Twenty questions with noise: Bayes optimal policies for entropy loss

We consider the problem of twenty questions with noisy answers, in which we seek to find a target by repeatedly choosing a set, asking an oracle whether the target lies in this set, and obtaining an answer corrupted by noise. Starting with a prior distribution on the target's location, we seek to minimize the expected entropy of the posterior distribution. We formulate this problem as a dynamic program and show that any policy optimizing the one-step expected reduction in entropy is also optimal over the full horizon. Two such Bayes optimal policies are presented: one generalizes the probabilistic bisection policy due to Horstein and the other asks a deterministic set of questions. We study the structural properties of the latter, and illustrate its use in a computer vision application.

Is dosing of therapeutic immunoglobulins optimal? A review of a three-decade long debate in europe.

The consumption of immunoglobulins (Ig) is increasing due to better recognition of antibody deficiencies, an aging population, and new indications. This review aims to examine the various dosing regimens and research developments in the established and in some of the relevant off-label indications in Europe. The background to the current regulatory settings in Europe is provided as a backdrop for the latest developments in primary and secondary immunodeficiencies and in immunomodulatory indications. In these heterogeneous areas, clinical trials encompassing different routes of administration, varying intervals, and infusion rates are paving the way toward more individualized therapy regimens. In primary antibody deficiencies, adjustments in dosing and intervals will depend on the clinical presentation, effective IgG trough levels and IgG metabolism. Ideally, individual pharmacokinetic profiles in conjunction with the clinical phenotype could lead to highly tailored treatment. In practice, incremental dosage increases are necessary to titrate the optimal dose for more severely ill patients. Higher intravenous doses in these patients also have beneficial immunomodulatory effects beyond mere IgG replacement. Better understanding of the pharmacokinetics of Ig therapy is leading to a move away from simplistic "per kg" dosing. Defective antibody production is common in many secondary immunodeficiencies irrespective of whether the causative factor was lymphoid malignancies (established indications), certain autoimmune disorders, immunosuppressive agents, or biologics. This antibody failure, as shown by test immunization, may be amenable to treatment with replacement Ig therapy. In certain immunomodulatory settings [e.g., idiopathic thrombocytopenic purpura (ITP)], selection of patients for Ig therapy may be enhanced by relevant biomarkers in order to exclude non-responders and thus obtain higher response rates. In this review, the developments in dosing of therapeutic immunoglobulins have been limited to high and some medium priority indications such as ITP, Kawasaki' disease, Guillain-Barré syndrome, chronic inflammatory demyelinating polyradiculoneuropathy, myasthenia gravis, multifocal motor neuropathy, fetal alloimmune thrombocytopenia, fetal hemolytic anemia, and dermatological diseases.

Defence on demand: mechanisms behind optimal defence patterns

Background The optimal defence hypothesis (ODH) predicts that tissues that contribute most to a plant's fitness and have the highest probability of being attacked will be the parts best defended against biotic threats, including herbivores. In general, young sink tissues and reproductive structures show stronger induced defence responses after attack from pathogens and herbivores and contain higher basal levels of specialized defensive metabolites than other plant parts. However, the underlying physiological mechanisms responsible for these developmentally regulated defence patterns remain unknown. Scope This review summarizes current knowledge about optimal defence patterns in above- and below-ground plant tissues, including information on basal and induced defence metabolite accumulation, defensive structures and their regulation by jasmonic acid (JA). Physiological regulations underlying developmental differences of tissues with contrasting defence patterns are highlighted, with a special focus on the role of classical plant growth hormones, including auxins, cytokinins, gibberellins and brassinosteroids, and their interactions with the JA pathway. By synthesizing recent findings about the dual roles of these growth hormones in plant development and defence responses, this review aims to provide a framework for new discoveries on the molecular basis of patterns predicted by the ODH. Conclusions Almost four decades after its formulation, we are just beginning to understand the underlying molecular mechanisms responsible for the patterns of defence allocation predicted by the ODH. A requirement for future advances will be to understand how developmental and defence processes are integrated.

Optimal Confidence Bands for Shape-Restricted Curves

Let Y be a stochastic process on [0,1] satisfying dY(t)=n 1/2 f(t)dt+dW(t) , where n≥1 is a given scale parameter (`sample size'), W is standard Brownian motion and f is an unknown function. Utilizing suitable multiscale tests, we construct confidence bands for f with guaranteed given coverage probability, assuming that f is isotonic or convex. These confidence bands are computationally feasible and shown to be asymptotically sharp optimal in an appropriate sense.

Combinations of dexmedetomidine and alfaxalone with butorphanol in cats: application of an innovative stepwise optimisation method to identify optimal clinical doses for intramuscular anaesthesia

OBJECTIVES The aim of this study was to optimise dexmedetomidine and alfaxalone dosing, for intramuscular administration with butorphanol, to perform minor surgeries in cats. METHODS Initially, cats were assigned to one of five groups, each composed of six animals and receiving, in addition to 0.3 mg/kg butorphanol intramuscularly, one of the following: (A) 0.005 mg/kg dexmedetomidine, 2 mg/kg alfaxalone; (B) 0.008 mg/kg dexmedetomidine, 1.5 mg/kg alfaxalone; (C) 0.012 mg/kg dexmedetomidine, 1 mg/kg alfaxalone; (D) 0.005 mg/kg dexmedetomidine, 1 mg/kg alfaxalone; and (E) 0.012 mg/kg dexmedetomidine, 2 mg/kg alfaxalone. Thereafter, a modified 'direct search' method, conducted in a stepwise manner, was used to optimise drug dosing. The quality of anaesthesia was evaluated on the basis of composite scores (one for anaesthesia and one for recovery), visual analogue scales and the propofol requirement to suppress spontaneous movements. The medians or means of these variables were used to rank the treatments; 'unsatisfactory' and 'promising' combinations were identified to calculate, through the equation first described by Berenbaum in 1990, new dexmedetomidine and alfaxalone doses to be tested in the next step. At each step, five combinations (one new plus the best previous four) were tested. RESULTS None of the tested combinations resulted in adverse effects. Four steps and 120 animals were necessary to identify the optimal drug combination (0.014 mg/kg dexmedetomidine, 2.5 mg/kg alfaxalone and 0.3 mg/kg butorphanol). CONCLUSIONS AND RELEVANCE The investigated drug mixture, at the doses found with the optimisation method, is suitable for cats undergoing minor clinical procedures.

Percutaneous screw fixation of the iliosacral joint: optimal screw pathways are frequently not completely intraosseous

INTRODUCTION In iliosacral screw fixation, the dimensions of solely intraosseous (secure) pathways, perpendicular to the ilio-sacral articulation (optimal) with corresponding entry (EP) and aiming points (AP) on lateral fluoroscopic projections, and the factors (demographic, anatomic) influencing these have not yet been described. METHODS In 100 CTs of normal pelvises, the height and width of the secure and optimal pathways were measured on axial and coronal views bilaterally (total measurements: n=200). Corresponding EP and AP were defined as either the location of the screw head or tip at the crossing of lateral innominate bones' cortices (EP) and sacral midlines (AP) within the centre of the pathway, respectively. EP and AP were transferred to the sagittal pelvic view using a coordinate system with the zero-point in the centre of the posterior cortex of the S1 vertebral body (x-axis parallel to upper S1 endplate). Distances are expressed in relation to the anteroposterior distance of the S1 upper endplate (in %). The influence of demographic (age, gender, side) and/or anatomic (PIA=pelvic incidence angle; TCA=transversal curvature angle, PID-Index=pelvic incidence distance-index; USW=unilateral sacral width-index) parameters on pathway dimensions and positions of EP and AP were assessed (multivariate analysis). RESULTS The width, height or both factors of the pathways were at least 7mm or more in 32% and 53% or 20%, respectively. The EP was on average 14±24% behind the centre of the posterior S1 cortex and 41±14% below it. The AP was on average 53±7% in the front of the centre of the posterior S1 cortex and 11±7% above it. PIA influenced the width, TCA, PID-Index the height of the pathways. PIA, PID-Index, and USW-Index significantly influenced EP and AP. Age, gender, and TCA significantly influenced EP. CONCLUSION Secure and optimal placement of screws of at least 7mm in diameter will be unfeasible in the majority of patients. Thoughtful preoperative planning of screw placement on CT scans is advisable to identify secure pathways with an optimal direction. For this purpose, the presented methodology of determining and transferring EPs and APs of corresponding pathways to the sagittal pelvic view using a coordinate system may be useful.

Hamlet's Mobility: The Reception of Shakespeare's Tragedy in US-American and Canadian Narrative Fiction

This essay presents a comprehensive study of how Hamlet figures in North American fiction. Gabriele Rippl takes her cue from Stephen Greenblatt’s notion of Shakespeare’s ‘theatrical mobility’ (Greenblatt, Cultural Mobility. Cambridge University Press, 2010). This initial mobility, based on the playwright’s own borrowings, appears to facilitate, or even instigate further migrations. Rippl proceeds to give an overview of adaptations of Shakespeare’s Hamlet in the USA and Canada, thus providing an insight into the historical and cultural uses to which the play has been put by authors such as John Updike or Margaret Atwood. Phenomena such as the ‘republicanization’ of Shakespeare (James Fenimore Cooper), or his appropriation for a feminist counter-discourse in Canada circumscribe a space for the negotiation of cultural and political identities.

Differentiating the Multipoint Expected Improvement for Optimal Batch Design

This work deals with parallel optimization of expensive objective functions which are modelled as sample realizations of Gaussian processes. The study is formalized as a Bayesian optimization problem, or continuous multi-armed bandit problem, where a batch of q > 0 arms is pulled in parallel at each iteration. Several algorithms have been developed for choosing batches by trading off exploitation and exploration. As of today, the maximum Expected Improvement (EI) and Upper Confidence Bound (UCB) selection rules appear as the most prominent approaches for batch selection. Here, we build upon recent work on the multipoint Expected Improvement criterion, for which an analytic expansion relying on Tallis’ formula was recently established. The computational burden of this selection rule being still an issue in application, we derive a closed-form expression for the gradient of the multipoint Expected Improvement, which aims at facilitating its maximization using gradient-based ascent algorithms. Substantial computational savings are shown in application. In addition, our algorithms are tested numerically and compared to state-of-the-art UCB-based batchsequential algorithms. Combining starting designs relying on UCB with gradient-based EI local optimization finally appears as a sound option for batch design in distributed Gaussian Process optimization.