13,498 research outputs found
Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback
Interaction via pulses is common in many natural systems, especially
neuronal. In this article we study one of the simplest possible systems with
pulse interaction: a phase oscillator with delayed pulsatile feedback. When the
oscillator reaches a specific state, it emits a pulse, which returns after
propagating through a delay line. The impact of an incoming pulse is described
by the oscillator's phase reset curve (PRC). In such a system we discover an
unexpected phenomenon: for a sufficiently steep slope of the PRC, a periodic
regular spiking solution bifurcates with several multipliers crossing the unit
circle at the same parameter value. The number of such critical multipliers
increases linearly with the delay and thus may be arbitrary large. This
bifurcation is accompanied by the emergence of numerous "jittering" regimes
with non-equal interspike intervals (ISIs). Each of these regimes corresponds
to a periodic solution of the system with a period roughly proportional to the
delay. The number of different "jittering" solutions emerging at the
bifurcation point increases exponentially with the delay. We describe the
combinatorial mechanism that underlies the emergence of such a variety of
solutions. In particular, we show how a periodic solution exhibiting several
distinct ISIs can imply the existence of multiple other solutions obtained by
rearranging of these ISIs. We show that the theoretical results for phase
oscillators accurately predict the behavior of an experimentally implemented
electronic oscillator with pulsatile feedback
Exchange Rate Economics
The paper summarizes the current theory of how a floating exchange rate is determined, dividing the subject into what determines the steady state and what determines the transition to steady state. The inadequacies of this model are examined, and an alternative “behavioral” model, which recognizes that the foreign exchange market is populated by both fundamentalists and chartists is presented. It is argued that the main importance of understanding the foreign exchange market for development strategy is to permit a correct appraisal of the dangers of Dutch disease. Empirically it seems that from the standpoint of promoting development it is preferable to have a mildly undervalued rate. The paper concludes by examining implications for exchange rate regimes.Exchange rates; behavioral model; Dutch disease
Development of spatial coarse-to-fine processing in the visual pathway
The sequential analysis of information in a coarse-to-fine manner is a
fundamental mode of processing in the visual pathway. Spatial frequency (SF)
tuning, arguably the most fundamental feature of spatial vision, provides
particular intuition within the coarse-to-fine framework: low spatial
frequencies convey global information about an image (e.g., general
orientation), while high spatial frequencies carry more detailed information
(e.g., edges). In this paper, we study the development of cortical spatial
frequency tuning. As feedforward input from the lateral geniculate nucleus
(LGN) has been shown to have significant influence on cortical coarse-to-fine
processing, we present a firing-rate based thalamocortical model which includes
both feedforward and feedback components. We analyze the relationship between
various model parameters (including cortical feedback strength) and responses.
We confirm the importance of the antagonistic relationship between the center
and surround responses in thalamic relay cell receptive fields (RFs), and
further characterize how specific structural LGN RF parameters affect cortical
coarse-to-fine processing. Our results also indicate that the effect of
cortical feedback on spatial frequency tuning is age-dependent: in particular,
cortical feedback more strongly affects coarse-to-fine processing in kittens
than in adults. We use our results to propose an experimentally testable
hypothesis for the function of the extensive feedback in the corticothalamic
circuit.Comment: 20 pages, 7 figures; substantial restructuring from previous versio
Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics
Neural activity patterns related to behavior occur at many scales in time and
space from the atomic and molecular to the whole brain. Here we explore the
feasibility of interpreting neurophysiological data in the context of many-body
physics by using tools that physicists have devised to analyze comparable
hierarchies in other fields of science. We focus on a mesoscopic level that
offers a multi-step pathway between the microscopic functions of neurons and
the macroscopic functions of brain systems revealed by hemodynamic imaging. We
use electroencephalographic (EEG) records collected from high-density electrode
arrays fixed on the epidural surfaces of primary sensory and limbic areas in
rabbits and cats trained to discriminate conditioned stimuli (CS) in the
various modalities. High temporal resolution of EEG signals with the Hilbert
transform gives evidence for diverse intermittent spatial patterns of amplitude
(AM) and phase modulations (PM) of carrier waves that repeatedly re-synchronize
in the beta and gamma ranges at near zero time lags over long distances. The
dominant mechanism for neural interactions by axodendritic synaptic
transmission should impose distance-dependent delays on the EEG oscillations
owing to finite propagation velocities. It does not. EEGs instead show evidence
for anomalous dispersion: the existence in neural populations of a low velocity
range of information and energy transfers, and a high velocity range of the
spread of phase transitions. This distinction labels the phenomenon but does
not explain it. In this report we explore the analysis of these phenomena using
concepts of energy dissipation, the maintenance by cortex of multiple ground
states corresponding to AM patterns, and the exclusive selection by spontaneous
breakdown of symmetry (SBS) of single states in sequences.Comment: 31 page
Computational study of resting state network dynamics
Lo scopo di questa tesi è quello di mostrare, attraverso una simulazione con il software The Virtual Brain, le più importanti proprietà della dinamica cerebrale durante il resting state, ovvero quando non si è coinvolti in nessun compito preciso e non si è sottoposti a nessuno stimolo particolare. Si comincia con lo spiegare cos’è il resting state attraverso una breve revisione storica della sua scoperta, quindi si passano in rassegna alcuni metodi sperimentali utilizzati nell’analisi dell’attività cerebrale, per poi evidenziare la differenza tra connettività strutturale e funzionale. In seguito, si riassumono brevemente i concetti dei sistemi dinamici, teoria indispensabile per capire un sistema complesso come il cervello. Nel capitolo successivo, attraverso un approccio ‘bottom-up’, si illustrano sotto il profilo biologico le principali strutture del sistema nervoso, dal neurone alla corteccia cerebrale. Tutto ciò viene spiegato anche dal punto di vista dei sistemi dinamici, illustrando il pionieristico modello di Hodgkin-Huxley e poi il concetto di dinamica di popolazione. Dopo questa prima parte preliminare si entra nel dettaglio della simulazione. Prima di tutto si danno maggiori informazioni sul software The Virtual Brain, si definisce il modello di network del resting state utilizzato nella simulazione e si descrive il ‘connettoma’ adoperato. Successivamente vengono mostrati i risultati dell’analisi svolta sui dati ricavati, dai quali si mostra come la criticità e il rumore svolgano un ruolo chiave nell'emergenza di questa attività di fondo del cervello. Questi risultati vengono poi confrontati con le più importanti e recenti ricerche in questo ambito, le quali confermano i risultati del nostro lavoro. Infine, si riportano brevemente le conseguenze che porterebbe in campo medico e clinico una piena comprensione del fenomeno del resting state e la possibilità di virtualizzare l’attività cerebrale
The Role of Data in Model Building and Prediction: A Survey Through Examples
The goal of Science is to understand phenomena and systems in order to
predict their development and gain control over them. In the scientific process
of knowledge elaboration, a crucial role is played by models which, in the
language of quantitative sciences, mean abstract mathematical or algorithmical
representations. This short review discusses a few key examples from Physics,
taken from dynamical systems theory, biophysics, and statistical mechanics,
representing three paradigmatic procedures to build models and predictions from
available data. In the case of dynamical systems we show how predictions can be
obtained in a virtually model-free framework using the methods of analogues,
and we briefly discuss other approaches based on machine learning methods. In
cases where the complexity of systems is challenging, like in biophysics, we
stress the necessity to include part of the empirical knowledge in the models
to gain the minimal amount of realism. Finally, we consider many body systems
where many (temporal or spatial) scales are at play and show how to derive from
data a dimensional reduction in terms of a Langevin dynamics for their slow
components
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