In-depth analysis and evaluation of diffusive glioma models

Glioma is one of the most aggressive types of brain tumor. Several mathematical models have been developed during the past two decades, toward simulating the mechanisms that govern the development of glioma. The most common models use the diffusion-reaction equation (DRE) for simulating the spatiotemporal variation of tumor cell concentration. Nevertheless, despite the applications presented, there has been little work on studying the details of the mathematical solution and implementation of the 3-D diffusion model and presenting a qualitative analysis of the algorithmic results. This paper presents a complete mathematical framework on the solution of the DRE using different numerical schemes. This framework takes into account all characteristics of the latest models, such as brain tissue heterogeneity, anisotropic tumor cell migration, chemotherapy, and resection modeling. The different numerical schemes presented have been evaluated based upon the degree to which the DRE exact solution is approximated. Experiments have been conducted both on real datasets and a test case for which there is a known algebraic expression of the solution. Thus, it is possible to calculate the accuracy of the different models.     

On the buckling and vibration of antisymmetric angle-ply laminated circular cylindrical shells

The buckling and free vibration problem of a thin composite antisymmetric angle-ply laminated circular cylindrical shell is studied. The Donnell-type equations of motion, in terms of the shell middle surface displacement components, are used and solved approximately by means of Galerkin's method. Numerical results are presented and the expectation that the bending-stretching coupling phenomenon rapidly dies out as the number of layers increases is confirmed.     

Patient effective dose and radiogenic risks from fluoroscopically assisted surgical reconstruction of femoral fractures

The objectives were to assess patient effective radiation dose from fluoroscopically guided surgical reconstruction of femoral fractures and provide normalized data for the estimation of patient effective dose and risks associated with such procedures performed in any laboratory. The fluoroscopic control required during surgical reconstruction of femoral fractures was classified into two types identified by beam orientation, i.e., posterior-anterior (PA) and lateral crosstable (LC) exposures. The duration and the dose area product (DAP) of each exposure were monitored in 24 patients with femoral fractures. Patient dose per DAP unit and per minute of fluoroscopy were measured at 14 radiosensitive organs/tissues using an anthropomorphic phantom and thermoluminescence dosimetry. The typical effective dose to patients with femoral fracture treated surgically in our institution was 11.6-21.7 microSv. This effective dose is estimated to cause an excess of 1.4 fatal cancers per million patients treated, and an excess of 0.4 hereditary disorders per million of births. Induction of deterministic skin injuries to treated patients is highly improbable at the dose levels found in this study. Patient effective dose and associated risks from a typical fluoroscopically guided surgical fixation of femoral fracture are low. However, they may be significantly elevated if treated patients are young individuals and/or the fluoroscopic exposure is prolonged. The present data may be used to determine effective dose to patients undergoing surgical reconstruction of femoral fracture in any institution.     

Switching networked attitude control of an unmanned quadrotor

In this article, a switching networked attitude controller for an unmanned quadrotor over a wireless sensor network is presented. To deal with the network induced time varying delays, the quadrotor is being modeled as a switching time varying linear system, while the applied switching output feedback control scheme, is calculated based on Linear Matrix Inequalities, and is able to guarantee the stability of the quadrotor under arbitrary changes in the time delays.     

Efficiently adapting graphical models for selectivity estimation

Query optimizers rely on statistical models that succinctly describe the underlying data. Models are used to derive cardinality estimates for intermediate relations, which in turn guide the optimizer to choose the best query execution plan. The quality of the resulting plan is highly dependent on the accuracy of the statistical model that represents the data. It is well known that small errors in the model estimates propagate exponentially through joins, and may result in the choice of a highly sub-optimal query execution plan. Most commercial query optimizers make the attribute value independence assumption: all attributes are assumed to be statistically independent. This reduces the statistical model of the data to a collection of one-dimensional synopses (typically in the form of histograms), and it permits the optimizer to estimate the selectivity of a predicate conjunction as the product of the selectivities of the constituent predicates. However, this independence assumption is more often than not wrong, and is considered to be the most common cause of sub-optimal query execution plans chosen by modern query optimizers. We take a step towards a principled and practical approach to performing cardinality estimation without making the independence assumption. By carefully using concepts from the field of graphical models, we are able to factor the joint probability distribution over all the attributes in the database into small, usually two-dimensional distributions, without a significant loss in estimation accuracy. We show how to efficiently construct such a graphical model from the database using only two-way join queries, and we show how to perform selectivity estimation in a highly efficient manner. We integrate our algorithms into the PostgreSQL DBMS. Experimental results indicate that estimation errors can be greatly reduced, leading to orders of magnitude more efficient query execution plans in many cases. Optimization time is kept in the range of tens of milliseconds, making this a practical approach for industrial-strength query optimizers.     

On a class of optimal abstractions of finite-state machines

Anabstraction A of an fsmM consists in partitioning its states, inputs, and outputs into groups, thus turning it into a non-deterministic fsmM _A. For fixed sets of states, inputs, and outputs, and abstraction generally maps a number of machinesM defined on these sets into the sameM _A. We would like to find anoptimal abstractionA ^* which minimizes this number, while lumping the states, inputs, and outputs into a specified number of classes. We extend these ideas to an fsmM operating in a random environment, and show that the abstraction results in a probabilistic fsm . Thinking of changes inM's output map as resulting in machinesM≠MM, we want to find anA ^* that minimizes the number ofMM which are such that the transition probabilities of their abstracted version are identical to those of the specification machine . SuchMM arise from statistically-undetectable output faults inM. Abstractions are directly applicable to the monitoring of a complex system by an observer for deviations from correct behavior (faults). Complex systems are usually accessible through restricted interfaces, which do not allow the observer to distinguish among all states, inputs, and outputs, thus rendering some faulty transitions undetectable. An optimal interface design will minimize the number of such undetectable faults. Assuming that only single-transition output faults occur inM, we show that each of the classes into which the abstraction lumps the outputs contributes a number of undetectable output faults. We then show that the problem of partitioning the outputs into a given number of classes that minimizes the maximum of these numbers is NP-complete. However, we give (a) an approximate minimization algorithm, running in time linear in the number of classes and quadratic in the number ofM's outputs, and (b) a lower bound on the minimum, computable in the same amount of time. The concept of optimal abstractions is illustrated by numerical results on combinational logic circuits that perform arithmetical operations. The results shed light on the trade-off between model simplification and the ability to detect erroneous behaviors in complex systems.     

Switching model predictive attitude control for a quadrotor helicopter subject to atmospheric disturbances

In this article a switching model predictive attitude controller for an unmanned quadrotor helicopter subject to atmospheric disturbances is presented. The proposed control scheme is computed based on a piecewise affine (PWA) model of the quadrotor's attitude dynamics, where the effects of the atmospheric turbulence are taken into consideration as additive disturbances. The switchings among the PWA models are ruled by the rate of the rotation angles and for each PWA system a corresponding model predictive controller is computed. The suggested algorithm is verified in experimental studies in the execution of sudden maneuvers subject to forcible wind disturbances. The quadrotor rejects the induced wind disturbances while performing accurate attitude tracking.     

Optimal pixel aspect ratio for enhanced 3D TV visualization

In multiview 3D TV, a pair of corresponding pixels in adjacent 2D views contributes to the reconstruction of voxels (3D pixels) in the 3D scene. We analyze this reconstruction process and determine the optimal pixel aspect ratio based on which the estimated object position can be improved given specific imaging or viewing configurations and constraints. By applying mathematical modeling, we deduce the optimal solutions for two general stereo configurations: parallel and with vergence. We theoretically show that for a given total resolution a finer horizontal resolution, compared to the usual uniform pixel distribution, in general, provides a better 3D visual experience for both configurations. The optimal value may vary depending on different configuration parameter values. We validate our theoretical results by conducting subjective studies using a set of simulated non-square discretized red–blue stereo pairs and show that human observers indeed have a better 3D viewing experience with an optimized vs. a non-optimized representation of 3D-models.     

Learning SO(3) Equivariant Representations with Spherical CNNs

International Journal of Computer Vision - We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification...