The spectrum of anti-GQ1B antibody syndrome: beyond Miller Fisher syndrome and Bickerstaff brainstem encephalitis.

INTRODUCTION: Since the initial identification of Miller Fisher syndrome (MFS) and Bickerstaff brainstem encephalitis (BBE),significant milestones have been achieved in understanding these diseases.Discoveries of common serum antibodies (IgG anti-GQ1b), antecedent infections, neurophysiological data, andneuroimaging suggested a shared autoimmune pathogenetic mechanism rather than distinct pathogenesis, leadingto the hypothesis that both diseases are part of a unified syndrome, termed "Fisher-Bickerstaff syndrome". The subsequent identification of atypical anti-GQ1b-positive forms expanded the classification to a broader condition known as "Anti-GQ1b-Antibody syndrome". METHODS: An exhaustive literature review was conducted, analyzing a substantial body of research spanning from the initialdescriptions of the syndrome's components to recent developments in diagnostic classification and researchperspectives. RESULTS: Anti-GQ1b syndrome encompasses a continuous spectrum of conditions defined by a common serological profilewith varying degrees of peripheral (PNS) and central nervous system (CNS) involvement. MFS and BBE represent theopposite ends of this spectrum, with MFS primarily affecting the PNS and BBE predominantly involving the CNS.Recently identified atypical forms, such as acute ophthalmoparesis, acute ataxic neuropathy withoutophthalmoparesis, Guillain-Barré syndrome (GBS) with ophthalmoparesis, MFS-GBS and BBE-GBS overlap syndromes,have broadened this spectrum. CONCLUSION: This work aims to provide an extensive, detailed, and updated overview of all aspects of the anti-GQ1b syndromewith the intention of serving as a stepping stone for further shaping thereof. Special attention was given to therecently identified atypical forms, underscoring their significance in redefining the boundaries of the syndrome.

Fishers (Pekania pennanti) are forest structure specialists when resting and generalists when moving: behavior influences resource selection in a northern Rocky Mountain fisher population.

BACKGROUND: Studies of animal habitat selection are important to identify and preserve the resources species depend on, yet often little attention is paid to how habitat needs vary depending on behavioral state. Fishers (Pekania pennanti) are known to be dependent on large, mature trees for resting and denning, but less is known about their habitat use when foraging or moving within a home range. METHODS: We used GPS locations collected during the energetically costly pre-denning season from 12 female fishers to determine fisher habitat selection during two critical behavioral activities: foraging (moving) or resting, with a focus on response to forest structure related to past forest management actions since this is a primary driver of fisher habitat configuration. We characterized behavior based on high-resolution GPS and collar accelerometer data and modeled fisher selection for these two behaviors within a home range (third-order selection). Additionally, we investigated whether fisher use of elements of forest structure or other important environmental characteristics changed as their availability changed, i.e., a functional response, for each behavior type. RESULTS: We found that fishers exhibited specialist selection when resting and generalist selection when moving, with resting habitat characterized by riparian drainages with dense canopy cover and moving habitat primarily influenced by the presence of mesic montane mixed conifer forest. Fishers were more tolerant of forest openings and other early succession elements when moving than resting. CONCLUSIONS: Our results emphasize the importance of considering the differing habitat needs of animals based on their movement behavior when performing habitat selection analyses. We found that resting fishers are more specialist in their habitat needs, while foraging fishers are more generalist and will tolerate greater forest heterogeneity from past disturbance.

Assessing spatiotemporal change in coral reef social-ecological systems.

Coral reef resilience is eroding at multiple spatial scales globally, with broad implications for coastal communities, and is thus a critical challenge for managing marine social-ecological systems (SESs). Many researchers believe that external stressors will cause key coral reefs to die by the end of the 21st century, virtually eliminating essential ecological and societal benefits. Here, we propose the use of resilience-based approaches to understand the dynamics of coral reef SESs and subsequent drivers of coral reef decline. Previous research has demonstrated the effectiveness of these methods, not only for tracking environmental change, but also for providing warning in advance of transitions, possibly allowing time for management interventions. The flexibility and utility of these methods make them ideal for assessing complex systems; however, they have not been used to study aquatic ecosystem dynamics at the global scale. Here, we evaluate these methods for examining spatiotemporal change in coral reef SESs across the global seascape and assess the subsequent impacts on coral reef resilience. We found that while univariate indicators failed to provide clear signals, multivariate resilience-based approaches effectively captured coral reef SES dynamics, unveiling distinctive patterns of variation throughout the global coral reef seascape. Additionally, our findings highlight global spatiotemporal variation, indicating patterns of degraded resilience. This degradation was reflected regionally, particularly in the Pacific Ocean and Indian Ocean SESs. These results underscore the utility of resilience-based approaches in assessing environmental change in SESs, detecting spatiotemporal variation at the global and regional scales, and facilitating more effective monitoring and management of coral reef SESs.

Simultaneous discovery of compounds dominated by either molding kinetics or geographical region of origin for moisture damaged cacao beans using orthogonally applied tile-based fisher ratio analysis of GC×GC-TOFMS data.

Herein, two "orthogonal" characteristics of moisture damaged cacao beans (temporally dependent molding kinetics versus the time-independent geographical region of origin) are simultaneously analyzed in a comprehensive two-dimensional (2D) gas chromatography time-of-flight mass spectrometry (GC×GC-TOFMS) dataset using tile-based Fisher ratio (F-ratio) analysis. Cacao beans from six geographical regions were analyzed once a day for six days following the initiation of moisture damage to trigger the molding process. Thus, there are two "extremes" to the experimental sample class design: six time points for the molding kinetics versus the six geographical regions of origin, resulting in a 6 × 6 element signal array referred to as a composite chemical fingerprint (CCF) for each analyte. Usually, this study would involve initial generation of two separate hit lists using F-ratio analysis, one hit list from inputting the data with the six time point classes, then another hit list from inputting the dataset from the perspective of geographic region of origin. However, analysis of two separate hit lists with the intent to distill them down to one hit list is extremely time-consuming and fraught with shortcomings due to the challenges associated with attempting to match analytes across two hit lists. To address this challenge, tile-based F-ratio analysis is "orthogonally applied" to each analyte CCF to simultaneously determine two F-ratios at the chromatographic 2D location (F-ratiokinetic and F-ratioregion) for each hit, by ranking a single hit list using the higher of the two F-ratios resulting in the discovery of 591 analytes. Further, using a pseudo-null distribution approach, at the 99.9% threshold over 400 analytes were deemed suitable for PCA classification. Using a more stringent 99.999% threshold, over 100 analytes were explored more deeply using PARAFAC to provide a purified mass spectrum.

A unified framework for perceived magnitude and discriminability of sensory stimuli.

The perception of sensory attributes is often quantified through measurements of sensitivity (the ability to detect small stimulus changes), as well as through direct judgments of appearance or intensity. Despite their ubiquity, the relationship between these two measurements remains controversial and unresolved. Here, we propose a framework in which they arise from different aspects of a common representation. Specifically, we assume that judgments of stimulus intensity (e.g., as measured through rating scales) reflect the mean value of an internal representation, and sensitivity reflects a combination of mean value and noise properties, as quantified by the statistical measure of Fisher information. Unique identification of these internal representation properties can be achieved by combining measurements of sensitivity and judgments of intensity. As a central example, we show that Weber's law of perceptual sensitivity can coexist with Stevens' power-law scaling of intensity ratings (for all exponents), when the noise amplitude increases in proportion to the representational mean. We then extend this result beyond the Weber's law range by incorporating a more general and physiology-inspired form of noise and show that the combination of noise properties and sensitivity measurements accurately predicts intensity ratings across a variety of sensory modalities and attributes. Our framework unifies two primary perceptual measurements-thresholds for sensitivity and rating scales for intensity-and provides a neural interpretation for the underlying representation.

On exact randomization-based covariate-adjusted confidence intervals.

Randomization-based inference using the Fisher randomization test allows for the computation of Fisher-exact P-values, making it an attractive option for the analysis of small, randomized experiments with non-normal outcomes. Two common test statistics used to perform Fisher randomization tests are the difference-in-means between the treatment and control groups and the covariate-adjusted version of the difference-in-means using analysis of covariance. Modern computing allows for fast computation of the Fisher-exact P-value, but confidence intervals have typically been obtained by inverting the Fisher randomization test over a range of possible effect sizes. The test inversion procedure is computationally expensive, limiting the usage of randomization-based inference in applied work. A recent paper by Zhu and Liu developed a closed form expression for the randomization-based confidence interval using the difference-in-means statistic. We develop an important extension of Zhu and Liu to obtain a closed form expression for the randomization-based covariate-adjusted confidence interval and give practitioners a sufficiency condition that can be checked using observed data and that guarantees that these confidence intervals have correct coverage. Simulations show that our procedure generates randomization-based covariate-adjusted confidence intervals that are robust to non-normality and that can be calculated in nearly the same time as it takes to calculate the Fisher-exact P-value, thus removing the computational barrier to performing randomization-based inference when adjusting for covariates. We also demonstrate our method on a re-analysis of phase I clinical trial data.

Comparison of scales for the evaluation of aneurysmal subarachnoid haemorrhage: a retrospective cohort study.

BACKGROUND/OBJECTIVES: Aneurysmal subarachnoid haemorrhage (aSAH) is a life-threatening event with major complications. Delayed cerebral infarct (DCI) occurs most frequently 7 days after aSAH and can last for a prolonged period. To determine the most predictive radiological scales in grading subarachnoid or ventricular haemorrhage or both for functional outcome at 3 months in a large aSAH population, we conducted a single-centre retrospective study. METHODS: A 3-year single-centre retrospective cohort study of 230 patients hospitalised for aSAH was analysed. Initial computed tomography (CT) scans in patients hospitalised for aSAH were blindly assessed using eight grading systems: the Fisher grade, modified Fisher grade, Barrow Neurological Institute scale, Hijdra scale, Intraventricular Haemorrhage (IVH) score, Graeb score and LeRoux score. RESULTS: Of 200 patients with aSAH who survived to day 7 and were included for DCI analysis, 39% of cases were complicated with DCI. The Hijdra scale was the best predictor for DCI, with a receiver operating characteristic area under the curve (ROCAUC) of 0.80 (95% confidence interval (CI), 0.74-0.85). The IVH score was the most effective grading system for predicting acute hydrocephalus, with a ROCAUC of 0.85 (95% CI, 0.79-0.89). In multivariate analysis, the Hijdra scale was the best predictor of the occurrence of DCI (hazard ratio, 1.18; 95% CI, 1.10-1.25). CONCLUSIONS: Although these results have yet to be prospectively confirmed, our findings suggest that the Hijdra scale may be a good predictor of DCI and could be useful in daily clinical practice. CLINICAL RELEVANCE STATEMENT: Better assessment of subarachnoid haemorrhage patients would allow for better prognostication and management of expectations, as well as referral for appropriate services and helping to appropriate use limited critical care resources. KEY POINTS: Aneurysmal subarachnoid haemorrhage is a life-threatening event that causes severe disability and leads to major complications such as delayed cerebral infarction. Accurate assessment of the amount of blood in the subarachnoid spaces on computed tomography with the Hijdra scale can better predict the risk of delayed cerebral infarct. The Hijdra scale could be a good triage tool for subarachnoid haemorrhage patients.

Navigating the complexity of Guillain-Barré syndrome and Miller-Fisher syndrome overlap syndrome: a pediatric case report.

Guillain-Barré syndrome/Miller-Fisher syndrome (GBS/MFS) overlap syndrome is an extremely rare variant of Guillain-Barré syndrome (GBS) in which Miller-Fisher syndrome (MFS) coexists with other characteristics of GBS, such as limb weakness, paresthesia, and facial paralysis. We report the clinical case of a 12-year-old patient, with no pathological history, who acutely presents with ophthalmoplegia, areflexia, facial diplegia, and swallowing and phonation disorders, followed by progressive, descending, and symmetrical paresis affecting first the upper limbs and then the lower limbs. An albuminocytological dissociation was found in the cerebrospinal fluid study. Magnetic resonance imaging of the spinal cord showed enhancement and thickening of the cauda equina roots. The patient was treated with immunoglobulins with a favorable clinical outcome.

Iterative experimental design and identifiability analysis of composite material failure models.

The parameter identification of failure models for composite plies can be cumbersome, due to multiple effects as the consequence of brittle fracture. Our work proposes an iterative, nonlinear design of experiments (DoE) approach that finds the most informative experimental data to identify the parameters of the Tsai-Wu, Tsai-Hill, Hoffman, Hashin, max stress and Puck failure models. Depending on the data, the models perform differently, therefore, the parameter identification is validated by the Euclidean distance of the measured points to the closest ones on the nominal surface. The resulting errors provide a base for the ranking of the models, which helps to select the best fitting. Following the validation, the sensitivity of the best model is calculated by partial differentiation, and a theoretical surface is generated. Lastly, an iterative design of the experiments is implemented to select the optimal set of experiments from which the parameters can be identified from the least data by minimizing the fitting error. In this way, the number of experiments required for the identification of a model of a composite material can be significantly reduced. We demonstrate how the proposed method selected the most optimal experiments out of generated data. The results indicate that if the dataset contains enough information, the method is robust and accurate. If the data set lacks the necessary information, novel material tests can be proposed based on the optimal points of the parameters' sensitivity of the generated failure model surface.

Effect of the Task Approach, Airway Clearance, Kinesthetic Exercise (TASKS) Paediatric Rehabilitation Protocol on Miller-Fisher Syndrome Variant of Guillain-Barré Syndrome: A Case Report.

Miller-Fisher syndrome (MFS) is a rare variant of Guillain-Barré syndrome (GBS) with varying incidence rates geographically. MFS is primarily diagnosed based on clinical features, such as ataxia and areflexia, although other neurological symptoms may also present. A case of MFS has been presented, characterized by complaints of ataxia, areflexia, bilateral foot and hand pain and difficulty in swallowing. In this regard, a paediatric rehabilitation approach has been adopted, utilizing outcome measures, such as the Erasmus Guillain-Barre Syndrome Respiratory Insufficiency Score-Kids, WeeFIM and paediatric balance scale, in addition to clinical evaluation. It is worth noting that the presented case demonstrates the importance of accurately diagnosing and treating this rare neurological condition MFS. Through the implementation of appropriate rehabilitation strategies, it is possible to enhance patients' quality of life.

Latent mutations in the ancestries of alleles under selection.

We consider a single genetic locus with two alleles A1 and A2 in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming the allele frequencies follow a Wright-Fisher diffusion and have reached stationarity, we describe the asymptotic behaviors of the conditional gene genealogy and the latent mutations of a sample with known allele counts, when the count n1 of allele A1 is fixed, and when either or both the sample size n and the selection strength |α| tend to infinity. Our study extends previous work under neutrality to the case of non-neutral rare alleles, asserting that when selection is not too strong relative to the sample size, even if it is strongly positive or strongly negative in the usual sense (α→-∞ or α→+∞), the number of latent mutations of the n1 copies of allele A1 follows the same distribution as the number of alleles in the Ewens sampling formula. On the other hand, very strong positive selection relative to the sample size leads to neutral gene genealogies with a single ancient latent mutation. We also demonstrate robustness of our asymptotic results against changing population sizes, when one of |α| or n is large.

Green economic growth in BRIC and CIVETS countries: The effects of trade openness and sustainable development goals.

This study aims to analyze the impact of trade openness and Sustainable Development Goals, Financial Development, and Technology on the economic growth of Brazil, Russia, India, China and Colombia, Indonesia, Vietnam, Egypt, Turkey, South Africa countries. The present analysis employs a balanced panel data set from 1996 to 2022. This study also uses various tests, such as the Johansen-Fisher cointegration and Granger causality test. The study's findings suggest that economic growth, trade openness, Sustainable Development Goals, financial development, inflation, technology, labor forces, and financial openness have a long-term relationship among them. In the long run, a positive relationship exists between economic growth, trade openness, and the sustainable development goals index in (BRIC) and (CIVETS) countries. Based on the heterogeneous panel non-causality tests, the findings demonstrate that trade openness and Sustainable Development Goals are a unidirectional causality between trade openness, Sustainable Development Goals, and economic growth.

Electrocardiographic abnormalities are prognostic of the clinical outcomes and mortality of patients with subarachnoid hemorrhages.

PURPOSE: We explored the relationships between electrocardiographic (ECG) abnormalities and the clinical outcomes and mortality of patients with non-traumatic aneurysmal subarachnoid hemorrhages (SAHs). METHODS: This retrospective cohort study enrolled consecutive adult patients who presented to emergency departments with non-traumatic aneurysmal SAHs. We recorded their demographics, clinical characteristics, and ECG findings, and explored the relationships between ECG abnormalities, on the one hand, and 28-day mortality and prognosis, on the other. RESULTS: We enrolled 158 patients, 76 females (48.10%) and 82 males (51.90%) of average age 54.70 ± 7.07 years. A total of 107 patients (67.72%) exhibited at least one ECG abnormality, most commonly a T-wave change (n = 54, 34.18%). Such patients evidenced significantly higher Hunt-Hess and Fisher scale scores than those without abnormalities (both p < 0.001). Patients with abnormal ECG findings experienced more unfavorable outcomes and higher mortality than others (both p < 0.001). ECG abnormalities, including PR prolongation, pathological Q waves, QRS widening, left bundle branch blocks, premature ventricular contractions, ST segment changes, and T-wave changes, were more common in non-survivors and patients with Hunt-Hess scores of 4-5 compared to survivors and those with Hunt-Hess scores <4, respectively. Moreover, increased age and presence of abnormal ECG findings were independent predictors of mortality in aneurysmal SAHs. CONCLUSIONS: Patients with abnormal ECG findings exhibited unfavorable clinical outcomes and increased mortality rates. Abnormal ECG findings combined with higher Hunt-Hess or Fischer grade scores usefully predict adverse clinical outcomes in and mortality of SAH patients.

Low frequency signal detection via correlated Ramsey measurements.

The low frequency region of the spectrum is a challenging regime for quantum probes. We support the idea that, in this regime, performing Ramsey measurements carefully controlling the time at which each measurement is initiated is an excellent signal detection strategy. We use the Fisher information to demonstrate a high quality performance in the low frequency regime, compared to more elaborated measurement sequences, and to optimize the correlated Ramsey sequence according to any given experimental parameters, showing that correlated Ramsey rivals with state-of-the-art protocols, and can even outperform commonly employed sequences such as dynamical decoupling in the detection of low frequency signals. Contrary to typical quantum detection protocols for oscillating signals, which require adjusting the time separation between pulses to match the half period of the target signal, and consequently see their scope limited to signals whose period is shorter than the characteristic decoherence time of the probe, or to those protocols whose target is primarily static signals, the time-tagged correlated Ramsey sequence simultaneously tracks the amplitude and the phase information of the target signal, regardless of its frequency, which crucially permits correlating measurements in post-processing, leading to efficient spectral reconstruction.

Construction of "De-Capacity Reduction" financial performance index for Chinese coal industry enterprises --based on Fisher discriminant analysis.

In February 2016, the Chinese government focused on removing excess capacity in coal industry enterprises, and the research goal of the paper was to determine how much impact this will have on the financial performance of coal industry enterprises. The paper collected the financial performance indicators of Chinese state-owned coal industry enterprises from 2011 to 2021, and discriminant analysis was used to calculate the financial performance index evaluation system. The conclusions are: (1) From 2011 to 2016, the financial performance index of Chinese state-owned coal industry enterprises before De-Capacity continued to decline, from 2.062 in 2011 to 1.639 in 2016; In 2017-2021, the financial performance index of Chinese state-owned coal industry enterprises after De-Capacity continued to rise, from 1.482 in 2017 to 1.515 in 2021. (2) From 2011 to 2020, the cumulative financial performance index for the whole trade of state-owned coal industry in the past decade was 18.340, with state-owned large coal industry enterprises having the best financial performance, with a 10-year cumulative index of 20.618, followed by state-owned medium-sized coal industry enterprises, with a 10-year cumulative index of 17.944, and the worst among state-owned small coal industry enterprises, with a 10-year cumulative index of 17.271. (3) If the market adjustment started in 2012 is also considered as a component of "De-Capacity", two pressures from the market and the government have prompted the transformation of state-owned coal industry enterprises. The industry wide financial performance index has increased from 1.554 in 2012 to 1.559 in 2020, with an average annual increase of 0.04 %.

Clinical, paraclinical and outcome features of 166 patients with acute anti-GQ1b antibody syndrome.

BACKGROUND & PURPOSE: In this retrospective study, we aimed at defining the clinical, paraclinical and outcome features of acute neurological syndromes associated with anti-GQ1b antibodies. RESULTS: We identified 166 patients with neurological symptoms appearing in less than 1 month and anti-GQ1b antibodies in serum between 2012 and 2022. Half were female (51%), mean age was 50 years (4-90), and the most frequent clinical features were areflexia (80% of patients), distal upper and lower limbs sensory symptoms (78%), ophthalmoplegia (68%), sensory ataxia (67%), limb muscle weakness (45%) and bulbar weakness (45%). Fifty-three patients (32%) presented with complete (21%) and incomplete (11%) Miller Fisher syndrome (MFS), thirty-six (22%) with Guillain-Barre syndrome (GBS), one (0.6%) with Bickerstaff encephalitis (BE), and seventy-three (44%) with mixed MFS, GBS & BE clinical features. Nerve conduction studies were normal in 46% of cases, showed demyelination in 28%, and axonal loss in 23%. Anti-GT1a antibodies were found in 56% of cases, increased cerebrospinal fluid protein content in 24%, and Campylobacter jejuni infection in 7%. Most patients (83%) were treated with intravenous immunoglobulins, and neurological recovery was complete in 69% of cases at 1 year follow-up. One patient died, and 15% of patients relapsed. Age > 70 years, initial Intensive Care Unit (ICU) admission, and absent anti-GQ1b IgG antibodies were predictors of incomplete recovery at 12 months. No predictors of relapse were identified. CONCLUSION: This study from Western Europe shows acute anti-GQ1b antibody syndrome presents with a large clinical phenotype, a good outcome in 2/3 of cases, and frequent relapses.

A mechanistic model of gossip, reputations, and cooperation.

Social reputations facilitate cooperation: those who help others gain a good reputation, making them more likely to receive help themselves. But when people hold private views of one another, this cycle of indirect reciprocity breaks down, as disagreements lead to the perception of unjustified behavior that ultimately undermines cooperation. Theoretical studies often assume population-wide agreement about reputations, invoking rapid gossip as an endogenous mechanism for reaching consensus. However, the theory of indirect reciprocity lacks a mechanistic description of how gossip actually generates consensus. Here, we develop a mechanistic model of gossip-based indirect reciprocity that incorporates two alternative forms of gossip: exchanging information with randomly selected peers or consulting a single gossip source. We show that these two forms of gossip are mathematically equivalent under an appropriate transformation of parameters. We derive an analytical expression for the minimum amount of gossip required to reach sufficient consensus and stabilize cooperation. We analyze how the amount of gossip necessary for cooperation depends on the benefits and costs of cooperation, the assessment rule (social norm), and errors in reputation assessment, strategy execution, and gossip transmission. Finally, we show that biased gossip can either facilitate or hinder cooperation, depending on the direction and magnitude of the bias. Our results contribute to the growing literature on cooperation facilitated by communication, and they highlight the need to study strategic interactions coupled with the spread of social information.

Intrinsic Information-Theoretic Models.

With this follow-up paper, we continue developing a mathematical framework based on information geometry for representing physical objects. The long-term goal is to lay down informational foundations for physics, especially quantum physics. We assume that we can now model information sources as univariate normal probability distributions N (µ, σ0), as before, but with a constant σ0 not necessarily equal to 1. Then, we also relaxed the independence condition when modeling m sources of information. Now, we model m sources with a multivariate normal probability distribution Nm(µ,Σ0) with a constant variance-covariance matrix Σ0 not necessarily diagonal, i.e., with covariance values different to 0, which leads to the concept of modes rather than sources. Invoking Schrödinger's equation, we can still break the information into m quantum harmonic oscillators, one for each mode, and with energy levels independent of the values of σ0, altogether leading to the concept of "intrinsic". Similarly, as in our previous work with the estimator's variance, we found that the expectation of the quadratic Mahalanobis distance to the sample mean equals the energy levels of the quantum harmonic oscillator, being the minimum quadratic Mahalanobis distance at the minimum energy level of the oscillator and reaching the "intrinsic" Cramér-Rao lower bound at the lowest energy level. Also, we demonstrate that the global probability density function of the collective mode of a set of m quantum harmonic oscillators at the lowest energy level still equals the posterior probability distribution calculated using Bayes' theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. While these new assumptions certainly add complexity to the mathematical framework, the results proven are invariant under transformations, leading to the concept of "intrinsic" information-theoretic models, which are essential for developing physics.

The Inverse of Exact Renormalization Group Flows as Statistical Inference.

We build on the view of the Exact Renormalization Group (ERG) as an instantiation of Optimal Transport described by a functional convection-diffusion equation. We provide a new information-theoretic perspective for understanding the ERG through the intermediary of Bayesian Statistical Inference. This connection is facilitated by the Dynamical Bayesian Inference scheme, which encodes Bayesian inference in the form of a one-parameter family of probability distributions solving an integro-differential equation derived from Bayes' law. In this note, we demonstrate how the Dynamical Bayesian Inference equation is, itself, equivalent to a diffusion equation, which we dub Bayesian Diffusion. By identifying the features that define Bayesian Diffusion and mapping them onto the features that define the ERG, we obtain a dictionary outlining how renormalization can be understood as the inverse of statistical inference.

Design of randomized clinical trials with a binary endpoint: Conditional versus unconditional analyses of a two-by-two table.

When designing a randomized clinical trial to compare two treatments, the sample size required to have desired power with a specified type 1 error depends on the hypothesis testing procedure. With a binary endpoint (e.g., response), the trial results can be displayed in a 2 × 2 table. If one does the analysis conditional on the number of positive responses, then using Fisher's exact test has an actual type 1 error less than or equal to the specified nominal type 1 error. Alternatively, one can use one of many unconditional "exact" tests that also preserve the type 1 error and are less conservative than Fisher's exact test. In particular, the unconditional test of Boschloo is always at least as powerful as Fisher's exact test, leading to smaller required sample sizes for clinical trials. However, many statisticians have argued over the years that the conditional analysis with Fisher's exact test is the only appropriate procedure. Since having smaller clinical trials is an extremely important consideration, we review the general arguments given for the conditional analysis of a 2 × 2 table in the context of a randomized clinical trial. We find the arguments not relevant in this context, or, if relevant, not completely convincing, suggesting the sample-size advantage of the unconditional tests should lead to their recommended use. We also briefly suggest that since designers of clinical trials practically always have target null and alternative response rates, there is the possibility of using this information to improve the power of the unconditional tests.