arXiv subjects

Marcelo O. Magnasco

Publications and source records attributed to Marcelo O. Magnasco.

At least 19 recordsLinked to original sources

arXiv2024

Input-driven circuit reconfiguration in critical recurrent neural networks

Changing a circuit dynamically, without actually changing the hardware itself, is called reconfiguration, and is of great importance due to its manifold technological applications. Circuit reconfiguration appears to be a feature of the cerebral cortex, and hence understanding the neuroarchitectural and dynamical features underlying self-reconfiguration may prove key to elucidate brain function. We present a very simple single-layer recurrent network, whose signal pathways can be reconfigured "on the fly" using only its inputs, with no changes to its synaptic weights. We use the low spatio-temporal frequencies of the input to landscape the ongoing activity, which in turn permits or denies the propagation of traveling waves. This mechanism uses the inherent properties of dynamically-critical systems, which we guarantee through unitary convolution kernels. We show this network solves the classical connectedness problem, by allowing signal propagation only along the regions to be evaluated for connectedness and forbidding it elsewhere.

cond-mat.stat-mech↗

arXiv2024

On the dynamics of convolutional recurrent neural networks near their critical point

We examine the dynamical properties of a single-layer convolutional recurrent network with a smooth sigmoidal activation function, for small values of the inputs and when the convolution kernel is unitary, so all eigenvalues lie exactly at the unit circle. Such networks have a variety of hallmark properties: the outputs depend on the inputs via compressive nonlinearities such as cubic roots, and both the timescales of relaxation and the length-scales of signal propagation depend sensitively on the inputs as power laws, both diverging as the input to 0. The basic dynamical mechanism is that inputs to the network generate ongoing activity, which in turn controls how additional inputs or signals propagate spatially or attenuate in time. We present analytical solutions for the steady states when the network is forced with a single oscillation and when a background value creates a steady state of ongoing activity, and derive the relationships shaping the value of the temporal decay and spatial propagation length as a function of this background value.

cond-mat.stat-mech↗

arXiv2023

Convolutional unitary or orthogonal recurrent neural networks

Recurrent neural networks are extremely powerful yet hard to train. One of their issues is the vanishing gradient problem, whereby propagation of training signals may be exponentially attenuated, freezing training. Use of orthogonal or unitary matrices, whose powers neither explode nor decay, has been proposed to mitigate this issue, but their computational expense has hindered their use. Here we show that in the specific case of convolutional RNNs, we can define a convolutional exponential and that this operation transforms antisymmetric or anti-Hermitian convolution kernels into orthogonal or unitary convolution kernels. We explicitly derive FFT-based algorithms to compute the kernels and their derivatives. The computational complexity of parametrizing this subspace of orthogonal transformations is thus the same as the networks' iteration.

cs.LG↗

arXiv2020

Masks and COVID-19: a causal framework for imputing value to public-health interventions

During the COVID-19 pandemic, the scientific community developed predictive models to evaluate potential governmental interventions. However, the analysis of the effects these interventions had is less advanced. Here, we propose a data-driven framework to assess these effects retrospectively. We use a regularized regression to find a parsimonious model that fits the data with the least changes in the Rt parameter. Then, we postulate each jump in Rt as the effect of an intervention. Following the do-operator prescriptions, we simulate the counterfactual case by forcing Rt to stay at the pre-jump value. We then attribute a value to the intervention from the difference between true evolution and simulated counterfactual. We show that the recommendation to use facemasks for all activities would reduce the number of cases by 170000 (95% CI 160000 to 180000) in Connecticut, Massachusetts, and New York State. The framework presented here might be used in any case where cause and effects are sparse in time.

q-bio.PE↗

arXiv2014

Extracting Hidden Hierarchies in 3D Distribution Networks

Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function. Yet, the set of tools that can characterize such a weighted cycle-rich architecture in a physically relevant, mathematically compact way is sparse. In order to fill this void, we have developed a new algorithm that rests on an abstraction of the physical `tiling' in the case of a two dimensional network to an effective tiling of an abstract surface in space that the network may be thought to sit in. Generically these abstract surfaces are richer than the flat plane and as a result there are now two families of fundamental units that may aggregate upon cutting weakest links -- the plaquettes of the tiling and the longer `topological' cycles associated with the abstract surface itself. Upon sequential removal of the weakest links, as determined by the edge weight, neighboring plaquettes merge and a tree characterizing this merging process results. The properties of this characteristic tree can provide the physical and topological data required to describe the architecture of the network and to build physical models. The new algorithm can be used for automated phenotypic characterization of any weighted network whose structure is dominated by cycles, such as mammalian vasculature in the organs, the root networks of clonal colonies like quaking aspen, or the force networks in jammed granular matter.

q-bio.QM↗

arXiv2014

Structural Self-Assembly and Glassy Dynamics in Locally Adaptive Networks

Transport networks play a key role across four realms of eukaryotic life: slime molds, fungi, plants, and animals. In addition to the developmental algorithms that build them, many also employ adaptive strategies to respond to stimuli, damage, and other environmental changes. We model these adapting network architectures using a generic dynamical system on weighted graphs and find in simulation that these networks ultimately develop a hierarchical organization of the final weighted architecture accompanied by the formation of a system-spanning backbone. In addition, we find that the long term equilibration dynamics exhibit glassy behavior characterized by long periods of slow changes punctuated by bursts of reorganization events.

nlin.AO↗

arXiv2013

A Geometric Knotspace Template

Early last century witnessed both the complete classification of 2-dimensional manifolds and a proof that classification of 4-dimensional manifolds is undecidable, setting up 3-dimensional manifolds as a central battleground of topology to this day. A rather important subset of the 3-manifolds has turned out to be the knotspaces, the manifolds left when a thin tube around a knot in 3D space is excised. Given a knot diagram it would be desirable to provide as compact a description of its knotspace as feasible; hitherto this has been done by computationally tessellating the knotspace of a given knot into polyhedral complexes using ad hoc methods of uncontrolled computational complexity. Here we present an extremely compact representation of the knotspace obtainable directly from a knot diagram; more technically, an explicit, geometrically-inspired polygonal tessellation of a deformation retract of the knotspace of arbitrary knots and links. Our template can be constructed directly from a planar presentation of the knot with C crossings using at most 12C polygons bounded by 64C edges, in time O(C). We show the utility of our template by deriving a novel presentation of the fundamental group, from which we motivate a measure of complexity of the knot diagram.

math.GT↗

arXiv2013

Minimal Bounds on Nonlinearity in Auditory Processing

Time-reversal symmetry breaking is a key feature of nearly all natural sounds, caused by the physics of sound production. While attention has been paid to the response of the auditory system to "natural stimuli," very few psychophysical tests have been performed. We conduct psychophysical measurements of time-frequency acuity for both "natural" notes (sharp attack, long decay) and time-reversed ones. Our results demonstrate significantly greater precision, arising from enhanced temporal acuity, for such "natural" sounds over both their time-reversed versions and theoretically optimal gaussian pulses, without a corresponding decrease in frequency acuity. These data rule out models of auditory processing that obey a modified "uncertainty principle" between temporal and frequency acuity and suggest the existence of statistical priors for naturalistic stimuli, in the form of sharp-attack, long-decay notes. We are additionally able to calculate a minimal theoretical bound on the order of the nonlinearity present in auditory processing. We find that only matching pursuit, spectral derivatives, and reassigned spectrograms are able to satisfy this criterion.

q-bio.NC↗

arXiv2013

Human Time-Frequency Acuity Beats the Fourier Uncertainty Principle

The time-frequency uncertainty principle states that the product of the temporal and frequency extents of a signal cannot be smaller than $1/(4π)$. We study human ability to simultaneously judge the frequency and the timing of a sound. Our subjects often exceeded the uncertainty limit, sometimes by more than tenfold, mostly through remarkable timing acuity. Our results establish a lower bound for the nonlinearity and complexity of the algorithms employed by our brains in parsing transient sounds, rule out simple "linear filter" models of early auditory processing, and highlight timing acuity as a central feature in auditory object processing.

q-bio.NC↗

arXiv2012

A Topological Phase Transition in the Scheidegger Model of River Networks

We investigate the canonical Scheidegger Model of river network morphology for the case of convergent and divergent underlying topography, by embedding it on a cone. We find two distinct phases corresponding to few, long basins and many, short basins, respectively, separated by a singularity in number of basins, indicating a phase transition. Quantifying basin shape through Hack's Law $l\sim a^h$ gives distinct values for the exponent $h$, providing a method of testing our hypotheses. The generality of our model suggests implications for vascular morphology, in particular differing number and shapes of arterial and venous trees.

q-bio.TO↗

arXiv2012

A phase transition in the first passage of a Brownian process through a fluctuating boundary: implications for neural coding

Finding the first time a fluctuating quantity reaches a given boundary is a deceptively simple-looking problem of vast practical importance in physics, biology, chemistry, neuroscience, economics and industry. Problems in which the bound to be traversed is itself a fluctuating function of time include widely studied settings in neural coding, such as neuronal integrators with irregular inputs and internal noise. We show that the probability p(t) that a Gauss-Markov process will first exceed the boundary at time t suffers a phase transition as a function of the roughness of the boundary, as measured by its Hölder exponent H, with critical value Hc = 1/2. For smoother boundaries, H > 1/2, the probability density is a continuous func- tion of time. For rougher boundaries, H < 1/2, the probability is concentrated on a Cantor-like set of zero measure: the probability density becomes divergent, almost everywhere either zero or infin- ity. The critical point Hc = 1/2 corresponds to a widely-studied case in the theory of neural coding, where the external input integrated by a model neuron is a white-noise process, such as uncorrelated but precisely balanced excitatory and inhibitory inputs. We argue this transition corresponds to a sharp boundary between rate codes, in which the neural firing probability varies smoothly, and temporal codes, in which the neuron fires at sharply-defined times regardless of the intensity of internal noise.

q-bio.NC↗

arXiv2011

Quantifying loopy network architectures

Biology presents many examples of planar distribution and structural networks having dense sets of closed loops. An archetype of this form of network organization is the vasculature of dicotyledonous leaves, which showcases a hierarchically-nested architecture containing closed loops at many different levels. Although a number of methods have been proposed to measure aspects of the structure of such networks, a robust metric to quantify their hierarchical organization is still lacking. We present an algorithmic framework, the hierarchical loop decomposition, that allows mapping loopy networks to binary trees, preserving in the connectivity of the trees the architecture of the original graph. We apply this framework to investigate computer generated graphs, such as artificial models and optimal distribution networks, as well as natural graphs extracted from digitized images of dicotyledonous leaves and vasculature of rat cerebral neocortex. We calculate various metrics based on the Asymmetry, the cumulative size distribution and the Strahler bifurcation ratios of the corresponding trees and discuss the relationship of these quantities to the architectural organization of the original graphs. This algorithmic framework decouples the geometric information (exact location of edges and nodes) from the metric topology (connectivity and edge weight) and it ultimately allows us to perform a quantitative statistical comparison between predictions of theoretical models and naturally occurring loopy graphs.

q-bio.QM↗

arXiv2009

A Fast $\mathcal{L}_p$ Spike Alignment Metric

The metrization of the space of neural responses is an ongoing research program seeking to find natural ways to describe, in geometrical terms, the sets of possible activities in the brain. One component of this program are the {\em spike metrics}, notions of distance between two spike trains recorded from a neuron. Alignment spike metrics work by identifying "equivalent" spikes in one train and the other. We present an alignment spike metric having $\mathcal{L}_p$ underlying geometrical structure; the $\mathcal{L}_2$ version is Euclidean and is suitable for further embedding in Euclidean spaces by Multidimensional Scaling methods or related procedures. We show how to implement a fast algorithm for the computation of this metric based on bipartite graph matching theory.

q-bio.NC↗

arXiv2009

Damage and fluctuations induce loops in optimal transport networks

Leaf venation is a pervasive example of a complex biological network, endowing leaves with a transport system and mechanical resilience. Transport networks optimized for efficiency have been shown to be trees, i.e. loopless. However, dicotyledon leaf venation has a large number of closed loops, which are functional and able to transport fluid in the event of damage to any vein, including the primary veins. Inspired by leaf venation, we study two possible reasons for the existence of a high density of loops in transport networks: resilience to damage and fluctuations in load. In the first case, we seek the optimal transport network in the presence of random damage by averaging over damage to each link. In the second case, we seek the network that optimizes transport when the load is sparsely distributed: at any given time most sinks are closed. We find that both criteria lead to the presence of loops in the optimum state.

physics.bio-ph↗

arXiv2008

Dynamical and Statistical Criticality in a Model of Neural Tissue

For the nervous system to work at all, a delicate balance of excitation and inhibition must be achieved. However, when such a balance is sought by global strategies, only few modes remain balanced close to instability, and all other modes are strongly stable. Here we present a simple model of neural tissue in which this balance is sought locally by neurons following `anti-Hebbian' behavior: {\sl all} degrees of freedom achieve a close balance of excitation and inhibition and become "critical" in the dynamical sense. At long timescales, the modes of our model oscillate around the instability line, so an extremely complex "breakout" dynamics ensues in which different modes of the system oscillate between prominence and extinction. We show the system develops various anomalous statistical behaviours and hence becomes self-organized critical in the statistical sense.

q-bio.NC↗

arXiv2007

A Haar-like Construction for the Ornstein Uhlenbeck Process

The classical Haar construction of Brownian motion uses a binary tree of triangular wedge-shaped functions. This basis has compactness properties which make it especially suited for certain classes of numerical algorithms. We present a similar basis for the Ornstein-Uhlenbeck process, in which the basis elements approach asymptotically the Haar functions as the index increases, and preserve the following properties of the Haar basis: all basis elements have compact support on an open interval with dyadic rational endpoints; these intervals are nested and become smaller for larger indices of the basis element, and for any dyadic rational, only a finite number of basis elements is nonzero at that number. Thus the expansion in our basis, when evaluated at a dyadic rational, terminates in a finite number of steps. We prove the covariance formulae for our expansion and discuss its statistical interpretation and connections to asymptotic scale invariance.

math.PR↗

arXiv2006

Structure, Scaling and Phase Transition in the Optimal Transport Network

We minimize the dissipation rate of an electrical network under a global constraint on the sum of powers of the conductances. We construct the explicit scaling relation between currents and conductances, and show equivalence to a a previous model [J. R. Banavar {\it et al} Phys. Rev. Lett. {\bf 84}, 004745 (2000)] optimizing a power-law cost function in an abstract network. We show the currents derive from a potential, and the scaling of the conductances depends only locally on the currents. A numerical study reveals that the transition in the topology of the optimal network corresponds to a discontinuity in the slope of the power dissipation.

cond-mat.dis-nn↗

arXiv2004

Computational Models of Adult Neurogenesis

Experimental results in recent years have shown that adult neurogenesis is a significant phenomenon in the mammalian brain. Little is known, however, about the functional role played by the generation and destruction of neurons in the context of and adult brain. Here we propose two models where new projection neurons are incorporated. We show that in both models, using incorporation and removal of neurons as a computational tool, it is possible to achieve a higher computational efficiency that in purely static, synapse-learning driven networks. We also discuss the implication for understanding the role of adult neurogenesis in specific brain areas.

q-bio.NC↗