Model categories for orthogonal calculus

We restate the notion of orthogonal calculus in terms of model categories. This provides a cleaner set of results and makes the role of O(n)-equivariance clearer. Thus we develop model structures for the category of n-polynomial and n-homogeneous functors, along with Quillen pairs relating them. We then classify n-homogeneous functors, via a zig-zag of Quillen equivalences, in terms of spectra with an O(n)-action. This improves upon the classification theorem of Weiss. As an application, we develop a variant of orthogonal calculus by replacing topological spaces with orthogonal spectra.

Power Allocation Strategies across N Orthogonal Channels at Both Source and Relay

A wireless relay network with one source, one relay and one destination is considered, where nodes communicate via N orthogonal channels. We develop optimal power allocation strategies at both the source and relay for maximizing the overall source-destination capacity under individual power constraints at the source and relay. Some properties of the optimal solution are studied. © 2012 IEEE.

Comparison of adaptive beamforming and orthogonal STBC with outdated feedback

We compare the achievable performance of adaptive beamforming (A-BF) and adaptive orthogonal space time block coding (A-OSTBC) with outdated channel feedback. We extend our single user setup to multiuser diversity systems employing adaptive modulation, and illustrate the impact of feedback delay on the multiuser diversity gain with either A-OSTBC or A-BF. Using closed-form expressions for spectral efficiency and average BER of a multiuser diversity system derived in this paper, we prove that the A-BF scheme outperforms the A-OSTBC scheme with no feedback delay. However, when the feedback delay is large, the A-OSTBC scheme achieves better performance due to the reduced diversity advantage of A-BF. We observe that more transmit antennas bring higher spectral efficiency for BF. With small feedback delay, this becomes inverted using OSTBC, due to the effect of channel-hardening. Interestingly, however, we show that A-OSTBC with multiple users enjoys improved spectral efficiency when the number of transmit antennas is increased and the feedback delay is significant

Orthogonal space-time block coded rate-adaptive modulation with outdated feedbasck

Abstract-Channel state information (CSI) at the transmitter can be used to adapt transmission rate or antenna gains in multi-antenna systems. We propose a rate-adaptive M-QAM scheme equipped with orthogonal space-time block coding with simple outdated, finite-rate feedback over independent flat fading channels. We obtain closed-form expressions for the average BER and throughput for our scheme, and analyze the effects of possibly delayed feedback on the performance gains. We derive optimal switching thresholds maximizing the average throughput under average and outage BER constraints with outdated feedback. Our numerical results illustrate the immunity of our optimal thresholds to delayed feedback.

Power allocation strategies across N orthogonal channels for single-relay networks at both source and relay

We consider a wireless relay network with one source, one relay and one destination, where communications between nodes are preformed over N orthogonal channels. This, for example, is the case when orthogonal frequency division multiplexing is employed for data communications. Since the power available at the source and relay is limited, we study optimal power allocation strategies at the source and relay in order to maximize the overall source-destination capacity. Depending on the availability of the channel state information at both the source and relay or only at the relay, power allocation is performed at both the source and relay or only at the relay. Considering different setups for the problem, various optimization problems are formulated and solved. Some properties of the optimal solution are also proved.

Implementation of a non-orthogonal model for the finite element simulation of textile composite draping

In the pursuit of producing high quality, low-cost composite aircraft structures, out-of-autoclave manufacturing processes for textile reinforcements are being simulated with increasing accuracy. This paper focuses on the continuum-based, finite element modelling of textile composites as they deform during the draping process. A non-orthogonal constitutive model tracks yarn orientations within a material subroutine developed for Abaqus/Explicit, resulting in the realistic determination of fabric shearing and material draw-in. Supplementary material characterisation was experimentally performed in order to define the tensile and non-linear shear behaviour accurately. The validity of the finite element model has been studied through comparison with similar research in the field and the experimental lay-up of carbon fibre textile reinforcement over a tool with double curvature geometry, showing good agreement.

Orthogonal Vector Approach for Synthesis of Multi-beam Directional Modulation Transmitters

An orthogonal vector approach is proposed for the synthesis of multi-beam directional modulation (DM) transmitters. These systems have the capability of concurrently projecting independent data streams into different specified spatial directions while simultaneously distorting signal constellations in all other directions. Simulated bit error rate (BER) spatial distributions are presented for various multi-beam system configurations in order to illustrate representative examples of physical layer security performance enhancement that can be achieved.

Orthogonal targeting of EGFRvIII expressing glioblastomas through simultaneous EGFR and PLK1 inhibition

We identified a synthetic lethality between PLK1 silencing and the expression of an oncogenic Epidermal Growth Factor Receptor, EGFRvIII. PLK1 promoted homologous recombination (HR), mitigating EGFRvIII induced oncogenic stress resulting from DNA damage accumulation. Accordingly, PLK1 inhibition enhanced the cytotoxic effects of the DNA damaging agent, temozolomide (TMZ). This effect was significantly more pronounced in an Ink4a/Arf(-/-) EGFRvIII glioblastoma model relative to an Ink4a/Arf(-/-) PDGF-β model. The tumoricidal and TMZ-sensitizing effects of BI2536 were uniformly observed across Ink4a/Arf(-/-) EGFRvIII glioblastoma clones that acquired independent resistance mechanisms to EGFR inhibitors, suggesting these resistant clones retain oncogenic stress that required PLK1 compensation. Although BI2536 significantly augmented the anti-neoplastic effect of EGFR inhibitors in the Ink4a/Arf(-/-) EGFRvIII model, durable response was not achieved until TMZ was added. Our results suggest that optimal therapeutic effect against glioblastomas requires a "multi-orthogonal" combination tailored to the molecular physiology associated with the target cancer genome.

Investigation of chip formation and fracture toughness in orthogonal cutting of UD-CFRP

Features of chip formation can inform the mechanism of a machining process. In this paper, a series of orthogonal cutting experiments were carried out on unidirectional carbon fiber reinforced polymer (UD-CFRP) under cutting speed of 0.5 m/min. The specially designed orthogonal cutting tools and high-speed camera were used in this paper. Two main factors are found to influence the chip morphology, namely the depth of cut (DOC) and the fiber orientation (angle 휃), and the latter of which plays a more dominant role. Based on the investigation of chip formation, a new approach is proposed for predicting fracture toughness of the newly machined surface and the total energy consumption during CFRP orthogonal cutting is introduced as a function of the surface energy of machined surface, the energy consumed to overcome friction, and the energy for chip fracture. The results show that the proportion of energy spent on tool-chip friction is the greatest, and the proportions of energy spent on creating new surface decrease with the increasing of fiber angle.

Two-Stage Orthogonal Least Squares Methods for Neural Network Construction

A number of neural networks can be formulated as the linear-in-the-parameters models. Training such networks can be transformed to a model selection problem where a compact model is selected from all the candidates using subset selection algorithms. Forward selection methods are popular fast subset selection approaches. However, they may only produce suboptimal models and can be trapped into a local minimum. More recently, a two-stage fast recursive algorithm (TSFRA) combining forward selection and backward model refinement has been proposed to improve the compactness and generalization performance of the model. This paper proposes unified two-stage orthogonal least squares methods instead of the fast recursive-based methods. In contrast to the TSFRA, this paper derives a new simplified relationship between the forward and the backward stages to avoid repetitive computations using the inherent orthogonal properties of the least squares methods. Furthermore, a new term exchanging scheme for backward model refinement is introduced to reduce computational demand. Finally, given the error reduction ratio criterion, effective and efficient forward and backward subset selection procedures are proposed. Extensive examples are presented to demonstrate the improved model compactness constructed by the proposed technique in comparison with some popular methods.