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Dirichlet process mixture models for non-stationary data streams
Get PDFIn recent years, we have seen a handful of work on inference algorithms over non-stationary data streams. Given their flexibility, Bayesian non-parametric models are a good candidate for these scenarios. However, reliable streaming inference under the concept drift phenomenon is still an open problem for these models. In this work, we propose a variational inference algorithm for Dirichlet process mixture models. Our proposal deals with the concept drift by including an exponential forgetting over the prior global parameters. Our algorithm allows adapting the learned model to the concept drifts automatically. We perform experiments in both synthetic and real data, showing that the proposed model outperforms state-of-the-art variational methods in density estimation, clustering and parameter tracking
Molecular Insight into the Self-Assembly Process of Cellulose Iβ Microfibril
Get PDFThe self-assembly process of β-D-glucose oligomers on the surface of cellulose Iβ microfibril involves crystallization, and this process is analyzed herein, in terms of the length and flexibility of the oligomer chain, by means of molecular dynamics (MD) simulations. The characterization of this process involves the structural relaxation of the oligomer, the recognition of the cellulose I microfibril, and the formation of several hydrogen bonds (HBs). This process is monitored on the basis of the changes in non-bonded energies and the interaction with hydrophilic and hydrophobic crystal faces. The oligomer length is considered a parameter for capturing insight into the energy landscape and its stability in the bound form with the cellulose I microfibril. We notice that the oligomer–microfibril complexes are more stable by increasing the number of hydrogen bond interactions, which is consistent with a gain in electrostatic energy. Our studies highlight the interaction with hydrophilic crystal planes on the microfibril and the acceptor role of the flexible oligomers in HB formation. In addition, we study by MD simulation the interaction between a protofibril and the cellulose I microfibril in solution. In this case, the main interaction consists of the formation of hydrogen bonds between hydrophilic faces, and those HBs involve donor groups in the protofibril
Effects of noise on leaky integrate-and-fire neuron models for neuromorphic computing applications
Get PDFArtificial neural networks (ANNs) have been extensively used
for the description of problems arising from biological systems and for
constructing neuromorphic computing models. The third generation of
ANNs, namely, spiking neural networks (SNNs), inspired by biological
neurons enable a more realistic mimicry of the human brain. A large
class of the problems from these domains is characterized by the necessity to deal with the combination of neurons, spikes and synapses via
integrate-and-fire neuron models. Motivated by important applications
of the integrate-and-fire of neurons in neuromorphic computing for biomedical studies, the main focus of the present work is on the analysis of
the effects of additive and multiplicative types of random input currents
together with a random refractory period on a leaky integrate-and-fire
(LIF) synaptic conductance neuron model. Our analysis is carried out
via Langevin stochastic dynamics in a numerical setting describing a
cell membrane potential. We provide the details of the model, as well
as representative numerical examples, and discuss the effects of noise
on the time evolution of the membrane potential as well as the spiking
activities of neurons in the LIF synaptic conductance model scrutinized
here. Furthermore, our numerical results demonstrate that the presence
of a random refractory period in the LIF synaptic conductance system
may substantially influence an increased irregularity of spike trains of
the output neuron
Topological equisingularity: oldproblems froma new perspective (With an appendix by G. -M. Greuel and G. Pfister on Singular)
No full textAn Optimizing Method for Performance and Resource Utilization in Quantum Machine Learning Circuits
Get PDFQuantum computing is a new and advanced topic that refers to calculations based on the principles of quantum mechanics. Itmakes certain kinds of problems be solved easier compared to classical computers. This advantage of quantum computingcan be used to implement many existing problems in different fields incredibly effectively. One important field that quantumcomputing has shown great results in machine learning. Until now, many different quantum algorithms have been presented toperform different machine learning approaches. In some special cases, the execution time of these quantum algorithms will bereduced exponentially compared to the classical ones. But at the same time, with increasing data volume and computationtime, taking care of systems to prevent unwanted interactions with the environment can be a daunting task and since thesealgorithms work on machine learning problems, which usually includes big data, their implementation is very costly in terms ofquantum resources. Here, in this paper, we have proposed an approach to reduce the cost of quantum circuits and to optimizequantum machine learning circuits in particular. To reduce the number of resources used, in this paper an approach includingdifferent optimization algorithms is considered. Our approach is used to optimize quantum machine learning algorithms forbig data. In this case, the optimized circuits run quantum machine learning algorithms in less time than the original onesand by preserving the original functionality. Our approach improves the number of quantum gates by 10.7% and 14.9% indifferent circuits and the number of time steps is reduced by three and 15 units, respectively. This is the amount of reduction forone iteration of a given sub-circuit U in the main circuit. For cases where this sub-circuit is repeated more times in the maincircuit, the optimization rate is increased. Therefore, by applying the proposed method to circuits with big data, both cost andperformance are improved
Deep learning enhanced principal component analysis for structural health monitoring
Get PDFThis paper proposes a Deep Learning Enhanced Principal Component Analysis (PCA) approach for outlier detection to assess the structural condition of bridges. We employ partially explainable autoencoder architecture to replicate and enhance the data compression and reconstruction ability of PCA. The particularity of the method lies in the addition of residual connections to account for nonlinearities. We apply the proposed method to monitoring data obtained from two bridges under real operation conditions and compare the results before and after adding the residual connections. Results show that the addition of residual connections enhances the outlier detection ability of the network, allowing to detect lighter damages
Classification of bursting patterns: A tale of two ducks
Get PDFBursting is one of the fundamental rhythms that excitable cells can generate either in response to incoming stimuli or intrinsically. It has been a topic of intense research in computational biology for several decades. The classification of bursting oscillations in excitable systems has been the subject of active research since the early 1980s and is still ongoing. As a by-product it establishes analytical and numerical foundations for studying complex temporal behaviors in multiple-timescale models of cellular activity. In this review, we first present the seminal works of Rinzel and Izhikevich in classifying bursting patterns of excitable systems. We recall a complementary mathematical classification approach by Bertram et al., and then by Golubitsky et al., which together with the Rinzel-Izhikevich proposals provide the state-of-the-art foundations to these classifications. Beyond classical approaches, we review a recent bursting example that falls outside the previous classification systems. Generalizing this example leads us to propose an extended classification, which requires the analysis of both fast and slow subsystems of an underlying slow-fast model and allows the dissection of a larger class of bursters. Namely, we provide a general framework for bursting systems with both subthreshold and superthreshold oscillations. A new class of bursters with at least two slow variables is then added, which we denote folded-node bursters, to convey the idea that the bursts are initiated or annihilated via a folded-node singularity. Key to this mechanism are so-called canard or duck orbits, organizing the underpinning excitability structure. We describe the two main families of folded-node bursters, depending upon the phase (active/spiking or silent/non-spiking) of the bursting cycle during which folded-node dynamics occurs. We classify both families and give examples of minimal systems displaying these novel bursting patterns. Finally, we provide a biophysical example by reinterpreting a generic conductance-based episodic burster as a folded-node burster, showing that the associated framework can explain its subthreshold oscillations over a larger parameter region than the fast-subsystem approach
On the Schrödinger map for regular helical polygons in the hyperbolic space
Get PDFThe main purpose of this article is to understand the evolution of X t = X s ∧− X ss , with X(s, 0) a regular polygonal curve with a nonzero torsion in the three-dimensional Minkowski space. Unlike in the case of the Euclidean space, a nonzero torsion now implies two different helical curves. This generalizes recent works by the author with de la Hoz and Vega on helical polygons in the Euclidean space as well as planar polygons in the Minkowski space. Numerical experiments in this article show that the trajectory of the point X(0, t) exhibits new variants of Riemann’s non-differentiable function whose structure depends on the initial torsion in the problem. As a result, we observe that the smooth solutions (helices, straight line) in the Minkowski space show the same instability as displayed by their Euclidean counterparts and curves with zero-torsion. These numerical observations are in agreement with some recent theoretical results obtained by Banica and Vega
The Frisch–Parisi formalism for fluctuations of the Schrödinger equation
Get PDFWe consider the solution of the Schrödinger equation in when the initial datum tends to the Dirac comb. Let be the fluctuations in time of , for , after removing a smooth background. We prove that the Frisch--Parisi formalism holds for , which is morally a simplification of the Riemann's non-differentiable curve . Our motivation is to understand the evolution of the vortex filament equation of polygonal filaments, which are related to .BERC 2022-2025,
FJC2019-039804-I,
RYC2018-025477-I,
Ikerbasque,
PGC2018-094522-B-I0
Modelling Holling type II functional response in deterministic and stochastic food chain models with mass conservation
Get PDFThe Rosenzweig-MacArthur predator-prey model is the building block in modeling food chain, food webs and ecosystems. There are a number of hidden assumptions involved in the derivation. For instance the prey population growth is logistic without predation but also with predation. In order to reveal these we will start with modelling a resource-predator-prey system in a closed spatially homogeneous environment. This allows us to keep track of the nutrient flow. With an instantaneous remineralisation of the products excreted in the environment by the populations and dead body mass there is conservation of mass. This allows for a model dimension reduction and yields the mass balance predator-prey model. When furthermore the searching and handling processes are much faster that the population changing rates, the trophic interaction is described by a Holling type II functional response, also assumed in the Rosenzweig-MacArthur model. The derivation uses an extended deterministic model with number of searching and handling predators as model variables where the ratio of the predator/prey body masses is used as a mechanistic time-scale parameter. This extended model is also used as a starting point for the derivation of a stochastic model. We will investigate the stochastic effects of random switching between searching and handling of the predators and predator dying. Prey growth by consumption of ambient resources is still deterministic and therefore the stochastic model is hybrid. The transient dynamics is studied by numerical Monte Carlo simulations and also the quasi-equilibrium distribution for the population quantities is calculated. The body mass of the prey individual is the scaling parameter in the stochastic model formulation. This allows for a quantification of the mean-field approximation criterion for the justification of replacement of the stochastic by a deterministic model.Marie Skłodowska-Curie grant agreement No. 79249