A Proof of the Grundy domination strong product conjecture

The Grundy domination number of a simple graph $G = (V,E)$ is the length of the longest sequence of unique vertices $S = (v_1, \ldots, v_k)$, $v_i \in V$, that satisfies the property $N[v_i] \setminus \cup_{j=1}^{i-1}N[v_j] \neq \emptyset$ for each $i \in [k]$. Here, $N(v) = \{u : uv \in E\}$ and $N[v] = N(v) \cup \{v\}$. In this note, we prove a recent conjecture about the Grundy domination number of the strong product of two graphs. We then discuss how this result relates to the zero forcing number of the strong product of graphs

Dispersive Shock Waves in Lattices: A Dimension Reduction Approach

Dispersive shock waves (DSWs), which connect states of different amplitude via a modulated wave train, form generically in nonlinear dispersive media subjected to abrupt changes in state. The primary tool for the analytical study of DSWs is Whitham\u27s modulation theory. While this framework has been successfully employed in many space-continuous settings to describe DSWs, the Whitham modulation equations are virtually intractable in most spatially discrete systems. In this article, we illustrate the relevance of the reduction of the DSW dynamics to a planar ODE in a broad class of lattice examples. Solutions of this low-dimensional ODE accurately describe the orbits of the DSW in self-similar coordinates and the local averages in a manner consistent with the modulation equations. We use data-driven and quasi-continuum approaches within the context of a discrete system of conservation laws to demonstrate how the underlying low dimensional structure of DSWs can be identified and analyzed. The connection of these results to Whitham modulation theory is also discussed

Tank Tests of Twin Seaplane Floats

The following report contains the most essential data for the hydrodynamic portion of the twin-float problem. The following points were successfully investigated: 1) difference between stationary and nonstationary flow; 2) effect of the shape of the step; 3) effect of distance between floats; 4) effect of nose-heavy and tail-heavy moments; 5) effect of the shape of floats; 6) maneuverability

Tight-binding study of high-pressure phase transitions in titanium: alpha to omega and beyond

We use a tight-binding total energy method, with parameters determined from a fit to first-principles calculations, to examine the newly discovered gamma phase of titanium. Our parameters were adjusted to accurately describe the alpha Ti-omega Ti phase transition, which is misplaced by density functional calculations. We find a transition from omega Ti to gamma Ti at 102 GPa, in good agreement with the experimental value of 116 GPa. Our results suggest that current density functional calculations will not reproduce the omega Ti-gamma Ti phase transition, but will instead predict a transition from omega Ti to the bcc beta Ti phase.Comment: 3 encapsulated Postscript figures, submitted to Phyical Review Letter

Kaon production in heavy-ion collisions and maximum mass of neutron stars

We determine an `empirical' kaon dispersion relation by analysing and fitting recent experimental data on kaon production in heavy-ion collisions. We then investigate its effects on hadronic equation of state at high densities and on neutron star properties. We find that the maximum mass of neutron stars can be lowered by about 0.4$M_\odot$, once kaon condensation as constrained by our empirical dispersion relation is introduced. We emphasize the growing interplay between hadron physics, relativistic heavy-ion physics and the physics of compact objects in astrophysics.Comment: 6 pages with 3 postscript figures, to appear in Physical Review Letter

Community views on ‘Can perinatal services safely identify Aboriginal and Torres Strait Islander parents experiencing complex trauma?’

Family and extended kinship systems which nurture healthy, happy children are central to Aboriginal and Torres Strait Islander cultures. Since colonisation, Aboriginal and Torres Strait Islander communities have been impacted by intergenerational cycles of trauma, stemming from colonial violence, genocidal policies and discrimination, including the forced removal of children from their families. Becoming a parent offers a unique life-course opportunity for trauma recovery and preventing intergenerational trauma. However, identifying or ‘recognising’ complex trauma carries significant risk of harm for Aboriginal and Torres Strait Islander parents due to reactive prenatal child protection involvement potentially compounding experiences of trauma, and limited benefits due to lack of culturally appropriate support. The Aboriginal-led participatory Healing the Past by Nurturing the Future project aims to co-design safe, accessible and feasible perinatal awareness, recognition, assessment and support strategies for Aboriginal and Torres Strait Islander parents experiencing complex trauma. This paper presents views of 38 workshop participants to determine prerequisites for ensuring benefits outweigh risks of assessment to safely recognise parents experiencing complex trauma, consistent with screening criteria. Six essential elements were identified from thematic analysis: high-quality holistic care; cultural, social and emotional safety; empowerment, choice and control; flexible person-centred approaches; trusting relationships; and sensitive, skilled communication

Co-Evolution of quasispecies: B-cell mutation rates maximize viral error catastrophes

Co-evolution of two coupled quasispecies is studied, motivated by the competition between viral evolution and adapting immune response. In this co-adaptive model, besides the classical error catastrophe for high virus mutation rates, a second ``adaptation-'' catastrophe occurs, when virus mutation rates are too small to escape immune attack. Maximizing both regimes of viral error catastrophes is a possible strategy for an optimal immune response, reducing the range of allowed viral mutation rates to a minimum. From this requirement one obtains constraints on B-cell mutation rates and receptor lengths, yielding an estimate of somatic hypermutation rates in the germinal center in accordance with observation.Comment: 4 pages RevTeX including 2 figure

Community perspectives of complex trauma assessment for Aboriginal parents: 'Its important, but how these discussions are held is critical'

Background and Purpose: Becoming a parent can be an exciting and also challenging transition, particularly for parents who have experienced significant hurt in their own childhoods, and may be experiencing ‘complex trauma.’ Aboriginal and Torres Strait Islander (Aboriginal) people also experience historical trauma. While the parenting transition is an important time to offer support for parents, it is essential to ensure that the benefits of identifying parents experiencing complex trauma outweigh any risks (e.g., stigmatization). This paper describes views of predominantly Aboriginal stakeholders regarding (1) the relative importance of domains proposed for complex trauma assessment, and (2) how to conduct these sensitive discussions with Aboriginal parents. Setting and Methods: A co-design workshop was held in Alice Springs (Central Australia) as part of an Aboriginal-led community-based participatory action research project. Workshop participants were 57 predominantly Aboriginal stakeholders with expertise in community, clinical, policy and academic settings. Twelve domains of complex trauma-related distress had been identified in existing assessment tools and through community consultation. Using story-telling and strategies to create safety for discussing complex and sensitive issues, and delphi-style methods, stakeholders rated the level of importance of the 12 domains; and discussed why, by whom, where and how experiences of complex trauma should be explored. Main Findings: The majority of stakeholders supported the importance of assessing each of the proposed complex trauma domains with Aboriginal parents. However, strong concerns were expressed regarding where, by whom and how this should occur. There was greater emphasis and consistency regarding ‘qualities’ (e.g., caring), rather than specific ‘attributes’ (e.g., clinician). Six critical overarching themes emerged: ensuring emotional and cultural safety; establishing relationships and trust; having capacity to respond appropriately and access support; incorporating less direct cultural communication methods (e.g., yarning, dadirri); using strengths-based approaches and offering choices to empower parents; and showing respect, caring and compassion. Conclusion: Assessments to identify Aboriginal parents experiencing complex trauma should only be considered when the prerequisites of safety, trusting relationships, respect, compassion, adequate care, and capacity to respond are assured. Offering choices and cultural and strengths-based approaches are also critical. Without this assurance, there are serious concerns that harms may outweigh any benefits for Aboriginal parents