The classic cake cutting problem concerns the fair allocation of a heterogeneous resource among interested agents. In this paper, we study a public goods variant of the problem, where instead of competing with one another for the cake, the agents all share the same subset of the cake which must be chosen subject to a length constraint. We focus on the design of truthful and fair mechanisms in the presence of strategic agents who have piecewise uniform utilities over the cake. On the one hand, we show that the leximin solution is truthful and moreover maximizes an egalitarian welfare measure among all truthful and position oblivious mechanisms. On the other hand, we demonstrate that the maximum Nash welfare solution is truthful for two agents but not in general. Our results assume that mechanisms can block each agent from accessing parts that the agent does not claim to desire; we provide an impossibility result when blocking is not allowed.
Polyimine covalent adaptable networks (CANs) exhibit several dynamic characteristics (such as recyclability and reprocessability) that are beneficial for compensating for the disadvantages of traditional petroleum-based synthetic thermosetting resins, and are therefore suggested as potential substitutes for environmentally unfriendly resins. However, owing to the lack of sufficient stability of imine bonds and their linked molecular chains, most polyimine CANs do not exhibit superior properties in applications with high stability requirements, such as strong water resistance, high heat resistance, and excellent mechanical strength. In this study, we designed and synthesized a new class of fully aromatic polyimine CANs to improve the stability of imine bonds and molecular chains employing the conjugation effect of the two benzene rings to C=N and fully aromatic structures. In contrast, these CANs simultaneously demonstrate superior water resistance (water absorption: 0.14–0.15%) and heat resistance (5% weight loss ( T d5% ): 434–441 °C; glass transition temperature ( T g ): 217–239 °C) than that of previously reported polyimine CANs (water absorption: 0.90–90%; T d5% : 200–348 °C; T g : 47–215 °C). They have outstanding mechanical properties that are almost unaffected by adsorbed water. Meanwhile, the resins exhibited remarkable resistance to ordinary acids, bases, oxidants, salts, solvents, and oils, except for several special solvents. In addition, like other polyimine CANs, they maintain their dynamic behavior characteristics, including degradability, recyclability, malleability, reprocessability, and rehealability. This study provides a new method for improving the comprehensive performance of polyimine CANs.
In pursuit of participatory budgeting (PB) outcomes with broader fairness guarantees, we initiate the study of lotteries over discrete PB outcomes. As the projects have heterogeneous costs, the amount spent may not be equal ex ante and ex post. To address this, we develop a technique to bound the amount by which the ex-post spend differs from the ex-ante spend---the property is termed budget balanced up to one project (BB1). With respect to fairness, we take a best-of-both-worlds perspective, seeking outcomes that are both ex-ante and ex-post fair. Towards this goal, we initiate a study of ex-ante fairness properties in PB, including Individual Fair Share (IFS), Unanimous Fair Share (UFS) and their stronger variants, as well as Group Fair Share (GFS). We show several incompatibility results between these ex-ante fairness notions and existing ex-post concepts based on justified representation. One of our main contributions is a randomized algorithm which simultaneously satisfies ex-ante Strong UFS, ex-post full justified representation (FJR) and ex-post BB1 for PB with binary utilities.
Abstract The wireless magnetic induction MIMO system can enhance the data transmission rate in near-field magnetic induction communication, but it also suffers from severe inter-channel interference issues. This paper introduces precoding techniques into the wireless magnetic induction MIMO system, employing the zero-forcing precoding algorithm to eliminate interference between different channels. Firstly, leveraging the characteristic that the channel state of magnetic induction transmit-receive coils is determined solely by the physical parameters of the coils, channel estimation is performed to obtain the channel gain matrix for wireless magnetic induction communication. Subsequently, the obtained channel matrix is subjected to zero-forcing precoding to eliminate interference caused by coupling between different channels. Simulation results indicate that the data transmission rate of the wireless magnetic induction MIMO system is significantly higher after applying zero-forcing precoding compared to the rate without it. Additionally, the system’s data transmission rate decreases as the distance between the transmitting and receiving coils increases.
Abstract Magnetic induction communication is a technology that utilizes magnetic field variations to transmit information. Compared to traditional electromagnetic wave communication, magnetic induction communication performs excellently in environments where electromagnetic waves are difficult to propagate, such as underwater and in soil. However, the current transmission rate of magnetic induction communication is relatively low. The magnetic induction MISO communication system addresses the issue of low transmission rates in cross-medium communication. However, it overlooks the impact of the transmission coil group arrangement on transmission rates. This paper investigates the effect of the transmission coil group arrangement on communication performance and proposes an arc-shaped magnetic induction MISO communication system. The transmission rate performance is analyzed, and the impact of the angle between the transmitting and receiving coils on the reception rate is studied. An expression for the channel gain increment is provided, along with its variation trend with the angle. When the position of the receiving coil is fixed, the expression yields the maximum increment of the shaped channel gain. Simulation results demonstrate that the data transmission rate of the shaped system is approximately 10% higher than that of the unshaped system.
In pursuit of participatory budgeting (PB) outcomes with broader fairness guarantees, we initiate the study of lotteries over discrete PB outcomes. As the projects have heterogeneous costs, the amount spent may not be equal ex ante and ex post. To address this, we develop a technique to bound the amount by which the ex-post spend differs from the ex-ante spend -- the property is termed budget balanced up to one project (BB1). With respect to fairness, we take a best-of-both-worlds perspective, seeking outcomes that are both ex-ante and ex-post fair. Towards this goal, we initiate a study of ex-ante fairness properties in PB, including Individual Fair Share (IFS), Unanimous Fair Share (UFS) and their stronger variants, as well as Group Fair Share (GFS). We show several incompatibility results between these ex-ante fairness notions and existing ex-post concepts based on justified representation. One of our main contributions is a randomized algorithm which simultaneously satisfies ex-ante Strong UFS, ex-post full justified representation (FJR) and ex-post BB1 for PB with binary utilities.
In approval-based budget division, a budget needs to be distributed to some candidates based on the voters' approval ballots over these candidates. In the pursuit of simple, well-behaved, and approximately fair rules for this setting, we introduce the class of sequential payment rules, where each voter controls a part of the budget and repeatedly spends his share on his approved candidates to determine the final distribution. We show that all sequential payment rules satisfy a demanding population consistency notion and we identify two particularly appealing rules within this class called the maximum payment rule (MP) and the $\frac{1}{3}$-multiplicative sequential payment rule ($\frac{1}{3}$-MP). More specifically, we prove that (i) MP is, apart from one other rule, the only monotonic sequential payment rule and gives a $2$-approximation to a fairness notion called average fair share, and (ii) $\frac{1}{3}$-MP gives a $\frac{3}{2}$-approximation to average fair share, which is optimal among sequential payment rules.
We consider a voting scenario in which the resource to be voted upon may consist of both indivisible and divisible goods. This setting generalizes both the well-studied model of multiwinner voting and the recently introduced model of cake sharing. Under approval votes, we propose two variants of the extended justified representation (EJR) notion from multiwinner voting, a stronger one called EJR for mixed goods (EJR-M) and a weaker one called EJR up to 1 (EJR-1). We extend three multiwinner voting rules to our setting -- GreedyEJR, the method of equal shares (MES), and proportional approval voting (PAV) -- and show that while all three generalizations satisfy EJR-1, only the first one provides EJR-M. In addition, we derive tight bounds on the proportionality degree implied by EJR-M and EJR-1, and investigate the proportionality degree of our proposed rules.
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