Applications of BGP-reflection functors: isomorphisms of cluster algebras

Given a symmetrizable generalized Cartan matrix $A$, for any index $k$, one can define an automorphism associated with $A,$ of the field $\mathbf{Q}(u_1, >..., u_n)$ of rational functions of $n$ independent indeterminates $u_1,..., u_n.$ It is an isomorphism between two cluster algebras associated to the matrix $A$ (see section 4 for precise meaning). When $A$ is of finite type, these isomorphisms behave nicely, they are compatible with the BGP-reflection functors of cluster categories defined in [Z1, Z2] if we identify the indecomposable objects in the categories with cluster variables of the corresponding cluster algebras, and they are also compatible with the "truncated simple reflections" defined in [FZ2, FZ3]. Using the construction of preprojective or preinjective modules of hereditary algebras by Dlab-Ringel [DR] and the Coxeter automorphisms (i.e., a product of these isomorphisms), we construct infinitely many cluster variables for cluster algebras of infinite type and all cluster variables for finite types.Comment: revised versio

Using LDGM Codes and Sparse Syndromes to Achieve Digital Signatures

In this paper, we address the problem of achieving efficient code-based digital signatures with small public keys. The solution we propose exploits sparse syndromes and randomly designed low-density generator matrix codes. Based on our evaluations, the proposed scheme is able to outperform existing solutions, permitting to achieve considerable security levels with very small public keys.Comment: 16 pages. The final publication is available at springerlink.co

Responsiveness of the PROMIS and its Concurrent Validity with Other Region- and Condition-specific PROMs in Patients Undergoing Carpal Tunnel Release

Background The Patient-reported Outcome Measurement Information System (PROMIS) continues to be an important universal patient-reported outcomes measure (PROM) in orthopaedic surgery. However, there is concern about the performance of the PROMIS as a general health questionnaire in hand surgery compared with the performance of region- and condition-specific PROMs such as the Michigan Hand Questionnaire (MHQ) and the Boston Carpal Tunnel Questionnaire (BCTQ), respectively. To ensure that PROMIS domains capture patient-reported outcomes to the same degree as region- and condition-specific PROMs do, comparing PROM performance is necessary. Questions/purposes (1) Which PROMs demonstrate high responsiveness among patients undergoing carpal tunnel release (CTR)? (2) Which of the PROMIS domains (Physical Function [PF], Upper Extremity [UE], and Pain Interference [PI]) demonstrate concurrent validity with the HHQ and BCTQ domains? Methods In this prospective study, between November 2014 and October 2016, patients with carpal tunnel syndrome visiting a single surgeon who elected to undergo CTR completed the BCTQ, MHQ, and PROMIS UE, PF, and PI domains at each visit. A total of 101 patients agreed to participate. Of these, 31 patients (31%) did not return for a followup visit at least 6 weeks after CTR and were excluded, leaving a final sample of 70 patients (69%). We compared the PROMIS against region- and condition-specific PROMs in terms of responsiveness and concurrent validity. Responsiveness was determined using Cohen’s d or the effect-size index (ESI). The larger the absolute value of the ESI, the greater the effect size. Using the ESI allows surgeons to better quantify the impact of CTR, with a medium ESI (that is, 0.5) representing a visible clinical change to a careful observer. Concurrent validity was determined using Spearman’s correlation coefficient with correlation strengths categorized as excellent (\u3e 0.7), excellent-good (0.61-0.70), good (0.4-0.6), and poor (\u3c 0.4). Significance was set a priori at p \u3c 0.05. Results Among PROMIS domains, the PI demonstrated the best responsiveness (ESI = 0.74; 95% CI, 0.39-1.08), followed by the UE (ESI = -0.66; 95% CI, -1.00 to -0.31). For the MHQ, the Satisfaction domain had the largest effect size (ESI = -1.48; 95% CI, -1.85 to -1.09), while for the BCTQ, the Symptom Severity domain had the best responsiveness (ESI = 1.54; 95% CI, 1.14-1.91). The PROMIS UE and PI domains demonstrated excellent-good to excellent correlations to the total MHQ and BCTQ–Functional Status scores (preoperative UE to MHQ: ρ = 0.68; PI to MHQ: ρ = 0.74; UE to BCTQ–Functional Status: ρ = 0.74; PI to BCTQ–Functional Status: ρ = 0.67; all p \u3c 0.001), while the PROMIS PF demonstrated poor correlations with the same domains (preoperative PF to MHQ; ρ = 0.33; UE to BCTQ–Functional Status: ρ = 0.39; both p \u3c 0.01). Conclusions The PROMIS UE and PI domains demonstrated slightly worse responsiveness than the MHQ and BCTQ domains that was nonetheless acceptable. The PROMIS PF domain was unresponsive. All three PROMIS domains correlated with the MHQ and BCTQ, but the PROMIS UE and PI domains had notably stronger correlations to the MHQ and BCTQ domains than the PF domain did. We feel that the PROMIS UE and PI can be used to evaluate the clinical outcomes of patients undergoing CTR, while also providing more robust insight into overall health status because they are general PROMs. However, we do not recommend the PROMIS PF for evaluating patients undergoing CTR. Level of Evidence Level II, diagnostic study

The Impact of a Canine-Assisted Reading Program on Readers Needing Extra Practice

Canines can provide emotional support, create a nonjudgmental environment, facilitate positive social interactions, and shape student behavior. This study investigated the impact of a canine-assisted reading program on four second-grade students\u27 reading fluency and attitudes toward reading. Oral reading fluency (ORF) was measured using ORF probes, and students\u27 attitudes toward reading were measured with the Elementary Reading Attitude Survey. Although ORF skills did not improve significantly following the program, students\u27 attitudes toward reading did. Implications regarding innovative strategies for reading fluency programs, including canine-assisted methods, are discussed, with emphasis on the importance of maintaining reading enjoyment among readers needing extra practice

The Evolution of Distorted Rotating Black Holes III: Initial Data

In this paper we study a new family of black hole initial data sets corresponding to distorted ``Kerr'' black holes with moderate rotation parameters, and distorted Schwarzschild black holes with even- and odd-parity radiation. These data sets build on the earlier rotating black holes of Bowen and York and the distorted Brill wave plus black hole data sets. We describe the construction of this large family of rotating black holes. We present a systematic study of important properties of these data sets, such as the size and shape of their apparent horizons, and the maximum amount of radiation that can leave the system during evolution. These data sets should be a very useful starting point for studying the evolution of highly dynamical black holes and can easily be extended to 3D.Comment: 16 page

Spectroscopy of 194^{194}Po

Prompt, in-beam $\gamma$ rays following the reaction $^{170}$Yb + 142 MeV $^{28}$Si were measured at the ATLAS facility using 10 Compton-suppressed Ge detectors and the Fragment Mass Analyzer. Transitions in $^{194}$Po were identified and placed using $\gamma$-ray singles and coincidence data gated on the mass of the evaporation residues. A level spectrum up to J$\approx$10$\hbar$ was established. The structure of $^{194}$Po is more collective than that observed in the heavier polonium isotopes and indicates that the structure has started to evolve towards the more collective nature expected for deformed nuclei.Comment: 8 pages, revtex 3.0, 4 figs. available upon reques