@article{12216,
  abstract     = {Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter says that quantum operations can never increase the relative entropy. The monotonicity versions often have many advantages, and often have direct physical application, as in the example just mentioned. Moreover, the monotonicity results are often valid for a larger class of maps than, say, quantum operations (which are completely positive). In this paper we prove several new monotonicity results, the first of which is a monotonicity theorem that has as a simple corollary a celebrated concavity theorem of Epstein. Our starting points are the monotonicity versions of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs of these in their general forms using interpolation. We then prove our new monotonicity theorems by several duality arguments.},
  author       = {Carlen, Eric A. and Zhang, Haonan},
  issn         = {0024-3795},
  journal      = {Linear Algebra and its Applications},
  keywords     = {Discrete Mathematics and Combinatorics, Geometry and Topology, Numerical Analysis, Algebra and Number Theory},
  pages        = {289--310},
  publisher    = {Elsevier},
  title        = {{Monotonicity versions of Epstein's concavity theorem and related inequalities}},
  doi          = {10.1016/j.laa.2022.09.001},
  volume       = {654},
  year         = {2022},
}

@article{11556,
  abstract     = {We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We test the performance and accuracy of the extended methods and compare their performance with efficient deterministic finite-difference method applied to the same model. We validate the stochastic methods on the test problems and apply them to verify the existence of oscillating regimes in the aggregation-fragmentation kinetics recently detected in deterministic simulations. We confirm the emergence of steady oscillations of densities in such systems and prove the stability of the
oscillations with respect to fluctuations and noise.},
  author       = {Kalinov, Aleksei and Osinskiy, A.I. and Matveev, S.A. and Otieno, W. and Brilliantov, N.V.},
  issn         = {0021-9991},
  journal      = {Journal of Computational Physics},
  keywords     = {Computer Science Applications, Physics and Astronomy (miscellaneous), Applied Mathematics, Computational Mathematics, Modeling and Simulation, Numerical Analysis},
  publisher    = {Elsevier},
  title        = {{Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics}},
  doi          = {10.1016/j.jcp.2022.111439},
  volume       = {467},
  year         = {2022},
}