scholarly journals A Two-Player Iterated Survival Game

2018 ◽  
Author(s):  
John Wakeley ◽  
Martin Nowak

AbstractWe describe an iterated game between two players, in which the payoff is to survive a number of steps. Expected payoffs are probabilities of survival. A key feature of the game is that individuals have to survive on their own if their partner dies. We consider individuals with hardwired, unconditional behaviors or strategies. When both players are present, each step is a symmetric two-player game. The overall survival of the two individuals forms a Markov chain. As the number of iterations tends to infinity, all probabilities of survival decrease to zero. We obtain general, analytical results for n-step payoffs and use these to describe how the game changes as n increases. In order to predict changes in the frequency of a cooperative strategy over time, we embed the survival game in three different models of a large, well-mixed population. Two of these models are deterministic and one is stochastic. Offspring receive their parent’s type without modification and fitnesses are determined by the game. Increasing the number of iterations changes the prospects for cooperation. All models become neutral in the limit (n → ∞). Further, if pairs of cooperative individuals survive together with high probability, specifically higher than for any other pair and for either type when it is alone, then cooperation becomes favored if the number of iterations is large enough. This holds regardless of the structure of pairwise interactions in a single step. Even if the single-step interaction is a Prisoner’s Dilemma, the cooperative type becomes favored. Enhanced survival is crucial in these iterated evolutionary games: if players in pairs start the game with a fitness deficit relative to lone individuals, the prospects for cooperation can become even worse than in the case of a single-step game.

2017 ◽  
Vol 14 (134) ◽  
pp. 20170223 ◽  
Author(s):  
Edward D. Lee ◽  
Bryan C. Daniels ◽  
David C. Krakauer ◽  
Jessica C. Flack

In biological systems, prolonged conflict is costly, whereas contained conflict permits strategic innovation and refinement. Causes of variation in conflict size and duration are not well understood. We use a well-studied primate society model system to study how conflicts grow. We find conflict duration is a ‘first to fight’ growth process that scales superlinearly, with the number of possible pairwise interactions. This is in contrast with a ‘first to fail’ process that characterizes peaceful durations. Rescaling conflict distributions reveals a universal curve, showing that the typical time scale of correlated interactions exceeds nearly all individual fights. This temporal correlation implies collective memory across pairwise interactions beyond those assumed in standard models of contagion growth or iterated evolutionary games. By accounting for memory, we make quantitative predictions for interventions that mitigate or enhance the spread of conflict. Managing conflict involves balancing the efficient use of limited resources with an intervention strategy that allows for conflict while keeping it contained and controlled.


Author(s):  
Toshiaki Iwase ◽  
Tushaar Vishal Shrimanker ◽  
Ruben Rodriguez-Bautista ◽  
Onur Sahin ◽  
Anjali James ◽  
...  

The purpose of this study was to determine the change in overall survival (OS) for patients with de novo metastatic breast cancer (dnMBC) over time. We conducted a retrospective cohort study with 1981 patients with dnMBC diagnosed between January 1995 and December 2017 at The University of Texas MD Anderson Cancer Center. OS was measured from the date of diagnosis of dnMBC. OS was compared between patients diagnosed during different time periods: 5-year periods and periods defined according to when key agents were approved for clinical use. The median OS was 3.4 years. The 5- and 10-year OS rates improved over time across both types of time periods. A subgroup analysis showed that OS improved significantly over time for the estrogen-receptor-positive/HER2-positive (ER+/HER2+) subtype, and exhibited a tendency toward improvement over time for the ER-negative (ER-)/HER2+ subtype. Median OS was significantly longer in patients with non-inflammatory breast cancer (P = .02) and in patients with ER+ disease, progesterone-receptor-positive disease, HER2+ disease, lower nuclear grade, locoregional therapy, and metastasis to a single organ (all P <.0001). These findings showed that OS at 5 and 10 years after diagnosis in patients with dnMBC improved over time. The significant improvements in OS over time for the ER+/HER2+ subtype and the tendency toward improvement for ER-/HER2+ subtype suggest the contribution of HER2-targeted therapy to survival.


2005 ◽  
Vol 62 (11) ◽  
pp. 2573-2585 ◽  
Author(s):  
Hal Whitehead ◽  
Tonya Wimmer

A population of northern bottlenose whales (Hyperoodon ampullatus) inhabits the waters along the edge of the Scotian Shelf. The most important habitat of this population is the Gully, a large submarine canyon, where animals were photographically identified between 1988 and 2003. Open mark–recapture models, including mixture models that allow for heterogeneity in identifiability and (or) mortality among individuals, were fitted to identification-history data. Models without heterogeneity in identifiability had poor fit to the data and underestimated population size. The population is estimated to contain about 163 animals (95% confidence interval 119–214), with no statistically significant temporal trend. About 12% of the population has a high probability of being identified within the Gully in any year. Many of them are mature males. The remainder is less likely to be identified in the Gully during any year, spend generally shorter periods in the Gully even in years when they are found, and are more likely to be female. This and other work indicate a poorly mixed population inhabiting the canyons and other deeper waters off the Scotian Shelf. Non parametric bootstrap methods were used to validate the estimation procedure and to estimate the efficiency of future fieldwork scenarios.


Sarcoma ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jules Lansu ◽  
Winan J. Van Houdt ◽  
Michael Schaapveld ◽  
Iris Walraven ◽  
Michiel A. J. Van de Sande ◽  
...  

Background. The purpose of this study was to evaluate the overall survival (OS) and associated characteristics for patients with Myxoid Liposarcoma (MLS) over time in The Netherlands. Methods. A population-based study was performed of patients with primary localized (n = 851) and metastatic (n = 50) MLS diagnosed in The Netherlands between 1989 and 2016, based on data from the National Cancer Registry. Results. The median age of the MLS patients was 49 years, and approximately two-thirds was located in the lower limb. An association was revealed between age and the risk of having a Round Cell (RC) tumor. OS rates for primary localized MLS were 93%, 83%, 78%, and 66% after 1, 3, 5, and 10 years, respectively. The median OS for patients with metastatic disease at diagnosis was 10 months. Increasing age (Hazard Ratio (HR) 1.05, p=0.00), a tumor size >5 cm (HR 2.18; p=0.00), and tumor location (trunk HR 1.29; p=0.09, upper limb HR 0.83; p=0.55, and “other” locations HR 2.73; p=0.00, as compared to lower limb) were independent prognostic factors for OS. The percentage of patients treated with radiotherapy (RT) increased over time, and preoperative RT gradually replaced postoperative RT. In contrast to patients with localized disease, significant improvement of OS was observed in patients with metastatic disease over time. Conclusions. In this large nationwide cohort, tumor size and tumor location were independent prognostic factors for OS. Furthermore, a higher probability of an RC tumor with increasing age was suggested. An increased use of RT over the years did not translate into improved OS for localized MLS.


Cancers ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1239 ◽  
Author(s):  
Abbema ◽  
Vissers ◽  
Vos-Geelen ◽  
Lemmens ◽  
Janssen-Heijnen ◽  
...  

Previous studies showed substantial improvement of survival rates in patients with cancer in the last two decades. However, lower survival rates have been reported for older patients compared to younger patients. In this population-based study, we analyzed treatment patterns and the survival of patients with breast cancer (BC) and colorectal cancer (CRC). Patients with stages I–III BC and CRC and diagnosed between 2003 and 2012 were selected from the Netherlands Cancer Registry (NCR). Trends in treatment modalities were evaluated with the Cochran-Armitage trend test. Trends in five-year overall survival were calculated with the Cox hazard regression model. The Ederer II method was used to calculate the five-year relative survival. The relative excess risk of death (RER) was estimated using a multivariate generalized linear model. During the study period, 98% of BC patients aged <75 years underwent surgery, whereas for patients ≥75 years, rates were 79.3% in 2003 and 66.7% in 2012 (p < 0.001). Most CRC patients underwent surgery irrespective of age or time period, although patients with rectal cancer aged ≥75 years received less surgery or radiotherapy over the entire study period than younger patients. The administration of adjuvant chemotherapy increased over time for CRC and BC patients, except for BC patients aged ≥75 years. The five-year relative survival improved only in younger BC patients (adjusted RER 0.95–0.96 per year), and was lower for older BC patients (adjusted RER 1.00, 95% Confidence Interval (CI) 0.98–1.02, and RER 1.00; 95% CI 0.98–1.01 per year for 65–74 years and ≥75 years, respectively). For CRC patients, the five-year relative survival improved over time for all ages (adjusted RER on average was 0.95 per year). In conclusion, the observed survival trends in BC and CRC patients suggest advances in cancer treatment, but with striking differences in survival between older and younger patients, particularly for BC patients.


2013 ◽  
Vol 31 (15_suppl) ◽  
pp. 3574-3574
Author(s):  
Paul Ruff ◽  
Radek Lakomy ◽  
Jana Prausová ◽  
Guy A. Van Hazel ◽  
Vladimir Moiseyenko ◽  
...  

3574 Background: VELOUR, a large, international, randomized, placebo (pbo)-controlled study, compared efficacy and safety of FOLFIRI with ziv-aflibercept (known as aflibercept outside the United States) or with pbo in 1,226 metastatic colorectal cancer patients who received prior oxaliplatin treatment. Ziv-aflibercept demonstrated statistically significant, clinically meaningful improvements in median overall survival (OS) (13.5 vs 12.06 mos; hazard ratio [HR]=0.817, P=0.0032), progression-free survival, and response rate. This analysis estimates treatment effect and safety over time course of the study. Methods: HRs by 6-mo time periods were estimated using piecewise Cox proportional hazard model. NCI-CTCAE v3.0 was used to grade adverse event (AE) severity. Results: HR improved over time (Table), consistent with survival curves that continue to separate past the median time point, indicating that the magnitude of ziv-aflibercept treatment effect continues to increase over time. Incidence of grade 3 AEs (45.1% vs 62.0%) was higher in the ziv-aflibercept/FOLFIRI arm; incidences of grade 4 AEs were 17.4% (pbo) vs 21.4% (ziv-aflibercept). More common AEs only occurred in a small proportion of ziv-aflibercept/FOLFIRI cycles (eg, grade ≥3 hypertension and diarrhea occurred in 3.6% and 2.8% of cycles, respectively). The majority of grade 3/4 AEs occurred in early treatment (first 3-4 cycles). Most patients experienced only a single episode of grade ≥3 AEs with ziv-aflibercept/FOLFIRI. Importantly, AEs in VELOUR did not impact patients’ ability to receive chemotherapy. Conclusions: Treatment with ziv-aflibercept/FOLFIRI showed continuous, consistent improvement in OS over time. While combined grade 3/4 AEs were higher with ziv-aflibercept, AEs occurred early in treatment in a small proportion of total cycles; the majority were single-episode in nature. Clinical trial information: NCT00561470. [Table: see text]


2016 ◽  
Vol 34 (2_suppl) ◽  
pp. 320-320
Author(s):  
Andrew J. Armstrong ◽  
Celestia S. Higano ◽  
A. Oliver Sartor ◽  
Nicholas J. Vogelzang ◽  
William R. Berry ◽  
...  

320 Background: Sip-T is an autologous cellular immunotherapy approved by the FDA for the treatment of asymptomatic or minimally symptomatic metastatic castration-resistant prostate cancer. PROCEED (NCT01306890) is a phase 4 registry evaluating men receiving sip-T therapy in the US. Patient characteristics and treatment trends were assessed from 2011 to 2013, when several agents with an overall survival benefit became commercially available. Methods: For patients enrolled from 2011 to 2013, baseline patient and disease characteristics at the first sip-T infusion, trends in prior therapy, and pre–sip-T baseline prostate-specific antigen (PSA) levels were examined year over year. Results: From 2011 to 2013, 1902 patients were enrolled and received ≥ 1 sip-T infusion: 2011, n = 145; 2012, n = 967; 2013, n = 790. During this time period, enrollment of African American men nearly doubled from 6.9% to 13.4%, and central venous catheter use to facilitate sip-T infusion decreased (from 53.8% to 44.1%). Median baseline lactate dehydrogenase (LDH) levels and the number of lymph node metastases also decreased as well as median baseline PSA values (17.8 ng/mL to 11.9 ng/mL [P = 0.002]). Prior use of first-generation anti-androgens (from 73.1% to 60.5%), ketoconazole (17.2% vs. 6.3%), and estrogen (4.8% vs. 1.6%) decreased along with prior docetaxel use (19.3% vs. 7.5%). In contrast, prior investigational use of abiraterone acetate (from 3.4% to 8.9%) and enzalutamide (1.4% vs. 3.2%) increased over time. Conclusions: Over the duration of PROCEED, the decrease in baseline PSA, lower LDH, fewer nodal metastases, and decline in prior docetaxel use suggest that sip-T is being used earlier in the course of metastatic castration-resistant disease. Moreover, second-line hormonal therapy use with agents that do not improve overall survival appears to be substituted by therapies that do. This decrease in second-line hormonal therapies during PROCEED could suggest a real-world preference for earlier sip-T use. Clinical trial information: NCT01306890.


2018 ◽  
Vol 36 (4_suppl) ◽  
pp. 239-239
Author(s):  
Nina J. Karlin ◽  
Shailja Amin ◽  
Matthew Buras ◽  
Heidi E. Kosiorek ◽  
Patricia M. Verona ◽  
...  

239 Background: The aim of this case-control study was to determine the impact of DM on survival in pancreatic cancer patients, and to examine the impact of pancreatic cancer on glycemic control in DM. Methods: Ninety-two patients with newly diagnosed pancreatic cancer from 2007 to 2015 with DM were identified from the institutional Cancer Registry and matched to ninety-two pancreatic cancer patients without DM according to age, gender, and year of pancreatic cancer diagnosis. The file was linked to the electronic medical record to obtain information on DM and pancreatic cancer therapies, and laboratory results. Overall survival (OS) was estimated with the Kaplan-Meier method and compared by Cox regression analysis. Mixed models were used to compare hemoglobin A1c (HbA1c) and glucose over time. Results: Mean age of the entire pancreatic cancer cohort was 70 years, most (92%) were white, most common (88%) histology was adenocarcinoma, and majority (41%) were stage IV. No differences in age, race/ethnicity, histology, or tumor stage were detected between patients with and without DM, although DM patients had higher body mass index (P = 0.014). Mean ca 19-9 (U/ml) was 804 for diabetics, and 395 for non-diabetics. Among those with DM the mean HbA1c during the year following cancer diagnosis was 7.3%. Time (days since diagnosis) was significant in DM patients (p = 0.014) as HbA1c decreased over time. Mean glucose during the year following diagnosis among DM patients was significantly higher compared to non-DM patients [160.6 (SD = 38.0) versus 117.2 (SD = 19.0); p < 0.001]. Both groups had a decline in glucose over time (p = 0.008). In Kaplan-Meier survival analysis (median follow-up time of 11.9 months), 2 year overall survival was estimated at 15% [95% CI: 8-24%] for DM patients versus 26% [95% CI: 17-36%] in non-DM patients. Hazard ratio (for matched pairs) was 1.15 (95% CI: 0.75-1.77; p = 0.51). Conclusions: DM did not adversely impact survival in patients with pancreatic cancer. Pancreatic cancer did not affect glycemic control. Elevated ca 19-9 in diabetic patients may be an unreliable marker for gauging disease progression.


2020 ◽  
Vol 16 (4) ◽  
pp. 400-402
Author(s):  
Nasir Ganikhodjaev ◽  
Pah Chin Hee

In this work, we introduce Rock-Paper-Scissors lattice model on Cayley tree of second order generated by Rock-Paper-Scissors game. In this strategic 2-player game, the rule is simple: rock beats scissors, scissors beat paper, and paper beats rock. A payoff matrix  of this game is a skew-symmetric. It is known that quadratic stochastic operator generated by this matrix is non-ergodic transformation. The Hamiltonian of Rock-Paper-Scissors Lattice Model is defined by this skew-symmetric payoff matrix . In this paper, we discuss a connection between three fields of research: evolutionary games, quadratic stochastic operators, and lattice models of statistical physics. We prove that a phase diagram of the Rock-Paper-Scissors model consists of translation-invariant and periodic Gibbs measure with period 3.


Blood ◽  
2018 ◽  
Vol 132 (Supplement 1) ◽  
pp. 2163-2163
Author(s):  
Kyung Taek Hong ◽  
Hyoung Jin Kang ◽  
Hong Yul Ahn ◽  
Jung Yoon Choi ◽  
Sang Hoon Song ◽  
...  

Abstract Introduction: Haploidentical related donor (Haplo) and umbilical cord blood (UCB) stem cell sources represent common alternative donor strategies used when a matched sibling donor or matched unrelated donor is not available for hematopoietic stem cell transplantation (HSCT). The aim of this study was to compare the results of graft source on outcome of children and adolescents with hematologic malignancies after Haplo and UCB transplantation in the setting of targeted busulfan-based myeloablative conditioning using intensive pharmacokinetic (PK) monitoring. Patients and methods: We retrospectively analyzed outcomes in 140 pediatric patients with hematologic malignancies who received allogeneic HSCT from Haplo donors (n=36), UCB (n=24), and unrelated donors (n=80) in Seoul National University Children's Hospital from January 2009 to February 2018. Because UCB transplantation had been conducted until 2016 while Haplo transplantation using posttransplantation cyclophosphamide (PTCy) was started from 2014 in our institution, differences over time of HSCT must be considered to compare them. Therefore, unrelated HSCT group was divided into Unrelated A group (n=51) who received HSCT from 2009 to 2013 and Unrelated B group (n=29) from 2014, which were compared first with the purpose of using them as a control to compare Haplo and UCB groups. Patients who received the first allogenic HSCT using an intensive PK monitoring, targeted busulfan-based myeloablative conditioning were included. The majority of UCB and unrelated groups received busulfan, fludarabine ± etoposide regimen with antithymocyte globulin. For graft-versus-host disease (GVHD) prophylaxis, cyclosporine and mycophenolate mofetil were used in UCB group while tacrolimus and methotrexate in unrelated groups. Busulfan, fludarabine and cyclophosphamide with PTCy, tacrolimus and methotrexate for GVHD prophylaxis were used in Haplo group. Results: First of all, Unrelated A group was compared to Unrelated B group. The median follow-up time were 5.7 years (0.2-9.5) and 1.8 years (0.3-4.5) in the Unrelated A and Unrelated B groups, respectively. The event-free survival (EFS) rates at 2 years (78.1±5.8% versus 72.3±9.1%, P=0.917) and overall survival (OS) rates at 2 years (83.7±5.3% versus 77.8±9.1%, P=0.874) in Unrelated A and B groups were similar. Under the assumption that there was no significant survival difference over time of HSCT from 2009 to 2013 and that from 2014 in our institution, the outcomes of Haplo and UCB groups were compared subsequently. The median follow-up time were 4.8 years (0.1-9.3) and 1.8 years (0.3-4.5), respectively. The median time to neutrophil and platelet recovery were 15 days (13-21) versus 14 days (12-40) (P=0.059), and 27 days (13-71) versus 46 days (21-77) (P<0.001) in Haplo and UCB groups, respectively. Engraftment failure occurred in 1 patient of UCB group. The cumulative incidence (CI) rates of acute GVHD grade II-IV, grade III-IV, and extensive chronic GVHD in Haplo and UCB groups were 38.9% versus 54.2% (P=0.479), 2.8% versus 29.2% (P=0.004), and 11.7% versus 12.5% (P=0.906), respectively. The CI rates of nonrelapse mortality were significantly lower in Haplo group (0% versus 33.6%, P<0.001), while the relapse incidences were not different (18.3% versus 8.6%, P=0.272). The event-free survival (EFS) rates at 2 years (79.3±7.0% versus 54.2±10.2% %, P=0.034) and overall survival (OS) rates at 2 years (85.8±6.7% versus 65.7±9.9%, P=0.029) in Haplo and UCB groups were significantly different. Conclusion: In this study, the CI rates of nonrelapse mortality and acute GVHD III-IV was lower in Haplo group than in UCB transplants, which translates into a better EFS and OS rate in Haplo group. Our results suggest that haploidentical HSCT with PTCy using intensive PK monitoring, targeted busulfan-based myeloablative conditioning regimen is a safe and promising alternative option for patients with hematological malignancies who lack an HLA-matched donor. Disclosures No relevant conflicts of interest to declare.


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