Discovering Almost Any Hidden Motif from Multiple Sequences in Polynomial Time with Low Sample Complexity and High Success Probability

2009 ◽  
pp. 231-240
Author(s):  
Bin Fu ◽  
Ming-Yang Kao ◽  
Lusheng Wang
Keyword(s):  
Polynomial Time ◽  
Success Probability ◽  
Sample Complexity ◽  
High Success Probability ◽  
Multiple Sequences

scholarly journals A quantum algorithm to approximate the linear structures of Boolean functions

2016 ◽  
Vol 28 (1) ◽  
pp. 1-13 ◽  
Author(s):  
HONGWEI LI ◽  
LI YANG
Keyword(s):  
Boolean Functions ◽  
High Probability ◽  
Success Probability ◽  
Quantum Algorithm ◽  
Linear Structure ◽  
Differential Uniformity ◽  
Linear Structures ◽  
High Success Probability ◽  
Time Required ◽  
Quantum Speedup

A quantum algorithm to determine approximations of linear structures of Boolean functions is presented and analysed. Similar results have already been published (see Simon's algorithm) but only for some promise versions of the problem, and it has been shown that no exponential quantum speedup can be obtained for the general (no promise) version of the problem. In this paper, no additional promise assumptions are made. The approach presented is based on the method used in the Bernstein–Vazirani algorithm to identify linear Boolean functions and on ideas from Simon's period finding algorithm. A proper combination of these two approaches results here to a polynomial-time approximation to the linear structures set. Specifically, we show how the accuracy of the approximation with high probability changes according to the running time of the algorithm. Moreover, we show that the time required for the linear structure determine problem with high success probability is related to so called relative differential uniformity δf of a Boolean function f. Smaller differential uniformity is, shorter time is needed.

scholarly journals Deciding unitary equivalence between matrix polynomials and sets of bipartite quantum states

2011 ◽  
Vol 11 (9&10) ◽  
pp. 813-819
Author(s):  
Eric Chitambar ◽  
Carl Miller ◽  
Yaoyun Shi
Keyword(s):  
Success Probability ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Quantum States ◽  
Unitary Equivalence ◽  
Matrix Polynomials ◽  
Unitary Transformations ◽  
The Matrix ◽  
Pure States ◽  
High Success Probability

In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$ matrix polynomials are unitarily equivalent; i.e. $UA_iV^\dagger=B_i$ for $0\leq i\leq m$ where $U$ and $V$ are unitary and $(A_i, B_i)$ are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices $U$ and $V$.

A NEW FAULT-TOLERANT BROADCAST ROUTING ALGORITHM ON MESH NETWORKS

2010 ◽  
Vol 11 (03n04) ◽  
pp. 175-187 ◽  
Author(s):  
GAOCAI WANG ◽  
JIANER CHEN ◽  
CHUANG LIN
Keyword(s):  
Failure Probability ◽  
Mesh Networks ◽  
Fault Tolerant ◽  
Routing Algorithm ◽  
Success Probability ◽  
Network Size ◽  
Large Size ◽  
Broadcast Routing ◽  
Network Topologies ◽  
High Success Probability

Mesh networks are a kind of very important network topologies in massively multicomputer parallel systems. One-to-all or broadcast communication is one of the most important routing patterns and can be applied in many important applications. With the continuous increment in network size, routing in large size mesh networks with faults is unavoidable. In this paper, we propose a new fault-tolerant, local-information-based, and distributed broadcast routing algorithm based on the concept of k-submesh in all-port mesh networks. We suppose that each node has independent failure probability, under the assumption, we analyze the fault tolerance of our algorithm. We show that our routing algorithm is highly fault tolerant and has a high success probability to broadcast messages. For example, we formally prove that if the node failure probability is bounded by 0.12%, our broadcast routing algorithm works successfully with probability at least 99%. Simulation results show that our algorithm is efficient and effective in practice and theory, and the time steps of our algorithm is very close to the optimum.

scholarly journals INCREMENTS OF UNCORRELATED TIME SERIES CAN BE PREDICTED WITH A UNIVERSAL 75% PROBABILITY OF SUCCESS

2000 ◽  
Vol 11 (04) ◽  
pp. 713-720 ◽  
Author(s):  
D. SORNETTE ◽  
J. V. ANDERSEN
Keyword(s):  
Time Series ◽  
General Result ◽  
Success Probability ◽  
Temperature Time Series ◽  
Global Temperature ◽  
Times Series ◽  
Paradoxical Result ◽  
Probability Of Success ◽  
High Success Probability ◽  
Temperature Time

We present a simple and general result that the sign of the variations or increments of uncorrelated times series are predictable with a remarkably high success probability of 75% for symmetric sign distributions. The origin of this paradoxical result is explained in details. We also present some tests on synthetic, financial and global temperature time series.

EFFICIENT SCHEME FOR PREPARING POLARIZATION-ENTANGLED PHOTONIC CLUSTER STATES BASED ON CROSS-KERR NONLINEARITY

2011 ◽  
Vol 09 (05) ◽  
pp. 1319-1327
Author(s):  
MENG-ZHENG ZHU ◽  
GUANG-YU YUAN
Keyword(s):  
Cluster State ◽  
Success Probability ◽  
Kerr Nonlinearity ◽  
Optical Systems ◽  
Distinct Advantage ◽  
Optical Elements ◽  
Cluster States ◽  
Present Scheme ◽  
Linear Optical ◽  
High Success Probability

A scheme is proposed for generating a polarization four-photon cluster, which is believed to be suitable to achieve the one-way quantum computing via single-qubit projective measurements, with the help of only cross-Kerr nonlinearity and current linear optical systems. Compared with the existing schemes, the distinct advantage of the present scheme is that cluster states can be achieved with high success probability close to unity. Our scheme is experimentally demanding but efficient. Based on the present scheme, the cluster state of 3N + 1 photons can be obtained with the help of linear optical elements.

scholarly journals Quantum Algorithm for Attacking RSA Based on Fourier Transform and Fixed-Point

2021 ◽  
Vol 26 (6) ◽  
pp. 489-494
Author(s):  
Yahui WANG ◽  
Huanguo ZHANG
Keyword(s):  
Fixed Point ◽  
Polynomial Time ◽  
Multiplicative Group ◽  
Success Probability ◽  
Quantum Algorithm ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Rsa Cryptosystem ◽  
Shor's Algorithm ◽  
Quantum Polynomial

Shor in 1994 proposed a quantum polynomial-time algorithm for finding the order r of an element a in the multiplicative group Zn*, which can be used to factor the integer n by computing [see formula in PDF]and hence break the famous RSA cryptosystem. However, the order r must be even. This restriction can be removed. So in this paper, we propose a quantum polynomial-time fixed-point attack for directly recovering the RSA plaintext M from the ciphertext C, without explicitly factoring the modulus n. Compared to Shor’s algorithm, the order r of the fixed-point C for RSA(e, n) satisfying [see formula in PDF] does not need to be even. Moreover, the success probability of the new algorithm is at least [see formula in PDF] and higher than that of Shor’s algorithm, though the time complexity for both algorithms is about the same.

Financing successful small business projects

2014 ◽  
Vol 52 (2) ◽  
pp. 365-377 ◽  
Author(s):  
Irene Comeig ◽  
Esther B. Del Brio ◽  
Matilde O. Fernandez-Blanco
Keyword(s):  
Interest Rates ◽  
Project Success ◽  
Success Probability ◽  
Credit Rationing ◽  
Bank Loans ◽  
Data Set ◽  
Content Type ◽  
Loan Contracts ◽  
Access To Credit ◽  
High Success Probability

Purpose – The current credit rationing strongly influences the viability of SMEs innovation projects. In this context, the practice of screening borrowers by project success probability has become a paramount consideration for both lenders and firms. The aim of this paper is to test the screening role of loan contracts that consider collateral-interest margins simultaneously. Design/methodology/approach – This paper presents an empirical analysis that uses a unique data set composed of 323 bank loans granted by 28 banks to SMEs backed by a Spanish Mutual Guarantee Institution. Findings – The results show that appropriate combinations of collateral and interest rates can distinguish between borrowers with different project success probability: low success probability borrowers finance its projects without collateral and with high interest rates, whereas high success probability borrowers accept loans with real estate collateral and low interest rates. Practical implications – This screening mechanism reduces credit rationing, thus increasing good projects' access to credit. Originality/value – This study provides the first empirical evidence on the effectiveness of collateral-interest pairs as a self-selection mechanism.

PROBABILISTIC MULTIPARTY-CONTROLLED REMOTE PREPARATION OF AN ARBITRARY m-QUDIT STATE VIA POSITIVE OPERATOR-VALUED MEASUREMENT

2012 ◽  
Vol 10 (05) ◽  
pp. 1250062 ◽  
Author(s):  
ZHAO LI ◽  
PING ZHOU
Keyword(s):  
Positive Operator ◽  
Success Probability ◽  
Entangled States ◽  
System State ◽  
Practical Application ◽  
Original State ◽  
Remote Preparation ◽  
High Success Probability ◽  
The Relationship ◽  
Controlled Remote Preparation

We present a scheme for multiparty-controlled remote preparation of an arbitrary m-qudit (d-dimensional quantum system) state via positive operator-valued measurement (POVM) by using nonmaximally entangled states as the quantum channel, not resorting to auxiliary qubits. The sender performs an optimal POVM measurement on her m particles with measurement operators that depend on the original state, the controllers perform generalized X-basis measurement X d and the receiver can prepare the original state if he cooperates with all the controllers and the sender. The scheme has the advantage of having high success probability for remote preparing an arbitrary m-qudit state and more convenient than others in a practical application. Moreover, it discusses the relationship between the probability that the receiver obtains the originally state and the coefficients of the entangled states.

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