Deciding Kleene Algebra Terms Equivalence in Coq

This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.

Linear algebra with applications

Lecture slides and notes for a PhD level course on linear algebra for electrical engineers and computer scientists. This course is given in in the framework of the School of Electronics and Computer Science Mathematics Training Courses https://secure.ecs.soton.ac.uk/notes/pg_maths/ (ECS password required)

Reviewing the sustainability/stationarity of current account imbalances with tests for bounded integration

We investigate for 26 OECD economies whether their current account imbalances to GDP are driven by stochastic trends. Regarding bounded stationarity as the more natural counterpart of sustainability, results from Phillips–Perron tests for unit root and bounded unit root processes are contrasted. While the former hint at stationarity of current account imbalances for 12 economies, the latter indicate bounded stationarity for only six economies. Through panel-based test statistics, current account imbalances are diagnosed as bounded non-stationary. Thus, (spurious) rejections of the unit root hypothesis might be due to the existence of bounds reflecting hidden policy controls or financial crises.

A treatise on universal algebra, with applications.

Available on demand as hard copy or computer file from Cornell University Library.

An introduction to algebra : with notes and observations : designed for the use of schools and places of public education : to which is added an appendix on the application of algebra to geometry /

Mode of access: Internet.

Algebra, with Arithmetic and mensuration, from the Sanscrit of Brahmegupta and Bháscara.

The 12th and 18th chapters, Gaṇitādhyāya and Kuṭṭakādhyāya, of Brahmagupta's Brahmasiddhānta ; and the first two parts, Līlāvatī and Bījagaṇita, of Bhāskara's Siddhāntaśirḿanṇi.

Circulating antibodies against Plasmodium falciparum histidine-rich proteins 2 interfere with antigen detection by rapid diagnostic tests

Background Rapid diagnostic tests (RDTs) for detection of Plasmodium falciparum infection that target P. falciparum histidine-rich protein 2 (PfHRP2), a protein that circulates in the blood of patients infected with this species of malaria, are widely used to guide case management. Understanding determinants of PfHRP2 availability in circulation is therefore essential to understanding the performance of PfHRP2-detecting RDTs. Methods The possibility that pre-formed host anti-PfHRP2 antibodies may block target antigen detection, thereby causing false negative test results was investigated in this study. Results Anti-PfHRP2 antibodies were detected in 19/75 (25%) of plasma samples collected from patients with acute malaria from Cambodia, Nigeria and the Philippines, as well as in 3/28 (10.7%) asymptomatic Solomon Islands residents. Pre-incubation of plasma samples from subjects with high-titre anti-PfHRP2 antibodies with soluble PfHRP2 blocked the detection of the target antigen on two of the three brands of RDTs tested, leading to false negative results. Pre-incubation of the plasma with intact parasitized erythrocytes resulted in a reduction of band intensity at the highest parasite density, and a reduction of lower detection threshold by ten-fold on all three brands of RDTs tested. Conclusions These observations indicate possible reduced sensitivity for diagnosis of P. falciparum malaria using PfHRP2-detecting RDTs among people with high levels of specific antibodies and low density infection, as well as possible interference with tests configured to detect soluble PfHRP2 in saliva or urine samples. Further investigations are required to assess the impact of pre-formed anti-PfHRP2 antibodies on RDT performance in different transmission settings.

Algebra, or universal mathematics: revived 1738 with notes and additions : manuscript, [after 1738]

Instructional book in algebra with exercises.

Four-dimensional current algebra from Chern-Simons theory

We study an abelian Chern-Simons theory on a five-dimensional manifold with boundary. We find it to be equivalent to a higher-derivative generalization of the abelian Wess-Zumino-Witten model on the boundary. It contains a U(1) current algebra with an operational extension.

Relativistic quark models and the current algebra

In this thesis we are concerned with finding representations of the algebra of SU(3) vector and axial-vector charge densities at infinite momentum (the "current algebra") to describe the mesons, idealizing the real continua of multiparticle states as a series of discrete resonances of zero width. Such representations would describe the masses and quantum numbers of the mesons, the shapes of their Regge trajectories, their electromagnetic and weak form factors, and (approximately, through the PCAC hypothesis) pion emission or absorption amplitudes.

We assume that the mesons have internal degrees of freedom equivalent to being made of two quarks (one an antiquark) and look for models in which the mass is SU(3)-independent and the current is a sum of contributions from the individual quarks. Requiring that the current algebra, as well as conditions of relativistic invariance, be satisfied turns out to be very restrictive, and, in fact, no model has been found which satisfies all requirements and gives a reasonable mass spectrum. We show that using more general mass and current operators but keeping the same internal degrees of freedom will not make the problem any more solvable. In particular, in order for any two-quark solution to exist it must be possible to solve the "factorized SU(2) problem," in which the currents are isospin currents and are carried by only one of the component quarks (as in the K meson and its excited states).

In the free-quark model the currents at infinite momentum are found using a manifestly covariant formalism and are shown to satisfy the current algebra, but the mass spectrum is unrealistic. We then consider a pair of quarks bound by a potential, finding the current as a power series in 1/m where m is the quark mass. Here it is found impossible to satisfy the algebra and relativistic invariance with the type of potential tried, because the current contributions from the two quarks do not commute with each other to order 1/m³. However, it may be possible to solve the factorized SU(2) problem with this model.

The factorized problem can be solved exactly in the case where all mesons have the same mass, using a covariant formulation in terms of an internal Lorentz group. For a more realistic, nondegenerate mass there is difficulty in covariantly solving even the factorized problem; one model is described which almost works but appears to require particles of spacelike 4-momentum, which seem unphysical.

Although the search for a completely satisfactory model has been unsuccessful, the techniques used here might eventually reveal a working model. There is also a possibility of satisfying a weaker form of the current algebra with existing models.