Quantum computing for finance

Quantum computers are expected to surpass the computational capabilities of classical computers and have a transformative impact on numerous industry sectors. We present a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on stochastic modeling, optimization, and machine learning. This Review is aimed at physicists, so it outlines the classical techniques used by the financial industry and discusses the potential advantages and limitations of quantum techniques. Finally, we look at the challenges that physicists could help tackle

On FPGA implementations for bioinformatics, neural prosthetics and reinforcement learning problems.

Mak Sui Tung Terrence.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 132-142).Abstracts in English and Chinese.Abstract --- p.iList of Tables --- p.ivList of Figures --- p.vAcknowledgements --- p.ixChapter 1. --- Introduction --- p.1Chapter 1.1 --- Bioinformatics --- p.1Chapter 1.2 --- Neural Prosthetics --- p.4Chapter 1.3 --- Learning in Uncertainty --- p.5Chapter 1.4 --- The Field Programmable Gate Array (FPGAs) --- p.7Chapter 1.5 --- Scope of the Thesis --- p.10Chapter 2. --- A Hybrid GA-DP Approach for Searching Equivalence Sets --- p.14Chapter 2.1 --- Introduction --- p.16Chapter 2.2 --- Equivalence Set Criterion --- p.18Chapter 2.3 --- Genetic Algorithm and Dynamic Programming --- p.19Chapter 2.3.1 --- Genetic Algorithm Formulation --- p.20Chapter 2.3.2 --- Bounded Mutation --- p.21Chapter 2.3.3 --- Conditioned Crossover --- p.22Chapter 2.3.4 --- Implementation --- p.22Chapter 2.4 --- FPGAs Implementation of GA-DP --- p.24Chapter 2.4.1 --- System Overview --- p.25Chapter 2.4.2 --- Parallel Computation for Transitive Closure --- p.26Chapter 2.4.3 --- Genetic Operation Realization --- p.28Chapter 2.5 --- Discussion --- p.30Chapter 2.6 --- Limitation and Future Work --- p.33Chapter 2.7 --- Conclusion --- p.34Chapter 3. --- An FPGA-based Architecture for Maximum-Likelihood Phylogeny Evaluation --- p.35Chapter 3.1 --- Introduction --- p.36Chapter 3.2 --- Maximum-Likelihood Model --- p.39Chapter 3.3 --- Hardware Mapping for Pruning Algorithm --- p.41Chapter 3.3.1 --- Related Works --- p.41Chapter 3.3.2 --- Number Representation --- p.42Chapter 3.3.3 --- Binary Tree Representation --- p.43Chapter 3.3.4 --- Binary Tree Traversal --- p.45Chapter 3.3.5 --- Maximum-Likelihood Evaluation Algorithm --- p.46Chapter 3.4 --- System Architecture --- p.49Chapter 3.4.1 --- Transition Probability Unit --- p.50Chapter 3.4.2 --- State-Parallel Computation Unit --- p.51Chapter 3.4.3 --- Error Computation --- p.54Chapter 3.5 --- Discussion --- p.56Chapter 3.5.1 --- Hardware Resource Consumption --- p.56Chapter 3.5.2 --- Delay Evaluation --- p.57Chapter 3.6 --- Conclusion --- p.59Chapter 4. --- Field Programmable Gate Array Implementation of Neuronal Ion Channel Dynamics --- p.61Chapter 4.1 --- Introduction --- p.62Chapter 4.2 --- Background --- p.63Chapter 4.2.1 --- Analog VLSI Model for Hebbian Synapse --- p.63Chapter 4.2.2 --- A Unifying Model of Bi-directional Synaptic Plasticity --- p.64Chapter 4.2.3 --- Non-NMDA Receptor Channel Regulation --- p.65Chapter 4.3 --- FPGAs Implementation --- p.65Chapter 4.3.1 --- FPGA Design Flow --- p.65Chapter 4.3.2 --- Digital Model of NMD A and AMPA receptors --- p.65Chapter 4.3.3 --- Synapse Modification --- p.67Chapter 4.4 --- Results --- p.68Chapter 4.4.1 --- Simulation Results --- p.68Chapter 4.5 --- Discussion --- p.70Chapter 4.6 --- Conclusion --- p.71Chapter 5. --- Continuous-Time and Discrete-Time Inference Networks for Distributed Dynamic Programming --- p.72Chapter 5.1 --- Introduction --- p.74Chapter 5.2 --- Background --- p.77Chapter 5.2.1 --- Markov decision process (MDPs) --- p.78Chapter 5.2.2 --- Learning in the MDPs --- p.80Chapter 5.2.3 --- Bellman Optimal Criterion --- p.80Chapter 5.2.4 --- Value Iteration --- p.81Chapter 5.3 --- A Computational Framework for Continuous-Time Inference Network --- p.82Chapter 5.3.1 --- Binary Relation Inference Network --- p.83Chapter 5.3.2 --- Binary Relation Inference Network for MDPs --- p.85Chapter 5.3.3 --- Continuous-Time Inference Network for MDPs --- p.87Chapter 5.4 --- Convergence Consideration --- p.88Chapter 5.5 --- Numerical Simulation --- p.90Chapter 5.5.1 --- Example 1: Random Walk --- p.90Chapter 5.5.2 --- Example 2: Random Walk on a Grid --- p.94Chapter 5.5.3 --- Example 3: Stochastic Shortest Path Problem --- p.97Chapter 5.5.4 --- Relationships Between λ and γ --- p.99Chapter 5.6 --- Discrete-Time Inference Network --- p.100Chapter 5.6.1 --- Results --- p.101Chapter 5.7 --- Conclusion --- p.102Chapter 6. --- On Distributed g-Learning Network --- p.104Chapter 6.1 --- Introduction --- p.105Chapter 6.2 --- Distributed Q-Learniing Network --- p.108Chapter 6.2.1 --- Distributed Q-Learning Network --- p.109Chapter 6.2.2 --- Q-Learning Network Architecture --- p.111Chapter 6.3 --- Experimental Results --- p.114Chapter 6.3.1 --- Random Walk --- p.114Chapter 6.3.2 --- The Shortest Path Problem --- p.116Chapter 6.4 --- Discussion --- p.120Chapter 6.4.1 --- Related Work --- p.121Chapter 6.5 --- FPGAs Implementation --- p.122Chapter 6.5.1 --- Distributed Registering Approach --- p.123Chapter 6.5.2 --- Serial BRAM Storing Approach --- p.124Chapter 6.5.3 --- Comparison --- p.125Chapter 6.5.4 --- Discussion --- p.127Chapter 6.6 --- Conclusion --- p.128Chapter 7. --- Summary --- p.129Bibliography --- p.132AppendixChapter A. --- Simplified Floating-Point Arithmetic --- p.143Chapter B. --- "Logarithm, Exponential and Division Implementation" --- p.144Chapter B.1 --- Introduction --- p.144Chapter B.2 --- Approximation Scheme --- p.145Chapter B.2.1 --- Logarithm --- p.145Chapter B.2.2 --- Exponentiation --- p.147Chapter B.2.3 --- Division --- p.148Chapter C. --- Analog VLSI Implementation --- p.150Chapter C.1 --- Site Function --- p.150Chapter C.1.1 --- Multiplication Cell --- p.150Chapter C.2 --- The Unit Function --- p.153Chapter C.3 --- The Inference Network Computation --- p.154Chapter C.4 --- Layout --- p.157Chapter C.5 --- Fabrication --- p.159Chapter C.5.1 --- Testing and Characterization --- p.16

Stability Problems for Stochastic Models: Theory and Applications II

Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia

A survey of random processes with reinforcement

The models surveyed include generalized P\'{o}lya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are discussed in statistics, biology, economics and a number of other areas.Comment: Published at http://dx.doi.org/10.1214/07-PS094 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

A Survey of Stochastic Simulation and Optimization Methods in Signal Processing

International audienceModern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational inference techniques. This has driven the development of statistical SP methods based on stochastic simulation and optimization. Stochastic simulation and optimization algorithms are computationally intensive tools for performing statistical inference in models that are anal ytically intractable and beyond the scope of deterministic inference methods. They have been recently successfully applied to many difficult problems involving complex statistical models and sophisticated (often Bayesian) statistical inference techniques. This survey paper offers an introduction to stochastic simulation and optimization methods in signal and image processing. The paper addresses a variety of high-dimensional Markov chain Monte Carlo (MCMC) methods as well as deterministic surrogate methods, such as variational Bayes, the Bethe approach, belief and expectation propagation and approximate message passing algorithms. It also discusses a range of optimization methods that have been adopted to solve stochastic problems, as well as stochastic methods for deterministic optimization. Subsequently, area as of overlap between simulation and optimization, in particular optimization-within-MCMC and MCMC-driven optimization are discussed