Degenerations for derived categories

We propose a theory of degenerations for derived module categories, analogous to degenerations in module varieties for module categories. In particular we define two types of degenerations, one algebraic and the other geometric. We show that these are equivalent, analogously to the Riemann-Zwara theorem for module varieties. Applications to tilting complexes are given, in particular that any two-term tilting complex is determined by its graded module structure

Modulation Classification for MIMO-OFDM Signals via Approximate Bayesian Inference

The problem of modulation classification for a multiple-antenna (MIMO) system employing orthogonal frequency division multiplexing (OFDM) is investigated under the assumption of unknown frequency-selective fading channels and signal-to-noise ratio (SNR). The classification problem is formulated as a Bayesian inference task, and solutions are proposed based on Gibbs sampling and mean field variational inference. The proposed methods rely on a selection of the prior distributions that adopts a latent Dirichlet model for the modulation type and on the Bayesian network formalism. The Gibbs sampling method converges to the optimal Bayesian solution and, using numerical results, its accuracy is seen to improve for small sample sizes when switching to the mean field variational inference technique after a number of iterations. The speed of convergence is shown to improve via annealing and random restarts. While most of the literature on modulation classification assume that the channels are flat fading, that the number of receive antennas is no less than that of transmit antennas, and that a large number of observed data symbols are available, the proposed methods perform well under more general conditions. Finally, the proposed Bayesian methods are demonstrated to improve over existing non-Bayesian approaches based on independent component analysis and on prior Bayesian methods based on the `superconstellation' method.Comment: To be appear in IEEE Trans. Veh. Technolog

Quantitative Assessment of the Anatomical Footprint of the C1 Pedicle Relative to the Lateral Mass: A Guide for C1 Lateral Mass Fixation

Study Design: Anatomic study. Objectives: To determine the relationship of the anatomical footprint of the C1 pedicle relative to the lateral mass (LM). Methods: Anatomic measurements were made on fresh frozen human cadaveric C1 specimens: pedicle width/height, LM width/height (minimum/maximum), LM depth, distance between LM’s medial aspect and pedicle’s medial border, distance between LM’s lateral aspect to pedicle’s lateral border, distance between pedicle’s inferior aspect and LM’s inferior border, distance between arch’s midline and pedicle’s medial border. The percentage of LM medial to the pedicle and the distance from the center of the LM to the pedicle’s medial wall were calculated. Results: A total of 42 LM were analyzed. The C1 pedicle’s lateral aspect was nearly confluent with the LM’s lateral border. Average pedicle width was 9.0 ± 1.1 mm, and average pedicle height was 5.0 ± 1.1 mm. Average LM width and depth were 17.0 ± 1.6 and 17.2 ± 1.6 mm, respectively. There was 6.9 ± 1.5 mm of bone medial to the medial C1 pedicle, which constituted 41% ± 9% of the LM’s width. The distance from C1 arch’s midline to the medial pedicle was 13.5 ± 2.0 mm. The LM’s center was 1.6 ± 1 mm lateral to the medial pedicle wall. There was on average 3.5 ± 0.6 mm of the LM inferior to the pedicle inferior border. Conclusions: The center of the lateral mass is 1.6 ± 1 mm lateral to the medial wall of the C1 pedicle and approximately 15 mm from the midline. There is 6.9 ± 1.5 mm of bone medial to the medial C1 pedicle. Thus, the medial aspect of C1 pedicle may be used as an anatomic reference for locating the center of the C1 LM for screw fixation