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We study the fair and efficient allocation of a set of indivisible goods among agents, where each good has several copies, and each agent has an additively separable concave valuation function with a threshold. These valuations capture the property of diminishing marginal returns, and they are more general than the well-studied case of additive valuations. We present a polynomial-time algorithm that approximates the optimal Nash social welfare (NSW) up to a factor of e1/e ≈ 1.445. This matches with the state-of-the-art approximation factor for additive valuations. The computed allocation also satisfies the popular fairness guarantee of envy-freeness up to one good (EF1) up to a factor of 2 + ε. For instances without thresholds, it is also approximately Pareto-optimal. For instances satisfying a large market property, we show an improved approximation factor. Lastly, we show that the upper bounds on the optimal NSW introduced in Cole and Gkatzelis (2018) and Barman et al. (2018) have the same value.

E-TEST (Einstein Telescope Euregio-Meuse-Rhin Site and Technology) is a project recently funded by the European program Ineterreg Euregio Meuse-Rhine. This program is dedicated to innovative cross boarder activities between Belgium, The Netherlands and Germany. With a total budget of15MC and a consortium of 11 partners from the three countries, the objective of the project is twofold. Firstly, to develop an eco-friendly and non-invasive imaging of the geological conditions as well as the development of an observatory of the underground in the EMR region. Secondly, to develop technologies necessary for 3rd generation gravitational wave detectors. In particular, it is proposed to develop a prototype of large suspended cryogenic silicon mirror, isolated from seismic vibrations at low frequency. The total budget of the project is equally spread over the two activities. The first activity is not discussed at all in this report. The E-TEST prototype will have some key unique features: a silicon mirror of 100 kg, a radiative cooling strategy (non contact), a low-frequency hybrid isolation stage, cryogenic sensors and electronics, a laser and optics at 2 microns, a low thermal noise coating.

Although non-genetic inheritance is thought to play an important role in plant ecology and evolution, evidence for adaptive transgenerational plasticity is scarce. Here, we investigated the consequences of copper excess on offspring defences and fitness in the giant duckweed (Spirodela polyrhiza) across multiple asexual generations. We found that exposing large monoclonal populations (>10,000 individuals) for 30 generations to copper excess decreased plant fitness during the first few generations but increased their fitness in consecutive generations under recurring stress when plants were grown for 5 generations under control conditions prior recurring conditions. Similarly, propagating individual plants as single descendants for 5 or 10 generations under copper excess decreased plant fitness when 5 generations and improved plant fitness when 10 generations passed between initial and recurring stress; thus, transgenerational stress responses likely contributed to the observed variations in offspring fitness of long-term copper exposed populations. Fitness benefits under recurring stress were partially associated with avoidance of excessive copper accumulation, which in turn correlated with transgenerationally modified flavonoid concentrations. Taken together, these data demonstrate time-dependent adaptive transgenerational responses under recurring stress, which highlights the importance of non-genetic inheritance for plant ecology and evolution.

Sub-picosecond magnetisation manipulation via femtosecond optical pumping has attracted wide attention ever since its original discovery in 1996. However, the spatial evolution of the magnetisation is not yet well understood, in part due to the difficulty in experimentally probing such rapid dynamics. Here, we find evidence of a universal rapid magnetic order recovery in ferrimagnets with perpendicular magnetic anisotropy via nonlinear magnon processes. We identify magnon localisation and coalescence processes, whereby localised magnetic textures nucleate and subsequently interact and grow in accordance with a power law formalism. A hydrodynamic representation of the numerical simulations indicates that the appearance of noncollinear magnetisation via optical pumping establishes exchange-mediated spin currents with an equivalent 100% spin polarised charge current density of 107 A cm−2. Such large spin currents precipitate rapid recovery of magnetic order after optical pumping. The magnon processes discussed here provide new insights for the stabilization of desired meta-stable states., The understanding of the magnetisation evolution upon femtosecond optical pumping remains elusive. The authors perform resonant X-ray magnetic scattering measurements and multiscale simulations that reveal rapid magnetic order recovery in ferrimagnets via nonlinear magnon processes.

We consider the task of assigning indivisible goods to a set of agents in a fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is to maximize the geometric mean of the utilities of the agents. Each good comes in multiple items or copies, and the utility of an agent diminishes as it receives more items of the same good. The utility of a bundle of items for an agent is the sum of the utilities of the items in the bundle. Each agent has a utility cap beyond which he does not value additional items. We give a polynomial time approximation algorithm that maximizes Nash social welfare up to a factor of $e^{1/e} \approx 1.445$.

Sub-picosecond magnetisation manipulation via femtosecond optical pumping has attracted wide attention ever since its original discovery in 1996. However, the spatial evolution of the magnetisation is not yet well understood, in part due to the difficulty in experimentally probing such rapid dynamics. Here, we find evidence of rapid magnetic order recovery in materials with perpendicular magnetic anisotropy via nonlinear magnon processes. We identify both localisation and coalescence regimes, whereby localised magnetic textures nucleate and subsequently evolve in accordance with a power law formalism. Coalescence is observed for optical excitations both above and below the switching threshold. Simulations indicate that the ultrafast generation of noncollinear magnetisation via optical pumping establishes exchange-mediated spin currents with an equivalent 100% spin polarised charge current density of $10^8$ A/cm$^2$. Such large spin currents precipitate rapid recovery of magnetic order after optical pumping. These processes suggest an ultrafast optical route for the stabilization of desired meta-stable states, e.g., isolated skyrmions.

The nonlinear Schr��dinger (NLS) equation and the Whitham modulation equations both describe slowly varying, locally periodic nonlinear wavetrains, albeit in differing amplitude-frequency domains. In this paper, we take advantage of the overlapping asymptotic regime that applies to both the NLS and Whitham modulation descriptions in order to develop a universal analytical description of dispersive shock waves (DSWs) generated in Riemann problems for a broad class of integrable and non-integrable nonlinear dispersive equations. The proposed method extends DSW fitting theory that prescribes the motion of a DSW's edges into the DSW's interior, i.e., this work reveals the DSW structure. Our approach also provides a natural framework in which to analyze DSW stability. We consider several representative, physically relevant examples that illustrate the efficacy of the developed general theory. Comparisons with direct numerical simulations show that inclusion of higher order terms in the NLS equation enables a remarkably accurate description of the DSW structure in a broad region that extends from the harmonic, small amplitude edge., 29 pages, 6 figures

Competitive equilibrium is a central concept in economics with numerous applications beyond markets, such as scheduling, fair allocation of goods, or bandwidth distribution in networks. Computation of competitive equilibria has received a significant amount of interest in algorithmic game theory, mainly for the prominent case of Fisher markets. Natural and decentralized processes like tatonnement and proportional response dynamics (PRD) converge quickly towards equilibrium in large classes of Fisher markets. Almost all of the literature assumes that the market is a static environment and that the parameters of agents and goods do not change over time. In contrast, many large real-world markets are subject to frequent and dynamic changes. In this paper, we provide the first provable performance guarantees of discrete-time tatonnement and PRD in markets that are subject to perturbation over time. We analyze the prominent class of Fisher markets with CES utilities and quantify the impact of changes in supplies of goods, budgets of agents, and utility functions of agents on the convergence of tatonnement to market equilibrium. Since the equilibrium becomes a dynamic object and will rarely be reached, our analysis provides bounds expressing the distance to equilibrium that will be maintained via tatonnement and PRD updates. Our results indicate that in many cases, tatonnement and PRD follow the equilibrium rather closely and quickly recover conditions of approximate market clearing. Our approach can be generalized to analyzing a general class of Lyapunov dynamical systems with changing system parameters, which might be of independent interest.

We present the first constant-factor approximation algorithm for maximizing the Nash social welfare when allocating indivisible items to agents with budget-additive valuation functions. Budget-additive valuations represent an important class of submodular functions. They have attracted a lot of research interest in recent years due to many interesting applications. For every $\varepsilon > 0$, our algorithm obtains a $(2.404 + \varepsilon)$-approximation in time polynomial in the input size and $1/\varepsilon$. Our algorithm relies on rounding an approximate equilibrium in a linear Fisher market where sellers have earning limits (upper bounds on the amount of money they want to earn) and buyers have utility limits (upper bounds on the amount of utility they want to achieve). In contrast to markets with either earning or utility limits, these markets have not been studied before. They turn out to have fundamentally different properties. Although the existence of equilibria is not guaranteed, we show that the market instances arising from the Nash social welfare problem always have an equilibrium. Further, we show that the set of equilibria is not convex, answering a question of [Cole et al, EC 2017]. We design an FPTAS to compute an approximate equilibrium, a result that may be of independent interest.

We present the first analysis of Fisher markets with buyers that have budget-additive utility functions. Budget-additive utilities are elementary concave functions with numerous applications in online adword markets and revenue optimization problems. They extend the standard case of linear utilities and have been studied in a variety of other market models. In contrast to the frequently studied CES utilities, they have a global satiation point which can imply multiple market equilibria with quite different characteristics. Our main result is an efficient combinatorial algorithm to compute a market equilibrium with a Pareto-optimal allocation of goods. It relies on a new descending-price approach and, as a special case, also implies a novel combinatorial algorithm for computing a market equilibrium in linear Fisher markets. We complement these positive results with a number of hardness results for related computational questions. We prove that it is NP-hard to compute a market equilibrium that maximizes social welfare, and it is PPAD-hard to find any market equilibrium with utility functions with separate satiation points for each buyer and each good., 21 pages

In dispersive media, hydrodynamic singularities are resolved by coherent wavetrains known as dispersive shock waves (DSWs). Only dynamically expanding, temporal DSWs are possible in one-dimensional media. The additional degree of freedom inherent in two-dimensional media allows for the generation of time-independent DSWs that exhibit spatial expansion. Spatial oblique DSWs, dispersive analogs of oblique shocks in classical media, are constructed utilizing Whitham modulation theory for a class of nonlinear Schr��dinger boundary value problems. Self-similar, simple wave solutions of the modulation equations yield relations between the DSW's orientation and the upstream/downstream flow fields. Time dependent numerical simulations demonstrate a convective or absolute instability of oblique DSWs in supersonic flow over obstacles. The convective instability results in an effective stabilization of the DSW., 23 pages, 7 figures

The magnetic dissipative droplet is a strongly nonlinear wave structure that can be stabilized in a thin film ferromagnet exhibiting perpendicular magnetic anisotropy by use of spin transfer torque. These structures have been observed experimentally at room temperature, showcasing their robustness against noise. Here, we quantify the effects of thermal noise by deriving the stochastic equations of motion for a droplet based on soliton perturbation theory. First, it is found that deterministic droplets are linearly unstable at large bias currents, subject to a drift instability. When the droplet is linearly stable, our framework allows us to analytically compute the droplet's generation linewidth and center variance. Additionally, we study the influence of non-local and Oersted fields with micromagnetic simulations, providing insight into their effect on the generation linewidth. These results motivate detailed experiments on the current and temperature-dependent linewidth as well as drift instability statistics of droplets, which are important figures-of-merit in the prospect of droplet-based applications., 10 pages, 6 figures

Summary Background Patients with chronic obstructive pulmonary disease (COPD) have few options for treatment. The efficacy and safety of the phosphodiesterase-4 inhibitor roflumilast have been investigated in studies of patients with moderate-to-severe COPD, but not in those concomitantly treated with longacting inhaled bronchodilators. The effect of roflumilast on lung function in patients with COPD that is moderate to severe who are already being treated with salmeterol or tiotropium was investigated. Methods In two double-blind, multicentre studies done in an outpatient setting, after a 4-week run-in, patients older than 40 years with moderate-to-severe COPD were randomly assigned to oral roflumilast 500 μg or placebo once a day for 24 weeks, in addition to salmeterol (M2-127 study) or tiotropium (M2-128 study). The primary endpoint was change in prebronchodilator forced expiratory volume in 1 s (FEV 1 ). Analysis was by intention to treat. The studies are registered with ClinicalTrials.gov, number NCT00313209 for M2-127, and NCT00424268 for M2-128. Findings In the salmeterol plus roflumilast trial, 466 patients were assigned to and treated with roflumilast and 467 with placebo; in the tiotropium plus roflumilast trial, 371 patients were assigned to and treated with roflumilast and 372 with placebo. Compared with placebo, roflumilast consistently improved mean prebronchodilator FEV 1 by 49 mL (p 1 was noted in both groups. Furthermore, roflumilast had beneficial effects on other lung function measurements and on selected patient-reported outcomes in both groups. Nausea, diarrhoea, weight loss, and, to a lesser extent, headache were more frequent in patients in the roflumilast groups. These adverse events were associated with increased patient withdrawal. Interpretation Roflumilast improves lung function in patients with COPD treated with salmeterol or tiotropium, and could become an important treatment for these patients. Funding Nycomed.

Coalition formation is a fundamental problem in the organization of many multi-agent systems. In large populations, the formation of coalitions is often restricted by structural visibility and locality constraints under which agents can reorganize. We capture and study this aspect using a novel network-based model for dynamic locality within the popular framework of hedonic coalition formation games. We analyze the effects of network-based visibility and structure on the convergence of coalition formation processes to stable states. Our main result is a tight characterization of the structures based on which dynamic coalition formation can stabilize quickly. Maybe surprisingly, polynomial-time convergence can be achieved if and only if coalition formation is based on complete or star graphs.

We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to another agent. Each agent has a complete preference list over all other agents it can be matched with. However, depending on the constraints and the current state of the game, not all possible partners are available for matching at all times. For correlated preferences, we propose and study a general class of hedonic coalition formation games that we call coalition formation games with constraints. This class includes and extends many recently studied variants of stable matching, such as locally stable matching, socially stable matching, or friendship matching. Perhaps surprisingly, we show that all these variants are encompassed in a class of "consistent" instances that always allow a polynomial improvement sequence to a stable state. In addition, we show that for consistent instances there always exists a polynomial sequence to every reachable state. Our characterization is tight in the sense that we provide exponential lower bounds when each of the requirements for consistency is violated. We also analyze matching with uncorrelated preferences, where we obtain a larger variety of results. While socially stable matching always allows a polynomial sequence to a stable state, for other classes different additional assumptions are sufficient to guarantee the same results. For the problem of reaching a given stable state, we show NP-hardness in almost all considered classes of matching games.

Motivated by recent experimental results, we study beating darkdark (DD) solitons as a prototypical coherent structure that emerges in two-component BoseEinstein condensates. We showcase their connection to darkbright solitons via SO(2) rotation, and infer from it both their intrinsic beating frequency and their frequency of oscillation inside a parabolic trap. We identify them as exact periodic orbits in the Manakov limit of equal inter- and intra-species nonlinearity strengths with and without the trap and showcase the persistence of such states upon weak deviations from this limit. We also consider large deviations from the Manakov limit illustrating that this breathing state may be broken apart into darkanti-dark soliton states. Finally, we consider the dynamics and interactions of two beating DD solitons in the absence and in the presence of the trap, inferring their typically repulsive interaction. © 2012 IOP Publishing Ltd.

We consider the discrete eigenvalues of the operator $H_\eps=-��+V(\x)+\eps^2Q(\eps\x)$, where $V(\x)$ is periodic and $Q(\y)$ is localized on $\R^d,\ \ d\ge1$. For $\eps>0$ and sufficiently small, discrete eigenvalues may bifurcate (emerge) from spectral band edges of the periodic Schr��dinger operator, $H_0 = -��_\x+V(\x)$, into spectral gaps. The nature of the bifurcation depends on the homogenized Schr��dinger operator $L_{A,Q}=-\nabla_\y\cdot A \nabla_\y +\ Q(\y)$. Here, $A$ denotes the inverse effective mass matrix, associated with the spectral band edge, which is the site of the bifurcation., 26 pages, 3 figures, to appear SIAM J. Math. Anal

The processes of merging and splitting dilute-gas Bose-Einstein condensates are studied in the nonadiabatic, high-density regime. Rich dynamics are found. Depending on the experimental parameters, uniform soliton trains containing more than ten solitons or the formation of a high-density bulge as well as quantum (or dispersive) shock waves are observed experimentally within merged BECs. Our numerical simulations indicate the formation of many vortex rings. In the case of splitting a BEC, the transition from sound-wave formation to dispersive shock-wave formation is studied by use of increasingly stronger splitting barriers. These experiments realize prototypical dispersive shock situations., Comment: 10 pages, 8 figures

Resistance breeding in apple has a long tradition at the Institute of Fruit Breeding now Julius Kuehn-institute in Dresden-Pillnitz. The breeding was aimed at the production of multiple resistance cultivars to allow a more sustainable and environmentally friendly production of apple. In the last decades a series of resistant cultivars (Re®-cultivars) bred in Dresden-Pillnitz has been released, ‘Recolor’ and ‘Rekarda’ in 2006. The main topic in the resistance breeding programme was scab resistance and the donor of scab resistance in most cultivars was Malus x floribunda 821. Due to the development of strains that are able to overcome resistance genes inherited by M. x floribunda 821 and due to the fact that single resistance genes can be broken easily, pyramiding of resistance genes is necessary. Besides scab, fire blight and powdery mildew are the main disease for which a pyramiding of genes is aspired in Pillnitz. Biotechnical approaches are necessary for the early detection of pyramided resistance genes in breeding clones. This paper will give an overview of the resistance breeding of apple in Pillnitz and the methods used.

A nonlinear model of spin-wave excitation involving a point contact in a thin ferromagnetic film that includes the Oersted magnetic field contribution is presented. We consider the case of an external dc field applied perpendicular to the film plane. The two-dimensional vectorial model reduces to an exact one-dimensional equation of motion. Large-amplitude vortex modes are computed, which represent a fundamental shift in the geometrical understanding of spin transfer nano-oscillators. Odd symmetry forces the magnetization to be pinned in the center of the point contact. Using the spin transfer efficiency as a single fitting parameter, the calculated dependence of frequency on current and contact size is in good agreement with recent experimental data. These vortex states are geometrically very different from previously computed cylindrical modes that exhibit even symmetry when the Oersted field is ignored., Comment: The authors have withdrawn this manuscript because the highly symmetric vortex mode has been found to be numerically unstable to 2D perturbations

Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to emphasize the plausibility of results, none of these algorithms has been shown to actually compute optimal partitions. We here settle the unknown complexity status of modularity maximization by showing that the corresponding decision version is NP-complete in the strong sense. As a consequence, any efficient, i.e. polynomial-time, algorithm is only heuristic and yields suboptimal partitions on many instances., Comment: 10 pages, 1 figure

We study efficient algorithms for a natural learning problem in markets. There is one seller with m divisible goods and n buyers with unknown individual utility functions and budgets of money. The seller can repeatedly announce prices and observe aggregate demand bundles requested by the buyers. The goal of the seller is to learn the utility functions and budgets of the buyers. Our scenario falls into the classic domain of ''revealed preference'' analysis. Problems with revealed preference have recently started to attract increased interest in computer science due to their fundamental nature in understanding customer behavior in electronic markets. The goal of revealed preference analysis is to observe rational agent behavior, to explain it using a suitable model for the utility functions, and to predict future agent behavior. Our results are the first polynomial-time algorithms to learn utility and budget parameters via revealed preference queries in classic Fisher markets with multiple buyers. Our analysis concentrates on linear, CES, and Leontief markets, which are the most prominent classes studied in the literature. Some of our results extend to general Arrow-Debreu exchange markets.