Introduction to Categories and Categorical Logic

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain numerous exercises, and hopefully will prove useful for self-study by those seeking a first introduction to the subject, with fairly minimal prerequisites. The coverage is by no means comprehensive, but should provide a good basis for further study; a guide to further reading is included. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions. An Appendix contains a summary of what we will need, and it may be useful to review this first. In addition, some prior exposure to abstract algebra - vector spaces and linear maps, or groups and group homomorphisms - would be helpful.Comment: 96 page

Ramsey numbers and adiabatic quantum computing

The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers $R(m,n)$ with $m,n\geq 3$, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers $R(m,n)$. We show how the computation of $R(m,n)$ can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for $5\leq s\leq 7$. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class QMA.Comment: 4 pages, 1 table, no figures, published versio

Stroke and bleeding risk in atrial fibrillation: navigating the alphabet soup of risk-score acronyms (CHADS2, CHA2DS2-VASc, R2CHADS2, HAS-BLED, ATRIA, and more)

: atrial fibrillation, stroke, bleeding, risk assessment.Stroke prevention is central to the management of patients with atrial fibrillation (AF). As effective stroke prophylaxis essentially requires oral anticoagulants (OAC) an understanding of the risks and benefits of OAC therapy is needed. While AF increases stroke risk 5-fold, this risk is not homogeneous. Many stroke risk factors also confer an increased risk of bleeding. Various stroke and bleeding risk stratification schemes have been developed to help inform clinical decision making. These scores were derived and validated in different study cohorts, ranging from highly selected clinical trial cohorts to 'real world' populations. Thus, their performance and classification accuracy varies depending on their derivation cohort(s). In the present review, we provide an overview of currently available stroke and bleeding risk stratification schemes. We particularly focus on the CHA2DS2-VASc and HAS-BLED schemes, as these are recommended by the latest European guidelines on AF management. Other risk stratification schemes (CHADS2, R2CHADS2, ATRIA, HEMORRHAGES, QStroke, etc.) and their place in the decision-making are also considered

Pairing and alpha-like quartet condensation in N=Z nuclei

We discuss the treatment of isovector pairing by an alpha-like quartet condensate which conserves exactly the particle number, the spin and the isospin. The results show that the quartet condensate describes accurately the isovector pairing correlations in the ground state of systems with an equal number of protons and neutronsComment: 4 pages, to appear in Journal of Physics: Conference Serie

Pseudo-Goldstone Boson Effects in Top-Antitop Productions at High Energy Hadron Colliders and Testing Technicolor Models

We study the top quark pair production process p+p(anti-p)-->top+antitop in various kinds of technicolor (TC) models at the Fermilab Tevatron Run II and the CERN LHC. The s-channel neutral pseudo-Goldstone bosons (PGB's) contribute dominately to the production amplitudes from its coupling to the gluons through the triangle loops of techniquarks and the top quark. Cross sections in different TC models with s-channel PGB contributions are calculated. It is shown that the PGB effects can be experimentally tested and different TC models under consideration can be distinguished at the LHC. Therefore, the p+p-->top+antitop process at the LHC provides feasible tests of the TC models.Comment: 10 pages in RevTex and 4 PS-files for the figures. Paramemter range is changed, and some references are added. Version for publication in Phys. Rev.

Universal Parametric Correlations of Conductance Peaks in Quantum Dots

We compute the parametric correlation function of the conductance peaks in chaotic and weakly disordered quantum dots in the Coulomb blockade regime and demonstrate its universality upon an appropriate scaling of the parameter. For a symmetric dot we show that this correlation function is affected by breaking time-reversal symmetry but is independent of the details of the channels in the external leads. We derive a new scaling which depends on the eigenfunctions alone and can be extracted directly from the conductance peak heights. Our results are in excellent agreement with model simulations of a disordered quantum dot.Comment: 12 pages, RevTex, 2 Postscript figure

Temporal Trends in Incidence, Prevalence, and Mortality of Atrial Fibrillation in Primary Care

Background Incidence and prevalence of atrial fibrillation ( AF ) are expected to increase dramatically; however, we currently lack comprehensive data on temporal trends in unselected clinical populations. Methods and Results Analysis of the UK Clinical Practice Research Datalink ( CPRD ) from 1998 to 2010 of patients with incident AF , excluding major valvular disease, linked to hospital admission data and national statistics. Fifty‐seven thousand eight hundred eighteen adults were identified with mean age 74.2 ( SD , 11.7) years and 48.3% women. Overall age‐adjusted incidence of AF per 1000 person years was 1.11 (95% CI , 1.09–1.13) in 1998–2001, 1.33 (1.31–1.34) in 2002–2006, and 1.33 (1.31–1.35) in 2007–2010. Ongoing increases in incidence were noted for patients aged ≥75 years, with similar temporal patterns in women and men. Associated comorbidities varied over time, with a constant prevalence of previous stroke, increases in hypertension and diabetes mellitus, and decreases in ischemic heart disease. Among patients aged 55 to 74 years, there was a significant reduction in mortality over time ( P &lt;0.001), but mortality rates in patients aged ≥75 years remained static at 14% to 15% per year ( P =0.84). Projections of AF prevalence demonstrated a constant yearly rise, increasing from 700 000 patients in 2010 to between 1.3 and 1.8 million patients with AF in the United Kingdom by 2060. Conclusions In a large general practice population, incident AF increased and then plateaued overall, with a continued increase in patients aged ≥75 years. The large projected increase in AF prevalence associated with temporal changes in AF ‐related comorbidities suggests the need for comprehensive implementation of AF prevention and management strategies. </jats:sec