Bottleneck Routing Games with Low Price of Anarchy

We study {\em bottleneck routing games} where the social cost is determined by the worst congestion on any edge in the network. In the literature, bottleneck games assume player utility costs determined by the worst congested edge in their paths. However, the Nash equilibria of such games are inefficient since the price of anarchy can be very high and proportional to the size of the network. In order to obtain smaller price of anarchy we introduce {\em exponential bottleneck games} where the utility costs of the players are exponential functions of their congestions. We find that exponential bottleneck games are very efficient and give a poly-log bound on the price of anarchy: $O(\log L \cdot \log |E|)$, where $L$ is the largest path length in the players' strategy sets and $E$ is the set of edges in the graph. By adjusting the exponential utility costs with a logarithm we obtain games whose player costs are almost identical to those in regular bottleneck games, and at the same time have the good price of anarchy of exponential games.Comment: 12 page

Factors Affecting Gummy Butter.

11 p

Resonance regimes of scattering by small bodies with impedance boundary conditions

The paper concerns scattering of plane waves by a bounded obstacle with complex valued impedance boundary conditions. We study the spectrum of the Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic behavior of the solutions of the scattering problem. The study includes the case when $k=0$ is an eigenvalue or a resonance. The transformation from the impedance to the Dirichlet boundary condition as impedance grows is described. A relation between poles and zeroes of the scattering matrix in the non-self adjoint case is established. The results are applied to a problem of scattering by an obstacle with a springy coating. The paper describes the dependence of the impedance on the properties of the material, that is on forces due to the deviation of the boundary of the obstacle from the equilibrium position

Does the Babcock--Leighton Mechanism Operate on the Sun?

The contribution of the Babcock-Leighton mechanism to the generation of the Sun's poloidal magnetic field is estimated from sunspot data for three solar cycles. Comparison of the derived quantities with the A-index of the large-scale magnetic field suggests a positive answer to the question posed in the title of this paper.Comment: 5 pages, 2 figures, to apper in Astronomy Letter

Cloud-Chamber Observations of Some Unusual Neutral V Particles Having Light Secondaries

From six cloud-chamber photographs of unusual V0 decay events, the following conclusions are drawn: (1) there is a neutral V particle that decays into two particles lighter than κ mesons with a Q value too small to be consistent with a θ0(π, π, 214 Mev) particle; (2) some of these events cannot be explained in terms of the decay of a τ0(π0, π-, π+, Q∼80 Mev) particle; (3) these events can be explained by any one of a number of three-body decay schemes, but two different types of V particles must be postulated if two-body decays are assumed

Upward Three-Dimensional Grid Drawings of Graphs

A \emph{three-dimensional grid drawing} of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line segments representing the edges do not cross. Our aim is to produce three-dimensional grid drawings with small bounding box volume. We prove that every $n$-vertex graph with bounded degeneracy has a three-dimensional grid drawing with $O(n^{3/2})$ volume. This is the broadest class of graphs admiting such drawings. A three-dimensional grid drawing of a directed graph is \emph{upward} if every arc points up in the z-direction. We prove that every directed acyclic graph has an upward three-dimensional grid drawing with $(n^3)$ volume, which is tight for the complete dag. The previous best upper bound was $O(n^4)$. Our main result is that every $c$-colourable directed acyclic graph ($c$ constant) has an upward three-dimensional grid drawing with $O(n^2)$ volume. This result matches the bound in the undirected case, and improves the best known bound from $O(n^3)$ for many classes of directed acyclic graphs, including planar, series parallel, and outerplanar

Coercivity enhancement in exchange biased systems driven by interfacial magnetic frustration

We report the temperature and cooling field dependence of the coercivity of exchange biased MnF2/Fe bilayers. When the antiferromagnetic surface is in a state of maximum magnetic frustration and the net exchange bias is zero, we observe a strong enhancement of the coercivity, which is proportional to the exchange coupling between the layers. Hence, the coercivity can be tuned in a reproducible and repeatable fashion in the same sample. We propose that a frustrated interface provides local energy minima which effectively pin the propagating domain walls in the ferromagnet, leading to an enhanced coercivity

First-order phase transition vs. spin-state quantum-critical scenarios in strain-tuned epitaxial cobaltite thin films

Pr-containing perovskite cobaltites exhibit unusual valence transitions, coupled to coincident structural, spin-state, and metal-insulator transitions. Heteroepitaxial strain was recently used to control these phenomena in the model (Pr$_{1-y}$Y$_y$)$_{1-x}$Ca$_x$CoO$_{3-\delta}$ system, stabilizing a nonmagnetic insulating phase under compression (with a room-temperature valence/spin-state/metal-insulator transition) and a ferromagnetic metallic phase under tension, thus exposing a potential spin-state quantum critical point. The latter has been proposed in cobaltites and can be probed in this system as a function of a disorder-free variable (strain). We study this here via thickness-dependent strain relaxation in compressive SrLaAlO$_4$(001)/(Pr$_{0.85}$Y$_{0.15}$)$_{0.70}$Ca$_{0.30}$CoO$_{3-\delta}$ epitaxial thin films to quasi-continuously probe structural, electronic, and magnetic behaviors across the nonmagnetic-insulator/ferromagnetic-metal boundary. High-resolution X-ray diffraction, electronic transport, magnetometry, polarized neutron reflectometry, and temperature-dependent magnetic force microscopy provide a detailed picture, including abundant evidence of temperature- and strain-dependent phase coexistence. This indicates a first-order phase transition as opposed to spin-state quantum-critical behavior, which we discuss theoretically via a phenomenological Landau model for coupled spin-state and magnetic phase transitions.Comment: main text + supplementary materia

Forming a consensus opinion to inform long COVID support mechanisms and interventions: a modified Delphi approach

BackgroundCurrent approaches to support patients living with post-COVID condition, also known as Long COVID, are highly disparate with limited success in managing or resolving a well-documented and long-standing symptom burden. With approximately 2.1 million people living with the condition in the UK alone and millions more worldwide, there is a desperate need to devise support strategies and interventions for patients.MethodsA three-round Delphi consensus methodology was distributed internationally using an online survey and was completed by healthcare professionals (including clinicians, physiotherapists, and general practitioners), people with long COVID, and long COVID academic researchers (round 1 n = 273, round 2 n = 186, round 3 n = 138). Across the three rounds, respondents were located predominantly in the United Kingdom (UK), with 17.3–15.2% (round 1, n = 47; round 2 n = 32, round 2 n = 21) of respondents located elsewhere (United States of America (USA), Austria, Malta, United Arab Emirates (UAE), Finland, Norway, Malta, Netherlands, Iceland,Canada, Tunisie, Brazil, Hungary, Greece, France, Austrailia, South Africa, Serbia, and India). Respondents were given ∼5 weeks to complete the survey following enrolment, with round one taking place from 02/15/2022 to 03/ 28/22, round two; 05/09/2022 to 06/26/2022, and round 3; 07/14/2022 to 08/09/2022. A 5-point Likert scale of agreement was used and the opportunity to include free text responses was provided in the first round.FindingsFifty-five statements reached consensus (defined as >80% agree and strongly agree), across the domains of i) long COVID as a condition, ii) current support and care available for long COVID, iii) clinical assessments for long COVID, and iv) support mechanisms and rehabilitation interventions for long COVID, further sub-categorised by consideration, inclusion, and focus. Consensus reached proposes that long COVID requires specialised, comprehensive support mechanisms and that interventions should form a personalised care plan guided by the needs of the patients. Supportive approaches should focus on individual symptoms, including but not limited tofatigue, cognitive dysfunction, and dyspnoea, utilising pacing, fatigue management, and support returning to daily activities. The mental impact of living with long COVID, tolerance to physical activity, emotional distress and well-being, and research of pre-existing conditions with similar symptoms, such as myalgic encephalomyelitis,should also be considered when supporting people with long COVID.InterpretationWe provide an outline that achieved consensus with stakeholders that could be used to inform the design and implementation of bespoke long COVID support mechanisms