Characterizations of Super-regularity and its Variants

Convergence of projection-based methods for nonconvex set feasibility problems has been established for sets with ever weaker regularity assumptions. What has not kept pace with these developments is analogous results for convergence of optimization problems with correspondingly weak assumptions on the value functions. Indeed, one of the earliest classes of nonconvex sets for which convergence results were obtainable, the class of so-called super-regular sets introduced by Lewis, Luke and Malick (2009), has no functional counterpart. In this work, we amend this gap in the theory by establishing the equivalence between a property slightly stronger than super-regularity, which we call Clarke super-regularity, and subsmootheness of sets as introduced by Aussel, Daniilidis and Thibault (2004). The bridge to functions shows that approximately convex functions studied by Ngai, Luc and Th\'era (2000) are those which have Clarke super-regular epigraphs. Further classes of regularity of functions based on the corresponding regularity of their epigraph are also discussed.Comment: 15 pages, 2 figure

Activity Identification and Local Linear Convergence of Douglas--Rachford/ADMM under Partial Smoothness

Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within this class of algorithms, Douglas--Rachford (DR) and alternating direction method of multipliers (ADMM) are designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local convergence behaviour of DR (resp. ADMM) when the involved functions (resp. their Legendre-Fenchel conjugates) are moreover partly smooth. More precisely, when both of the two functions (resp. their conjugates) are partly smooth relative to their respective manifolds, we show that DR (resp. ADMM) identifies these manifolds in finite time. Moreover, when these manifolds are affine or linear, we prove that DR/ADMM is locally linearly convergent. When $J$ and $G$ are locally polyhedral, we show that the optimal convergence radius is given in terms of the cosine of the Friedrichs angle between the tangent spaces of the identified manifolds. This is illustrated by several concrete examples and supported by numerical experiments.Comment: 17 pages, 1 figure, published in the proceedings of the Fifth International Conference on Scale Space and Variational Methods in Computer Visio

Simulating Dynamical Features of Escape Panic

One of the most disastrous forms of collective human behaviour is the kind of crowd stampede induced by panic, often leading to fatalities as people are crushed or trampled. Sometimes this behaviour is triggered in life-threatening situations such as fires in crowded buildings; at other times, stampedes can arise from the rush for seats or seemingly without causes. Tragic examples within recent months include the panics in Harare, Zimbabwe, and at the Roskilde rock concert in Denmark. Although engineers are finding ways to alleviate the scale of such disasters, their frequency seems to be increasing with the number and size of mass events. Yet, systematic studies of panic behaviour, and quantitative theories capable of predicting such crowd dynamics, are rare. Here we show that simulations based on a model of pedestrian behaviour can provide valuable insights into the mechanisms of and preconditions for panic and jamming by incoordination. Our results suggest practical ways of minimising the harmful consequences of such events and the existence of an optimal escape strategy, corresponding to a suitable mixture of individualistic and collective behaviour.Comment: For related information see http://angel.elte.hu/~panic, http://www.helbing.org, http://angel.elte.hu/~fij, and http://angel.elte.hu/~vicse

Fermentation kinetics including product and substrate inhibitions plus biomass death: a mathematical analysis

Fermentation is generally modelled by kinetic equations giving the time evolutions for biomass, substrate, and product concentrations. Although these equations can be solved analytically in simple cases if substrate/product inhibition and biomass death are included, they are typically solved numerically. We propose an analytical treatment of the kinetic equations --including cell death and an arbitrary number of inhibitions-- in which constant yield needs not be assumed. Equations are solved in phase space, i.e. the biomass concentration is written explicitly as a function of the substrate concentration.Comment: 4 pages, 4 figure

Impact of disorder on dynamics and ordering in the honeycomb-lattice iridate Na2IrO3

Kitaev's honeycomb spin-liquid model and its proposed realization in materials such as α-RuCl3, Li2IrO3, and Na2IrO3 continue to present open questions about how the dynamics of a spin liquid are modified in the presence of non-Kitaev interactions as well as the presence of inhomogeneities. Here we use Na23 nuclear magnetic resonance to probe both static and dynamical magnetic properties in single-crystal Na2IrO3. We find that the NMR shift follows the bulk susceptibility above 30 K but deviates from it below; moreover below TN the spectra show a broad distribution of internal magnetic fields. Both of these results provide evidence for inequivalent magnetic sites at low temperature, suggesting inhomogeneities are important for the magnetism. The spin-lattice relaxation rate is isotropic and diverges at TN, suggesting that the Kitaev cubic axes may control the critical quantum spin fluctuations. In the ordered state, we observe gapless excitations, which may arise from site substitution, emergent defects from milder disorder, or possibly be associated with nearby quantum paramagnetic states distinct from the Kitaev spin liquid

Dark Ages Cold Period: A literature review and directions for future research

Several late Quaternary studies have recorded cold and disturbed climates centred during the mid-first millennium AD and discussed these conditions under the term ‘Dark Ages Cold Period’ (DACP). A review of 114 palaeoclimate papers indicated that cold climates were common in the Northern Hemisphere between AD 400 and 765. There are also suggestions that some regions may have been relatively wet during the DACP, while those around the Mediterranean and the China/Tibetan Plateau indicate coinciding droughts. A set of environmental responses, however, indicate a delayed DACP interval (AD 509–865) postdating the actual climate signal. Previously, the DACP has been linked with the North Atlantic ice-rafting event at about 1400 years ago, while some evidence suggests an involvement of the North Atlantic Oscillation and/or El Niño–Southern Oscillation. More recently, another proposed phase of widespread cooling, the ‘Late Antique Little Ice Age’ (LALIA), overlaps with the DACP and has been tentatively linked with volcanic aerosol and solar irradiance variations reinforcing the climatic downturn since AD 536. Importantly, a higher number of proxy records extending over the first millennium AD is required for more rigorous assessments of climate variability and the forcing during these centuries and to disentangle the DACP and LALIA fingerprints in the proxy data, particularly to determine whether the DACP and the LALIA are distinct features. Also a richer network of both climate and environmental proxies is needed to evaluate the human–environment interactions, during the historical Migration Period, and thus through the DACP

On Automated Lemma Generation for Separation Logic with Inductive Definitions

Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas relating the inductive definitions. We propose a novel approach for generating these lemmas automatically which is based on simple syntactic criteria and deterministic strategies for applying them. Our approach focuses on iterative programs, although it can be applied to recursive programs as well, and specifications that describe not only the shape of the data structures, but also their content or their size. Empirically, we find that our approach is powerful enough to deal with sophisticated benchmarks, e.g., iterative procedures for searching, inserting, or deleting elements in sorted lists, binary search tress, red-black trees, and AVL trees, in a very efficient way

Retrospective model-based inference guides model-free credit assignment

An extensive reinforcement learning literature shows that organisms assign credit efficiently, even under conditions of state uncertainty. However, little is known about credit-assignment when state uncertainty is subsequently resolved. Here, we address this problem within the framework of an interaction between model-free (MF) and model-based (MB) control systems. We present and support experimentally a theory of MB retrospective-inference. Within this framework, a MB system resolves uncertainty that prevailed when actions were taken thus guiding an MF credit-assignment. Using a task in which there was initial uncertainty about the lotteries that were chosen, we found that when participants’ momentary uncertainty about which lottery had generated an outcome was resolved by provision of subsequent information, participants preferentially assigned credit within a MF system to the lottery they retrospectively inferred was responsible for this outcome. These findings extend our knowledge about the range of MB functions and the scope of system interactions

Disfluency in dialogue:an intentional signal from the speaker?

Disfluency is a characteristic feature of spontaneous human speech, commonly seen as a consequence of problems with production. However, the question remains open as to why speakers are disfluent: Is it a mechanical by-product of planning difficulty, or do speakers use disfluency in dialogue to manage listeners' expectations? To address this question, we present two experiments investigating the production of disfluency in monologue and dialogue situations. Dialogue affected the linguistic choices made by participants, who aligned on referring expressions by choosing less frequent names for ambiguous images where those names had previously been mentioned. However, participants were no more disfluent in dialogue than in monologue situations, and the distribution of types of disfluency used remained constant. Our evidence rules out at least a straightforward interpretation of the view that disfluencies are an intentional signal in dialogue. © 2012 Psychonomic Society, Inc

Influence of bioreaction on a long-term operation of a submerged membrane adsorption hybrid system

This study investigates the long-term performance of a submerged membrane adsorption hybrid system (SMAHS) for organic matter removal from synthetic wastewater representing biologically treated wastewater by using a low dose of powdered activated carbon (PAC). A simple periodic backwash system is used to de-clog the hollow fiber membrane. In this reactor, bioreaction takes place due to the growth of the biomass in the system. This hybrid system was able to remove effectively the small- and large-molecular weight organic matters from 270 to 36,270 Da. The effect of PAC replacement in the reactor was also studied and it was shown that PAC replacement could enhance both biological activity and adsorption. With PAC replacement of 2.5%(total amount) per day, the total organic carbon (TOC) removal efficiency was 10% higher than without PAC replacement. In another long-term experiment, the TOC removal efficiency was maintained over 85% even after 55-day operation (with PAC replacement rate of 2.5%(total amount) every two days). © 2006