize accurately the content of the ineligible subject-matter categories, much less specify why they are ineligible. Removing these physicalist errors dissipates much of the fog in this area. In its wake emerges a second distinct theme of ineligibility case law: the intimation by the courts of a set of embryonic “functionality” concerns, which seek to restrict patents to zones of applied rather than basic knowledge. But these concerns have remained inchoate, owing to their entanglement in a physicalist web. Thus, reconstructing eligibility doctrine requires extricating incipient functionality concerns from the physicalist thicket, developing their independent policy bases, and finally, properly following through on their doctrinal implications. Doing so yields three large gains. First, it provides the first unified account of this body of law, something that scholars had despaired of realizing. Second, it advances a distinctive “platform” rationale for why basic research should remain outside the patent system, and be sustained instead by publicly funded peer production. Third, it cures each of the three defects marring eligibility’s existing doctrinal framework: (1) under “step one” of the framework, it clarifies what precisely is the content of the ineligible categories; (2) under “step two” of the framework, it radically improves the analysis of how a claim with such ineligible content may be rendered eligible; and (3) finally, when moving from eligibility into an analysis of the substantive requirements of patentability, it clarifies how to follow the courts’ (heretofore nebulous) injunction that claims must be evaluated “as a whole.

Self-medication amongst university students of Karachi: prevalence, knowledge and attitudes

OBJECTIVE: To determine the prevalence, attitude and knowledge of self-medication amongst university students of Karachi, Pakistan. METHODS: This cross-sectional, study was conducted from Jan-Feb 2007. A convenience sample was taken from 2 medical and 2 non-medical universities of the city of Karachi, Pakistan. Data was analyzed using SPSS v 14 and associations were tested using the Chi square test. RESULTS: Of the 572 participants (mean age=21 +/- 1.8 years, Male: Female ratio=1:1.5), 295 were medical and 277 were non-medical students. The prevalence of self-medication was 76%. Forty three percent students stated that they alter the regimen of prescribed medicines while 61.9% stated that they stop taking a prescribed medicine without consulting a doctor. The most common reason for self-medication was previous experience (50.1%) and the most common symptoms were headache (72.4%), flu (65.5%), and fever (55.2%). Commonly used medicines were analgesics (88.3%), antipyretics (65.1%) and antibiotics (35.2%). Eighty seven percent of students thought self-medication could be harmful and 82.5% students thought that it was necessary to consult a doctor before taking a new medicine. There was no significant difference between the self medication practices of medical and non medical students (p=0.8) CONCLUSION: Prevalence of self-medication is high in the educated youth, despite majority being aware of its harmful effects. There is a need to educate the youth to ensure safe practices. Strict policies need to be implemented on the advertising and selling of medications to prevent this problem from escalating

The Fundamental Building Blocks of Social Relations Regarding Resources: Hohfeld in Europe and Beyond

In the hundred years since Hohfeld published his two “Fundamental Legal Conceptions” articles, the “bundle-of-rights” view of property associated with his work has come to enjoy the status of conventional wisdom in American legal scholarship. Seen as a corrective to lay conceptions and a predecessor “Blackstonian” view of property as the “sole and despotic dominion” of an “owner” over a thing, the central insight of Hohfeldian analysis is standardly taken to be that property is not a single “thing” but rather a “bundle of rights” with respect to things and persons. In recent years, however, this Hohfeldian view has come under increasing attack by critics calling to replace the bundle-of-rights picture with a return to lay or neo-Blackstonian conceptions of property, as the “right to a thing,” “thing-ownership” or, simply, “the law of things.” Yet what precisely is at stake in this dispute has remained somewhat nebulous. In the words of one critic, although all sides to the debate “agree that the thing versus ad hoc bundle contrast is significant, it is surprisingly difficult to specify what the contrast really means. The crux of the problem, we suggest, is a fundamental mischaracterization of the Hohfeldian analysis of property—by both critics and defenders. The “bundle of rights” label obscures from view a distinct—and more fundamental—dimension of Hohfeldian analysis, namely that property is a social relation. And as or more important than getting right the precise content of each of these claims is understanding their inter-connection: the “social relations” claim is the fundamental platform of the analysis, generating in its turn the “bundle of rights” claim as a conclusion. Indeed, if a short moniker were wanted for Hohfeldian analysis, much preferable to the “bundle of rights” would be the “relational” conception of property.Moreover, each of these components of Hohfeldian analysis—social relations and bundle of rights—is fundamentally distinct from a third set of points with which they are commonly fused, concerning the dematerialization of the objects and interests of property. It is the blurring of what are three distinct lines of analysis—what we may call dephysicalization, disaggregation and dematerialization—that has led many to the conclusion that Hohfeldian analysis results in the “disintegration” of property, rendering it no longer a distinct concept or field of law. An outcome embraced by some (neo-Hohfeldians) and decried by others (neo-Blackstonians). This conclusion, we believe, is both too hasty and imprecise. Imprecise because it fails to locate the contest between Hohfeldian and neo-Blackstonian conceptions of property as pivoting around not one, but at least two and perhaps three, points of contrast, tracking each of the central but distinct lines of Hohfeldian analysis: dephysicalization, disaggregation and dematerialization. It is too hasty because the dephysicalization of property, as a social relation, poses no problems; and while disaggregation and dematerialization may indeed lead to troubling—if very distinct—forms of disintegration, the fault lies less with the specific content of Hohfeld’s claims than with a failure, post-Hohfeld, to follow through on his underlying method and structure of analysis in a constructive fashion. And so the solution to disintegration, we urge, is not a “rethingification” of property but rather its “reintegration”—by carrying forward the method of Hohfeldian analysis in two constructive directions: (a) a resource-specific answer to the question of “what is property about?” and (b) in answer to “what does property consist of?” an architectural analysis of the basic entitlements that serve as the fundamental building blocks of all property forms