Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)

Context-free and context-sensitive dynamics in recurrent neural networks

Continuous-valued recurrent neural networks can learn mechanisms for processing context-free languages. The dynamics of such networks is usually based on damped oscillation around fixed points in state space and requires that the dynamical components are arranged in certain ways. It is shown that qualitatively similar dynamics with similar constraints hold for a(n)b(n)c(n), a context-sensitive language. The additional difficulty with a(n)b(n)c(n), compared with the context-free language a(n)b(n), consists of 'counting up' and 'counting down' letters simultaneously. The network solution is to oscillate in two principal dimensions, one for counting up and one for counting down. This study focuses on the dynamics employed by the sequential cascaded network, in contrast to the simple recurrent network, and the use of backpropagation through time. Found solutions generalize well beyond training data, however, learning is not reliable. The contribution of this study lies in demonstrating how the dynamics in recurrent neural networks that process context-free languages can also be employed in processing some context-sensitive languages (traditionally thought of as requiring additional computation resources). This continuity of mechanism between language classes contributes to our understanding of neural networks in modelling language learning and processing.

The intersection of people, technology and local space. PPGIS and Web in practice for participatory planning

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies

Towards cryogenic liquid –vapor energy storage units for space applications

Dissertation to obtain the Doctoral degree in Physics Engineering

Connecting free volume with shape memory properties in noncytotoxic gamma-irradiated polycyclooctene

The free volume holes of a shape memory polymer have been analysed considering that the empty space between molecules is necessary for the molecular motion, and the shape memory response is based on polymer segments acting as molecular switches through variable flexibility with temperature or other stimuli. Therefore, thermomechanical analysis (TMA) and positron annihilation lifetime spectroscopy (PALS) have been applied to analyse shape recovery and free volume hole sizes in gamma irradiated polycyclooctene (PCO) samples, as a non-cytotoxic alternative to more conventional PCO crosslinked via peroxide for future applications in medicine. Thus, a first approach relating structure, free volume holes and shape memory properties in gamma irradiated PCO is presented. The results suggest that free volume holes caused by gamma irradiation in PCO samples facilitate the recovery process by improving movement of polymer chains and open t possibilities for the design and control of the macroscopic response.

Cat(0) and Cat (-1) dimensions of torsion free

We show that a particular free-by-cyclic group has CAT(0) dimension equal to 2, but CAT(-1) dimension equal to 3. We also classify the minimal proper 2-dimensional CAT(0) actions of this group; they correspond, up to scaling, to a 1-parameter family of locally CAT(0) piecewise Euclidean metrics on a fixed presentation complex for the group. This information is used to produce an infinite family of 2-dimensional hyperbolic groups, which do not act properly by isometries on any proper CAT(0) metric space of dimension 2. This family includes a free-by-cyclic group with free kernel of rank 6.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

Navigator-gated free-breathing three-dimensional balanced fast field echo (TrueFISP) coronary magnetic resonance angiography.

RATIONALE AND OBJECTIVES: Recent developments of MR imaging equipment enabled high-quality steady state-free-precession (Balanced FFE, True-FISP) MR-imaging with a substantial 'T2 like' contrast, resulting in a high signal intensity of the blood-pool without the application of exogenous contrast agents. It is hypothesized that Balanced-FFE may be valuable for contrast enhancement in 3D free-breathing coronary MRA. MATERIALS AND METHODS: Navigator-gated free-breathing cardiac triggered coronary MRA was performed in 10 healthy adult subjects and three patients with radiograph defined coronary artery disease using a segmented k-space 3D Balanced FFE imaging sequence. RESULTS: High contrast-to-noise ratio between the blood-pool and the myocardium (29 +/- 8) and long segment visualization of both coronary arteries could be obtained in about 5 minutes during free breathing using the present navigator-gated Balanced-FFE coronary MRA approach. First patient results demonstrated successful display of coronary artery stenoses. CONCLUSION: Balanced FFE offers a potential alternative for endogenous contrast enhancement in navigator-gated free-breathing 3D coronary MRA. The obtained results together with the relatively short scanning time warrant further studies in larger patient collectives.

Self-Navigation with Compressed Sensing for 2D Translational Motion Correction in Free-Breathing Coronary MRI: A Feasibility Study.

PURPOSE: Respiratory motion correction remains a challenge in coronary magnetic resonance imaging (MRI) and current techniques, such as navigator gating, suffer from sub-optimal scan efficiency and ease-of-use. To overcome these limitations, an image-based self-navigation technique is proposed that uses "sub-images" and compressed sensing (CS) to obtain translational motion correction in 2D. The method was preliminarily implemented as a 2D technique and tested for feasibility for targeted coronary imaging. METHODS: During a 2D segmented radial k-space data acquisition, heavily undersampled sub-images were reconstructed from the readouts collected during each cardiac cycle. These sub-images may then be used for respiratory self-navigation. Alternatively, a CS reconstruction may be used to create these sub-images, so as to partially compensate for the heavy undersampling. Both approaches were quantitatively assessed using simulations and in vivo studies, and the resulting self-navigation strategies were then compared to conventional navigator gating. RESULTS: Sub-images reconstructed using CS showed a lower artifact level than sub-images reconstructed without CS. As a result, the final image quality was significantly better when using CS-assisted self-navigation as opposed to the non-CS approach. Moreover, while both self-navigation techniques led to a 69% scan time reduction (as compared to navigator gating), there was no significant difference in image quality between the CS-assisted self-navigation technique and conventional navigator gating, despite the significant decrease in scan time. CONCLUSIONS: CS-assisted self-navigation using 2D translational motion correction demonstrated feasibility of producing coronary MRA data with image quality comparable to that obtained with conventional navigator gating, and does so without the use of additional acquisitions or motion modeling, while still allowing for 100% scan efficiency and an improved ease-of-use. In conclusion, compressed sensing may become a critical adjunct for 2D translational motion correction in free-breathing cardiac imaging with high spatial resolution. An expansion to modern 3D approaches is now warranted.

Aortic vessel wall magnetic resonance imaging at 3.0 Tesla: a reproducibility study of respiratory navigator gated free-breathing 3D black blood magnetic resonance imaging.

The purpose of this study was to evaluate a free-breathing three-dimensional (3D) dual inversion-recovery (DIR) segmented k-space gradient-echo (turbo field echo [TFE]) imaging sequence at 3T for the quantification of aortic vessel wall dimensions. The effect of respiratory motion suppression on image quality was tested. Furthermore, the reproducibility of the aortic vessel wall measurements was investigated. Seven healthy subjects underwent 3D DIR TFE imaging of the aortic vessel wall with and without respiratory navigator. Subsequently, this sequence with respiratory navigator was performed twice in 10 healthy subjects to test its reproducibility. The signal-to-noise (SNR), contrast-to-noise ratio (CNR), vessel wall sharpness, and vessel wall volume (VWV) were assessed. Data were compared using the paired t-test, and the reproducibility of VWV measurements was evaluated using intraclass correlation coefficients (ICCs). SNR, CNR, and vessel wall sharpness were superior in scans performed with respiratory navigator compared to scans performed without. The ICCs concerning intraobserver, interobserver, and interscan reproducibility were excellent (0.99, 0.94, and 0.95, respectively). In conclusion, respiratory motion suppression substantially improves image quality of 3D DIR TFE imaging of the aortic vessel wall at 3T. Furthermore, this optimized technique with respiratory motion suppression enables assessment of aortic vessel wall dimensions with high reproducibility.

Pairing in a two-component ultracold Fermi gas: Phases with broken-space symmetries

We explore the phase diagram of a two-component ultracold atomic Fermi gas interacting with zero-range forces in the limit of weak coupling. We focus on the dependence of the pairing gap and the free energy on the variations in the number densities of the two species while the total density of the system is held fixed. As the density asymmetry is increased, the system exhibits a transition from a homogenous Bardeen-Cooper-Schrieffer (BCS) phase to phases with spontaneously broken global space symmetries. One such realization is the deformed Fermi surface superfluidity (DFS) which exploits the possibility of deforming the Fermi surfaces of the species into ellipsoidal form at zero total momentum of Cooper pairs. The critical asymmetries at which the transition from DFS to the unpaired state occurs are larger than those for the BCS phase. In this precritical region the DFS phase lowers the pairing energy of the asymmetric BCS state. We compare quantitatively the DFS phase to another realization of superconducting phases with broken translational symmetry: the single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell phase, which is characterized by a nonvanishing center-of-mass momentum of the Cooper pairs. The possibility of the detection of the DFS phase in the time-of-flight experiments is discussed and quantified for the case of 6Li atoms trapped in two different hyperfine states.

Nucleation rates in flat and curved space

Nucleation rates for tunneling processes in Minkowski and de Sitter space are investigated, taking into account one loop prefactors. In particular, we consider the creation of membranes by an antisymmetric tensor field, analogous to Schwinger pair production. This can be viewed as a model for the decay of a false (or true) vacuum at zero temperature in the thin wall limit. Also considered is the spontaneous nucleation of strings, domain walls, and monopoles during inflation. The instantons for these processes are spherical world sheets or world lines embedded in flat or de Sitter backgrounds. We find the contribution of such instantons to the semiclassical partition function, including the one loop corrections due to small fluctuations around the spherical world sheet. We suggest a prescription for obtaining, from the partition function, the distribution of objects nucleated during inflation. This can be seen as an extension of the usual formula, valid in flat space, according to which the nucleation rate is twice the imaginary part of the free energy. For the case of pair production, the results reproduce those that can be obtained using second quantization methods, confirming the validity of instanton techniques in de Sitter space. Throughout the paper, both the gravitational field and the antisymmetric tensor field are assumed external.