Joint spectrum shrinking maps on projections

Let $\mathcal H$ be a finite dimensional complex Hilbert space with dimension $n \ge 3$ and $\mathcal P(\mathcal H)$ the set of projections on $\mathcal H$. Let $\varphi: \mathcal P(\mathcal H) \to \mathcal P(\mathcal H)$ be a surjective map. We show that $\varphi$ shrinks the joint spectrum of any two projections if and only if it is joint spectrum preserving for any two projections and thus is induced by a ring automorphism on $\mathbb C$ in a particular way. In addition, for an arbitrary $k \ge 3$, $\varphi$ shrinks the joint spectrum of any $k$ projections if and only if it is induced by a unitary or an anti-unitary. Assume that $\phi$ is a surjective map on the Grassmann space of rank one projections. We show that $\phi$ is joint spectrum preserving for any $n$ rank one projections if and only if it can be extended to a surjective map on $\mathcal P(\mathcal{H})$ which is spectrum preserving for any two projections. Moreover, for any $k >n$, $\phi$ is joint spectrum shrinking for any $k$ rank one projections if and only if it is induced by a unitary or an anti-unitary.Comment: 14 page

LP-BFGS attack: An adversarial attack based on the Hessian with limited pixels

Deep neural networks are vulnerable to adversarial attacks. Most white-box attacks are based on the gradient of models to the input. Since the computation and memory budget, adversarial attacks based on the Hessian information are not paid enough attention. In this work, we study the attack performance and computation cost of the attack method based on the Hessian with a limited perturbation pixel number. Specifically, we propose the Limited Pixel BFGS (LP-BFGS) attack method by incorporating the BFGS algorithm. Some pixels are selected as perturbation pixels by the Integrated Gradient algorithm, which are regarded as optimization variables of the LP-BFGS attack. Experimental results across different networks and datasets with various perturbation pixel numbers demonstrate our approach has a comparable attack with an acceptable computation compared with existing solutions.Comment: 5 pages, 4 figure

A dynamic simulation model for financing strategy management of infrastructure PPP projects

Strategic management is vital for significant infrastructure public-private partnership (PPP) projects characterised by a heavy and irreversible investment over a long period. In PPP projects, the financing strategy relates to the capital structure of the project and the coordination of the participants’ requirements. In this paper, a system dynamics (SD) model is described to analyse the impacts of two types of financing strategies on the needs of creditors, the government, and private investors, considering the dynamic and complex characteristics of infrastructure PPP projects. The proposed model has been implemented on a PPP highway project. A number of experiments were conducted over a 33-year strategic planning horizon as a means of assessing the long-term effects of different financing strategies. The experimental results reveal that the model is a useful tool that could support decision-makers in identifying the intervals with different management focus of financing risk and comparing different financing strategies to choose the optimal one. It is especially helpful for the government to select a financing strategy for infrastructure PPP projects with capital limitations

Image abstraction painting of flow-like stylization

U radu se predstavlja tehnika ne-fotorealističkog prikaza u kojoj se iz fotografije dobiva stilizirana apstraktna slika s tonovima koji se prelijevaju. Zasnovana na Kuwahara filtrima i integralnim spiralnim linijama, naša metoda simultano apstrahira oblike i boje, zadržavajući u isto vrijeme osnovna obilježja slika. Posebno razvijamo metodu proširenja i detekcije ruba i usmjeravamo pažnju na specifična obilježja i rubne dijelove slike. Predloženi je algoritam promjenljiv i iterativan te se stupanj prelijevanja tonova i apstrakcije može regulirati. Eksperimentalni rezultati pokazuju da je učinkovitost naše metode u postizanju koherentne i stilizirane apstrakcije zadovoljavajuća, uz zadržavanje osnovnih obilježja iz zadanih fotografija.This paper presents a non-photorealistic rendering technique for producing flow-like abstraction stylization from a photograph. Based on anisotropic Kuwahara filtering in conjunction with line integral convolution, our method abstracts shapes and colors simultaneously while preserving features of images. In particular, we develop an edge detection and dilation method, to draw attention to salient features and image boundaries. This proposed algorithm is incremental and iterative, and therefore the degree of flow and abstraction can be controlled. Experimental results demonstrate that the effectiveness of our method in producing a coherent and flow-like abstraction stylization is satisfactory yet preserving features and directions from photographs

On Two-Level State-Dependent Routing Polling Systems with Mixed Service

Based on priority differentiation and efficiency of the system, we consider an N+1 queues’ single-server two-level polling system which consists of one key queue and N normal queues. The novel contribution of the present paper is that we consider that the server just polls active queues with customers waiting in the queue. Furthermore, key queue is served with exhaustive service and normal queues are served with 1-limited service in a parallel scheduling. For this model, we derive an expression for the probability generating function of the joint queue length distribution at polling epochs. Based on these results, we derive the explicit closed-form expressions for the mean waiting time. Numerical examples demonstrate that theoretical and simulation results are identical and the new system is efficient both at key queue and normal queues