Mixing Time of Markov Chains, Dynamical Systems and Evolution

In this paper we study the mixing time of evolutionary Markov chains over populations of a fixed size (N) in which each individual can be one of m types. These Markov chains have the property that they are guided by a dynamical system from the m-dimensional probability simplex to itself. Roughly, given the current state of the Markov chain, which can be viewed as a probability distribution over the m types, the next state is generated by applying this dynamical system to this distribution, and then sampling from it N times. Many processes in nature, from biology to sociology, are evolutionary and such chains can be used to model them. In this study, the mixing time is of particular interest as it determines the speed of evolution and whether the statistics of the steady state can be efficiently computed. In a recent result [Panageas, Srivastava, Vishnoi, Soda, 2016], it was suggested that the mixing time of such Markov chains is connected to the geometry of this guiding dynamical system. In particular, when the dynamical system has a fixed point which is a global attractor, then the mixing is fast. The limit sets of dynamical systems, however, can exhibit more complex behavior: they could have multiple fixed points that are not necessarily stable, periodic orbits, or even chaos. Such behavior arises in important evolutionary settings such as the dynamics of sexual evolution and that of grammar acquisition. In this paper we prove that the geometry of the dynamical system can also give tight mixing time bounds when the dynamical system has multiple fixed points and periodic orbits. We show that the mixing time continues to remain small in the presence of several unstable fixed points and is exponential in N when there are two or more stable fixed points. As a consequence of our results, we obtain a phase transition result for the mixing time of the sexual/grammar model mentioned above. We arrive at the conclusion that in the interesting parameter regime for these models, i.e., when there are multiple stable fixed points, the mixing is slow. Our techniques strengthen the connections between Markov chains and dynamical systems and we expect that the tools developed in this paper should have a wider applicability

Ibrutinib Unmasks Critical Role of Bruton Tyrosine Kinase in Primary CNS Lymphoma.

Bruton tyrosine kinase (BTK) links the B-cell antigen receptor (BCR) and Toll-like receptors with NF-κB. The role of BTK in primary central nervous system (CNS) lymphoma (PCNSL) is unknown. We performed a phase I clinical trial with ibrutinib, the first-in-class BTK inhibitor, for patients with relapsed or refractory CNS lymphoma. Clinical responses to ibrutinib occurred in 10 of 13 (77%) patients with PCNSL, including five complete responses. The only PCNSL with complete ibrutinib resistance harbored a mutation within the coiled-coil domain of CARD11, a known ibrutinib resistance mechanism. Incomplete tumor responses were associated with mutations in the B-cell antigen receptor-associated protein CD79B

Peripheral blood clinical laboratory variables associated with outcomes following combination nivolumab and ipilimumab immunotherapy in melanoma

Both the combination of nivolumab + ipilimumab and single-agent anti-PD- 1 immunotherapy have demonstrated survival benefit for patients with advanced melanoma. As the combination has a high rate of serious side effects, further analyses in randomized trials of combination versus anti-PD- 1 immunotherapy are needed to understand who benefits most from the combination. Clinical laboratory values that were routinely collected in randomized studies may provide information on the relative benefit of combination immunotherapy. To prioritize which clinical laboratory factors to ultimately explore in these randomized studies, we performed a single-center, retrospective analysis of patients with advanced melanoma who received nivolumab + ipilimumab either as part of a clinical trial (n = 122) or commercial use (n = 87). Baseline routine laboratory values were correlated with overall survival (OS) and overall response rate (ORR). Kaplan–Meier estimation and Cox regression were performed. Median OS was 44.4 months, 95% CI (32.9, Not Reached). A total of 110 patients (53%) responded (CR/PR). Significant independent variables for favorable OS included the following: high relative eosinophils, high relative basophils, low absolute monocytes, low LDH, and a low neutrophil-to- lymphocyte ratio. These newly identified factors, along with those previously reported to be associated with anti-PD- 1 monotherapy outcomes, should be studied in the randomized trials of nivolumab + ipilimumab versus anti-PD- 1 monotherapies to determine whether they help define the patients who benefit most from the combination versus anti-PD- 1 alone

Automated office blood pressure measurements in primary care are misleading in more than one third of treated hypertensives: The VALENTINE-Greece Home Blood Pressure Monitoring study

Abstract Background This study assessed the diagnostic reliability of automated office blood pressure (OBP) measurements in treated hypertensive patients in primary care by evaluating the prevalence of white coat hypertension (WCH) and masked uncontrolled hypertension (MUCH) phenomena. Methods Primary care physicians, nationwide in Greece, assessed consecutive hypertensive patients on stable treatment using OBP (1 visit, triplicate measurements) and home blood pressure (HBP) measurements (7 days, duplicate morning and evening measurements). All measurements were performed using validated automated devices with bluetooth capacity (Omron M7 Intelli-IT). Uncontrolled OBP was defined as ≥140/90 mmHg, and uncontrolled HBP was defined as ≥135/85 mmHg. Results A total of 790 patients recruited by 135 doctors were analyzed (age: 64.5 ± 14.4 years, diabetics: 21.4%, smokers: 20.6%, and average number of antihypertensive drugs: 1.6 ± 0.8). OBP (137.5 ± 9.4/84.3 ± 7.7 mmHg, systolic/diastolic) was higher than HBP (130.6 ± 11.2/79.9 ± 8 mmHg; difference 6.9 ± 11.6/4.4 ± 7.6 mmHg, p Conclusions In primary care, automated OBP measurements are misleading in approximately 40% of treated hypertensive patients. HBP monitoring is mandatory to avoid overtreatment of subjects with WCH phenomenon and prevent undertreatment and subsequent excess cardiovascular disease in MUCH

Treatment in advanced colorectal cancer: what, when and how?

Treatment of advanced colorectal cancer (CRC) increasingly requires a multidisciplinary approach and multiple treatment options add to the complexity of clinical decision-making. Recently novel targeted therapy against angiogenesis and epidermal growth factor receptor completed a plethora of phase III studies. The addition of bevacizumab to chemotherapy improved the efficacy over chemotherapy alone in both first and second line settings, although the magnitude of benefit may not be as great when a more optimal chemotherapy platform is used. Studies performed thus far did not address conclusively whether bevacizumab should be continued in subsequent lines of treatment. Anti-angiogenesis tyrosine kinase inhibitors have not shown any additional benefit over chemotherapy alone so far. Although some benefits were seen with cetuximab in all settings of treating advanced CRC, K-ras mutation status provides an important determinant of who would not benefit from such a treatment. Caution should be exercised in combining anti-angiogenesis with anti-EGFR strategy until further randomised data become available. In this review, we have focused on the implications of these trial results on the everyday management decisions of treating advanced CRC