Computing balanced solutions for large international kidney exchange schemes when cycle length is unbounded

The preferred treatment for kidney failure is a transplant; however, demand for donor kidneys far outstrips supply. Kidney exchange, an innovation where willing but incompatible patient-donor pairs can exchange organs- — via barter cycles and altruist-initiated chains —provides a life-saving alternative.Typically, fielded exchanges act myopically, considering only the current pool of pairs when planning the cycles and chains. Yet kidney exchange is inherently dynamic, with participants arriving and departing. Also, many planned exchange transplants do not go to surgery due to various failures. So, it is important to consider the future when matching. Motivated by our experience running the computational side of a large nationwide kidney exchange, we present FutureMatch, a framework for learning to match in a general dynamic model. FutureMatch takes as input a high-level objective (e.g., "maximize graft survival of transplants over time'') decided on by experts, then automatically (i) learns based on data how to make this objective concrete and (ii) learns the ``means'' to accomplish this goal — a task, in our experience, that humans handle poorly. It uses data from all live kidney transplants in the US since 1987 to learn the quality of each possible match; it then learns the potentials of elements of the current input graph offline (e.g., potentials of pairs based on features such as donor and patient blood types), translates these to weights, and performs a computationally feasible batch matching that incorporates dynamic, failure-aware considerations through the weights. We validate FutureMatch on real fielded exchange data. It results in higher values of the objective. Furthermore, even under economically inefficient objectives that enforce equity, it yields better solutions for the efficient objective (which does not incorporate equity) than traditional myopic matching that uses the efficiency objective.

The need for kidney exchange arises when a healthy person wishes to donate a kidney but is incompatible with her intended recipient. Two main factors determine compatibility of a donor with a patient: blood-type compatibility and tissue-type compatibility. Two or more incompatible pairs can form a cyclic exchange so that each patient can receive a kidney from a compatible donor. In addition, an exchange can be initiated by a non-directed donor (an altruistic donor who does not designate a particular intended patient), and in this case, a chain of exchanges need not form a closed cycle.Current exchange pools are of moderate size and have a dynamic flavor as pairs enroll over time. Further, they contain many highly sensitized patients, i.e., patients that are very unlikely to be tissue-type compatible with a blood-type compatible donor. One major decision clearinghouses are facing is how often to search for allocations (a set of disjoint exchanges). On one hand, waiting for more pairs to arrive before finding allocations will increase the number of matched pairs, especially with highly sensitized patients, and on the other hand, waiting is costly. This paper studies this intrinsic tradeoff between the waiting time, and the number of pairs matched under a myopic, current-like, matching algorithm called Chunk Matching (CM) that accumulates a given number of incompatible pairs, or a chunk, before searching for an allocation in the pool that consists of easy and hard to match patients.We perform sensitivity analysis on the chunk size given different types of allocations; first, we first study the performance of CM when it searches for allocations limited to cycles of length 2 and show that if the waiting period between two subsequent match runs is a sub-linear function of the problem size (or the entire time horizon), CM matches approximately the same number of pairs as the online scenario (matching each time a new incompatible pair joins the pool) does. Waiting, however, a linear fraction between every two runs will result in matching linearly more pairs compared to the online scenario. We then analyze CM when cycles of length both 2 and 3 are allowed. We show that for some regimes, sub-linear waiting will result in a linear addition of matches comparing to the online scenario. Finally, we study the efficiency of dynamic matching with chains (chains are initiated by a non-directed donor), and show that in the online scenario, adding one non-directed donor will increase linearly the number of matches that CM will find over the number of matches it will find without a chain.Our results may be of independent interest to the literature on dynamic matching in random graphs. Kidney exchange serves well as an example for which we have distributional information on the underlying graphs, thus we can exploit this information to make analysis and prediction far more accurate than the worst-case analysis can do. We believe our average-case analysis can have implications beyond the kidney exchange and can be applied to other dynamic allocation problems with such distributional information. Further, from a theoretical perspective, our paper initiates a novel direction in matching over time, deviating from the online scenarios.While this paper focuses on kidney exchange, there are many dynamic markets for barter exchange for which our findings apply. There is a growing number of websites that accommodate a marketplace for exchange of goods (often more than 2 goods), e.g. ReadItSwapIt.com and Swap.com. In these markets, the demand for goods, cycle lengths and waiting times play a significant role in efficiency.

**Read paper on the following link:** https://ifaamas.org/Proceedings/aamas2022/pdfs/p82.pdf **Abstract:** To overcome incompatibility issues, kidney patients may swap their donors. In international kidney exchange programmes (IKEPs), countries merge their national patient-donor pools. We consider a recent credit system where in each round, countries are given an initial kidney transplant allocation which is adjusted by a credit function yielding a target allocation. The goal is to find a solution in the patient-donor compatibility graph that approaches the target allocation as closely as possible, to ensure long-term stability of the international pool. As solutions, we use maximum matchings that lexicographically minimize the country deviations from the target allocation. We first give a polynomial-time algorithm for computing such matchings. We then perform, for the first time, a computational study for a {\it large} number of countries. For the initial allocations we use, besides two easy-to-compute solution concepts, two classical concepts: the Shapley value and nucleolus. These are hard to compute, but by using state-of-the-art software we show that they are now within reach for IKEPs of up to fifteen countries. Our experiments show that using lexicographically minimal maximum matchings instead of ones that only minimize the largest deviation from the target allocation (as previously done) may make an IKEP up to 52\% more balanced.

We tested re-optimisation strategies for international kidney exchange programmes using the simulator developed by the ENCKEP COST Action. Kidney exchange programmes (KEPs) are operating in most of the European countries to facilitate the exchange of kidney donors for the recipients with incompatible living donors. The optimal solutions for national and international KEPs are typically selected in every three months based on the compatibilities estimated on the individual immunological data. However, these estimations are not always accurate, and if a positive crossmatch is found in the laboratory crossmatch tests then the corresponding exchange cycle (or chain) must be cancelled. Depending on the matching process, the coordinators may use different re-optimisation strategies to repair the failed solutions. We examine the effects of using multiple rounds of re-optimisation with different optimisation strategies, such as fixing good cycles in the intermediate solutions or prioritising transplants with negative crossmatch tests in previous rounds. In the context of international KEPs we also consider the possibility of testing and prioritising national transplants in the solutions. We measure the performance of these policies regarding the number of transplants and the number of compatibility tests conducted in a time period. By extending our results presented in [16], we performed simulations for a large number of instances to measure the effects of various re-optimisation policies. Our main findings show a clear trade-off in the number of transplants versus the number of tests and re-optimisation rounds.

The b-matching game is a cooperative game defined on a graph. The game generalizes the matching game to allow each individual to have more than one partner. The game has several applications, such as the roommate assignment, the multi-item version of the seller-buyer assignment, and the international kidney exchange. Compared with the standard matching game, the b-matching game is computationally hard. In particular, the core non-emptiness problem and the core membership problem are co-NP-hard. Therefore, we focus on the convexity of the game, which is a sufficient condition of the core non-emptiness and often more tractable concept than the core non-emptiness. It also has several additional benefits. In this study, we give a necessary and sufficient condition of the convexity of the b-matching game. This condition also gives an O(n log n + m α(n)) time algorithm to determine whether a given game is convex or not, where n and m are the number of vertices and edges of a given graph, respectively, and α(・) is the inverse-Ackermann function. Using our characterization, we also give a polynomial-time algorithm to compute the Shapley value of a convex b-matching game.

We introduce generalized matching games defined on a graph $G=(V,E)$ with an edge weighting w and a partition $V=V_1 \cup \dots \cup V_n$ of~V. The player set is $N = \ 1, \dots, n\ $, and player $p \in N$ owns the vertices in $V_p$. The value $v(S)$ of coalition $S \subseteq N$ is the maximum weight of a matching in the subgraph of G induced by the vertices owned by players in S. If $|V_p|=1$ for every player~p we obtain the classical matching game. We prove that checking core non-emptiness is polynomial-time solvable if $|V_p|łeq 2$ for each p and co-\NP-hard if $|V_p|łeq 3$ for each p. We do so via pinpointing a relationship with b-matching games and also settle the complexity classification on testing core non-emptiness for b-matching games. We propose generalized matching games as a suitable model for international kidney exchange programs, where the vertices in V correspond to patient-donor pairs and each $V_p$ represents one country. For this setting we prove a number of complexity results.

Non-thermal atmospheric pressure plasmas (APPs) have attracted great interest due the potential cost reductions in manufacturing and processing of materials for a wide range of applications [1]. Although APPs present several challenges, considerable progress has been achieved in recent years with an increasing number of industrial and commercial applications utilizing different forms of APPs. One of the most attractive application of APPs is for the synthesis and processing of nanomaterials with specific focus on materials for energy applications.In this contribution we will present recent advances in both the synthesis and surface engineering of quantum confined silicon-based nanoparticles [2-5]. In particular we will discuss a range of synthesis methods that rely on atmospheric pressure plasmas for producing crystalline silicon nanoparticles as well as alloyed silicon-tin nanoparticles; these will include laser-produced plasmas, rf-APPs and plasmas in liquids. The analysis will include, in some of the cases, theoeretical models that highlight key mechanisms of nanoparticle heating [6].We will then discuss the integration of silicon-based nanoparticles in photovoltaic devices, demonstrating their contribution as down-converters and/or as part of the active layer. In this context we will show how APP-based surface engineering can offer great opportunities for tailoring surface properties of the nanoparticles. Device parameters will be presented and analysed for different device architectures.Finally, tha applicability of APPs in different aspect of photovoltaic device fabrication will be discussed presenting opportunities and challenges for large scale nanomanufacturing. Acknowledgement This work was partially supported by a NEDO project, the Royal Society International Exchange Scheme (IE120884), the Leverhulme International Network (IN-2012-136) and EPSRC (EP/K022237/1). DM also acknowledges the support of the JSPS Bridge Fellowship. SM and SA thank the financial support of the University of Ulster Vice-Chancellor Studentship.

Germane experience: Six Welsh student nurses are mastering the German language In preparation for an exchange visit to Osnabruck in the spring. It is one of the first international exchange schemes in the UK to involve diploma nursing students. The students, from the Department of Nursing and Midwifery at the University of Glamorgan, will spend 15 weeks sharing practical and theoretical knowledge with German nurses. They will work in surgical, care of the elderly and paediatric areas.

We measure the dielectric confinement length scales of triplet excitons in organic semiconductors by jointly measuring their microwave-domain electric and magnetic susceptibilities. We apply this technique to characterize triplet excitons in two singlet fission materials with distinct solid-state packing and correlate the extracted localization length scales with the role of the excitonic environment. By using the magnetic susceptibility simultaneously determined through our experiments, we compare the independently extracted dielectric and spin-spin localization length scales, highlighting the role of local anisotropy on the properties of excitonic triplet states.

Bone is the most common site for metastasis in prostate cancer (PCa), and identifying clinically useful biomarkers to predict the risk of currently incurable bone metastases is a major priority in PCa research. Extracellular adenosine triphosphate (ATP) was shown to be a major biochemical constituent of the tumor microenvironment and regulates the tumor and host interactions by acting at P2 purinergic receptors. Among the P2 receptors, the ion channel P2X purinergic receptor 7 (P2X7R) has an unusually long C-terminus containing 200 amino acids, which forms the molecular basis for the unique bi-function of P2X7R promoting cancer cell proliferation or inducing membrane permeabilization and apoptosis, upon activation by a low or high concentration of ATP, respectively. A cysteine-rich region and a guanosine diphosphate or triphosphate (GDP/GTP)-binding site located in the C-terminus are pivotal for the structural rearrangement of the second transmembrane domain helix and the globular ballast underneath during the membrane pore permeabilization [1]. Among the 10 human P2X7R splice variants (P2X7RA-J), the P2X7RA variant is the full-length "wild-type (WT)" receptor, while the truncated P2X7RB variant lacks the intracellular C-terminal tail. This naturally occurring P2X7RB isoform maintains ATP-stimulated channel activity but not pore permeabilization [2, 3]. P2X7RB is upregulated in epithelial cancer cells [3] and associated with the trophic activity of primary bone cancer [2, 4, 5]. These findings have highlighted the importance of defining the role of P2X7R C-terminal truncated variants in cancer progression, particularly considering that data on P2X7R in PCa bone metastasis is lacking, whereas clinical evidence offers contradictory results [6, 7]. To clarify the role of P2X7R in PCa, we collected biopsies and surgical specimens from 77 patients with PCa and 9 patients with benign prostatic hyperplasia (BPH) from three local hospitals in Qingdao, Shandong, China. Among these PCa patients, 20 (26.0%) had bone metastases at the time of diagnosis, while 57 (74.0%) had no bone metastases (Supplementary Table S1). To distinguish the full-length WT P2X7RA and the C-terminus truncated P2X7RB splice variants, we used two antibodies specifically against different domains of the P2X7R, including anti-P2X7R-Cter (C-terminal) antibody against the P2X7RA-specific C-terminal tail, thus detecting the P2X7RA isoform, whilst the anti-P2X7R-ec (extracellular) antibody against the extracellular domain and detecting both P2X7RA and P2X7RB [4]. The detailed Methods can be found in the Supplementary file. Therefore, P2X7RA was defined as positive staining for both anti-P2X7R-Cter and anti-P2X7R-ec, while P2X7RB was positive for anti-P2X7R-ec but negative for anti-P2X7R-Cter (Figure 1A). Of the 66 P2X7R expressing PCa specimens (anti-P2X7R-ec-positive), 47 (71.2%) expressed P2X7RA, and 19 (28.8%) expressed P2X7RB. Comparing the Gleason scores, P2X7RB-positive cases were 8.2% higher than P2X7RA-positive cases (P = 0.047, Figure 1B). P2X7RB was not expressed in BPH specimens (0/9) but was expressed in 25.9% of PCa cases without bone metastases (14/54) and 41.7% of cases with bone metastases (5/12). The fraction of P2X7RB-positive cases were positively correlated with PCa progression (r = 0.997, P = 0.048, Figure 1C), based on the average Gleason scores of different disease stages (PCa without bone metastases = 8.0, bone metastatic PCa = 8.9, Supplementary Figure S1A). Immunoreactivity analysis showed no significant difference in P2X7RA expression level among specimens from the BPH group and groups of PCa with or without bone metastases (Supplementary Figure S1B-C), which was consistent with the retrospective analysis of clinical datasets (Supplementary Figure S1D-E). Therefore, C-terminus truncated P2X7RB variants, but not full-length P2X7RA, were positively associated with PCa progression and bone metastases. As P2RX7 exon 13 encodes 85% length of the entire C-terminus and is key to C-terminal functions, CRISPR/Cas9 technique was used to generate a frameshift after residue position 451 in exon 13 (∆C) (Supplementary Figure S2, S3), to understand how P2X7R C-terminal disruptions affect PCa cell biology. In WT PCa cells, exposure to 300 μmol/L P2X7R-specific agonist BzATP induced ethidium bromide uptake, suggesting that P2X7R mediated membrane permeabilization to large molecules, a unique property of the P2X7R C-terminus. While in ∆C cells, this was significantly reduced (P < 0.001, Figure 1D). To examine whether ∆C P2X7R is still functional in PCa cells, we tested the BzATP-induced calcium influx. BzATP was able to induce a calcium influx in PC3 ∆C cells, which was inhibited by the P2X7R antagonist A740003 (Figure 1E). There was no significant difference in BzATP-induced calcium influx peak between PC3 WT and ∆C cells (P = 0.388, Figure 1F). In addition, PC3 ∆C cells showed a significantly reduced presence of the P2X7R C-terminus at the protein level (Supplementary Figure S3F-I). These data have confirmed that our P2X7R ∆C resembled the unique characteristics of C-terminal truncated P2X7RB isoform, i.e., maintaining channel activity but not membrane pore permeabilization [2]. To test whether the disruption of P2RX7 exon 13 altered the metastatic ability of PCa cells, we tracked bone tumors formed by WT and ∆C PC3 cells following intra-cardiac injection (Figure 1G). Mice injected with ∆C cells had almost twice the skeletal tumor frequency (number of skeletal tumors/mouse) of the WT group (4.2 vs. 2.3, P = 0.016, Figure 1H), with a significant 4-day reduction in survival compared to the WT group (median survival: 26 vs. 30 days, P = 0.042, Figure 1I). However, there were no significant differences in the individual tumor size (Supplementary Figure S4A), number of non-skeletal tumors (Supplementary Figure S4B), or tumor-induced bone destruction determined ex vivo using micro-CT (Supplementary Figure S4C-F). These were consistent with data from cellular assays showing that disrupting P2X7R C-terminus did not impair proliferation (Supplementary Figure S5) and suggested that the pro-bone metastasis effects in C-terminal disrupted PCa cells were bone tropism related rather than tumor growth per se. To provide an insight into what led to the enhanced metastatic potential of ∆C cells, we performed a metastasis-initiating cell assay [8] and found that PC3 ∆C cells had significantly increased numbers of bone tropic metastasis-initiating cells by 74.1% (P = 0.012, Figure 1J). We examined these cells' response to stimulation of pore-inducing high concentration of extracellular BzATP (300 μmol/L) and showed a significant reduction of induced apoptosis in PC3 ∆C cells (P = 0.030, Figure 1K) but an increased secretion of pro-metastatic cytokine IL-6 (Figure 1L). The enhanced presence of the metastasis-initiating cell subpopulation in P2X7R ∆C cells was probably linked to their ability to escape apoptosis. The P2X7R C-terminus, with the presence of palmitoylated cysteine residues, could be inserted into the plasma membrane and facilitated pore formation by preventing cholesterol interaction with P2X7R [9]. Disruption of the C-terminus, like in the P2X7RB isoform or ∆C cells, could significantly reduce the induction of apoptosis in cells under the stimulation of pore-inducing high concentration of extracellular nucleotides (e.g., 100-500 μmol/L extracellular ATP within solid tumors) [10]. Furthermore, when stimulated by extracellular BzATP, only ∆C cells secreted IL-6, a pro-inflammatory cytokine with strong pro-metastatic effects on bone metabolism, tumor cell survival, and angiogenesis. These findings warrant further investigation to clarify the exact regulatory mechanisms determining the metastatic fate of P2X7R ∆C cells. In conclusion, using both clinical and pre-clinical data, we showed that the disruption of the C-terminus of P2X7R was positively associated with PCa progression and bone metastasis. The C-terminal truncated P2X7RB isoform, rather than the full-length P2X7RA, could potentially be used as a prognostic marker to predict PCa bone metastasis. Haiping Song: Investigation, Formal analysis, Visualization and Funding acquisition; Hector Manuel Arredondo Carrera: Investigation, Formal analysis and Visualization; Alexandria Sprules: Investigation, Validation and Methodology; Ying Ji: Investigation and Validation; Tongsong Zhang: Investigation and Validation; Jiepei He: Investigation; Eleanor Lawrence: Investigation; Alison Gartland: Writing - Review & Editing; Jian Luo: Writing - Review & Editing and Funding acquisition; Ning Wang: Conceptualization, Writing - Original Draft, Supervision, Project administration, Funding acquisition. These studies received supports from the Royal Society/the National Natural Science Foundation of China (NSFC) and Qingdao Science and Technology Bureau Research Fund. We also wish to thank the following colleagues for their excellent technical support: Dr. Bin Ding, Pathology Department, Qingdao Tumor Hospital, China; Dr. Changqing Jiang, Pathology Department, Qingdao Municipal Hospital, China; Dr. Yunqing Chen, Pathology Department, the Affiliated Hospital of Medical College, Qingdao University, China; and Dr. Karan M Shah, Department of Oncology & Metabolism, The University of Sheffield, UK. The authors declare that they have no competing interests. This research was funded by the International Exchange Scheme – Cost Share Programme, jointly sponsored by the Royal Society, UK (grant number IEC∖NSFC∖170113) and the National Natural Science Foundation of China (NSFC) (grant number 8171101485). This research was also funded by the Qingdao Science and Technology Bureau Research Fund, China, grant number 18-6-1-98-nsh. Raw data for retrospective analysis can be accessed through the Gene Expression Omnibus (GEO) database (Accession Number: GDS1439 and GDS3289). The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request. For clinical samples, written informed consent was obtained from all patients, and the study was approved by the Ethical Review Committee of the Qingdao Tumor Hospital to ensure that rights and privacy of patients were protected (Approval Number: [Y]KY20200001). For animal studies, all procedures complied with the UK Animals (Scientific Procedures) Act 1986 and were reviewed and approved by the local Research Ethics Committees of the University of Sheffield under Home Office project license 70/8799 (Sheffield, UK). Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. 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