Globally optimal on-line learning rules for multi-layer neural networks

We present a method for determining the globally optimal on-line learning rule for a soft committee machine under a statistical mechanics framework. This rule maximizes the total reduction in generalization error over the whole learning process. A simple example demonstrates that the locally optimal rule, which maximizes the rate of decrease in generalization error, may perform poorly in comparison.

Globally optimal on-line learning rules

We present a method for determining the globally optimal on-line learning rule for a soft committee machine under a statistical mechanics framework. This work complements previous results on locally optimal rules, where only the rate of change in generalization error was considered. We maximize the total reduction in generalization error over the whole learning process and show how the resulting rule can significantly outperform the locally optimal rule.

The role of stochasticity in an information-optimal neural population code

In this paper we consider the optimisation of Shannon mutual information (MI) in the context of two model neural systems The first is a stochastic pooling network (population) of McCulloch-Pitts (MP) type neurons (logical threshold units) subject to stochastic forcing; the second is (in a rate coding paradigm) a population of neurons that each displays Poisson statistics (the so called 'Poisson neuron'). The mutual information is optimised as a function of a parameter that characterises the 'noise level'-in the MP array this parameter is the standard deviation of the noise, in the population of Poisson neurons it is the window length used to determine the spike count. In both systems we find that the emergent neural architecture and; hence, code that maximises the MI is strongly influenced by the noise level. Low noise levels leads to a heterogeneous distribution of neural parameters (diversity), whereas, medium to high noise levels result in the clustering of neural parameters into distinct groups that can be interpreted as subpopulations In both cases the number of subpopulations increases with a decrease in noise level. Our results suggest that subpopulations are a generic feature of an information optimal neural population.

Exchange rate economic exposure and hedging:the significance of currency options

This thesis focuses on the theoretical examination of the exchange rate economic (operating) exposure within the context of the theory of the firm, and proposes some hedging solutions using currency options. The examination of economic exposure is based on such parameters as firms' objectives, industry structure and production cost efficiency. In particular, it examines an hypothetical exporting firm with costs in domestic currency, which faces competition from foreign firms in overseas markets and has a market share expansion objective. Within this framework, the hypothesis is established that economic exposure, portrayed in a diagram connecting export prices and real exchange rates, is asymmetric (i.e. the negative effects depreciation are higher than the positive effects of a currency depreciation). In this case, export business can be seen as a real option, given by exporting firms to overseas customer. Different scenarios about the asymmetry hypothesis can be derived for different assumptions about the determinants of economic exposure. Having established the asymmetry hypothesis, the hedging against this exposure is analysed. The hypothesis is established, that a currency call option should be used in hedging against asymmetric economic exposure. Further, some advanced currency options stategies are discussed, and their use in hedging several scenarios of exposure is indicated, establishing the hypothesis that, the optimal options strategy is a function of the determinants of exposure. Some extensions on the theoretical analysis are examined. These include the hedging of multicurrency exposure using options, and the exposure of a purely domestic firm facing import competition. The empirical work addresses two issues: the empirical validity of the asymmetry hypothesis and the examination of the hedging effectiveness of currency options.

Theoretic analysis of IEEE 802.11 rate adaptation algorithm SampleRate

In this paper we investigate rate adaptation algorithm SampleRate, which spends a fixed time on bit-rates other than the currently measured best bit-rate. A simple but effective analytic model is proposed to study the steady-state behavior of the algorithm. Impacts of link condition, channel congestion and multi-rate retry on the algorithm performance are modeled. Simulations validate the model. It is also observed there is still a large performance gap between SampleRate and optimal scheme in case of high frame collision probability.

Susceptibility to pattern glare and the effect of spectral filters on rate of reading and visual search in stroke patients

The present thesis investigates pattern glare susceptibility following stroke and the immediate and prolonged impact of prescribing optimal spectral filters on reading speed, accuracy and visual search performance. Principal observations: A case report has shown that visual stress can occur following stroke. The use of spectral filters and precision tinted lenses proved to be a successful intervention in this case, although the parameters required modification following a further stroke episode. Stroke subjects demonstrate elevated levels of pattern glare compared to normative data values and a control group. Initial use of an optimal spectral filter in a stroke cohort increased reading speed by ~6% and almost halved error scores, findings not replicated in a control group. With the removal of migraine subjects reading speed increased by ~8% with an optimal filter and error scores almost halved. Prolonged use of an optimal spectral filter for stroke subjects, increased reading speed by >9% and error scores more than halved. When the same subjects switched to prolonged use of a grey filter, reading speed reduced by ~4% and error scores increased marginally. When a second group of stroke subjects used a grey filter first, reading speed decreased by ~3% but increased by ~3% with prolonged use of an optimal filter, with error scores almost halving; these findings persisted with migraine subjects excluded. Initial use of an optimal spectral filter improved visual search response time but not error scores in a stroke cohort with migraine subjects excluded. Neither prolonged use of an optimal nor grey filter improved response time or reduced error scores in a stroke group; these findings persisted with the exclusion of migraine subjects.

Adaptive resource allocation for multicast orthogonal frequency division multiple access systems with guaranteed BER and rate

In this paper, we propose a resource allocation scheme to minimize transmit power for multicast orthogonal frequency division multiple access systems. The proposed scheme allows users to have different symbol error rate (SER) across subcarriers and guarantees an average bit error rate and transmission rate for all users. We first provide an algorithm to determine the optimal bits and target SER on subcarriers. Because the worst-case complexity of the optimal algorithm is exponential, we further propose a suboptimal algorithm that separately assigns bit and adjusts SER with a lower complexity. Numerical results show that the proposed algorithm can effectively improve the performance of multicast orthogonal frequency division multiple access systems and that the performance of the suboptimal algorithm is close to that of the optimal one. Copyright © 2012 John Wiley & Sons, Ltd. This paper proposes optimal and suboptimal algorithms for minimizing transmitting power of multicast orthogonal frequency division multiple access systems with guaranteed average bit error rate and data rate requirement. The proposed scheme allows users to have different symbol error rate across subcarriers and guarantees an average bit error rate and transmission rate for all users. Copyright © 2012 John Wiley & Sons, Ltd.

Optimal span length in high-speed transmission systems with hybrid Raman-erbium-doped fiber amplification

We show, using nonlinearity management, that the optimal performance in high-bit-rate dispersion-managed fiber systems with hybrid amplification is achieved for a specific amplifier spacing that is different from the asymptotically vanishing length corresponding to ideally distributed amplification [Opt. Lett. 15, 1064 (1990)]. In particular, we prove the existence of a nontrivial optimal span length for 40-Gbit/s wavelength-division transmission systems with Raman-erbium-doped fiber amplification. Optimal amplifier lengths are obtained for several dispersion maps based on commonly used transmission fibers. © 2005 Optical Society of America.

A hierarchy of phase transitions in optimal neuronal coding:from binary to M-ary discrete optimal codes

We have investigated how optimal coding for neural systems changes with the time available for decoding. Optimization was in terms of maximizing information transmission. We have estimated the parameters for Poisson neurons that optimize Shannon transinformation with the assumption of rate coding. We observed a hierarchy of phase transitions from binary coding, for small decoding times, toward discrete (M-ary) coding with two, three and more quantization levels for larger decoding times. We postulate that the presence of subpopulations with specific neural characteristics could be a signiture of an optimal population coding scheme and we use the mammalian auditory system as an example.

Achievable performance gain of IEEE 802.11 multi-rate link adaptation algorithm with cross-layer design

Link quality-based rate adaptation has been widely used for IEEE 802.11 networks. However, network performance is affected by both link quality and random channel access. Selection of transmit modes for optimal link throughput can cause medium access control (MAC) throughput loss. In this paper, we investigate this issue and propose a generalised cross-layer rate adaptation algorithm. It considers jointly link quality and channel access to optimise network throughput. The objective is to examine the potential benefits by cross-layer design. An efficient analytic model is proposed to evaluate rate adaptation algorithms under dynamic channel and multi-user access environments. The proposed algorithm is compared to link throughput optimisation-based algorithm. It is found rate adaptation by optimising link layer throughput can result in large performance loss, which cannot be compensated by the means of optimising MAC access mechanism alone. Results show cross-layer design can achieve consistent and considerable performance gains of up to 20%. It deserves to be exploited in practical design for IEEE 802.11 networks.

Essays in dynamic optimal taxation: working experience, unemployment scarring and poverty

This thesis investigates the design of optimal tax systems in dynamic environments. The first essay characterizes the optimal tax system where wages depend on stochastic shocks and work experience. In addition to redistributive and efficiency motives, the taxation of inexperienced workers depends on a second-best requirement that encourages work experience, a social insurance motive and incentive effects. Calibrations using U.S. data yield higher expected optimal marginal income tax rates for experienced workers for most of the inexperienced workers. They confirm that the average marginal income tax rate increases (decreases) with age when shocks and work experience are substitutes (complements). Finally, more variability in experienced workers' earnings prospects leads to increasing tax rates since income taxation acts as a social insurance mechanism. In the second essay, the properties of an optimal tax system are investigated in a dynamic private information economy where labor market frictions create unemployment that destroys workers' human capital. A two-skill type model is considered where wages and employment are endogenous. I find that the optimal tax system distorts the first-period wages of all workers below their efficient levels which leads to more employment. The standard no-distortion-at-the-top result no longer holds due to the combination of private information and the destruction of human capital. I show this result analytically under the Maximin social welfare function and confirm it numerically for a general social welfare function. I also investigate the use of a training program and job creation subsidies. The final essay analyzes the optimal linear tax system when there is a population of individuals whose perceptions of savings are linked to their disposable income and their family background through family cultural transmission. Aside from the standard equity/efficiency trade-off, taxes account for the endogeneity of perceptions through two channels. First, taxing labor decreases income, which decreases the perception of savings through time. Second, taxation on savings corrects for the misperceptions of workers and thus savings and labor decisions. Numerical simulations confirm that behavioral issues push labor income taxes upward to finance saving subsidies. Government transfers to individuals are also decreased to finance those same subsidies.

Rate Maximization of Decode-and-Forward Relaying Systems with RF Energy Harvesting

We consider a three-node decode-and-forward (DF) half-duplex relaying system, where the source first harvests RF energy from the relay, and then uses this energy to transmit information to the destination via the relay. We assume that the information transfer and wireless power transfer phases alternate over time in the same frequency band, and their time fraction (TF) may change or be fixed from one transmission epoch (fading state) to the next. For this system, we maximize the achievable average data rate. Thereby, we propose two schemes: (1) jointly optimal power and TF allocation, and (2) optimal power allocation with fixed TF. Due to the small amounts of harvested power at the source, the two schemes achieve similar information rates, but yield significant performance gains compared to a benchmark system with fixed power and fixed TF allocation.

Joint Information and Jamming Beamforming for Secrecy Rate Maximization in Cognitive Radio Networks

In this paper, we consider the secure beamforming design for an underlay cognitive radio multiple-input singleoutput broadcast channel in the presence of multiple passive eavesdroppers. Our goal is to design a jamming noise (JN) transmit strategy to maximize the secrecy rate of the secondary system. By utilizing the zero-forcing method to eliminate the interference caused by JN to the secondary user, we study the joint optimization of the information and JN beamforming for secrecy rate maximization of the secondary system while satisfying all the interference power constraints at the primary users, as well as the per-antenna power constraint at the secondary transmitter. For an optimal beamforming design, the original problem is a nonconvex program, which can be reformulated as a convex program by applying the rank relaxation method. To this end, we prove that the rank relaxation is tight and propose a barrier interior-point method to solve the resulting saddle point problem based on a duality result. To find the global optimal solution, we transform the considered problem into an unconstrained optimization problem. We then employ Broyden-Fletcher-Goldfarb-Shanno (BFGS) method to solve the resulting unconstrained problem which helps reduce the complexity significantly, compared to conventional methods. Simulation results show the fast convergence of the proposed algorithm and substantial performance improvements over existing approaches.

Optimal Power Allocation for Multiuser Secure Communication in Cooperative Relaying Networks

We consider a cooperative relaying network in which a source communicates with a group of users in the presence of one eavesdropper. We assume that there are no source-user links and the group of users receive only retransmitted signal from the relay. Whereas, the eavesdropper receives both the original and retransmitted signals. Under these assumptions, we exploit the user selection technique to enhance the secure performance. We first find the optimal power allocation strategy when the source has the full channel state information (CSI) of all links. We then evaluate the security level through: i) ergodic secrecy rate and ii) secrecy outage probability when having only the statistical knowledge of CSIs.

The role of heart rate as a risk marker for predicting adverse outcomes

Cardiovascular disease is one of the leading causes of death around the world. Resting heart rate has been shown to be a strong and independent risk marker for adverse cardiovascular events and mortality, and yet its role as a predictor of risk is somewhat overlooked in clinical practice. With the aim of highlighting its prognostic value, the role of resting heart rate as a risk marker for death and other adverse outcomes was further examined in a number of different patient populations. A systematic review of studies that previously assessed the prognostic value of resting heart rate for mortality and other adverse cardiovascular outcomes was presented. New analyses of nine clinical trials were carried out. Both the original and extended Cox model that allows for analysis of time-dependent covariates were used to evaluate and compare the predictive value of baseline and time-updated heart rate measurements for adverse outcomes in the CAPRICORN, EUROPA, PROSPER, PERFORM, BEAUTIFUL and SHIFT populations. Pooled individual patient meta-analyses of the CAPRICORN, EPHESUS, OPTIMAAL and VALIANT trials, and the BEAUTIFUL and SHIFT trials, were also performed. The discrimination and calibration of the models applied were evaluated using Harrell’s C-statistic and likelihood ratio tests, respectively. Finally, following on from the systematic review, meta-analyses of the relation between baseline and time-updated heart rate, and the risk of death from any cause and from cardiovascular causes, were conducted. Both elevated baseline and time-updated resting heart rates were found to be associated with an increase in the risk of mortality and other adverse cardiovascular events in all of the populations analysed. In some cases, elevated time-updated heart rate was associated with risk of events where baseline heart rate was not. Time-updated heart rate also contributed additional information about the risk of certain events despite knowledge of baseline heart rate or previous heart rate measurements. The addition of resting heart rate to the models where resting heart rate was found to be associated with risk of outcome improved both discrimination and calibration, and in general, the models including time-updated heart rate along with baseline or the previous heart rate measurement had the highest and similar C-statistics, and thus the greatest discriminative ability. The meta-analyses demonstrated that a 5bpm higher baseline heart rate was associated with a 7.9% and an 8.0% increase in the risk of all-cause and cardiovascular death, respectively (both p less than 0.001). Additionally, a 5bpm higher time-updated heart rate (adjusted for baseline heart rate in eight of the ten studies included in the analyses) was associated with a 12.8% (p less than 0.001) and a 10.9% (p less than 0.001) increase in the risk of all-cause and cardiovascular death, respectively. These findings may motivate health care professionals to routinely assess resting heart rate in order to identify individuals at a higher risk of adverse events. The fact that the addition of time-updated resting heart rate improved the discrimination and calibration of models for certain outcomes, even if only modestly, strengthens the case that it be added to traditional risk models. The findings, however, are of particular importance, and have greater implications for the clinical management of patients with pre-existing disease. An elevated, or increasing heart rate over time could be used as a tool, potentially alongside other established risk scores, to help doctors identify patient deterioration or those at higher risk, who might benefit from more intensive monitoring or treatment re-evaluation. Further exploration of the role of continuous recording of resting heart rate, say, when patients are at home, would be informative. In addition, investigation into the cost-effectiveness and optimal frequency of resting heart rate measurement is required. One of the most vital areas for future research is the definition of an objective cut-off value for the definition of a high resting heart rate.