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This paper presents Krylov subspace model order reduction of linear dynamical systems with quadratic output. To reach this goal, the quadratic transfer function with two variables is taken into consideration. The Krylov subspaces are established at the finite and the infinite frequency points where both the one-sided and the two-sided projection cases are discussed. The moment matching is accordingly studied and the quadratic transfer function of the reduced system resulting from the two-sided projection case can match more moments. Finally, numerical results illustrate the performance of the proposed Krylov model order reduction methodology. [ABSTRACT FROM AUTHOR]

Abstract In the design process of large adaptive mirrors numerical simulations represent the first step to evaluate the system design compliance in terms of performance, stability and robustness. For the next generation of Extremely Large Telescopes increased system dimensions and bandwidths lead to the need of modeling not only the deformable mirror alone, but also all the system supporting structure or even the full telescope. The capability to perform the simulations with an acceptable amount of time and computational resources is highly dependent on finding appropriate methods to reduce the size of the resulting dynamic models. In this paper we present a framework developed together with the company Microgate to create a reduced order structural model of a large adaptive mirror as a preprocessing step to the control system simulations. The reduced dynamic model is then combined with the remaining system components allowing to simulate the full adaptive mirror in a computationally efficient way. We analyze the feasibility of our reduced models for Microgate’s prototype of the adaptive mirror of the Giant Magellan Telescope.

In the design process of large adaptive mirrors numerical simulations represent the first step to evaluate the system design compliance in terms of performance, stability and robustness. For the next generation of Extremely Large Telescopes increased system dimensions and bandwidths lead to the need of modeling not only the deformable mirror alone, but also all the system supporting structure or even the full telescope. The capability to perform the simulations with an acceptable amount of time and computational resources is highly dependent on finding appropriate methods to reduce the size of the resulting dynamic models. In this paper we present a framework developed together with the company Microgate to create a reduced order structural model of a large adaptive mirror as a preprocessing step to the control system simulations. The reduced dynamic model is then combined with the remaining system components allowing to simulate the full adaptive mirror in a computationally efficient way. We analyze the feasibility of our reduced models for Microgate's prototype of the adaptive mirror of the Giant Magellan Telescope. [ABSTRACT FROM AUTHOR]

This paper presents an efficient heuristic to generate multi‐stage scenario trees for portfolio selection problems. In the case of two or more risky assets, investors need to account for the complex multivariate dependence among different assets. The dependence patterns have shown not only asymmetric and fat tails but also time‐varying, and the upper and lower tails have different effect on portfolio management. In this paper, we design a new scenario generation method by combining the GARCH‐type model and vine copula model to properly reflect these complex dependence patterns in multiple assets in a flexible way. A multi‐stage scenario tree is generated sequentially from this model by simultaneously utilizing the simulation and clustering methods. The scenarios' nodal probabilities are determined by solving an improved moment matching model, whose objective is to maintain the central moments and lower tails of the original distribution. The resulting scenario trees are then tested on a multi‐stage portfolio selection model. The experimental results prove the efficiency and advantages of our proposed scenario generation method over other existing models or methods and the positive influence of moment matching on our method. [ABSTRACT FROM AUTHOR]

This paper proposes a comprehensive model order reduction framework to enable fast power integrity verification at the system level. This approach is developed to compress models of complete power delivery networks of high-end multiprocessor systems, where electromagnetic models of board and package are connected through banks of per-core Fully Integrated Voltage Regulators to chip models and loads in a closed-loop configuration. Due to complexity in both dynamical behavior and number of signals to be monitored, a direct transient simulation at the system level is very challenging. We show that a careful topological formulation of the circuit equations leads to a global model format that enables a structured projection framework for the elimination of the redundant states. Within this framework, we present and compare two alternative approaches based on approximate interpolation and empirical balancing, here adapted for the application at hand. In both cases, the resulting system is proven to be unconditionally stable both in open and in closed-loop configuration. Transient simulation of the reduced system provides a speedup exceeding $100\times $ with respect to SPICE.

Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A Gaussian distribution provides a convenient density for such approaches; examples include the Laplace, penalized quasi-likelihood, Gaussian variational, and expectation propagation methods. Unfortunately, these all ignore potential posterior skewness. The recent work of Durante et al. [Skewed Bernstein-von Mises theorem and skew-modal approximations; 2023. ArXiv preprint arXiv:2301.03038.] addresses this using skew-modal (SM) approximations, and is theoretically justified by a skewed Bernstein-von Mises theorem. However, the SM approximation can be impractical to work with in terms of tractability and storage costs, and uses only local posterior information. We introduce a variety of matching-based approximation schemes using the standard skew-normal distribution to resolve these issues. Experiments were conducted to compare the performance of this skew-normal matching method (both as a standalone approximation and as a post-hoc skewness adjustment) with the SM and existing Gaussian approximations. We show that for small and moderate dimensions, skew-normal matching can be much more accurate than these other approaches. For post-hoc skewness adjustments, this comes at very little cost in additional computational time. [ABSTRACT FROM AUTHOR]

Dispersed phases like colloidal particles and emulsions are characterized by their particle size distribution. Narrow distributions can be represented by the monodisperse distribution. However, this is not the case for broader distributions. The so-called quadrature methods of moments assume any distribution as a bidisperse one in order to solve the corresponding population balance. The generalization of this approach (i.e., approximation of the actual particle size distribution according to a bidisperse one) is proposed in the present work. This approximation helps to compress the amount of numbers for the description of the distribution and facilitates the calculation of the properties of the dispersion (especially convenient in cases of complex calculations). In the present work, the procedure to perform the approximation is evaluated, and the best approach is found. It was shown that the approximation works well for the case of a lognormal distribution (as an example) for a moments order from 0 to 2 and for dispersivity up to 3. [ABSTRACT FROM AUTHOR]

Fusion of multimodal medical data provides multifaceted, disease-relevant information for diagnosis or prognosis prediction modeling. Traditional fusion strategies such as feature concatenation often fail to learn hidden complementary and discriminative manifestations from high-dimensional multimodal data. To this end, we proposed a methodology for the integration of multimodality medical data by matching their moments in a latent space, where the hidden, shared information of multimodal data is gradually learned by optimization with multiple feature collinearity and correlation constrains. We first obtained the multimodal hidden representations by learning mappings between the original domain and shared latent space. Within this shared space, we utilized several relational regularizations, including data attribute preservation, feature collinearity and feature-task correlation, to encourage learning of the underlying associations inherent in multimodal data. The fused multimodal latent features were finally fed to a logistic regression classifier for diagnostic prediction. Extensive evaluations on three independent clinical datasets have demonstrated the effectiveness of the proposed method in fusing multimodal data for medical prediction modeling. [ABSTRACT FROM AUTHOR]

This paper extends interpolatory model reduction to systems with (up to) quadratic-bilinear dynamics and quadratic-bilinear outputs. These systems are referred to as QB-QB systems and arise in a number of applications, including fluid dynamics, optimal control, and uncertainty quantification. In the interpolatory approach, the reduced order models (ROMs) are based on a Petrov-Galerkin projection, and the projection matrices are constructed so that transfer function components of the ROM interpolate the corresponding transfer function components of the original system. To extend the approach to systems with QB outputs, this paper derives system transfer functions and sufficient conditions on the projection matrices that guarantee the aforementioned interpolation properties. Alternatively, if the system has linear dynamics and quadratic outputs, one can introduce auxiliary state variables to transform it into a system with QB dynamics and linear outputs to which known interpolatory model reduction can be applied. This transformation approach is compared with the proposed extension that directly treats quadratic outputs. The comparison shows that transformation hides the problem structure. Numerical examples illustrate that keeping the original QB-QB structure leads to ROMs with better approximation properties. [ABSTRACT FROM AUTHOR]

We consider the problem of approximating a continuous random variable, characterized by a cumulative distribution function (cdf) F(x), by means of k points, x 1 < x 2 < ⋯ < x k , with probabilities p i , i = 1 , ⋯ , k . For a given k, a criterion for determining the x i and p i of the approximating k-point discrete distribution can be the minimization of some distance to the original distribution. Here we consider the weighted Cramér-von Mises distance between the original cdf F(x) and the step-wise cdf F ^ (x) of the approximating discrete distribution, characterized by a non-negative weighting function w(x). This problem has been already solved analytically when w(x) corresponds to the probability density function of the continuous random variable, w (x) = F ′ (x) , and when w(x) is a piece-wise constant function, through a numerical iterative procedure based on a homotopy continuation approach. In this paper, we propose and implement a solution to the problem for different choices of the weighting function w(x), highlighting how the results are affected by w(x) itself and by the number of approximating points k, in addition to F(x); although an analytic solution is not usually available, yet the problem can be numerically solved through an iterative method, which alternately updates the two sub-sets of k unknowns, the x i 's (or a transformation thereof) and the p i 's, till convergence. The main apparent advantage of these discrete approximations is their universality, since they can be applied to most continuous distributions, whether they possess or not the first moments. In order to shed some light on the proposed approaches, applications to several well-known continuous distributions (among them, the normal and the exponential) and to a practical problem where discretization is a useful tool are also illustrated. [ABSTRACT FROM AUTHOR]

Certificates are structured financial instruments that aim to provide investors with investment solutions tailored to their needs. Certificates can be modeled using a bond component and a derivative component, typically an options strategy. The pricing of certificates is typically performed using the Monte Carlo numerical methodology. Such method allows for projections of the underlying using series of random numbers. The results obtained display an error (standard deviation) that depends on the number of simulations used and on the specific characteristics of the structured product. This work has the objective of minimizing the experimental error, and, consequently, of accelerating the speed of convergence using statistical techniques known in the literature as variance reduction methods. The most popular stochastic dynamics have been analyzed, like the classical Black and Scholes model, the Local Volatility model and the Heston model. Three certificates are analyzed in the paper and they are characterized by different payoffs. The variance reduction techniques, implemented in different programming languages (Python, Matlab and R), are: Latin Hypercube, Stratified Sampling, Antithetic Variables, Importance Sampling, Moment Matching and Control Variates.

The lattice Boltzmann method (LBM) is a numerical scheme for solving fluid dynamics problems. One of the important and actively developing areas of LBM is correct construction of the scheme on nonuniform spatial grids. With nonuniform grids the total number of calculations can be significantly reduced. However, at the moment the construction of an LBM scheme near a boundary of grids with different spatial steps inevitably requires data interpolation, which may reduce the LBM approximation order and lead to violation of conservation laws. In this work, for the first time, we have developed and tested a method for constructing an athermal node-based LBM on nonuniform grids without interpolation, with the same time step for grids of different scales. The method is based on a two-stage transformation of populations corresponding to different on-grid stencils. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the use of close formula approximation for pricing European mortgage options. Under the assumption of logistic duration and normal mortgage rates the underlying price at the option expiry is approximated by shifted lognormal or regular lognormal distribution by matching moments. Once the price function is approximated by lognormal distributions, the option price can be computed directly as an integration of the distribution function over the payoff at the option expiry by using Black-Scholes-Merton close formula. We will see that lower curvature levels correspond to positively skewness price distributions and in this case lognormal approximation leads to close parametric formula representation in terms of all model parameters. The proposed methodologies are tested against Monte Carlo approach under different market and contract parameters and the tests confirmed that the close form approximation have a very good accuracy.

Grid refinement is used to reduce computing costs while maintaining the precision of fluid simulation. In the lattice Boltzmann method (LBM), grid refinement often uses interpolated values. Here, we developed a method in which interpolation in space and time is not required. For this purpose, we used the moment matching condition and rescaled the nonequilibrium part of the populations, thereby developing a recalibration procedure that allows for the transfer of information between different LBM stencils in the simulation domain. Then, we built a nonuniform lattice that uses stencils with different shapes on the transition. The resulting procedure was verified by performing benchmarks with the 2D Poisselle flow and the advected vortex. It is suggested that grids with adaptive geometry can be built with the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes an unsupervised multi-source domain adaptation algorithm with graph convolution network and multi-alignment in mixed latent space, which leverages domain labels, data structure, and category labels in a unified network but improves domain-invariant semantic representation by several innovations. Specifically, a novel data structure alignment is proposed to exploit the inherent properties of different domains while using current domain alignment and classification result alignment. Through this design, category consistency can be considered in both latent space, and domain and structure discrepancy between different source domains and the target domain can be eliminated. Moreover, we also use category alignment based on both CNN and GCN features to optimize category decision boundary. Experiment results show that the proposed method brings sufficient improvement especially for adaptation tasks with large shift in data distribution. [ABSTRACT FROM AUTHOR]

Dispersed phases like colloidal particles and emulsions are characterized by their particle size distribution. Narrow distributions can be represented by the monodisperse distribution. However, this is not the case for broader distributions. The so-called quadrature methods of moments assume any distribution as a bidisperse one in order to solve the corresponding population balance. The generalization of this approach (i.e., approximation of the actual particle size distribution according to a bidisperse one) is proposed in the present work. This approximation helps to compress the amount of numbers for the description of the distribution and facilitates the calculation of the properties of the dispersion (especially convenient in cases of complex calculations). In the present work, the procedure to perform the approximation is evaluated, and the best approach is found. It was shown that the approximation works well for the case of a lognormal distribution (as an example) for a moments order from 0 to 2 and for dispersivity up to 3.

Physical machine systems are represented in the form of differential equations. These differential equations may be of the higher order and difficult to analyses. Therefore, it is necessary to convert the higher-order to lower order which replicates approximately similar properties of the higher-order system (HOS). This article presents a novel approach to reducing the higher-order model. The approach is based on the hunting demeanor of the hawk and escaping of the prey. The proposed method unifies the Harris hawk algorithm and the moment matching technique. The method is applied on single input single output (SISO), multi-input multi-output (MIMO) linear time–invariant (LTI) systems. The proposed method is justified by examining the result. The results are compared using the step response characteristics and response error indices. The response indices are integral square error, integral absolute error, integral time absolute error. The step response characteristics such as rise time, peak, peak time, settling time of the proposed reduced order follows 97%–100% of the original system characteristics.

In this paper, we investigate the goodness-of-fit of the flexible four-parameter generalized Lambda Distribution (GLD) for high-frequency 5-min returns sampled from the DJI30 Index. Applying Moment Matching (MM) and Maximum Likelihood Estimation (MLE) techniques, we highlight the significance of the higher-order parameters of the GLD distribution to depict the asymmetric and fat-tailed behaviour observed in high-frequency returns data. We also show and explain why the MLE consistently outperforms the MM; especially in the presence of “outliers”. Finally, we use lambda-space scatterplots to introduce, clarify and discuss additional stylized facts of high-frequency index returns not found in the extant high-frequency literature.

A new method for data-driven interpolatory model reduction for discrete-time systems is presented in this paper. Using the so-called data informativity perspective, we define a framework that enables the computation of moments at given (possibly complex) interpolation points based on time-domain input–output data only, without explicitly identifying the high-order system. Instead, by characterizing the set of all systems explaining the data, necessary and sufficient conditions are provided under which all systems in this set share the same moment at a given interpolation point. Moreover, these conditions allow for explicitly computing these moments. Reduced-order models are then derived by employing a variation of the classical rational interpolation method. The condition to enforce moment matching model reduction with prescribed poles is also discussed as a means to obtain stable reduced-order models. An example of an electrical circuit illustrates this framework. [ABSTRACT FROM AUTHOR]

In recent years, Neural Machine Translation (NMT), which harnesses the power of neural networks, has achieved astonishing achievements. Despite its promise, NMT models can still not model prior external knowledge. Recent investigations have necessitated the adaptation of past expertise to both training and inference methods, resulting in translation inference issues. This paper proposes an extension of the moment matching framework that incorporates advanced prior knowledge without interfering with the inference process by using a matching mechanism between the model and empirical distributions. Our tests show that the suggested expansion outperforms the baseline and effectively over various language combinations. [ABSTRACT FROM AUTHOR]

In this paper, we compute a (local) optimal reduced order model that matches a prescribed set of moments of a stable linear time-invariant system of high dimension. We fix the interpolation points and parametrize the models achieving moment-matching in a set of free parameters. Based on the parametrization and using the H 2 -norm of the approximation error as the objective function, we derive a nonconvex optimization problem, i.e., we search for the optimal free parameters to determine the model yielding the minimal H 2 -norm of the approximation error. Furthermore, we provide the necessary first-order optimality conditions in terms of the controllability and the observability Gramians of a minimal realization of the error system. We then propose two gradient-type algorithms to compute the (local) optimal models, with mathematical guarantees on the convergence. We also derive convex semidefinite programming relaxations for the nonconvex Problem, under the assumption that the error system admits block-diagonal Gramians, and derive sufficient conditions to guarantee the block diagonalization. The solutions resulting at each step of the proposed algorithms guarantee the achievement of the imposed moment matching conditions. The second gradient-based algorithm exhibits the additional property that, when stopped, yields a stable approximation with a reduced H 2 -error norm. We illustrate the theory on a CD-player and on a discretized heat equation. [ABSTRACT FROM AUTHOR]

Grid refinement is used to reduce computing costs while maintaining the precision of fluid simulation. In the lattice Boltzmann method (LBM), grid refinement often uses interpolated values. Here, we developed a method in which interpolation in space and time is not required. For this purpose, we used the moment matching condition and rescaled the nonequilibrium part of the populations, thereby developing a recalibration procedure that allows for the transfer of information between different LBM stencils in the simulation domain. Then, we built a nonuniform lattice that uses stencils with different shapes on the transition. The resulting procedure was verified by performing benchmarks with the 2D Poisselle flow and the advected vortex. It is suggested that grids with adaptive geometry can be built with the proposed method.

This paper proposes a method to probabilistically quantify the moments (mean and variance) of excavated material during excavation by aggregating the prior moments of the grade blocks around the given bucket dig location. By modelling the moments as random probability density functions (pdf) at sampled locations, a formulation of the sums of Gaussian-based uncertainty estimation is presented that jointly estimates the location pdfs, as well as the prior values for uncertainty coming from ore body knowledge (obk) sub-block models. The method was tested in a region situated in the Brockman Iron Formation of the Hamersley Province, Western Australia. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the goodness-of-fit of the flexible four-parameter generalized Lambda Distribution (GLD) for high-frequency 5-min returns sampled from the DJI30 Index. Applying Moment Matching (MM) and Maximum Likelihood Estimation (MLE) techniques, we highlight the significance of the higher-order parameters of the GLD distribution to depict the asymmetric and fat-tailed behaviour observed in high-frequency returns data. We also show and explain why the MLE consistently outperforms the MM; especially in the presence of "outliers". Finally, we use lambda-space scatterplots to introduce, clarify and discuss additional stylized facts of high-frequency index returns not found in the extant high-frequency literature. [ABSTRACT FROM AUTHOR]

Because of the complexity of the nuclear reactor system, traditional statistical sampling methods, such as random sampling and Latin hypercube sampling, often lead to unstable uncertainty quantification results of the reactor physics analysis. In order to make the analysis results robust, traditional sampling methods require a large number of samples, which brings a huge computation cost. For this reason, this paper proposes a new sampling scheme based on the moment matching method to generate efficient samples for the uncertainty quantification of reactor physics calculations. A linear programming model is established to minimize the deviations of the first- and second-order moments. The generated samples can better reflect the statistical characteristics of the real distribution than classical sampling methods. A series of numerical experiments is carried out to demonstrate the superiority of the proposed moment matching sampling method, which can quickly provide more reliable uncertainty quantification results with a small sample size. [ABSTRACT FROM AUTHOR]

Count data are often subject to underreporting, especially in infectious disease surveillance. We propose an approximate maximum likelihood method to fit count time series models from the endemic‐epidemic class to underreported data. The approach is based on marginal moment matching where underreported processes are approximated through completely observed processes from the same class. Moreover, the form of the bias when underreporting is ignored or taken into account via multiplication factors is analyzed. Notably, we show that this leads to a downward bias in model‐based estimates of the effective reproductive number. A marginal moment matching approach can also be used to account for reporting intervals which are longer than the mean serial interval of a disease. The good performance of the proposed methodology is demonstrated in simulation studies. An extension to time‐varying parameters and reporting probabilities is discussed and applied in a case study on weekly rotavirus gastroenteritis counts in Berlin, Germany. [ABSTRACT FROM AUTHOR]

Linear dynamics are virtually always assumed when designing optimal controllers for wave energy converters (WECs), motivated by both their simplicity and computational convenience. Nevertheless, unlike traditional tracking control applications, the assumptions under which the linearization of WEC models is performed are challenged by the energy-maximizing controller itself, which intrinsically enhances device motion to maximize power extraction from incoming ocean waves. In this article, we present a moment-based energy-maximizing control strategy for WECs subject to nonlinear dynamics. We develop a framework under which the objective function (and system variables) can be mapped to a finite-dimensional tractable nonlinear program, which can be efficiently solved using state-of-the-art nonlinear programming solvers. Moreover, we show that the objective function belongs to a class of generalized convex functions when mapped to the moment domain, guaranteeing the existence of a global energy-maximizing solution and giving explicit conditions for when a local solution is, effectively, a global maximizer. The performance of the strategy is demonstrated through a case study, where we consider (state and input-constrained) energy maximization for a state-of-the-art CorPower-like WEC, subject to different hydrodynamic nonlinearities. [ABSTRACT FROM AUTHOR]

Featured Application: This work has developed an adaptive multipoint model reduction model based on the Arnoldi algorithm to obtain reduced-order models of a 3-D temperature field. In simulations of three-dimensional transient physics filled through a numerical approach, the order of the equation set of high-fidelity models is extremely high. To eliminate the large dimension of equations, a model order reduction (MOR) technique is introduced. In the existing MOR methods, the block Arnoldi algorithm-based MOR method is numerically stable, achieving a passively reduced order model. Nevertheless, this method performs poorly when it is applied to very wide-frequency transients. To eliminate this deficiency, multipoint MOR methods are emerging. However, it is hard to directly apply an existing multipoint MOR method to a 3-D transient field equation set. The implementation issues in a reduction process (such as the selection of expansion points, the number of moments matched at a point and the error bound) have not been explored in detail. In this respect, an adaptive multipoint model reduction model based on the Arnoldi algorithm is proposed to obtain the reduced-order models of a 3-D temperature field. The originality of this study is the proposal of a novel adaptive algorithm for selecting expansion points, matching moments automatically, using a posterior-error estimator based on temperature response coupled with a network topological method (NTM). The computational efficiency and accuracy of the proposed method are evaluated by the numerical results from solving the temperature field of a prototype insulated-gate bipolar transistor (IGBT). [ABSTRACT FROM AUTHOR]

Physical machine systems are represented in the form of differential equations. These differential equations may be of the higher order and difficult to analyses. Therefore, it is necessary to convert the higher-order to lower order which replicates approximately similar properties of the higher-order system (HOS). This article presents a novel approach to reducing the higher-order model. The approach is based on the hunting demeanor of the hawk and escaping of the prey. The proposed method unifies the Harris hawk algorithm and the moment matching technique. The method is applied on single input single output (SISO), multi-input multi-output (MIMO) linear time-invariant (LTI) systems. The proposed method is justified by examining the result. The results are compared using the step response characteristics and response error indices. The response indices are integral square error, integral absolute error, integral time absolute error. The step response characteristics such as rise time, peak, peak time, settling time of the proposed reduced order follows 97%-100% of the original system characteristics. [ABSTRACT FROM AUTHOR]

In this brief paper, we propose a time-domain data-driven method for model order reduction by two-sided moment matching for linear systems. An algorithm that asymptotically approximates a key interpolation matrix from time-domain samples of the so-called two-sided interconnection is provided. Exploiting this estimated interpolation matrix, we determine the unique reduced-order model of order ν , which asymptotically matches the moments at 2 ν distinct interpolation points. Furthermore, we discuss the impact that certain disturbances and data distortions may have on the algorithm. Finally, we illustrate the use of the proposed methodology by means of a benchmark model. [ABSTRACT FROM AUTHOR]

Dynamical systems are pervasive in almost all engineering and scientific applications. Simulating such systems is computationally very intensive. Hence, Model Order Reduction (MOR) is used to reduce them to a lower dimension. Most of the MOR algorithms require solving large sparse sequences of linear systems. Since using direct methods for solving such systems does not scale well in time with respect to the increase in the input dimension, efficient preconditioned iterative methods are commonly used. In one of our previous works, we have shown substantial improvements by reusing preconditioners for the parametric MOR (Singh et al. 2019). Here, we had proposed techniques for both, the non-parametric and the parametric cases, but had applied them only to the latter. We have three main contributions here. First, we demonstrate that preconditioners can be reused more effectively in the non-parametric case as compared to the parametric one. Second, we show that reusing preconditioners is an art via detailed algorithmic implementations in multiple MOR algorithms. Third and final, we demonstrate that reusing preconditioners for reducing a real-life industrial problem (of size 1.2 million), leads to relative savings of up to 64 % in the total computation time (in absolute terms a saving of 5 days).

An analogue can be made between: (a) the slow pace at which species adapt to an environment, which often results in the emergence of a new distinct species out of a once homogeneous genetic pool and (b) the slow changes that take place over time within a fund, mutating its investment style. A fund's track record provides a sort of genetic marker, which we can use to identify mutations. This has motivated our use of a biometric procedure to detect the emergence of a new investment style within a fund's track record. In doing so, we answer the question: What is the probability that a particular PM's performance is departing from the reference distribution used to allocate her capital? The EF3M algorithm, inspired by evolutionary biology, may help detect early stages of an evolutionary divergence in an investment style and trigger a decision to review a fund's capital allocation. © 2013 © 2013 Taylor & Francis.

Summary: In this paper, we present a new and straightforward approximation methodology for pricing a call option in a Black and Scholes market, characterized by stochastic interest rates. The method relies on a Gaussian moment matching technique applied to a conditional Black and Scholes formula, used to disentangle the distributional complexity of the underlying price process. The problem then reduces to exploiting the Gaussian density and the expression of the bond price induced by the interest rate. To check its accuracy and computational time, we implement it for a CIR interest rate model correlated with the underlying, using Monte Carlo simulations as a benchmark. The method performance turns out to be quite remarkable, even when compared with similar results obtained by the affine approximation technique presented in Grzelak and Oosterlee, and by the expansion formula introduced in Kim and Kunimoto. In the last section, we apply the method also to the pricing of Forward‐Starting options, to the evaluation of the credit spreads in the Merton structural approach to credit risk, and we outline a possible application to a stochastic volatility model. [ABSTRACT FROM AUTHOR]

Sequentially detecting multiple changepoints in a data stream is a challenging task. Difficulties relate to both computational and statistical aspects, and in the latter, specifying control parameters is a particular problem. Choosing control parameters typically relies on unrealistic assumptions, such as the distributions generating the data, and their parameters, being known. This is implausible in the streaming paradigm, where several changepoints will exist. Further, current literature is mostly concerned with streams of continuous-valued observations, and focuses on detecting a single changepoint. There is a dearth of literature dedicated to detecting multiple changepoints in transition matrices, which arise from a sequence of discrete states. This paper makes the following contributions: a complete framework is developed for adaptively and sequentially estimating a Markov transition matrix in the streaming data setting. A change detection method is then developed, using a novel moment matching technique, which can effectively monitor for multiple changepoints in a transition matrix. This adaptive detection and estimation procedure for transition matrices, referred to as ADEPT-M, is compared to several change detectors on synthetic data streams, and is implemented on two real-world data streams – one consisting of over nine million HTTP web requests, and the other being a well-studied electricity market data set. [ABSTRACT FROM AUTHOR]

The fully adaptive rational global Arnoldi method (AIRGA) for the modelorder reduction of second-order multi-input multi-output systems with proportional damping is revisited. The method automatically generates a reduced system approximating the transfer function. It is based on a moment-matching approach. The expansion points are determined iteratively. The reduced order and the number of moments matched per expansion point are determined adaptively using a heuristic based on an error estimation. A revised moment error expression is presented as well as some related findings.