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- Mixed Hodge structures on character varieties of nilpotent groupsPublication . A. A. Florentino, Carlos; Lawton, Sean; Silva, JaimeLet Hom0(Ƭ, G) be the connected component of the identity of the variety of representations of a finitely generated nilpotent group into a connected reductive complex affine algebraic group G. We determine the mixed Hodge structure on the representation variety Hom0(Ƭ, G) and on the character variety Hom0(Ƭ, G)//G. We obtain explicit formulae (both closed and recursive) for the mixed Hodge polynomial of these representation and character varieties.
- Periodic attractors of nonautonomous flat-topped tent systemsPublication . Silva, LuisIn this work we will consider a family of nonautonomous dynamical systems x(k)(+1) = f(k)(x(k), lambda), lambda is an element of [-1, 1] (N0), generated by a one-parameter family of flat-topped tent maps g(alpha) (x), i.e., f(k)(x, lambda) = g(lambda k) (x) for all k is an element of N-0. We will reinterpret the concept of attractive periodic orbit in this context, through the existence of some periodic, invariant and attractive nonautonomous sets and establish sufficient conditions over the parameter sequences for the existence of such periodic attractors.
- Fractal analysis and ferroelectric properties of Nd(Zn-1/Ti-2(1)/(2))O-3(NZT)Publication . Khamoushi, Kouros; Serpa, CristinaThe challenges in productivity of satellite mobile devices are growing rapidly to overcome the question of miniaturization. The intention is to supply the electrical and microwave properties of materials by discovering their outstanding electronic properties. Neodymium Zinc Titanate (NZT) can be a promising ferroelectric material due to its stable dielectric and microwave properties. The grain size and shape of NZT have a strong influence on overall material performances. Therefore, shape, reconstruction and property of the coming compound take an important part and can be predicted before being utilized in the devices. The significant of this research is to define ferroelectric properties of NZT and to characterize it by using Fractal Nature Analysis (FNA). FNA is a powerful mathematical technique that could be applied to improve the grain shape and interface reconstruction. The fractal structure is identified by its self-similarity. The self-similarity of an object means a repetition of shapes in smaller scales. A measure of this structure is computed using the Hausdorff dimension. It is for the first time in this investigation the Fractal analysis method is applied for the microwave materials microstructure reconstruction which makes this research an innovative work and will open the door for Curie-Weiss law fractal correction. In connection to our previous research for dielectric properties fractalization, we had some characterization and reconstruction data which include the Hausdorff dimension (HD).
- Trapped modes in a fluid with three layers topped by a rigid lidPublication . Cal, Filipe; Dias, Gonçalo A. S.; Pereira, Bruno M. M.We consider trapping of linear water waves by a submerged horizontal cylinder in a three-layer fluid topped by a rigid lid. Trapped modes correspond to time harmonic oscillations with finite energy of the fluid surrounding a submerged structure and can be found as eigenfunctions of a certain spectral boundary-value problem. Our main result is a geometric condition relating the cross sections of the submerged parts of the obstacles and the line integrals along the parts of the interfaces pierced by the obstacles and guaranteeing the existence of trapped modes: This follows from variational techniques applied to a suitable operator formulation of the problem. Several examples of structures (piercing or not the interfaces between the fluid layers) satisfying the condition and supporting trapped modes are given.
- Automatic completion of data gaps applied to a system of water pumpsPublication . Enguiça, Ricardo; Soares, FilipaWe consider a time series with real data from a water lift station, equipped with three water pumps which are activated and deactivated depending on certain starting and halting thresholds. Given the water level and the number of active pumps, both read every 5 min, we aim to infer when each pump was activated or deactivated. To do so, we build an algorithm that sets a hierarchy of criteria based on the past and future of a given interval to identify which thresholds have been crossed during that interval. We then fill the gaps between the 5 min time steps, modeling the water level continuously with a piecewise linear function. This filling takes into account not only every water level reading and every previously identified change of status, but also the fact that activation and deactivation of a pump has no immediate effect on water level. This allows for the fulfillment of the ultimate objective of the problem in its real context, which is to provide the water management company an estimate of how long each pump has been working. Additionally, our estimates correct the errors contained in the time series regarding the number of active pumps.
- Continuous/discontinuous Galerkin approximations for a fourth-order nonlinear problemPublication . Lopes, Nuno; Oliveira, H. B. deWe introduce a Continuous/Discontinuous Galerkin Finite Element Method (CDFEM) with interior penalty terms to solve a nonlinear fourth-order problem that appears in the analysis of the confinement of fluid flows governed by the Stokes system. For the associated continuous and discrete problems, we prove the existence and uniqueness of weak solutions. Consistency, stability and convergence of the method are shown analytically. To show the applicability and robustness of the numerical model, several test cases are performed.
- Short-term load forecasting using time series clusteringPublication . Martins, Ana Alexandra; Lagarto, João; Canacsinh, Hiren; Reis, Francisco; Cardoso, Maria MargaridaShort-term load forecasting plays a major role in energy planning. Its accuracy has a direct impact on the way power systems are operated and managed. We propose a new Clustering-based Similar Pattern Forecasting algorithm (CSPF) for short-term load forecasting. It resorts to a K-Medoids clustering algorithm to identify load patterns and to the COMB distance to capture differences between time series. Clusters' labels are then used to identify similar sequences of days. Temperature information is also considered in the day-ahead load forecasting, resorting to the K-Nearest Neighbor approach. CSPF algorithm is intended to provide the aggregate forecast of Portugal's national load, for the next day, with a 15-min discretization, based on data from the Portuguese Transport Network Operator (TSO). CSPF forecasting performance, as evaluated by RMSE, MAE and MAPE metrics, outperforms three alternative/baseline methods, suggesting that the proposed approach is promising in similar applications.
- Extinction or coexistence in periodic Kolmogorov systems of competitive typePublication . Coelho, Isabel; Rebelo, Carlota; Sovrano, ElisaWe study a periodic Kolmogorov system describing two species nonlinear competition. We discuss coexistence and extinction of one or both species, and describe the domain of attraction of nontrivial periodic solutions in the axes, under conditions that generalise Gopalsamy conditions. Finally, we apply our results to a model of microbial growth and to a model of phyto-plankton competition under the e_ect of toxins.
- Cl− kinetic-energy release distributions from chlorobenzene and related molecules in electron transfer experimentsPublication . Kumar, Sarvesh; Pereira, Pedro; Garcia, Gustavo; Limão-Vieira, PauloWe report a novel and comprehensive analysis of the chlorine anion (Cl−) kinetic energy release distributions (KERDs) from electron transfer experiments at 12, 40 and 118 eV collision energies in the centre-of-mass frame. These distributions have been obtained from the shape and width of Cl− time-offlight mass spectra from collisions of neutral potassium (K) atoms with a set of selected neutral chlorinated compounds, viz. C6H5Cl, C6D5Cl, C6H11Cl and C6Cl6. The reactions producing bond breaking of the temporary negative ions formed with an excess of internal energy in such collisions, are a result of intramolecular energy redistribution through the different available degrees of freedom due to statistical degradation via vibrational excitation and partly due to direct transformation into translational energy of the fragment anions. The Cl− low-energy kinetic energy release, εd, has been fitted with a statistical function and the role of the different available resonances in the collision dynamics has been discussed, allowing therefore to obtain relevant information on the electronic structure involved in negative ion formation. From Cl− kinetic-energy release maxima as a function of the collision energy, C6Cl6 shows the lowest values which have been attributed to the strong competition with the parent anion formation. In contrast, C6H11Cl shows the highest values which result from this molecular system having no π delocalized electrons over the ring, and the electronic state spectroscopy is mostly dictated by relevant σ* antibonding character along the C–Cl coordinate.
- A multivariable prediction model to select colorectal surgical patients for co-managementPublication . Bayão Horta, A.; Brás-Geraldes, Carlos; Salgado, Cátia; Vieira, Susana; Xavier, Miguel; Papoila, Ana LuisaIntroduction: Increased life expectancy leads to older and frailer surgical patients. Co-management between medical and surgical specialities has proven favourable in complex situations. Selection of patients for co-management is full of difficulties. The aim of this study was to develop a clinical decision support tool to select surgical patients for co-management. Material and Methods: Clinical data was collected from patient electronic health records with an ICD-9 code for colorectal surgery from January 2012 to December 2015 at a hospital in Lisbon. The outcome variable consists in co-management signalling. A dataset from 344 patients was used to develop the prediction model and a second data set from 168 patients was used for external validation. Results: Using logistic regression modelling the authors built a five variable (age, burden of comorbidities, ASA-PS status, surgical risk and recovery time) predictive referral model for co-management. This model has an area under the curve (AUC) of 0.86 (95% CI: 0.81 - 0.90), a predictive Brier score of 0.11, a sensitivity of 0.80, a specificity of 0.82 and an accuracy of 81.3%. Discussion: Early referral of high-risk patients may be valuable to guide the decision on the best level of post-operative clinical care. We developed a simple bedside decision tool with a good discriminatory and predictive performance in order to select patients for comanagement. Conclusion: A simple bed-side clinical decision support tool of patients for co-management is viable, leading to potential improvement in early recognition and management of postoperative complications and reducing the ‘failure to rescue’. Generalizability to other clinical settings requires adequate customization and validation.