152 research outputs found
First-passage phenomena in hierarchical networks
In this paper we study Markov processes and related first passage problems on
a class of weighted, modular graphs which generalize the Dyson hierarchical
model. In these networks, the coupling strength between two nodes depends on
their distance and is modulated by a parameter . We find that, in the
thermodynamic limit, ergodicity is lost and the "distant" nodes can not be
reached. Moreover, for finite-sized systems, there exists a threshold value for
such that, when is relatively large, the inhomogeneity of the
coupling pattern prevails and "distant" nodes are hardly reached. The same
analysis is carried on also for generic hierarchical graphs, where interactions
are meant to involve -plets () of nodes, finding that ergodicity is
still broken in the thermodynamic limit, but no threshold value for is
evidenced, ultimately due to a slow growth of the network diameter with the
size
Phase transition for the Maki-Thompson rumour model on a small-world network
We consider the Maki-Thompson model for the stochastic propagation of a
rumour within a population. We extend the original hypothesis of homogenously
mixed population by allowing for a small-world network embedding the model.
This structure is realized starting from a -regular ring and by inserting,
in the average, additional links in such a way that and are
tuneable parameter for the population architecture. We prove that this system
exhibits a transition between regimes of localization (where the final number
of stiflers is at most logarithmic in the population size) and propagation
(where the final number of stiflers grows algebraically with the population
size) at a finite value of the network parameter . A quantitative estimate
for the critical value of is obtained via extensive numerical simulations.Comment: 24 pages, 4 figure
A walk in the statistical mechanical formulation of neural networks
Neural networks are nowadays both powerful operational tools (e.g., for
pattern recognition, data mining, error correction codes) and complex
theoretical models on the focus of scientific investigation. As for the
research branch, neural networks are handled and studied by psychologists,
neurobiologists, engineers, mathematicians and theoretical physicists. In
particular, in theoretical physics, the key instrument for the quantitative
analysis of neural networks is statistical mechanics. From this perspective,
here, we first review attractor networks: starting from ferromagnets and
spin-glass models, we discuss the underlying philosophy and we recover the
strand paved by Hopfield, Amit-Gutfreund-Sompolinky. One step forward, we
highlight the structural equivalence between Hopfield networks (modeling
retrieval) and Boltzmann machines (modeling learning), hence realizing a deep
bridge linking two inseparable aspects of biological and robotic spontaneous
cognition. As a sideline, in this walk we derive two alternative (with respect
to the original Hebb proposal) ways to recover the Hebbian paradigm, stemming
from ferromagnets and from spin-glasses, respectively. Further, as these notes
are thought of for an Engineering audience, we highlight also the mappings
between ferromagnets and operational amplifiers and between antiferromagnets
and flip-flops (as neural networks -built by op-amp and flip-flops- are
particular spin-glasses and the latter are indeed combinations of ferromagnets
and antiferromagnets), hoping that such a bridge plays as a concrete
prescription to capture the beauty of robotics from the statistical mechanical
perspective.Comment: Contribute to the proceeding of the conference: NCTA 2014. Contains
12 pages,7 figure
Topological properties of hierarchical networks
Hierarchical networks are attracting a renewal interest for modelling the
organization of a number of biological systems and for tackling the complexity
of statistical mechanical models beyond mean-field limitations. Here we
consider the Dyson hierarchical construction for ferromagnets, neural networks
and spin-glasses, recently analyzed from a statistical-mechanics perspective,
and we focus on the topological properties of the underlying structures. In
particular, we find that such structures are weighted graphs that exhibit high
degree of clustering and of modularity, with small spectral gap; the robustness
of such features with respect to link removal is also studied. These outcomes
are then discussed and related to the statistical mechanics scenario in full
consistency. Lastly, we look at these weighted graphs as Markov chains and we
show that in the limit of infinite size, the emergence of ergodicity breakdown
for the stochastic process mirrors the emergence of meta-stabilities in the
corresponding statistical mechanical analysis
Meta-stable states in the hierarchical Dyson model drive parallel processing in the hierarchical Hopfield network
In this paper we introduce and investigate the statistical mechanics of
hierarchical neural networks: First, we approach these systems \`a la Mattis,
by thinking at the Dyson model as a single-pattern hierarchical neural network
and we discuss the stability of different retrievable states as predicted by
the related self-consistencies obtained from a mean-field bound and from a
bound that bypasses the mean-field limitation. The latter is worked out by
properly reabsorbing fluctuations of the magnetization related to higher levels
of the hierarchy into effective fields for the lower levels. Remarkably, mixing
Amit's ansatz technique (to select candidate retrievable states) with the
interpolation procedure (to solve for the free energy of these states) we prove
that (due to gauge symmetry) the Dyson model accomplishes both serial and
parallel processing. One step forward, we extend this scenario toward multiple
stored patterns by implementing the Hebb prescription for learning within the
couplings. This results in an Hopfield-like networks constrained on a
hierarchical topology, for which, restricting to the low storage regime (where
the number of patterns grows at most logarithmical with the amount of neurons),
we prove the existence of the thermodynamic limit for the free energy and we
give an explicit expression of its mean field bound and of the related improved
boun
Hierarchical neural networks perform both serial and parallel processing
In this work we study a Hebbian neural network, where neurons are arranged
according to a hierarchical architecture such that their couplings scale with
their reciprocal distance. As a full statistical mechanics solution is not yet
available, after a streamlined introduction to the state of the art via that
route, the problem is consistently approached through signal- to-noise
technique and extensive numerical simulations. Focusing on the low-storage
regime, where the amount of stored patterns grows at most logarithmical with
the system size, we prove that these non-mean-field Hopfield-like networks
display a richer phase diagram than their classical counterparts. In
particular, these networks are able to perform serial processing (i.e. retrieve
one pattern at a time through a complete rearrangement of the whole ensemble of
neurons) as well as parallel processing (i.e. retrieve several patterns
simultaneously, delegating the management of diff erent patterns to diverse
communities that build network). The tune between the two regimes is given by
the rate of the coupling decay and by the level of noise affecting the system.
The price to pay for those remarkable capabilities lies in a network's capacity
smaller than the mean field counterpart, thus yielding a new budget principle:
the wider the multitasking capabilities, the lower the network load and
viceversa. This may have important implications in our understanding of
biological complexity
From Dyson to Hopfield: Processing on hierarchical networks
We consider statistical-mechanical models for spin systems built on
hierarchical structures, which provide a simple example of non-mean-field
framework. We show that the coupling decay with spin distance can give rise to
peculiar features and phase diagrams much richer that their mean-field
counterpart. In particular, we consider the Dyson model, mimicking
ferromagnetism in lattices, and we prove the existence of a number of
meta-stabilities, beyond the ordered state, which get stable in the
thermodynamic limit. Such a feature is retained when the hierarchical structure
is coupled with the Hebb rule for learning, hence mimicking the modular
architecture of neurons, and gives rise to an associative network able to
perform both as a serial processor as well as a parallel processor, depending
crucially on the external stimuli and on the rate of interaction decay with
distance; however, those emergent multitasking features reduce the network
capacity with respect to the mean-field counterpart. The analysis is
accomplished through statistical mechanics, graph theory, signal-to-noise
technique and numerical simulations in full consistency. Our results shed light
on the biological complexity shown by real networks, and suggest future
directions for understanding more realistic models
Theatricality in Installation Artworks: An Overview
The article is an investigation into theatricality from various standpoints (among others those of Michael Fried, Claire Bishop, Juliane Rebentisch and Samuel Weber) in order to focus on different views on theatricality considered as partially emancipated from theatre and to verify if and to what extent each of them can apply to installation artworks as environments and intermedial devices. Ultimately the article propounds the idea of a paradoxical anti-theatrical theatricality of installation art, grasped in its very connection to site-specificity, critically engaging Martin Heideggerâs insights regarding the «Gestell» and the «work-being» of the work of art, as a general theoretical basis through which a particular focus of âspecificityâ of installation is endorsed
Lâesperienza estetica come esperienza di immagini. Walter Benjamin e Theodor W. Adorno
Both Walter Benjamin and Theodor W. Adorno consider âaesthetical experienceâ as an âimage experienceâ assuming a power of images âto set free forcesâ directed to produce or support aesthetical-political (Benjamin) or aesthetical-critical (Adorno) requirements. Profane illumination, âthinkimagesâ, phantasmagory, dialectical images, decayed âauraâ and technicalized images in Benjaminâs theory of aesthetical modernity. Expressive feature or âmimeticâ eloquence in nature and art countering reality, dismantled âauraâ in contemporary desacralized work of art, but also persisting âauraâ in its meaningful dimension in Adornoâs aesthetical theory
Adorno, Bloch e il campo d'azione dell'utopia. Un dialogo radiofonico.
Il saggio intende mettere a fuoco le rispettive proposte di Bloch e Adorno relative a un rinnovato pensiero dellâutopia, rinvenendo in entrambe una, sia pur differente, struttura âagonaleâ. Una breve citazione tratta da unâopera di Brecht, «manca qualcosa» (Mahagonny), Ăš il punto di avvio della discussione radiofonica avvenuta nel 1964 tra Bloch e Adorno sulle contraddizioni e gli anacronismi dellâutopico. Secondo Bloch la frase rivela la presenza dellâutopia nel processo dellâessere, il che rende la speranza una strategia di lotta. Bloch fonda il suo argomento sulla base della tesi della âprossimitĂ â dellâutopia e attraverso una fenomenologia della coscienza utopica che si confronta con vari processi della realtĂ e con simboli e âtopoiâ utopici incontrati lungo il cammino. Contro lâemergere di tali immagini del desiderio Adorno suggerisce che Ăš possibile parlare di utopia solo negativamente e che il âcampo dâazioneâ dellâutopia consiste piuttosto nel mutamento di tutte le categorie â e non solo di quelle sociali ÂŹâ attraverso il procedimento della negazione determinata. Sostengo infine che entrambi i filosofi non traspongono lâutopia in un tempo futuro per il fatto che essa assume un valore agonale e operativo, che vede lâutopico agire criticamente come una trascendenza âimmanenteâ dellâesperienza concreta.The essay aims at focusing on both Blochâs and Adornoâs proposals for a renewed utopian thinking, claiming their differently âagonisticâ structure. Brechtâs short sentence «Somethingâs missing» (Mahagonny) gives way to a discussion between Ernst Bloch and Theodor W. Adorno broadcasted by radio in 1964 on the contradictions and anachronism of âthe utopianâ. The sentence reveals according to Bloch the very presence of utopia in the process of being, which makes hope a struggling strategy. Bloch substantiates his argument with the thesis of the âproximityâ of utopia and with the use of a phenomenology of utopian consciousness engaged with various processes of reality and with symbols and utopic âtopoiâ encontered along the way. Against the emergence of such wish-images, Adorno suggests that we can talk about utopia only in a negative way and that the âoperational theatreâ of utopia is rather a changing of all categories â not only in the social field â through determined negation. I argue that for both philosophers utopia is not transposed into the future because of its agonistc and operational value: it performs critically as âimmanentâ transcendence of concrete experience
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