On feedback and stable price adjustment mechanisms

Given an excess demand function of an economy, say Z(p)$Z(p)$, a stable price adjustment mechanism (SPAM) guarantees convergence of solution path p(t,_p0)$p(t,p_0)$ to an equilibrium _peq$p_{\mathit{eq}}$ solution of Z(p)=0$Z(p)=0$. Besides, all equilibrium points of Z(p)$Z(p)$ are asymptotically stable. Some SPAMs have been proposed, including Newton and transpose Jacobian methods. Despite this powerful stability property of SPAMs, their acceptation in the economics community has been limited by a lack of interpretation. This paper focuses on this issue. Specifically, feedback control theory is used to link SPAMs and price dynamics models with control inputs, which match the economically intuitive Walrasian Hypothesis (i.e., prices change with excess demand sign). Under mild conditions, it is shown the existence of a feedback function that transforms the price dynamics into a desired SPAM. Hence, a SPAM is interpreted as a fundamental (e.g., Walrasian) price dynamics under the action of a feedback function aimed to stabilize the equilibrium set of the excess demand function.     

Comparisons of the discrete-dipole approximation and modified double interaction model methods to predict light scattering from small features on surfaces

Two numerical methods to model light scattering from illuminated features on surfaces are presented. The discrete-dipole approximation (DDA) method is considered, as well as the modified double interaction method (MDIM). The DDA method models electromagnetic scattering of continuous features using discrete dipoles placed on a lattice structure. Sommerfeld integral terms are used to model dipole/surface interaction in the near-field. The MDIM method first computes scattering from the features based in free space using other methods such as Mie theory or other standard light scattering codes (including DDA). The surface interaction is modeled as a first approximation by means of a geometrical shadowing effect and the Fresnel coefficients. Comparisons of the methods will be shown for light scattering from spherical features. The material properties of dielectric and metallic materials will be considered and the feature sizes will be varied. The prediction accuracy and computational requirements of each method will be investigated. For most cases, the studies will show that the DDA method is more accurate than the MDIM method for dielectric materials since the modeling of the feature and surface electromagnetic interaction is more accurate; however, the modified double interaction method may be advantageous over the discrete-dipole approximation method for metallic features because of lesser computational times and memory requirements.     

Using permutations to detect dependence between time series

In this paper, we propose an independence test between two time series which is based on permutations. The proposed test can be carried out by means of different common statistics such as Pearson’s chi-square or the likelihood ratio. We also point out why an exact test is necessary. Simulated and real data (return exchange rates between several currencies) reveal the capacity of this test to detect linear and nonlinear dependences.     

Is the US stock market becoming weakly efficient over time? Evidence from 80-year-long data

We propose a degree of market efficiency in terms of entropy concepts. The relative efficiency for the US stock market varies over time from 1929 to 2012, with a slight decline in the past 10 years.     

In situ studies of microbial inactivation during high pressure processing

High pressure processing (HPP) has been shown to reduce microbial concentration in foods. The mechanisms of microbial inactivation by HPP have been associated with damage to cell membranes. The real-time response of bacteria to HPP was measured to elucidate the mechanisms of inactivation, which can aid in designing more effective processes. Different pressure cycling conditions were used to expose Enterobacter aerogenes cells to HPP. Propidium iodide (PI) was used as a probe, which fluoresces after penetrating cells with damaged membranes and binding with nucleic acids. A HPP vessel with sapphire windows was used for measuring fluorescence in situ. Membrane damage was detected during pressurization and hold time, but not during depressurization. The drop in fluorescence was larger than expected after pressure cycles at higher pressure and longer times. This indicated possible reversible disassociation of ribosomes resulting in additional binding of PI to exposed RNA under pressure and its release after depressurization.     

Ceric Ion Initiated Graft Polymerization onto Poly(vinyl Alcohol)

This paper describes the kinetics of the ceric ion-initiated graft co-polymerization of vinyl acetate-acrylonitrile to poly(vinyl alcohol). The graft copolymerization rate R_p was found to be first order with respect to the total concentration of the comonomer mixture [M], the concentration of vinyl alcohol repeating units [PVA], and the mole fraction of vinyl acetate in the comonomer feed mixture. R_p was independent of cerous ion. The grafting rate was independent of ceric ion above a ceric concentration of 0.0020 M but first order in ceric ion below that concentration. Rp initially increased rapidly with [H⁺] to a maximum and then decreased and levelled off at hgher [H⁺]. The rate of ceric ion disappearance was first order in [PVA], independent of [MI, and increased with increasing [H⁺] with a leveling off at high [H⁺]. A reaction mechanism.