Route to chaos in a third-order phase-locked loop network

Phase-locked loops (PLLs) are widely used in applications related to control systems and telecommunication networks. Here we show that a single-chain master-slave network of third-order PLLs can exhibit stationary, periodic and chaotic behaviors, when the value of a single parameter is varied. Hopf, period-doubling and saddle-saddle bifurcations are found. Chaos appears in dissipative and non-dissipative conditions. Thus, chaotic behaviors with distinct dynamical features can be generated. A way of encoding binary messages using such a chaos-based communication system is suggested. (C) 2009 Elsevier B.V. All rights reserved.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.

Comparing lock-in ranges and transient responses of second- and third-order phase-locked loops in master-slave clock distribution networks

The distribution of clock signals throughout the nodes of a network is essential for several applications. in control and communication with the phase-locked loop (PLL) being the component for electronic synchronization process. In systems with master-slave (MS) strategies, the PLLs are the slave nodes responsible for providing reliable clocks in all nodes of the network. As PLLs have nonlinear phase detection, double-frequency terms appear and filtering becomes necessary. Imperfections in filtering process cause oscillations around the synchronous state worsening the performance of the clock distribution process. The behavior of one-way master-slave (OWMS) clock distribution networks is studied and performances of first- and second-order filter processes are compared, concerning lock-in ranges and responses to perturbations of the synchronous state. (c) 2007 Elsevier GmbH. All rights reserved.

Evaluation of algorithms used to order markers on genetic maps

When building genetic maps, it is necessary to choose from several marker ordering algorithms and criteria, and the choice is not always simple. In this study, we evaluate the efficiency of algorithms try (TRY), seriation (SER), rapid chain delineation (RCD), recombination counting and ordering (RECORD) and unidirectional growth (UG), as well as the criteria PARF (product of adjacent recombination fractions), SARF (sum of adjacent recombination fractions), SALOD (sum of adjacent LOD scores) and LHMC (likelihood through hidden Markov chains), used with the RIPPLE algorithm for error verification, in the construction of genetic linkage maps. A linkage map of a hypothetical diploid and monoecious plant species was simulated containing one linkage group and 21 markers with fixed distance of 3 cM between them. In all, 700 F(2) populations were randomly simulated with and 400 individuals with different combinations of dominant and co-dominant markers, as well as 10 and 20% of missing data. The simulations showed that, in the presence of co-dominant markers only, any combination of algorithm and criteria may be used, even for a reduced population size. In the case of a smaller proportion of dominant markers, any of the algorithms and criteria (except SALOD) investigated may be used. In the presence of high proportions of dominant markers and smaller samples (around 100), the probability of repulsion linkage increases between them and, in this case, use of the algorithms TRY and SER associated to RIPPLE with criterion LHMC would provide better results. Heredity (2009) 103, 494-502; doi:10.1038/hdy.2009.96; published online 29 July 2009

Cattle depredation by puma (Puma concolor) and jaguar (Panthera onca) in central-western Brazil

In this study, data on cattle depredation by puma (Puma concolor) and jaguar (Panthera onca) were recorded for six years (1998 - 2003) in a cattle ranch in central-western Brazil. Depredation represented 18.9% of the overall cattle mortality, being predominant on calves. in biomass, kills represented 0.4% (63.8 kg/km(2)) of the ranch`s annual stock. in economic loss, kills represented 0.3% of the cattle stock value. Depredation was mainly associated with cattle`s age class and location along with the time of birth of calves. The proportion of pastures next to forest with depredation (n=33, 48.5%) was not distinguished to the proportion of pastures not bordering forest with depredation (n=35, 51.5%). However, the proportion of pastures next to forest with depredation represented 54% (n=33) of the 61 total pastures that were at least partially surrounded by forest patches or riparian forests that comprised eight continuum blocks of forest fragments of different sizes in the ranch and adjacent areas. No kills occurred in the central portion (main house) of the farm, close to the headquarters where the pastures not bordering forest. The distances of the kills in relation to areas of native forest was 1317.48 +/- 941.03 m. In order to reduce depredation, calves should be kept as far as possible from forest areas and concentrated cattle breeding and calving seasons should be encouraged. (c) 2007 Elsevier Ltd. All rights reserved.

Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

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.

Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.

Fixed bed reactors with catalyst poisoning - first order kinetics.

The long performance of an isothermal fixed bed reactor undergoing catalyst poisoning is theoretically analyzed using the dispersion model. First order reaction with dth order deactivation is assumed and the model equations are solved by matched asymptotic expansions for large Peclet number. Simple closed-form solutions, uniformly valid in time, are obtained.

The relationship between multiple birth children's early phonological skills and later literacy

Previous studies have shown that multiple ; birth children (MBC) are prone to early phonological ;difficulties and later literacy problems. However, to date, ;there has been no systematic long-term follow-up of MBC with phonological difficulties in the preschool years to determine whether these difficulties predict later literacy problems. In this study, 20 MBC whose early speech and language skills had been previously documented were compared to normative data and 20 singleton controls on tasks assessing phonological ; processing and literacy. The major findings indicated that MBC performed significantly more poorly on some tasks :df phonological processing than singleton controls did. Further, the early phonological skills of MBC (i.e., the number of inappropriate phonological processes used) correlated with poor performance on visual rhyme recognition, word repetition, and phoneme detection tasks 5 years later. There was no significant relationship between early biological factors (birth weight and gestation period) and performance on the phonological processing and literacy-related subtests. These results cl-support the hypothesis that MBC's early speech and language difficulties are not merely a transient phase;of; development, but a real disorder, with consequences for later academic achievement.

Mice expressing the E7 oncogene of HPV16 in epithelium show central tolerance, and evidence of peripheral anergising tolerance, to E7-encoded cytotoxic T-lymphocyte epitopes

In order to derive mice which expressed both the E7 open reading frame transgene of human papillomavirus type 16 in skin and MHC class 1 restriction elements for several E7-encoded cytotoxic T-lymphocyte (CTL) epitopes, K14.HPV16E7 mice which express E7 in basal keratinocytes were crossed to the F1 generation with A2.1 K-b transgenic mice which express the MHC binding cleft domains of human HLA A*0201, and murine H-2(b). F1 mice (denoted K14E7xA2.1) expressed E7 in the thymus at least as early as 2-5 days before birth. Immunisation of FVBxA2.1 control mice (transgenic for HLA A*0201 and H-2(b) but not for E7), with two HLA A*0201-restricted epitopes of E7 and one H-2(b)-restricted CTL epitope of E7, gave strong primary CTL responses recognising epitope-pulsed or constitutively E7-expressing syngeneic target cells. In contrast, in immunised K14E7xA2.1 mice, the CTL responses to the H-2(b) epitope and one of the HLA A*0201 CTL epitopes were strongly down-regulated, and to the other HLA A*0201 epitope, completely abolished, as demonstrated by percentage specific killing by bulk splenocyte cultures in cyrotoxicity assays, and by CTL precursor frequency analysis, In thymus-transplanted bone marrow radiation chimeras in which the immune system of K14E7xA2.1 mice was replaced by a FVBxA2.1 immune system, specific immunisation did not result in reemergence of strong E7-directed CTL responses. In agreement with these in vitro findings, specific immunisation failed to significantly alter the course of E7-associated tumour development in K14E7xA2.1 mice. These data are consistent with a model of central deletional CTL tolerance to E7-encoded epitopes recognised in the context of two distinct MHC class 1 restriction elements, and with the possibility of peripheral T-cell anergy maintained by expression of E7 in the skin. (C) 1998 Academic Press.

Subcycling first- and second-order generalizations of the trapezoidal rule

Subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first- and second-order systems of equations arising in finite element analysis, as well as for integration using explicit/implicit partitions of a model. The author has recently extended this work to implicit/implicit multi-timestep partitions of both first- and second-order systems. In this paper, improved algorithms for multi-timestep implicit integration are introduced, that overcome some weaknesses of those proposed previously. In particular, in the second-order case, improved stability is obtained. Some of the energy conservation properties of the Newmark family of algorithms are shown to be preserved in the new multi-timestep extensions of the Newmark method. In the first-order case, the generalized trapezoidal rule is extended to multiple timesteps, in a simple way that permits an implicit/implicit partition. Explicit special cases of the present algorithms exist. These are compared to algorithms proposed previously. (C) 1998 John Wiley & Sons, Ltd.

Expression of galectin-1 in the mouse olfactory system

Primary sensory olfactory axons arise from the olfactory neuroepithelium that lines the nasal cavity and then project via the olfactory nerve into the olfactory bulb. The P-galactoside binding lectin, galectin-1,and its laminin ligand have been implicated in the growth of these axons along this pathway. In galectin-1 null mutant mice, a subpopulation of primary sensory olfactory axons fails to reach its targets in the olfactory bulb. In the present study we examined the spatiotemporal expression pattern of galectin-1 in normal mice in order to understand its role in the development of the olfactory nerve pathway. At E15.5, when olfactory axons have already contacted the olfactory bulb, galectin-1 was expressed in the cartilage and mesenchyme surrounding the nasal cavity but was absent from the olfactory neuroepithelium, nerve and bulb. Between E16.5 and birth galectin-1 began to be expressed by olfactory nerve ensheathing cells in the lamina propria of the neuroepithelium and nerve fibre layer. Galectin-1 was neither expressed by primary sensory neurons in the olfactory neuroepithelium nor by their axons in the olfactory nerve. Laminin, a galectin-1 ligand, also exhibited a similar expression pattern in the embryonic olfactory nerve pathway. Our results reveal that galectin-1 is dynamically expressed by glial elements within the nerve fibre layer during a discrete period in the developing olfactory nerve pathway. Previous studies have reported galectin-1 acts as a substrate adhesion molecule by cross-linking primary sensory olfactory neurons to laminin. Thus, the coordinate expression of galectin-1 and laminin in the embryonic nerve fibre layer suggests that these molecules support the adhesion and fasciculation of axons en route to their glomerular targets.

Off-diagonal long-range order in a supersymmetric integrable model of correlated electrons

A new model for correlated electrons is presented which is integrable in one-dimension. The symmetry algebra of the model is the Lie superalgebra gl(2\1) which depends on a continuous free parameter. This symmetry algebra contains the eta pairing algebra as a subalgebra which is used to show that the model exhibits Off-Diagonal Long-Range Order in any number of dimensions.

Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.