The subseries number

Every conditionally convergent series of real numbers has a divergent subseries. How many subsets of the natural numbers are needed so that every conditionally convergent series diverges on the subseries corresponding to one of these sets? The answer to this question is defined to be the subseries number, a new cardinal characteristic of the continuum. This cardinal is bounded below by $\aleph_1$ and above by the cardinality of the continuum, but it is not provably equal to either. We define three natural variants of the subseries number, and compare them with each other, with their corresponding rearrangement numbers, and with several well-studied cardinal characteristics of the continuum. Many consistency results are obtained from these comparisons, and we obtain another by computing the value of the subseries number in the Laver model

Formulas and flexibility in trade negotiations : sensitive agricultural products in the WTO's Doha agenda

Many trade negotiations involve large cuts in high tariffs, with flexibilities allowing much smaller cuts for an agreed number of politically-sensitive products. The effects of these flexibilities on market access opportunities are difficult to predict, creating particular problems for developing countries in assessing whether to support a proposed agreement. Some widely-used ad hoc approaches to identifying likely sensitive products -- such as the highest-bound-tariff rule -- suggest that the impacts of a limited number of such exceptions on average tariffs and on market access are likely to be minor. This paper uses a rigorous specification based on the apparent objectives of policy makers in setting the pre-negotiation tariff. Applying this approach with detailed data allows the authors to assess the implications of sensitive-product provisions for average agricultural tariffs, economic welfare, and market access under the Doha negotiations. The authors conclude that highest-tariff rules are likely to seriously underestimate the impacts on average tariffs, and that treating even 2 percent of tariff lines as sensitive is likely to have a sharply adverse impact on economic welfare. The impacts on market access are also adverse, but much smaller, perhaps reflecting the mercantilist focus of the negotiating process.Free Trade,International Trade and Trade Rules,Markets and Market Access,Debt Markets,Trade Policy

On Policies for Single-leg Revenue Management with Limited Demand Information

In this paper we study the single-item revenue management problem, with no information given about the demand trajectory over time. When the item is sold through accepting/rejecting different fare classes, Ball and Queyranne (2009) have established the tight competitive ratio for this problem using booking limit policies, which raise the acceptance threshold as the remaining inventory dwindles. However, when the item is sold through dynamic pricing instead, there is the additional challenge that offering a low price may entice high-paying customers to substitute down. We show that despite this challenge, the same competitive ratio can still be achieved using a randomized dynamic pricing policy. Our policy incorporates the price-skimming technique from Eren and Maglaras (2010), but importantly we show how the randomized price distribution should be stochastically-increased as the remaining inventory dwindles. A key technical ingredient in our policy is a new "valuation tracking" subroutine, which tracks the possible values for the optimum, and follows the most "inventory-conservative" control which maintains the desired competitive ratio. Finally, we demonstrate the empirical effectiveness of our policy in simulations, where its average-case performance surpasses all naive modifications of the existing policies

Usefulness and Usability of a Personal Health Record and Survivorship Care Plan for Colorectal Cancer Survivors: Survey Study

Background: As a result of improvements in cancer screening, treatment, and supportive care, nearly two-thirds of individuals diagnosed with colorectal cancer (CRC) live for 5 years after diagnosis. An ever-increasing population of CRC survivors creates a need for effective survivorship care to help manage and mitigate the impact of CRC and its treatment. Personal health records (PHRs) and survivorship care plans provide a means of supporting the long-term care of cancer survivors. Objective: The purpose of this study is to characterize the usefulness of a CRC PHR and survivorship care plan and to describe the usability of these technologies in a population of CRC survivors. To our knowledge, this is the first study to assess a PHR and survivorship care plan specifically targeting CRC survivors. Methods: Twenty-two patients with CRC were recruited from surgery clinics of an academic medical center and Veterans Affairs hospital in Indianapolis and provided access to an online Colorectal Cancer Survivor’s Personal Health Record (CRCS-PHR). Survey data were collected to characterize the usefulness of the CRCS-PHR and describe its usability in a population of CRC survivors. CRC survivors were surveyed 6 months after being provided online access. Means and proportions were used to describe the usefulness and ease of using the CRC website. Open-ended questions were qualitatively coded using the constant comparative method. Results: CRC survivors perceived features related to their health care (ie, summary of cancer treatment history, follow-up care schedule, description of side effects, and list of community resources) to be more useful than communication features (ie, creating online relationships with family members or caregivers, communicating with doctor, and secure messages). CRC survivors typically described utilizing traditional channels (eg, via telephone or in person) to communicate with their health care provider. Participants had overall positive perceptions with respect to ease of use and overall satisfaction. Major challenges experienced by participants included barriers to system log-in, lack of computer literacy or experience, and difficulty entering their patient information. Conclusions: For CRC, survivors may find the greater value in a PHR’s medical content than the communication functions, which they have available elsewhere. These findings regarding the usefulness and usability of a PHR for the management of CRC survivorship provide valuable insights into how best to tailor these technologies to patients’ needs. These findings can inform future design and development of PHRs for purposes of both cancer and chronic disease management

Algebraic Properties of Generalized Graph Laplacians: Resistor Networks, Critical Groups, and Homological Algebra

We propose an algebraic framework for generalized graph Laplacians which unifies the study of resistor networks, the critical group, and the eigenvalues of the Laplacian and adjacency matrices. Given a graph with boundary $G$ together with a generalized Laplacian $L$ with entries in a commutative ring $R$, we define a generalized critical group $\Upsilon_R(G,L)$. We relate $\Upsilon_R(G,L)$ to spaces of harmonic functions on the network using the Hom, Tor, and Ext functors of homological algebra. We study how these algebraic objects transform under combinatorial operations on the network $(G,L)$, including harmonic morphisms, layer-stripping, duality, and symmetry. In particular, we use layer-stripping operations from the theory of resistor networks to systematize discrete harmonic continuation. This leads to an algebraic characterization of the graphs with boundary that can be completely layer-stripped, an algorithm for simplifying computation of $\Upsilon_R(G,L)$, and upper bounds for the number of invariant factors in the critical group and the multiplicity of Laplacian eigenvalues in terms of geometric quantities.Comment: 73 pages, 27 figures. This revised version submitted to SIDMA on Jan. 9 201