The Method of Images in Cosmology

31 pages, 18 figures31 pages, 18 figuresWe apply the method of images to the exact initial data for cosmological models that contain a number of regularly arranged discrete masses. This allows us to join cosmological regions together by throats, and to construct wormholes in the initial data. These wormholes allow for the removal of the asymptotically flat "flange" regions that would otherwise exist on the far side of black holes. The method of images also provides us with a way to investigate the definition of mass is cosmology, and the cosmological consequences of the gravitational interaction energies between massive objects. We find evidence that the interaction energies within clusters of massive objects do indeed appear to contribute to the total energy budget in the cosmological regions of the space-time

Dynamics of a lattice Universe

We find a solution to Einstein field equations for a regular toroidal lattice of size L with equal masses M at the centre of each cell; this solution is exact at order M/L. Such a solution is convenient to study the dynamics of an assembly of galaxy-like objects. We find that the solution is expanding (or contracting) in exactly the same way as the solution of a Friedman-Lema\^itre-Robertson-Walker Universe with dust having the same average density as our model. This points towards the absence of backreaction in a Universe filled with an infinite number of objects, and this validates the fluid approximation, as far as dynamics is concerned, and at the level of approximation considered in this work.Comment: 14 pages. No figure. Accepted version for Classical and Quantum Gravit

A stacked long short-term memory approach for predictive blood glucose monitoring in women with gestational diabetes mellitus

Gestational diabetes mellitus (GDM) is a subtype of diabetes that develops during pregnancy. Managing blood glucose (BG) within the healthy physiological range can reduce clinical complications for women with gestational diabetes. The objectives of this study are to (1) develop benchmark glucose prediction models with long short-term memory (LSTM) recurrent neural network models using time-series data collected from the GDm-Health platform, (2) compare the prediction accuracy with published results, and (3) suggest an optimized clinical review schedule with the potential to reduce the overall number of blood tests for mothers with stable and within-range glucose measurements. A total of 190,396 BG readings from 1110 patients were used for model development, validation and testing under three different prediction schemes: 7 days of BG readings to predict the next 7 or 14 days and 14 days to predict 14 days. Our results show that the optimized BG schedule based on a 7-day observational window to predict the BG of the next 14 days achieved the accuracies of the root mean square error (RMSE) = 0.958 ± 0.007, 0.876 ± 0.003, 0.898 ± 0.003, 0.622 ± 0.003, 0.814 ± 0.009 and 0.845 ± 0.005 for the after-breakfast, after-lunch, after-dinner, before-breakfast, before-lunch and before-dinner predictions, respectively. This is the first machine learning study that suggested an optimized blood glucose monitoring frequency, which is 7 days to monitor the next 14 days based on the accuracy of blood glucose prediction. Moreover, the accuracy of our proposed model based on the fingerstick blood glucose test is on par with the prediction accuracies compared with the benchmark performance of one-hour prediction models using continuous glucose monitoring (CGM) readings. In conclusion, the stacked LSTM model is a promising approach for capturing the patterns in time-series data, resulting in accurate predictions of BG levels. Using a deep learning model with routine fingerstick glucose collection is a promising, predictable and low-cost solution for BG monitoring for women with gestational diabetes

Maximum tumor diameter is associated with event-free survival in PET-negative patients with stage I/IIA Hodgkin lymphoma.

Introduction: the high cure rates achieved in early-stage (ES) Hodgkin lymphoma (HL) are one of the great successes of hemato-oncology, but late treatment-related toxicity undermines long-term survival. Improving overall survival and quality of life further will require maintaining disease control while potentially de-escalating chemotherapy and/or omitting radiotherapy to reduce late toxicity. Accurate stratification of patients is required to facilitate individualized treatment approaches. Response assessment using 18F-fluorodeoxyglucose positron emission tomography (PET) is a powerful predictor of outcome in HL,1,2 and has been used in multiple studies, including the United Kingdom National Cancer Research Institute Randomised Phase III Trial to Determine the Role of FDG–PET Imaging in Clinical Stages IA/IIA Hodgkin’s Disease (UK NCRI RAPID) trial, to investigate whether patients achieving complete metabolic remission (CMR) can be treated with chemotherapy alone.3-5 These PET-adapted trials have demonstrated that omitting radiotherapy results in higher relapse rates, but without compromising overall survival.3-5 For the 75% of patients who achieved CMR in RAPID, neither baseline clinical risk stratification (favorable/unfavorable) nor PET (Deauville score 1/2) predicted disease relapse; additional biomarkers are needed.1 Tumor bulk has long been recognized as prognostic in HL,1,6 but there remains uncertainty about the significance and definition of bulk in the era of PET-adapted treatment.7 We performed a subsidiary analysis of RAPID to assess the prognostic value of baseline maximum tumor dimension (MTD) in patients achieving CMR. Methods: ee have previously reported the RAPID trial design, primary results, and outcomes according to pretreatment risk stratification and PET score.1,3 Patients were aged 16 to 75 years with untreated ES-HL and without B-symptoms or mediastinal bulk (mass > 1/3 internal mediastinal diameter at T5/6).6 Metabolic response after 3 cycles of ABVD chemotherapy (doxorubicin, bleomycin, vinblastine, and dacarbazine) was centrally assessed using PET (N = 562). Patients with CMR (ie, Deauville score 1-2) were randomly assigned to receive involved field radiotherapy (IFRT; n = 208) or no further therapy (NFT; n = 211). PET-positive patients (score, 3-5; n = 143) received a fourth cycle of ABVD and IFRT. Baseline disease assessment was performed by computed tomography, and bidimensional target lesion measurements were reported by local radiologists in millimeters. The association of baseline MTD with HL-related event-free survival (EFS: progression or HL-related death) and progression-free survival (PFS) (progression or any-cause death) was assessed using Kaplan-Meier and Cox regression analyses. Non-HL deaths were either related to primary treatment toxicity or occurred in HL remission.1 United Kingdom ethical approval for the RAPID trial was via the UK Multicentre Research ethics committee. Results and discussion: baseline patient characteristics have been previously described.1 Median age was 34 years (range, 16-75 years); 184 (37.4%) of 492 patients had unfavorable risk by European Organisation for Research and Treatment of Cancer criteria, and 155 (32.3%) of 480 by German Hodgkin Study Groupcriteria. Median MTD for patients achieving CMR was 3.0 cm (interquartile range, 2.0-4.0 cm) and 3.0 cm (interquartile range, 1.8-4.5 cm) in the NFT and IFRT groups, respectively, whereas PET-positive patients had a median MTD of 3.9 cm (interquartile range, 2.8-5.1 cm). After a median follow-up of 61.6 m, 44 HL progression events occurred: 21 NFT, 9 IFRT and 14 PET-positive. No patient received salvage treatment without documented progression. Only 5 HL-related deaths occurred (1 IFRT, 4 PET-positive), and 12 non-HL deaths (4 NFT, 6 IFRT, 2 PET-positive).1 For patients with CMR (N = 419), there was a strong association between MTD and EFS (hazard ratio [HR], 1.19; 95% confidence interval [CI], 1.02-1.39; P = .02), adjusting for treatment group, with an approximate 19% increase in HL risk per centimeter increase in MTD. The association was similar in both treatment groups (NFT HR, 1.20 [95% CI, 0.99-1.44; P = .06]; IFRT HR, 1.19 [95% CI, 0.92-1.55; P = .19]). The observed effect sizes did not markedly change after adjusting for baseline clinical risk factors, and similar results were observed for PFS (supplemental Table 1). In contrast, for PET-positive patients, there was no association between MTD and EFS (HR, 0.88; 95% CI, 0.70-1.11; P = .29) or PFS (HR, 0.87; 95% CI, 0.70-1.08; P = .21). In an exploratory analysis within the NFT group, MTD was dichotomized using increasing 1-cm intervals to investigate the relationship between MTD thresholds and EFS. The largest effect size was observed with an MTD threshold of ≥5 cm (Table 1). Similar results were observed for PFS; this threshold also performed best in time-dependent receiver operating characteristic curve analyses. It was not possible to assess MTD thresholds in the IFRT group with only 9 events. Among all randomized patients, 79 (18.9%) had MTD of ≥5 cm, the majority with mediastinal (n = 43), supraclavicular (n = 17), or cervical (n = 16) locations. Five-year EFS for patients with MTD of ≥5 cm randomly assigned to NFT and IFRT was 79.3% (n = 39; 95% CI, 66.6%-92.0%) and 94.9% (n = 40; 95% CI, 88.0%-100%), respectively (P = .03; Figure 1)

Cosmologies with Energy Exchange

We provide a simple mathematical description of the exchange of energy between two fluids in an expanding Friedmann universe with zero spatial curvature. The evolution can be reduced to a single non-linear differential equation which we solve in physically relevant cases and provide an analysis of all the possible evolutions. Particular power-law solutions exist for the expansion scale factor and are attractors at late times under particular conditions. We show how a number of problems studied in the literature, such as cosmological vacuum energy decay, particle annihilation, and the evolution of a population of evaporating black holes, correspond to simple particular cases of our model. In all cases we can determine the effects of the energy transfer on the expansion scale factor. We also consider the situation in the presence of anti-decaying fluids and so called phantom fluids which violate the dominant energy conditions.Comment: 12 pages, 1 figur

Evolution of a periodic eight-black-hole lattice in numerical relativity

The idea of black-hole lattices as models for the large-scale structure of the universe has been under scrutiny for several decades, and some of the properties of these systems have been elucidated recently in the context of the problem of cosmological backreaction. The complete, three-dimensional and fully relativistic evolution of these system has, however, never been tackled. We explicitly construct the first of these solutions by numerically integrating Einstein's equation in the case of an eight-black-hole lattice with the topology of S3.Comment: 21 pages, 13 figures. Corrected and clarified discussio

Positron Emission Tomography Score Has Greater Prognostic Significance Than Pretreatment Risk Stratification in Early-Stage Hodgkin Lymphoma in the UK RAPID Study.

PURPOSE: Accurate stratification of patients is an important goal in Hodgkin lymphoma (HL), but the role of pretreatment clinical risk stratification in the context of positron emission tomography (PET) -adapted treatment is unclear. We performed a subsidiary analysis of the RAPID trial to assess the prognostic value of pretreatment risk factors and PET score in determining outcomes. PATIENTS AND METHODS: Patients with stage IA to IIA HL and no mediastinal bulk underwent PET assessment after three cycles of doxorubicin, bleomycin, vinblastine, and dacarbazine; 143 PET-positive patients (PET score, 3 to 5) received a fourth doxorubicin, bleomycin, vinblastine, and dacarbazine cycle and involved-field radiotherapy, and 419 patients in complete metabolic remission were randomly assigned to receive involved-field radiotherapy (n = 208) or no additional treatment (n = 211). Cox regression was used to investigate the association between PET score and pretreatment risk factors with HL-specific event-free survival (EFS). RESULTS: High PET score was associated with inferior EFS, before (P .4). CONCLUSION: In RAPID, a positive PET scan did not carry uniform prognostic weight; only a PET score of 5 was associated with inferior outcomes. This suggests that in future trials involving patients without B symptoms or mediastinal bulk, a score of 5 rather than a positive PET result should be used to guide treatment escalation in early-stage HL

Regulating and Deregulating the Public Utilities 1830-2010

History can provide invaluable insights into important issues of the economic and social regulation of utilities, and offer lessons towards future debates. But the history of utility regulation – which speaks of changing, diverse and complex experiences around the world – was, unfortunately, sidelined or marginalised when economists and policymakers enthusiastically embraced the question of how to reform the utilities from the 1970s. This paper provides an overview of the three, overarching, `waves' of utility regulation from the nineteenth century to the present, documenting how, when and why the ways in which the roles of the state, the market and firms altered over time. It then contextualises and explains the main contributions of each of the papers included in this special issue of Business History, which cover energy, communications, water, transportation and other urban infrastructure regulation, across Western Europe, the United States and Australia

Energy-Conserving Lattice Boltzmann Thermal Model in Two Dimensions

A discrete velocity model is presented for lattice Boltzmann thermal fluid dynamics. This model is implemented and tested in two dimensions with a finite difference scheme. Comparison with analytical solutions shows an excellent agreement even for wide temperature differences. An alternative approximate approach is then presented for traditional lattice transport schemes

Soil Microbial Networks Shift Across a High-Elevation Successional Gradient.

While it is well established that microbial composition and diversity shift along environmental gradients, how interactions among microbes change is poorly understood. Here, we tested how community structure and species interactions among diverse groups of soil microbes (bacteria, fungi, non-fungal eukaryotes) change across a fundamental ecological gradient, succession. Our study system is a high-elevation alpine ecosystem that exhibits variability in successional stage due to topography and harsh environmental conditions. We used hierarchical Bayesian joint distribution modeling to remove the influence of environmental covariates on species distributions and generated interaction networks using the residual species-to-species variance-covariance matrix. We hypothesized that as ecological succession proceeds, diversity will increase, species composition will change, and soil microbial networks will become more complex. As expected, we found that diversity of most taxonomic groups increased over succession, and species composition changed considerably. Interestingly, and contrary to our hypothesis, interaction networks became less complex over succession (fewer interactions per taxon). Interactions between photosynthetic microbes and any other organism became less frequent over the gradient, whereas interactions between plants or soil microfauna and any other organism were more abundant in late succession. Results demonstrate that patterns in diversity and composition do not necessarily relate to patterns in network complexity and suggest that network analyses provide new insight into the ecology of highly diverse, microscopic communities