Precise Complexity of the Core in Dichotomous and Additive Hedonic Games

Hedonic games provide a general model of coalition formation, in which a set of agents is partitioned into coalitions, with each agent having preferences over which other players are in her coalition. We prove that with additively separable preferences, it is $\Sigma_2^p$-complete to decide whether a core- or strict-core-stable partition exists, extending a result of Woeginger (2013). Our result holds even if valuations are symmetric and non-zero only for a constant number of other agents. We also establish $\Sigma_2^p$-completeness of deciding non-emptiness of the strict core for hedonic games with dichotomous preferences. Such results establish that the core is much less tractable than solution concepts such as individual stability.Comment: ADT-2017, 15 pages in LNCS styl

Data-driven PDE discovery with evolutionary approach

The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation discovery techniques. The existing methods of PDE (partial derivative equations) discovery are bound with the sparse regression. However, sparse regression is restricting the resulting model form, since the terms for PDE are defined before regression. The evolutionary approach described in the article has a symbolic regression as the background instead and thus has fewer restrictions on the PDE form. The evolutionary method of PDE discovery (EPDE) is described and tested on several canonical PDEs. The question of robustness is examined on a noised data example

Finding the optimal design of a passive microfluidic mixer.

The ability to thoroughly mix two fluids is a fundamental need in microfluidics. While a variety of different microfluidic mixers have been designed by researchers, it remains unknown which (if any) of these mixers are optimal (that is, which designs provide the most thorough mixing with the smallest possible fluidic resistance across the mixer). In this work, we automatically designed and rationally optimized a microfluidic mixer. We accomplished this by first generating a library of thousands of different randomly designed mixers, then using the non-dominated sorting genetic algorithm II (NSGA-II) to optimize the random chips in order to achieve Pareto efficiency. Pareto efficiency is a state of allocation of resources (e.g. driving force) from which it is impossible to reallocate so as to make any one individual criterion better off (e.g. pressure drop) without making at least one individual criterion (e.g. mixing performance) worse off. After 200 generations of evolution, Pareto efficiency was achieved and the Pareto-optimal front was found. We examined designs at the Pareto-optimal front and found several design criteria that enhance the mixing performance of a mixer while minimizing its fluidic resistance; these observations provide new criteria on how to design optimal microfluidic mixers. Additionally, we compared the designs from NSGA-II with some popular microfluidic mixer designs from the literature and found that designs from NSGA-II have lower fluidic resistance with similar mixing performance. As a proof of concept, we fabricated three mixer designs from 200 generations of evolution and one conventional popular mixer design and tested the performance of these four mixers. Using this approach, an optimal design of a passive microfluidic mixer is found and the criteria of designing a passive microfluidic mixer are established

Novel sol–gel preparation of (PO)–(CaO)–(NaO)–(TiO) bioresorbable glasses (X = 0.05, 0.1, and 0.15)

Quaternary phosphate-based glasses in the PO–CaO–NaO–TiO system with a fixed PO and CaO content of 40 and 25 mol% respectively have been successfully synthesised via sol–gel method and bulk, transparent samples were obtained. The structure, elemental proportion, and thermal properties of stabilised sol–gel glasses have been characterised using X-ray diffraction (XRD), energy dispersive X-ray spectroscopy (EDX), P nuclear magnetic resonance (P NMR), titanium K-edge X-ray absorption near-edge structure (XANES), fourier transform infrared (FTIR) spectroscopy, and differential thermal analysis (DTA). The XRD results confirmed the amorphous nature for all stabilized sol–gel derived glasses. The EDX result shows the relatively low loss of phosphorus during the sol–gel process and Ti K-edge XANES confirmed titanium in the glass structure is in mainly six-fold coordination environment. The P NMR and FTIR results revealed that the glass structure consist of mainly Q and Q phosphate units and the Ti cation was acting as a cross-linking between phosphate units. In addition DTA results confirmed a decrease in the glass transition and crystallisation temperature with increasing NaO content. Ion release studies also demonstrated a decrease in degradation rates with increasing TiO content therefore supporting the use of these glasses for biomedical applications that require a degree of control over glass degradation. These sol–gel glasses also offer the potential to incorporate proactive molecules for drug delivery application due to the low synthesis temperature employed

Telling the tale of the first stars

HE 0107-5240 is a star in more than once sense of the word. Chemically, it is the most primitive object yet discovered, and it is at the centre of debate about the origins of the first elements in the Universe.Comment: 3 pages, 0 figures, published in Nature "News and Views," Apr. 24, 200

The prevalence and burden of subthreshold generalized anxiety disorder: A systematic review

Background: To review the prevalence and impact of generalized anxiety disorder (GAD) below the diagnostic threshold and explore its treatment needs in times of scarce healthcare resources.Methods: A systematic literature search was conducted until January 2013 using PUBMED/MEDLINE, PSYCINFO, EMBASE and reference lists to identify epidemiological studies of subthreshold GAD, i.e. GAD symptoms that do not reach the current thresholds of DSM-III-R, DSM-IV or ICD-10. Quality of all included studies was assessed and median prevalences of subthreshold GAD were calculated for different subpopulations.Results: Inclusion criteria led to 15 high-quality and 3 low-quality epidemiological studies with a total of 48,214 participants being reviewed. Whilst GAD proved to be a common mental health disorder, the prevalence for subthreshold GAD was twice that for the full syndrome. Subthreshold GAD is typically persistent, causing considerably more suffering and impairment in psychosocial and work functioning, benzodiazepine and primary health care use, than in non-anxious individuals. Subthreshold GAD can also increase the risk of onset and worsen the course of a range of comorbid mental health, pain and somatic disorders; further increasing costs. Results are robust against bias due to low study quality.Conclusions: Subthreshold GAD is a common, recurrent and impairing disease with verifiable morbidity that claims significant healthcare resources. As such, it should receive additional research and clinical attention. © 2014 Haller et al.; licensee BioMed Central Ltd

Supercritical heat transfer characteristics of couple stress convection flow from a vertical cylinder using an equation of state approach

The present work describes numerical simulations of the supercritical heat transfer characteristics of couple stress fluid flow from a vertical cylinder using the equation of state approach. Redlich-Kwong (RK-EOS) and Van der Waals (VW-EOS) equations of state (EOS) are deployed to derive the equation for the thermal expansion coefficient (β). The β values calculated based on RK-EOS are sufficiently close to the experimental values when compared with those based on VW-EOS. Due to the presence of couple stresses in the fluid, highly nonlinear coupled partial differential equations are generated. These primitive equations are reduced to dimensionless form by using suitable non-dimensional quantities. An unconditionally stable finite difference technique is used to solve the normalized conservation equations under physically viable boundary conditions, in order to describe the natural convection heat transfer characteristics of couple stress fluid external to a vertical cylinder in the supercritical region. For different values of the emerging physical parameters, numerical data for couple stress fluid for the case of Nitrogen is generated and presented in the form of graphs and tables. The present computations indicate that the velocity field is suppressed close to the cylinder whereas it is enhanced away from the cylinder with increasing values of reduced temperature in the supercritical fluid region. The reverse behavior is observed for reduced pressure. The present results are compared with the previous results and found to be in good agreement. Applications of the model include super-critical coating dynamics in the aerospace and medical industries