Sensitivity of the stationary distribution vector for an ergodic Markov chain

AbstractStationary distribution vectors p∞ for Markov chains with associated transition matrices T are important in the analysis of many models in the mathematical sciences, such as queuing networks, input-output economic models, and compartmental tracer analysis models. The purpose of this paper is to provide insight into the sensitivity of p∞ to perturbations in the transition probabilities of T and to understand some of the difficulties in computing an accurate p∞. The group inverse A# of I − T is shown to be of fundamental importance in understanding sensitivity or conditioning of p∞. The main result shows that if there is a state that is accessible from every other state and the corresponding column of T has no small off-diagonal elements, then p∞ cannot be sensitive to small perturbations in T. Ecological examples are given. A new algorithm for calculating A# is described

Biting into the Genome to Phenome Map: Developmental Genetic Modularity of Cichlid Fish Dentitions

Within vertebrates, teleost fishes provide a rich evolutionary context for studying the mechanisms of dental divergence because of the numerous axes along which their teeth have diverged phenotypically and presumably developmentally. Using both a review of teleost in situ hybridization and de novo transcriptome sequencing in a cichlid fish, we examined whether 341 gene homologs thought to play a role in developing mice teeth are expressed in the tooth-bearing jaws of teleosts. The similarities and putative differences in gene expression documented between the two most commonly used models, zebrafish and cichlids, highlight what can be learned from using a greater diversity of teleost model systems in studies of tooth development. Both types of gene expression analysis also provide substantial evidence for conservation of tooth gene expression from teleosts to mammals as well as between initial and replacement teeth. Additionally, we found that the cichlid oral and pharyngeal jaws share expression for a large percentage of genes that influence tooth development. Our transcriptome analyses also suggest sub-functionalization between gene paralogs expressed in teeth and paralogs expressed in other structures is likely a common pattern across teleost diversity. Teleost dentitions will continue to provide a potent system in which to examine the importance of both gene duplication as well as the conservation of gene expression for phenotypic diversification

The influence of anatomy app use on chiropractic students’ learning outcomes: a randomised controlled trial

Background: Anatomy apps supplement traditional learning; however, it is unknown if their use can improve students' outcome. The present study examined whether the use of anatomy apps improved student performance on a neuroanatomy assessment. Methods: Second-year anatomy students, enrolled in a Bachelor of Science with Chiropractic Major program, were randomly allocated to experimental and control groups in July 2015. Students completed the Self-Directed Learning Readiness Scale (SDLRS). The experimental group had access to iPads with four anatomy apps for three weekly classes (1.5 h each). One week after the last class, students were assessed by an online 30-question neuroanatomy test. Linear regression was used to examine the association between test scores and app use, gender, previous anatomy unit score and SDLRS scores. Students' views on apps were collected by focus group discussion immediately after the test. Results: Completed questionnaires were obtained from n = 25 control and n = 25 experimental students. There was no association between app use and neuroanatomy assessment score (B = 1.75, 95 % CI: -0.340-3.840, p = 0.099). Only previous anatomy unit score (B = 0.348, 95 % CI: 0.214-0.483, p < 0.001) affected neuroanatomy assessment scores. Students favored apps with clinical images and features including identification pins, sliding bars and rotatable 3D images. Conclusions: App use did not enhance learning outcomes in a second-year anatomy unit

Synchronizing Automata on Quasi Eulerian Digraph

In 1964 \v{C}ern\'{y} conjectured that each $n$-state synchronizing automaton posesses a reset word of length at most $(n-1)^2$. From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in $n$. Thus the main problem here is to prove quadratic (in $n$) upper bounds. Since 1964, this problem has been solved for few special classes of \sa. One of this result is due to Kari \cite{Ka03} for automata with Eulerian digraphs. In this paper we introduce a new approach to prove quadratic upper bounds and explain it in terms of Markov chains and Perron-Frobenius theories. Using this approach we obtain a quadratic upper bound for a generalization of Eulerian automata.Comment: 8 pages, 1 figur

Neutrino masses in the Lepton Number Violating MSSM

We consider the most general supersymmetric model with minimal particle content and an additional discrete Z_3 symmetry (instead of R-parity), which allows lepton number violating terms and results in non-zero Majorana neutrino masses. We investigate whether the currently measured values for lepton masses and mixing can be reproduced. We set up a framework in which Lagrangian parameters can be initialised without recourse to assumptions concerning trilinear or bilinear superpotential terms, CP-conservation or intergenerational mixing and analyse in detail the one loop corrections to the neutrino masses. We present scenarios in which the experimental data are reproduced and show the effect varying lepton number violating couplings has on the predicted atmospheric and solar mass^2 differences. We find that with bilinear lepton number violating couplings in the superpotential of the order 1 MeV the atmospheric mass scale can be reproduced. Certain trilinear superpotential couplings, usually, of the order of the electron Yukawa coupling can give rise to either atmospheric or solar mass scales and bilinear supersymmetry breaking terms of the order 0.1 GeV^2 can set the solar mass scale. Further details of our calculation, Lagrangian, Feynman rules and relevant generic loop diagrams, are presented in three Appendices.Comment: 48 pages, 7 figures, v2 references added, typos corrected, published versio

Association of delays in surgery for melanoma with insurance type

IMPORTANCE: Timely receipt of treatment for cancer is an important aspect of health care quality. It is unknown how delays of surgery for melanoma vary by insurance type. OBJECTIVE: To analyze factors associated with delays between diagnosis and surgery for melanoma in patients with Medicare, Medicaid, or private insurance. DESIGN, SETTING, AND PARTICIPANTS: Retrospective cohort study of patients who received a diagnosis of melanoma between 2004 and 2011 in North Carolina using data from the North Carolina Cancer Registry linked to administrative claims from Medicare, Medicaid, and private insurance. Inclusion criteria were incident patients with a diagnosis of melanoma stage 0 to III and with continuous insurance enrollment from at least 1 month prior to the month of diagnosis to 12 months after diagnosis of melanoma. MAIN OUTCOMES AND MEASURES: Surgical delay, defined as definitive surgical excision occurring more than 6 weeks after melanoma diagnosis. Generalized linear models with log link, Poisson distributions, and robust standard errors were used to estimate adjusted risk ratios (RRs) to model risk of delay in definitive surgery. RESULTS: A total of 7629 patients were included (4210 [55%] female; mean [SD] age, 64 [15] years), 48% (n = 3631) Medicare, 48% (n = 3667) privately insured, and 4% (n = 331) Medicaid patients. Privately insured patients were least likely to experience a delay in definitive surgery, followed by Medicare and Medicaid patients (519 [14%], 609 [17%], and 79 [24%], respectively; P < .001). After demographic adjustment, the risk of surgical delay was significantly increased in patients with Medicaid compared with private insurance (RR, 1.36; 95% CI, 1.09-1.70). Delays were more likely in nonwhite patients (RR, 1.38; 95% CI, 1.02-1.87). Surgical delays were less likely if the physician performing the surgery (RR, 0.82; 95% CI, 0.72-0.93) or the diagnosing clinician (RR, 0.81; 95% CI, 0.71-0.93) was a dermatologist as compared with a nondermatologist. CONCLUSION AND RELEVANCE: Surgical treatment delays were common but were less prevalent in patients diagnosed or surgically treated by a dermatologist. Medicaid patients experienced the most surgical delays. A reduction in delays in melanoma surgery could be achieved through better access to specialty care and cross-disciplinary coordination

Dynamics of Enceladus and Dione inside the 2:1 Mean-Motion Resonance under Tidal Dissipation

In a previous work (Callegari and Yokoyama 2007, Celest. Mech. Dyn. Astr. vol. 98), the main features of the motion of the pair Enceladus-Dione were analyzed in the frozen regime, i.e., without considering the tidal evolution. Here, the results of a great deal of numerical simulations of a pair of satellites similar to Enceladus and Dione crossing the 2:1 mean-motion resonance are shown. The resonance crossing is modeled with a linear tidal theory, considering a two-degrees-of-freedom model written in the framework of the general three-body planar problem. The main regimes of motion of the system during the passage through resonance are studied in detail. We discuss our results comparing them with classical scenarios of tidal evolution of the system. We show new scenarios of evolution of the Enceladus-Dione system through resonance not shown in previous approaches of the problem.Comment: 36 pages, 12 figures. Accepted in Celestial Mechanics and Dynamical Astronom

On the speed of convergence to stationarity of the Erlang loss system

We consider the Erlang loss system, characterized by $N$ servers, Poisson arrivals and exponential service times, and allow the arrival rate to be a function of $N.$ We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and display some bounds for the total variation distance between the time-dependent and stationary distributions. We also pay attention to time-dependent rates

(n,p) Studies at 120 MeV

This research was sponsored by the National Science Foundation Grant NSF PHY 87-1440

Itinerant Ferromagnetism in the Periodic Anderson Model

We introduce a novel mechanism for itinerant ferromagnetism, based on a simple two-band model. The model includes an uncorrelated and dispersive band hybridized with a second band which is narrow and correlated. The simplest Hamiltonian containing these ingredients is the Periodic Anderson Model (PAM). Using quantum Monte Carlo and analytical methods, we show that the PAM and an extension of it contain the new mechanism and exhibit a non-saturated ferromagnetic ground state in the intermediate valence regime. We propose that the mechanism, which does not assume an intra atomic Hund's coupling, is present in both the iron group and in some f electron compounds like Ce(Rh_{1-x} Ru_x)_3 B_2, La_x Ce_{1-x} Rh_3 B_2 and the uranium monochalcogenides US, USe, and UTe