Neural Network Modelling with Input Uncertainty: Theory and Application

It is generally assumed when using Bayesian inference methods for neural networks that the input data contains no noise. For real-world (errors in variable) problems this is clearly an unsafe assumption. This paper presents a Bayesian neural network framework which accounts for input noise provided that a model of the noise process exists. In the limit where the noise process is small and symmetric it is shown, using the Laplace approximation, that this method adds an extra term to the usual Bayesian error bar which depends on the variance of the input noise process. Further, by treating the true (noiseless) input as a hidden variable, and sampling this jointly with the network’s weights, using a Markov chain Monte Carlo method, it is demonstrated that it is possible to infer the regression over the noiseless input. This leads to the possibility of training an accurate model of a system using less accurate, or more uncertain, data. This is demonstrated on both the, synthetic, noisy sine wave problem and a real problem of inferring the forward model for a satellite radar backscatter system used to predict sea surface wind vectors.

Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the “phase” giving the state of the first queue and the “level” giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts’s R-matrix and show that the decay rate of the stationary distribution of the “level” process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.

A beam-forming network for a circular switched-beam phased array antenna

This paper reports on the design and development of a dividing/phasing network for a compact switched-beam array antenna for Land-vehicle mobile satellite communications, The device is formed by a switched radial divider/combiner and 1-bit phase shifters and generates a sufficient number of beams for the proper satellite tracking.

A new diffusion and flow theory for activated carbon from low pressure to capillary condensation range

In this paper, we develop a theory for diffusion and flow of pure sub-critical adsorbates in microporous activated carbon over a wide range of pressure, ranging from very low to high pressure, where capillary condensation is occurring. This theory does not require any fitting parameter. The only information needed for the prediction is the complete pore size distribution of activated carbon. The various interesting behaviors of permeability versus loading are observed such as the maximum permeability at high loading (occurred at about 0.8-0.9 relative pressure). The theory is tested with diffusion and flow of benzene through a commercial activated carbon, and the agreement is found to be very good in the light that there is no fitting parameter in the model. (C) 2001 Elsevier Science B.V. All rights reserved.

Use of liquid phase adsorption for characterizing pore network connectivity in activated carbon

A simple percolation theory-based method for determination of the pore network connectivity using liquid phase adsorption isotherm data combined with a density functional theory (DFT)-based pore size distribution is presented in this article. The liquid phase adsorption experiments have been performed using eight different esters as adsorbates and microporous-mesoporous activated carbons Filtrasorb-400, Norit ROW 0.8 and Norit ROX 0.8 as adsorbents. The density functional theory (DFT)-based pore size distributions of the carbons were obtained using DFT analysis of argon adsorption data. The mean micropore network coordination numbers, Z, of the carbons were determined based on DR characteristic plots and fitted saturation capacities using percolation theory. Based on this method, the critical molecular sizes of the model compounds used in this study were also obtained. The incorporation of percolation concepts in the prediction of multicomponent adsorption equilibria is also investigated, and found to improve the performance of the ideal adsorbed solution theory (IAST) model for the large molecules utilized in this study. (C) 2002 Elsevier Science B.V. All rights reserved.

Kinetics of adsorption on activated carbon: application of heterogeneous vacancy solution theory

The kinetics of single component adsorption on activated carbon is investigated here using a heterogeneous vacancy solution theory (VST) of adsorption. The adsorption isotherm is developed to account for the adsorbate non-ideality due to the size difference between the adsorbate molecule and the vacant site, while incorporating adsorbent heterogeneity through a pore-width-related potential energy. The transport process in the bidisperse carbon considers coupled mass transfer in both macropore and micropore phases simultaneously. Adsorbate diffusion in the micropore network is modeled through effective medium theory, thus considering pore network connectivity in the adsorbent, with the activation energy for adsorbate diffusion related to the adsorption energy, represented by the Steele 10-4-3 potential for carbons. Experimental data of five hydrocarbons, CO2 and SO2 on Ajax carbon at multiple temperatures, as well as three hydrocarbons on Norit carbon at three temperatures are first fitted by the heterogeneous VST model to obtain the isotherm parameters, followed by application of the kinetic model to uptake data on carbon particles of different sizes and geometry at various temperatures. For the hydrocarbons studied, the model can successfully correlate the experimental data for both adsorption equilibrium and kinetics. However, there is some deviation in the fit of the desorption kinetics for polar compounds such as CO2 and SO2, due to the inadequacy of the L-J potential model in this case. The significance of viscous transport in the micropores is also considered here and found to be negligible, consistent with recent molecular simulation studies. (C) 2002 Elsevier Science Ltd. All rights reserved.

Effect of pore-network connectivity on multicomponent adsorption of large molecules

The effect of pore-network connectivity on binary liquid-phase adsorption equilibria using the ideal adsorbed solution theory (LAST) was studied. The liquid-phase binary adsorption experiments used ethyl propionate, ethyl butyrate, and ethyl isovalerate as the adsorbates and commercial activated carbons Filtrasorb-400 and Norit ROW 0.8 as adsorbents. As the single-component isotherm, a modified Dubinin-Radushkevich equation was used. A comparison with experimental data shows that incorporating the connectivity of the pore network and considering percolation processes associated with different molecular sizes of the adsorptives in the mixture, as well as their different corresponding accessibility, can improve the prediction of binary adsorption equilibria using the LAST Selectivity of adsorption for the larger molecule in binary systems increases with an increase in the pore-network coordination number, as well with an increase in the mean pore width and in the spread of the pore-size distribution.

Re-entrant phase behaviour of network fluids: A patchy particle model with temperature-dependent valence

We study a model consisting of particles with dissimilar bonding sites ("patches"), which exhibits self-assembly into chains connected by Y-junctions, and investigate its phase behaviour by both simulations and theory. We show that, as the energy cost epsilon(j) of forming Y-junctions increases, the extent of the liquid-vapour coexistence region at lower temperatures and densities is reduced. The phase diagram thus acquires a characteristic "pinched" shape in which the liquid branch density decreases as the temperature is lowered. To our knowledge, this is the first model in which the predicted topological phase transition between a fluid composed of short chains and a fluid rich in Y-junctions is actually observed. Above a certain threshold for epsilon(j), condensation ceases to exist because the entropy gain of forming Y-junctions can no longer offset their energy cost. We also show that the properties of these phase diagrams can be understood in terms of a temperature-dependent effective valence of the patchy particles. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3605703]

Reentrant Phase Diagram of Network Fluids

We introduce a microscopic model for particles with dissimilar patches which displays an unconventional "pinched'' phase diagram, similar to the one predicted by Tlusty and Safran in the context of dipolar fluids [Science 290, 1328 (2000)]. The model-based on two types of patch interactions, which account, respectively, for chaining and branching of the self-assembled networks-is studied both numerically via Monte Carlo simulations and theoretically via first-order perturbation theory. The dense phase is rich in junctions, while the less-dense phase is rich in chain ends. The model provides a reference system for a deep understanding of the competition between condensation and self-assembly into equilibrium-polymer chains.

Transmission cost allocation using cooperative game theory: a comparative study

In this paper is presented a Game Theory based methodology to allocate transmission costs, considering cooperation and competition between producers. As original contribution, it finds the degree of participation on the additional costs according to the demand behavior. A comparative study was carried out between the obtained results using Nucleolus balance and Shapley Value, with other techniques such as Averages Allocation method and the Generalized Generation Distribution Factors method (GGDF). As example, a six nodes network was used for the simulations. The results demonstrate the ability to find adequate solutions on open access environment to the networks.

Neural-network approach to modeling liquid crystals in complex confinement

Finding the structure of a confined liquid crystal is a difficult task since both the density and order parameter profiles are nonuniform. Starting from a microscopic model and density-functional theory, one has to either (i) solve a nonlinear, integral Euler-Lagrange equation, or (ii) perform a direct multidimensional free energy minimization. The traditional implementations of both approaches are computationally expensive and plagued with convergence problems. Here, as an alternative, we introduce an unsupervised variant of the multilayer perceptron (MLP) artificial neural network for minimizing the free energy of a fluid of hard nonspherical particles confined between planar substrates of variable penetrability. We then test our algorithm by comparing its results for the structure (density-orientation profiles) and equilibrium free energy with those obtained by standard iterative solution of the Euler-Lagrange equations and with Monte Carlo simulation results. Very good agreement is found and the MLP method proves competitively fast, flexible, and refinable. Furthermore, it can be readily generalized to the richer experimental patterned-substrate geometries that are now experimentally realizable but very problematic to conventional theoretical treatments.

An implicit GTS allocation mechanism in IEEE 802.15.4 for time-sensitive wireless sensor networks: theory and practice

Timeliness guarantee is an important feature of the recently standardized IEEE 802.15.4 protocol, turning it quite appealing for Wireless Sensor Network (WSN) applications under timing constraints. When operating in beacon-enabled mode, this protocol allows nodes with real-time requirements to allocate Guaranteed Time Slots (GTS) in the contention-free period. The protocol natively supports explicit GTS allocation, i.e. a node allocates a number of time slots in each superframe for exclusive use. The limitation of this explicit GTS allocation is that GTS resources may quickly disappear, since a maximum of seven GTSs can be allocated in each superframe, preventing other nodes to benefit from guaranteed service. Moreover, the GTS may be underutilized, resulting in wasted bandwidth. To overcome these limitations, this paper proposes i-GAME, an implicit GTS Allocation Mechanism in beacon-enabled IEEE 802.15.4 networks. The allocation is based on implicit GTS allocation requests, taking into account the traffic specifications and the delay requirements of the flows. The i-GAME approach enables the use of one GTS by multiple nodes, still guaranteeing that all their (delay, bandwidth) requirements are satisfied. For that purpose, we propose an admission control algorithm that enables to decide whether to accept a new GTS allocation request or not, based not only on the remaining time slots, but also on the traffic specifications of the flows, their delay requirements and the available bandwidth resources. We show that our approach improves the bandwidth utilization as compared to the native explicit allocation mechanism defined in the IEEE 802.15.4 standard. We also present some practical considerations for the implementation of i-GAME, ensuring backward compatibility with the IEEE 801.5.4 standard with only minor add-ons. Finally, an experimental evaluation on a real system that validates our theoretical analysis and demonstrates the implementation of i-GAME is also presented

Towards a unified theory of health-disease: II. Holopathogenesis

This article presents a systematic framework for modeling several classes of illness-sickness-disease named as Holopathogenesis. Holopathogenesis is defined as processes of over-determination of diseases and related conditions taken as a whole, comprising selected facets of the complex object Health. First, a conceptual background of Holopathogenesis is presented as a series of significant interfaces (biomolecular-immunological, physiopathological-clinical, epidemiological-ecosocial). Second, propositions derived from Holopathogenesis are introduced in order to allow drawing the disease-illness-sickness complex as a hierarchical network of networks. Third, a formalization of intra- and inter-level correspondences, over-determination processes, effects and links of Holopathogenesis models is proposed. Finally, the Holopathogenesis frame is evaluated as a comprehensive theoretical pathology taken as a preliminary step towards a unified theory of health-disease.