
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 15-54 (No. 54) |
| Halaman | : | 67-76 |
| Abstrak | : | - |
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 15-54 (No. 54) |
| Halaman | : | 58-66 |
| Abstrak | : | - |
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 4) |
| Halaman | : | 1392-1421 |
| Abstrak | : | Understanding and predicting the dynamical properties of systems involving dry friction is a major concern in physics and engineering. It abounds in many mechanical processes, from the sound produced by a violin to the screeching of chalk on a blackboard to human infant crawling dynamics and friction-based locomotion of a multitude of living organisms (snakes, bacteria, scallops) to the displacement of mechanical structures (building, bridges, nuclear plants, massive industrial infrastructures) under earthquakes and beyond. Surprisingly, even for low-dimensional systems, the modeling of dry friction in the presence of random forcing has not been elucidated. In this paper, we propose a piecewise deterministic Markov process approach modeling a system with dry friction including different coefficients for the static and dynamic forces. In this mathematical framework, we derive the corresponding Kolmogorov equations to compute statistical quantities of interest related to the distributions of the static (sticked) and dynamic phases. We show ergodicity and provide a representation formula of the stationary measure using independent identically distributed portions of the trajectory (excursions). We also obtain deterministic characterizations of the Laplace transforms of the probability density functions of the durations of the static and dynamic phases. In particular, the analysis of the power spectral density of the velocity reveals a critical value of the noise correlation time below which the correlations of the dynamic behaviors coincide with those of the white noise limit. The existence of such a critical value was already mentioned in the physical literature [Geffert and Just, Phys. Rev. E, 95 (2017), 062111] |
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 15-54 (No. 54) |
| Halaman | : | 44-47 |
| Abstrak | : | - |
| Pengarang | : | Autry, Eric [et al...] |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 4) |
| Halaman | : | 1366-1391 |
| Abstrak | : | We develop a new Markov chain on graph partitions that makes relatively global moves yet is computationally feasible to be used as the proposal in the Metropolis-Hastings method. Our resulting algorithm is able to sample from a specified measure on partitions or spanning forests. Being able to sample from a specified measure is a requirement of what we consider as the gold standard in quantifying the extent to which a particular map is a gerrymander. Our proposal chain modifies the recently developed method called recombination (ReCom), which draws spanning trees on joined partitions and then randomly cuts them to repartition. We improve the computational efficiency by augmenting the statespace from partitions to spanning forests. The extra information accelerates the computation of the forward and backward proposal probabilities which are required for the Metropolis-Hastings algorithm. We demonstrate this method by sampling redistricting plans on several measures of interest and find promising convergence results on several key observables of interest. We also explore some limitations in the measures that are efficient to sample from and investigate the feasibility of using parallel tempering to extend this space of measures. |
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 83 (No. 4) |
| Halaman | : | 1341-1365 |
| Abstrak | : | This paper studies the phase-only reconstruction problem of recovering a complex valued signal x in \BbbC d from the phase of Ax where A is a given measurement matrix in \BbbC m\times d. The reconstruction, if possible, should be up to a positive scaling factor. By using the rank of discriminant matrices, uniqueness conditions are derived to characterize whether the underlying signal can be uniquely reconstructed. We are also interested in the problem of minimal measurement number. We show that at least 2d but no more than 4d - 2 measurements are needed for the reconstruction of all x \in \BbbC d, whereas the minimal measurement number is exactly 2d - 1 if we pursue the recovery of almost all signals. Moreover, when adapted to the phase-only reconstruction of x \in \BbbR d, our uniqueness conditions are more practical and general than existing ones. Our theoretical results can be straightforwardly extended to affine phase-only reconstruction where the phase of Ax+b is observed for some b\in \BbbC m. |
| Pengarang | : | Eka Darmaputera |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 15-54 (No. 54) |
| Halaman | : | 35-43 |
| Abstrak | : | - |
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 15-54 (No. 54) |
| Halaman | : | 21-34 |
| Abstrak | : | - |
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 15-54 (No. 54) |
| Halaman | : | 15-20 |
| Abstrak | : | - |
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Bina Darma |
| Volume / Edisi | : | 15-54 (No. 54) |
| Halaman | : | 6-14 |
| Abstrak | : | - |