At the tipping point, it is known that small incident can trigger dramatic societal shift. Gettin... more At the tipping point, it is known that small incident can trigger dramatic societal shift. Getting early-warning signals for such changes are valuable to avoid detrimental outcomes such as riots or collapses of nations. However, it is notoriously hard to capture the processes of such transitions in the real-world. Here, we demonstrate the occurrence of a major shift in public opinion in the form of political support. Instead of simple swapping of ruling parties, we study the regime shift of a party popularity based on its attractiveness by examining the American presidential elections during 1980-2012. A single irreversible transition is detected in 1991. Once a transition happens, recovery to the original level of attractiveness does not bring popularity of the political party back. Remarkably, this transition is corroborated by tell-tale early-warning signature of critical slowing down. Our approach is applicable to shifts in public attitude within any social system.
It has been known that assortative network structure plays an important role in spreading dynamic... more It has been known that assortative network structure plays an important role in spreading dynamics for unweighted networks. Yet its influence on weighted networks is not clear, in particular when weight is strongly correlated with the degrees of the nodes as we empirically observed in Twitter. Here we use the self-consistent probability method and revised nonperturbative heterogenous mean-field theory method to investigate this influence on both susceptible-infective-recovered (SIR) and susceptible-infective-susceptible (SIS) spreading dynamics. Both our simulation and theoretical results show that while the critical threshold is not significantly influenced by the assortativity, the prevalence in the supercritical regime shows a crossover under different degree-weight correlations. In particular, unlike the case of random mixing networks, in assortative networks, the negative degree-weight correlation leads to higher prevalence in their spreading beyond the critical transmissivity ...
We give a method for numerically evaluating the Wess–Zumino (WZ) term for an arbitrary SU(3) fiel... more We give a method for numerically evaluating the Wess–Zumino (WZ) term for an arbitrary SU(3) field configuration. We check the accuracy of the numerical method by evaluating the WZ-term for the 2π-rotation of a Skyrmion field configuration.
Major American Univ. Ph.D. Qualifying Questions and Solutions - Physics, 1991
The material for these volumes has been selected from the past twenty years' examination ques... more The material for these volumes has been selected from the past twenty years' examination questions for graduate students at University of California at Berkeley, Columbia University, the University of Chicago, MIT, State University of New York at Buffalo, Princeton University and University of Wisconsin.
Major American Univ. Ph.D. Qualifying Questions and Solutions - Physics, 1994
... of China Refereed by: Qiang Yuan-qi, Gu En-pu, Cheng Jia-fu, Li Ze-hua & Yang De-tian Edi... more ... of China Refereed by: Qiang Yuan-qi, Gu En-pu, Cheng Jia-fu, Li Ze-hua & Yang De-tian Edited by: Lim Yung-kuo ... 5 Toh Tuck Link, Singapore 596224 USA office: Suite 202, I060 Main Street, River Edge, NJ 0766I UK office: 57 Shelton Street, Covent Garden, London WC2H ...
The effect of the shape of six different periodic forces and second periodic forces on the onset ... more The effect of the shape of six different periodic forces and second periodic forces on the onset of horseshoe chaos are studied both analytically and numerically in a Duffing oscillator. The external periodic forces considered are sine wave, square wave, symmetric saw-tooth wave, asymmetric saw-tooth wave, rectified sine wave, and modulus of sine wave. An analytical threshold condition for the onset of horseshoe chaos is obtained in the Duffing oscillator driven by various periodic forces using the Melnikov method. Melnikov threshold curve is drawn in a parameter space. For all the forces except modulus of sine wave, the onset of cross-well asymptotic chaos is observed just above the Melnikov threshold curve for onset of horseshoe chaos. For the modulus of sine wave long time transient motion followed by a periodic attractor is realized. The possibility of controlling of horseshoe and asymptotic chaos in the Duffing oscillator by an addition of second periodic force is then analyzed...
The nonrelativistic propagator is derived by formulating the generalized Aharonov–Bohm effect, va... more The nonrelativistic propagator is derived by formulating the generalized Aharonov–Bohm effect, valid for any gauge group in a general multiply connected manifold, as a gauge artifact in the universal covering space. The loop phase factors and the free homotopy propagators arise naturally. An explicit expression for the propagator when there are two solenoids present is given.
It is shown that the transition functions that give the global structure of the fiber bundle play... more It is shown that the transition functions that give the global structure of the fiber bundle play an important role in the construction of the metric. The invariance properties of this metric under general gauge transformations are discussed and it is found that the usual requirement of a gauge-invariant metric leads to severe constraints on the gauge fields. To avoid them, it is shown that the metric should instead be covariant with respect to these transformations. Moreover the existence of global actions that are essential in the context of the consistency problem is also discussed. The presence of such actions is studied in both the principal and their associated bundles. In the case of a homogeneous bundle with G/H as the typical fiber, it is shown that a ‘‘spliced’’ bundle with G×N(H)/H as the structure group has to be used. The unified space is then taken as the bundle space of its associated bundle.
At the tipping point, it is known that small incident can trigger dramatic societal shift. Gettin... more At the tipping point, it is known that small incident can trigger dramatic societal shift. Getting early-warning signals for such changes are valuable to avoid detrimental outcomes such as riots or collapses of nations. However, it is notoriously hard to capture the processes of such transitions in the real-world. Here, we demonstrate the occurrence of a major shift in public opinion in the form of political support. Instead of simple swapping of ruling parties, we study the regime shift of a party popularity based on its attractiveness by examining the American presidential elections during 1980-2012. A single irreversible transition is detected in 1991. Once a transition happens, recovery to the original level of attractiveness does not bring popularity of the political party back. Remarkably, this transition is corroborated by tell-tale early-warning signature of critical slowing down. Our approach is applicable to shifts in public attitude within any social system.
It has been known that assortative network structure plays an important role in spreading dynamic... more It has been known that assortative network structure plays an important role in spreading dynamics for unweighted networks. Yet its influence on weighted networks is not clear, in particular when weight is strongly correlated with the degrees of the nodes as we empirically observed in Twitter. Here we use the self-consistent probability method and revised nonperturbative heterogenous mean-field theory method to investigate this influence on both susceptible-infective-recovered (SIR) and susceptible-infective-susceptible (SIS) spreading dynamics. Both our simulation and theoretical results show that while the critical threshold is not significantly influenced by the assortativity, the prevalence in the supercritical regime shows a crossover under different degree-weight correlations. In particular, unlike the case of random mixing networks, in assortative networks, the negative degree-weight correlation leads to higher prevalence in their spreading beyond the critical transmissivity ...
We give a method for numerically evaluating the Wess–Zumino (WZ) term for an arbitrary SU(3) fiel... more We give a method for numerically evaluating the Wess–Zumino (WZ) term for an arbitrary SU(3) field configuration. We check the accuracy of the numerical method by evaluating the WZ-term for the 2π-rotation of a Skyrmion field configuration.
Major American Univ. Ph.D. Qualifying Questions and Solutions - Physics, 1991
The material for these volumes has been selected from the past twenty years' examination ques... more The material for these volumes has been selected from the past twenty years' examination questions for graduate students at University of California at Berkeley, Columbia University, the University of Chicago, MIT, State University of New York at Buffalo, Princeton University and University of Wisconsin.
Major American Univ. Ph.D. Qualifying Questions and Solutions - Physics, 1994
... of China Refereed by: Qiang Yuan-qi, Gu En-pu, Cheng Jia-fu, Li Ze-hua & Yang De-tian Edi... more ... of China Refereed by: Qiang Yuan-qi, Gu En-pu, Cheng Jia-fu, Li Ze-hua & Yang De-tian Edited by: Lim Yung-kuo ... 5 Toh Tuck Link, Singapore 596224 USA office: Suite 202, I060 Main Street, River Edge, NJ 0766I UK office: 57 Shelton Street, Covent Garden, London WC2H ...
The effect of the shape of six different periodic forces and second periodic forces on the onset ... more The effect of the shape of six different periodic forces and second periodic forces on the onset of horseshoe chaos are studied both analytically and numerically in a Duffing oscillator. The external periodic forces considered are sine wave, square wave, symmetric saw-tooth wave, asymmetric saw-tooth wave, rectified sine wave, and modulus of sine wave. An analytical threshold condition for the onset of horseshoe chaos is obtained in the Duffing oscillator driven by various periodic forces using the Melnikov method. Melnikov threshold curve is drawn in a parameter space. For all the forces except modulus of sine wave, the onset of cross-well asymptotic chaos is observed just above the Melnikov threshold curve for onset of horseshoe chaos. For the modulus of sine wave long time transient motion followed by a periodic attractor is realized. The possibility of controlling of horseshoe and asymptotic chaos in the Duffing oscillator by an addition of second periodic force is then analyzed...
The nonrelativistic propagator is derived by formulating the generalized Aharonov–Bohm effect, va... more The nonrelativistic propagator is derived by formulating the generalized Aharonov–Bohm effect, valid for any gauge group in a general multiply connected manifold, as a gauge artifact in the universal covering space. The loop phase factors and the free homotopy propagators arise naturally. An explicit expression for the propagator when there are two solenoids present is given.
It is shown that the transition functions that give the global structure of the fiber bundle play... more It is shown that the transition functions that give the global structure of the fiber bundle play an important role in the construction of the metric. The invariance properties of this metric under general gauge transformations are discussed and it is found that the usual requirement of a gauge-invariant metric leads to severe constraints on the gauge fields. To avoid them, it is shown that the metric should instead be covariant with respect to these transformations. Moreover the existence of global actions that are essential in the context of the consistency problem is also discussed. The presence of such actions is studied in both the principal and their associated bundles. In the case of a homogeneous bundle with G/H as the typical fiber, it is shown that a ‘‘spliced’’ bundle with G×N(H)/H as the structure group has to be used. The unified space is then taken as the bundle space of its associated bundle.
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