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We consider the problem of robust polynomial regression, where one receives samples that are usually within a small additive error of a target polynomial, but have a chance of being arbitrary adversarial outliers. Previously, it was known how to efficiently estimate the target polynomial only when the outlier probability was subconstant in the degree of the target polynomial. We give an algorithm...
Ground states of local Hamiltonians can be generally highly entangled: any quantum circuit that generates them (even approximately) must be sufficiently deep to allow coupling (entanglement) between any pair of qubits. Until now this property was not known to be robust - the marginals of such states to a subset of the qubits containing all but a small constant fraction of them may be only locally...
Study on the design of a robust network against malicious attacks has gained increased interest in various areas such as wireless communications networks. One of the main obstacles towards finding the optimum robust network is the large number of possible network configurations. In this paper, we propose a novel method to design robust networks against malicious attacks based on the network degree...
An active queue management controller based on Hamiltonian energy theory for a class of nonlinear TCP network congestion system in the p resence of uncertain parameters and unknown external disturbances is derived. The restriction of inequality assumption is eliminated by introducing the MiniMax methods into dissipation Hamilton system. Sufficient conditions for the existence of MiniMax controller...
Many real-life systems have integrated circuits interacting with physical systems in safety critical applications. These systems are called hybrid systems. The safety analysis of integrated circuits used in such systems is typically done in isolation of the end application and associated physical system, and hence results in the need to take recourse to conservative design techniques utilizing costly...
Subgraph pattern matching is fundamental to graph analytics and has wide applications. Unfortunately, high computational complexity limits the robustness guarantees of existing algorithms: they do not scale for modern large graph datasets and/or they have limitations in terms of accuracy or in terms of the intricacy of the patterns supported. We present algorithms, theory, and empirical evidence that...
Subspace clustering is one of the active research problem associated with high-dimensional data. Here some of the standard techniques are reviewed to investigate existing methodologies. Although, there have been various forms of research techniques evolved recently, they do not completely mitigate the problems pertaining to noise sustainability and optimization of clustering accuracy. Hence, a novel...
Low rank matrix approximation, in the presence of missing data and outliers, has previously shown its significance as a theoretic foundation in a wide spectrum of tabulated information processing applications. To fit low rank models, minimizing the nuclear norm of matrices is a popular scheme, the computational load of which, however, is heavy. While bilinear factorization can largely mitigate the...
The layout of High-speed rail network determines its performance of the flexibility, connectivity and reliability. Based on complex network theory, this paper constructs Chinese high-speed rail networks(CHSRN) at three periods, and analyzes their complex properties. Using a comprehensive evaluation index combined with degree and betweenness of nodes to discover the important stations, this paper simulates...
In this paper, we consider the problem of hybrid multi-input multi-output (MIMO) transceiver design for a non regenerative hybrid two-way amplify-forward (AF) relay based millimeter wave (mmWave) communication system. We propose two low complexity mmWave system designs based on the quality of available channel state information (CSI). We first propose the design of transceivers and a two- way AF relay,...
Fountain codes are used in many applications where the channels are time varying and it is difficult at the transmitter to predict the appropriate code rate. In this situation, fixedrate codes are not suitable. Despite the good performance of fountain codes, universally optimal codes do not exist in the finite-length regime. In this paper, we design new fountain codes that are robust to the communication...
We introduce Cyclone codes which are rateless erasure resilient codes. They combine Pair codes with Luby Transform (LT) codes by computing a code symbol from a random set of data symbols using bitwise XOR and cyclic shift operations. The number of data symbols is chosen according to the Robust Soliton distribution. XOR and cyclic shift operations establish a unitary commutative ring if data symbols...
It has been shown that for a general-valued constraint language Γ the following statements are equivalent: (1) any instance of VCSP(Γ) can be solved to optimality using a constant level of the Sherali-Adams LP hierarchy; (2) any instance of VCSP(Γ) can be solved to optimality using the third level of the Sherali-Adams LP hierarchy; (3) the support of Γ satisfies the “bounded width condition”, i.e...
Descriptive Complexity has been very successful in characterizing complexity classes of decision problems in terms of the properties definable in some logics. However, descriptive complexity for counting complexity classes, such as FP and #P, has not been systematically studied, and it is not as developed as its decision counterpart. In this paper, we propose a framework based on Weighted Logics to...
Prefrontal cortex (PFC) is thought to support the ability to focus on goal-relevant information by filtering out irrelevant information, a process akin to dimensionality reduction. Here, we find direct evidence of goal-directed data compression within medial PFC during learning, such that the degree of neural compression predicts an individual’s ability to selectively attend to concept-specific information...
In recent times, user activities on web-based social networks has increased enormously irrespective of time and place that generates a variety of datasets which further offers tremendous scope for both mining and knowledge discovery. Due to a large number of Social Networking websites and interactions among people via these sites, rapid growth in social networks has taken place. Community detection...
This paper proposes a new adaptive watermarking algorithm leveraging combined knowledge of spatial and frequency domains to ensure the robustness and security of the embedded watermark and the transparency of the carrier image. The scheme makes use of the perceptual characteristics of human visual system and the local correlation of the image. The wavelet coefficients of the image are divided into...
We present the design and implementation of a parallel and fully algebraic preconditioner based on an approximate sparse factorization using low-rank matrix compression. The sparse factorization uses a multifrontal algorithm with fill-in occurring in dense frontal matrices. These frontal matrices are approximated as hierarchically semi-separable matrices, which are constructed using a randomized sampling...
We present LS-ELAS, a line segment extension to the ELAS algorithm, which increases the performance and robustness. LS-ELAS is a binocular dense stereo matching algorithm, which computes the disparities in constant time for most of the pixels in the image and in linear time for a small subset of the pixels (support points). Our approach is based on line segments to determine the support points instead...
Global 3D point cloud registration has been solved by finding putative matches between the point clouds for establishing alignment hypotheses. A naive approach would try to perform exhaustive search of triplets with a cubic runtime complexity in the number of data points. Super4PCS reduces this complexity to linear by making use of sets of 4 coplanar points. This paper proposes 2-Point-Normal Sets...
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