Ergodic Properties of Triangular Billiards: A Numerical Study

Polygonal billiards represent one of the simplest examples of systems with anomalous dynamics. So far, they have resisted numerous attempts to fully describe their dynamical behaviour. There is still a lack of complete understanding of even some basic features, such as ergodicity or the decay of correlations. In this thesis, we study the dynamical properties of triangular billiards using numerical means. We highlight the importance of the billiard table geometry, more specifically symmetry, for the resulting dynamics. We show that while typical triangular billiards appear to show correlation decay as expected by the community, symmetric billiards may not even be ergodic with respect to the uniform distribution in phase space. We provide compelling evidence that symmetry plays a decisive role in the dynamics. We further show that the relation between dynamical properties of symmetric and right-angled triangular billiards shows a rich interplay

Anomalous dynamics in symmetric triangular irrational billiards

We identify a symmetry induced mechanism which dominates the long time behaviour in symmetric triangular billiards. We rigorously prove the existence of invariant sets in symmetric irrational billiards on which the dynamics is governed by an interval exchange transformation. Counterintuitively, this property of symmetric irrational billiards is analogous to the case of general rational billiards, and it highlights the non-trivial impact of symmetries in non-hyperbolic dynamical systems. Our findings provide an explanation for the logarithmic subdiffusive relaxation processes observed in certain triangular billiards. In addition we are able to settle a long standing conjecture about the existence of non-periodic and not everywhere dense trajectories in triangular billiards

Impact of symmetry on ergodic properties of triangular billiards

Polygonal billiards constitute some of the simplest yet counterintuitive dynamical systems in physics. Even basic features of the dynamics, such as ergodicity of the microcanonical distribution or the decay of correlations have not been settled in general. In this Letter, we will highlight the importance of symmetries of the billiard table for the resulting dynamics. Although typical triangular billiards appear to show correlation decay, symmetric billiards may not even be ergodic with respect to the uniform distribution in phase space

Efficacy and safety of Id-protein-loaded dendritic cell vaccine in patients with multiple myeloma \u2013 Phase II study results

In a\u202fphase II clinical study, pretreated multiple myeloma patients with relapsing or stable disease received autologous anticancer vaccine containing dendritic cells loaded with Id-protein. Patients received a\u202ftotal of 6 vaccine doses intradermally in monthly intervals. No clinical responses were observed. During the follow-up with a\u202fmedian of 33.1 months (range: 11-43 months), the disease remained stable in 7/11 (64%) of patients. Immune responses measured by ELISpot were noted in 3/11 (27%) and DTH skin test for Id-protein was positive in 8/11 (73%) of patients; out of those, 1/11 (9%) and 5/11 (46%), respectively, had preexisting immune response to Id-protein before the vaccination began. Outcomes were compared to those of a\u202fcontrol group of 13 patients. A\u202ftrend to lower cumulative incidence of progression in the vaccinated group was observed at 12 months from the first vaccination (p= 0.099). More patients from the control group compared to vaccinated patients required active anticancer therapy [4/11 (36%) vs. 8/13 (62%)]. Vaccines based on dendritic cells loaded with Id-protein are safe and induce specific immune response in multiple myeloma patients. Our results suggest that the vaccination could stabilize the disease in approximately two-thirds of patients

Enhanced stimulation of human tumor-specific T cells by dendritic cells matured in the presence of interferon-gamma and multiple toll-like receptor agonists

Dendritic cell (DC) vaccines have been demonstrated to elicit immunological responses in numerous cancer immunotherapy trials. However, long-lasting clinical effects are infrequent. We therefore sought to establish a protocol to generate DC with greater immunostimulatory capacity. Immature DC were generated from healthy donor monocytes by culturing in the presence of IL-4 and GM-CSF and were further differentiated into mature DC by the addition of cocktails containing different cytokines and toll-like receptor (TLR) agonists. Overall, addition of IFN gamma and the TLR7/8 agonist R848 during maturation was essential for the production of high levels of IL-12p70 which was further augmented by adding the TLR3 agonist poly I:C. In addition, the DC matured with IFN gamma, R848, and poly I:C also induced upregulation of several other pro-inflammatory and Th1-skewing cytokines/chemokines, co-stimulatory receptors, and the chemokine receptor CCR7. For most cytokines and chemokines the production was even further potentiated by addition of the TLR4 agonist LPS. Concurrently, upregulation of the anti-inflammatory cytokine IL-10 was modest. Most importantly, DC matured with IFN gamma, R848, and poly I:C had the ability to activate IFN gamma production in allogeneic T cells and this was further enhanced by adding LPS to the cocktail. Furthermore, epitope-specific stimulation of TCR-transduced T cells by peptide- or whole tumor lysate-loaded DC was efficiently stimulated only by DC matured in the full maturation cocktail containing IFN gamma and the three TLR ligands R848, poly I:C, and LPS. We suggest that this cocktail is used for future clinical trials of anti-cancer DC vaccines