Geometry of Spectral Curves and All Order Dispersive Integrable System

We propose a definition for a Tau function and a spinor kernel (closely related to Baker-Akhiezer functions), where times parametrize slow (of order 1/N) deformations of an algebraic plane curve. This definition consists of a formal asymptotic series in powers of 1/N, where the coefficients involve theta functions whose phase is linear in N and therefore features generically fast oscillations when N is large. The large N limit of this construction coincides with the algebro-geometric solutions of the multi-KP equation, but where the underlying algebraic curve evolves according to Whitham equations. We check that our conjectural Tau function satisfies Hirota equations to the first two orders, and we conjecture that they hold to all orders. The Hirota equations are equivalent to a self-replication property for the spinor kernel. We analyze its consequences, namely the possibility of reconstructing order by order in 1/N an isomonodromic problem given by a Lax pair, and the relation between "correlators", the tau function and the spinor kernel. This construction is one more step towards a unified framework relating integrable hierarchies, topological recursion and enumerative geometry

An efficient data exchange mechanism for chained network functions

Thanks to the increasing success of virtualization technologies and processing capabilities of computing devices, the deployment of virtual network functions is evolving towards a unified approach aiming at concentrating a huge amount of such functions within a limited number of commodity servers. To keep pace with this trend, a key issue to address is the definition of a secure and efficient way to move data between the different virtualized environments hosting the functions and a centralized component that builds the function chains within a single server. This paper proposes an efficient algorithm that realizes this vision and that, by exploiting the peculiarities of this application domain, is more efficient than classical solutions. The algorithm that manages the data exchanges is validated by performing a formal verification of its main safety and security properties, and an extensive functional and performance evaluation is presented

Towards a unified definition of solar limb during central eclipses and daily transits

The diameter of the Sun has been measured using Baily's beads during central eclipses, observed with portable telescopes. A blend of tiny emission lines produced in the first several hundred kilometers above the photosphere gives a light signal which prolonges the light curves of the beads. The simple criterion of light OFF/ON adopted in the previous approaches to define the timing of photosphere's disappearance/reappearance is modified. The technique of the limb darkening function reconstruction from the Baily's beads light curves is introduced here.Comment: 9 pages, 6 figures, Proc. of the 2nd Galileo-Xu Guangqi Meeting, Ventimiglia - Villa Hanbury, Italy, 11-16 July 201

Mathematical Definitions of Scene and Scenario for Analysis of Automated Driving Systems in Mixed-Traffic Simulations

This paper introduces a unified mathematical definition for describing commonly used terms encountered in systematical analysis of automated driving systems in mixed-traffic simulations. The most significant contribution of this work is in translating the terms that are clarified previously in literature into a mathematical set and function based format. Our work can be seen as an incremental step towards further formalisation of Domain-Specific-Language (DSL) for scenario representation. We also extended the previous work in the literature to allow more complex scenarios by expanding the model-incompliant information using set-theory to represent the perception capacity of the road-user agents. With this dynamic perception definition, we also support interactive scenarios and are not limited to reactive and pre-defined agent behavior. Our main focus is to give a framework to represent realistic road-user behavior to be used in simulation or computational tool to examine interaction patterns in mixed-traffic conditions. We believe that, by formalising the verbose definitions and extending the previous work in DSL, we can support automatic scenario generation and dynamic/evolving agent behavior models for simulating mixed traffic situations and scenarios. In addition, we can obtain scenarios that are realistic but also can represent rare-conditions that are difficult to extract from field-tests and real driving data repositories

Towards a unified approach to information-disturbance tradeoffs in quantum measurements

We show that the global balance of information dynamics for general quantum measurements given in [F. Buscemi, M. Hayashi, and M. Horodecki, Phys.Rev.Lett. 100, 210504 (2008)] makes it possible to unify various and generally inequivalent approaches adopted in order to derive information-disturbance tradeoffs in quantum theory. We focus in particular on those tradeoffs, constituting the vast majority of the literature on the subject, where disturbance is defined either in terms of average output fidelity or of entanglement fidelity

Adversarial Attack and Defense on Graph Data: A Survey

Deep neural networks (DNNs) have been widely applied to various applications including image classification, text generation, audio recognition, and graph data analysis. However, recent studies have shown that DNNs are vulnerable to adversarial attacks. Though there are several works studying adversarial attack and defense strategies on domains such as images and natural language processing, it is still difficult to directly transfer the learned knowledge to graph structure data due to its representation challenges. Given the importance of graph analysis, an increasing number of works start to analyze the robustness of machine learning models on graph data. Nevertheless, current studies considering adversarial behaviors on graph data usually focus on specific types of attacks with certain assumptions. In addition, each work proposes its own mathematical formulation which makes the comparison among different methods difficult. Therefore, in this paper, we aim to survey existing adversarial learning strategies on graph data and first provide a unified formulation for adversarial learning on graph data which covers most adversarial learning studies on graph. Moreover, we also compare different attacks and defenses on graph data and discuss their corresponding contributions and limitations. In this work, we systemically organize the considered works based on the features of each topic. This survey not only serves as a reference for the research community, but also brings a clear image researchers outside this research domain. Besides, we also create an online resource and keep updating the relevant papers during the last two years. More details of the comparisons of various studies based on this survey are open-sourced at https://github.com/YingtongDou/graph-adversarial-learning-literature.Comment: In submission to Journal. For more open-source and up-to-date information, please check our Github repository: https://github.com/YingtongDou/graph-adversarial-learning-literatur