Robust Controller Design of Networked Control Systems with Nonlinear Uncertainties

We address robust stabilization problem for networked control systems with nonlinear uncertainties and packet losses by modelling such systems as a class of uncertain switched systems. Based on theories on switched Lyapunov functions, we derive the robustly stabilizing conditions for state feedback stabilization and design packet-loss dependent controllers by solving some matrix inequalities. A numerical example and some simulations are worked out to demonstrate the effectiveness of the proposed design method.

Modeling corneal surfaces with rational functions for high-speed videokeratoscopy data compression

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.

Bias in the nonlinear filter generator output sequence

Nonlinear filter generators are common components used in the keystream generators for stream ciphers and more recently for authentication mechanisms. They consist of a Linear Feedback Shift Register (LFSR) and a nonlinear Boolean function to mask the linearity of the LFSR output. Properties of the output of a nonlinear filter are not well studied. Anderson noted that the m-tuple output of a nonlinear filter with consecutive taps to the filter function is unevenly distributed. Current designs use taps which are not consecutive. We examine m-tuple outputs from nonlinear filter generators constructed using various LFSRs and Boolean functions for both consecutive and uneven (full positive difference sets where possible) tap positions. The investigation reveals that in both cases, the m-tuple output is not uniform. However, consecutive tap positions result in a more biased distribution than uneven tap positions, with some m-tuples not occurring at all. These biased distributions indicate a potential flaw that could be exploited for cryptanalysis.

Bias in the nonlinear filter generator output sequence

Nonlinear filter generators are common components used in the keystream generators for stream ciphers and more recently for authentication mechanisms. They consist of a Linear Feedback Shift Register (LFSR) and a nonlinear Boolean function to mask the linearity of the LFSR output. Properties of the output of a nonlinear filter are not well studied. Anderson noted that the m-tuple output of a nonlinear filter with consecutive taps to the filter function is unevenly distributed. Current designs use taps which are not consecutive. We examine m-tuple outputs from nonlinear filter generators constructed using various LFSRs and Boolean functions for both consecutive and uneven (full positive difference sets where possible) tap positions. The investigation reveals that in both cases, the m-tuple output is not uniform. However, consecutive tap positions result in a more biased distribution than uneven tap positions, with some m-tuples not occurring at all. These biased distributions indicate a potential flaw that could be exploited for cryptanalysis

Nonlinear diffusion and exclusion processes with contact interactions

Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.

Nuclear localization of NPR1 is required for activation of PR gene expression

Systemic acquired resistance (SAR) is a broad-spectrum resistance in plants that involves the upregulation of a battery of pathogenesis-related (PR) genes. NPR1 is a key regulator in the signal transduction pathway that leads to SAR. Mutations in NPR1 result in a failure to induce PR genes in systemic tissues and a heightened susceptibility to pathogen infection, whereas overexpression of the NPR1 protein leads to increased induction of the PR genes and enhanced disease resistance. We analyzed the subcellular localization of NPR1 to gain insight into the mechanism by which this protein regulates SAR. An NPR1–green fluorescent protein fusion protein, which functions the same as the endogenous NPR1 protein, was shown to accumulate in the nucleus in response to activators of SAR. To control the nuclear transport of NPR1, we made a fusion of NPR1 with the glucocorticoid receptor hormone binding domain. Using this steroid-inducible system, we clearly demonstrate that nuclear localization of NPR1 is essential for its activity in inducing PR genes.

Quantifying spatial structure in experimental observations and agent-based simulations using pair-correlation functions

We define a pair-correlation function that can be used to characterize spatiotemporal patterning in experimental images and snapshots from discrete simulations. Unlike previous pair-correlation functions, the pair-correlation functions developed here depend on the location and size of objects. The pair-correlation function can be used to indicate complete spatial randomness, aggregation or segregation over a range of length scales, and quantifies spatial structures such as the shape, size and distribution of clusters. Comparing pair-correlation data for various experimental and simulation images illustrates their potential use as a summary statistic for calibrating discrete models of various physical processes.

Analysis of nonlinear sequences and streamciphers

Streamciphers are common cryptographic algorithms used to protect the confidentiality of frame-based communications like mobile phone conversations and Internet traffic. Streamciphers are ideal cryptographic algorithms to encrypt these types of traffic as they have the potential to encrypt them quickly and securely, and have low error propagation. The main objective of this thesis is to determine whether structural features of keystream generators affect the security provided by stream ciphers.These structural features pertain to the state-update and output functions used in keystream generators. Using linear sequences as keystream to encrypt messages is known to be insecure. Modern keystream generators use nonlinear sequences as keystream.The nonlinearity can be introduced through a keystream generator's state-update function, output function, or both. The first contribution of this thesis relates to nonlinear sequences produced by the well-known Trivium stream cipher. Trivium is one of the stream ciphers selected in a final portfolio resulting from a multi-year project in Europe called the ecrypt project. Trivium's structural simplicity makes it a popular cipher to cryptanalyse, but to date, there are no attacks in the public literature which are faster than exhaustive keysearch. Algebraic analyses are performed on the Trivium stream cipher, which uses a nonlinear state-update and linear output function to produce keystream. Two algebraic investigations are performed: an examination of the sliding property in the initialisation process and algebraic analyses of Trivium-like streamciphers using a combination of the algebraic techniques previously applied separately by Berbain et al. and Raddum. For certain iterations of Trivium's state-update function, we examine the sets of slid pairs, looking particularly to form chains of slid pairs. No chains exist for a small number of iterations.This has implications for the period of keystreams produced by Trivium. Secondly, using our combination of the methods of Berbain et al. and Raddum, we analysed Trivium-like ciphers and improved on previous on previous analysis with regards to forming systems of equations on these ciphers. Using these new systems of equations, we were able to successfully recover the initial state of Bivium-A.The attack complexity for Bivium-B and Trivium were, however, worse than exhaustive keysearch. We also show that the selection of stages which are used as input to the output function and the size of registers which are used in the construction of the system of equations affect the success of the attack. The second contribution of this thesis is the examination of state convergence. State convergence is an undesirable characteristic in keystream generators for stream ciphers, as it implies that the effective session key size of the stream cipher is smaller than the designers intended. We identify methods which can be used to detect state convergence. As a case study, theMixer streamcipher, which uses nonlinear state-update and output functions to produce keystream, is analysed. Mixer is found to suffer from state convergence as the state-update function used in its initialisation process is not one-to-one. A discussion of several other streamciphers which are known to suffer from state convergence is given. From our analysis of these stream ciphers, three mechanisms which can cause state convergence are identified.The effect state convergence can have on stream cipher cryptanalysis is examined. We show that state convergence can have a positive effect if the goal of the attacker is to recover the initial state of the keystream generator. The third contribution of this thesis is the examination of the distributions of bit patterns in the sequences produced by nonlinear filter generators (NLFGs) and linearly filtered nonlinear feedback shift registers. We show that the selection of stages used as input to a keystream generator's output function can affect the distribution of bit patterns in sequences produced by these keystreamgenerators, and that the effect differs for nonlinear filter generators and linearly filtered nonlinear feedback shift registers. In the case of NLFGs, the keystream sequences produced when the output functions take inputs from consecutive register stages are less uniform than sequences produced by NLFGs whose output functions take inputs from unevenly spaced register stages. The opposite is true for keystream sequences produced by linearly filtered nonlinear feedback shift registers.

Understanding the abnormal brain activity in epilepsy as a potential predictor of the onset of an epileptic seizure

The Brain Research Institute (BRI) uses various types of indirect measurements, including EEG and fMRI, to understand and assess brain activity and function. As well as the recovery of generic information about brain function, research also focuses on the utilisation of such data and understanding to study the initiation, dynamics, spread and suppression of epileptic seizures. To assist with the future focussing of this aspect of their research, the BRI asked the MISG 2010 participants to examine how the available EEG and fMRI data and current knowledge about epilepsy should be analysed and interpreted to yield an enhanced understanding about brain activity occurring before, at commencement of, during, and after a seizure. Though the deliberations of the study group were wide ranging in terms of the related matters considered and discussed, considerable progress was made with the following three aspects. (1) The science behind brain activity investigations depends crucially on the quality of the analysis and interpretation of, as well as the recovery of information from, EEG and fMRI measurements. A number of specific methodologies were discussed and formalised, including independent component analysis, principal component analysis, profile monitoring and change point analysis (hidden Markov modelling, time series analysis, discontinuity identification). (2) Even though EEG measurements accurately and very sensitively record the onset of an epileptic event or seizure, they are, from the perspective of understanding the internal initiation and localisation, of limited utility. They only record neuronal activity in the cortical (surface layer) neurons of the brain, which is a direct reflection of the type of electrical activity they have been designed to record. Because fMRI records, through the monitoring of blood flow activity, the location of localised brain activity within the brain, the possibility of combining fMRI measurements with EEG, as a joint inversion activity, was discussed and examined in detail. (3) A major goal for the BRI is to improve understanding about ``when'' (at what time) an epileptic seizure actually commenced before it is identified on an eeg recording, ``where'' the source of this initiation is located in the brain, and ``what'' is the initiator. Because of the general agreement in the literature that, in one way or another, epileptic events and seizures represent abnormal synchronisations of localised and/or global brain activity the modelling of synchronisations was examined in some detail. References C. M. Michel, G. Thut, S. Morand, A. Khateb, A. J. Pegna, R. Grave de Peralta, S. Gonzalez, M. Seeck and T. Landis, Electric source imaging of human brain functions, Brain Res. Rev. , 36 (2--3), 2001, 108--118. doi:10.1016/S0165-0173(01)00086-8 S. Ogawa, R. S. Menon, S. G. Kim and K. Ugurbil, On the characteristics of functional magnetic resonance imaging of the brain, Annu. Rev. Bioph. Biom. , 27 , 1998, 447--474. doi:10.1146/annurev.biophys.27.1.447 C. D. Binnie and H. Stefan, Modern electroencephalography: its role in epilepsy management, Clin. Neurophysiol. , 110 (10), 1999, 1671--1697. doi:10.1016/S1388-2457(99)00125-X J. X. Tao, A. Ray, S. Hawes-Ebersole and J. S. Ebersole, Intracranial eeg substrates of scalp eeg interictal spikes, Epilepsia , 46 (5), 2005, 669--76. doi:10.1111/j.1528-1167.2005.11404.x S. Ogawa, D. W. Tank, R. Menon, J. M. Ellermann, S. G. Kim, H. Merkle and K. Ugurbil, Intrinsic signal changes accompanying sensory stimulation: Functional brain mapping with magnetic resonance imaging, P. Natl. Acad. Sci. USA , 89 (13), 1992, 5951--5955. doi:10.1073/pnas.89.13.5951 J. Engel Jr., Report of the ilae classification core group, Epilepsia , 47 (9), 2006, 1558--1568. doi:10.1111/j.1528-1167.2006.00215.x L. Lemieux, A. Salek-Haddadi, O. Josephs, P. Allen, N. Toms, C. Scott, K. Krakow, R. Turner and D. R. Fish, Event-related fmri with simultaneous and continuous eeg: description of the method and initial case r port, NeuroImage , 14 (3), 2001, 780--7. doi:10.1006/nimg.2001.0853 P. Federico, D. F. Abbott, R. S. Briellmann, A. S. Harvey and G. D. Jackson, Functional mri of the pre-ictal state, Brain , 128 (8), 2005, 1811-7. doi:10.1093/brain/awh533 C. S. Hawco, A. P. Bagshaw, Y. Lu, F. Dubeau and J. Gotman, bold changes occur prior to epileptic spikes seen on scalp eeg, NeuroImage , 35 (4), 2007, 1450--1458. doi:10.1016/j.neuroimage.2006.12.042 F. Moeller, H. R. Siebner, S. Wolff, H. Muhle, R. Boor, O. Granert, O. Jansen, U. Stephani and M. Siniatchkin, Changes in activity of striato-thalamo-cortical network precede generalized spike wave discharges, NeuroImage , 39 (4), 2008, 1839--1849. doi:10.1016/j.neuroimage.2007.10.058 V. Osharina, E. Ponchel, A. Aarabi, R. Grebe and F. Wallois, Local haemodynamic changes preceding interictal spikes: A simultaneous electrocorticography (ecog) and near-infrared spectroscopy (nirs) analysis in rats, NeuroImage , 50 (2), 2010, 600--607. doi:10.1016/j.neuroimage.2010.01.009 R. S. Fisher, W. Boas, W. Blume, C. Elger, P. Genton, P. Lee and J. Engel, Epileptic seizures and epilepsy: Definitions proposed by the international league against epilepsy (ilae) and the international bureau for epilepsy (ibe), Epilepsia , 46 (4), 2005, 470--472. doi:10.1111/j.0013-9580.2005.66104.x H. Berger, Electroencephalogram in humans, Arch. Psychiat. Nerven. , 87 , 1929, 527--570. C. M. Michel, M. M. Murray, G. Lantz, S. Gonzalez, L. Spinelli and R. G. de Peralta, eeg source imaging, Clin. Neurophysiol. , 115 (10), 2004, 2195--2222. doi:10.1016/j.clinph.2004.06.001 P. L. Nunez and R. B. Silberstein, On the relationship of synaptic activity to macroscopic measurements: Does co-registration of eeg with fmri make sense?, Brain Topogr. , 13 (2), 2000, 79--96. doi:10.1023/A:1026683200895 S. Ogawa, T. M. Lee, A. R. Kay and D. W. Tank, Brain magnetic resonance imaging with contrast dependent on blood oxygenation, P. Natl. Acad. Sci. USA , 87 (24), 1990, 9868--9872. doi:10.1073/pnas.87.24.9868 J. S. Gati, R. S. Menon, K. Ugurbil and B. K. Rutt, Experimental determination of the bold field strength dependence in vessels and tissue, Magn. Reson. Med. , 38 (2), 1997, 296--302. doi:10.1002/mrm.1910380220 P. A. Bandettini, E. C. Wong, R. S. Hinks, R. S. Tikofsky and J. S. Hyde, Time course EPI of human brain function during task activation, Magn. Reson. Med. , 25 (2), 1992, 390--397. K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppelm, M. S. Cohen and R. Turner, Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation, P. Natl. Acad. Sci. USA , 89 (12), 1992, 5675--5679. doi:10.1073/pnas.89.12.5675 J. Frahm, K. D. Merboldt and W. Hnicke, Functional mri of human brain activation at high spatial resolution, Magn. Reson. Med. , 29 (1), 1993, 139--144. P. A. Bandettini, A. Jesmanowicz, E. C. Wong and J. S. Hyde, Processing strategies for time-course data sets in functional MRI of the human brain, Magn. Reson. Med. , 30 (2), 1993, 161--173. K. J. Friston, P. Jezzard and R. Turner, Analysis of functional MRI time-series, Hum. Brain Mapp. , 1 (2), 1994, 153--171. B. Biswal, F. Z. Yetkin, V. M. Haughton and J. S. Hyde, Functional connectivity in the motor cortex of resting human brain using echo-planar mri, Mag. Reson. Med. , 34 (4), 1995, 537--541. doi:10.1002/mrm.1910340409 K. J. Friston, J. Ashburner, C. D. Frith, J. Poline, J. D. Heather and R. S. J. Frackowiak, Spatial registration and normalization of images, Hum. Brain Mapp. , 3 (3), 1995, 165--189. K. J. Friston, S. Williams, R. Howard, R. S. Frackowiak and R. Turner, Movement-related effects in fmri time-series, Magn. Reson. Med. , 35 (3), 1996, 346--355. G. H. Glover, T. Q. Li and D. Ress, Image-based method for retrospective correction of physiological motion effects in fmri: Retroicor, Magn. Reson. Med. , 44 (1), 2000, 162--167. doi:10.1002/1522-2594(200007)44:13.0.CO;2-E K. J. Friston, O. Josephs, G. Rees and R. Turner, Nonlinear event-related responses in fmri, Magn. Reson. Med. , 39 (1), 1998, 41--52. doi:10.1002/mrm.1910390109 K. Ugurbil, L. Toth and D. Kim, How accurate is magnetic resonance imaging of brain function?, Trends Neurosci. , 26 (2), 2003, 108--114. doi:10.1016/S0166-2236(02)00039-5 D. S. Kim, I. Ronen, C. Olman, S. G. Kim, K. Ugurbil and L. J. Toth, Spatial relationship between neuronal activity and bold functional mri, NeuroImage , 21 (3), 2004, 876--885. doi:10.1016/j.neuroimage.2003.10.018 A. Connelly, G. D. Jackson, R. S. Frackowiak, J. W. Belliveau, F. Vargha-Khadem and D. G. Gadian, Functional mapping of activated human primary cortex with a clinical mr imaging system, Radiology , 188 (1), 1993, 125--130. L. Allison, Hidden Markov Models, Technical Report , School of Computer and Software Engineering, Monash University, 2000. R. J. Elliott, L. Aggoun and J.B. Moore, Hidden Markov Models: Estimation and Control, Appl. Math.-Czech. , 2004. B. Bhavnagri, Discontinuities of plane functions projected from a surface with methods for finding these , Technical Report, 2009. B. Bhavnagri, Computer Vision using Shape Spaces , Technical Report,1996, University of Adelaide. B. Bhavnagri, A method for representing shape based on an equivalence relation on polygons, Pattern Recogn. , 27 (2), 1994, 247--260. doi:10.1016/0031-3203(94)90057-4 D. F. Abbott, A. B. Waites, A. S. Harvey and G. D. Jackson, Exploring epileptic seizure onset with fmri, NeuroImage , 36(S1) (344TH-PM), 2007. M. C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science , 197 , 1977, 287--289. S. H. Strogatz, SYNC - The Emerging Science of Spontaneous Order , Theia, New York, 2003. J. W. Kim, J. A. Roberts and P. A. Robinson, Dynamics of epileptic seizures: Evolution, spreading, and suppression, J. Theor. Biol. , 257 (4), 2009, 527--532. doi:10.1016/j.jtbi.2008.12.009 Y. Kuramoto, T. Aoyagi, I. Nishikawa, T. Chawanya T and K. Okuda, Neural network model carrying phase information with application to collective dynamics, J. Theor. Phys. , 87 (5), 1992, 1119--1126. V. B. Mountcastle, The columnar organization of the neocortex, Brain , 120 (4), 1997, 701. doi:10.1093/brain/120.4.701 F. L. Silva, W. Blanes, S. N. Kalitzin, J. Parra, P. Suffczynski and D. N. Velis, Epilepsies as dynamical diseases of brain systems: Basic models of the transition between normal and epileptic activity, Epilepsia , 44 (12), 2003, 72--83. F. H. Lopes da Silva, W. Blanes, S. N. Kalitzin, J. Parra, P. Suffczynski and D. N. Velis, Dynamical diseases of brain systems: different routes to epileptic seizures, ieee T. Bio-Med. Eng. , 50 (5), 2003, 540. L.D. Iasemidis, Epileptic seizure prediction and control, ieee T. Bio-Med. Eng. , 50 (5), 2003, 549--558. L. D. Iasemidis, D. S. Shiau, W. Chaovalitwongse, J. C. Sackellares, P. M. Pardalos, J. C. Principe, P. R. Carney, A. Prasad, B. Veeramani, and K. Tsakalis, Adaptive epileptic seizure prediction system, ieee T. Bio-Med. Eng. , 50 (5), 2003, 616--627. K. Lehnertz, F. Mormann, T. Kreuz, R.G. Andrzejak, C. Rieke, P. David and C. E. Elger, Seizure prediction by nonlinear eeg analysis, ieee Eng. Med. Biol. , 22 (1), 2003, 57--63. doi:10.1109/MEMB.2003.1191451 K. Lehnertz, R. G. Andrzejak, J. Arnhold, T. Kreuz, F. Mormann, C. Rieke, G. Widman and C. E. Elger, Nonlinear eeg analysis in epilepsy: Its possible use for interictal focus localization, seizure anticipation, and prevention, J. Clin. Neurophysiol. , 18 (3), 2001, 209. B. Litt and K. Lehnertz, Seizure prediction and the preseizure period, Curr. Opin. Neurol. , 15 (2), 2002, 173. doi:10.1097/00019052-200204000-00008 B. Litt and J. Echauz, Prediction of epileptic seizures, Lancet Neurol. , 1 (1), 2002, 22--30. doi:10.1016/S1474-4422(02)00003-0 M. M{a}kiranta, J. Ruohonen, K Suominen, J. Niinim{a}ki, E. Sonkaj{a}rvi, V. Kiviniemi, T. Sepp{a}nen, S. Alahuhta, V. J{a}ntti and O. Tervonen, {bold} signal increase preceeds eeg spike activity--a dynamic penicillin induced focal epilepsy in deep anesthesia, NeuroImage , 27 (4), 2005, 715--724. doi:10.1016/j.neuroimage.2005.05.025 K. Lehnertz, F. Mormann, H. Osterhage, A. M{u}ller, J. Prusseit, A. Chernihovskyi, M. Staniek, D. Krug, S. Bialonski and C. E. Elger, State-of-the-art of seizure prediction, J. Clin. Neurophysiol. , 24 (2), 2007, 147. doi:10.1097/WNP.0b013e3180336f16 F. Mormann, T. Kreuz, C. Rieke, R. G. Andrzejak, A. Kraskov, P. David, C. E. Elger and K. Lehnertz, On the predictability of epileptic seizures, Clin. Neurophysiol. , 116 (3), 2005, 569--587. doi:10.1016/j.clinph.2004.08.025 F. Mormann, R. G. Andrzejak, C. E. Elger and K. Lehnertz, Seizure prediction: the long and winding road, Brain , 130 (2), 2007, 314--333. doi:10.1093/brain/awl241 Z. Rogowski, I. Gath and E. Bental, On the prediction of epileptic seizures, Biol. Cybern. , 42 (1), 1981, 9--15. Y. Salant, I. Gath, O. Henriksen, Prediction of epileptic seizures from two-channel eeg, Med. Biol. Eng. Comput. , 36 (5), 1998, 549--556. doi:10.1007/BF02524422 J. Gotman and D.J. Koffler, Interictal spiking increases after seizures but does not after decrease in medication, Evoked Potential , 72 (1), 1989, 7--15. J. Gotman and M. G. Marciani, Electroencephalographic spiking activity, drug levels, and seizure occurence in epileptic patients, Ann. Neurol. , 17 (6), 1985, 59--603. A. Katz, D. A. Marks, G. McCarthy and S. S. Spencer, Does interictal spiking change prior to seizures?, Electroen. Clin. Neuro. , 79 (2), 1991, 153--156. A. Granada, R. M. Hennig, B. Ronacher, A. Kramer and H. Herzel, Phase Response Curves: Elucidating the dynamics of couples oscillators, Method Enzymol. , 454 (A), 2009, 1--27. doi:10.1016/S0076-6879(08)03801-9 doi:10.1016/S0076-6879(08)03801-9 H. Kantz and T. Schreiber, Nonlinear time series analysis , 2004, Cambridge Univ Press. M. V. L. Bennett and R. S Zukin, Electrical coupling and neuronal synchronization in the mammalian brain, Neuron , 41 (4), 2004, 495 --511. doi:10.1016/S0896-6273(04)00043-1 L.D. Iasemidis, J. Chris Sackellares, H. P. Zaveri and W. J. Williams, Phase space topography and the Lyapunov exponent of electrocorticograms in partial seizures, Brain Topogr. , 2 (3), 1990, 187--201. doi:10.1007/BF01140588 M. Le Van Quyen, J. Martinerie, V. Navarro, M. Baulac and F. J. Varela, Characterizing neurodynamic changes before seizures, J. Clin. Neurophysiol. , 18 (3), 2001, 191. J. Martinerie, C. Adam, M. Le Van Quyen, M. Baulac, S. Clemenceau, B. Renault and F. J. Varela, Epileptic seizures can be anticipated by non-linear analysis, Nat. Med. , 4 (10), 1998, 1173--1176. doi:10.1038/2667 A. Pikovsky, M. Rosenblum, J. Kurths and R. C. Hilborn, Synchronization: A universal concept in nonlinear science, Amer. J. Phys. , 70 , 2002, 655. H. R. Wilson and J. D. Cowan, Excitatory and inhibitory interactions in localized populations of model neurons, Biophys. J. , 12 (1), 1972, 1--24. D. Cumin and C. P. Unsworth, Generalising the Kuramoto model for the study of neuronal synchronisation in the brain, Physica D , 226 (2), 2007, 181--196. doi:10.1016/j.physd.2006.12.004 F. K. Skinner, H. Bazzazi and S. A. Campbell, Two-cell to N-cell heterogeneous, inhibitory networks: Precise linking of multistable and coherent properties, J. Comput. Neurosci. , 18 (3), 2005, 343--352. doi:10.1007/s10827-005-0331-1 W. W. Lytton, Computer modelling of epilepsy, Nat. Rev. Neurosci. , 9 (8), 2008, 626--637. doi:10.1038/nrn2416 R. D. Traub, A. Bibbig, F. E. N. LeBeau, E. H. Buhl and M. A. Whittington, Cellular mechanisms of neuronal population oscillations in the hippocampus in vitro, Ann. Rev. , 2004. R. D. Traub, A. Draguhn, M. A. Whittington, T. Baldeweg, A. Bibbig, E. H. Buhl and D. Schmitz, Axonal gap junc ions between principal neurons: A novel source of network oscillations, and perhaps epileptogenesis., Rev. Neuroscience , 13 (1), 2002, 1. doi:10.1146/annurev.neuro.27.070203.144303 M. Scheffer, J. Bascompte, W. A. Brock, V. Brovkin, S. R. Carpenter, V. Dakos, H. Held, E. H. van Nes, M. Rietkerk and G. Sugihara, Early-warning signals for critical transitions, Nature , 461 (7260), 2009, 53--59. doi:10.1038/nature08227 K. Murphy, A Brief Introduction to Graphical Models and Bayesian Networks , 2008, http://www.cs.ubc.ca/murphyk/Bayes/bnintro.html . R. C. Bradley, An elementary

Nonlinear secret sharing immune against cheating

The paper investigates the design of secret sharing that is immune against cheating (as defined by the Tompa-Woll attack). We examine secret sharing with binary shares and secrets. Bounds on the probability of successful cheating are given for two cases. The first case relates to secret sharing based on bent functions and results in a non-perfect scheme. The second case considers perfect secret sharing built on highly nonlinear balanced Boolean functions.

Structural damage detection method using frequency response functions

Structural damage detection using measured dynamic data for pattern recognition is a promising approach. These pattern recognition techniques utilize artificial neural networks and genetic algorithm to match pattern features. In this study, an artificial neural network–based damage detection method using frequency response functions is presented, which can effectively detect nonlinear damages for a given level of excitation. The main objective of this article is to present a feasible method for structural vibration–based health monitoring, which reduces the dimension of the initial frequency response function data and transforms it into new damage indices and employs artificial neural network method for detecting different levels of nonlinearity using recognized damage patterns from the proposed algorithm. Experimental data of the three-story bookshelf structure at Los Alamos National Laboratory are used to validate the proposed method. Results showed that the levels of nonlinear damages can be identified precisely by the developed artificial neural networks. Moreover, it is identified that artificial neural networks trained with summation frequency response functions give higher precise damage detection results compared to the accuracy of artificial neural networks trained with individual frequency response functions. The proposed method is therefore a promising tool for structural assessment in a real structure because it shows reliable results with experimental data for nonlinear damage detection which renders the frequency response function–based method convenient for structural health monitoring.

Information-theoretic analysis of brain white matter fiber orientation distribution functions

We propose a new information-theoretic metric, the symmetric Kullback-Leibler divergence (sKL-divergence), to measure the difference between two water diffusivity profiles in high angular resolution diffusion imaging (HARDI). Water diffusivity profiles are modeled as probability density functions on the unit sphere, and the sKL-divergence is computed from a spherical harmonic series, which greatly reduces computational complexity. Adjustment of the orientation of diffusivity functions is essential when the image is being warped, so we propose a fast algorithm to determine the principal direction of diffusivity functions using principal component analysis (PCA). We compare sKL-divergence with other inner-product based cost functions using synthetic samples and real HARDI data, and show that the sKL-divergence is highly sensitive in detecting small differences between two diffusivity profiles and therefore shows promise for applications in the nonlinear registration and multisubject statistical analysis of HARDI data.

The Expanded Human Kallikrein (KLK) gene family : genomic organisation, tissue specific expression and potential functions

The tissue kallikreins are serine proteases encoded by highly conserved multigene families. The rodent kallikrein (KLK) families are particularly large, consisting of 13 26 genes clustered in one chromosomal locus. It has been recently recognised that the human KLK gene family is of a similar size (15 genes) with the identification of another 12 related genes (KLK4-KLK15) within and adjacent to the original human KLK locus (KLK1-3) on chromosome 19q13.4. The structural organisation and size of these new genes is similar to that of other KLK genes except for additional exons encoding 5 or 3 untranslated regions. Moreover, many of these genes have multiple mRNA transcripts, a trait not observed with rodent genes. Unlike all other kallikreins, the KLK4-KLK15 encoded proteases are less related (25–44%) and do not contain a conventional kallikrein loop. Clusters of genes exhibit high prostatic (KLK2-4, KLK15) or pancreatic (KLK6-13) expression, suggesting evolutionary conservation of elements conferring tissue specificity. These genes are also expressed, to varying degrees, in a wider range of tissues suggesting a functional involvement of these newer human kallikrein proteases in a diverse range of physiological processes.