A very brief introduction to quantum computing and quantum information theory for mathematicians

This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic representation theory. Proofs of most statements can be found in standard references

Investigation of phase separation within the generalized Lin-Taylor model for a binary liquid mixture of large hexagonal and small triangular particles

The generalized Lin-Taylor model defined on the hexagonal lattice is used to investigate the phase separation in an asymmetric binary liquid mixture consisting of large A (hexagons) and small B (triangles) particles. By considering interaction energies between A-A and A-B pairs of particles that occupy nearest-neighbour cells of the hexagonal lattice, we have derived an exact solution for the considered model system having established a mapping correspondence with the two-dimensional Ising model on its dual triangular lattice. Altogether, six different types of coexistence curves including those with reentrant miscibility regions (i.e. closed-loop coexistence curves) were found in dependence on the relative strength between both coupling constants.Comment: 8 pages, 4 figures, presented at 7th Liblice conference on the Statistical Mechanics of Liquids to be held in Lednice on June 11-16, 200

Letters of condolence: assessing attitudes and variability in practice amongst oncologists and palliative care doctors in Yorkshire

Background: Following a patient’s death, some doctors routinely write a letter of condolence to the bereaved family. Practice appears to vary widely but this is poorly documented, particularly in the UK setting. We wished to explore the attitudes of oncologists and palliative care consultants towards writing letters of condolence to patient’s families. Methods: A sample of oncology and palliative care consultants from across Yorkshire were invited via email to complete an anonymous online survey. The survey aimed to identify current practice regarding condolence letter writing and respondents attitudes towards this. Results: A total of 47 (72%) recipients completed the survey, comprised of clinical oncologists (45%), medical oncologists (42%), and palliative care consultants (13%). The majority (87%) reported sending condolence letters, but amongst this group, only 49% indicated they do this ‘often’ or ‘always’. When asked whether they would use a standard template letter, should it be made available, 77% of participants responded negatively. Many later commented that a template with room for flexibility would be better received. The majority (72%) were also not in favour of the introduction of policies to try to unify practices. Conclusions: Practices and attitudes towards condolence letter writing are variable. The participants in this study felt strongly about when and how they wished to express condolences. A single unifying policy seems unlikely to be appropriate or feasible

On Resource-bounded versions of the van Lambalgen theorem

The van Lambalgen theorem is a surprising result in algorithmic information theory concerning the symmetry of relative randomness. It establishes that for any pair of infinite sequences $A$ and $B$, $B$ is Martin-L\"of random and $A$ is Martin-L\"of random relative to $B$ if and only if the interleaved sequence $A \uplus B$ is Martin-L\"of random. This implies that $A$ is relative random to $B$ if and only if $B$ is random relative to $A$ \cite{vanLambalgen}, \cite{Nies09}, \cite{HirschfeldtBook}. This paper studies the validity of this phenomenon for different notions of time-bounded relative randomness. We prove the classical van Lambalgen theorem using martingales and Kolmogorov compressibility. We establish the failure of relative randomness in these settings, for both time-bounded martingales and time-bounded Kolmogorov complexity. We adapt our classical proofs when applicable to the time-bounded setting, and construct counterexamples when they fail. The mode of failure of the theorem may depend on the notion of time-bounded randomness

Brentano’s lectures on positivism (1893-1894) and his relationship to Ernst Mach

This paper is mainly about Brentano’s commentaries on Ernst Mach in his lectures “Contemporary philosophical questions” which he held one year before he left Austria. I will first identify the main sources of Brentano’s interests in Comte’s and J. S. Mill’s positivism during his Würzburg period. The second section provides a short overview of Brentano’s 1893-1894 lectures and his criticism of Comte, Kirchhoff, and Mill. The next sections bear on Brentano’s criticism of Mach’s monism and Brentano’s argument against the reduction of the mental based on his theory of intentionality. The last section is about Brentano’s proposal to replace the identity relation in Mach’s theory of elements by that of intentional correlation. I conclude with a remark on the history of philosophy in Austria

Perinatal changes in fetal ventricular geometry, myocardial performance and cardiac function in normal term pregnancies.

Background: The fetal heart at term is exposed to an increase in hemodynamic work as a consequence of fetal growth, increased circulating volume and alteration in loading patterns due to maturational changes in fetoplacental circulation. The extent to which these cardiovascular changes influence the human fetal and neonatal cardiac adaptation has not been fully elucidated. The aim of this study was to evaluate perinatal cardiovascular changes in ventricular geometry and myocardial performance in normal term fetuses. Methods: Prospective study of 108 uncomplicated pregnancies delivering at term. M-mode, twodimensional (2D) or B-mode, pulsed wave (PW) Doppler, PW tissue Doppler and 2D speckle tracking imaging were performed a few days before, and within 24 hours of birth. Results: Analysis of paired fetal and neonatal echoes demonstrated significant perinatal changes (p<0.0001 for all) in right ventricular (RV) and left ventricular (LV) geometry (RV/LV enddiastolic dimension ratio: 1.2 vs. 0.8, RV sphericity index: 0.53 vs. 0.40, LV sphericity index: 0.46 vs. 0.49). There were corresponding significant (p<0.001 for all) perinatal changes in global myocardial performance: LV myocardial performance index (MPI’): 0.60 vs. 0.47, RV MPI’: 0.61 vs. 0.42; systolic function: LV longitudinal systolic strain rate: -1.4 /s vs. -1.0 /s, RV longitudinal systolic strain rate: -1.5 /s vs. -1.0 /s; RV systolic annular peak velocity (S’): 5.3 cm/s vs. 6.5 cm/s; and diastolic function: LV diastolic annular peak velocity ratio (E’/A’): 0.8 vs.1.1. Conclusion: The findings support the concept that the perinatal period is associated with major changes in fetal ventricular geometry and cardiac function in response to significant alterations in loading conditions. Improved knowledge of perinatal cardiac changes in normal fetuses could facilitate better understanding of cardiac adaptation in normal and pathological pregnancies

Concurrent adaptation to opposing visual displacements during an alternating movement.

It has been suggested that, during tasks in which subjects are exposed to a visual rotation of cursor feedback, alternating bimanual adaptation to opposing rotations is as rapid as unimanual adaptation to a single rotation (Bock et al. in Exp Brain Res 162:513–519, 2005). However, that experiment did not test strict alternation of the limbs but short alternate blocks of trials. We have therefore tested adaptation under alternate left/right hand movement with opposing rotations. It was clear that the left and right hand, within the alternating conditions, learnt to adapt to the opposing displacements at a similar rate suggesting that two adaptive states were formed concurrently. We suggest that the separate limbs are used as contextual cues to switch between the relevant adaptive states. However, we found that during online correction the alternating conditions had a significantly slower rate of adaptation in comparison to the unimanual conditions. Control conditions indicate that the results are not directly due the alternation between limbs or to the constant switching of vision between the two eyes. The negative interference may originate from the requirement to dissociate the visual information of these two alternating displacements to allow online control of the two arms

Minority Becomes Majority in Social Networks

It is often observed that agents tend to imitate the behavior of their neighbors in a social network. This imitating behavior might lead to the strategic decision of adopting a public behavior that differs from what the agent believes is the right one and this can subvert the behavior of the population as a whole. In this paper, we consider the case in which agents express preferences over two alternatives and model social pressure with the majority dynamics: at each step an agent is selected and its preference is replaced by the majority of the preferences of her neighbors. In case of a tie, the agent does not change her current preference. A profile of the agents' preferences is stable if the preference of each agent coincides with the preference of at least half of the neighbors (thus, the system is in equilibrium). We ask whether there are network topologies that are robust to social pressure. That is, we ask if there are graphs in which the majority of preferences in an initial profile always coincides with the majority of the preference in all stable profiles reachable from that profile. We completely characterize the graphs with this robustness property by showing that this is possible only if the graph has no edge or is a clique or very close to a clique. In other words, except for this handful of graphs, every graph admits at least one initial profile of preferences in which the majority dynamics can subvert the initial majority. We also show that deciding whether a graph admits a minority that becomes majority is NP-hard when the minority size is at most 1/4-th of the social network size.Comment: To appear in WINE 201