Post-Newtonian constraints on f(R) cosmologies in metric formalism

We compute the complete post-Newtonian limit of the metric form of f(R) gravities using a scalar-tensor representation. By comparing the predictions of these theories with laboratory and solar system experiments, we find a set of inequalities that any lagrangian f(R) must satisfy. The constraints imposed by those inequalities allow us to find explicit bounds to the possible nonlinear terms of the lagrangian. We conclude that the lagrangian f(R) must be almost linear in R and that corrections that grow at low curvatures are incompatible with observations. This result shows that modifications of gravity at very low cosmic densities cannot be responsible for the observed cosmic speed-up.Comment: 10 pages, no figures, revtex

Supergravity Computations without Gravity Complications

The conformal compensator formalism is a convenient and versatile representation of supergravity (SUGRA) obtained by gauge fixing conformal SUGRA. Unfortunately, practical calculations often require cumbersome manipulations of component field terms involving the full gravity multiplet. In this paper, we derive an alternative gauge fixing for conformal SUGRA which decouples these gravity complications from SUGRA computations. This yields a simplified tree-level action for the matter fields in SUGRA which can be expressed compactly in terms of superfields and a modified conformal compensator. Phenomenologically relevant quantities such as the scalar potential and fermion mass matrix are then straightforwardly obtained by expanding the action in superspace.Comment: 10 pages; v2: references update

Response to the Letter to the Editor

This paper has attracted interest around the world from the media (both TV and newspapers). In addition, we have received letters, emails and telephone calls. One of our favorites was a voicemail message asking us to return a call to Australia at which point we would learn who really killed JFK. We welcome the opportunity to respond to the letter to the editor from Mr. Fiorentino. Mr. Fiorentino claims that our ``statement relating to the likelihood of a second assassin based on the premise of three or more separate bullets is demonstrably false.'' In response we would like to simply quote from page 327 of Gerald Posner's book Case Closed, one of the most well known works supporting the single assassin theory: ``If Connally was hit by another bullet, it had to be fired from a second shooter, since the Warren Commission's own reconstructions showed that Oswald could not have operated the bolt and refired in 1.4 seconds.'' Mr. Fiorentino also claims that the ``second fatal flaw is the use of a rather uncomplicated formula based on Bayes Theorem.'' Let $E$ denote the evidence and $T$ denote the theory that there were just two bullets (and hence a single shooter). We used Bayes Theorem to hypothetically calculate $P(T|E)$ from $P(E|T)$ and the prior probability $P(T)$. In order to make $P(T|E)$ ten times more likely than $P(\bar{T}|E)$, the ratio of the prior probabilities [i.e., $P(T) / P(\bar{T})$] would have to be greater than 15. Thus, we again conclude that this casts serious doubt on Dr. Guinn's conclusion that the evidence supported just two bullets. Sadly, this is far from the first time that probability has been misunderstood and/or misapplied in a case of public interest. A notable British example is the Clark case. See Nobles and Schiff (2005) for details. Finally, we welcome and, in fact, encourage members of the scientific community to provide alternative analyses of the data.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS154 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Online Pattern Matching for String Edit Distance with Moves

Edit distance with moves (EDM) is a string-to-string distance measure that includes substring moves in addition to ordinal editing operations to turn one string to the other. Although optimizing EDM is intractable, it has many applications especially in error detections. Edit sensitive parsing (ESP) is an efficient parsing algorithm that guarantees an upper bound of parsing discrepancies between different appearances of the same substrings in a string. ESP can be used for computing an approximate EDM as the L1 distance between characteristic vectors built by node labels in parsing trees. However, ESP is not applicable to a streaming text data where a whole text is unknown in advance. We present an online ESP (OESP) that enables an online pattern matching for EDM. OESP builds a parse tree for a streaming text and computes the L1 distance between characteristic vectors in an online manner. For the space-efficient computation of EDM, OESP directly encodes the parse tree into a succinct representation by leveraging the idea behind recent results of a dynamic succinct tree. We experimentally test OESP on the ability to compute EDM in an online manner on benchmark datasets, and we show OESP's efficiency.Comment: This paper has been accepted to the 21st edition of the International Symposium on String Processing and Information Retrieval (SPIRE2014

Design Patent Infringement Needs a Free Expression Defense (La infracción de patentes de diseño necesita una defensa de libre expresión)

English Abstract: As elsewhere in the world, design patents are propagating copiously in U.S. intellectual property law. Notwithstanding their fertility, design patents face potentially prohibitive and as yet unexplored legal challenges. One possibility is that the U.S. Congress might lack the very power to authorize design patents. Another possibility – our subject here, with implications for design patents in Europe and around the world – is that design patents violate fundamental rights if there is not a defense to infringement founded in the freedom of expression. Spanish Abstract: Las patentes de diseño se propagan en abundancia en el derecho de la propiedad intelectual. Mientras tanto, las patentes de diseño enfrentan desafíos legales aún inexplorados. Enfocándose en la ley estadounidense, este artículo postula que las patentes de diseño violan los derechos fundamentales si no hay una defensa a la infracción fundada en la libertad de expresión. Diseño es único entre las patentes debido a su capacidad expresiva. Por lo tanto, debe acomodarse a la libertad de expresión con defensa de uso o trato justo, comparable a la ley de los derechos de autor

The Constitutionality of Design Patents

Design patents have been part of American law since 1842. In that time, only just over 600,000 design patents have been issued, with more than half of these being granted in the last twenty years. This quantity is dramatically fewer than the number of utility patents issued which is rapidly approaching 9,000,000 issued patents. Possibly because of the low usage of design patents over time, no case law and little literature address the constitutional issues raised by them. This article intends to overcome that shortcoming. Two constitutional aspects of design patents will be examined. First, congressional authority to adopt the design patent laws will be examined. The Constitution in Article I, Section 8, Clause 8 grants Congress specific powers to adopt both patents and copyrights. When a design is examined, it is unclear that it is an invention making its patentability suspect. At the same time, establishing a design as a writing is not problematic, leading to its eligibility for copyright. In this case, the clause itself must be examined to determine if something that qualifies only for copyright protection can nevertheless be granted a patent. The words chosen in the clause, particularly based on the way some of them were used in the Eighteenth Century, suggest that the answer is “no.” Of course, any historical analysis of the Constitution may prove to be an inaccurate predictor of how modern courts would address an issue, but this analysis does suggest a significant Article I problem for design patents. Second, even if the Article I problem can be overcome, serious First Amendment issues are raised. Unlike a utility patent, design patents are far more likely to have direct impacts on speech. If so, the patent laws would have to accommodate that speech unless there is a compelling governmental need for it to not do so. Copyright law, for example, avoids much of this First Amendment conflict through the recognition of the Fair Use Defense under 17 U.S.C. § 107 which allow society to use copyrighted materials despite the legal protection where important First Amendment issues are raised. Patent law has no such defense, but may need one to avoid constitutional problems

The Constitutionality of Design Patents

Design patents have been part of American law since 1842. In that time, only just over 600,000 design patents have been issued, with more than half of these being granted in the last twenty years. This quantity is dramatically fewer than the number of utility patents issued which is rapidly approaching 9,000,000 issued patents. Possibly because of the low usage of design patents over time, no case law and little literature address the constitutional issues raised by them. This article intends to overcome that shortcoming. Two constitutional aspects of design patents will be examined. First, congressional authority to adopt the design patent laws will be examined. The Constitution in Article I, Section 8, Clause 8 grants Congress specific powers to adopt both patents and copyrights. When a design is examined, it is unclear that it is an invention making its patentability suspect. At the same time, establishing a design as a writing is not problematic, leading to its eligibility for copyright. In this case, the clause itself must be examined to determine if something that qualifies only for copyright protection can nevertheless be granted a patent. The words chosen in the clause, particularly based on the way some of them were used in the Eighteenth Century, suggest that the answer is “no.” Of course, any historical analysis of the Constitution may prove to be an inaccurate predictor of how modern courts would address an issue, but this analysis does suggest a significant Article I problem for design patents. Second, even if the Article I problem can be overcome, serious First Amendment issues are raised. Unlike a utility patent, design patents are far more likely to have direct impacts on speech. If so, the patent laws would have to accommodate that speech unless there is a compelling governmental need for it to not do so. Copyright law, for example, avoids much of this First Amendment conflict through the recognition of the Fair Use Defense under 17 U.S.C. § 107 which allow society to use copyrighted materials despite the legal protection where important First Amendment issues are raised. Patent law has no such defense, but may need one to avoid constitutional problems

Free subgroups of one-relator relative presentations

Suppose that G is a nontrivial torsion-free group and w is a word over the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\}. It is proved that for n\ge2 the group \~G= always contains a nonabelian free subgroup. For n=1 the question about the existence of nonabelian free subgroups in \~G is answered completely in the unimodular case (i.e., when the exponent sum of x_1 in w is one). Some generalisations of these results are discussed.Comment: V3: A small correction in the last phrase of the proof of Theorem 1. 4 page