Constructive quantum scaling of unitary matrices

In this work, we present a method of decomposition of arbitrary unitary matrix \(U\in \mathbf {U}(2^k)\) into a product of single-qubit negator and controlled-\(\sqrt{\text{ NOT }}\) gates. Since the product results with negator matrix, which can be treated as complex analogue of bistochastic matrix, our method can be seen as complex analogue of Sinkhorn–Knopp algorithm, where diagonal matrices are replaced by adding and removing an one-qubit ancilla. The decomposition can be found constructively, and resulting circuit consists of \(O(4^k)\) entangling gates, which is proved to be optimal. An example of such transformation is presented.     

Central limit theorem for reducible and irreducible open quantum walks

In this work we aim at proving central limit theorems for open quantum walks on \({\mathbb {Z}}^d\). We study the case when there are various classes of vertices in the network. In particular, we investigate two ways of distributing the vertex classes in the network. First, we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a transition invariant distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.     

Studies on a New Concept of 3D Data Integration about Reaches and Forces of a Disabled Person on a Wheelchair (CAD Methods in Car and Market Ergonomics)

The article presents a new concept of combining the three dimensions (3D) of a person's manipulation space. The data concern information about the reach of the arms and biomechanical data about limiting the load of a disabled person sitting in a wheelchair. Measurement data were acquired empirically, on original measuring station. The data included, respectively, arms' reach (static and dynamic) or, alternatively, measurements of limiting forces. The obtained data were processed into virtual 3D surfaces of arms' reach and forces. These surfaces provide the required graphic model of anthropotechnical and biomechanical data. Developed model was utilized to perform a virtual analysis of the accessibility of a disabled person to technical means: in a market sale space and in the ergonomic analysis into the space of a personal car. The presented method of 3D graphic modeling of anthropometrical and biomechanical data can be universally applied in ergonomic designing of work stations not only for disabled persons. © 2011 Wiley Periodicals, Inc.     

Code reordering using local random extraction and insertion (LREI) operator for GPGPU-based track-before-detect systems

Track-before-detect (TBD) algorithms are used for tracking systems, where the object’s signal is below the noise floor (low-SNR objects). A lot of computations and memory transfers for real-time signal processing are necessary. GPGPU in parallel processing devices for TBD algorithms is well suited. Finding optimal or suboptimal code, due to lack of documentation for low-level programming of GPGPUs is not possible. High-level code optimization is necessary and the evolutionary approach, based on the single parent and single child is considered, that is local search approach. Brute force search technique is not feasible, because there are N! code variants, where N is the number of motion vectors components. The proposed evolutionary operator—LREI (local random extraction and insertion) allows source code reordering for the reduction of computation time due to better organization of memory transfer and the texture cache content. The starting point, based on the sorting and the minimal execution time metric is proposed. The unbiased random and biased sorting techniques are compared using experimental approach. Tests shows significant improvements of the computation speed, about 8 % over the conventional code for CUDA code. The time period of optimization for the sample code is about 1 h (1,000 iterations) for the considered recursive spatio-temporal TBD algorithm.     

Hydrophilic polycarbonate chips for generation of oil-in-water (O/W) and water-in-oil-in-water (W/O/W) emulsions

Modification of the surfaces of polycarbonate (PC) with the use of a solution of tin (II) chloride renders them hydrophilic. The surface draping is stable against exposure to water and to alcohols. Exposure to alkanes reduces but does not diminish the effect. The method is compatible—in using the same solvent and temperature—with the hydrophobic modification of PC (Jankowski et al. in Lab Chip 11:1151–1156, 2011). The combination of these methods makes it possible to generate single and multiple monodisperse emulsions with the use of flow-focusing junctions in systems made in PC—a material that is suitable for fabrication of multilayer, high-throughput microfluidic devices.     

Hydrophilic polycarbonate chips for generation of oil-in-water (O/W) and water-in-oil-in-water (W/O/W) emulsions

Modification of the surfaces of polycarbonate (PC) with the use of a solution of tin (II) chloride renders them hydrophilic. The surface draping is stable against exposure to water and to alcohols. Exposure to alkanes reduces but does not diminish the effect. The method is compatible—in using the same solvent and temperature—with the hydrophobic modification of PC Jankowski et al. ( Lab Chip 11:748–752, 2011). The combination of these methods makes it possible to generate single and multiple monodisperse emulsions with the use of flow-focusing junctions in systems made in PC—material that is suitable for fabrication of multilayer, high throughput microfluidic devices.     

Control of Robot Manipulators in Terms of Quasi-Velocities

In this paper we present new control algorithms for robots with dynamics described in terms of quasi-velocities (Kozłowski, Identification of articulated body inertias and decoupled control of robots in terms of quasi-coordinates. In: Proc. of the 1996 IEEE International Conference on Robotics and Automation, pp. 317–322. IEEE, Piscataway, 1996a; Zeitschrift für Angewandte Mathematik und Mechanik 76(S3):479–480, 1996c; Robot control algorithms in terms of quasi-coordinates. In: Proc. of the 34 Conference on Decision and Control, pp. 3020–3025, Kobe, 11–13 December 1996, 1996d). The equations of motion are written using spatial quantities such as spatial velocities, accelerations, forces, and articulated body inertia matrices (Kozłowski, Standard and diagonalized Lagrangian dynamics: a comparison. In: Proc. of the 1995 IEEE Int. Conf. on Robotics and Automation, pp. 2823–2828. IEEE, Piscataway, 1995b; Rodriguez and Kreutz, Recursive Mass Matrix Factorization and Inversion, An Operator Approach to Open- and Closed-Chain Multibody Dynamics, pp. 88–11. JPL, Dartmouth, 1998). The forward dynamics algorithms incorporate new control laws in terms of normalized quasi-velocities. Two cases are considered: end point trajectory tracking and trajectory tracking algorithm, in general. It is shown that by properly choosing the Lyapunov function candidate a dynamic system with appropriate feedback can be made asymptotically stable and follows the desired trajectory in the task space. All of the control laws have a new architecture in the sense that they are derived, in the so-called quasi-velocity and quasi-force space, and at any instant of time generalized positions and forces can be recovered from order recursions, where denotes the number of degrees of freedom of the manipulator. This paper also contains the proposition of a sliding mode control, originally introduced by Slotine and Li (Int J Rob Res 6(3):49–59, 1987), which has been extended to the sliding mode control in the quasi-velocity and quasi-force space. Experimental results illustrate behavior of the new control schemes and show the potential of the approach in the quasi-velocity and quasi-force space. Authors are with Chair of Control and Systems Engineering.