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Let S be a compact surface with boundary and F be the set of the orbits of a traversing flow on S. If the flow is generic, its orbit space is a spine G of S, namely G is a graph embedded in S and S is a regular neighbourhood of G. Moreover an extra structure on G turns it into a flow-spine, from which one can reconstruct S and F. In this paper we study properly immersed curves C in S. We do this by considering generic C's and their apparent contour relative to F, namely the set of points of G corresponding to orbits that either are tangent to C, or go through a self-intersection of C, or meet the boundary of C. We translate this apparent contour into a decoration of G that allows one to reconstruct C, and then we allow C to vary up to homotopy within a fixed generic F, and next also F to vary up to homotopy, and we identify a finite set of local moves on decorated graphs that translate these homotopies., Comment: 39 pages, 50 figures

In this note we provide a new partial solution to the Hurwitz existence problem for surface branched covers. Namely, we consider candidate branch data with base surface the sphere and one partition of the degree having length two, and we fully determine which of them are realizable and which are exceptional. The case where the covering surface is also the sphere was solved somewhat recently by Pakovich, and we deal here with the case of positive genus. We show that the only other exceptional candidate data, besides those of Pakovich (five infinite families and one sporadic case), are a well-known very specific infinite family in degree 4 (indexed by the genus of the candidate covering surface, which can attain any value), five sporadic cases (four in genus 1 and one in genus 2), and another infinite family in genus 1 also already known. Since the degree is a composite number for all these exceptional data, our findings provide more evidence for the prime-degree conjecture. Our argument proceeds by induction on the genus and on the number of branching points, so our results logically depend on those of Pakovich, and we do not employ the technology of constellations on which his proof is based., Comment: 37 pages, 21 figures. Incorporated reviewer's suggestions. To appear in Illinois J. Math

Linear stability theory (LST) is often used to model the large-scale flow structures in the turbulent mixing region and near pressure field of high-speed jets. For perfectly-expanded single round jets, these models predict the dominance of $m=0$ and $m = 1$ helical modes for the lower frequency range, in agreement with empirical data. When LST is applied to twin-jet systems, four solution families appear following the odd/even behaviour of the pressure field about the symmetry planes. The interaction between the unsteady pressure fields of the two jets also results in their coupling. The individual modes of the different solution families no longer correspond to helical motions, but to flapping oscillations of the jet plumes. In the limit of large jet separations, when the jet coupling vanishes, the eigenvalues corresponding to the $m=1$ mode in each family are identical, and a linear combination of them recovers the helical motion. Conversely, as the jet separation decreases, the eigenvalues for the $m=1$ modes of each family diverge, thus favouring a particular flapping oscillation over the others and preventing the appearance of helical motions. The dominant mode of oscillation for a given jet Mach number $M_j$ and temperature ratio $T_R$ depends on the Strouhal number $St$ and jet separation $s$. Increasing both $M_j$ and $T_R$ independently is found to augment the jet coupling and modify the $(St,s)$ map of the preferred oscillation mode. Present results predict the preference of two modes when the jet interaction is relevant, namely varicose and especially sinuous flapping oscillations on the nozzles plane.

Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearised Navier-Stokes system for a few low wavenumbers. Resulting Galerkin systems comprise ordinary differential equations, with a number of degrees of freedom ranging from 144 to 600, which may be integrated to large times without sign of numerical instability. The reduced-order models so obtained are also found to match statistics of direct numerical simulations at Reynolds number 500 and 1200 with reasonable accuracy, despite a truncation of orders of magnitude in the degrees of freedom of the system. The present models offer thus an interesting compromise between simplicity and accuracy in a canonical wall-bounded flow, with relatively few modes representing coherent structures in the flow and their dominant dynamics., Comment: 10 pages, 4 figures

Fuzzy Cognitive Maps (FCMs) have emerged as an interpretable signed weighted digraph method consisting of nodes (concepts) and weights which represent the dependencies among the concepts. Although FCMs have attained considerable achievements in various time series prediction applications, designing an FCM model with time-efficient training method is still an open challenge. Thus, this paper introduces a novel univariate time series forecasting technique, which is composed of a group of randomized high order FCM models labeled R-HFCM. The novelty of the proposed R-HFCM model is relevant to merging the concepts of FCM and Echo State Network (ESN) as an efficient and particular family of Reservoir Computing (RC) models, where the least squares algorithm is applied to train the model. From another perspective, the structure of R-HFCM consists of the input layer, reservoir layer, and output layer in which only the output layer is trainable while the weights of each sub-reservoir components are selected randomly and keep constant during the training process. As case studies, this model considers solar energy forecasting with public data for Brazilian solar stations as well as Malaysia dataset, which includes hourly electric load and temperature data of the power supply company of the city of Johor in Malaysia. The experiment also includes the effect of the map size, activation function, the presence of bias and the size of the reservoir on the accuracy of R-HFCM method. The obtained results confirm the outperformance of the proposed R-HFCM model in comparison to the other methods. This study provides evidence that FCM can be a new way to implement a reservoir of dynamics in time series modelling.

Among various soft computing approaches for time series forecasting, Fuzzy Cognitive Maps (FCM) have shown remarkable results as a tool to model and analyze the dynamics of complex systems. FCM have similarities to recurrent neural networks and can be classified as a neuro-fuzzy method. In other words, FCMs are a mixture of fuzzy logic, neural network, and expert system aspects, which act as a powerful tool for simulating and studying the dynamic behavior of complex systems. The most interesting features are knowledge interpretability, dynamic characteristics and learning capability. The goal of this survey paper is mainly to present an overview on the most relevant and recent FCM-based time series forecasting models proposed in the literature. In addition, this article considers an introduction on the fundamentals of FCM model and learning methodologies. Also, this survey provides some ideas for future research to enhance the capabilities of FCM in order to cover some challenges in the real-world experiments such as handling non-stationary data and scalability issues. Moreover, equipping FCMs with fast learning algorithms is one of the major concerns in this area.

The prediction of residential power usage is essential in assisting a smart grid to manage and preserve energy to ensure efficient use. An accurate energy forecasting at the customer level will reflect directly into efficiency improvements across the power grid system, however forecasting building energy use is a complex task due to many influencing factors, such as meteorological and occupancy patterns. In addiction, high-dimensional time series increasingly arise in the Internet of Energy (IoE), given the emergence of multi-sensor environments and the two way communication between energy consumers and the smart grid. Therefore, methods that are capable of computing high-dimensional time series are of great value in smart building and IoE applications. Fuzzy Time Series (FTS) models stand out as data-driven non-parametric models of easy implementation and high accuracy. Unfortunately, the existing FTS models can be unfeasible if all features were used to train the model. We present a new methodology for handling high-dimensional time series, by projecting the original high-dimensional data into a low dimensional embedding space and using multivariate FTS approach in this low dimensional representation. Combining these techniques enables a better representation of the complex content of multivariate time series and more accurate forecasts., Comment: 18 pages, 3 figures

We propose a new approach to predict the modulation of wavepackets in shock-containing jets. With a modelled ideally expanded mean flow as input, an approximation of the shock-cell structure is obtained from the parabolised stability equations (PSE) at zero frequency. This solution is then used to define a new shock-containing mean flow, which is a function of the shock-cell wavenumber at each streamwise station. Linearisation of the Navier-Stokes equations around this quasi-periodic mean flow allows us to postulate a solution based on the Floquet ansatz, and further manipulation of the equations leads to a system called the parabolised Floquet equations (PFE) that bears several similarities to PSE. The modulation wavenumbers are marched spatially together with the central Kelvin-Helmholtz wavenumber, leading to a modulated wavepacket as the final solution. The limitations of PFE are highlighted, and the method is applied to two sample cases: a canonical slowly diverging jet at low supersonic Mach number and an overexpanded jet, for which large-eddy simulation (LES) data is available. Overall, good agreement is observed between the wavepackets predicted by PFE and the leading spectral proper orthogonal decomposition (SPOD) modes from the LES, suggesting that the method is able to capture the underlying physical mechanism associated with wavepacket modulation: the extraction of energy from the mean flow by the Kelvin-Helmholtz mode and a redistribution of energy to modulation wavenumbers due to the interaction with the shock-cell structure., Comment: Submitted to the Journal of Fluid Mechanics

This paper explores the screech closure mechanism for different axisymmetric modes in shock-containing jets. While many of the discontinuities in tonal frequency exhibited by screeching jets can be associated with a change in the azimuthal mode, there has to date been no explanation for the existence of multiple axisymmetric modes at different frequencies. This paper provides just such an explanation. As shown in previous works, specific wavenumbers arise from the interaction of waves in the flow with the shocks. This provides new paths for driving upstream-travelling waves that can potentially close the resonance loop. Predictions using locally parallel and spatially periodic linear stability analyses and the wavenumber spectrum of the shock-cell structure suggest that the A1 mode resonance is closed by a wave generated when the Kelvin-Helmholtz mode interacts with the leading wavenumber of the shock-cell structure. The A2 mode is closed by a wave that arises due to interaction between the Kelvin-Helmholtz wave and a secondary wavenumber peak, which arises from the spatial variation of the shock-cell wavelength. The predictions are shown to closely match experimental data, and possible justifications for the dominance of each mode are provided based on the growth rates of the absolute instability., Comment: Submitted to the Journal of Fluid Mechanics

We present an analysis of the linear stability characteristics of shock-containing jets. The flow is linearised around a spatially periodic mean, which acts as a surrogate for a mean flow with a shock-cell structure, leading to a set of partial differential equations with periodic coefficients in space. Disturbances are written using the Floquet ansatz and Fourier modes in the streamwise direction, leading to an eigenvalue problem for the Floquet exponent. The characteristics of the solution are directly compared to the locally parallel case, and some of the features are similar. The inclusion of periodicity induces minor changes in the growth rate and phase velocity of the relevant modes for small shock amplitudes. On the other hand, the eigenfunctions are now subject to modulation related to the periodicity of the flow. Analysis of the spatio-temporal growth rates led to the identification of a saddle point between the Kelvin-Helmholtz mode and the guided jet mode, characterising an absolute instability mechanism. Frequencies and mode shapes related to the saddle points for two conditions (associated with axisymmetric and helical modes) are compared with screech frequencies and the most energetic coherent structures of screeching jets, resulting in a good agreement for both. The analysis shows that a periodic shock-cell structure has an impulse response that grows upstream, leading to oscillator behaviour. The results suggest that screech can occur in the absence of a nozzle, and that the upstream reflection condition is not essential for screech frequency selection. Connections to previous models are also discussed., Comment: Submitted to the Journal of Fluid Mechanics

The present work studies the non-linear dynamics of a shear layer, driven by a body force and confined between parallel walls, a simplified setting to study transitional and turbulent shear layers. It was introduced by Nogueira \& Cavalieri (J. Fluid Mech. 907, A32, 2021), and is here studied using a reduced-order model based on a Galerkin projection of the Navier-Stokes system. By considering a confined shear layer with free-slip boundary conditions on the walls, periodic boundary conditions in streamwise and spanwise directions may be used, simplifying the system and enabling the use of methods of dynamical systems theory. A basis of eight modes is used in the Galerkin projection, representing the mean flow, Kelvin-Helmholtz vortices, rolls, streaks and oblique waves, structures observed in the cited work, and also present in shear layers and jets. A dynamical system is obtained, and its transition to chaos is studied. Increasing Reynolds number $Re$ leads to pitchfork and Hopf bifurcations, and the latter leads to a limit cycle with amplitude modulation of vortices, as in the DNS by Nogueira \& Cavalieri. Further increase of $Re$ leads to the appearance of a chaotic saddle, followed by the emergence of quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging crisis for higher $Re$, leading to chaotic dynamics with amplitude modulation and phase jumps of vortices. This is reminiscent of observations of coherent structures in turbulent jets, suggesting that the model represents dynamics consistent with features of shear layers and jets., Comment: 28 pages, 18 figures

The interaction between various wavelike structures in screeching jets is considered via both experimental measurements and linear stability theory. Velocity snapshots of screeching jets are used to produce a reduced order model of the screech cycle via proper orthogonal decomposition. Streamwise Fourier filtering is then applied to isolate the negative and positive wavenumber components, which for the waves of interest in this jet correspond to upstream and downstream-travelling waves. A global stability analysis on an experimentally derived base flow is conducted, demonstrating a close match to the results obtained via experiment, indicating that the mechanisms considered here are well represented in a linear framework. In both analyses, three distinct wavelike structures are evident. These three waves are those first shown by Tam & Hu (1989) to be supported by a cylindrical vortex sheet. One is the Kelvin-Helmholtz mode. Another is the upstream-travelling guided jet mode that has been a topic of recent discussion. The third component, with positive phase velocity, has not previously been identified in screeching jets. We provide evidence that this downstream-travelling wave is a duct-like mode similar to that recently identified in high-subsonic jets by Towne et al. (2017). We further demonstrate that both of the latter two waves are generated by the interaction between the Kelvin-Helmholtz wavepacket and the shock cells in the flow, according to a theory first proposed in Tam & Tanna (1982). Finally, we consider the periodic spatial modulation of the coherent velocity fluctuation evident in screeching jets, and show that this modulation is the result of the superposition of the three wavelike structures, with no evidence that the shocks in the flow modulate the growth of the Kelvin-Helmholtz wavepacket., Comment: 27 pages, 10 figures. Submitted to the Journal of Fluid Mechanics

Enterprise architecture (EA) has been present in scientific literature since the 1980s and has branched out into several research fields. EA delivers value by presenting business and ICT leaders with recommendations for adjusting policies and projects to achieve business goals. Although there are many works on the EA application in healthcare systems, the literature lacks studies that provide a systematic approach to this topic specifically. This work presents a deep and broad Systematic Literature Review (SLR) to select studies demonstrating current EA practices in healthcare systems. The researchers established an SLR protocol returning 280 primary studies after the first step of the Data Selection and a consolidated inclusion of 46 articles after the second step. They assessed the level of disagreement during the team's evaluations using Cohen's Kappa. This SLR revealed essential aspects of state-of-the-art EA application in healthcare systems, such as the most used methodologies and tools, best practices, and criteria considered for their choice. It also analyzed the main positive impacts, challenges, and critical success factors described by the studies' authors based on empirical approaches. Besides, this work brings the main publication channels and the most influential authors on the topic of EA in Healthcare systems., Comment: 22 pages

The COVID-19 pandemic due to the SARS-CoV-2 coronavirus has directly impacted the public health and economy worldwide. To overcome this problem, countries have adopted different policies and non-pharmaceutical interventions for controlling the spread of the virus. This paper proposes the COVID-ABS, a new SEIR (Susceptible-Exposed-Infected-Recovered) agent-based model that aims to simulate the pandemic dynamics using a society of agents emulating people, business and government. Seven different scenarios of social distancing interventions were analyzed, with varying epidemiological and economic effects: (1) do nothing, (2) lockdown, (3) conditional lockdown, (4) vertical isolation, (5) partial isolation, (6) use of face masks, and (7) use of face masks together with 50% of adhesion to social isolation. In the impossibility of implementing scenarios with lockdown, which present the lowest number of deaths and highest impact on the economy, scenarios combining the use of face masks and partial isolation can be the more realistic for implementation in terms of social cooperation. The COVID-ABS model was implemented in Python programming language, with source code publicly available. The model can be easily extended to other societies by changing the input parameters, as well as allowing the creation of a multitude of other scenarios. Therefore, it is a useful tool to assist politicians and health authorities to plan their actions against the COVID-19 epidemic., Comment: 37 pages, 17 figures

In this paper we introduce a Non-Stationary Fuzzy Time Series (NSFTS) method with time varying parameters adapted from the distribution of the data. In this approach, we employ Non-Stationary Fuzzy Sets, in which perturbation functions are used to adapt the membership function parameters in the knowledge base in response to statistical changes in the time series. The proposed method is capable of dynamically adapting its fuzzy sets to reflect the changes in the stochastic process based on the residual errors, without the need to retraining the model. This method can handle non-stationary and heteroskedastic data as well as scenarios with concept-drift. The proposed approach allows the model to be trained only once and remain useful long after while keeping reasonable accuracy. The flexibility of the method by means of computational experiments was tested with eight synthetic non-stationary time series data with several kinds of concept drifts, four real market indices (Dow Jones, NASDAQ, SP500 and TAIEX), three real FOREX pairs (EUR-USD, EUR-GBP, GBP-USD), and two real cryptocoins exchange rates (Bitcoin-USD and Ethereum-USD). As competitor models the Time Variant fuzzy time series and the Incremental Ensemble were used, these are two of the major approaches for handling non-stationary data sets. Non-parametric tests are employed to check the significance of the results. The proposed method shows resilience to concept drift, by adapting parameters of the model, while preserving the symbolic structure of the knowledge base., Comment: 21 pages, 7 figures, submitted to Applied Soft Computing

The cross-spectral density (CSD) of the non-linear forcing in resolvent analyses is here quantified for the first time for turbulent channel flows. Direct numerical simulations (DNS) at $Re_{\tau} =179$ and $Re_{\tau} =543$ are performed. The CSDs are computed for highly energetic structures typical of buffer-layer and large-scale motions, for different temporal frequencies. The CSD of the non-linear forcing is shown not to be uncorrelated (white) in space, which implies the forcing is structured. Since the non-linear forcing is non-solenoidal by construction and the velocity of an incompressible flow is affected only by the solenoidal part of the forcing, this solenoidal part is evaluated. It is shown that the solenoidal part of the non-linear forcing is the combination of oblique streamwise vortices and a streamwise component which counteract each other, as in a destructive interference. It is shown that a rank-2 approximation of the forcing, with only the most energetic SPOD (spectral proper orthogonal decomposition) modes, leads to the bulk of the response. The projections of the non-linear forcing onto the right-singular vectors of the resolvent are evaluated. The left-singular vectors of the resolvent associated with very low-magnitude singular values are non-negligible since the non-linear forcing term has a non-negligible projection onto the linear sub-optimals of resolvent analysis. The same projections are computed when the forcing is modelled with an eddy-viscosity approach. It is clarified that this modelling improves the accuracy of the prediction since the projections are closer to those associated with the non-linear forcing from DNS data.

An analysis of the statistics of the non-linear terms in resolvent analysis is performed in this work for turbulent Couette flow at low Reynolds number. Data from a direct numerical simulation of a minimal flow unit, at Reynolds number 400, is post-processed using Fourier analysis in both time and space, leading to the covariance matrix of the velocity. From the same data, we computed the non-linear terms of the Navier-Stokes equations (treated as forcing in the present formulation), which allowed us to compute the covariance matrix of the forcing for this case. The two covariances are related exactly by the resolvent operator; based on this, we explore the recovery of the velocity statistics from the statistics of the forcing as a function of the components of the forcing term. This is carried out for the dominant structures in this flow, which participate in the self-sustaining cycle of turbulence: (i) streamwise vortices and streaks, and (ii) spanwise coherent fluctuations of spanwise velocity. The present results show a dominance by four of the non-linear terms for the prediction of the full statistics of streamwise vortices and streaks; a single term is seen to be dominant for spanwise motions. A relevant feature observed in these cases is that forcing terms have significant coherence in space; moreover, different forcing components are also coherent between them. This leads to constructive and destructive interferences that greatly modify the flow response, and should thus be accounted for in modelling work.

Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin-Helmholtz, and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211-237) at low Strouhal number ($St$) and non-zero azimuthal wavenumbers ($m$). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes, and sensitivity analysis distinguishes the three mechanisms and the regions of frequency-wavenumber space where each dominates, finding lift-up to be dominant as $St/m \rightarrow 0$. Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core., Comment: 35 pages, 23 figures, Accepted in J. Fluid Mech

We consider surface branch data with base surface the sphere, odd degree d, three branching points, and two partitions of d of the form (2,...,2,1) and (2,...,2,2h+1). If the third partition has length L, this datum satisfies the Riemann-Hurwitz necessary condition for realizability if h-L is odd and at least -1. For several small values of h and L (namely, for h+L<6) we explicitly compute the number n of realizations of the datum up to the equivalence relation given by the action of automorphisms (even unoriented ones) of both the base and the covering surface. The expression of n depends on arithmetic properties of the entries of the third partition. In particular we find that in the only case where n is 0 these entries have a common divisor, in agreement with a conjecture of Edmonds-Kulkarny-Stong and a stronger one of Zieve., Comment: 27 pages, 16 figures. arXiv admin note: text overlap with arXiv:1807.11067, arXiv:1805.00317

To a branched cover f between orientable surfaces one can associate a certain branch datum D(f), that encodes the combinatorics of the cover. This D(f) satisfies a compatibility condition called the Riemann-Hurwitz relation. The old but still partly unsolved Hurwitz problem asks whether for a given abstract compatible branch datum D there exists a branched cover f such that D(f)=D. One can actually refine this problem and ask how many these f's exist, but one must of course decide what restrictions one puts on such f's, and choose an equivalence relation up to which one regards them. And it turns out that quite a few natural choices are possible. In this short note we carefully analyze all these choices and show that the number of actually distinct ones is only three. To see that these three choices are indeed different we employ Grothendieck's dessins d'enfant., Comment: 15 pages, 1 figure

We continue our computation, using a combinatorial method based on Gronthendieck's dessins d'enfant, of the number of (weak) equivalence classes of surface branched covers matching certain specific branch data. In this note we concentrate on data with the surface of genus g as source surface, the sphere as target surface, 3 branching points, degree 2k, and local degrees over the branching points of the form [2,...,2], [2h+1,3,2,...,2], [d_1,...,d_l]. We compute the corresponding (weak) Hurwitz numbers for several values of g and h, getting explicit arithmetic formulae in terms of the d_i's., Comment: 25 pages, 10 figures

We prove that there exists no branched cover from the torus to the sphere with degree 3h and 3 branching points in the target with local degrees (3,...,3), (3,...,3), (4,2,3,...,3) at their preimages. The result was already established by Izmestiev, Kusner, Rote, Springborn, and Sullivan, using geometric techniques, and by Corvaja and Zannier with a more algebraic approach, whereas our proof is topological and completely elementary: besides the definitions, it only uses the fact that on the torus a simple closed curve can only be trivial (in homology, or equivalently bounding a disc, or equivalently separating) or non-trivial., Comment: To appear in Rendiconti Lincei - Matematica e Applicazioni. 14 pages, many pictures

We compute the number of (weak) equivalence classes of branched covers from a surface of genus g to the sphere, with 3 branching points, degree 2k, and local degrees over the branching points of the form (2,...,2), (2h+1,1,2,...,2), (d_1,...,d_m), for several values of g and h. We obtain explicit formulae of arithmetic nature in terms of the d_i's. Our proofs employ a combinatorial method based on Grothendieck's dessins d'enfant., Comment: To appear in European Journal of Combinatorics (2018); 23 pages, 12 figures

This note has an experimental nature and contains no new theorems. We introduce certain moves for classical knot diagrams that for all the very many examples we have tested them on give a monotonic complete simplification. A complete simplification of a knot diagram D is a sequence of moves that transform D into a diagram D' with the minimal possible number of crossings for the isotopy class of the knot represented by D. The simplification is monotonic if the number of crossings never increases along the sequence. Our moves are certain Z1, Z2, Z3 generalizing the classical Reidemeister moves R1, R2, R3, and another one C (together with a variant) aimed at detecting whether a knot diagram can be viewed as a connected sum of two easier ones. We present an accurate description of the moves and several results of our implementation of the simplification procedure based on them, publicly available on the web., Comment: 38 pages, 33 figures

Sub-Nyquist time frequency packing technique was demonstrated for the first time in a super channel field trial transmission over long-haul distances. The technique allows a limited spectral occupancy even with low order modulation formats. The transmission was successfully performed on a deployed Australian link between Sydney and Melbourne which included 995 km of uncompensated SMF with coexistent traffic. 40 and 100 Gb/s co-propagating channels were transmitted together with the super-channel in a 50 GHz ITU-T grid without additional penalty. The super-channel consisted of eight sub-channels with low-level modulation format, i.e. DP-QPSK, guaranteeing better OSNR robustness and reduced complexity with respect to higher order formats. At the receiver side, coherent detection was used together with iterative maximum-a-posteriori (MAP) detection and decoding. A 975 Gb/s DP-QPSK super-channel was successfully transmitted between Sydney and Melbourne within four 50GHz WSS channels (200 GHz). A maximum potential SE of 5.58 bit/s/Hz was achieved with an OSNR=15.8 dB, comparable to the OSNR of the installed 100 Gb/s channels. The system reliability was proven through long term measurements. In addition, by closing the link in a loop back configuration, a potential SE*d product of 9254 bit/s/Hz*km was achieved.

Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra combinatorial structures on T. We then analyze how to change these extra structures on T, and T itself, without changing s, thereby getting a combinatorial realization, in the usual "objects/moves" sense, of the set of all pairs (M,s). Our moves have a local nature, except one, that has a global flavour but is explicitly described anyway. We also provide an alternative approach where the global move is replaced by simultaneous local ones., Comment: 49 pages, many figures

We provide a combinatorial presentation of the set F of 3-dimensional generic flows, namely the set of pairs (M,v) with M a compact oriented 3-manifold and v a nowhere-zero vector field on M having generic behaviour along the boundary of M, with M viewed up to diffeomorphism and v up to homotopy on M fixed on the boundary. To do so we introduce a certain class S of finite 2-dimensional polyhedra with extra combinatorial structures, and some moves on S, exhibiting a surjection f:S->F such that f(P0)=f(P1) if and only if P0 and P1 are related by the moves. To obtain this result we first consider the subset F0 of F consisting of flows having all orbits homeomorphic to closed segments or points, constructing a combinatorial counterpart S0 for F0 and then adapting it to F., Comment: 26 pages, 24 figures

We consider hyperbolic 3-manifolds with either non-empty compact geodesic boundary, or some toric cusps, or both. For any such M we analyze what portion of the volume of M can be recovered by inserting in M boundary collars and cusp neighbourhoods with disjoint embedded interiors. Our main result is that this portion can only be maximal in some combinatorially extremal configurations. The techniques we employ are VERY elementary but the result is in our opinion of some interest., Comment: 15 pages

We consider in this paper the minimally twisted chain link with 5 components in the 3-sphere, and we analyze the Dehn surgeries on it, namely the Dehn fillings on its exterior M5. The 3-manifold M5 is a nicely symmetric hyperbolic one, filling which one gets a wealth of hyperbolic 3-manifolds having 4 or fewer (including 0) cusps. In view of Thurston's hyperbolic Dehn filling theorem it is then natural to face the problem of classifying all the exceptional fillings on M5, namely those yielding non-hyperbolic 3-manifolds. Here we completely solve this problem, also showing that, thanks to the symmetries of M5 and of some hyperbolic manifolds resulting from fillings of M5, the set of exceptional fillings on M5 is described by a very small amount of information., Comment: 46 pages, 10 figures. This new version uses the "hikmot" libraries to verify the numeric computations made by SnapPy