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Xiang Ming Chen - One of the best experts on this subject based on the ideXlab platform.
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measurement error of temperature coefficient of resonant frequency for microwave dielectric materials by mathrm te _ mathrm 01 delta mode resonant Cavity Method
IEEE Transactions on Microwave Theory and Techniques, 2016Co-Authors: Jun Yao Zhu, Xiang Ming ChenAbstract:The temperature coefficient of resonant frequency of a microwave dielectric material ( $\tau _{f,s}$ ) is defined as the $\tau _{f}$ of an ideal resonant system that is homogeneously filled with this material, while it is usually measured as the $\tau _{f}$ of a nonideal resonant system ( $\tau _{f,r}$ ) such as a Cavity dielectric resonator. In the present work, finite element analysis is used to investigate the measurement error of ${\tau }_{f,s}$ by $\mathrm{TE}_{01\delta }$ -mode resonant Cavity Method, for which the sample is placed on a support and far from the Cavity walls. Several error sources contribute to the total measurement error, which is usually several ppm/°C and decreases with the dielectric constant of the sample ( ${\varepsilon }_{r,s}$ ). Besides, the measurement error is strongly dependent on the Cavity size. In comparison, the measurement error is much lower and usually within 1 ppm/°C for TE011-mode parallel plate Method, where the sample is clamped between two metal plates. It is suggested to measure ${\tau }_{f,s}$ by TE011-mode parallel plate Method but not by $\mathrm{TE}_{01\delta }$ -mode resonant Cavity Method if ${\tau }_{f,s}$ is treated as ${\tau }_{f,r}$ , especially when ${\varepsilon }_{r,s}$ is low and high measurement accuracy is needed. If $\mathrm{TE}_{01\delta }$ -mode resonant Cavity Method is used to measure ${\tau }_{f,s}$ , the result must be corrected with the aid of numerical calculation to improve the measurement accuracy.
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Measurement Error of Temperature Coefficient of Resonant Frequency for Microwave Dielectric Materials by $\mathrm{TE}_{\mathrm {01\delta }}$ -Mode Resonant Cavity Method
IEEE Transactions on Microwave Theory and Techniques, 2016Co-Authors: Jun Yao Zhu, Xiang Ming ChenAbstract:The temperature coefficient of resonant frequency of a microwave dielectric material ( $\tau _{f,s}$ ) is defined as the $\tau _{f}$ of an ideal resonant system that is homogeneously filled with this material, while it is usually measured as the $\tau _{f}$ of a nonideal resonant system ( $\tau _{f,r}$ ) such as a Cavity dielectric resonator. In the present work, finite element analysis is used to investigate the measurement error of ${\tau }_{f,s}$ by $\mathrm{TE}_{01\delta }$ -mode resonant Cavity Method, for which the sample is placed on a support and far from the Cavity walls. Several error sources contribute to the total measurement error, which is usually several ppm/°C and decreases with the dielectric constant of the sample ( ${\varepsilon }_{r,s}$ ). Besides, the measurement error is strongly dependent on the Cavity size. In comparison, the measurement error is much lower and usually within 1 ppm/°C for TE011-mode parallel plate Method, where the sample is clamped between two metal plates. It is suggested to measure ${\tau }_{f,s}$ by TE011-mode parallel plate Method but not by $\mathrm{TE}_{01\delta }$ -mode resonant Cavity Method if ${\tau }_{f,s}$ is treated as ${\tau }_{f,r}$ , especially when ${\varepsilon }_{r,s}$ is low and high measurement accuracy is needed. If $\mathrm{TE}_{01\delta }$ -mode resonant Cavity Method is used to measure ${\tau }_{f,s}$ , the result must be corrected with the aid of numerical calculation to improve the measurement accuracy.
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Effect of Sample Size on Measurement Reliability of Microwave Dielectric Properties of Low-Loss Materials by a Resonant Cavity Method
Ferroelectrics, 2012Co-Authors: Xiang Ming ChenAbstract:The microwave dielectric properties of SrTiO3 and CaNdAlO4 single crystals were measured by the resonant Cavity Method, and the effect of sample size on measurement reliability was investigated. High measurement accuracy could always be achieved for SrTiO3, while the measurement was completely unreliable for CaNdAlO4 with small sizes. The difference was attributed to the much higher dielectric constant and electric energy filling factor of SrTiO3. It is indicated that the sample with much smaller size than usual might also be used for the resonant Cavity Method, as long as the electric energy filling factor of the sample was high enough.
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Evaluation of microwave dielectric properties of giant permittivity materials by a modified resonant Cavity Method
Applied Physics Letters, 2007Co-Authors: Xiang Ming ChenAbstract:A modified resonant Cavity Method was developed to evaluate the microwave dielectric properties of giant permittivity materials, which were difficult to determine accurately using previous Methods. A small-sized sample was used for measurement in the present work, and the microwave dielectric properties could be measured accurately over a wide frequency range with the aid of low-loss reference ceramics. The measurement was conducted on CaCu3Ti4O12 ceramics from 3.38to10.16GHz. The permittivity of CaCu3Ti4O12 ceramics was around 84 over the above frequency range and decreased slightly with increasing frequency, while the dielectric loss decreased significantly from 0.17 to 0.055.
Marc Mezard - One of the best experts on this subject based on the ideXlab platform.
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Cavity Method : Message Passing from a Physics perspective
2016Co-Authors: Gino Del Ferraro, Chuang Wang, Dani Martí, Marc MezardAbstract:In this three-sections lecture Cavity Method is introduced as heuristic framework from a Physics perspective to solve probabilistic graphical models and it is presented both at the replica symmetri ...
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Cavity Method: Message Passing from a Physics Perspective
arXiv: Disordered Systems and Neural Networks, 2014Co-Authors: Gino Del Ferraro, Chuang Wang, Dani Martí, Marc MezardAbstract:In this three-sections lecture Cavity Method is introduced as heuristic framework from a Physics perspective to solve probabilistic graphical models and it is presented both at the replica symmetric (RS) and 1-step replica symmetry breaking (1RSB) level. This technique has been applied with success on a wide range of models and problems such as spin glasses, random constrain satisfaction problems (rCSP), error correcting codes etc. Firstly, the RS Cavity solution for Sherrington-Kirkpatrick model---a fully connected spin glass model---is derived and its equivalence to the RS solution obtained using replicas is discussed. Then, the general Cavity Method for diluted graphs is illustrated both at RS and 1RSB level. The latter was a significant breakthrough in the last decade and has direct applications to rCSP. Finally, as example of an actual problem, K-SAT is investigated using belief and survey propagation.
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The Cavity Method for quantum disordered systems: from transverse random field ferromagnets to directed polymers in random media
Journal of Statistical Mechanics: Theory and Experiment, 2011Co-Authors: O Dimitrova, Marc MezardAbstract:After reviewing the basics of the Cavity Method in classical systems, we show how its quantum version, with some appropriate approximation scheme, can be used to study a system of spins with random ferromagnetic interactions and a random transverse field. The quantum Cavity equations describing the ferromagnetic–paramagnetic phase transition can be transformed into the well-known problem of a classical directed polymer in a random medium. The glass transition of this polymer problem translates into the existence of a 'Griffiths phase' close to the quantum phase transition of the quantum spin problem, where the physics is dominated by rare events. The physical behaviour of random transverse-field ferromagnets on the Bethe lattice is found to be very similar to that found in finite-dimensional systems, and the quantum Cavity Method gets back the known exact results of the one-dimensional problem.
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The Cavity Method for quantum disordered systems: from transverse random field ferromagnets to directed polymers in random media
2010Co-Authors: O Dimitrova, Marc MezardAbstract:After reviewing the basics of the Cavity Method in classical systems, we show how its quantum version, with some appropriate approximation scheme, can be used to study a system of spins with random ferromagnetic interactions and a random transverse field. The quantum Cavity equations describing the ferromagnetic-paramagnetic phase transition can be transformed into the well-known problem of a classical directed polymer in a random medium. The glass transition of this polymer problem translates ino the existence of a `Griffith phase' close to the quantum phase transition of the quantum spin problem, where the physics is dominated by rare events.
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threshold values of random k sat from the Cavity Method
Random Structures and Algorithms, 2006Co-Authors: Stephan Mertens, Marc Mezard, Riccardo ZecchinaAbstract:Using the Cavity equations of Mezard, Parisi, and Zecchina [Science 297 (2002), 812]; Mezard and Zecchina, [Phys Rev E 66 (2002), 056126] we derive the various threshold values for the number of clauses per variable of the random K-satisfiability problem, generalizing the previous results to K ≥ 4. We also give an analytic solution of the equations, and some closed expressions for these thresholds, in an expansion around large K. The stability of the solution is also computed. For any K, the satisfiability threshold is found to be in the stable region of the solution, which adds further credit to the conjecture that this computation gives the exact satisfiability threshold.© 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006
Jun Yao Zhu - One of the best experts on this subject based on the ideXlab platform.
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measurement error of temperature coefficient of resonant frequency for microwave dielectric materials by mathrm te _ mathrm 01 delta mode resonant Cavity Method
IEEE Transactions on Microwave Theory and Techniques, 2016Co-Authors: Jun Yao Zhu, Xiang Ming ChenAbstract:The temperature coefficient of resonant frequency of a microwave dielectric material ( $\tau _{f,s}$ ) is defined as the $\tau _{f}$ of an ideal resonant system that is homogeneously filled with this material, while it is usually measured as the $\tau _{f}$ of a nonideal resonant system ( $\tau _{f,r}$ ) such as a Cavity dielectric resonator. In the present work, finite element analysis is used to investigate the measurement error of ${\tau }_{f,s}$ by $\mathrm{TE}_{01\delta }$ -mode resonant Cavity Method, for which the sample is placed on a support and far from the Cavity walls. Several error sources contribute to the total measurement error, which is usually several ppm/°C and decreases with the dielectric constant of the sample ( ${\varepsilon }_{r,s}$ ). Besides, the measurement error is strongly dependent on the Cavity size. In comparison, the measurement error is much lower and usually within 1 ppm/°C for TE011-mode parallel plate Method, where the sample is clamped between two metal plates. It is suggested to measure ${\tau }_{f,s}$ by TE011-mode parallel plate Method but not by $\mathrm{TE}_{01\delta }$ -mode resonant Cavity Method if ${\tau }_{f,s}$ is treated as ${\tau }_{f,r}$ , especially when ${\varepsilon }_{r,s}$ is low and high measurement accuracy is needed. If $\mathrm{TE}_{01\delta }$ -mode resonant Cavity Method is used to measure ${\tau }_{f,s}$ , the result must be corrected with the aid of numerical calculation to improve the measurement accuracy.
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Measurement Error of Temperature Coefficient of Resonant Frequency for Microwave Dielectric Materials by $\mathrm{TE}_{\mathrm {01\delta }}$ -Mode Resonant Cavity Method
IEEE Transactions on Microwave Theory and Techniques, 2016Co-Authors: Jun Yao Zhu, Xiang Ming ChenAbstract:The temperature coefficient of resonant frequency of a microwave dielectric material ( $\tau _{f,s}$ ) is defined as the $\tau _{f}$ of an ideal resonant system that is homogeneously filled with this material, while it is usually measured as the $\tau _{f}$ of a nonideal resonant system ( $\tau _{f,r}$ ) such as a Cavity dielectric resonator. In the present work, finite element analysis is used to investigate the measurement error of ${\tau }_{f,s}$ by $\mathrm{TE}_{01\delta }$ -mode resonant Cavity Method, for which the sample is placed on a support and far from the Cavity walls. Several error sources contribute to the total measurement error, which is usually several ppm/°C and decreases with the dielectric constant of the sample ( ${\varepsilon }_{r,s}$ ). Besides, the measurement error is strongly dependent on the Cavity size. In comparison, the measurement error is much lower and usually within 1 ppm/°C for TE011-mode parallel plate Method, where the sample is clamped between two metal plates. It is suggested to measure ${\tau }_{f,s}$ by TE011-mode parallel plate Method but not by $\mathrm{TE}_{01\delta }$ -mode resonant Cavity Method if ${\tau }_{f,s}$ is treated as ${\tau }_{f,r}$ , especially when ${\varepsilon }_{r,s}$ is low and high measurement accuracy is needed. If $\mathrm{TE}_{01\delta }$ -mode resonant Cavity Method is used to measure ${\tau }_{f,s}$ , the result must be corrected with the aid of numerical calculation to improve the measurement accuracy.
Riccardo Zecchina - One of the best experts on this subject based on the ideXlab platform.
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Performance of a Cavity-Method-based algorithm for the prize-collecting Steiner tree problem on graphs
Physical Review E, 2012Co-Authors: Indaco Biazzo, Alfredo Braunstein, Riccardo ZecchinaAbstract:We study the behavior of an algorithm derived from the Cavity Method for the prize-collecting steiner tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the Cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide range of existing benchmarks, networks, and random graphs. Specifically, we consider an enhanced derivative of the Goemans-Williamson heuristics and the dhea solver, a branch and cut integer linear programming based approach. The comparison shows that the Cavity algorithm outperforms the two algorithms in most large instances both in running time and quality of the solution. Finally we prove a few optimality properties of the solutions provided by our algorithm, including optimality under the two postprocessing procedures defined in the Goemans-Williamson derivative and global optimality in some limit cases.
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threshold values of random k sat from the Cavity Method
Random Structures and Algorithms, 2006Co-Authors: Stephan Mertens, Marc Mezard, Riccardo ZecchinaAbstract:Using the Cavity equations of Mezard, Parisi, and Zecchina [Science 297 (2002), 812]; Mezard and Zecchina, [Phys Rev E 66 (2002), 056126] we derive the various threshold values for the number of clauses per variable of the random K-satisfiability problem, generalizing the previous results to K ≥ 4. We also give an analytic solution of the equations, and some closed expressions for these thresholds, in an expansion around large K. The stability of the solution is also computed. For any K, the satisfiability threshold is found to be in the stable region of the solution, which adds further credit to the conjecture that this computation gives the exact satisfiability threshold.© 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006
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Threshold values of Random K-SAT from the Cavity Method
arXiv: Computational Complexity, 2003Co-Authors: Stephan Mertens, Marc Mezard, Riccardo ZecchinaAbstract:Using the Cavity equations of \cite{mezard:parisi:zecchina:02,mezard:zecchina:02}, we derive the various threshold values for the number of clauses per variable of the random $K$-satisfiability problem, generalizing the previous results to $K \ge 4$. We also give an analytic solution of the equations, and some closed expressions for these thresholds, in an expansion around large $K$. The stability of the solution is also computed. For any $K$, the satisfiability threshold is found to be in the stable region of the solution, which adds further credit to the conjecture that this computation gives the exact satisfiability threshold.
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The random K-satisfiability problem: from an analytic solution to an efficient algorithm
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2002Co-Authors: Marc Mezard, Riccardo ZecchinaAbstract:We study the problem of satisfiability of randomly chosen clauses, each with K Boolean variables. Using the Cavity Method at zero temperature, we find the phase diagram for the K=3 case. We show the existence of an intermediate phase in the satisfiable region, where the proliferation of metastable states is at the origin of the slowdown of search algorithms. The fundamental order parameter introduced in the Cavity Method, which consists of surveys of local magnetic fields in the various possible states of the system, can be computed for one given sample. These surveys can be used to invent new types of algorithms for solving hard combinatorial optimizations problems. One such algorithm is shown here for the 3-sat problem, with very good performances.
Florent Krzakala - One of the best experts on this subject based on the ideXlab platform.
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Information-theoretic thresholds from the Cavity Method
Advances in Mathematics, 2018Co-Authors: Amin Coja-oghlan, Florent Krzakala, Will Perkins, Lenka ZdeborovaAbstract:Abstract Vindicating a sophisticated but non-rigorous physics approach called the Cavity Method, we establish a formula for the mutual information in statistical inference problems induced by random graphs and we show that the mutual information holds the key to understanding certain important phase transitions in random graph models. We work out several concrete applications of these general results. For instance, we pinpoint the exact condensation phase transition in the Potts antiferromagnet on the random graph, thereby improving prior approximate results (Contucci et al., 2013) [34] . Further, we prove the conjecture from Krzakala et al. (2007) [55] about the condensation phase transition in the random graph coloring problem for any number q ≥ 3 of colors. Moreover, we prove the conjecture on the information-theoretic threshold in the disassortative stochastic block model (Decelle et al., 2011) [35] . Additionally, our general result implies the conjectured formula for the mutual information in Low-Density Generator Matrix codes (Montanari, 2005) [73] .
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information theoretic thresholds from the Cavity Method
Symposium on the Theory of Computing, 2017Co-Authors: Amin Cojaoghlan, Florent Krzakala, Will Perkins, Lenka ZdeborovaAbstract:Vindicating a sophisticated but non-rigorous physics approach called the Cavity Method, we establish a formula for the mutual information in statistical inference problems induced by random graphs. This general result implies the conjecture on the information-theoretic threshold in the disassortative stochastic block model [Decelle et al.: Phys. Rev. E (2011)] and allows us to pinpoint the exact condensation phase transition in random constraint satisfaction problems such as random graph coloring, thereby proving a conjecture from [Krzakala et al.: PNAS (2007)]. As a further application we establish the formula for the mutual information in Low-Density Generator Matrix codes as conjectured in [Montanari: IEEE Transactions on Information Theory (2005)]. The proofs provide a conceptual underpinning of the replica symmetric variant of the Cavity Method, and we expect that the approach will find many future applications.
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Information-theoretic thresholds from the Cavity Method
2017Co-Authors: Amin Coja-oghlan, Florent Krzakala, Will Perkins, Lenka ZdeborovaAbstract:Vindicating a sophisticated but non-rigorous physics approach called the Cavity Method, we establish a formula for the mutual information in statistical inference problems induced by random graphs and we show that the mutual information holds the key to understanding certain important phase transitions in random graph models. We work out several concrete applications of these general results. For instance, we pinpoint the exact condensation phase transition in the Potts antiferromagnet on the random graph, thereby improving prior approximate results [Contucci et al.: Communications in Mathematical Physics 2013]. Further, we prove the conjecture from [Krzakala et al.: PNAS 2007] about the condensation phase transition in the random graph coloring problem for any number q ≥ 3 of colors. Moreover , we prove the conjecture on the information-theoretic threshold in the disassortative stochastic block model [Decelle et al.: Phys. Rev. E 2011]. Additionally, our general result implies the conjectured formula for the mutual information in Low-Density Generator Matrix codes [Montanari: IEEE Transactions on Information Theory 2005].
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STOC - Information-theoretic thresholds from the Cavity Method
Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2017, 2017Co-Authors: Amin Coja-oghlan, Florent Krzakala, Will Perkins, Lenka ZdeborovaAbstract:Vindicating a sophisticated but non-rigorous physics approach called the Cavity Method, we establish a formula for the mutual information in statistical inference problems induced by random graphs. This general result implies the conjecture on the information-theoretic threshold in the disassortative stochastic block model [Decelle et al.: Phys. Rev. E (2011)] and allows us to pinpoint the exact condensation phase transition in random constraint satisfaction problems such as random graph coloring, thereby proving a conjecture from [Krzakala et al.: PNAS (2007)]. As a further application we establish the formula for the mutual information in Low-Density Generator Matrix codes as conjectured in [Montanari: IEEE Transactions on Information Theory (2005)]. The proofs provide a conceptual underpinning of the replica symmetric variant of the Cavity Method, and we expect that the approach will find many future applications.
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Generalization of the Cavity Method for adiabatic evolution of Gibbs states
Physical Review B, 2010Co-Authors: Lenka Zdeborova, Florent KrzakalaAbstract:Mean-field glassy systems have a complicated energy landscape and an enormous number of different Gibbs states. In this paper, we introduce a generalization of the Cavity Method in order to describe the adiabatic evolution of these glassy Gibbs states as an external parameter, such as the temperature, is tuned. We give a general derivation of the Method and describe in details the solution of the resulting equations for the fully connected $p$-spin model, the XOR-satisfiability (SAT) problem and the antiferromagnetic Potts glass (coloring problem). As direct results of the states following Method we present a study of very slow Monte Carlo annealings, the demonstration of the presence of temperature chaos in these systems and the identification of an easy/hard transition for simulated annealing in constraint optimization problems. We also discuss the relation between our approach and the Franz-Parisi potential, as well as with the reconstruction problem on trees in computer science. A mapping between the states following Method and the physics on the Nishimori line is also presented.
