Rare-event analysis of mixed Poisson random variables, and applications in staffing

A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to be significantly overdispersed. This motivates that in this paper we consider a mixed Poisson arrival process with arrival rates that are resampled every $N^{a}$ time units, where $a> 0$ and $N$ a scaling parameter. In the first part of the paper we analyse the asymptotic tail distribution of this doubly stochastic arrival process. That is, for large $N$ and i.i.d. arrival rates $X_1, \dots, X_N$, we focus on the evaluation of $P_N(A)$, the probability that the scaled number of arrivals exceeds $NA$. Relying on elementary techniques, we derive the exact asymptotics of $P_N(A)$: For $a 3$ we identify (in closed-form) a function $\tilde{P}_N(A)$ such that $P_N(A) / P_N(A)$ tends to $1$ as $N \to \infty$. For $a \in [\frac{1}{3},\frac{1}{2})$ and $a\in [2, 3)$ we find a partial solution in terms of an asymptotic lower bound. For the special case that the $X_i$s are gamma distributed, we establish the exact asymptotics across all $a> 0$. In addition, we set up an asymptotically efficient importance sampling procedure that produces reliable estimates at low computational cost. The second part of the paper considers an infinite-server queue assumed to be fed by such a mixed Poisson arrival process. Applying a scaling similar to the one in the definition of $P_N(A)$, we focus on the asymptotics of the probability that the number of clients in the system exceeds $NA$. The resulting approximations can be useful in the context of staffing. Our numerical experiments show that, astoundingly, the required staffing level can actually decrease when service times are more variable

Vaccine manufacturing capacity expansion – An approach to meet global needs based on Covid-19 learnings

COVID-19 has spurred the deployment of large sums of capital and major multilateral involvement in building vaccine manufacturing capacity in LMICs; however, manufacturing facilities will not be functional or sustainable without a skilled workforce to operate them. The Bill & Melinda Gates Foundation has developed a three-pronged approach to (1) Understand manufacturer needs; (2) Train via innovative and accessible materials; and (3) Build a sustainable ecosystem through linked initiatives. Please click Download on the upper right corner to see the full abstract. Please click Additional File below for the presentation

Countertransference reactions to psychotherapy group work with HIV positive children

Abstract Powerful and diverse countertransference reactions in psychotherapy group work with HIV positive children can be understood to indicate a site of mourning in the life of the group. Data from six interviews with five individuals conducting broadly psychodynamic group work with HIV positive children was analysed according to Thematic Content Analysis. The countertransference responses of the participants are understood as communications of the group unconscious, as well as expressions of the participants’ own unresolved unconscious difficulties. Working with HIV positive children confronts the participants with mortality and activates their earliest losses. A sense of strangeness and displacement, denial, idealisation, feelings of persecution, fantasies of rescue, rage, despair and hopelessness emerge in the countertransference and can be considered indicative of defences against mourning. These defences alternate with an engagement with the work of mourning and are represented in the countertransference as the relinquishment of omnipotence, awareness of fusion, containment, the recognition of the child’s resilience and uniqueness and the promotion of the child’s autonomy and expression. These findings may facilitate containment for therapists working with HIV positive children by offering an explanation of powerful and diverse countertransference responses as indicating a site of mourning, thereby promoting increased receptivity to unexpressed grief in therapy with these children

'Madame Royal'. Eine kritisch-diskursanalytische Untersuchung zur printmedialen Repräsentation von Polit-Figuren im medialen Diskurs am Beispiel des französischen Präsidentschaftswahlkampfes

The article illustrates 'nomination” as a special form of reference, containing an evaluative perspective of the language user on extra-linguistic entities (cf. REISIGL 2003. In the media discourse nomination referring to people appears as classification or as anthroponyms and can be instrumentalized. The corpus consists of the nominations of the candidates to the presidential election in France 2007, the nominations contained in the daily press of the 3 months preceding the election. In the field of nomination as anthroponyms it could be shown that in the media discourse the use of the family name alone and the use of both first name and family name can be considered as neutral, while the use of a nickname or the first name alone establishes a relation of inferiority, a phenomenon that could be observed only in the case of the female candidate Ségolène Royal. Nomination as classification of the other hand established the following representations: The hyper real figure of Nicolas Sarkozy was represented as an authoritarian, strong, experienced politician with a problematic character and a migration-background. Ségolène Royal was constructed as an emotional woman who is hardly known in the political landscape and has little political experience. François Bayrou was represented as a solid, Christian down-to-earth personality, at the third place behind the other two and Jean Marie Le Pen as extreme right wing and the oldest candidate behind the other three. It could be shown that nominations (as classifications or anthroponyms) construct representations of the candidates which correspond even before the elections to their result

Comorbidity of Arithmetic and Reading Disorder: Basic Number Processing and Calculation in Children With Learning Impairments

The aim of the present study was to investigate the cognitive profiles of primary school children (age 82-133 months) on a battery of basic number processing and calculation tasks. The sample consisted of four groups matched for age and IQ: arithmetic disorder only (AD;n = 20), reading disorder only (RD;n = 40), a comorbid group (n = 27), and an unimpaired control group (n = 40). Multiple 2 (RD vs. No RD) x 2 (AD vs. No AD) factorial ANCOVAs showed that children with RD had selective impairments in counting and number transcoding efficiency. In contrast, children with AD performed poorly in most tasks, including symbolic and nonsymbolic magnitude comparisons, subitizing, number line estimation, number sets, number transcoding accuracy, and calculation. These findings provide further support that AD is characterized by multiple, heterogeneous underlying deficits. In contrast, RD is associated with specific number processing impairments only if tasks require verbal processing. Taken together, the results fully support the assumption of comorbid additivity of AD and RD

Antibiotics for preventing recurrent urinary tract infection: Systematic review and meta-analysis

Recurrent urinary tract infections are a common health problem. The only comprehensive synthesis on antibiotic prophylaxis in the last 15 years has been a guideline-embedded meta-analysis. We conducted a systematic review and meta-analysis of randomized controlled trials published up to October 13, 2020, evaluating patients age ≥12 years with either ≥2 episodes of lower urinary tract infection (UTI) within 6 months or ≥3 in the past year. Placebo or antibiotics were allowed as comparators. Study quality was low. In the 11 placebo-controlled trials, the risk for developing UTI was 85% lower with prophylaxis in comparison with placebo (risk ratio [RR], 0.15; 95% CI, 0.08-0.29). In the 9 head-to-head trials, the efficacy of the antibiotic agents appeared similar: The pooled RR indicated no difference between nitrofurantoin and comparators (RR, 1.01; 95% CI, 0.74-1.37), nor trimethoprim (+/- sulfamethoxazole; RR, 1.34; 95% CI, 0.89-2.03) or norfloxacin and comparators (RR, 1.17; 95% CI, 0.43-1.70). Studies comparing intermittent (postcoital) with continuous strategies revealed intermittent application to be equally effective

Antibiotics for Preventing Recurrent Urinary Tract Infection: Systematic Review and Meta-analysis.

Recurrent urinary tract infections are a common health problem. The only comprehensive synthesis on antibiotic prophylaxis in the last 15 years has been a guideline-embedded meta-analysis. We conducted a systematic review and meta-analysis of randomized controlled trials published up to October 13, 2020, evaluating patients age ≥12 years with either ≥2 episodes of lower urinary tract infection (UTI) within 6 months or ≥3 in the past year. Placebo or antibiotics were allowed as comparators. Study quality was low. In the 11 placebo-controlled trials, the risk for developing UTI was 85% lower with prophylaxis in comparison with placebo (risk ratio [RR], 0.15; 95% CI, 0.08-0.29). In the 9 head-to-head trials, the efficacy of the antibiotic agents appeared similar: The pooled RR indicated no difference between nitrofurantoin and comparators (RR, 1.01; 95% CI, 0.74-1.37), nor trimethoprim (+/- sulfamethoxazole; RR, 1.34; 95% CI, 0.89-2.03) or norfloxacin and comparators (RR, 1.17; 95% CI, 0.43-1.70). Studies comparing intermittent (postcoital) with continuous strategies revealed intermittent application to be equally effective