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.     

Surface monitoring based on light scattering by metal nanosensors

Light scattering from objects in the proximity of surfaces is of fundamental importance in a variety of surface- and field-enhanced optical sensing, spectroscopy and microscopy applications. Here, we present surface monitoring techniques based on the spectral analysis of the scattered light by metal nanoparticles which act as sensors (nanosensors) of sample substrates interacting with them. We will focus on the detection of surface inhomogeneities by studying the modifications undergone by the local fields produced in the surrounding of the nanosensor, giving rise to spectral changes in its Plasmon Resonances. We will also describe an alternative technique where the sample information is obtained from the changes induced in the linear polarization degree of the far field scattered by the tip and due to the interaction with the sample.     

Early Detection of Breast Cancer: Synthesis and Characterization of Novel Target Specific NIR-Fluorescent Estrogen Conjugate for Molecular Optical Imaging

Estrogen induced proliferation of existing mutant cells is widely understood to be the major risk determining factor in the development of breast cancer. Hence determination of the Estrogen Receptor[ER] status is of paramount importance. We have carried out the synthesis and characterization of a novel NIR fluorescent dye conjugate aimed at measuring ER+ve status in-vivo. The conjugate was synthesized by ester formation between 17-β estradiol and a cyanine dye namely: bis-1, 1-(4-sulfobutyl) indotricarbocyanine-5-carboxylic acid, sodium salt. The replacement of the sodium ion in the ester by a larger glucosammonium ion was found to enhance the hydrophilicity and reduce the toxic effect on cell lines. The excitation and emission peaks for the dye were recorded as 750 and 788 nm respectively; ideal for non-invasive optical imaging owing to minimal tissue attenuation and auto-fluorescence at these wavelengths. The dye (NIRDC1) has a significant drop in plasma-protein binding therefore leading to marked improvement in pharmacokinetic profile such as dye evacuation in comparison to ICG. In addition the dye showed enhanced fluorescence quantum yield, molar extinction coefficient and linearity in fluorescence relative to ICG. This dye can be potentially used as a target specific exogenous contrast agent in molecular optical imaging for early detection of breast cancer.     

Correlations in a Mozart's music score (K-73x) with palindromic and upside-down structure

In this work, we study long-range correlations in a “Scherzo-Duetto di Mozart” score (K-73x) for two violins. This is a fascinating piece, as the second violin part is upside down on the same sheet below the first violin, and some parts are like a palindrome. Given such ingenious structure, it is expected the existence of long-range correlations in the score structure. In order to quantify long-range correlations, we considered the music score as a sequence of integer numbers, each of them corresponding to last common denominator units of note. By using detrended fluctuation analysis (DFA), correlations are quantified by means of the scaling exponent that reflects the type of correlations for a given distance between neighbors note. The following conclusions can be drawn from the analysis: (a) For about 10-25 neighbor note distances, correlations are similar to 1/f-noise. This is an interesting finding since it has been shown that pleasant sounds for humans display a behavior similar to 1/f noise. (b) As the neighbor note distance increases, the long-range correlations decays continuously. For some score sections, the music score behaves like non-correlated (i.e., purely random) noise. Summing up, the results show that the studied Mozart's score contains a certain degree of correlation for relatively small note distances, and becomes close to non-correlated behavior for long note distances. We considered also the sequence constructed by considering the distance between the simultaneously played notes of the two violins. Interestingly, for relatively small neighbor note distances, a scaling behavior similar to that found for individual violins is also displayed. In some sense, this is an expression of the specific structure (palindromes plus upside down construction) used by Mozart in the composition of this music score. Although we focused on a particular high-art music score, our results suggest that modern methods borrowed from statistical physics can be useful for the systematic study of music composition techniques.     

Multivariate analysis in provenance studies: Cerrillos obsidians case, Peru

We present the preliminary results of a provenance study of obsidians samples from Cerrillos (ca. 800–100 b.c.) using Mössbauer Spectroscopy. The Cerrillos archaeological site, located in the Upper Ica Valley, Peru, is the only Paracas ceremonial center excavated so far. The archaeological data collected suggest the existence of a complex social and economic organization on the south coast of Peru. Provenance research of obsidian provides valuable information about the selection of lithic resources by our ancestors and eventually about the existence of communication routes and exchange networks. We characterized 18 obsidian artifacts samples by Mössbauer spectroscopy from Cerrillos. The spectra, recorded at room temperature using different velocities, are mainly composed of broad asymmetric doublets due to the superposition of at least two quadrupole doublets corresponding to Fe²⁺ in two different sites (species A and B), one weak Fe³⁺ doublet (specie C) and magnetic components associated to the presence of small particles of magnetite. Multivariate statistical analysis of the Mössbauer data (hyperfine parameters) allows to defined two main groups of obsidians, reflecting different geographical origins.     

Characterizing turbulence in globally coupled maps with stochastic finite automata

We describe a method to discriminate between ordered and turbulent behavior in a general class of collective systems known as Globally Coupled Maps (GCM). Our method is able to discover an unknown small ordered region inside the turbulent phase of GCM parameter space. The computational nature of the method is the main novelty of our approach; it is another example of how measures based on computational notions of structure may provide new information in the study of dynamical systems.     

Hydrogenated amorphous silicon films obtained by a low pressure dc glow discharge

Films of a-Si: H have been deposited by means of a dc hot cathode discharge of SiH₄ with electrostatic confinement at a pressure as low as 0.4 Pa. The plasma used is quite quiescent as has been observed by means of reproducible Langmuir probe measurements. Substrates have been placed at different locations in between the electrodes, some of them facing the anode and the others facing the cathode.Films deposited on substrates facing the cathode present a granular, non-columnar, structure, an IR spectrum with only SiH absorption peaks, and a very low photoresponse. Films deposited on substrates facing the anode have a similar IR spectrum but are homogeneous, have lower hydrogen content, and present a high photoresponse. The optical absorption coefficient shows in all samples thenE=C(E–E₀) ^x behaviour, but with exponentx=3 and notx=2 as is usually considered in a-SiH.     

Delayed feedback control of phase synchronisation in a neuronal network model

The human cerebral cortex can be separated into cortical areas forming a clustered network structure. We build two different clustered networks, where one network is based on a healthy brain and the other according to a brain affected by a neurodegenerative process. Each cortical area has a subnetwork with small-world properties. We verify that both networks exhibit rich-club organisation and phase synchronisation. Due to the fact that neuronal synchronisation can be related to brain diseases, we consider the delayed feedback control as a method to suppress synchronous behaviours. In this work, it is presented that depending on the feedback parameters, intensity and time delay, phase synchronisation in both networks can be suppressed. Therefore, one of our main results is to show that delayed feedback control can be used to suppress undesired synchronous behaviours not only in the healthy brain, but also in the brain marked by neurodegenerative processes.