Service Provisioning for Multi-source IoT Applications in Mobile Edge Computing

We are embracing an era of Internet of Things (IoT). The latency brought by unstable wireless networks caused by limited resources of IoT devices seriously impacts the quality of services of users, particularly the service delay they experienced. Mobile Edge Computing (MEC) technology provides promising solutions to delay-sensitive IoT applications, where cloudlets (edge servers) are co-located with wireless access points in the proximity of IoT devices. The service response latency for IoT applications can be significantly shortened due to that their data processing can be performed in a local MEC network. Meanwhile, most IoT applications usually impose Service Function Chain (SFC) enforcement on their data transmission, where each data packet from its source gateway of an IoT device to the destination (a cloudlet) of the IoT application must pass through each Virtual Network Function (VNF) in the SFC in an MEC network. However, little attention has been paid on such a service provisioning of multi-source IoT applications in an MEC network with SFC enforcement. In this article, we study service provisioning in an MEC network for multi-source IoT applications with SFC requirements and aiming at minimizing the cost of such service provisioning, where each IoT application has multiple data streams from different sources to be uploaded to a location (cloudlet) in the MEC network for aggregation, processing, and storage purposes. To this end, we first formulate two novel optimization problems: the cost minimization problem of service provisioning for a single multi-source IoT application, and the service provisioning problem for a set of multi-source IoT applications, respectively, and show that both problems are NP-hard. Second, we propose a service provisioning framework in the MEC network for multi-source IoT applications that consists of uploading stream data from multiple sources of the IoT application to the MEC network, data stream aggregation and routing through the VNF instance placement and sharing, and workload balancing among cloudlets. Third, we devise an efficient algorithm for the cost minimization problem built upon the proposed service provisioning framework, and further extend the solution for the service provisioning problem of a set of multi-source IoT applications. We finally evaluate the performance of the proposed algorithms through experimental simulations. Simulation results demonstrate that the proposed algorithms are promising.

On optimal cloaking-by-mapping transformations

A central ingredient of cloaking-by-mapping is the diffeomorphisn which transforms an annulus with a small hole into an annulus with a finite size hole, while being the identity on the outer boundary of the annulus. The resulting meta-material is anisotropic, which makes it difficult to manufacture. The problem of minimizing anisotropy among radial transformations has been studied in [4]. In this work, as in [4], we formulate the problem of minimizing anisotropy as an energy minimization problem. Our main goal is to provide strong evidence for the conjecture that for cloaks with circular boundaries, non-radial transformations do not lead to lower degree of anisotropy. In the final section, we consider cloaks with non-circular boundaries and show that in this case, non-radial cloaks may be advantageous, when it comes to minimizing anisotropy.

Quantum and Classical Log-Bounded Automata for the Online Disjointness Problem

We consider online algorithms with respect to the competitive ratio. In this paper, we explore one-way automata as a model for online algorithms. We focus on quantum and classical online algorithms. For a specially constructed online minimization problem, we provide a quantum log-bounded automaton that is more effective (has less competitive ratio) than classical automata, even with advice, in the case of the logarithmic size of memory. We construct an online version of the well-known Disjointness problem as a problem. It was investigated by many researchers from a communication complexity and query complexity point of view.

A Proximal Algorithm with Convergence Guarantee for a Nonconvex Minimization Problem Based on Reproducing Kernel Hilbert Space

The underlying function in reproducing kernel Hilbert space (RKHS) may be degraded by outliers or deviations, resulting in a symmetry ill-posed problem. This paper proposes a nonconvex minimization model with ℓ0-quasi norm based on RKHS to depict this degraded problem. The underlying function in RKHS can be represented by the linear combination of reproducing kernels and their coefficients. Thus, we turn to estimate the related coefficients in the nonconvex minimization problem. An efficient algorithm is designed to solve the given nonconvex problem by the mathematical program with equilibrium constraints (MPEC) and proximal-based strategy. We theoretically prove that the sequences generated by the designed algorithm converge to the nonconvex problem’s local optimal solutions. Numerical experiment also demonstrates the effectiveness of the proposed method.

An accelerated majorization-minimization algorithm with convergence guarantee for non-Lipschitz wavelet synthesis model *

We consider a wavelet based image reconstruction model with the ℓ p (0 < p < 1) quasi-norm regularization, which is a non-convex and non-Lipschitz minimization problem. For solving this model, Figueiredo et al (2007 IEEE Trans. Image Process. 16 2980–2991) utilized the classical majorization-minimization framework and proposed the so-called Isoft algorithm. This algorithm is computationally efficient, but whether it converges or not has not been concluded yet. In this paper, we propose a new algorithm to accelerate the Isoft algorithm, which is based on Nesterov’s extrapolation technique. Furthermore, a complete convergence analysis for the new algorithm is established. We prove that the whole sequence generated by this algorithm converges to a stationary point of the objective function. This convergence result contains the convergence of Isoft algorithm as a special case. Numerical experiments demonstrate good performance of our new algorithm.

A minimization problem for the sum of weighted convolutions’ difference and a novel approach to the inverse problem of ECG- and PPG-signals recovering

In this paper, we consider an unstudied problem of approximation of an observed pulse train by by a quasiperiodic signal generated by a pulse with a given pattern (reference) shape. The quasiperiodicity allows variation of time intervals between repetitions of the pattern pulse, as well as nonlinear expansions of the pattern in time. Such inverse problems are common in electrocardiogram (ECG) and photoplethysmogram (PPG) features extraction. The following two variants of the problem are considered. In the first variant, the number of the pulse repetitions is unknown, while in the second one, that number is given. The polynomial-time solvability of the both variants of the problem is constructively proved.

Dynamic Decals

Pervasive interfaces can present relevant information anywhere in our environment, and they are thus challenged by the non rectilinearity of the display surface (e.g. circular table) and by the presence of objects that can partially occlude the interface (e.g. a book or cup on the table). To tackle this problem, we propose a novel solution based on two core contributions: the decomposition of the interface into deformable graphical units, called Dynamic Decals, and the control of their position and behaviour by a constraint-based approach. Our approach dynamically deforms the interface when needed while minimizing the impact on its visibility and layout properties. To do so, we extend previous work on implicit deformations to propose and experimentally validate functions defining different decal shapes and new deformers modeling decal deformations when they collide. Then, we interactively optimize the decal placements according to the interface geometry and their interrelations. Relations are modeled as constraints and the interface evolution results from an easy and efficient to solve minimization problem. Our approach is validated by a user study showing that, compared to two baselines, Dynamic decals is an aesthetically pleasant interface that preserves visibility, layout and aesthetic properties.