Strong Secrecy for Erasure Wiretap Channels

We show that duals of certain low-density parity-check (LDPC) codes, when used in a standard coset coding scheme, provide strong secrecy over the binary erasure wiretap channel (BEWC). This result hinges on a stopping set analysis of ensembles of LDPC codes with block length $n$ and girth $\geq 2k$, for some $k \geq 2$. We show that if the minimum left degree of the ensemble is $l_\mathrm{min}$, the expected probability of block error is \calO(\frac{1}{n^{\lceil l_\mathrm{min} k /2 \rceil - k}}) when the erasure probability $\epsilon < \epsilon_\mathrm{ef}$, where $\epsilon_\mathrm{ef}$ depends on the degree distribution of the ensemble. As long as $l_\mathrm{min} > 2$ and $k > 2$, the dual of this LDPC code provides strong secrecy over a BEWC of erasure probability greater than $1 - \epsilon_\mathrm{ef}$.Comment: Submitted to the Information Theory Workship (ITW) 2010, Dubli

A better conversations approach for people living with dysarthria

In this chapter, the authors describe better conversations with dysarthria (BCD) therapy featuring a man living with Parkinson’s disease and his communication partner. A better conversations approach aims to help people with communication difficulties to have more enjoyable interactions. The authors outline the pre-post therapy assessment process, the intervention itself and highlight a specific outcome relating to responses to the communication partner’s turns. They also present data on the acceptability of BCD. This is the first BCD therapy case to be published and as such provides an important reference point for future work in this field

The pivot point between problem presentation and advice in a health helpline service

This paper examines interactions between callers to a health helpline and specialist nurses. Helpline call-takers must judge the appropriate moment to move from listening to the caller's problem to offering them the appropriate service. In a study of Parkinson's UK nurse call-takers, we find that the pivot is the point at which the caller reports the upshot of their trouble in terms of an impact on their daily life. Indeed, if the caller seems likely not to produce this upshot report, it is generated by the call-taker. Using the methods of Conversation Analysis we analyse how these upshot formulations are reached, and how the call-taker subsequently edits them to deliver a service that stays within their institutional guidelines. The findings contribute to sociological and clinical understandings about how health problems are framed and managed interactionally in order to reach a deliverable outcome for both participants in a helpline environment

Symmetric Toda, gradient flows, and tridiagonalization

The Toda lattice (1967) is a Hamiltonian system given by $n$ points on a line governed by an exponential potential. Flaschka (1974) showed that the Toda lattice is integrable by interpreting it as a flow on the space of symmetric tridiagonal $n\times n$ matrices, while Moser (1975) showed that it is a gradient flow on a projective space. The symmetric Toda flow of Deift, Li, Nanda, and Tomei (1986) generalizes the Toda lattice flow from tridiagonal to all symmetric matrices. They showed the flow is integrable, in the classical sense of having $d$ integrals in involution on its $2d$-dimensional phase space. The system may be viewed as integrable in other ways as well. Firstly, Symes (1980, 1982) solved it explicitly via $QR$-factorization and conjugation. Secondly, Deift, Li, Nanda, and Tomei (1986) 'tridiagonalized' the system into a family of tridiagonal Toda lattices which are solvable and integrable. In this paper we derive their tridiagonalization procedure in a natural way using the fact that the symmetric Toda flow is diffeomorphic to a twisted gradient flow on a flag variety, which may then be decomposed into flows on a product of Grassmannians. These flows may in turn be embedded into projective spaces via Pl\"ucker embeddings, and mapped back to tridiagonal Toda lattice flows using Moser's construction. In addition, we study the tridiagonalized flows projected onto a product of permutohedra, using the twisted moment map of Bloch, Flaschka, and Ratiu (1990). These ideas are facilitated in a natural way by the theory of total positivity, building on our previous work (2023).Comment: 21 page

Prognostication As an Interactionally Delicate Matter: A Conversation Analytic Study of Hospice Multidisciplinary Team Meeting

Prognostication has been found to be a delicate matter in interactions between palliative care professionals and patients. Studies have investigated how these discussions are managed and how speakers orient to their delicate nature. However, the degree to which prognostication is a delicate matter in discussions between palliative care professionals themselves has yet to be investigated. This study explored how hospice multidisciplinary team (MDT) members oriented to the delicacy of prognostication during their meetings. Video-recordings of 24 hospice MDT meetings were transcribed and analyzed using Conversation Analysis. In-depth analysis of the interactions showed how prognostic discussions were oriented to as delicate. This was displayed through markers such as pauses and self-repair organization including cutting off words and restarts, and through accounts accompanying the prognosis. In this way, it was seen that prognostication was not necessarily straightforward. This was further evidenced when prognostic requests were problematic to respond to. It is noteworthy that prognostic discussions are delicate during hospice MDT meetings. Potential reasons may reach further than the taboo of death and lie within prognostic uncertainty and accountability. Research is warranted to explore what causes this delicacy and whether specific support is needed for hospice staff