Time reversibility from visibility graphs of nonstationary processes

Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of both natural and horizontal visibility graphs associated to several non-stationary processes, and we pay particular attention to their capacity to assess time irreversibility. Non-stationary signals are (infinitely) irreversible by definition (independently of whether the process is Markovian or producing entropy at a positive rate), and thus the link between entropy production and time series irreversibility has only been explored in non-equilibrium stationary states. Here we show that the visibility formalism naturally induces a new working definition of time irreversibility, which allows to quantify several degrees of irreversibility for stationary and non-stationary series, yielding finite values that can be used to efficiently assess the presence of memory and off-equilibrium dynamics in non-stationary processes without needs to differentiate or detrend them. We provide rigorous results complemented by extensive numerical simulations on several classes of stochastic processes

Flow cytometric analysis of cytologic specimens in hematologic disease Presented in part before the International Academy of Pathology, Washington, D.C., February 28-March 3, 1988 (Lab Invest 1988; S8:37A).

Cytologic evaluation of body fluids and fine needle aspirations (FNA) is frequently required in patients with hematologic diseases. In this study we have correlated immunophenotyping and DNA analysis by flow cytometry with cytologic findings and tissue biopsies from 20 patients with body fluid specimens and 5 with FNA. Nineteen of 25 cases, including all FNA cases, had an immunophenotype consistent with malignancy: 12 monoclonal lymphomas, 2 T-cell lymphomas, 2 T-ALL and 3 non-T-ALL. By cytologic examination, 14 of these 19 cases were positive for malignant cells, 2 suspicious and 3 negative; the latter 5 cases, including 2 FNA cases, had small monoclonal B-cell populations detected by flow cytometry. Six cases had a benign immunophenotype; cytologic examination was benign in 4 of these and suspicious for lymphoma in 2. Our results show the feasibility of using flow cytometry to evaluate body fluids or FNA and demonstrate that small malignant populations that may be missed by routine cytology can be detected by flow cytometry.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/38530/1/1860030103_ftp.pd

Influence of Luddism on innovation diffusion

We generalize the classical Bass model of innovation diffusion to include a new class of agents - Luddites - that oppose the spread of innovation. Our model also incorporates ignorants, susceptibles, and adopters. When an ignorant and a susceptible meet, the former is converted to a susceptible at a given rate, while a susceptible spontaneously adopts the innovation at a constant rate. In response to the rate of adoption, an ignorant may become a Luddite and permanently reject the innovation. Instead of reaching complete adoption, the final state generally consists of a population of Luddites, ignorants, and adopters. The evolution of this system is investigated analytically and by stochastic simulations. We determine the stationary distribution of adopters, the time needed to reach the final state, and the influence of the network topology on the innovation spread. Our model exhibits an important dichotomy: When the rate of adoption is low, an innovation spreads slowly but widely; in contrast, when the adoption rate is high, the innovation spreads rapidly but the extent of the adoption is severely limited by Luddites

Left Ventricular Ejection Time on Echocardiography Predicts Long-Term Mortality in Light Chain Amyloidosis

Mathematical models of diffusive transport underpin our understanding of chemical, biochemical and biological transport phenomena. Analysis of such models often focusses on relatively simple geometries and deals with diffusion through highly idealised homogeneous media. In contrast, practical applications of diffusive transport theory inevitably involve dealing with more complicated geometries as well as dealing with heterogeneous media. One of the most fundamental properties of diffusive transport is the concept of mean particle lifetime or mean exit time, which are particular applications of the concept of first passage time, and provide the mean time required for a diffusing particle to reach an absorbing boundary. Most formal analysis of mean particle lifetime applies to relatively simple geometries, often with homogeneous (spatially-invariant) material properties. In this work, we present a general framework that provides exact mathematical insight into the mean particle lifetime, and higher moments of particle lifetime, for point particles diffusing in heterogeneous discs and spheres with radial symmetry. Our analysis applies to geometries with an arbitrary number and arrangement of distinct layers, where transport in each layer is characterised by a distinct diffusivity. We obtain exact closed-form expressions for the mean particle lifetime for a diffusing particle released at an arbitrary location and we generalise these results to give exact, closed-form expressions for any higher-order moment of particle lifetime for a range of different boundary conditions. Finally, using these results we construct new homogenization formulae that provide an accurate simplified description of diffusion through heterogeneous discs and spheres.Comment: 19 pages, 3 figures, accepted version of paper published in The Journal of Chemical Physic

Switch Hitting in Baseball: Apparent Rule-following, not Matching

Many studies, including some dealing with shot selection in basketball and play selection in football, demonstrate that the generalized matching equation provides a good description of the allocation of time and effort to alternative responses as a function of the consequences of those alternatives. We examined whether it did so with respect to left- and right-handed at bats (alternative responses) and left- and right-handed total bases earned, runs batted in, and home runs (three consequences) for the outstanding baseball switch-hitters Mickey Mantle, Eddie Murray, and Pete Rose. With all hitters, undermatching, suggesting insensitivity to the consequences of behavior (reinforcement), was evident and there was substantial bias towards left-handed at bats. These players apparently chose handedness based on the rule “bat opposite the pitcher,” not on differential consequences obtained in major league games. The present findings are significant in representing a counter-instance of demonstrations of a matching relationship in sports in particular and in human behavior in general and in calling attention to the need for further study of the variables that affect choice