On-off and multistate intermittencies in cascaded random distributed feedback fibre laser

A range of physical and engineering systems exhibit an irregular complex dynamics featuring alternation of quiet and burst time intervals called the intermittency. The intermittent dynamics most popular in laser science is the on-off intermittency [1]. The on-off intermittency can be understood as a conversion of the noise in a system close to an instability threshold into effective time-dependent fluctuations which result in the alternation of stable and unstable periods. The on-off intermittency has been recently demonstrated in semiconductor, Erbium doped and Raman lasers [2-5]. Recently demonstrated random distributed feedback (random DFB) fiber laser has an irregular dynamics near the generation threshold [6,7]. Here we show the intermittency in the cascaded random DFB fiber laser. We study intensity fluctuations in a random DFB fiber laser based on nitrogen doped fiber. The laser generates first and second Stokes components 1120 nm and 1180 nm respectively under an appropriate pumping. We study the intermittency in the radiation of the second Stokes wave. The typical time trace near the generation threshold of the second Stokes wave (Pth) is shown at Fig. 1a. From the number of long enough time-traces we calculate statistical distribution between major spikes in time dynamics, Fig. 1b. To eliminate contribution of high frequency components of spikes we use a low pass filter along with the reference value of the output power. Experimental data is fitted by power law, ~(P-Pth)y, where is a mean time between pikes. There are two different intermittency regimes. Just above Pth, the mean time is approximated by the -3/2 power law. The -3/2 power law is typical to the on-off intermittency with hopping between two states (first and second Stokes waves in our case) [7]. At higher power, the mean time is approximated by -4 power law, that indicates a change in intermittency type to multistate. Multistable dynamics is observed in erbium-doped fiber lasers [8]. The origin of multiples states in our system could be probably connected with polarization hopping or other reasons and should be further investigated. We have presented a first experimental statistical characterisation of the on-off and multistate intermittencies that occur in the generation of the second Stokes wave in nitrogen doped random DFB fiber laser. References [1] H. Fujisaka and T. Yamada, “A New Intermittency in Coupled Dynamical Systems,” Prog. Theor. Phys. 74, 918 (1985). [2] S. Osborne, A. Amann, D. Bitauld, and S. O’Brien, “On-off intermittency in an optically injected semiconductor laser,” Phys. Rev. E 85, 056204 (2012). [3] S. Sergeyev, K. O'Mahoney, S. Popov, and A. T. Friberg, “Coherence and anticoherence resonance in high-concentration erbium-doped fiber laser,” Opt. Lett. 35, 3736 (2010). [4] A.E. El-Taher, S.V. Sergeyev, E.G. Turitsyna, P. Harper, and S. K. Turitsyn, “Intermittent Self-Pulsing in a Fiber Raman Laser”, In proc. Conf. Nonlin. Photon., paper ID 1367139, Colorado Springs, USA, 2012 [5] S.K. Turitsyn, S.A. Babin, A.E. El-Taher, P. Harper, D.V. Churkin, S.I. Kablukov, J.D. Ania-Castañón, V. Karalekas, and E.V. Podivilov, “Random distributed feedback fibre laser”, Nat. Photon..4, 231 (2010). [6] I. D. Vatnik, D. V. Churkin, S. A. Babin, and S. K. Turitsyn, "Cascaded random distributed feedback Raman fiber laser operating at 1.2 μm," Opt. Express 19, 18486 (2011). [7] W. Feller, An introduction to probability theory and its applications, Vol. 1, 3rd ed. (Wiley, New-York, 1968). [8] G. Huerta-Cuellar, A.N. Pisarchik, and Y.O. Barmenkov, “Experimental characterization of hopping dynamics in a multistable fiber laser,” Phys. Rev. E 78, 035202(R) (2008).

Probabilistic Approach to the Neumann Problem for a Symmetric Operator

2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.

The existence of an inverse limit of inverse system of measure spaces - a purely measurable case

The existence of an inverse limit of an inverse system of (probability) measure spaces has been investigated since the very beginning of the birth of the modern probability theory. Results from Kolmogorov [10], Bochner [2], Choksi [5], Metivier [14], Bourbaki [3] among others have paved the way of the deep understanding of the problem under consideration. All the above results, however, call for some topological concepts, or at least ones which are closely related topological ones. In this paper we investigate purely measurable inverse systems of (probability) measure spaces, and give a sucient condition for the existence of a unique inverse limit. An example for the considered purely measurable inverse systems of (probability) measure spaces is also given.

Defense against node compromise in sensor network security

Recent advances in electronic and computer technologies lead to wide-spread deployment of wireless sensor networks (WSNs). WSNs have wide range applications, including military sensing and tracking, environment monitoring, smart environments, etc. Many WSNs have mission-critical tasks, such as military applications. Thus, the security issues in WSNs are kept in the foreground among research areas. Compared with other wireless networks, such as ad hoc, and cellular networks, security in WSNs is more complicated due to the constrained capabilities of sensor nodes and the properties of the deployment, such as large scale, hostile environment, etc. Security issues mainly come from attacks. In general, the attacks in WSNs can be classified as external attacks and internal attacks. In an external attack, the attacking node is not an authorized participant of the sensor network. Cryptography and other security methods can prevent some of external attacks. However, node compromise, the major and unique problem that leads to internal attacks, will eliminate all the efforts to prevent attacks. Knowing the probability of node compromise will help systems to detect and defend against it. Although there are some approaches that can be used to detect and defend against node compromise, few of them have the ability to estimate the probability of node compromise. Hence, we develop basic uniform, basic gradient, intelligent uniform and intelligent gradient models for node compromise distribution in order to adapt to different application environments by using probability theory. These models allow systems to estimate the probability of node compromise. Applying these models in system security designs can improve system security and decrease the overheads nearly in every security area. Moreover, based on these models, we design a novel secure routing algorithm to defend against the routing security issue that comes from the nodes that have already been compromised but have not been detected by the node compromise detecting mechanism. The routing paths in our algorithm detour those nodes which have already been detected as compromised nodes or have larger probabilities of being compromised. Simulation results show that our algorithm is effective to protect routing paths from node compromise whether detected or not.

Defense Against Node Compromise in Sensor Network Security

Recent advances in electronic and computer technologies lead to wide-spread deployment of wireless sensor networks (WSNs). WSNs have wide range applications, including military sensing and tracking, environment monitoring, smart environments, etc. Many WSNs have mission-critical tasks, such as military applications. Thus, the security issues in WSNs are kept in the foreground among research areas. Compared with other wireless networks, such as ad hoc, and cellular networks, security in WSNs is more complicated due to the constrained capabilities of sensor nodes and the properties of the deployment, such as large scale, hostile environment, etc. Security issues mainly come from attacks. In general, the attacks in WSNs can be classified as external attacks and internal attacks. In an external attack, the attacking node is not an authorized participant of the sensor network. Cryptography and other security methods can prevent some of external attacks. However, node compromise, the major and unique problem that leads to internal attacks, will eliminate all the efforts to prevent attacks. Knowing the probability of node compromise will help systems to detect and defend against it. Although there are some approaches that can be used to detect and defend against node compromise, few of them have the ability to estimate the probability of node compromise. Hence, we develop basic uniform, basic gradient, intelligent uniform and intelligent gradient models for node compromise distribution in order to adapt to different application environments by using probability theory. These models allow systems to estimate the probability of node compromise. Applying these models in system security designs can improve system security and decrease the overheads nearly in every security area. Moreover, based on these models, we design a novel secure routing algorithm to defend against the routing security issue that comes from the nodes that have already been compromised but have not been detected by the node compromise detecting mechanism. The routing paths in our algorithm detour those nodes which have already been detected as compromised nodes or have larger probabilities of being compromised. Simulation results show that our algorithm is effective to protect routing paths from node compromise whether detected or not.

Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference.

Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufri\`{e}re Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.

Increasing the power of genome wide association studies in natural populations using repeated measures : evaluation and implementation

1. Genomewide association studies (GWAS) enable detailed dissections of the genetic basis for organisms' ability to adapt to a changing environment. In long-term studies of natural populations, individuals are often marked at one point in their life and then repeatedly recaptured. It is therefore essential that a method for GWAS includes the process of repeated sampling. In a GWAS, the effects of thousands of single-nucleotide polymorphisms (SNPs) need to be fitted and any model development is constrained by the computational requirements. A method is therefore required that can fit a highly hierarchical model and at the same time is computationally fast enough to be useful. 2. Our method fits fixed SNP effects in a linear mixed model that can include both random polygenic effects and permanent environmental effects. In this way, the model can correct for population structure and model repeated measures. The covariance structure of the linear mixed model is first estimated and subsequently used in a generalized least squares setting to fit the SNP effects. The method was evaluated in a simulation study based on observed genotypes from a long-term study of collared flycatchers in Sweden. 3. The method we present here was successful in estimating permanent environmental effects from simulated repeated measures data. Additionally, we found that especially for variable phenotypes having large variation between years, the repeated measurements model has a substantial increase in power compared to a model using average phenotypes as a response. 4. The method is available in the R package RepeatABEL. It increases the power in GWAS having repeated measures, especially for long-term studies of natural populations, and the R implementation is expected to facilitate modelling of longitudinal data for studies of both animal and human populations.

Spatial modeling of data with excessive zeros applied to reindeer pellet-group counts

We analyze a real data set pertaining to reindeer fecal pellet-group counts obtained from a survey conducted in a forest area in northern Sweden. In the data set, over 70% of counts are zeros, and there is high spatial correlation. We use conditionally autoregressive random effects for modeling of spatial correlation in a Poisson generalized linear mixed model (GLMM), quasi-Poisson hierarchical generalized linear model (HGLM), zero-inflated Poisson (ZIP), and hurdle models. The quasi-Poisson HGLM allows for both under- and overdispersion with excessive zeros, while the ZIP and hurdle models allow only for overdispersion. In analyzing the real data set, we see that the quasi-Poisson HGLMs can perform better than the other commonly used models, for example, ordinary Poisson HGLMs, spatial ZIP, and spatial hurdle models, and that the underdispersed Poisson HGLMs with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLMs. Spatial count response with an extremely high proportion of zeros, and underdispersion can be successfully modeled using the quasi-Poisson HGLM with spatial random effects.

Improving CAS Capabilities: New Rules for Computing Improper Integrals

There are diferent applications in Engineering that require to compute improper integrals of the first kind (integrals defined on an unbounded domain) such as: the work required to move an object from the surface of the earth to in nity (Kynetic Energy), the electric potential created by a charged sphere, the probability density function or the cumulative distribution function in Probability Theory, the values of the Gamma Functions(wich useful to compute the Beta Function used to compute trigonometrical integrals), Laplace and Fourier Transforms (very useful, for example in Differential Equations).

A Microdata Analysis Approach to Transport Infrastructure Maintenance

Maintenance of transport infrastructure assets is widely advocated as the key in minimizing current and future costs of the transportation network. While effective maintenance decisions are often a result of engineering skills and practical knowledge, efficient decisions must also account for the net result over an asset's life-cycle. One essential aspect in the long term perspective of transport infrastructure maintenance is to proactively estimate maintenance needs. In dealing with immediate maintenance actions, support tools that can prioritize potential maintenance candidates are important to obtain an efficient maintenance strategy. This dissertation consists of five individual research papers presenting a microdata analysis approach to transport infrastructure maintenance. Microdata analysis is a multidisciplinary field in which large quantities of data is collected, analyzed, and interpreted to improve decision-making. Increased access to transport infrastructure data enables a deeper understanding of causal effects and a possibility to make predictions of future outcomes. The microdata analysis approach covers the complete process from data collection to actual decisions and is therefore well suited for the task of improving efficiency in transport infrastructure maintenance. Statistical modeling was the selected analysis method in this dissertation and provided solutions to the different problems presented in each of the five papers. In Paper I, a time-to-event model was used to estimate remaining road pavement lifetimes in Sweden. In Paper II, an extension of the model in Paper I assessed the impact of latent variables on road lifetimes; displaying the sections in a road network that are weaker due to e.g. subsoil conditions or undetected heavy traffic. The study in Paper III incorporated a probabilistic parametric distribution as a representation of road lifetimes into an equation for the marginal cost of road wear. Differentiated road wear marginal costs for heavy and light vehicles are an important information basis for decisions regarding vehicle miles traveled (VMT) taxation policies. In Paper IV, a distribution based clustering method was used to distinguish between road segments that are deteriorating and road segments that have a stationary road condition. Within railway networks, temporary speed restrictions are often imposed because of maintenance and must be addressed in order to keep punctuality. The study in Paper V evaluated the empirical effect on running time of speed restrictions on a Norwegian railway line using a generalized linear mixed model.

Inconsistencies of a purported probability current in the Duffin-Kemmer-Petiau theory

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A history of the mathematical theory of probability from the time of Pascal to that of Laplace.

Mode of access: Internet.

Some theorems in the theory of probability, with special reference to their importance in the theory of homograde correlation ...

Mode of access: Internet.

Theory of probability with applications /

At the head of title page: Princeton University Station, Division 2, National Defense Research Committee.