ABSTRACT:

One of the issues of admission control in communication networks is to determine regions of the values of the parameters ensuring given QoS guarantees. It is thus important to obtain estimates of the packet loss probability. Since the latter has to be small, e.g., 10^(-5) - 10^(-9) , it is natural to resort to asymptotics. In this talk I will concentrate on estimating the probabilities of large queue lengths in tandem queues. More specifically, I will discuss an approximation based on moderate deviation asymptotics in heavy traffic. An interesting part of the derivation is a study of a certain variational problem which admits an explicit solution.

ABSTRACT:

Application of semidefinite programming to 0-1 integer programming has been one of the most studied topics in operations research. This is partly due to the seminal work by Goemans and Williamson (1995) who achieved 0.878 approximation-guarantee on the max-cut problem. In this seminar, we introduce semidefinite programming and its application to the max-cut problem.

ABSTRACT:

Multi-valued and universal binary neurons (MVN and UBN) operate with the complex-valued weights and complex-valued activation functions that are the functions of the argument of the weighted sum. MVN is based on the general principles of multiple-valued threshold logic over the field of complex numbers and UBN is based on the idea of P-realizable Boolean functions, which makes it possible to learn the non-threshold Boolean functions on a single neuron.

The MVN inputs and output are lying on the unit circle, and its activation function maps the complex plane into the unit circle. The MVN learning algorithm is reduced to the movement along the unit circle. The MVN learning algorithm is based on a simple linear error correction rule and it is derivative-free. The functionality of a single MVN is much higher than the functionality of other traditionally used neurons. It is very interesting that the states of "maximum excitation" and "maximum inhibition" of MVN coincide with each other, while a "medium" state is equidistant from them. Thus, the neuron can change its state from excitatory to inhibitory and vice versa either passing all intermediate states or in the shortest possible way. This MVN paradigm can be very interesting for the simulations of the natural neurons.

The most impressive and recently developed application of MVN is a multilayer feedforward neural network based on multi-valued neurons (MLMVN). The backpropagation learning algorithm for the MLMVN is derivative-free. Being similar to the classical backpropagation algorithm, it has important distinctions that make it more stable and less heuristic. These distinctions are derivative-free learning and a self adaptation of the learning rate for the hidden neurons. The MLMVN is a powerful tool for solving multiple-class classification, recognition and prediction problems. It outperforms a classical backpropagation network, different kernel-based networks including SVM in terms of complexity and classification/prediction rate solving a number of popular benchmark problems. Some successful real world applications of the MLMVN have been recently developed (blur identification for solving the image restoration problem and classification of microarray gene expression data). The MLMVN with just one hidden layer containing 4 neurons and one output neuron can be used as a universal generator of the genetic code.

The activation function of UBN similarly to the MVN activation functions is also a function of the argument of the weighted sum: a complex plane is separated onto equal sectors, where the activation function is equal to 1 or -1 depending on the sector's parity. This makes possible learning of the nonlinearly separable Boolean functions on a single neuron. Thus, the functionality of UBN is incompatibly higher than the functionality of the traditional single perceptron. For example, the classical nonlinearly separable problems XOR and Parity N (for arbitrary N) can be easily solved using a single UBN. The UBN learning algorithm similarly to the MVN learning algorithm is also reduced to the movement along the unit circle, and it is based on the linear error correcting learning rule.

The presentation will be illustrated by a number of impressive examples of using MVN, MLMVN and UBN for solving different problems.

ABSTRACT:

The San Francisco Fire Department positions ambulances for emergency response. An integer programming model places ambulances to minimize the distance to call volume. As ambulances go out on calls, using the original model to reposition all remaining ambulances is an impractical solution. Rather, additional constraints were added to the model to determine the best way to reposition a limited number of ambulances. This real time information can be fed to the dispatcher to improve response times.

ABSTRACT:

In many models of exposure-related lung carcinogenesis, including traditional linearized multistage models and more recent two-stage clonal expansion (TSCE) models, cells progress between stages – possibly undergoing proliferation in some stages – at rates that may depend (usually linearly) on biologically effective doses. Biologically effective doses, in turn, may depend nonlinearly on administered doses, due to pharmacokinetic nonlinearities. This talk presents a mathematical analysis of the expected number of cells in the last (“malignant”) stage of such a “multistage clonal expansion” (MSCE) model as a function of dose rate and age. The solution displays symmetries such that several distinct sets of parameter values provide identical fits to all epidemiological data, yet make significantly different predictions about the effects on risk of changes in the composition of exposure. Effects of interventions on age-specific cancer risks in an MSCE model can be either large or small, but which is the case cannot be predicted from pre-intervention epidemiological data alone. Rather, biological data that break the mathematical symmetry are required to obtain unambiguous predictions. From epidemiological data alone, only a set of equally likely alternative predictions can be made for the effects on risk of such interventions.