On the complexity of role updating feasibility problem in RBAC

In Role Based Access Control (RBAC) systems, it is necessary and important to update the role–permission assignments in order to reflect the evolutions of the system transactions. However, role updating is generally complex and challenging, especially for large-scale RBAC systems. This is because the resulting state is usually expected to meet various requirements and constraints. In this paper, we focus on a fundamental problem of role updating in RBAC, which determines whether there exists a valid role–permission assignment, i.e., whether it can satisfy all the requirements of the role updating and without violating any role–capacity or permission–capacity constraint. We formally define such a problem as the Role Updating Feasibility Problem (RUFP), and study the computational complexity of RUFP in different subcases. Our results show that although several subcases are solvable in linear time, this problem is NP-complete in the general case.     

Holographic algorithms on bases of rank 2

An essential problem in the design of holographic algorithms is to decide whether the required signatures can be realized under a suitable basis transformation (SRP). For holographic algorithms with matchgates on domain size 2, , ,  and  have built a systematical theory. In this paper, we reduce SRP on domain size k≥3$k\ge 3$ to SRP on domain size 2 for holographic algorithms with matchgates on bases of rank 2. Furthermore, we generalize the collapse theorem of [3] to domain size k≥3$k\ge 3$.     

Multi-label core vector machine with a zero label

Multi-label core vector machine (Rank-CVM) is an efficient and effective algorithm for multi-label classification. But there still exist two aspects to be improved: reducing training and testing computational costs further, and detecting relevant labels effectively. In this paper, we extend Rank-CVM via adding a zero label to construct its variant with a zero label, i.e., Rank-CVMz, which is formulated as the same quadratic programming form with a unit simplex constraint and non-negative ones as Rank-CVM, and then is solved by Frank–Wolfe method efficiently. Attractively, our Rank-CVMz has fewer variables to be solved than Rank-CVM, which speeds up training procedure dramatically. Further, the relevant labels are effectively detected by the zero label. Experimental results on 12 benchmark data sets demonstrate that our method achieves a competitive performance, compared with six existing multi-label algorithms according to six indicative instance-based measures. Moreover, on the average, our Rank-CVMz runs 83 times faster and has slightly fewer support vectors than its origin Rank-CVM.     

Drawing non‐layered tidy trees in linear time

The well‐known Reingold–Tilford algorithm produces tidy‐layered drawings of trees: drawings where all nodes at the same depth are vertically aligned. However, when nodes have varying heights, layered drawing may use more vertical space than necessary. A non‐layered drawing of a tree places children at a fixed distance from the parent, thereby giving a more vertically compact drawing. Moreover, non‐layered drawings can also be used to draw trees where the vertical position of each node is given, by adding dummy nodes. In this paper, we present the first linear‐time algorithm for producing non‐layered drawings. Our algorithm is a modification of the Reingold–Tilford algorithm, but the original complexity proof of the Reingold–Tilford algorithm uses an invariant that does not hold for the non‐layered case. We give an alternative proof of the algorithm and its extension to non‐layered drawings. To improve drawings of trees of unbounded degree, extensions to the Reingold–Tilford algorithm have been proposed. These extensions also work in the non‐layered case, but we show that they then cause a O(n²) run‐time. We then propose a modification to these extensions that restores the O(n) run‐time. Copyright © 2013 John Wiley & Sons, Ltd.     

Positive state controllability of positive linear systems

Controllability of positive systems by positive inputs arises naturally in applications where both external and internal variables must remain positive for all time. In many applications, particularly in population biology, the need for positive inputs is often overly restrictive. Relaxing this requirement, the notion of positive state controllability of positive systems is introduced. A connection between positive state controllability and positive input controllability of a related system is established and used to obtain Kalman-like controllability criteria. In doing so we aim to encourage further study in this underdeveloped area.     

On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, a particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to the nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding horizon control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system.     

Adaptive block size for dense QR factorization in hybrid CPU–GPU systems via statistical modeling

QR factorization is a computational kernel of scientific computing. How can the latest computer be used to accelerate this task? We investigate this topic by proposing a dense QR factorization algorithm with adaptive block sizes on a hybrid system that contains a central processing unit (CPU) and a graphic processing unit (GPU). To maximize the use of CPU and GPU, we develop an adaptive scheme that chooses block size at each iteration. The decision is based on statistical surrogate models of performance and an online monitor, which avoids unexpected occasional performance drops. We modify the highly optimized CPU–GPU based QR factorization in MAGMA to implement the proposed schemes. Numerical results suggest that our approaches are efficient and can lead to near-optimal block sizes. The proposed algorithm can be extended to other one-sided factorizations, such as LU and Cholesky factorizations.     

Closed‐Loop Identification for Control of Linear Parameter Varying Systems

This paper deals with system identification for control of linear parameter varying systems. In practical applications, it is often important to be able to identify small plant changes in an incremental manner without shutting down the system and/or disconnecting the controller; unfortunately, closed‐loop system identification is more difficult than open‐loop identification. In this paper we prove that the so‐called Hansen scheme, a technique known from linear time‐invariant systems theory for transforming closed‐loop system identification problems into open‐loop‐like problems, can be extended to accommodate linear parameter varying systems as well. We investigate the identified subsystem's parameter dependency and observe that, under mild assumptions, the identified subsystem is affine in the parameter vector. Various identification methods are compared in direct and Hansen Scheme setups in simulation studies, and the application of the Hansen Scheme is seen to improve the identification performance.     

Observability Analysis of Continuous‐Time LTI Systems with Limited Derivative Data

We consider continuous‐time LTI systems with either unknown‐input or with lack of information about the input and output derivatives. We compute the unknown‐input observability subspace and the observability subspace with unknown derivatives of input and output. We first formulate the unknown‐input observability subspace via projection matrices, then show that through having the unknown‐input observability subspace, one can easily evaluate the effect of known input and output signals but unknown derivatives on the observability subspace. Our method is demonstrated on the dynamics of a longitudinal aircraft in steady‐state flight.