arXiv subjects

Marcelo Magnasco

Publications and source records attributed to Marcelo Magnasco.

6 recordsLinked to original sources

arXiv2019

A Center Manifold Reduction Technique for a System of Randomly Coupled Oscillators

In dynamical systems theory, a fixed point of the dynamics is called nonhyperbolic if the linearization of the system around the fixed point has at least one eigenvalue with zero real part. The center manifold existence theorem guarantees the local existence of an invariant subspace of the dynamics, known as a center manifold, around such nonhyperbolic fixed points. A growing number of theoretical and experimental studies suggest that some neural systems utilize nonhyperbolic fixed points and corresponding center manifolds to display complex, nonlinear dynamics and to flexibly adapt to wide-ranging sensory input parameters. In this paper, we present a technique to study the statistical properties of high-dimensional, nonhyperbolic dynamical systems with random connectivity and examine which statistical properties determine both the shape of the center manifold and the corresponding reduced dynamics on it. This technique also gives us constraints on the family of center manifold models that could arise from a large-scale random network. We demonstrate this approach on an example network of randomly coupled damped oscillators.

math.DS↗

arXiv2018

A Time Domain Acoustic Model for the Production of Rodent Ultrasonic Vocalizations

Mammalian ultrasonic vocalization (USV) has been a subject of interest for decades. This interest has mainly been driven by the intelligence of dolphins and other odontocetes. However the semantic content of odontocete USV and its mechanism of production remain poorly understood. Serendipitously however many rodent species have convergently evolved the ability to produce USVs in a similar manner. In this paper we use rodent USV as a model process to help us gain insight into the production mechanism for mammalian USV as a whole. We derive a model that describes the production of rodent USVs by considering the interaction of an unstable jet, emerging from the vocal folds, with the passive resonance modes of the upper vocal tract. Thus our model is also a solution to a special case of the jet susceptibility problem. The derived model takes the form of a set of coupled nonlinear time domain ODEs, whose solutions are controlled by biologically relevant parameters such as subglottal pressure and vocal fold radius. In our analysis of the model we find the existence of a subglottal blowing pressure threshold ($p \approx 710$ Pa), above which steady acoustic oscillations occur. Furthermore we also reproduce the $22$ kHz rat alarm call at realistic blowing pressures ($p \approx 1500$ Pa)

physics.bio-ph↗

arXiv2018

A Nonhyperbolic Toy Model of Cochlear Dynamics

Cochlea displays complex and highly nonlinear behavior in response to wide-ranging auditory stimuli. While there have been many recent advancements in the modeling of cochlear dynamics, it remains unclear what mathematical structures underlie the essential features of the extended cochlea. We construct a dynamical system consisting of a series of strongly coupled critical oscillators to show that high-dimensional nonhyperbolic dynamics can account for high-order compressive nonlinearities, amplification of weak input, frequency selectivity, and traveling waves of activity. As a single Hopf bifurcation generically gives rise to features of cochlea at a local level, the nonhyperbolicity mechanism proposed in this paper can be seen as a higher-dimensional analogue for the entire extended cochlea.

physics.bio-ph↗

arXiv2018

Adaptive Scales of Spatial Integration and Response Latencies in a Critically-Balanced Model of the Primary Visual Cortex

The brain processes visual inputs having structure over a large range of spatial scales. The precise mechanisms or algorithms used by the brain to achieve this feat are largely unknown and an open problem in visual neuroscience. In particular, the spatial extent in visual space over which primary visual cortex (V1) performs evidence integration has been shown to change as a function of contrast and other visual parameters, thus adapting scale in visual space in an input-dependent manner. We demonstrate that a simple dynamical mechanism---dynamical criticality---can simultaneously account for the well-documented input-dependence characteristics of three properties of V1: scales of integration in visuotopic space, extents of lateral integration on the cortical surface, and response latencies.

q-bio.NC↗

arXiv2002

A study of accuracy and precision in oligonucleotide arrays: extracting more signal at large concentrations

Despite the success and popularity of oligonucleotide arrays as a high-throughput technique for measuring mRNA expression levels, quantitative calibration studies have until now been limited. The main reason is that suitable data was not available. However, calibration data recently produced by Affymetrix now permits detailed studies of the intensity dependent sensitivity. Given a certain transcript concentration, it is of particular interest to know whether current analysis methods are capable of detecting differential expression ratios of 2 or higher. Using the calibration data, we demonstrate that while current techniques are capable of detecting changes in the low to mid concentration range, the situation is noticeably worse for high concentrations. In this regime, expression changes as large as 4 fold are severely biased, and changes of 2 are often undetectable. Such effects are mainly the consequence of the sequence specific binding properties of probes, and not the result of optical saturation in the fluorescence measurements. GeneChips are manufactured such that each transcript is probed by a set of sequences with a wide affinity range. We show that this property can be used to design a method capable of reducing the high intensity bias. The idea behind our methods is to transfers the weight of a measurement to a subset of probes with optimal linear response at a given concentration, which can be achieved using local embedding techniques.

physics.bio-ph↗

arXiv2001

DNA hybridization to mismatched templates: a chip study

High-density oligonucleotide arrays are among the most rapidly expanding technologies in biology today. In the {\sl GeneChip} system, the reconstruction of the target concentration depends upon the differential signal generated from hybridizing the target RNA to two nearly identical templates: a perfect match (PM) and a single mismatch (MM) probe. It has been observed that a large fraction of MM probes repeatably bind targets better than the PMs, against the usual expectation from sequence-specific hybridization; this is difficult to interpret in terms of the underlying physics. We examine this problem via a statistical analysis of a large set of microarray experiments. We classify the probes according to their signal to noise ($S/N$) ratio, defined as the eccentricity of a (PM, MM) pair's `trajectory' across many experiments. Of those probes having large $S/N$ ($>3$) only a fraction behave consistently with the commonly assumed hybridization model. Our results imply that the physics of DNA hybridization in microarrays is more complex than expected, and they suggest new ways of constructing estimators for the target RNA concentration.

physics.bio-ph↗