Laws relating runs, long runs, and steps in gambler's ruin, with persistence in two strata

Define a certain gambler's ruin process \mathbf{X}_{j}, \mbox{ \ }j\ge 0, such that the increments $\varepsilon_{j}:=\mathbf{X}_{j}-\mathbf{X}_{j-1}$ take values $\pm1$ and satisfy $P(\varepsilon_{j+1}=1|\varepsilon_{j}=1, |\mathbf{X}_{j}|=k)=P(\varepsilon_{j+1}=-1|\varepsilon_{j}=-1,|\mathbf{X}_{j}|=k)=a_k$, all $j\ge 1$, where $a_k=a$ if $0\le k\le f-1$, and $a_k=b$ if $f\le k<N$. Here $0<a, b <1$ denote persistence parameters and $f ,N\in \mathbb{N}$ with $f<N$. The process starts at $\mathbf{X}_0=m\in (-N,N)$ and terminates when $|\mathbf{X}_j|=N$. Denote by ${\cal R}'_N$, ${\cal U}'_N$, and ${\cal L}'_N$, respectively, the numbers of runs, long runs, and steps in the meander portion of the gambler's ruin process. Define $X_N:=\left ({\cal L}'_N-\frac{1-a-b}{(1-a)(1-b)}{\cal R}'_N-\frac{1}{(1-a)(1-b)}{\cal U}'_N\right )/N$ and let $f\sim\eta N$ for some $0<\eta <1$. We show $\lim_{N\to\infty} E\{e^{itX_N}\}=\hat{\varphi}(t)$ exists in an explicit form. We obtain a companion theorem for the last visit portion of the gambler's ruin.Comment: Presented at 8th International Conference on Lattice Path Combinatorics, Cal Poly Pomona, Aug., 2015. The 2nd version has been streamlined, with references added, including reference to a companion document with details of calculations via Mathematica. The 3rd version has 2 new figures and improved presentatio

Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials

Relationship between diameter asymmetry and blood flow in the pre-communicating (A1) segment of the anterior cerebral arteries

BACKGROUND: Asymmetry in diameter between pre-communicating (A1) segments of the anterior cerebral arteries is related to anterior communicating artery aneurysm formation. Diameter asymmetry definitions vary and have not been related to blood flow measurements using the same imaging modality. We aimed to evaluate the relationship between A1-diameter asymmetry and blood flow asymmetry and to define a hemodynamically significant cut-off value for A1-diameter asymmetry. We assessed sex differences between different groups of A1-asymmetry. MATERIALS AND METHODS: 3-Tesla time-of-flight MRA and 4D-phase-contrast MRI were performed in 122 healthy participants. Diameter and blood flow measurements were performed halfway in both A1-segments. Participants were subdivided based on A1-diameter asymmetry: ≤10% (symmetric); 11-20%; 21-30%; 31-40%; and >40% (increasing asymmetry) groups. We studied the relationship between A1-diameter asymmetry and corresponding flow asymmetry (scatterplot and correlation). A hemodynamic-based cutoff value for A1-asymmetry was determined by comparing dominant A1 blood flow in the asymmetry groups to the mean blood flow of the symmetric A1-group (linear mixed-effects model). Sex-related differences in A1-diameter, blood flow and asymmetry were assessed with t-tests. RESULTS: A1-diameter asymmetry was linearly related to blood flow asymmetry between dominant and non-dominant sides. A1-diameter asymmetry >30% yielded statistically significant increased blood flow in the dominant A1 compared to symmetric A1s. Men had statistically significant larger A1-diameters, higher blood flow and a similar degree of A1-diameter asymmetry compared to women. CONCLUSION: A1-diameter asymmetry is linearly related to blood flow asymmetry. A >30% A1-asymmetry can be used as hemodynamically significant cut-off value. There were no sex-related differences in A1-diameter asymmetry

Staying at work with back pain: patients' experiences of work-related help received from GPs and other clinicians. A qualitative study

<p>Abstract</p> <p>Background</p> <p>Low back pain commonly affects work ability, but little is known about the work-related help and advice that patients receive from GPs and other clinicians. The purpose of this study was to explore the experiences of employed people with back pain and their perceptions of how GPs and other clinicians have addressed their work difficulties.</p> <p>Methods</p> <p>A qualitative approach with thematic analysis was used. Individual interviews were carried out with twenty-five employed patients who had been referred for back pain rehabilitation. All had expressed concern about their ability to work due to low back pain.</p> <p>Results</p> <p>The perception of the participants was that GPs and other clinicians had provided little or no work-focused guidance and support and rarely communicated with employers. Sickness certification was the main method that GPs used to manage participants' work problems. Few had received assistance with temporary modifications and many participants had remained in work despite the advice they had received. There was little expectation of what GPs and other clinicians could offer to address work issues.</p> <p>Conclusions</p> <p>These findings question the ability of GPs and other clinicians to provide work-focused support and advice to patients with low back pain. Future research is recommended to explore how the workplace problems of patients can be best addressed by health professionals.</p

Hands-on time during cardiopulmonary resuscitation is affected by the process of teambuilding: a prospective randomised simulator-based trial

BACKGROUND: Cardiac arrests are handled by teams rather than by individual health-care workers. Recent investigations demonstrate that adherence to CPR guidelines can be less than optimal, that deviations from treatment algorithms are associated with lower survival rates, and that deficits in performance are associated with shortcomings in the process of team-building. The aim of this study was to explore and quantify the effects of ad-hoc team-building on the adherence to the algorithms of CPR among two types of physicians that play an important role as first responders during CPR: general practitioners and hospital physicians. METHODS: To unmask team-building this prospective randomised study compared the performance of preformed teams, i.e. teams that had undergone their process of team-building prior to the onset of a cardiac arrest, with that of teams that had to form ad-hoc during the cardiac arrest. 50 teams consisting of three general practitioners each and 50 teams consisting of three hospital physicians each, were randomised to two different versions of a simulated witnessed cardiac arrest: the arrest occurred either in the presence of only one physician while the remaining two physicians were summoned to help ("ad-hoc"), or it occurred in the presence of all three physicians ("preformed"). All scenarios were videotaped and performance was analysed post-hoc by two independent observers. RESULTS: Compared to preformed teams, ad-hoc forming teams had less hands-on time during the first 180 seconds of the arrest (93 +/- 37 vs. 124 +/- 33 sec, P > 0.0001), delayed their first defibrillation (67 +/- 42 vs. 107 +/- 46 sec, P > 0.0001), and made less leadership statements (15 +/- 5 vs. 21 +/- 6, P > 0.0001). CONCLUSION: Hands-on time and time to defibrillation, two performance markers of CPR with a proven relevance for medical outcome, are negatively affected by shortcomings in the process of ad-hoc team-building and particularly deficits in leadership. Team-building has thus to be regarded as an additional task imposed on teams forming ad-hoc during CPR. All physicians should be aware that early structuring of the own team is a prerequisite for timely and effective execution of CPR

Financial and monetary policy responses to oil price shocks: evidence from oil-importing and oil-exporting countries

In this study, we investigate the financial and monetary policy responses to oil price shocks using a Structural VAR framework. We distinguish between net oil-importing and net oil-exporting countries. Since the 80s, a significant number of empirical studies have been published investigating the effect of oil prices on macroeconomic and financial variables. Most of these studies though, do not make a distinction between oil-importing and oil-exporting economies. Overall, our results indicate that the level of inflation in both net oil-exporting and net oil-importing countries is significantly affected by oil price innovations. Furthermore, we find that the response of interest rates to an oil price shock depends heavily on the monetary policy regime of each country. Finally, stock markets operating in net oil-importing countries exhibit a negative response to increased oil prices. The reverse is true for the stock market of the net oil-exporting countries. We find evidence that the magnitude of stock market responses to oil price shocks is higher for the newly established and/or less liquid stock market