Relative Periodic Solutions of the Complex Ginzburg-Landau Equation

A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the one-dimensional complex Ginzburg-Landau equation (CGLE) with periodic boundary conditions. A relative periodic solution is a solution that is periodic in time, up to a transformation by an element of the equation's symmetry group. With the method used, relative periodic solutions are represented by a space-time Fourier series modified to include the symmetry group element and are sought as solutions to a system of nonlinear algebraic equations for the Fourier coefficients, group element, and time period. The 77 relative periodic solutions found for the CGLE exhibit a wide variety of temporal dynamics, with the sum of their positive Lyapunov exponents varying from 5.19 to 60.35 and their unstable dimensions from 3 to 8. Preliminary work indicates that weighted averages over the collection of relative periodic solutions accurately approximate the value of several functionals on typical trajectories.Comment: 32 pages, 12 figure

On sketching approximations for symmetric Boolean CSPs

A Boolean maximum constraint satisfaction problem, Max-CSP($f$), is specified by a predicate $f:\{-1,1\}^k\to\{0,1\}$. An $n$-variable instance of Max-CSP($f$) consists of a list of constraints, each of which applies $f$ to $k$ distinct literals drawn from the $n$ variables. For $k=2$, Chou, Golovnev, and Velusamy [CGV20, FOCS 2020] obtained explicit ratios characterizing the $\sqrt n$-space streaming approximability of every predicate. For $k \geq 3$, Chou, Golovnev, Sudan, and Velusamy [CGSV21, arXiv:2102.12351] proved a general dichotomy theorem for $\sqrt n$-space sketching algorithms: For every $f$, there exists $\alpha(f)\in (0,1]$ such that for every $\epsilon>0$, Max-CSP($f$) is $(\alpha(f)-\epsilon)$-approximable by an $O(\log n)$-space linear sketching algorithm, but $(\alpha(f)+\epsilon)$-approximation sketching algorithms require $\Omega(\sqrt{n})$ space. In this work, we give closed-form expressions for the sketching approximation ratios of multiple families of symmetric Boolean functions. Letting $\alpha'_k = 2^{-(k-1)} (1-k^{-2})^{(k-1)/2}$, we show that for odd $k \geq 3$, $\alpha(k$AND$) = \alpha'_k$, and for even $k \geq 2$, $\alpha(k$AND$) = 2\alpha'_{k+1}$. We also resolve the ratio for the "at-least-$(k-1)$-$1$'s" function for all even $k$; the "exactly-$\frac{k+1}2$-$1$'s" function for odd $k \in \{3,\ldots,51\}$; and fifteen other functions. We stress here that for general $f$, according to [CGSV21], closed-form expressions for $\alpha(f)$ need not have existed a priori. Separately, for all threshold functions, we give optimal "bias-based" approximation algorithms generalizing [CGV20] while simplifying [CGSV21]. Finally, we investigate the $\sqrt n$-space streaming lower bounds in [CGSV21], and show that they are incomplete for $3$AND.Comment: 27 pages; same results but significant changes in presentatio

Transforming Development and Disaster Risk

Abstract: This article focuses on the complex relationship between development and disaster risk. Development and disaster risk are closely linked as the people and assets exposed to risk, as well as their vulnerability and capacity, are largely determined by development processes. Transformation is key to moving from current development patterns that increase, create or unfairly distribute risks, to forms of development that are equitable, resilient and sustainable. Based on a review of existing literature, we present three opportunities that have the potential to lead to transformation in the development-disaster risk relationship: (i) exposing development-disaster risk trade-offs in development policy and decision-making; (ii) prioritizing equity and social justice in approaches to secure resilience; and (iii) enabling transformation through adaptive governance. This research aims to contribute to breaking down existing barriers in research, policy and practice between the disaster risk reduction, climate change adaptation, and development communities by providing cross-sectoral opportunities to operationalize theoretical knowledge on transformation. It also helps to clarify the connections between different global agendas by positioning transformation as a potential bridging concept to link disconnected policy processes. This paper argues for empirical research to test the opportunities presented here and further define transformative pathways at multiple scales

What We Measure Matters:The Case of the Missing Development Data in Sendai Framework for Disaster Risk Reduction Monitoring

International audienceThe Sendai Framework for Disaster Risk Reduction 2015-2030's (SFDRR) framing moved away from disaster risk as a natural phenomenon to the examination of the inequality and injustice at the root of human vulnerability to hazards and disasters. Yet, its achievements have not seriously challenged the long-established capitalist systems of oppression that hinder the development leading to disaster risk creation. This article is an exploratory mapping exercise of and a collective reflection on Sustainable Development Goals (SDGs) and SFDRR indicators-and their use in measuring progress towards disaster risk reduction (DRR). We highlight that despite the rhetoric of vulnerability, the measurement of progress towards DRR remains event/hazard-centric. We argue that the measurement of disaster risk could be greatly enhanced by the integration of development data in future iterations of global DRR frameworks for action

Adherence to Treatment Recommendations in Chronic Disease: What is (im)Possible? Expert conclusions from the 30th ECOG workshop 2021 Abstracts

Obesity is a chronic disease, in which treatment outcomes are highly dependent on patient and family adherence to behavioural recommendations. The role of healthy eating, physical activity, medication adherence as well as adherence to pre- and post-bariatric surgery protocols are of utmost importance for long-term treatment outcomes. Even the best interventions are not likely to reach their maximum benefit without significant levels of adherence on the part of the individual and family. Traditionally, the annual meeting of the European Childhood Obesity Group (ECOG) includes an expert workshop addressing one specific topic within the field of childhood obesity. During the 30th annual meeting, hosted by the University of Pécs, Hungary, as a virtual meeting, "adherence to treatment recommendations in obesity as a chronic disease" was addressed. The discussions that developed during the workshop are summarized in the following article

Refined Criteria for Gradual Typing

Siek and Taha [2006] coined the term gradual typing to describe a theory for integrating static and dynamic typing within a single language that 1) puts the programmer in control of which regions of code are statically or dynamically typed and 2) enables the gradual evolution of code between the two typing disciplines. Since 2006, the term gradual typing has become quite popular but its meaning has become diluted to encompass anything related to the integration of static and dynamic typing. This dilution is partly the fault of the original paper, which provided an incomplete formal characterization of what it means to be gradually typed. In this paper we draw a crisp line in the sand that includes a new formal property, named the gradual guarantee, that relates the behavior of programs that differ only with respect to their type annotations. We argue that the gradual guarantee provides important guidance for designers of gradually typed languages. We survey the gradual typing literature, critiquing designs in light of the gradual guarantee. We also report on a mechanized proof that the gradual guarantee holds for the Gradually Typed Lambda Calculus

Obesity Stigma: Is the ‘Food Addiction’ Label Feeding the Problem?

Obesity is often attributed to an addiction to high-calorie foods. However, the effect of "food addiction" explanations on weight-related stigma remains unclear. In two online studies, participants (n = 439, n = 523, respectively, recruited from separate samples) read a vignette about a target female who was described as 'very overweight'. Participants were randomly allocated to one of three conditions which differed in the information provided in the vignette: (1) in the "medical condition", the target had been diagnosed with food addiction by her doctor; (2) in the "self-diagnosed condition", the target believed herself to be a food addict; (3) in the control condition, there was no reference to food addiction. Participants then completed questionnaires measuring target-specific stigma (i.e., stigma towards the female described in the vignette), general stigma towards obesity (both studies), addiction-like eating behavior and causal beliefs about addiction (Study 2 only). In Study 1, participants in the medical and self-diagnosed food addiction conditions demonstrated greater target-specific stigma relative to the control condition. In Study 2, participants in the medical condition had greater target-specific stigma than the control condition but only those with low levels of addiction-like eating behavior. There was no effect of condition on general weight-based stigma in either study. These findings suggest that the food addiction label may increase stigmatizing attitudes towards a person with obesity, particularly within individuals with low levels of addiction-like eating behavior