Equitable Labelings of Caterpillar Graphs

The Graceful Tree Conjecture in graph theory has been open for almost half a century. The conjecture states that the vertices of any tree can be labeled with distinct integers between 0 and the number of edges of the tree in a way that the edges can be uniquely identified by the absolute value of the difference between their vertex labels. One possible approach to prove the conjecture is to prove the more general k-equitable tree conjecture. In a k-equitable labeling we assign integers from the set {0,1,2,…,k-1} to the vertices. Each edge will receive a label that is the absolute value of the difference of its vertex labels. We want to distribute the labels as equally as possible both for the edges and for the vertices. The conjecture states that this kind of labeling is possible for every tree and every k. This conjecture is equivalent to the graceful tree conjecture when k is the number of vertices of the tree. It has already been proven that every tree is 2-equitable and 3-equitable. We attempt to show a part of the k-equitable tree conjecture by choosing a large collection of trees called caterpillars, and examining different values of k

Enforcing Intellectual Property Rights

We study the determinants of patent suits and their outcomes over the period 1978-1999 by linking detailed information from the U.S. patent office, the federal court system, and industry sources. The probability of being involved in a suit is very heterogeneous, being much higher for valuable patents and for patents owned by individuals and smaller firms. Thus the patent system generates incentives, net of expected enforcement costs, that differ across inventors. Patentees with a large portfolio of patents to trade, or having other characteristics that encourage 'cooperative' interaction with disputants, more successfully avoid court actions. At the same time, key post-suit outcomes do not depend on observed characteristics. This is good news: advantages in settlement are exercised quickly, before extensive legal proceedings consume both court and firm resources. But it is bad news in that the more frequent involvement of smaller patentees in court actions is not offset by a more rapid resolution of their suits. However, our estimates of the heterogeneity in litigation risk can facilitate development of private patent litigation insurance to mitigate this adverse affect of high enforcement costs.

Enforcing Intellectual Property Rights

We study the determinants of patent suits and their outcomes over the period 1978-1999 by linking detailed information from the U.S. patent office, the federal court system, and industry sources. The probability of being involved in a suit is heterogeneous, being much higher for valuable patents and for patents owned by individuals and smaller firms. Thus the patent system generates incentives, net of expected enforcement costs, that differ across inventors. Patentees with a large portfolio of patents to trade, or having other characteristics that encourage "cooperative" interaction with disputants, more successfully avoid court actions. At the same time, key post-suit outcomes do not depend on observed characteristics. This is good news: advantages in settlement are exercised quickly, before extensive legal proceedings consume both court and firm resources. But it is bad news in that the more frequent involvement of smaller patentees in court actions is not offset by a more rapid resolution of their suits. However, our estimates of the heterogeneity in litigation risk can facilitate development of private patent litigation to mitigate this adverse effect of high enforcement costs.Parents, court actions, settement.

Review of \u3cem\u3eThe Rise of the Military Welfare State. Jennifer Mittelstadt. Reviewed by Mark Olson

Jennifer Mittelstadt, The Rise of the Military Welfare State. Harvard University Press (2015), 344 pages, $29.95 (hardcover)

Review of \u3cem\u3eThe Age of American Unreason in a Culture of Lies\u3c/em\u3e by Susan Jacoby

Review of The Age of American Unreason in a Culture of Lies by Susan Jacoby, Vintage (2019)

Practice-oriented controversies and borrowed epistemic credibility in current evolutionary biology: phylogeography as a case study

Although there is increasing recognition that theory and practice in science are intimately intertwined, philosophy of science perspectives on scientific controversies have been historically focused on theory rather than practice. As a step in the construction of frameworks for understanding controversies linked to scientific practices, here we introduce the notion of borrowed epistemic credibility (BEC), to describe the situation in which scientists, in order to garner support for their own stances, exploit similarities between tenets in their own field and accepted statements or positions properly developed within other areas of expertise. We illustrate the scope of application of our proposal with the analysis of a heavily methods-grounded, recent controversy in phylogeography, a biological subdiscipline concerned with the study of the historical causes of biogeographical variation through population genetics- and phylogenetics-based computer analyses of diversity in DNA sequences, both within species and between closely related taxa. Toward this end, we briefly summarize the arguments proposed by selected authors representing each side of the controversy: the ‘nested clade analysis’ school versus the ‘statistical phylogeography’ orientation. We claim that whereas both phylogeographic ‘research styles’ borrow epistemic credibility from sources such as formal logic, the familiarity of results from other scientific areas, the authority of prominent scientists, or the presumed superiority of quantitative vs. verbal reasoning, ‘theory’ plays essentially no role as a foundation of the controversy. Besides underscoring the importance of strictly methodological and other non-theoretical aspects of controversies in current evolutionary biology, our analysis suggests a perspective with potential usefulness for the re-examination of more general philosophy of biology issues, such as the nature of historical inference, rationality, justification, and objectivity

Dominant and Nash Strategy Mechanisms for the Assignment Problem

In this paper, I examine the problem of matching or assigning a fixed set of goods or services to a fixed set of agents. I characterize the social choice correspondences that can be implemented in dominant and Nash strategies when transfers are not allowed. This is an extension of the literature that was begun by Gibbard (1973) and Satterthwaite (1975), who independently proved that if a mechanism is nonmanipulable it is dictatorial. For the classes of mechanisms that are described in the paper, the results imply that the only mechanisms that are implementable in dominant and Nash strategies are choice mechanisms that rely only on ordinal rankings. I also describe a subclass of mechanisms that are Pareto optimal. In addition, the results explain the modeling conventions found in the literature - that when nontransfer mechanisms are studied individuals are endowed with ordinal preferences, and when transfer mechanisms are studied individuals are endowed with cardinal preferences

Morphogenesis of Photoreceptors in the Chick Retina: An Electron Microscopic Study

An electron microscopic investigation of the morphogenesis of photoreceptor cells in the domestic fowl (Gallus gallus) retina is presented in this study. The fine structural observations illustrate photoreceptor development ranging from five to twenty-one days of incubation and one to two days post-hatching. Retinal tissues were fixed in buffered aldehyde fixative, post-fixed in buffered 2% osmium tetroxide and otherwise conventionally prepared for electron microscopy. The neural (sensory) retina of the chick is largely occupied by undifferentiated cells within the outer neuroblastic layer from the 5th to 9th days of incubation. This layer is later divided into the inner and outer nuclear layers as a result of the establishment of the outer plexi- form layer. The ellipsoid cells of the outer nuclear layer will develop as the photoreceptors of the chick retina. Numerous centrioles are conspicuous within these cells at the level of the outer limiting membrane. The first indication of differentiation in the photoreceptor proper occurs during the 9th to 11th days, as the apical cytoplasm of the future receptor cells extends beyond the outer limiting membrane. These bulbous cytoplasmic projections occupy the optic ventricle and represent the forming inner segments with their characteristic ellipsoid. By the 16th day, the inner segments are extensively elongated. They are divided into the following two definitive portions: (1) the ellipsoid which occupies the distal one-third and (2) the myoid which represents the proximal two-thirds. During the 17th day, irregularly arranged membranous discs are observed within the forming outer segments. This portion of the photoreceptor proper develops as a modified cilium which originates from a basal body within the ellipsoid region of the inner segment. The membranous discs are closely associated with the microtubules of the connecting cilium and many are continuous with cylindrical tubules measuring 240 to 400 A in diameter. The discs (135 A thick) become oriented at right angles to the plasmalemrna by the 19th day. Some of the membranous discs are continuous with the plasmalemrna. Groups of discs are found within the pigment epithelium during the second day post-hatching. This observation indicates that the pigment epithelium actively participates in the removal of membranous discs. During the early stages of photoreceptor development, the basal portions of the receptor cells are not very conspicuous, with the exception of a large nucleus. By the 16th day basal arborizations begin to develop. Extensive synaptic terminals are plentiful and extend into the outer plexiform layer by the 19th day. They contain numerous synaptic vesicles and synaptic ribbons. Both conventional and invaginated (ribbon) synapses occur between the photoreceptors and secondary neurons (bipolar and horizontal cells). This study indicates that the morphogenesis of photoreceptors in the chick retina corresponds well with that in other vertebrate species. Moreover, the basic fine structure of the mature photoreceptor correlates favorably with that in a number of vertebrates, including amphibians, other avian species and numerous mammals

Gas dynamics in interacting and merging galaxies.

In this dissertation I develop a three dimensional model of the dynamics of gas clouds in interacting galaxies. The gas clouds move under the combined gravitational influence of two galaxies passing close to each other. By performing a multipole expansion of the gravitational field I am able to include the effects of self-gravity within a galaxy. This also allows me to model the case in which the two galaxies merge. The gas clouds are allowed to interact with one another by colliding. They either coalesce to form a larger cloud or are disrupted, depending on their relative kinetic energy as compared to the total gravitational binding energy of the two-cloud system. Various cases are considered in this dissertation by varying such parameters as impact parameter, inclination of the gaseous disk of a galaxy to the orbital plane of the two, interacting galaxies, relative velocity of the galaxies, the mass ratio of the galaxies, and the presence of gas in the second galaxy. As the strength of the interaction increases the more disturbed the interstellar medium becomes. The clouds collide at an increased rate and with larger velocities so that the fraction of collisions which disrupt the clouds rises as the strength of the interaction increases. The region of the galaxy where increased rates of collision are induced also becomes more and more concentrated toward the center of the galaxy. Since interacting galaxies are observed to have elevated star formation rates, I conclude that the star formation induced by the interaction of two galaxies is related to the high velocity, disruptive cloud-cloud collisions. Monitoring the amount of gas mass involved in such collisions allows me to estimate the star formation rate and the luminosity produced by these stars. Considering parameters such as inclination, bound and unbound orbits, the mass of the perturbing galaxy, and the possible presence of gas in both galaxies, I find that the scatter in observations of the infrared luminosity to gas mass ratio can be explained