Information Invariance and Quantum Probabilities

We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The requirement of invariance of the information under a continuous change of the set of mutually complementary measurements uniquely singles out a measure of information, which is quadratic in probabilities. The assumption which gives the same scaling of the number of degrees of freedom with the dimension as in quantum theory follows essentially from the assumption that all physical states of a higher dimensional system are those and only those from which one can post-select physical states of two-dimensional systems. The requirement that no more than one bit of information (as quantified by the quadratic measure) is contained in all possible post-selected two-dimensional systems is equivalent to the positivity of density operator in quantum theory.Comment: 8 pages, 1 figure. This article is dedicated to Pekka Lahti on the occasion of his 60th birthday. Found. Phys. (2009

Effects of rapid prey evolution on predator-prey cycles

We study the qualitative properties of population cycles in a predator-prey system where genetic variability allows contemporary rapid evolution of the prey. Previous numerical studies have found that prey evolution in response to changing predation risk can have major quantitative and qualitative effects on predator-prey cycles, including: (i) large increases in cycle period, (ii) changes in phase relations (so that predator and prey are cycling exactly out of phase, rather than the classical quarter-period phase lag), and (iii) "cryptic" cycles in which total prey density remains nearly constant while predator density and prey traits cycle. Here we focus on a chemostat model motivated by our experimental system [Fussmann et al. 2000,Yoshida et al. 2003] with algae (prey) and rotifers (predators), in which the prey exhibit rapid evolution in their level of defense against predation. We show that the effects of rapid prey evolution are robust and general, and furthermore that they occur in a specific but biologically relevant region of parameter space: when traits that greatly reduce predation risk are relatively cheap (in terms of reductions in other fitness components), when there is coexistence between the two prey types and the predator, and when the interaction between predators and undefended prey alone would produce cycles. Because defense has been shown to be inexpensive, even cost-free, in a number of systems [Andersson and Levin 1999, Gagneux et al. 2006,Yoshida et al. 2004], our discoveries may well be reproduced in other model systems, and in nature. Finally, some of our key results are extended to a general model in which functional forms for the predation rate and prey birth rate are not specified.Comment: 35 pages, 8 figure

Committed Global Warming Risks Triggering Multiple Climate Tipping Points

Many scenarios for limiting global warming to 1.5°C assume planetary-scale carbon dioxide removal sufficient to exceed anthropogenic emissions, resulting in radiative forcing falling and temperatures stabilizing. However, such removal technology may prove unfeasible for technical, environmental, political, or economic reasons, resulting in continuing greenhouse gas emissions from hard-to-mitigate sectors. This may lead to constant concentration scenarios, where net anthropogenic emissions remain non-zero but small, and are roughly balanced by natural carbon sinks. Such a situation would keep atmospheric radiative forcing roughly constant. Fixed radiative forcing creates an equilibrium “committed” warming, captured in the concept of “equilibrium climate sensitivity.” This scenario is rarely analyzed as a potential extension to transient climate scenarios. Here, we aim to understand the planetary response to such fixed concentration commitments, with an emphasis on assessing the resulting likelihood of exceeding temperature thresholds that trigger climate tipping points. We explore transients followed by respective equilibrium committed warming initiated under low to high emission scenarios. We find that the likelihood of crossing the 1.5°C threshold and the 2.0°C threshold is 83% and 55%, respectively, if today's radiative forcing is maintained until achieving equilibrium global warming. Under the scenario that best matches current national commitments (RCP4.5), we estimate that in the transient stage, two tipping points will be crossed. If radiative forcing is then held fixed after the year 2100, a further six tipping point thresholds are crossed. Achieving a trajectory similar to RCP2.6 requires reaching net-zero emissions rapidly, which would greatly reduce the likelihood of tipping events

Non-AIDS defining cancers in the D:A:D Study - time trends and predictors of survival : A cohort study

Background: Non-AIDS defining cancers (NADC) are an important cause of morbidity and mortality in HIV-positive individuals. Using data from a large international cohort of HIV-positive individuals, we described the incidence of NADC from 2004-2010, and described subsequent mortality and predictors of these.Methods: Individuals were followed from 1st January 2004/enrolment in study, until the earliest of a new NADC, 1st February 2010, death or six months after the patient's last visit. Incidence rates were estimated for each year of follow-up, overall and stratified by gender, age and mode of HIV acquisition. Cumulative risk of mortality following NADC diagnosis was summarised using Kaplan-Meier methods, with follow-up for these analyses from the date of NADC diagnosis until the patient's death, 1st February 2010 or 6 months after the patient's last visit. Factors associated with mortality following NADC diagnosis were identified using multivariable Cox proportional hazards regression.Results: Over 176,775 person-years (PY), 880 (2.1%) patients developed a new NADC (incidence: 4.98/1000PY [95% confidence interval 4.65, 5.31]). Over a third of these patients (327, 37.2%) had died by 1st February 2010. Time trends for lung cancer, anal cancer and Hodgkin's lymphoma were broadly consistent. Kaplan-Meier cumulative mortality estimates at 1, 3 and 5 years after NADC diagnosis were 28.2% [95% CI 25.1-31.2], 42.0% [38.2-45.8] and 47.3% [42.4-52.2], respectively. Significant predictors of poorer survival after diagnosis of NADC were lung cancer (compared to other cancer types), male gender, non-white ethnicity, and smoking status. Later year of diagnosis and higher CD4 count at NADC diagnosis were associated with improved survival. The incidence of NADC remained stable over the period 2004-2010 in this large observational cohort.Conclusions: The prognosis after diagnosis of NADC, in particular lung cancer and disseminated cancer, is poor but has improved somewhat over time. Modifiable risk factors, such as smoking and low CD4 counts, were associated with mortality following a diagnosis of NADC. © 2013 Worm et al.; licensee BioMed Central Ltd

A just world on a safe planet: a Lancet Planetary Health–Earth Commission report on Earth-system boundaries, translations, and transformations

The health of the planet and its people are at risk. The deterioration of the global commons—ie, the natural systems that support life on Earth—is exacerbating energy, food, and water insecurity, and increasing the risk of disease, disaster, displacement, and conflict. In this Commission, we quantify safe and just Earth-system boundaries (ESBs) and assess minimum access to natural resources required for human dignity and to enable escape from poverty. Collectively, these describe a safe and just corridor that is essential to ensuring sustainable and resilient human and planetary health and thriving in the Anthropocene. We then discuss the need for translation of ESBs across scales to inform science-based targets for action by key actors (and the challenges in doing so), and conclude by identifying the system transformations necessary to bring about a safe and just future. Our concept of the safe and just corridor advances research on planetary boundaries and the justice and Earth-system aspects of the Sustainable Development Goals. We define safe as ensuring the biophysical stability of the Earth system, and our justice principles include minimising harm, meeting minimum access needs, and redistributing resources and responsibilities to enhance human health and wellbeing. The ceiling of the safe and just corridor is defined by the more stringent of the safe and just ESBs to minimise significant harm and ensure Earth-system stability. The base of the corridor is defined by the impacts of minimum global access to food, water, energy, and infrastructure for the global population, in the domains of the variables for which we defined the ESBs. Living within the corridor is necessary, because exceeding the ESBs and not meeting basic needs threatens human health and life on Earth. However, simply staying within the corridor does not guarantee justice because within the corridor resources can also be inequitably distributed, aggravating human health and causing environmental damage. Procedural and substantive justice are necessary to ensure that the space within the corridor is justly shared. We define eight safe and just ESBs for five domains—the biosphere (functional integrity and natural ecosystem area), climate, nutrient cycles (phosphorus and nitrogen), freshwater (surface and groundwater), and aerosols—to reduce the risk of degrading biophysical life-support systems and avoid tipping points. Seven of the ESBs have already been transgressed: functional integrity, natural ecosystem area, climate, phosphorus, nitrogen, surface water, and groundwater. The eighth ESB, air pollution, has been transgressed at the local level in many parts of the world. Although safe boundaries would ensure Earth-system stability and thus safeguard the overall biophysical conditions that have enabled humans to flourish, they do not necessarily safeguard everyone against harm or allow for minimum access to resources for all. We use the concept of Earth-system justice—which seeks to ensure wellbeing and reduce harm within and across generations, nations, and communities, and between humans and other species, through procedural and distributive justice—to assess safe boundaries. Earth-system justice recognises unequal responsibility for, and unequal exposure and vulnerability to, Earth-system changes, and also recognises unequal capacities to respond and unequal access to resources. We also assess the extent to which safe ESBs could minimise irreversible, existential, and other major harms to human health and wellbeing through a review of who is affected at each boundary. Not all safe ESBs are just, in that they do not minimise all significant harm (eg, that associated with the climate change, aerosol, or nitrogen ESBs). Billions of people globally do not have sufficient access to energy, clean water, food, and other resources. For climate change, for example, tens of millions of people are harmed at lower levels of warming than that defined in the safe ESB, and thus to avoid significant harm would require a more stringent ESB. In other domains, the safe ESBs align with the just ESBs, although some need to be modified, or complemented with local standards, to prevent significant harm (eg, the aerosols ESB). We examine the implications of achieving the social SDGs in 2018 through an impact modelling exercise, and quantify the minimum access to resources required for basic human dignity (level 1) as well as the minimum resources required to enable escape from poverty (level 2). We conclude that without social transformation and redistribution of natural resource use (eg, from top consumers of natural resources to those who currently do not have minimum access to these resources), meeting minimum-access levels for people living below the minimum level would increase pressures on the Earth system and the risks of further transgressions of the ESBs. We also estimate resource-access needs for human populations in 2050 and the associated Earth-system impacts these could have. We project that the safe and just climate ESB will be overshot by 2050, even if everybody in the world lives with only the minimum required access to resources (no more, no less), unless there are transformations of, for example, the energy and food systems. Thus, a safe and just corridor will only be possible with radical societal transformations and technological changes. Living within the safe and just corridor requires operationalisation of ESBs by key actors across all levels, which can be achieved via cross-scale translation (whereby resources and responsibilities for impact reductions are equitably shared among actors). We focus on cities and businesses because of the magnitude of their impacts on the Earth system, and their potential to take swift action and act as agents of change. We explore possible approaches for translating each ESB to cities and businesses via the sequential steps of transcription, allocation, and adjustment. We highlight how different elements of Earth-system justice can be reflected in the allocation and adjustment steps by choosing appropriate sharing approaches, informed by the governance context and broader enabling conditions. Finally we discuss system transformations that could move humanity into a safe and just corridor and reduce risks of instability, injustice, and harm to human health. These transformations aim to minimise harm and ensure access to essential resources, while addressing the drivers of Earth-system change and vulnerability and the institutional and social barriers to systemic transformations, and include reducing and reallocating consumption, changing economic systems, technology, and governance

Hierarchy of Scales in Language Dynamics

Methods and insights from statistical physics are finding an increasing variety of applications where one seeks to understand the emergent properties of a complex interacting system. One such area concerns the dynamics of language at a variety of levels of description, from the behaviour of individual agents learning simple artificial languages from each other, up to changes in the structure of languages shared by large groups of speakers over historical timescales. In this Colloquium, we survey a hierarchy of scales at which language and linguistic behaviour can be described, along with the main progress in understanding that has been made at each of them − much of which has come from the statistical physics community. We argue that future developments may arise by linking the different levels of the hierarchy together in a more coherent fashion, in particular where this allows more effective use of rich empirical data sets

Non-AIDS defining cancers in the D:A:D Study-time trends and predictors of survival : a cohort study

BACKGROUND:Non-AIDS defining cancers (NADC) are an important cause of morbidity and mortality in HIV-positive individuals. Using data from a large international cohort of HIV-positive individuals, we described the incidence of NADC from 2004-2010, and described subsequent mortality and predictors of these.METHODS:Individuals were followed from 1st January 2004/enrolment in study, until the earliest of a new NADC, 1st February 2010, death or six months after the patient's last visit. Incidence rates were estimated for each year of follow-up, overall and stratified by gender, age and mode of HIV acquisition. Cumulative risk of mortality following NADC diagnosis was summarised using Kaplan-Meier methods, with follow-up for these analyses from the date of NADC diagnosis until the patient's death, 1st February 2010 or 6 months after the patient's last visit. Factors associated with mortality following NADC diagnosis were identified using multivariable Cox proportional hazards regression.RESULTS:Over 176,775 person-years (PY), 880 (2.1%) patients developed a new NADC (incidence: 4.98/1000PY [95% confidence interval 4.65, 5.31]). Over a third of these patients (327, 37.2%) had died by 1st February 2010. Time trends for lung cancer, anal cancer and Hodgkin's lymphoma were broadly consistent. Kaplan-Meier cumulative mortality estimates at 1, 3 and 5 years after NADC diagnosis were 28.2% [95% CI 25.1-31.2], 42.0% [38.2-45.8] and 47.3% [42.4-52.2], respectively. Significant predictors of poorer survival after diagnosis of NADC were lung cancer (compared to other cancer types), male gender, non-white ethnicity, and smoking status. Later year of diagnosis and higher CD4 count at NADC diagnosis were associated with improved survival. The incidence of NADC remained stable over the period 2004-2010 in this large observational cohort.CONCLUSIONS:The prognosis after diagnosis of NADC, in particular lung cancer and disseminated cancer, is poor but has improved somewhat over time. Modifiable risk factors, such as smoking and low CD4 counts, were associated with mortality following a diagnosis of NADC