On homotopy spheres of low dimension

Let M be a smooth compact manifold homotopy equivalent to the 4-sphere S^4. Then M x R^1 is homeomorphism co S^4 x R^1.

Classic Nintendo games are (computationally) hard

We prove NP-hardness results for five of Nintendo's largest video game franchises: Mario, Donkey Kong, Legend of Zelda, Metroid, and Pokémon. Our results apply to generalized versions of Super Mario Bros.1-3, The Lost Levels, and Super Mario World; Donkey Kong Country 1-3; all Legend of Zelda games; all Metroid games; and all Pokémon role-playing games. In addition, we prove PSPACE-completeness of the Donkey Kong Country games and several Legend of Zelda games.

Single particle motion of polymeric, colloidal, and biological materials

Small particles and their dynamics are of widespread interest due both to their unique properties and their ubiquity. Here, we investigate several classes of small particles: colloids, polymers, and liposomes. All these particles, due to their size on the order of microns, exhibit significant similarity in that they are large enough to be visualized in microscopes, but small enough to be significantly influenced by thermal (or Brownian) motion. Further, similar optical microscopy and experimental techniques are commonly employed to investigate all these particles. In this work, we develop single particle tracking techniques, which allow thorough characterization of individual particle dynamics, observing many behaviors which would be overlooked by methods which time or ensemble average. The various particle systems are also similar in that frequently, the signal-to-noise ratio represented a significant concern. In many cases, development of image analysis and particle tracking methods optimized to low signal-to-noise was critical to performing experimental observations. The simplest particles studied, in terms of their interaction potentials, were chemically homogeneous (though optically anisotropic) hard-sphere colloids. Using these spheres, we explored the comparatively underdeveloped conjunction of translation and rotation and particle hydrodynamics. Developing off this, the dynamics of clusters of spherical colloids were investigated, exploring how shape anisotropy influences the translation and rotation respectively. Transitioning away from uniform hard-sphere potentials, the interactions of amphiphilic colloidal particles were explored, observing the effects of hydrophilic and hydrophobic interactions upon pattern assembly and inter-particle dynamics. Interaction potentials were altered in a different fashion by working with suspensions of liposomes, which, while homogeneous, introduce the possibility of deformation. Even further degrees of freedom were introduced by observing the interaction of particles and then polymers within polymer suspensions or along lipid tubules. Throughout, while examination of the trajectories revealed that while by some measures, the averaged behaviors accorded with expectation, often closer examination made possible by single particle tracking revealed novel and unexpected phenomena.

Shape and chemically anisotropic colloidal particles: A theoretical study of their structure, phase behavior, and slow dynamics

A detailed non-equilibrium state diagram of shape-anisotropic particle fluids is constructed. The effects of particle shape are explored using Naive Mode Coupling Theory (NMCT), and a single particle Non-linear Langevin Equation (NLE) theory. The dynamical behavior of non-ergodic fluids are discussed. We employ a rotationally frozen approach to NMCT in order to determine a transition to center of mass (translational) localization. Both ideal and kinetic glass transitions are found to be highly shape dependent, and uniformly increase with particle dimensionality. The glass transition volume fraction of quasi 1- and 2- dimensional particles fall monotonically with the number of sites (aspect ratio), while 3-dimensional particles display a non-monotonic dependence of glassy vitrification on the number of sites. Introducing interparticle attractions results in a far more complex state diagram. The ideal non-ergodic boundary shows a glass-fluid-gel re-entrance previously predicted for spherical particle fluids. The non-ergodic region of the state diagram presents qualitatively different dynamics in different regimes. They are qualified by the different behaviors of the NLE dynamic free energy. The caging dominated, repulsive glass regime is characterized by long localization lengths and barrier locations, dictated by repulsive hard core interactions, while the bonding dominated gel region has short localization lengths (commensurate with the attraction range), and barrier locations. There exists a small region of the state diagram which is qualified by both glassy and gel localization lengths in the dynamic free energy. A much larger (high volume fraction, and high attraction strength) region of phase space is characterized by short gel-like localization lengths, and long barrier locations. The region is called the attractive glass and represents a 2-step relaxation process whereby a particle first breaks attractive physical bonds, and then escapes its topological cage. The dynamic fragility of fluids are highly particle shape dependent. It increases with particle dimensionality and falls with aspect ratio for quasi 1- and 2- dimentional particles. An ultralocal limit analysis of the NLE theory predicts universalities in the behavior of relaxation times, and elastic moduli. The equlibrium phase diagram of chemically anisotropic Janus spheres and Janus rods are calculated employing a mean field Random Phase Approximation. The calculations for Janus rods are corroborated by the full liquid state Reference Interaction Site Model theory. The Janus particles consist of attractive and repulsive regions. Both rods and spheres display rich phase behavior. The phase diagrams of these systems display fluid, macrophase separated, attraction driven microphase separated, repulsion driven microphase separated and crystalline regimes. Macrophase separation is predicted in highly attractive low volume fraction systems. Attraction driven microphase separation is charaterized by long length scale divergences, where the ordering length scale determines the microphase ordered structures. The ordering length scale of repulsion driven microphase separation is determined by the repulsive range. At the high volume fractions, particles forgo the enthalpic considerations of attractions and repulsions to satisfy hard core constraints and maximize vibrational entropy. This results in site length scale ordering in rods, and the sphere length scale ordering in Janus spheres, i.e., crystallization. A change in the Janus balance of both rods and spheres results in quantitative changes in spinodal temperatures and the position of phase boundaries. However, a change in the block sequence of Janus rods causes qualitative changes in the type of microphase ordered state, and induces prominent features (such as the Lifshitz point) in the phase diagrams of these systems. A detailed study of the number of nearest neighbors in Janus rod systems reflect a deep connection between this local measure of structure, and the structure factor which represents the most global measure of order.

Three dimensional study to quantify the relationship between facial hard and soft tissue movement as a result of orthognathic surgery

Introduction Prediction of soft tissue changes following orthognathic surgery has been frequently attempted in the past decades. It has gradually progressed from the classic “cut and paste” of photographs to the computer assisted 2D surgical prediction planning; and finally, comprehensive 3D surgical planning was introduced to help surgeons and patients to decide on the magnitude and direction of surgical movements as well as the type of surgery to be considered for the correction of facial dysmorphology. A wealth of experience was gained and numerous published literature is available which has augmented the knowledge of facial soft tissue behaviour and helped to improve the ability to closely simulate facial changes following orthognathic surgery. This was particularly noticed following the introduction of the three dimensional imaging into the medical research and clinical applications. Several approaches have been considered to mathematically predict soft tissue changes in three dimensions, following orthognathic surgery. The most common are the Finite element model and Mass tensor Model. These were developed into software packages which are currently used in clinical practice. In general, these methods produce an acceptable level of prediction accuracy of soft tissue changes following orthognathic surgery. Studies, however, have shown a limited prediction accuracy at specific regions of the face, in particular the areas around the lips. Aims The aim of this project is to conduct a comprehensive assessment of hard and soft tissue changes following orthognathic surgery and introduce a new method for prediction of facial soft tissue changes.   Methodology The study was carried out on the pre- and post-operative CBCT images of 100 patients who received their orthognathic surgery treatment at Glasgow dental hospital and school, Glasgow, UK. Three groups of patients were included in the analysis; patients who underwent Le Fort I maxillary advancement surgery; bilateral sagittal split mandibular advancement surgery or bimaxillary advancement surgery. A generic facial mesh was used to standardise the information obtained from individual patient’s facial image and Principal component analysis (PCA) was applied to interpolate the correlations between the skeletal surgical displacement and the resultant soft tissue changes. The identified relationship between hard tissue and soft tissue was then applied on a new set of preoperative 3D facial images and the predicted results were compared to the actual surgical changes measured from their post-operative 3D facial images. A set of validation studies was conducted. To include: • Comparison between voxel based registration and surface registration to analyse changes following orthognathic surgery. The results showed there was no statistically significant difference between the two methods. Voxel based registration, however, showed more reliability as it preserved the link between the soft tissue and skeletal structures of the face during the image registration process. Accordingly, voxel based registration was the method of choice for superimposition of the pre- and post-operative images. The result of this study was published in a refereed journal. • Direct DICOM slice landmarking; a novel technique to quantify the direction and magnitude of skeletal surgical movements. This method represents a new approach to quantify maxillary and mandibular surgical displacement in three dimensions. The technique includes measuring the distance of corresponding landmarks digitized directly on DICOM image slices in relation to three dimensional reference planes. The accuracy of the measurements was assessed against a set of “gold standard” measurements extracted from simulated model surgery. The results confirmed the accuracy of the method within 0.34mm. Therefore, the method was applied in this study. The results of this validation were published in a peer refereed journal. • The use of a generic mesh to assess soft tissue changes using stereophotogrammetry. The generic facial mesh played a major role in the soft tissue dense correspondence analysis. The conformed generic mesh represented the geometrical information of the individual’s facial mesh on which it was conformed (elastically deformed). Therefore, the accuracy of generic mesh conformation is essential to guarantee an accurate replica of the individual facial characteristics. The results showed an acceptable overall mean error of the conformation of generic mesh 1 mm. The results of this study were accepted for publication in peer refereed scientific journal. Skeletal tissue analysis was performed using the validated “Direct DICOM slices landmarking method” while soft tissue analysis was performed using Dense correspondence analysis. The analysis of soft tissue was novel and produced a comprehensive description of facial changes in response to orthognathic surgery. The results were accepted for publication in a refereed scientific Journal. The main soft tissue changes associated with Le Fort I were advancement at the midface region combined with widening of the paranasal, upper lip and nostrils. Minor changes were noticed at the tip of the nose and oral commissures. The main soft tissue changes associated with mandibular advancement surgery were advancement and downward displacement of the chin and lower lip regions, limited widening of the lower lip and slight reversion of the lower lip vermilion combined with minimal backward displacement of the upper lip were recorded. Minimal changes were observed on the oral commissures. The main soft tissue changes associated with bimaxillary advancement surgery were generalized advancement of the middle and lower thirds of the face combined with widening of the paranasal, upper lip and nostrils regions. In Le Fort I cases, the correlation between the changes of the facial soft tissue and the skeletal surgical movements was assessed using PCA. A statistical method known as ’Leave one out cross validation’ was applied on the 30 cases which had Le Fort I osteotomy surgical procedure to effectively utilize the data for the prediction algorithm. The prediction accuracy of soft tissue changes showed a mean error ranging between (0.0006mm±0.582) at the nose region to (-0.0316mm±2.1996) at the various facial regions.

An Approach to Manage Reconfigurations and Reduce Area Cost in Hard Real-Time Reconfigurable Systems

This article presents a methodology to build real-time reconfigurable systems that ensure that all the temporal constraints of a set of applications are met, while optimizing the utilization of the available reconfigurable resources. Starting from a static platform that meets all the real-time deadlines, our approach takes advantage of run-time reconfiguration in order to reduce the area needed while guaranteeing that all the deadlines are still met. This goal is achieved by identifying which tasks must be always ready for execution in order to meet the deadlines, and by means of a methodology that also allows reducing the area requirements.

Erosive potential of sugar-free hard candies dissolved in water and artificial saliva

Aim: To compare the acidity of sugar-free hard candies dissolved in water and artificial saliva. Methods: Sugar-free Flopi Florestal hard candies (grape, strawberry, cherry, orange, ginger, lemon balm, fennel) were selected and grouped in 2 groups: G-1 (candies dissolved in distilled water) and G-2 (candies dissolved in artificial saliva). Candies were triturated with a porcelain pestle, yielding two samples of 20 g. Samples were dissolved in 120 mL distilled water (G-1) and 120 mL artificial saliva (20 mM NaHCO3, 3 mM NaH2PO4.H2O and 1 mM CaCl2.2H2O) (G-2), obtaining three samples of 30 mL for each of the flavors and groups. pH was measured using potentiometer and combined glass electrode. Titratable acidity was evaluated by adding 100 μL 1M NaOH aliquots until reaching pH 5.5. For statistical analysis, analysis of variance (ANOVA) was used. Means were compared by the Tukey test at 5% significance level (p<0.05) Results: All flavors of G-1 showed pH values below 5.5. Comparison of groups in the same flavor showed a significant increase in pH in flavors of G-2. Comparison of the titratable acidity between G-1 and G-2, showed that fruit flavors were significantly different from each other, with reduced acidity in G-2. Conclusions: All evaluated candies are acid, and dilution in artificial saliva raised their pH and lowered their titratable acidity, reducing their erosive potential.

Positron Emission Tomography (PET) Tumor Segmentation and Quantification: Development of New Algorithms

Tumor functional volume (FV) and its mean activity concentration (mAC) are the quantities derived from positron emission tomography (PET). These quantities are used for estimating radiation dose for a therapy, evaluating the progression of a disease and also use it as a prognostic indicator for predicting outcome. PET images have low resolution, high noise and affected by partial volume effect (PVE). Manually segmenting each tumor is very cumbersome and very hard to reproduce. To solve the above problem I developed an algorithm, called iterative deconvolution thresholding segmentation (IDTS) algorithm; the algorithm segment the tumor, measures the FV, correct for the PVE and calculates mAC. The algorithm corrects for the PVE without the need to estimate camera’s point spread function (PSF); also does not require optimizing for a specific camera. My algorithm was tested in physical phantom studies, where hollow spheres (0.5-16 ml) were used to represent tumors with a homogeneous activity distribution. It was also tested on irregular shaped tumors with a heterogeneous activity profile which were acquired using physical and simulated phantom. The physical phantom studies were performed with different signal to background ratios (SBR) and with different acquisition times (1-5 min). The algorithm was applied on ten clinical data where the results were compared with manual segmentation and fixed percentage thresholding method called T50 and T60 in which 50% and 60% of the maximum intensity respectively is used as threshold. The average error in FV and mAC calculation was 30% and -35% for 0.5 ml tumor. The average error FV and mAC calculation were ~5% for 16 ml tumor. The overall FV error was ~10% for heterogeneous tumors in physical and simulated phantom data. The FV and mAC error for clinical image compared to manual segmentation was around -17% and 15% respectively. In summary my algorithm has potential to be applied on data acquired from different cameras as its not dependent on knowing the camera’s PSF. The algorithm can also improve dose estimation and treatment planning.

Spheres of Influence: A Few Reflections on the Concept

In the frame of the Ukrainian crisis the question of spheres of influence has returned to political discourse. This may be an awkward subject, but what if we only deny the existence of such power constellations as spheres of influence? Do spheres of influence exist, or are they relics of history, and mere rhetoric? And if they exist, where can we find them? The hypothesis in this article is that instead of being a tangible reality, spheres of influence are obscure and contested political constructions, which nevertheless can have an impact on political behaviour. To demonstrate this, the article will first introduce a few examples of the current use of the concept. Secondly, a few remarks follow concerning the different IR schools of thought, and conceptual history as a method. Next, the article turns to discussing a few dictionaries and the empirical material for the present inquiry, which consists of recent textbooks, i.e. the current political science curriculum in one particular university, at the University of Tampere, Finland. More empirical cases deal with the division of Africa, the post-WWII situation, and the Hungarian revolution of 1956.