1,721,138 research outputs found
Epileptic seizures can be anticipated by geometric-topological entropy analysis
Full text linkEpilepsy is a complex brain disorder characterized by an hypersynchronous activity of neural ensemble in the brain. Nowadays electroencephalography (EEG) is the golden stan- dard for studying, monitoring and diagnosing epilepsy. Signals (time series), recorded by EEG, represent a description of the dynamics of the brain. Epilepsy is an emergent behavior given by a phase transition between a non-epileptic state (pre-ictal state) and an epileptic one (ictal state) of the neural hypergraph [1-2]. Traditional linear techniques applied to EEG show some limitation to identify these transitions while the non-linear ones seem to be more promising. The understanding of the underlying mechanisms of ictogenesis and propagation requires a suitable formal method to compute the model that supports the anticipation of ictal states. Recently, Topological Data Analysis and topological entropy [3-4], the so-called persistent entropy, are proven to be encouraging for distinguishing healthy from unhealthy patients by showing numerical evidence of the occurrence of phase transitions. We extend the previous work by providing a theoretical justification, based on statistical indexes (skewness and kurtosis), persistent entropy and topological invariants (Betti numbers), of the preliminary numerical results which describe the occurrence of a phase transition; moreover, we also intend to investigate the role of geometric entropy in quantifying the complexity of the networks since a change of complexity is also an indicator of a phase transition [5].
References
1. Varela F.J.; Naturalizing Phenomenology: Issues in Contemporary Phenomenology and Cognitive Science Edited by Jean, Petitot, Francisco J. Varela, Bernard Pachoud abd Jean-Michel Roy Stanford University Press, Stanford Chapter 9, pp.266-329
2. Piangerelli M.; Merelli E.; RNN-based Model for Self-adaptive Systems - The Emer- gence of Epilepsy in the Human Brain. IJCCI (NCTA).2014: 356-361
3. Merelli E.; Piangerelli M.; Rucco M.; Toller D.; A topological approach for multivariate time series characterization: the epileptic brain.2015
4. Rucco M.; Castiglione F.; Merelli E.; Pettini M.; Characterization of idiotypic immune network through Persistent Entropy. In Proc. Complex2015
5. Franzosi R.; Felice D.; Mancini M.; Pettini M.; A geometric entropy detecting the Erdös-Rényi phase transition. EPL.201
Theorem on the Origin of Phase Transitions
Full text linkFor physical systems described by smooth, finite-range, and confining microscopic interaction potentials [Formula presented] with continuously varying coordinates, we announce and outline the proof of a theorem that establishes that, unless the equipotential hypersurfaces of configuration space [Formula presented], [Formula presented], change topology at some [Formula presented] in a given interval [Formula presented] of values [Formula presented] of [Formula presented], the Helmoltz free energy must be at least twice differentiable in the corresponding interval of inverse temperature [Formula presented] also in the [Formula presented] limit. Thus, the occurrence of a phase transition at some [Formula presented] is necessarily the consequence of the loss of diffeomorphicity among the [Formula presented] and the [Formula presented], which is the consequence of the existence of critical points of [Formula presented] on [Formula presented], that is, points where [Formula presented]. © 2004 The American Physical Society
Source- vs topographic-forcing in pyroclastic currents. the case of the Orvieto-Bagnoregio Ignimbrite, Vulsini, central Italy
Full text linkThe main pyroclastic flow unit of the Orvieto-Bagnoregio Ignimbrite (Vulsini, central Italy) provides a striking example of increasing thickness with distance from the vent, accompanied by opposite size-distance trends for lithic and juvenile clasts. Lithic clasts show normal lateral grading, while dense (1120-1400 kg/m3) scoria clasts show inverse lateral grading. The latter trends are attributed to the opposite density contrast with respect to the flow medium of gas and fine particles and put a constraint to the minimum density of the transporting flow. Thus, the study example approaches the high concentration, non-turbulent end-member of pyroclastic currents. By applying the topological aspect ratio approach, we infer a forced behavior of the parent flow in proximal to intermediate settings, due to sustained feeding with high mass discharge rate at source. In distal settings, the source-forced regime was enhanced by topographic forcing due to channeling along radial topographic lows, thus resulting in increasing bulk density and runout of the current. By analogy with the mobility of dry debris flows, the sliding component of transport prevailed from proximal to intermediate settings, accounting for the prevailing tendency of the pyroclastic current to transport than to deposit, thus forming a relatively thin deposit with normal lateral grading of lithics. The spreading component dominated toward the distal settings, resulting in increasing pyroclast accumulation (up to tens of meters of thickness) and delayed deposition of coarsest scoria clasts as far as the final runout
Process-based modelling towards the simulation of long-distance electrodynamic interactions of biomolecules
No full textOur work is focussed on the computational study of the molecular interactions in biological systems. We hypothesise the use of process algebras to highlight the relation between the complexity of the functions carried out by a biological entity and the type of interactions tying the elementary units that compose its structure. This approach is intended to define predictive models able to generate new knowledge, on the system itself, complementary to the one obtained via empirical methods.
We investigated the way in which the interactions between nucleotides determine the three-dimensional conformation of RNAs and hence their functions. With the aid of formal models based on process algebras, we compared the folding process of proteins with the one performed by RNAs. We formally proved the existence of an abstraction level in which these two kinds of processes show a congruence in their behaviour. Such result allows us to identify and model the distinguishing features of the studied biological processes only on the basis of the known properties of the interactions that bind the nucleotides (in RNAs) and the amino acids (in proteins). This was possible thanks to the expressiveness of a specific process algebra, the Milner’s CCS (Calculus of Communicating Systems)1.
We are also working on an application of the proposed modelling approach to the studies carried out at the CPT (Centre de Physique Théorique, Aix-Marseille University), on the long-distance electrodynamic interactions of biomolecules2. The main idea is to develop a simulator able to solve the problem of the possible interpenetrations of the represented molecules. It would be also intended to yield information on the temporal evolution of the molecular interactions.
Applications of our approach in modelling the processes involved in the gene expression would allow the identification of mutations in human gene pathologies; on the other hand, simulations of protein interactions would be the basis of in-silico studies of the formation of protein aggregates, like amyloid plaques in neurodegenerative diseases.
References:
1) Milner, R. Communication and Concurrency; Upper Saddle River, 1989, NJ, USA: Prentice-Hall, Inc.
2) Gori, M. et al. Investigation of Brownian diffusion and long-distance electrodynamic interactions of biomolecules. Noise and Fluctuations (ICNF), 2015, International Conference on. IEEE, pp. 1 – 4
Topological origin of phase transitions in the absence of critical points of the energy landscape
No full textDifferent arguments led us to surmise that the deep origin of phase transitions has to be identified with suitable topological changes of potential-related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of equipotential energy submanifolds of configuration space. However, it has been recently shown that the 2D lattice -model provides a counterexample that falsifies the mentioned theorems. On the basis of a numerical investigation, the present work indicates the way to overcome this difficulty: in spite of the absence of critical points of the potential in correspondence of the transition energy, also the phase transition of this model stems from a change of topology of both the energy and potential level sets. But in this case the topology changes are asymptotic (). This fact is not obvious since the symmetry-breaking transition could be given measure-based explanations in presence of trivial topology
EXPERIMENTAL-EVIDENCE OF SUPPRESSION OF CHAOS BY RESONANT PARAMETRIC PERTURBATIONS
No full textExperimental results are reported concerning the possibility of reducing and even suppressing chaoticity in a bistable magnetoelastic beam system by means of parametric periodic perturbations. The experimental parameters are chosen such that a strange attractor is observed. Then a parametric perturbation is added. When its frequency approaches some resonant value, laminar phases are observed of increasing duration up to complete regularization of the motion at exact resonance
Lyapunov exponents from geodesic spread in configuration space
Full text linkThe exact form of the Jacobi–Levi-Civita (JLC) equation for geodesic spread is here explicitly worked out at arbitrary dimension for the configuration space manifold [Formula Presented] of a standard Hamiltonian system, equipped with the Jacobi (or kinetic energy) metric [Formula Presented] As the Hamiltonian flow corresponds to a geodesic flow on [Formula Presented] the JLC equation can be used to study the degree of instability of the Hamiltonian flow. It is found that the solutions of the JLC equation are closely resembling the solutions of the standard tangent dynamics equation which is used to compute Lyapunov exponents. Therefore the instability exponents obtained through the JLC equation are in perfect quantitative agreement with usual Lyapunov exponents. This work completes a previous investigation that was limited only to two degrees of freedom systems. © 1997 The American Physical Society
Further results on the equipartition threshold in large nonlinear Hamiltonian system
No full textNumerical simulations show the existence of an ergodicity threshold in the Fermi-Pasta-Ulam α model. This feature is common to a large class of nonlinear Hamiltonian systems
Energy transfer to the phonons of a macromolecule through light pumping
Full text linkIn the present paper we address the problem of the energy downconversion of the light absorbed by a protein into its internal vibrational modes. We consider the case in which the light receptors are fluorophores either naturally co-expressed with the protein or artificially covalently bound to some of its amino acids. In a recent work [Phys. Rev. X 8, 031061 (2018)], it has been experimentally found that by shining a laser light on the fluorophores attached to a protein the energy fed to it can be channeled into the normal mode of lowest frequency of vibration thus making the subunits of the protein coherently oscillate. Even if the phonon condensation phenomenon has been theoretically explained, the first step - the energy transfer from electronic excitation into phonon excitation - has been left open. The present work is aimed at filling this gap
Riemannian geometry of Hamiltonian chaos: Hints for a general theory RID A-2864-2010
No full textWe aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam β model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity. © 2008 The American Physical Society
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