745 research outputs found
Frequency responses of age-structured populations: Pacific salmon as an example
Increasing evidence of the effects of changing climate on physical ocean
conditions and long-term changes in fish populations adds to the need to
understand the effects of stochastic forcing on marine populations. Cohort
resonance is of particular interest because it involves selective sensitivity
to specific time scales of environmental variability, including that of mean
age of reproduction, and, more importantly, very low frequencies (i.e.,
trends). We present an age-structured model for two Pacific salmon species with
environmental variability in survival rate and in individual growth rate, hence
spawning age distribution. We use computed frequency response curves and
analysis of the linearized dynamics to obtain two main results. First, the
frequency response of the population is affected by the life history stage at
which variability affects the population; varying growth rate tends to excite
periodic resonance in age structure, while varying survival tends to excite
low-frequency fluctuation with more effect on total population size. Second,
decreasing adult survival strengthens the cohort resonance effect at all
frequencies, a finding that addresses the question of how fishing and climate
change will interact.Comment: much revised: the version accepted by Theoretical Population Biolog
Invasion speeds for structured populations in fluctuating environments
We live in a time where climate models predict future increases in
environmental variability and biological invasions are becoming increasingly
frequent. A key to developing effective responses to biological invasions in
increasingly variable environments will be estimates of their rates of spatial
spread and the associated uncertainty of these estimates. Using stochastic,
stage-structured, integro-difference equation models, we show analytically that
invasion speeds are asymptotically normally distributed with a variance that
decreases in time. We apply our methods to a simple juvenile-adult model with
stochastic variation in reproduction and an illustrative example with published
data for the perennial herb, \emph{Calathea ovandensis}. These examples
buttressed by additional analysis reveal that increased variability in vital
rates simultaneously slow down invasions yet generate greater uncertainty about
rates of spatial spread. Moreover, while temporal autocorrelations in vital
rates inflate variability in invasion speeds, the effect of these
autocorrelations on the average invasion speed can be positive or negative
depending on life history traits and how well vital rates ``remember'' the
past
Dissipative Deep Neural Dynamical Systems
In this paper, we provide sufficient conditions for dissipativity and local
asymptotic stability of discrete-time dynamical systems parametrized by deep
neural networks. We leverage the representation of neural networks as pointwise
affine maps, thus exposing their local linear operators and making them
accessible to classical system analytic and design methods. This allows us to
"crack open the black box" of the neural dynamical system's behavior by
evaluating their dissipativity, and estimating their stationary points and
state-space partitioning. We relate the norms of these local linear operators
to the energy stored in the dissipative system with supply rates represented by
their aggregate bias terms. Empirically, we analyze the variance in dynamical
behavior and eigenvalue spectra of these local linear operators with varying
weight factorizations, activation functions, bias terms, and depths.Comment: Under review at IEEE Open Journal of Control System
Stock Market Valuation : the Role of the Macroeconomic Risk Premium
Using annual and quarterly data since 1952, we estimate a fundamentals- based empirical model for the earning-price ratio of US stocks. The key fundamental-variable is a time-varying discount rate, decomposed into a time-varying measure for the real interest rate and the equity risk premium. Applying the Johansen procedure, we implicitly estimate the equity risk premium with cointegration test in an error correction model. This equity risk premium is determined by GDP volatility and price inflation. In a lesser extent, the share of U.S. equities held by institutional investors can explain the risk premium. Demographic variables explain the earning-price ratio but only as a short-run phenomenon. Our results suggest that change in the macroeconomic equity risk premium has driven much of the recent run-up in stock prices.Johansen Procedure, Valuation Ratios, Equity Risk Premium, Present Value Model.
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