Structure and Randomness of Continuous-Time Discrete-Event Processes

Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models---memoryful, state-dependent versions of renewal processes. Calculating these quantities requires introducing novel mathematical objects ({\epsilon}-machines of hidden semi-Markov processes) and new information-theoretic methods to stochastic processes.Comment: 10 pages, 2 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/ctdep.ht

Musculoskeletal Manifestations of COVID-19: A Systematic Search and Review

Coronavirus disease (COVID-19) started its journey around the world from Wuhan, China and gradually became a pandemic. COVID-19 often affects the respiratory system, but symptoms may include fatigue, myalgia, arthralgia, arthritis, and spine and bone pain as presenting complaints. In the present systematic search and review, we aim to highlight the musculoskeletal manifestations during COVID-19. PubMed Central and Google Scholar search engines were searched for the key words “muscle pain”, “joint pain”, “body ache”, and “fatigue”, in Covid-19 patients. After screening, a total of 76 articles dated between January 1 and July 1, 2020 met the inclusion criteria and were included in the study. All articles were published in English comprising 36,558 COVID-19 cases. In cross-sectional studies, fatigue was found in 55%, myalgia in 26%, and arthralgia in 20% of cases, respectively. In cohort studies, fatigue was found in 35%, myalgia in 15%, and arthralgia in 5%, respectively. Sporadic case reports also mention back pain, bone pain, myositis, and arthritis as presenting symptoms of COVID-19. Fatigue was the most frequent musculoskeletal (MSK) manifestation of COVID-19 followed by myalgia and joint pain. The frequency of the different MSK manifestations in COVID-19 may vary widely among different geographic regions. MSK like fatigue, myalgia and arthralgia are frequent symptoms in COVID-19 patients and may vary in different countries

Information anatomy of stochastic equilibria

A stochastic nonlinear dynamical system generates information, as measured by its entropy rate. Some-the ephemeral information-is dissipated and some-the bound information-is actively stored and so affects future behavior. We derive analytic expressions for the ephemeral and bound information in the limit of infinitesimal time discretization for two classical systems that exhibit dynamical equilibria: first-order Langevin equations (i) where the drift is the gradient of an analytic potential function and the diffusion matrix is invertible and (ii) with a linear drift term (Ornstein-Uhlenbeck), but a noninvertible diffusion matrix. In both cases, the bound information is sensitive to the drift and diffusion, while the ephemeral information is sensitive only to the diffusion matrix and not to the drift. Notably, this information anatomy changes discontinuously as any of the diffusion coefficients vanishes, indicating that it is very sensitive to the noise structure. We then calculate the information anatomy of the stochastic cusp catastrophe and of particles diffusing in a heat bath in the overdamped limit, both examples of stochastic gradient descent on a potential landscape. Finally, we use our methods to calculate and compare approximations for the time-local predictive information for adaptive agents

Structure and Randomness of Continuous-Time Discrete-Event Processes

Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models---memoryful, state-dependent versions of renewal processes. Calculating these quantities requires introducing novel mathematical objects ({\epsilon}-machines of hidden semi-Markov processes) and new information-theoretic methods to stochastic processes

Inferring an Observer's Prediction Strategy in Sequence Learning Experiments

Cognitive systems exhibit astounding prediction capabilities that allow them to reap rewards from regularities in their environment. How do organisms predict environmental input and how well do they do it? As a prerequisite to answering that question, we first address the limits on prediction strategy inference, given a series of inputs and predictions from an observer. We study the special case of Bayesian observers, allowing for a probability that the observer randomly ignores data when building her model. We demonstrate that an observer's prediction model can be correctly inferred for binary stimuli generated from a finite-order Markov model. However, we can not necessarily infer the model's parameter values unless we have access to several "clones" of the observer. As stimuli become increasingly complicated, correct inference requires exponentially more data points, computational power, and computational time. These factors place a practical limit on how well we are able to infer an observer's prediction strategy in an experimental or observational setting

A 600-ka Arctic sea-ice record from Mendeleev Ridge based on ostracodes

Arctic paleoceanography and sea-ice history were reconstructed from epipelagic and benthic ostracodes from a sediment core (HLY0503-06JPC, 800 m water depth) located on the Mendeleev Ridge, Western Arctic Ocean. The calcareous microfaunal record (ostracodes and foraminifers) covers several glacial/interglacial cycles back to estimated Marine Isotope Stage 13 (MIS 13, ∼500 ka) with an average sedimentation rate of ∼0.5 cm/ka for most of the stratigraphy (MIS 5–13). Results based on ostracode assemblages and an unusual planktic foraminiferal assemblage in MIS 11 dominated by a temperate-water species Turborotalita egelida show that extreme interglacial warmth, high surface ocean productivity, and possibly open ocean convection characterized MIS 11 and MIS 13 (∼400 and 500 ka, respectively). A major shift in western Arctic Ocean environments toward perennial sea ice occurred after MIS 11 based on the distribution of an ice-dwelling ostracode Acetabulastoma arcticum. Spectral analyses of the ostracode assemblages indicate sea ice and mid-depth ocean circulation in western Arctic Ocean varied primarily at precessional (∼22 ka) and obliquity (∼40 ka) frequencies