The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Geir E Dullerud - One of the best experts on this subject based on the ideXlab platform.
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distributed Symmetric Function computation in noisy wireless sensor networks
IEEE Transactions on Information Theory, 2007Co-Authors: Lei Ying, R Srikant, Geir E DullerudAbstract:In this correspondence, we consider a wireless sensor network consisting of n sensors, and each sensor has a measurement, which is an integer value belonging to the set {().....m-1}, so that it can be represented by [log2 m] bits. The network has a special node called the fusion center whose goal is to compute a Symmetric Function of these measurements. The problem studied is to minimize the total transmission energy used by the network when computing this Function, subject to the constraint that this computation be correct with high probability. We assume the wireless channels are binary Symmetric channels with a probability of error p, and that each sensor uses ralpha units of energy to transmit each bit, where r is the transmission range of the sensor.
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distributed Symmetric Function computation in noisy wireless sensor networks with binary data
Modeling and Optimization in Mobile Ad-Hoc and Wireless Networks, 2006Co-Authors: Lei Ying, R Srikant, Geir E DullerudAbstract:We consider a wireless sensor network consisting of n sensors, each having a recorded bit, the sensor’s measurement, which has been set to either “0” or “1”. The network has a special node called the fusion center whose goal is to compute a Symmetric Function of these bits; i.e., a Function that depends only on the number of sensors that have a “1.” The sensors convey information to the fusion center in a multi-hop fashion to enable the Function computation. The problem studied is to minimize the total transmission energy used by the network when computing this Function, subject to the constraint that this computation is correct with high probability. We assume the wireless channels are binary Symmetric channels with a probability of error p, and that each sensor uses rαunits of energy to transmit each bit, where r is the transmission range of the sensor. The main result in this paper is an algorithm whose energy usage is Θ (n(loglogn)(√logn/n)α), and we also show that any algorithm satisfying the performance constraints must necessarily have energy usage Ω (n(√logn/n)α). Then, we consider the case where the sensor network observes N events, and each node records one bit per event, thus having N bits to convey. The fusion center now wants to compute N Symmetric Functions, one for each of the events.
Kaizhong Guan - One of the best experts on this subject based on the ideXlab platform.
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a class of Symmetric Functions for multiplicatively convex Function
Mathematical Inequalities & Applications, 2007Co-Authors: Kaizhong GuanAbstract:A new Symmetric Function, which generalizes Hamy Symmetric Function, is defined. Its properties, including Schur-geometric convexity, are investigated. Some analytic inequalities are also established. Mathematics subject classification (2000): 26A51, 26D15, 0E05.
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schur convexity of the complete elementary Symmetric Function
Journal of Inequalities and Applications, 2006Co-Authors: Kaizhong GuanAbstract:We prove that the complete elementary Symmetric FunctionOpen image in new window and the FunctionOpen image in new window are Schur-convex Functions inOpen image in new window, whereOpen image in new window are nonnegative integers,Open image in new window,Open image in new window. For which, some inequalities are established by use of the theory of majorization. A problem given by K. V. Menon (Duke Mathematical Journal 35 (1968), 37–45) is also solved.
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the hamy Symmetric Function and its generalization
Mathematical Inequalities & Applications, 2006Co-Authors: Kaizhong GuanAbstract:In the paper we investigate and generalize the Hamy Symmetric Function: Fn(x, r) = ∑ 1 i1
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schur convexity of the complete Symmetric Function
Mathematical Inequalities & Applications, 2006Co-Authors: Kaizhong GuanAbstract:This paper investigates Schur-convexity of the complete Symmetric Function cr(x) = ∑ i1+...+in=r x i1 1 ...x in n and the Function φr(x) = cr(x) cr−1(x) , where i1, ..., in are non-negative integers and r 1. Some inequalities, including Ky Fan type inequality, are established by use of the theory of majorization. It is also concerned with an open problem proposed by Menon [1]. Mathematics subject classification (2000): 05E05, 26E60, 26D20.
Lei Ying - One of the best experts on this subject based on the ideXlab platform.
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distributed Symmetric Function computation in noisy wireless sensor networks
IEEE Transactions on Information Theory, 2007Co-Authors: Lei Ying, R Srikant, Geir E DullerudAbstract:In this correspondence, we consider a wireless sensor network consisting of n sensors, and each sensor has a measurement, which is an integer value belonging to the set {().....m-1}, so that it can be represented by [log2 m] bits. The network has a special node called the fusion center whose goal is to compute a Symmetric Function of these measurements. The problem studied is to minimize the total transmission energy used by the network when computing this Function, subject to the constraint that this computation be correct with high probability. We assume the wireless channels are binary Symmetric channels with a probability of error p, and that each sensor uses ralpha units of energy to transmit each bit, where r is the transmission range of the sensor.
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distributed Symmetric Function computation in noisy wireless sensor networks with binary data
Modeling and Optimization in Mobile Ad-Hoc and Wireless Networks, 2006Co-Authors: Lei Ying, R Srikant, Geir E DullerudAbstract:We consider a wireless sensor network consisting of n sensors, each having a recorded bit, the sensor’s measurement, which has been set to either “0” or “1”. The network has a special node called the fusion center whose goal is to compute a Symmetric Function of these bits; i.e., a Function that depends only on the number of sensors that have a “1.” The sensors convey information to the fusion center in a multi-hop fashion to enable the Function computation. The problem studied is to minimize the total transmission energy used by the network when computing this Function, subject to the constraint that this computation is correct with high probability. We assume the wireless channels are binary Symmetric channels with a probability of error p, and that each sensor uses rαunits of energy to transmit each bit, where r is the transmission range of the sensor. The main result in this paper is an algorithm whose energy usage is Θ (n(loglogn)(√logn/n)α), and we also show that any algorithm satisfying the performance constraints must necessarily have energy usage Ω (n(√logn/n)α). Then, we consider the case where the sensor network observes N events, and each node records one bit per event, thus having N bits to convey. The fusion center now wants to compute N Symmetric Functions, one for each of the events.
Pavlo Pylyavskyy - One of the best experts on this subject based on the ideXlab platform.
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p partition products and fundamental quasi Symmetric Function positivity
Advances in Applied Mathematics, 2008Co-Authors: Thomas Lam, Pavlo PylyavskyyAbstract:We show that certain differences of productsK"Q"@?"R","@qK"Q"@?"R","@q-K"Q","@qK"R","@q of P-partition generating Functions are positive in the basis of fundamental quasi-Symmetric Functions L"@a. This result interpolates between recent Schur positivity and monomial positivity results of the same flavor. We study the case of chains in detail, introducing certain ''cell transfer'' operations on compositions and a related ''L-positivity'' poset. We introduce and study quasi-Symmetric Functions called wave Schur Functions and use them to establish, in the case of chains, that K"Q"@?"R","@qK"Q"@?"R","@q-K"Q","@qK"R","@q is itself equal to a single generating Function K"P","@q for a labeled poset (P,@q). In the course of our investigations we establish some factorization properties of the ring QSym of quasi-Symmetric Functions.
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p partition products and fundamental quasi Symmetric Function positivity
arXiv: Combinatorics, 2006Co-Authors: Thomas Lam, Pavlo PylyavskyyAbstract:We show that certain differences of products of $P$-partition generating Functions are positive in the basis of fundamental quasi-Symmetric Functions L_\alpha. This result interpolates between recent Schur positivity and monomial positivity results of the same flavor. We study the case of chains in detail, introducing certain ``cell transfer'' operations on compositions and an interesting related ``L-positivity'' poset. We introduce and study quasi-Symmetric Functions called ``wave Schur Functions'' and use them to establish, in the case of chains, that the difference of products we study is itself equal to a single generating Function K_{P,\theta} for a labeled poset (P,\theta). In the course of our investigations we establish some factorization properties of the ring of quasiSymmetric Functions.
Alexander Garbali - One of the best experts on this subject based on the ideXlab platform.
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the domain wall partition Function for the izergin korepin nineteen vertex model at a root of unity
Journal of Statistical Mechanics: Theory and Experiment, 2016Co-Authors: Alexander GarbaliAbstract:We study the domain wall partition Function Z N for the ${{U}_{q}}\left(A_{2}^{(2)}\right)$ (Izergin–Korepin) integrable nineteen-vertex model on a square lattice of size N. Z N is a Symmetric Function of two sets of parameters: horizontal ${{\zeta}_{1}},..,{{\zeta}_{N}}$ and vertical ${{z}_{1}},..,{{z}_{N}}$ rapidities. For generic values of the parameter q we derive the recurrence relation for the domain wall partition Function relating Z N+1 to ${{P}_{N}}{{Z}_{N}}$ , where P N is the proportionality factor in the recurrence, which is a polynomial Symmetric in two sets of variables ${{\zeta}_{1}},..,{{\zeta}_{N}}$ and ${{z}_{1}},..,{{z}_{N}}$ . After setting $q={{\text{e}}^{\text{i}\pi /3}}$ the recurrence relation simplifies and we solve it in terms of a Jacobi–Trudi-like determinant of polynomials generated by P N .
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the domain wall partition Function for the izergin korepin 19 vertex model at a root of unity
arXiv: Mathematical Physics, 2014Co-Authors: Alexander GarbaliAbstract:We study the domain wall partition Function $Z_N$ for the $U_q(A_2^{(2)})$ (Izergin-Korepin) integrable $19$-vertex model on a square lattice of size $N$. $Z_N$ is a Symmetric Function of two sets of parameters: horizontal $\zeta_1,..,\zeta_N$ and vertical $z_1,..,z_N$ rapidities. For generic values of the parameter $q$ we derive the recurrence relation for the domain wall partition Function relating $Z_{N+1}$ to $P_N Z_N$, where $P_N$ is the proportionality factor in the recurrence, which is a polynomial Symmetric in two sets of variables $\zeta_1,..,\zeta_N$ and $z_1,..,z_N$. After setting $q^3=-1$ the recurrence relation simplifies and we solve it in terms of a Jacobi-Trudi-like determinant of polynomials generated by $P_N$.
