Counting Independent Sets and Colorings on Random Regular Bipartite Graphs

We give a fully polynomial-time approximation scheme (FPTAS) to count the number of independent sets on almost every Delta-regular bipartite graph if Delta >= 53. In the weighted case, for all sufficiently large integers Delta and weight parameters lambda = Omega~ (1/(Delta)), we also obtain an FPTAS on almost every Delta-regular bipartite graph. Our technique is based on the recent work of Jenssen, Keevash and Perkins (SODA, 2019) and we also apply it to confirm an open question raised there: For all q >= 3 and sufficiently large integers Delta=Delta(q), there is an FPTAS to count the number of q-colorings on almost every Delta-regular bipartite graph

SDA: Simple Discrete Augmentation for Contrastive Sentence Representation Learning

Contrastive learning methods achieve state-of-the-art results in unsupervised sentence representation learning. Although playing essential roles in contrastive learning, data augmentation methods applied on sentences have not been fully explored. Current SOTA method SimCSE utilizes a simple dropout mechanism as continuous augmentation which outperforms discrete augmentations such as cropping, word deletion and synonym replacement. To understand the underlying rationales, we revisit existing approaches and attempt to hypothesize the desiderata of reasonable data augmentation methods: balance of semantic consistency and expression diversity. Based on the hypothesis, we propose three simple yet effective discrete sentence augmentation methods, i.e., punctuation insertion, affirmative auxiliary and double negation. The punctuation marks, auxiliaries and negative words act as minimal noises in lexical level to produce diverse sentence expressions. Unlike traditional augmentation methods which randomly modify the sentence, our augmentation rules are well designed for generating semantically consistent and grammatically correct sentences. We conduct extensive experiments on both English and Chinese semantic textual similarity datasets. The results show the robustness and effectiveness of the proposed methods

Secure Split Learning against Property Inference, Data Reconstruction, and Feature Space Hijacking Attacks

Split learning of deep neural networks (SplitNN) has provided a promising solution to learning jointly for the mutual interest of a guest and a host, which may come from different backgrounds, holding features partitioned vertically. However, SplitNN creates a new attack surface for the adversarial participant, holding back its practical use in the real world. By investigating the adversarial effects of highly threatening attacks, including property inference, data reconstruction, and feature hijacking attacks, we identify the underlying vulnerability of SplitNN and propose a countermeasure. To prevent potential threats and ensure the learning guarantees of SplitNN, we design a privacy-preserving tunnel for information exchange between the guest and the host. The intuition is to perturb the propagation of knowledge in each direction with a controllable unified solution. To this end, we propose a new activation function named R3eLU, transferring private smashed data and partial loss into randomized responses in forward and backward propagations, respectively. We give the first attempt to secure split learning against three threatening attacks and present a fine-grained privacy budget allocation scheme. The analysis proves that our privacy-preserving SplitNN solution provides a tight privacy budget, while the experimental results show that our solution performs better than existing solutions in most cases and achieves a good tradeoff between defense and model usability.Comment: 23 page

Distributed fusion filter over lossy wireless sensor networks with the presence of non-Gaussian noise

The information transmission between nodes in a wireless sensor networks (WSNs) often causes packet loss due to denial-of-service (DoS) attack, energy limitations, and environmental factors, and the information that is successfully transmitted can also be contaminated by non-Gaussian noise. The presence of these two factors poses a challenge for distributed state estimation (DSE) over WSNs. In this paper, a generalized packet drop model is proposed to describe the packet loss phenomenon caused by DoS attacks and other factors. Moreover, a modified maximum correntropy Kalman filter is given, and it is extended to distributed form (DM-MCKF). In addition, a distributed modified maximum correntropy Kalman filter incorporating the generalized data packet drop (DM-MCKF-DPD) algorithm is provided to implement DSE with the presence of both non-Gaussian noise pollution and packet drop. A sufficient condition to ensure the convergence of the fixed-point iterative process of the DM-MCKF-DPD algorithm is presented and the computational complexity of the DM-MCKF-DPD algorithm is analyzed. Finally, the effectiveness and feasibility of the proposed algorithms are verified by simulations

Stabilisation by delay feedback control for highly nonlinear hybrid stochastic differential equations

Given an unstable hybrid stochastic differential equation (SDE, also known as an SDE with Markovian switching), can we design a delay feed- back control to make the controlled hybrid SDE become asymptotically stable? The paper [14] by Mao et al. was the first to study the stabilisation by de- lay feedback controls for hybrid SDEs, though the stabilization by non-delay feedback controls had been well studied. A critical condition imposed in [14] is that both drift and diffusion coefficients of the given hybrid SDE need to satisfy the linear growth condition. However, many hybrid SDE models in the real world do not fulfill this condition (namely, they are highly nonlinear) and hence there is a need to develop a new theory for these highly nonlinear SDE models. The aim of this paper is to design delay feedback controls in order to stabilise a class of highly nonlinear hybrid SDEs whose coefficients satisfy the polynomial growth condition

Self‐Assembly of Wireframe DNA Nanostructures from Junction Motifs

Wireframe frameworks have been investigated for the construction of complex nanostructures from a scaffolded DNA origami approach; however, a similar framework is yet to be fully explored in a scaffold‐free “LEGO” approach. Herein, we describe a general design scheme to construct wireframe DNA nanostructures entirely from short synthetic strands. A typical edge of the resulting structures in this study is composed of two parallel duplexes with crossovers on both ends, and three, four, or five edges radiate out from a certain vertex. By using such a self‐assembly scheme, we produced planar lattices and polyhedral objects.Verzweigte Angelegenheit: DNA‐Verzweigungsmotive mit Anordnungen in bestimmten Winkeln wurden entwickelt. Mit ihnen wurden zweidimensionale Drahtgitterstrukturen und dreidimensionale Polyeder konstruiert.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151370/1/ange201906408.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151370/2/ange201906408-sup-0001-misc_information.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151370/3/ange201906408_am.pd

Self‐Assembly of Wireframe DNA Nanostructures from Junction Motifs

Wireframe frameworks have been investigated for the construction of complex nanostructures from a scaffolded DNA origami approach; however, a similar framework is yet to be fully explored in a scaffold‐free “LEGO” approach. Herein, we describe a general design scheme to construct wireframe DNA nanostructures entirely from short synthetic strands. A typical edge of the resulting structures in this study is composed of two parallel duplexes with crossovers on both ends, and three, four, or five edges radiate out from a certain vertex. By using such a self‐assembly scheme, we produced planar lattices and polyhedral objects.Conjunction junction, what’s your function? Junction motifs of specific angle arrangements are designed. 2D wireframe lattices and 3D wireframe polyhedra are constructed accordingly.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151279/1/anie201906408-sup-0001-misc_information.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151279/2/anie201906408_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151279/3/anie201906408.pd

Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state

Although the mean square stabilisation of hybrid systems by feedback controls based on discretetime observations of state and mode has been studied by several authors since 2013 (see, e.g., [17,19,27,31]), the corresponding almost sure stabilisation problem has little been investigated. Recent Mao [18] is the first to study the almost sure stabilisation of a given unstable system x(t) = f(x(t)) by a linear discretetime stochastic feedback control Ax([t/τ]τ)dB(t) (namely the stochastically controlled system has the form dx(t) = f(x(t))dt + Ax([t/τ]τ)dB(t)), where B(t) is a scalar Brownian, τ > 0 and [t/τ] is the integer part of t/τ. In this paper, we will consider a much more general problem. That is, we will to study the almost sure stabilisation of a given unstable hybrid system x(t) = f(x(t), r(t)) by nonlinear discrete-time stochastic feedback control u(x([t/τ]τ), r([t/τ]τ))dB(t) (so the stochastically controlled system is a hybrid stochastic system of the form dx(t) = f(x(t), r(t))dt + u(x([t/τ]τ), r([t/τ]τ))dB(t)), where B(t) is a multi-dimensional Brownian motion and r(t) is a Markov chain