Small Error Probability Research Articles

Nonadaptive Group Testing Based on Sparse Pooling Graphs

An information theoretical analysis of nonadaptive group testing schemes based on sparse pooling graphs is presented. A pooling graph is a bipartite graph for which the adjacency matrix is a pooling matrix. The binary status of the objects to be tested are modeled by independent identically distributed. Bernoulli random variables with probability $p$ . An $(l, r, n)$ -regular pooling graph is a bipartite graph in which the left nodes have degree $l$ , the right nodes have degree $r$ , and $n$ is the number of left nodes. The main contribution of this paper is a direct coding theorem that gives the conditions for the existence of an estimator that can achieve an arbitrarily small probability of error. An estimator is a function that uses observations to infer the state of an object. The direct coding theorem is proved by averaging the upper bound on the probability of the estimation error of the typical set estimator over an $(l, r, n)$ -regular pooling graph ensemble. Numerical results indicate sharp threshold behaviors in the asymptotic regime. These results can provide a concrete benchmark for nonadaptive group testing of existing and emerging detection algorithms over a noiseless system.

Indexing and querying color sets of images

We aim to study the set of color sets of continuous regions of an image given as a matrix of m rows over n≥m columns where each element in the matrix is an integer from [1,σ] named a color. The set of distinct colors in a region is called fingerprint. We aim to compute, index and query the fingerprints of all rectangular regions named rectangles. The set of all such fingerprints is denoted by F. A rectangle is maximal if it is not contained in a greater rectangle with the same fingerprint. The set of all locations of maximal rectangles is denoted by L. We first explain how to determine all the |L| maximal locations with their fingerprints in expected time O(nm2σ) using a Monte Carlo algorithm (with polynomially small probability of error) or within deterministic O(nm2σlog⁡(|L|nm2+2)) time. We then show how to build a data structure which occupies O(nmlog⁡n+|L|) space such that a query which asks for all the maximal locations with a given fingerprint f can be answered in time O(|f|+log⁡log⁡n+k), where k is the number of maximal locations with fingerprint f. If the query asks only for the presence of the fingerprint, then the space usage becomes O(nmlog⁡n+|F|) while the query time becomes O(|f|+log⁡log⁡n). We eventually consider the special case of squared regions (squares).

Performance of LDPC Decoders With Missing Connections

Due to process variation in nanoscale manufacturing, there may be permanently missing connections in information processing hardware. Due to timing errors in circuits, there may be missed messages in intra-chip communications, equivalent to transiently missing connections. In this work, we investigate the performance of message-passing LDPC decoders in the presence of missing connections. We prove concentration and convergence theorems that validate the use of density evolution performance analysis. Arbitrarily small error probability is not possible with missing connections, but we find suitably defined decoding thresholds for communication systems with binary erasure channels under peeling decoding, as well as binary symmetric channels under Gallager A and B decoding. We see that decoding is robust to missing wires, as decoding thresholds degrade smoothly. Moreover, there is a stochastic facilitation effect in Gallager B decoders with missing connections. We also compare the decoding sensitivity with respect to channel noise and missing wiring.

Doubly infinite separation of quantum information and communication

We prove the existence of (one-way) communication tasks with a subconstant versus superconstant asymptotic gap, which we call "doubly infinite," between their quantum information and communication complexities. We do so by studying the exclusion game [C. Perry et al., Phys. Rev. Lett. 115, 030504 (2015)] for which there exist instances where the quantum information complexity tends to zero as the size of the input $n$ increases. By showing that the quantum communication complexity of these games scales at least logarithmically in $n$, we obtain our result. We further show that the established lower bounds and gaps still hold even if we allow a small probability of error. However in this case, the $n$-qubit quantum message of the zero-error strategy can be compressed polynomially.

Quantum computation with coherent spin states and the close Hadamard problem

We study a model of quantum computation based on the continuously-parameterized yet finite-dimensional Hilbert space of a spin system. We explore the computational powers of this model by analyzing a pilot problem we refer to as the close Hadamard problem. We prove that the close Hadamard problem can be solved in the spin system model with arbitrarily small error probability in a constant number of oracle queries. We conclude that this model of quantum computation is suitable for solving certain types of problems. The model is effective for problems where symmetries between the structure of the information associated with the problem and the structure of the unitary operators employed in the quantum algorithm can be exploited.

Tight Bounds for Sliding Bloom Filters

A Bloom filter is a method for reducing the space (memory) required for representing a set by allowing a small error probability. In this paper we consider a Sliding Bloom Filter: a data structure that, given a stream of elements, supports membership queries of the set of the last n elements (a sliding window), while allowing a small error probability and a slackness parameter. The problem of sliding Bloom filters has appeared in the literature in several communities, but this work is the first theoretical investigation of it. We formally define the data structure and its relevant parameters and analyze the time and memory requirements needed to achieve them. We give a low space construction that runs in $$O(1)$$ time per update with high probability (that is, for all sequences with high probability all operations take constant time) and provide an almost matching lower bound on the space that shows that our construction has the best possible space consumption up to an additive lower order term.

Capacity–Delay–Error Boundaries: A Composable Model of Sources and Systems

This paper develops a notion of capacity-delay-error (CDE) boundaries as a performance model of networked sources and systems. The goal is to provision effective capacities that sustain certain statistical delay guarantees with a small probability of error. We use a stochastic non-equilibrium approach that models the variability of traffic and service to formalize the influence of delay constraints on the effective capacity. Permitting unbounded delays, known ergodic capacity results from information theory are recovered in the limit. We prove that the model has the property of additivity, which enables composing CDE boundaries obtained for sources and systems as if in isolation. A method for construction of CDE boundaries is devised based on moment-generating functions, which includes the large body of results from the theory of effective bandwidths. Solutions for essential sources, channels, and respective coders are derived, including Huffman coding, MPEG video, Rayleigh fading, and hybrid automatic repeat request. Results for tandem channels and for the composition of sources and channels are shown.

Network Codes Resilient to Jamming and Eavesdropping

We consider the problem of communicating information over a network secretly and reliably in the presence of a hidden adversary who can eavesdrop and inject malicious errors. We provide polynomial-time distributed network codes that are information-theoretically rate-optimal for this scenario, improving on the rates achievable in prior work by Ngai Our main contribution shows that as long as the sum of the number of links the adversary can jam (denoted by ZO) and the number of links he can eavesdrop on (denoted by ZI) is less than the network capacity (denoted by C) (i.e., ), our codes can communicate (with vanishingly small error probability) a single bit correctly and without leaking any information to the adversary. We then use this scheme as a module to design codes that allow communication at the source rate of C- ZO when there are no security requirements, and codes that allow communication at the source rate of C- ZO- ZI while keeping the communicated message provably secret from the adversary. Interior nodes are oblivious to the presence of adversaries and perform random linear network coding; only the source and destination need to be tweaked. We also prove that the rate-region obtained is information-theoretically optimal. In proving our results, we correct an error in prior work by a subset of the authors in this paper.

Thermal pure quantum states of many-particle systems

We generalize the thermal pure quantum (TPQ) formulation of statistical mechanics, in such a way that it is applicable to systems whose Hilbert space is infinite dimensional. Assuming particle systems, we construct the grand-canonical TPQ (gTPQ) state, which is the counterpart of the grand-canonical Gibbs state of the ensemble formulation. A single realization of the gTPQ state gives all quantities of statistical-mechanical interest, with exponentially small probability of error. This formulation not only sheds new light on quantum statistical mechanics but also is useful for practical computations. As an illustration, we apply it to the Hubbard model, on a one-dimensional (1D) chain and on a two-dimensional (2D) triangular lattice. For the 1D chain, our results agree well with the exact solutions over wide ranges of temperature, chemical potential, and the on-site interaction. For the 2D triangular lattice, for which exact results are unknown, we obtain reliable results over a wide range of temperature. We also find that finite-size effects are much smaller in the gTPQ state than in the canonical TPQ state. This also shows that in the ensemble formulation the grand-canonical Gibbs state of a finite-size system simulates an infinite system much better than the canonical Gibbs state.

From Polar to Reed-Muller Codes: A Technique to Improve the Finite-Length Performance

We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM codes have a smaller error probability than polar codes under MAP decoding. This motivates us to introduce a family of codes that interpolates between RM and polar codes, call this family C-inter = {C-alpha:alpha is an element of[0;1]}, where C alpha vertical bar(alpha=1) is the original polar code, and C alpha vertical bar(alpha=0) is an RM code. Based on numerical observations, we remark that the error probability under MAP decoding is an increasing function of alpha. MAP decoding has in general exponential complexity, but empirically the performance of polar codes at finite block lengths is boosted by moving along the family C-inter even under low-complexity decoding schemes such as, for instance, belief propagation or successive cancellation list decoder. We demonstrate the performance gain via numerical simulations for transmission over the erasure channel as well as the Gaussian channel.

Quantum illumination with photon-subtracted continuous-variable entanglement

Quantum illumination is a protocol where quantum resources are utilized to detect a low-reflectivity object embedded in a bright thermal noise bath. For example, quantum illumination with a two-mode squeezed state (TMSS) provides a 6 dB advantage in the error-probability exponent over the optimal classical illumination. We here consider quantum illumination with the photon-subtracted two-mode squeezed state (PSTMSS). Our result is twofold. First, we show that a much smaller error probability ${P}_{\mathrm{err}}$ could be obtained, meaning that much smaller resources will be required in quantum illumination for a fixed ${P}_{\mathrm{err}}$. Second, quantum illumination with PSTMSS appreciably outperforms its classic correspondence in both low- and high-noise operating regimes, extending the regimes in which quantum illumination is optimal for target detection.

Fast Sparse Superposition Codes Have Near Exponential Error Probability for <formula formulatype="inline"><tex Notation="TeX">$R<{\cal C}$</tex></formula>

For the additive white Gaussian noise channel with average codeword power constraint, sparse superposition codes are developed. These codes are based on the statistical high-dimensional regression framework. In a previous paper, we investigated decoding using the optimal maximum-likelihood decoding scheme. Here, a fast decoding algorithm, called the adaptive successive decoder, is developed. For any rate R less than the capacity C, communication is shown to be reliable with nearly exponentially small error probability. Specifically, for blocklength n, it is shown that the error probability is exponentially small in n/logn.

Investigation of the mechanism of improvement in improved Nyquist filters

In this study, the authors have investigated the mechanism that determines improved Nyquist filters (INFs) to perform better in the presence of timing errors. The authors have explored the role of low- and high-frequency regions in the range [B(1 − α), B], where B is the bandwidth corresponding to T = 1/2B in producing a smaller error probability in the presence of symbol timing error. The authors first have analysed the performance of the POWER pulse and evidenced the role of the slope of the frequency characteristic in the vicinity of B(1 − α), determined the optimal values of the exponent β and derived a formula that links β and the slope value at B(1 − α + α/100) to the normalised time offset. Then, the authors have proposed five new INFs with piece-wise polynomial frequency characteristic, and investigated the influence of component frequency bands and shapes on the error probability, when the impulse response is sampled with a time offset. The authors consider that the slope of the frequency characteristic in the transition band in the vicinity of B(1 − α) has a direct effect on the error probability. Finally, the authors have presented the performance evaluation and practical engineering challenges brought in by the use of the new pulses in an N-subcarrier orthogonal frequency-division multiplexing (OFDM) systems in order to reduce inter-carrier interference power.

Dynamic Matrix Rank with Partial Lookahead

We consider the problem of maintaining information about the rank of a matrix M under changes to its entries. For an n×n matrix M, we show an amortized upper bound of O(n ω−1) arithmetic operations per change for this problem, where ω<2.373 is the exponent for matrix multiplication, under the assumption that there is a lookahead of up to Θ(n) locations. That is, we know up to the next Θ(n) locations (i 1,j 1),(i 2,j 2),…, whose entries are going to change, in advance; however we do not know the new entries in these locations in advance. We get the new entries in these locations in a dynamic manner. The dynamic matrix rank problem was first studied by Frandsen and Frandsen who showed an upper bound of O(n 1.575) and a lower bound of Ω(n) for this problem and later Sankowski showed an upper bound of O(n 1.495) for this problem when allowing randomization and a small probability of error. These algorithms do not assume any lookahead. For the dynamic matrix rank problem with lookahead, Sankowski and Mucha showed a randomized algorithm (with a small probability of error) that is more efficient than these algorithms.

Competing-provers protocols for circuit evaluation

Let C be a (fan-in 2) Boolean circuit of size s and depth d, and let x be an input for C. Assume that a verifier that knows C but doesn't know x can access the low degree extension of x at one random point. Two competing provers try to convince the verifier that C(x)=0 and C(x)=1, respectively, and assume that one of the provers is honest.For any r≥1, we give an r rounds protocol with communication complexity d1/r poly log(s) that convinces the verifier in the correct value of C(x) (with small probability of error). In particular, when we allow only one round, the protocol exchanges d ⋅ poly log(s) bits, and when we allow r=O(log(d)/log log(s)) rounds, the protocol exchanges only poly log(s) bits.Moreover, the complexity of the verifier and honest provers in this protocol is poly(s), and if in addition the circuit is log(s)-space uniform, the complexity of the verifier is d1/r poly log(s).The protocol is obtained by combining the delegation protocol of Goldwasser, Kalai and Rothblum [5] and the competing provers protocols of Feige and Kilian [3] and some new techniques. We suggest two applications of these results:Delegating computation to competing clouds: The main motivation behind the protocol of [5] was delegating computation to a cloud. Using our new protocol, a verifier can delegate computation to two (or more) competing clouds. If at least one of the clouds is reliable the verifier can trust that the computation is correct (with high probability). The advantage over the protocol of [5] is that the communication complexity and the number of rounds in our protocol are significantly lower.Communication complexity with competing provers, and circuit lower bounds: Aaronson and Wigderson [1] suggested the model of communication complexity with competing provers, where two competing provers try to convince two players that f(x,y)=0 and f(x,y)=1, respectively, where x is an input held by the first player and y is an input held by the second player. By scaling down the competing provers protocols of [3], they showed that strong enough lower bounds for the communication complexity of f, in this model, imply lower bounds for the computational complexity of f.Our results strengthen this connection. More precisely, we show that if f can be computed by a Boolean circuit of size s and depth d then for any r≥1 there is an r rounds protocol for f, in this model, with communication complexity d1/r poly log(s). This can be viewed as a possible direction towards proving circuit lower bounds. For instance, in order to prove f∉NC, it suffices to show that any one round protocol for f, in this model, requires the exchange of ω(poly log(n)) bits. This gives a relatively simple combinatorial property that implies strong circuit lower bounds.

基于3S技术的图们江流域湿地生态安全评价与预警研究

PDF HTML阅读 XML下载 导出引用 引用提醒 基于3S技术的图们江流域湿地生态安全评价与预警研究 DOI: 10.5846/stxb201211241666 作者: 作者单位: 长白山生物资源与功能分子教育部重点实验室;延边大学理学院地理系,临邑县第一中学,延边大学 理学院地理系,延边大学 理学院地理系,临邑县第一中学 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然基金资助项目（41361015，40961011，41071333）；吉林省科技厅国际合作项目（20120740）；吉林省科技发展计划项目（20130206007SF） Study on ecological safety evaluation and warning of wetlands in Tumen River watershed based on 3S technology Author: Affiliation: Key Laboratory of Natural Resources of Changbai Mountain Functional Molecules,Yanji Jilin China;Geography Department College of Sciences,Yanbian University,Yanji Jilin China,The first middle school in Linyi,Linyi Shandong,Geography Department College of Sciences,Yanbian University,Yanji Jilin,Geography Department College of Sciences,Yanbian University,Yanji Jilin,The first middle school in Linyi,Linyi Shandong Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:图们江是我国重要的国际性河流之一，随着我国经济的迅速崛起，图们江地区进入到多国合作联合开发阶段，该区环境也因此受到了不同程度的干扰和破坏，对该区域进行湿地生态安全评价与预警研究，可为图们江流域生态环境的可持续发展提供依据。以图们江流域湿地生态安全为出发点，基于PSR模型构建了适合该区域生态环境的生态安全评价指标体系，在3S技术支持下，通过解译1976年、1990年、2000年、2010年4个年份的TM/MSS影像，获取了这4个时期的景观格局指标数据，并运用层次分析法确定指标权重；在使用逻辑斯蒂增长曲线模型对各个指标进行单指标评价的基础上，使用综合评价法对各个时期的图们江流域湿地生态安全进行评价，最终得到1976年、1990年生态安全值分别为0.650、0.620，湿地生态系统比较安全，2000年、2010年生态安全值分别为0.536、0.454，湿地生态系统处于预警状态，应及时对该区域湿地生态系统进行保护。基于灰色预测模型构建湿地生态安全预测模型，经检验，模型精度较高，可以进行图们江流域湿地生态安全的预测研究。做出了图们江流域未来40a的湿地生态安全预测，分别为0.3903、0.3345、0.2866、0.2456，湿地生态系统处于中度预警状态，并有向重度预警发展的趋势，生态安全面临的威胁越来越严重，急需对本区域湿地生态系统进行保护与管理。 Abstract:Wetlands, forests and oceans form the three global ecosystems. Wetlands are the natural integration of aquatic and semi-aquatic creatures in a wet environment.Wetlands are an important natural resource and one of the most important environments for human survival. They not only offer the raw materials for human life and human production but also play an important role in ameliorating weather conditions, flood storage, and the control and reduction of environmental pollution. Wetlands have thus been called the "kidney of the earth".Global and regional problems such as environmental pollution, soil erosion and so on, have become more and more serious with the rapid development of human society. These problems create a serious threat to society, economic development and perhaps even human survival. People are discovering it is not military or political activity which threatens to restrict economic development, but ecological crises which are creating long term effects. Also, people are gradually realizing that ecological stability is critical to both broad scale ecosystem integrity and guaranteeing sustainable development. It is the region or country other ecological safety of the carrier and the foundation. The development of human society depends on creating sustainable development with a system which secures the survival of ecological systems. Therefore, the study of ecological sustainability has become a field of concern.Tumen river is one of the key international rivers in China. The region has already entered into multinational cooperation in developmental stages with the Chinese economy rising rapidly. The environment has been getting interfered with and destroyed in different degrees. This study can provide a scientific basis for sustainable development of ecological environment of the Tumen river basin. In this study, we used the Tumen river watershed wetland ecological security for the purpose built wetland ecology safety evaluation system based on Pressure-Status-Response (PSR) concept model, and got landscape dates of 1976,1990,2000 and 2010 by using 3S technology. We used experts' evaluation index combined with AHP evaluation to give the weight and got the final comprehensive evaluation in the use of the logistical growth curve model for each index based on the assessment of a single index. The study finally got the ecological secure values that were respectively 0.650,0.620 in 1976 and 1990, the ecological system was in a safe state; the ecological secure values were respectively 0.536 and 0.454 in 2000 and 2010, which shows that the ecological system was in a state of early warning. The wetland ecological system should be immediately protected. Based on this, we used the grey prediction model to build a wetland ecological safety prediction model and did accuracy testing for the model. The Simulation error, correlation and the mean square error ratio, and the small error probability were primary concerns but the model accuracy was high enough for the Tumen river wetland ecological safety prediction. Finally this study made a prediction for the Tumen river basin wetland ecological safety for 40 years, the results were respectively 0.3903, 0.3345, 0.2866 and 0.2456. The wetland ecological system was in a moderate warning state and the trend of the situation continued to become more severe. Ecological security threat is very serious and this area needs more protection and management for the wetland ecosystem to survive. 参考文献 相似文献 引证文献

Errors and Their Mitigation at the Kirchhoff-Law-Johnson-Noise Secure Key Exchange

A method to quantify the error probability at the Kirchhoff-law-Johnson-noise (KLJN) secure key exchange is introduced. The types of errors due to statistical inaccuracies in noise voltage measurements are classified and the error probability is calculated. The most interesting finding is that the error probability decays exponentially with the duration of the time window of single bit exchange. The results indicate that it is feasible to have so small error probabilities of the exchanged bits that error correction algorithms are not required. The results are demonstrated with practical considerations.

GMM-based visual attention for target selection of indoor robotic tasks

Purpose – Indoor robotic tasks frequently specify objects. For these applications, this paper aims to propose an object-based attention method using task-relevant feature for target selection. The task-relevant feature(s) are deduced from the learned object representation in semantic memory (SM), and low dimensional bias feature templates are obtained using Gaussian mixture model (GMM) to get an efficient attention process. This method can be used to select target in a scene which forms a task-specific representation of the environment and improves the scene understanding by driving the robot to a position in which the objects of interest can be detected with a smaller error probability. Design/methodology/approach – Task definition and object representation in SM are proposed, and bias feature templates are obtained using GMM deduction for features from high dimension to low dimension. Mean shift method is used to segment the visual scene into discrete proto-objects. Given a task-specific object, the top...

Deterministic Function Computation with Chemical Reaction Networks.

Chemical reaction networks (CRNs) formally model chemistry in a well-mixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology, CRNs are a promising language for the design of artificial molecular control circuitry. Nonetheless, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs is not well understood. CRNs have been shown to be efficiently Turing-universal (i.e., able to simulate arbitrary algorithms) when allowing for a small probability of error. CRNs that are guaranteed to converge on a correct answer, on the other hand, have been shown to decide only the semilinear predicates (a multi-dimensional generalization of "eventually periodic" sets). We introduce the notion of function, rather than predicate, computation by representing the output of a function f : ℕ k → ℕ l by a count of some molecular species, i.e., if the CRN starts with x1, …, xk molecules of some "input" species X1, …, Xk , the CRN is guaranteed to converge to having f(x1, …, xk ) molecules of the "output" species Y1, …, Yl . We show that a function f : ℕ k → ℕ l is deterministically computed by a CRN if and only if its graph {(x, y) ∈ ℕ k × ℕ l ∣ f(x) = y} is a semilinear set. Finally, we show that each semilinear function f (a function whose graph is a semilinear set) can be computed by a CRN on input x in expected time O(polylog ∥x∥1).

COMPARISON OF TWO PHASE UNWRAPPING METHODS FOR PSP TIME SERIES ANALYSIS

Abstract. Phase unwrapping is a key issue for PSP (Permanent Scatters Pairs) time series analysis. In this paper, the LLL method and grid search method are applied for determining elevation error and velocity difference in LOS for each PSP, and the RMS is used to assess the correctness of the solution. The Delaunay triangulation is used to formulate PSPs, which are used to unwrap elevations and velocities of all PSs with respect to a given reference point. The simulation examples with real SAR satellite orbits show that if the atmosphere noise is less than 2 radians and the random noise is less than 10 degrees, LLL method can obtain correct solution while grid search can obtain solution with a small error probability.