Constructing random matrices to represent real ecosystems

Models of complex systems with n components typically have order n² parameters because each component can potentially interact with every other. When it is impractical to measure these parameters, one may choose random parameter values and study the emergent statistical properties at the system level. Many influential results in theoretical ecology have been derived from two key assumptions: that species interact with random partners at random intensities and that intraspecific competition is comparable between species. Under these assumptions, community dynamics can be described by a community matrix that is often amenable to mathematical analysis. We combine empirical data with mathematical theory to show that both of these assumptions lead to results that must be interpreted with caution. We examine 21 empirically derived community matrices constructed using three established, independent methods. The empirically derived systems are more stable by orders of magnitude than results from random matrices. This consistent disparity is not explained by existing results on predator-prey interactions. We investigate the key properties of empirical community matrices that distinguish them from random matrices. We show that network topology is less important than the relationship between a species’ trophic position within the food web and its interaction strengths. We identify key features of empirical networks that must be preserved if random matrix models are to capture the features of real ecosystems.

In vitro release of nonoxynol-9 from silicone matrix intravaginal rings

The controlled-release characteristics of matrix silicone intravaginal rings loaded with between 100 and 971 mg of nonoxynol-9 have been investigated with a view to developing a ring that may offer a new female-controlled method for the prevention of transmission of sexually transmitted diseases, particularly HIV. Intravaginal rings containing 253, 487 and 971 mg of nonoxynol-9 provided a daily release of 2 mg or more over the 8-day release period, the minimal amount of nonoxynol-9 considered to provide an effective vaginal concentration for the prevention of HIV. Furthermore, the maximum daily release of N9 was about 6 mg, an amount significantly smaller than that observed for other nonoxynol-9 products whose large daily doses may in fact increase the occurrence of HIV by causing epithelial damage to the vaginal tissue. The release mechanism of the liquid nonoxynol-9 from the intravaginal rings has also been investigated and compared to models describing the release of solid drugs from the rings. It has been demonstrated through release studies and surface microscopy that a drug depletion zone is not established in such liquid-loaded intravaginal ring systems, with implications for the release kinetics. (C) 2003 Elsevier B.V. All rights reserved.

Extracting S-matrix poles for resonances from numerical scattering data: Type-II Pade reconstruction

We present a FORTRAN 77 code for evaluation of resonance pole positions and residues of a numerical scattering matrix element in the complex energy (CE) as well as in the complex angular momentum (CAM) planes. Analytical continuation of the S-matrix element is performed by constructing a type-II Pade approximant from given physical values (Bessis et al. (1994) [421: Vrinceanu et al. (2000) [24]; Sokolovski and Msezane (2004) [23]). The algorithm involves iterative 'preconditioning' of the numerical data by extracting its rapidly oscillating potential phase component. The code has the capability of adding non-analytical noise to the numerical data in order to select 'true' physical poles, investigate their stability and evaluate the accuracy of the reconstruction. It has an option of employing multiple-precision (MPFUN) package (Bailey (1993) [451) developed by D.H. Bailey wherever double precision calculations fail due to a large number of input partial waves (energies) involved. The code has been successfully tested on several models, as well as the F + H-2 -> HE + H, F + HD : HE + D, Cl + HCI CIH + Cl and H + D-2 -> HD + D reactions. Some detailed examples are given in the text.

A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.

A micromechanics approach for damage modeling of polymer matrix composites

A new model for damage evolution in polymer matrix composites is presented. The model is based on a combination of two constituent-level models and an interphase model. This approach reduces the number of empirical parameters since the two constituent- level models are formulated for isotropic materials, namely fiber and matrix. Decomposition of the state variables down to the micro-scale is accomplished by micromechanics. Phenomenological damage evolution models are then postulated for each constituent. Determination of material parameters is made from available experimental data. The required experimental data can be obtained with standard tests. Comparison between model predictions and additional experimental data is presented.

A spatio-temporal 2D-models framework for human pose recovery in monocular sequences

This paper addresses the pose recovery problem of a particular articulated object: the human body. In this model-based approach, the 2D-shape is associated to the corresponding stick figure allowing the joint segmentation and pose recovery of the subject observed in the scene. The main disadvantage of 2D-models is their restriction to the viewpoint. To cope with this limitation, local spatio-temporal 2D-models corresponding to many views of the same sequences are trained, concatenated and sorted in a global framework. Temporal and spatial constraints are then considered to build the probabilistic transition matrix (PTM) that gives a frame to frame estimation of the most probable local models to use during the fitting procedure, thus limiting the feature space. This approach takes advantage of 3D information avoiding the use of a complex 3D human model. The experiments carried out on both indoor and outdoor sequences have demonstrated the ability of this approach to adequately segment pedestrians and estimate their poses independently of the direction of motion during the sequence. (c) 2008 Elsevier Ltd. All rights reserved.

Photon collisions with atoms and ions within an intermediate-energy R-matrix framework

Recent experimental advances in light technology necessitate the availability of sophisticated theoretical models which can incorporate an accurate treatment of double-electron continua. We describe here a new intermediate-energy R-matrix approach to photoionisation and photo-double-ionisation and illustrate its feasibilty by application to photoionisation and photo-double-ionisation of He, and photodetachment and photo-double-detachment of H^-. Results are shown to be in excellent agreement with previous theoretical and experimental studies. This work is a key step in the development of a multipurpose R-matrix code for multiple-electron ejection. © 2012 American Physical Society

Atomic harmonic generation in time-dependent R-matrix theory

We have developed the capability to determine accurate harmonic spectra for multielectron atoms within time-dependent R-matrix (TDRM) theory. Harmonic spectra can be calculated using the expectation value of the dipole length, velocity, or acceleration operator. We assess the calculation of the harmonic spectrum from He irradiated by 390-nm laser light with intensities up to 4 x 10(14) W cm(-2) using each form, including the influence of the multielectron basis used in the TDRM code. The spectra are consistent between the different forms, although the dipole acceleration calculation breaks down at lower harmonics. The results obtained from TDRM theory are compared with results from the HELIUM code, finding good quantitative agreement between the methods. We find that bases which include pseudostates give the best comparison with the HELIUM code, but models comprising only physical orbitals also produce accurate results.

Learning Effective and Interpretable Semantic Models using Non-Negative Sparse Embedding

In this paper, we introduce an application of matrix factorization to produce corpus-derived, distributional
models of semantics that demonstrate cognitive plausibility. We find that word representations
learned by Non-Negative Sparse Embedding (NNSE), a variant of matrix factorization, are sparse,
effective, and highly interpretable. To the best of our knowledge, this is the first approach which
yields semantic representation of words satisfying these three desirable properties. Though extensive
experimental evaluations on multiple real-world tasks and datasets, we demonstrate the superiority
of semantic models learned by NNSE over other state-of-the-art baselines.

An R-matrix approach for plasma modelling and the interpretation of astrophysical observation

Over the last decade an Auburn-Rollins-Strathclyde consortium has developed several suites of parallel R-matrix codes [1, 2, 3] that can meet the fundamental data needs required for the interpretation of astrophysical observation and/or plasma experiments. Traditionally our collisional work on light fusion-related atoms has been focused towards spectroscopy and impurity transport for magnetically confined fusion devices. Our approach has been to provide a comprehensive data set for the excitation/ionization for every ion stage of a particular element. As we progress towards a burning fusion plasma, there is a demand for the collisional processes involving tungsten, which has required a revitalization of the relativistic R-matrix approach. The implementation of these codes on massively parallel supercomputers has facilitated the progression to models involving thousands of levels in the close-coupling expansion required by the open d and f sub-shell systems of mid Z tungsten. This work also complements the electron-impact excitation of Fe-Peak elements required by astrophysics, in particular the near neutral species, which offer similar atomic structure challenges. Although electron-impact excitation work is our primary focus in terms of fusion application, the single photon photoionisation codes are also being developed in tandem, and benefit greatly from this ongoing work.