General Fragmentation Trees

We show that the genealogy of any self-similar fragmentation process can be encoded in a compact measured real tree. Under some Malthusian hypotheses, we compute the fractal Hausdorff dimension of this tree through the use of a natural measure on the set of its leaves. This generalizes previous work of Haas and Miermont which was restricted to conservative fragmentation processes

On the exponential functional of Markov Additive Processes, and applications to multi-type self-similar fragmentation processes and trees

A Markov Additive Process is a bi-variate Markov process $(\xi,J)=\big((\xi_t,J_t),t\geq0\big)$ which should be thought of as a multi-type L\'evy process: the second component $J$ is a Markov chain on a finite space $\{1,\ldots,K\}$, and the first component $\xi$ behaves locally as a L\'evy process, with local dynamics depending on $J$. In the subordinator-like case where $\xi$ is nondecreasing, we establish several results concerning the moments of $\xi$ and of its exponential functional $I_{\xi}=\int_{0}^{\infty} e^{-\xi_t}\mathrm dt,$ extending the work of Carmona et al., and Bertoin and Yor. We then apply these results to the study of multi-type self-similar fragmentation processes: these are self-similar analogues of Bertoin's homogeneous multi-type fragmentation processes Notably, we encode the genealogy of the process in a tree, and under some Malthusian hypotheses, compute its Hausdorff dimension in a generalisation of our previous work.Comment: Minor corrections and typo

Holistic and leadership approaches to international regulation: confronting nature conservation and developmental challenges. A response to Farnese

International nature protection law has developed without a coherent plan, with disparate governance instruments each largely evolving within their own separate sphere. Yet, many other issues are closely linked to the challenges of nature degradation, such as developmental challenges, climate change, food security and food safety, disease prevention and rural poverty . These interconnections have partly been recognized in Agenda 21 and more recently in the Aichi Biodiversity Targets. This response draws on and extrapolates further the conclusions of Farnese in ‘The Prevention Imperative’, published in this issue, of Transnational Environmental Law and argues for a more coherent approach and effective leadership in this area of global regulation along with a more flexible and holistic approach to governance responses

Scaling limits of k-ary growing trees

For each integer $k \geq 2$, we introduce a sequence of $k$-ary discrete trees constructed recursively by choosing at each step an edge uniformly among the present edges and grafting on "its middle" $k-1$ new edges. When $k=2$, this corresponds to a well-known algorithm which was first introduced by R\'emy. Our main result concerns the asymptotic behavior of these trees as $n$ becomes large: for all $k$, the sequence of $k$-ary trees grows at speed $n^{1/k}$ towards a $k$-ary random real tree that belongs to the family of self-similar fragmentation trees. This convergence is proved with respect to the Gromov-Hausdorff-Prokhorov topology. We also study embeddings of the limiting trees when $k$ varies

Theoretical And Experimental Studies Of Collision-Induced Electronic Energy Transfer From v=0-3 Of The E(0g+) Ion-Pair State Of Br2: Collisions With He And Ar

Collisions of Br(2), prepared in the E(0(g)(+)) ion-pair (IP) electronic state, with He or Ar result in electronic energy transfer to the D, D(\u27), and beta IP states. These events have been examined in experimental and theoretical investigations. Experimentally, analysis of the wavelength resolved emission spectra reveals the distribution of population in the vibrational levels of the final electronic states and the relative efficiencies of He and Ar collisions in promoting a specific electronic energy transfer channel. Theoretically, semiempirical rare gas-Br(2) potential energy surfaces and diabatic couplings are used in quantum scattering calculations of the state-to-state rate constants for electronic energy transfer and distributions of population in the final electronic state vibrational levels. Agreement between theory and experiment is excellent. Comparison of the results with those obtained for similar processes in the IP excited I(2) molecule points to the general importance of Franck-Condon effects in determining vibrational populations, although this effect is more important for He collisions than for Ar collisions

Equitability revisited: why the “equitable threat score” is not equitable

In the forecasting of binary events, verification measures that are “equitable” were defined by Gandin and Murphy to satisfy two requirements: 1) they award all random forecasting systems, including those that always issue the same forecast, the same expected score (typically zero), and 2) they are expressible as the linear weighted sum of the elements of the contingency table, where the weights are independent of the entries in the table, apart from the base rate. The authors demonstrate that the widely used “equitable threat score” (ETS), as well as numerous others, satisfies neither of these requirements and only satisfies the first requirement in the limit of an infinite sample size. Such measures are referred to as “asymptotically equitable.” In the case of ETS, the expected score of a random forecasting system is always positive and only falls below 0.01 when the number of samples is greater than around 30. Two other asymptotically equitable measures are the odds ratio skill score and the symmetric extreme dependency score, which are more strongly inequitable than ETS, particularly for rare events; for example, when the base rate is 2% and the sample size is 1000, random but unbiased forecasting systems yield an expected score of around −0.5, reducing in magnitude to −0.01 or smaller only for sample sizes exceeding 25 000. This presents a problem since these nonlinear measures have other desirable properties, in particular being reliable indicators of skill for rare events (provided that the sample size is large enough). A potential way to reconcile these properties with equitability is to recognize that Gandin and Murphy’s two requirements are independent, and the second can be safely discarded without losing the key advantages of equitability that are embodied in the first. This enables inequitable and asymptotically equitable measures to be scaled to make them equitable, while retaining their nonlinearity and other properties such as being reliable indicators of skill for rare events. It also opens up the possibility of designing new equitable verification measures

Effects of Acute Stress on Psychophysiology in Armed Tactical Occupations: A Narrative Review

The ability to perform under extreme pressure is one of the most sought-after qualities in both sports and tactical (military, law enforcement, fire, and rescue, etc.) occupations. While tactical performance relies on both physical and mental capabilities to achieve a desired outcome, it is often hampered by the stressful environments in which these personnel work. The acute stress experienced by tactical personnel can interfere with occupational performance, impacting both physical execution of tasks and decision-making. This narrative review discusses the implications of acute stress on the psychophysiology and physical performance of personnel serving in armed tactical occupations