Time-optimal control of a 3-level quantum system and its generalization

We solve the problem of steering a three-level quantum system from one eigen-state to another in minimum time and study its possible extension to the time-optimal control problem for a general n-level quantum system. For the three-level system we find all optimal controls by finding two types of symmetry in the problems: ℤ × S3 discrete symmetry and 51 continuous symmetry, and exploiting them to solve the problem through discrete reduction and symplectic reduction. We then study the geometry, in the same framework, which occurs in the time-optimal control of a general n-level quantum system. Copyright ©2007 Watam Press.

Continuous dynamical systems that realize discrete optimization on the hypercube

We study the problem of finding a local minimum of a multilinear function E over the discrete set {0,1}n. The search is achieved by a gradient-like system in [0,1]n with cost function E. Under mild restrictions on the metric, the stable attractors of the gradient-like system are shown to produce solutions of the problem, even when they are not in the vicinity of the discrete set {0,1}n. Moreover, the gradient-like system connects with interior point methods for linear programming and with the analog neural network studied by Vidyasagar (IEEE Trans. Automat. Control 40 (8) (1995) 1359), in the same context. © 2004 Elsevier B.V. All rights reserved.

A new approach to the analytical and numerical form-finding of tensegrity structures

We develop a new formulation for the form-finding of tensegrity structures in which the primary variables are the Cartesian components of element lengths. Both an analytical and a numerical implementation of the formulation are described; each require a description of the connectivity of the tensegrity, with the iterative numerical method also requiring a random starting vector of member force densities. The analytical and numerical form-finding of tensegrity structures is demonstrated through six examples, and the results obtained are compared and contrasted with those available in the literature to verify the accuracy and viability of the suggested methods. © 2013 Elsevier Ltd. All rights reserved.

The inverse problem in magnetic force microscopy--inferring sample magnetization from MFM images.

Nanomagnetic structures have the potential to surpass silicon's scaling limitations both as elements in hybrid CMOS logic and as novel computational elements. Magnetic force microscopy (MFM) offers a convenient characterization technique for use in the design of such nanomagnetic structures. MFM measures the magnetic field and not the sample's magnetization. As such the question of the uniqueness of the relationship between an external magnetic field and a magnetization distribution is a relevant one. To study this problem we present a simple algorithm which searches for magnetization distributions consistent with an external magnetic field and solutions to the micromagnetic equations' qualitative features. The algorithm is not computationally intensive and is found to be effective for our test cases. On the basis of our results we propose a systematic approach for interpreting MFM measurements.

Application of the multi-objective Alliance algorithm to a benchmark aerodynamic optimization problem

This paper introduces a new version of the multiobjective Alliance Algorithm (MOAA) applied to the optimization of the NACA 0012 airfoil section, for minimization of drag and maximization of lift coefficients, based on eight section shape parameters. Two software packages are used: XFoil which evaluates each new candidate airfoil section in terms of its aerodynamic efficiency, and a Free-Form Deformation tool to manage the section geometry modifications. Two versions of the problem are formulated with different design variable bounds. The performance of this approach is compared, using two indicators and a statistical test, with that obtained using NSGA-II and multi-objective Tabu Search (MOTS) to guide the optimization. The results show that the MOAA outperforms MOTS and obtains comparable results with NSGA-II on the first problem, while in the other case NSGA-II is not able to find feasible solutions and the MOAA is able to outperform MOTS. © 2013 IEEE.

Gene structure and transcription of IRF-2 in the mandarin fish Siniperca chuatsi with the finding of alternative transcripts and microsatellite in the coding region

The gene of interferon regulatory factor-2 (IRF-2) has been cloned from the mandarin fish (Siniperca chuatsi). The IRF-2 gene has 6,418 nucleotides (nt) and contains eight exons and seven introns, encoding two mRNAs. The two IRF-2 mRNAs each contained an open reading frame of 873 nt, which both translate into the same 291 amino acids but differed in their 5' untranslated region: one mRNA was transcribed initially from the exon 1 bypassing exon 2, while the other was transcribed from the exon 2. The microsatellites (CA repeats) could be found in the carboxyl terminal region of mandarin fish IRF-2, which result in the truncated form molecules. The microsatellites' polymorphism was investigated, and eight alleles were found in 16 individuals. The microsatellites were also examined in IRF-2 of several freshwater perciform fishes. The transcription of the IRF-2 in different tissues with or without poly inosine-cytidine stimulation was analyzed by real-time PCR, and the constitutive transcription of both molecules could be detected in all the tissues examined.

Obtaining the shape of a moving object with a specular surface

This paper addresses the basic problem of recovering the 3D surface of an object that is observed in motion by a single camera and under a static but unknown lighting condition. We propose a method to establish pixelwise correspondence between input images by way of depth search by investigating optimal subsets of intensities rather than employing all the relevant pixel values. The thrust of our algorithm is that it is capable of dealing with specularities which appear on the top of shading variance that is caused due to object motion. This is in terms of both stages of finding sparse point correspondence and dense depth search. We also propose that a linearised image basis can be directly computed by the procudure of finding the correspondence. We illustrate the performance of the theoretical propositions using images of real objects. © 2009. The copyright of this document resides with its authors.

System Dynamics and Scenario Planning: Implementation Challenges

In this paper we discuss key implementation challenges of a systems approach that combines System Dynamics, Scenario Planning and Qualitative Data Analysis methods in tackling a complex problem. We present the methods and the underlying framework. We then detail the main difficulties encountered in designing and planning the Scenario Planning workshop and how they were overcome, such as finding and involving the stakeholders and customising the process to fit within timing constraints. After presenting the results from this application, we argue that the consultants or system analysts need to engage with the stakeholders as process facilitators and not as system experts in order to gain commitment, trust and to improve information sharing. They also need be ready to adapt their tools and processes as well as their own thinking for more effective complex problem solving.

Finding resonance: Adaptive frequency oscillators for dynamic legged locomotion

There is much to gain from providing walking machines with passive dynamics, e.g. by including compliant elements in the structure. These elements can offer interesting properties such as self-stabilization, energy efficiency and simplified control. However, there is still no general design strategy for such robots and their controllers. In particular, the calibration of control parameters is often complicated because of the highly nonlinear behavior of the interactions between passive components and the environment. In this article, we propose an approach in which the calibration of a key parameter of a walking controller, namely its intrinsic frequency, is done automatically. The approach uses adaptive frequency oscillators to automatically tune the intrinsic frequency of the oscillators to the resonant frequency of a compliant quadruped robot The tuning goes beyond simple synchronization and the learned frequency stays in the controller when the robot is put to halt. The controller is model free, robust and simple. Results are presented illustrating how the controller can robustly tune itself to the robot, as well as readapt when the mass of the robot is changed. We also provide an analysis of the convergence of the frequency adaptation for a linearized plant, and show how that analysis is useful for determining which type of sensory feedback must be used for stable convergence. This approach is expected to explain some aspects of developmental processes in biological and artificial adaptive systems that "develop" through the embodied system-environment interactions. © 2006 IEEE.

Excision of Sleeping Beauty transposons: parameters and applications to gene therapy

A major problem in gene therapy is the determination of the rates at which gene transfer has occurred. Our work has focused on applications of the Sleeping Beauty (SB) transposon system as a non-viral vector for gene therapy. Excision of a transposon from a donor molecule and its integration into a cellular chromosome are catalyzed by SB transposase. In this study, we used a plasmid-based excision assay to study the excision step of transposition. We used the excision assay to evaluate the importance of various sequences that border the sites of excision inside and outside the transposon in order to determine the most active sequences for transposition from a donor plasmid. These findings together with our previous results in transposase binding to the terminal repeats suggest that the sequences in the transposon-junction of SB are involved in steps subsequent to DNA binding but before excision, and that they may have a role in transposase-transposon interaction. We found that SB transposons leave characteristically different footprints at excision sites in different cell types, suggesting that alternative repair machineries operate in concert with transposition. Most importantly, we found that the rates of excision correlate with the rates of transposition. We used this finding to assess transposition in livers of mice that were injected with the SB transposon and transposase. The excision assay appears to be a relatively quick and easy method to optimize protocols for delivery of genes in SB transposons to mammalian chromosomes in living animals. Copyright (C) 2004 John Wiley Sons, Ltd.

reducing symmetries to generate easier sat instances

Finding countermodels is an effective way of disproving false conjectures. In first-order predicate logic, model finding is an undecidable problem. But if a finite model exists, it can be found by exhaustive search. The finite model generation problem in the first-order logic can also be translated to the satisfiability problem in the propositional logic. But a direct translation may not be very efficient. This paper discusses how to take the symmetries into account so as to make the resulting problem easier. A static method for adding constraints is presented, which can be thought of as an approximation of the least number heuristic (LNH). Also described is a dynamic method, which asks a model searcher like SEM to generate a set of partial models, and then gives each partial model to a propositional prover. The two methods are analyzed, and compared with each other.

on lin-bose problem

This paper study generalized Serre problem proposed by Lin and Bose in multidimensional system theory context [Multidimens. Systems and Signal Process. 10 (1999) 379; Linear Algebra Appl. 338 (2001) 125]. This problem is stated as follows. Let F ∈ Al×m be a full row rank matrix, and d be the greatest common divisor of all the l × l minors of F. Assume that the reduced minors of F generate the unit ideal, where A = K[x 1,...,xn] is the polynomial ring in n variables x 1,...,xn over any coefficient field K. Then there exist matrices G ∈ Al×l and F1 ∈ A l×m such that F = GF1 with det G = d and F 1 is a ZLP matrix. We provide an elementary proof to this problem, and treat non-full rank case.