Knot Theory: from Fox 3-colorings of links to Yang-Baxter homology and Khovanov homology

This paper is an extended account of my "Introductory Plenary talk at Knots in Hellas 2016" conference We start from the short introduction to Knot Theory from the historical perspective, starting from Heraclas text (the first century AD), mentioning R.Llull (1232-1315), A.Kircher (1602-1680), Leibniz idea of Geometria Situs (1679), and J.B.Listing (student of Gauss) work of 1847. We spend some space on Ralph H. Fox (1913-1973) elementary introduction to diagram colorings (1956). In the second section we describe how Fox work was generalized to distributive colorings (racks and quandles) and eventually in the work of Jones and Turaev to link invariants via Yang-Baxter operators, here the importance of statistical mechanics to topology will be mentioned. Finally we describe recent developments which started with Mikhail Khovanov work on categorification of the Jones polynomial. By analogy to Khovanov homology we build homology of distributive structures (including homology of Fox colorings) and generalize it to homology of Yang-Baxter operators. We speculate, with supporting evidence, on co-cycle invariants of knots coming from Yang-Baxter homology. Here the work of Fenn-Rourke-Sanderson (geometric realization of pre-cubic sets of link diagrams) and Carter-Kamada-Saito (co-cycle invariants of links) will be discussed and expanded. Dedicated to Lou Kauffman for his 70th birthday.Comment: 35 pages, 31 figures, for Knots in Hellas II Proceedings, Springer, part of the series Proceedings in Mathematics & Statistics (PROMS

Spatio-temporal analysis of the role of climate in inter-annual variation of malaria incidence in Zimbabwe

BACKGROUND: On the fringes of endemic zones climate is a major determinant of inter-annual variation in malaria incidence. Quantitative description of the space-time effect of this association has practical implications for the development of operational malaria early warning system (MEWS) and malaria control. We used Bayesian negative binomial models for spatio-temporal analysis of the relationship between annual malaria incidence and selected climatic covariates at a district level in Zimbabwe from 1988–1999. RESULTS: Considerable inter-annual variations were observed in the timing and intensity of malaria incidence. Annual mean values of average temperature, rainfall and vapour pressure were strong positive predictors of increased annual incidence whereas maximum and minimum temperature had the opposite effects. Our modelling approach adjusted for unmeasured space-time varying risk factors and showed that while year to year variation in malaria incidence is driven mainly by climate, the resultant spatial risk pattern may to large extent be influenced by other risk factors except during high and low risk years following the occurrence of extremely wet and dry conditions, respectively. CONCLUSION: Our model revealed a spatially varying risk pattern that is not attributable only to climate. We postulate that only years characterized by extreme climatic conditions may be important for developing climate based MEWS and for delineating areas prone to climate driven epidemics. However, the predictive value of climatic risk factors identified in this study still needs to be evaluated

An approach to computing downward closures

The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful abstraction, algorithms for computing a finite automaton for the downward closure of a given language have been established only for few language classes. This work presents a simple general method for computing downward closures. For language classes that are closed under rational transductions, it is shown that the computation of downward closures can be reduced to checking a certain unboundedness property. This result is used to prove that downward closures are computable for (i) every language class with effectively semilinear Parikh images that are closed under rational transductions, (ii) matrix languages, and (iii) indexed languages (equivalently, languages accepted by higher-order pushdown automata of order 2).Comment: Full version of contribution to ICALP 2015. Comments welcom

Brachial and Cerebrovascular Functions Are Enhanced in Postmenopausal Women after Ingestion of Chocolate with a High Concentration of Cocoa.

Background: Cocoa contains polyphenols that are thought to be beneficial for vascular health.Objective: We assessed the impact of chocolate containing distinct concentrations of cocoa on cerebrovascular function and cognition.Methods: Using a counterbalanced within-subject design, we compared the acute impact of consumption of energy-matched chocolate containing 80%, 35%, and 0% single-origin cacao on vascular endothelial function, cognition, and cerebrovascular function in 12 healthy postmenopausal women (mean ± SD age: 57.3 ± 5.3 y). Participants attended a familiarization session, followed by 3 experimental trials, each separated by 1 wk. Outcome measures included cerebral blood flow velocity (CBFv) responses, recorded before and during completion of a computerized cognitive assessment battery (CogState); brachial artery flow-mediated dilation (FMD); and hemodynamic responses (heart rate and blood pressure).Results: When CBFv data before and after chocolate intake were compared between conditions through the use of 2-factor ANOVA, an interaction effect (P = 0.003) and main effects for chocolate (P = 0.043) and time (P = 0.001) were evident. Post hoc analysis revealed that both milk chocolate (MC; 35% cocoa; P = 0.02) and dark chocolate (DC; 80% cocoa; P = 0.003) induced significantly lower cerebral blood flow responses during the cognitive tasks, after normalizing for changes in arterial pressure. DC consumption also increased brachial FMD compared with the baseline value before chocolate consumption (P = 0.002), whereas MC and white chocolate (0% cocoa) caused no change (P-interaction between conditions = 0.034).Conclusions: Consumption of chocolate containing high concentrations of cocoa enhanced vascular endothelial function, which was reflected by improvements in FMD. Cognitive function outcomes did not differ between conditions; however, cerebral blood flow responses during these cognitive tasks were lower in those consuming MC and DC. These findings suggest that chocolate containing high concentrations of cocoa may modify the relation between cerebral metabolism and blood flow responses in postmenopausal women. This trial was registered at www.ANZCTR.orgau as ACTRN12616000990426

Survivin as a therapeutic target in Sonic hedgehog-driven medulloblastoma.

Medulloblastoma (MB) is a highly malignant brain tumor that occurs primarily in children. Although surgery, radiation and high-dose chemotherapy have led to increased survival, many MB patients still die from their disease, and patients who survive suffer severe long-term side effects as a consequence of treatment. Thus, more effective and less toxic therapies for MB are critically important. Development of such therapies depends in part on identification of genes that are necessary for growth and survival of tumor cells. Survivin is an inhibitor of apoptosis protein that regulates cell cycle progression and resistance to apoptosis, is frequently expressed in human MB and when expressed at high levels predicts poor clinical outcome. Therefore, we hypothesized that Survivin may have a critical role in growth and survival of MB cells and that targeting it may enhance MB therapy. Here we show that Survivin is overexpressed in tumors from patched (Ptch) mutant mice, a model of Sonic hedgehog (SHH)-driven MB. Genetic deletion of survivin in Ptch mutant tumor cells significantly inhibits proliferation and causes cell cycle arrest. Treatment with small-molecule antagonists of Survivin impairs proliferation and survival of both murine and human MB cells. Finally, Survivin antagonists impede growth of MB cells in vivo. These studies highlight the importance of Survivin in SHH-driven MB, and suggest that it may represent a novel therapeutic target in patients with this disease

Proof Theory and Ordered Groups

Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups (l-groups). These calculi are then used to provide new proofs of theorems arising in the theory of ordered groups. More precisely: an analytic calculus for abelian l-groups is generated using an ordering theorem for abelian groups; a calculus is generated for l-groups and new decidability proofs are obtained for the equational theory of this variety and extending finite subsets of free groups to right orders; and a calculus for representable l-groups is generated and a new proof is obtained that free groups are orderable

Apparent mass of small children: Experimental measurements

A test facility and protocol were developed for measuring the seated, vertical, whole-body vibration response of small children of less than 18 kg in mass over the frequency range from 1 to 45 Hz. The facility and protocol adhered to the human vibration testing guidelines of BS7085 and to current codes of ethics for research involving children. Additional procedures were also developed which are not currently defined in the guidelines, including the integral involvement of the parents and steps taken to maximize child happiness. Eight children were tested at amplitudes of 0.8 and 1.2 m/s2 using band-limited, Gaussian, white noise acceleration signals defined over the frequency interval from 1 to 50 Hz. Driving point apparent mass modulus and phase curves were determined for all eight children at both test amplitudes. All results presented a single, principal, anti-resonance, and were similar to data reported for primates and for adult humans seated in an automotive posture which provided backrest support. The mean frequency of the apparent mass peak was 6.25 Hz for the small children, as compared to values between 6.5 - 8.5 Hz for small primates and values between 6.5 - 8.6 Hz for adults seated with backrest support. The peak value of the mean, normalized, apparent mass was 1.54 for the children, which compares to values from 1.19 to 1.45 reported in the literature for small primates and 1.28 for adults seated with backrest support. ISO standard 5982, which specifies a mean, normalized, apparent mass modulus peak of 1.50 at a frequency of 4.0 Hz for adults seated without backrest support, provides significant differences

An invisibility cloak using silver nanowires

In this paper, we use the parameter retrieval method together with an analytical effective medium approach to design a well-performed invisible cloak, which is based on an empirical revised version of the reduced cloak. The designed cloak can be implemented by silver nanowires with elliptical cross-sections embedded in a polymethyl methacrylate host. This cloak is numerically proved to be robust for both the inner hidden object as well as incoming detecting waves, and is much simpler thus easier to manufacture when compared with the earlier proposed one [Nat. Photon. 1, 224 (2007)].Comment: 7 pages, 4 figures, 2 table

Comparative population structure of <i>Plasmodium malariae</i> and <i>Plasmodium falciparum</i> under different transmission settings in Malawi

&lt;b&gt;Background:&lt;/b&gt; Described here is the first population genetic study of Plasmodium malariae, the causative agent of quartan malaria. Although not as deadly as Plasmodium falciparum, P. malariae is more common than previously thought, and is frequently in sympatry and co-infection with P. falciparum, making its study increasingly important. This study compares the population parameters of the two species in two districts of Malawi with different malaria transmission patterns - one seasonal, one perennial - to explore the effects of transmission on population structures. &lt;BR/&gt; &lt;b&gt;Methods:&lt;/b&gt; Six species-specific microsatellite markers were used to analyse 257 P. malariae samples and 257 P. falciparum samples matched for age, gender and village of residence. Allele sizes were scored to within 2 bp for each locus and haplotypes were constructed from dominant alleles in multiple infections. Analysis of multiplicity of infection (MOI), population differentiation, clustering of haplotypes and linkage disequilibrium was performed for both species. Regression analyses were used to determine association of MOI measurements with clinical malaria parameters. &lt;BR/&gt; &lt;b&gt;Results:&lt;/b&gt; Multiple-genotype infections within each species were common in both districts, accounting for 86.0% of P. falciparum and 73.2% of P. malariae infections and did not differ significantly with transmission setting. Mean MOI of P. falciparum was increased under perennial transmission compared with seasonal (3.14 vs 2.59, p = 0.008) and was greater in children compared with adults. In contrast, P. malariae mean MOI was similar between transmission settings (2.12 vs 2.11) and there was no difference between children and adults. Population differentiation showed no significant differences between villages or districts for either species. There was no evidence of geographical clustering of haplotypes. Linkage disequilibrium amongst loci was found only for P. falciparum samples from the seasonal transmission setting. &lt;BR/&gt; &lt;b&gt;Conclusions:&lt;/b&gt; The extent of similarity between P. falciparum and P. malariae population structure described by the high level of multiple infection, the lack of significant population differentiation or haplotype clustering and lack of linkage disequilibrium is surprising given the differences in the biological features of these species that suggest a reduced potential for out-crossing and transmission in P. malariae. The absence of a rise in P. malariae MOI with increased transmission or a reduction in MOI with age could be explained by differences in the duration of infection or degree of immunity compared to P. falciparum