pth Moment Exponential Stability of Stochastic Recurrent Neural Networks with Markovian Switching

This paper investigates the problem of the pth moment exponential stability for a class of stochastic recurrent neural networks with Markovian jump parameters. With the help of Lyapunov function, stochastic analysis technique, generalized Halanay inequality and Hardy inequality, some novel sufficient conditions on the pth moment exponential stability of the considered system are derived. The results obtained in this paper are completely new and complement and improve some of the previously known results (Liao and Mao, Stoch Anal Appl, 14:165–185, 1996; Wan and Sun, Phys Lett A, 343:306–318, 2005; Hu et al., Chao Solitions Fractals, 27:1006–1010, 2006; Sun and Cao, Nonlinear Anal Real, 8:1171–1185, 2007; Huang et al., Inf Sci, 178:2194–2203, 2008; Wang et al., Phys Lett A, 356:346–352, 2006; Peng and Liu, Neural Comput Appl, 20:543–547, 2011). Moreover, a numerical example is also provided to demonstrate the effectiveness and applicability of the theoretical results.     

An Efficient Algorithm for ℓ 0 Minimization in Wavelet Frame Based Image Restoration

Wavelet frame based models for image restoration have been extensively studied for the past decade (Chan et al. in SIAM J. Sci. Comput. 24(4):1408–1432, 2003; Cai et al. in Multiscale Model. Simul. 8(2):337–369, 2009; Elad et al. in Appl. Comput. Harmon. Anal. 19(3):340–358, 2005; Starck et al. in IEEE Trans. Image Process. 14(10):1570–1582, 2005; Shen in Proceedings of the international congress of mathematicians, vol. 4, pp. 2834–2863, 2010; Dong and Shen in IAS lecture notes series, Summer program on “The mathematics of image processing”, Park City Mathematics Institute, 2010). The success of wavelet frames in image restoration is mainly due to their capability of sparsely approximating piecewise smooth functions like images. Most of the wavelet frame based models designed in the past are based on the penalization of the ? ₁ norm of wavelet frame coefficients, which, under certain conditions, is the right choice, as supported by theories of compressed sensing (Candes et al. in Appl. Comput. Harmon. Anal., 2010; Candes et al. in IEEE Trans. Inf. Theory 52(2):489–509, 2006; Donoho in IEEE Trans. Inf. Theory 52:1289–1306, 2006). However, the assumptions of compressed sensing may not be satisfied in practice (e.g. for image deblurring and CT image reconstruction). Recently in Zhang et al. (UCLA CAM Report, vol. 11-32, 2011), the authors propose to penalize the ? ₀ “norm” of the wavelet frame coefficients instead, and they have demonstrated significant improvements of their method over some commonly used ? ₁ minimization models in terms of quality of the recovered images. In this paper, we propose a new algorithm, called the mean doubly augmented Lagrangian (MDAL) method, for ? ₀ minimizations based on the classical doubly augmented Lagrangian (DAL) method (Rockafellar in Math. Oper. Res. 97–116, 1976). Our numerical experiments show that the proposed MDAL method is not only more efficient than the method proposed by Zhang et al. (UCLA CAM Report, vol. 11-32, 2011), but can also generate recovered images with even higher quality. This study reassures the feasibility of using the ? ₀ “norm” for image restoration problems.     

Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems

The stochastic collocation method (Babu?ka et al. in SIAM J Numer Anal 45(3):1005–1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411–2442, 2008a; SIAM J Numer Anal 46(5):2309–2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118–1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289–294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229–275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41–44):3187–3206, 2009; Arch Comput Methods Eng 17:435–454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions $O(1)$ to moderate dimensions $O(10)$ and to high dimensions $O(100)$ . The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs.     

Some types of filters in residuated lattices

In this paper, inspired by some types of $BL$ -algebra filters (deductive systems) introduced in Haveshki et al. (Soft Comput 10:657–664, 2006), Kondo and Dudek (Soft Comput 12:419–423, 2008) and Turunen (Arch Math Log 40:467–473, 2001), we defined residuated lattice versions of them and study them in connection with Van Gasse et al. (Inf Sci 180(16):3006–3020, 2010), Lianzhen and Kaitai (Inf Sci 177:5725–5738, 2007), Zhu and Xu (Inf Sci 180:3614–3632, 2010). Also we consider some relations between these filters and quotient residuated lattice that are constructed via these filters.     

On anonymizing transactions with sensitive items

K-anonymity (Samarati and Sweeny 1998; Samarati, IEEE Trans Knowl Data Eng, 13(6):1010–1027, 2001; Sweeny, Int J Uncertain, Fuzziness Knowl-Based Syst, 10(5):557–570, 2002) and its variants, l-diversity (Machanavajjhala et al., ACM TKDD, 2007) and tcloseness (Li et al. 2007) among others are anonymization techniques for relational data and transaction data, which are used to protect privacy against re-identification attacks. A relational dataset D is k-anonymous if every record in D has at least k-1 other records with identical quasi-identifier attribute values. The combination of released data with external data will never allow the recipient to associate each released record with less than k individuals (Samarati, IEEE Trans Knowl Data Eng, 13(6):1010–1027, 2001). However, the current concept of k-anonymity on transaction data treats all items as quasi-identifiers. The anonymized data set has k identical transactions in groups and suffers from lower data utility (He and Naughton 2009; He et al. 2011; Liu and Wang 2010; Terrovitis et al., VLDB J, 20(1):83–106, 2011; Terrovitis et al. 2008). To improve the utility of anonymized transaction data, this work proposes a novel anonymity concept on transaction data that contain both quasi-identifier items (QID) and sensitive items (SI). A transaction that contains sensitive items must have at least k-1 other identical transactions (Ghinita et al. IEEE TKDE, 33(2):161–174, 2011; Xu et al. 2008). For a transaction that does not contain a sensitive item, no anonymization is required. A transaction dataset that satisfies this property is said to be sensitive k-anonymous. Three algorithms, Sensitive Transaction Neighbors (STN) Gray Sort Clustering (GSC) and Nearest Neighbors for K-anonymization (K-NN), are developed. These algorithms use adding/deleting QID items and only adding SI to achieve sensitive k-anonymity on transaction data. Additionally, a simple “privacy value” is proposed to evaluate the degree of privacy for different types of k-anonymity on transaction data. Extensive numerical simulations were carried out to demonstrate the characteristics of the proposed algorithms and also compared to other types of k-anonymity approaches. The results show that each technique possesses its own advantage under different criteria such as running time, operation, and information loss. The results obtained here can be used as a guideline of the selection of anonymization technique on different data sets and for different applications.     

A new spatial IP assignment method for IP-based wireless sensor networks

Wireless sensor networks (WSNs), one of the commercial wireless mesh networks (WMNs), are envisioned to provide an effective solution for sensor-based AmI (Ambient Intelligence) systems and applications. To enable the communications between AmI sensor networks and the most popular TCP/IP networks seamlessly, the best solution model is to run TCP/IP directly on WSNs (Mulligan et al. 2009; Hui and Culler 2008; Han and Mam 2007; Kim et al. 2007; Xiaohua et al. 2004; Dunkels et al. 2004; Dunkels et al. 2004; Dunkels 2001; Dunkels et al. 2004). In this case, an IP assignment method is required to assign each sensor node a unique IP address. SIPA (Dunkels et al. 2004) is the best known IP assignment method that uses spatial relations and locations of sensor nodes to assign their IP addresses. It has been applied in Contiki (Dunkels et al. 2004), a famous WSN operating system, to support the 6LowPAN protocol. In Chang et al. (2009), we proposed the SLIPA (Scan-Line IP Assignment) algorithm to improve the assignment success rate (ASR) obtained by SIPA. SLIPA can achieve a good ASR when sensor nodes are uniformly distributed. However, if sensor nodes are deployed by other distributions, the improvements would be limited. This paper proposes a new spatial IP assignment method, called SLIPA-Q (SLIPA with equal-quantity partition), to improve SLIPA. Experiments show that, by testing the proposed method 1,000 times with 1,000 randomly deployed sensor nodes, the average ASR obtained by SLIPA-Q is over two times of that obtained by SLIPA. Under the same 88% ASR, the average numbers of sensor nodes those can be successfully assigned by SLIPA-Q, SLIPA, and SIPA are 950, 850, and 135, respectively. Comparing to previous spatial IP assignment methods, SLIPA-Q can achieve dramatic improvements in ASR for assigning IP addresses to a large set of sensor nodes.     

WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-Dimensional Compressible Two-Medium Flows

High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in (Parés, SIAM J.?Numer. Anal. 44:300?C321, 2006; Castro et al., Math. Comput. 75:1103?C1134, 2006; J.?Sci. Comput. 39:67?C114, 2009). Recently, it has been observed in (Abgrall and Karni, J.?Comput. Phys. 229:2759?C2763, 2010) that this approach may have some computational issues and shortcomings. In this paper, a modification to the high order path-conservative scheme in (Castro et al., Math. Comput. 75:1103?C1134, 2006) is proposed to improve its computational performance and to overcome some of the shortcomings. This modification is based on the high order finite volume WENO scheme with subcell resolution and it uses an exact Riemann solver to catch the right paths at the discontinuities. An application to one-dimensional compressible two-medium flows of nonconservative or primitive Euler equations is carried out to show the effectiveness of this new approach.     

Thermal actuator for accurate positioning read/write element in hard disk drive

Flying height control (TFC) sliders with thermal actuation, which make it possible to control head disk spacing, have been introduced in commercial products for compensating the flying height loss and reducing the risk of head disk contacts, thus to increase the bit density (Gupta et al. in ASME J Tribol 123:380–387, 2001; Juang and Bogy in ASME J Tribol 129:570–578, 2007; Kurita et al. in Microsyst Technol 12:369–375, 2006; Shiramatsu et al. in IEEE Trans Magn 42:2513–2515, 2006). However, with the increasing of areal density, it is also necessary to increase the track density. To increase track density, it is required to improve the performances of head positioning system in terms of fast transition from one track to another (track seeking), fast and accurate settling, and precise track following of the target track. Dual-actuator systems (Choe in A thermal driven micro actuator for hard disk drive. In: Proceedings of the APMRC 2010, Nov 10–12, 2010, Singapore, 2010; Bain et al. in Electrothermal actuator for hard disk drive application. In: Proceedings of the APMRC 2010, Nov. 10–12, 2010, Singapore, 2010; Furukawa et al. in Fabrication and test of thermal actuator. In: ISPS 2011, Jun. 13–14, Santa Clara, CA, USA, 2011) have been proposed to meet these requirements. These dual-actuator systems consist of a voice-coil-motor (VCM) as a first-stage actuator and a transducer (piezoelectric, electromagnetic, electrostatic and thermal) as a second-stage actuator. The second-stage actuator could be designed to actuate the movement of suspension (suspension driven), slider (slider driven) or head element (head driven). Most of reported dual-actuator systems were made to be suspension driven or slider driven. Recently, Choe by (A thermal driven micro actuator for hard disk drive. In: Proceedings of the APMRC 2010, Nov. 10–12, 2010, Singapore, 2010) and Bain et al. by (Electrothermal actuator for hard disk drive application. In: Proceedings of the APMRC 2010, Nov. 10–12, 2010, Singapore, 2010) reported to use thermal actuators for driving head movement. They attained a thermal transient of less than 10?μs using 2-D finite element simulation. Using thermal actuators to accurately position read/write element could be a promising technology for mass production for future HDD. This kind of control theme was termed as thermal positioning control (TPC). The objective of TPC actuator design is to achieve large actuation stroke as well as increase frequency bandwidth. In our studies, the design procedure may involve several steps: (1) Fundamental studies with simple TPC slider structure by finite element simulations to explore the feasibility of TPC actuation and estimate working frequency range. Also we may be able to find out the problems which induced by TPC actuator. (2) Prototyped TPC slider, and tested its frequency characteristics to confirm the feasibility and achievability of TPC actuation. (3) Increases TPC actuation stroke and frequency bandwidth by improving TPC slider structures and servo control schemes. This paper explores the feasibility studies of TPC slider by finite element simulation. The principle and structural modeling of slider with TPC heater was first introduced. Then static–static simulation was carried out to study the steady deformation displacement at read/write element and transient analysis was conducted to estimate the deformation displacement response. It was found that 7?nm deformation stroke at read/write element could be attained at steady state with 50?mW input power, and the deformation displacement was about 1.7?nm after power was applied to TPC heater 1.5?ms (frequency of 1?kHz based on first order delay system). Meanwhile, it was found that protrusion on the air bearing surface (ABS) becomes a problem for the slider’s flying performance, thus the ABS design was improved to reduce protrusion’s effect, and cross-talk effect between TFC and TPC actuators was then investigated.     

Algebraic flux correction for nonconforming finite element discretizations of scalar transport problems

This paper is concerned with the extension of the algebraic flux-correction (AFC) approach (Kuzmin in Computational fluid and solid mechanics, Elsevier, Amsterdam, pp 887–888, 2001; J Comput Phys 219:513–531, 2006; Comput Appl Math 218:79–87, 2008; J Comput Phys 228:2517–2534, 2009; Flux-corrected transport: principles, algorithms, and applications, 2nd edn. Springer, Berlin, pp 145–192, 2012; J Comput Appl Math 236:2317–2337, 2012; Kuzmin et al. in Comput Methods Appl Mech Eng 193:4915–4946, 2004; Int J Numer Methods Fluids 42:265–295, 2003; Kuzmin and Möller in Flux-corrected transport: principles, algorithms, and applications. Springer, Berlin, 2005; Kuzmin and Turek in J Comput Phys 175:525–558, 2002; J Comput Phys 198:131–158, 2004) to nonconforming finite element methods for the linear transport equation. Accurate nonoscillatory approximations to convection-dominated flows are obtained by stabilizing the continuous Galerkin method by solution-dependent artificial diffusion. Its magnitude is controlled by a flux limiter. This concept dates back to flux-corrected transport schemes. The unique feature of AFC is that all information is extracted from the system matrices which are manipulated to satisfy certain mathematical constraints. AFC schemes have been devised with conforming $P_1$ and $Q_1$ finite elements in mind but this is not a prerequisite. Here, we consider their extension to the nonconforming Crouzeix–Raviart element (Crouzeix and Raviart in RAIRO R3 7:33–76, 1973) on triangular meshes and its quadrilateral counterpart, the class of rotated bilinear Rannacher–Turek elements (Rannacher and Turek in Numer Methods PDEs 8:97–111, 1992). The underlying design principles of AFC schemes are shown to hold for (some variant of) both elements. However, numerical tests for a purely convective flow and a convection–diffusion problem demonstrate that flux-corrected solutions are overdiffusive for the Crouzeix–Raviart element. Good resolution of smooth and discontinuous profiles is attested to $Q_1^\mathrm{nc}$ approximations on quadrilateral meshes. A synthetic benchmark is used to quantify the artificial diffusion present in conforming and nonconforming high-resolution schemes of AFC-type. Finally, the implementation of efficient sparse matrix–vector multiplications is addressed.     

Vibration study and classification of rotor faults in PM synchronous motor

Thanks for the precision engineering technology, motor, especially Permanent Magnet Synchronous Motor can be made as Micro-motor. However, any imprecise rotor parts of this meticulous motor could lead to undesirable vibration and acoustic noise (Yu et al. in 3D influence of unbalanced magnetic pull induced by misalignment rotor in PMSM, APMRC2012, 2012; Bi et al. in Influence of axial asymmetrical rotor in PMAC motor operation, ICEMS, 2011; Bi et al. in Influence of rotor eccentricity to unbalanced-magnetic-pull in pm synchronous motor, ICEMS06, 2006). This paper presents five types of rotor faults design and vibration study of these five types of faults in motor is conducted. Based on the vibration pattern, fuzzy mathematics is employed to classify these five types of rotor faults.     

A Uniform Paradigm to Succinctly Encode Various Families of Trees

We propose a uniform method to encode various types of trees succinctly. These families include ordered (ordinal), k-ary (cardinal), and unordered (free) trees. We will show the approach is intrinsically suitable for obtaining entropy-based encodings of trees (such as the degree-distribution entropy). Previously-existing succinct encodings of trees use ad hoc techniques to encode each particular family of trees. Additionally, the succinct encodings obtained using the uniform approach improve upon the existing succinct encodings of each family of trees; in the case of ordered trees, it simplifies the encoding while supporting the full set of navigational operations. It also simplifies the implementation of many supported operations. The approach applied to k-ary trees yields a succinct encoding that supports both cardinal-type operations (e.g. determining the child label i) as well as the full set of ordinal-type operations (e.g. reporting the number of siblings to the left of a node). Previous work on succinct encodings of k-ary trees does not support both types of operations simultaneously (Benoit et al. in Algorithmica 43(4):275–292, 2005; Raman et al. in ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 233–242, 2002). For unordered trees, the approach achieves the first succinct encoding. The approach is based on two recursive decompositions of trees into subtrees. Recursive decomposition of a structure into substructures is a common technique in succinct encodings and has even been used to encode (ordered) trees (Geary et al. in ACM Trans. Algorithms 2(4):510–534, 2006; He et al. in ICALP, pp. 509–520, 2007) and dynamic binary trees (Munro et al. in ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 529–536, 2001; Storm in Representing dynamic binary trees succinctly, Master’s thesis, 2000). The main distinction of the approach in this paper is that a tree is decomposed into subtrees in a manner that the subtrees are maximally isolated from each other. This intermediate decomposition result is interesting in its own right and has proved useful in other applications (Farzan et al. in ICALP (1), pp. 451–462, 2009; Farzan and Munro in ICALP (1), pp. 439–450, 2009; Farzan and Kamali in ICALP, 2011).     

Hermitian Compact Interpolation on the Cubed-Sphere Grid

The cubed-sphere grid is a spherical grid made of six quasi-cartesian square-like patches. It was originally introduced in Sadourny (Mon Weather Rev 100:136–144, 1972). We extend to this grid the design of high-order finite-difference compact operators (Collatz, The numerical treatment of differential equations. Springer, Berlin, 1960; Lele, J Comput Phys 103:16–42, 1992). The present work is limitated to the design of a fourth-order accurate spherical gradient. The treatment at the interface of the six patches relies on a specific interpolation system which is based on using great circles in an essential way. The main interest of the approach is a fully symmetric treatment of the sphere. We numerically demonstrate the accuracy of the approximate gradient on several test problems, including the cosine-bell test-case of Williamson et al. (J Comput Phys 102:211–224, 1992) and a deformational test-case reported in Nair and Lauritzen (J Comput Phys 229:8868–8887, 2010).     

Principal tests and verification of a resonance-based solar harvester utilizing micro/nano technology

The authors propose an analysis of a model solar element based on the principle of a resonance system facilitating the transformation of the external form of incident energy into electrical energy. A similar principle provides the basis for harvesters designed to operate at lower frequencies, (Jirku et al. Microsyst Technol 16:677–690, 2010; Wen et al. In: Proceedings of World Automation Congress, Maui, 2000). In these harvesters, the efficiency of the energy form transformation can be controlled from the frequency spectrum of an external source.     

Fast Phylogeny Reconstruction Through Learning of Ancestral Sequences

Given natural limitations on the length DNA sequences, designing phylogenetic reconstruction methods which are reliable under limited information is a crucial endeavor. There have been two approaches to this problem: reconstructing partial but reliable information about the tree (Mossel in IEEE Comput. Biol. Bioinform. 4:108–116, 2007; Daskalakis et al. in SIAM J. Discrete Math. 25:872–893, 2011; Daskalakis et al. in Proc. of RECOMB 2006, pp. 281–295, 2006; Gronau et al. in Proc. of the 19th Annual SODA 2008, pp. 379–388, 2008), and reaching “deeper” in the tree through reconstruction of ancestral sequences. In the latter category, Daskalakis et al. (Proc. of the 38th Annual STOC, pp. 159–168, 2006) settled an important conjecture of M. Steel (My favourite conjecture. Preprint, 2001), showing that, under the CFN model of evolution, all trees on n leaves with edge lengths bounded by the Ising model phase transition can be recovered with high probability from genomes of length O(logn) with a polynomial time algorithm. Their methods had a running time of O(n ¹⁰). Here we enhance our methods from Daskalakis et al. (Proc. of RECOMB 2006, pp. 281–295, 2006) with the learning of ancestral sequences and provide an algorithm for reconstructing a sub-forest of the tree which is reliable given available data, without requiring a-priori known bounds on the edge lengths of the tree. Our methods are based on an intuitive minimum spanning tree approach and run in O(n ³) time. For the case of full reconstruction of trees with edges under the phase transition, we maintain the same asymptotic sequence length requirements as in Daskalakis et al. (Proc. of the 38th Annual STOC, pp. 159–168, 2006), despite the considerably faster running time.     

The Duo-Item Bisection Auction

This paper proposes an iterative sealed-bid auction for selling multiple heterogeneous items to bidders interested in buying at most one item. It generalizes the single item bisection auction (Grigorieva et al. Econ Theory, 30:107–118, 2007) to the environment with multiple heterogeneous items. We focus on the case with two items for sale. We show that the auction elicits a minimal amount of information on preferences required to find the Vickrey–Clark–Groves outcome (Clarke, Public Choice, XI:17–33, 1971; Groves, Econometrica, 61:617–631, 1973; Vickrey, J Finance, 16:8–37, 1961), when there are two items for sale and an arbitrary number of bidders.     

Technical, legal and ethical dilemmas: distinguishing risks arising from malware and cyber-attack tools in the ‘cloud’—a forensic computing perspective

While hype around the benefits of ‘cloud computing’increase, challenges in maintaining data security and data privacy have also been recognised as significant vulnerabilities (Ristenpart et al. in Proceedings of the 14th ACM conference on computer and communications security, pp 103–115, 2009; Pearson in CLOUD’09, pp 44–52, 2009; Vouk in J Comput Inf Technol 4:235–246, 2008). These vulnerabilities generate a range of questions relating to the capacity of organisations relying on cloud solutions to effectively manage risk. This has become particularly the case as the threats faced by organisations have moved increasingly away from indiscriminate malware to more targeted cyber-attack tools. From forensic computing perspective it has also been recognised that ‘cloud solutions’ pose additional challenges for forensic computing specialists including discoverability and chain of evidence (Ruan et al. in Adv Digital Forensics VII:35–46, 2011; Reilly et al. in Int J Multimedia Image Process 1:26–34, 2011). However, to date there has been little consideration of how the differences between indiscriminate malware and targeted cyber-attack tools further problematize the capacity of organisations to manage risk. This paper also considers these risks and differentiates between technical, legal and ethical dilemmas posed. The paper also highlights the need for organisations to be aware of these issues when deciding to move to cloud solutions.     

A Comparison of Iterated Optimal Stopping and Local Policy Iteration for American Options Under Regime Switching

A theoretical analysis tool, iterated optimal stopping, has been used as the basis of a numerical algorithm for American options under regime switching (Le and Wang in SIAM J Control Optim 48(8):5193–5213, 2010). Similar methods have also been proposed for American options under jump diffusion (Bayraktar and Xing in Math Methods Oper Res 70:505–525, 2009) and Asian options under jump diffusion (Bayraktar and Xing in Math Fin 21(1):117–143, 2011). An alternative method, local policy iteration, has been suggested in Huang et al. (SIAM J Sci Comput 33(5):2144–2168, 2011), and Salmi and Toivanen (Appl Numer Math 61:821–831, 2011). Worst case upper bounds on the convergence rates of these two methods suggest that local policy iteration should be preferred over iterated optimal stopping (Huang et al. in SIAM J Sci Comput 33(5):2144–2168, 2011). In this article, numerical tests are presented which indicate that the observed performance of these two methods is consistent with the worst case upper bounds. In addition, while these two methods seem quite different, we show that either one can be converted into the other by a simple rearrangement of two loops.     

Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective

In the past decades, Model Order Reduction (MOR) has demonstrated its robustness and wide applicability for simulating large-scale mathematical models in engineering and the sciences. Recently, MOR has been intensively further developed for increasingly complex dynamical systems. Wide applications of MOR have been found not only in simulation, but also in optimization and control. In this survey paper, we review some popular MOR methods for linear and nonlinear large-scale dynamical systems, mainly used in electrical and control engineering, in computational electromagnetics, as well as in micro- and nano-electro-mechanical systems design. This complements recent surveys on generating reduced-order models for parameter-dependent problems (Benner et al. in 2013; Boyaval et al. in Arch Comput Methods Eng 17(4):435–454, 2010; Rozza et al. Arch Comput Methods Eng 15(3):229–275, 2008) which we do not consider here. Besides reviewing existing methods and the computational techniques needed to implement them, open issues are discussed, and some new results are proposed.     

Analytic expressions of quantum correlations in qutrit Werner states

Quantum correlations in qutrit Werner states are extensively investigated with five popular methods, namely, original quantum discord (OQD) (Ollivier and Zurek in Phys Rev Lett 88:017901, 2001), measurement-induced disturbance (MID) (Luo in Phys Rev A 77:022301, 2008), ameliorated MID (AMID) (Girolami et al. in J Phys A Math Theor 44:352002, 2011), relative entropy (RE) (Modi et al. in Phys Rev Lett 104:080501, 2010) and geometric discord (GD) (Daki? et al. in Phys Rev Lett 105:190502, 2010). Two different analytic expressions of quantum correlations are derived. Quantum correlations captured by the former four methods are same and bigger than those obtained via the GD method. Nonetheless, they all qualitatively characterize quantum correlations in the concerned states. Moreover, as same as the qubit case, there exist quantum correlations in separable qutrit Werner states, too.