BCR algorithm and the T(b)T(b) theorem

We show using the Beylkin-Coifman-Rokhlin algorithm in the Haar basis that any singular integral operator can be written as the sum of a bounded operator on $L^p$, $1<p<\infty$, and of a perfect dyadic singular integral operator. This allows to deduce a local $T(b)$ theorem for singular integral operators from the one for perfect dyadic singular integral operators obtained by Hofmann, Muscalu, Thiele, Tao and the first author.Comment: Change of title. New abstract and new introductio

Differences between <i>Trypanosoma brucei gambiense</i> groups 1 and 2 in their resistance to killing by Trypanolytic factor 1

&lt;p&gt;&lt;b&gt;Background:&lt;/b&gt; The three sub-species of &lt;i&gt;Trypanosoma brucei&lt;/i&gt; are important pathogens of sub-Saharan Africa. &lt;i&gt;T. b. brucei&lt;/i&gt; is unable to infect humans due to sensitivity to trypanosome lytic factors (TLF) 1 and 2 found in human serum. &lt;i&gt;T. b. rhodesiense&lt;/i&gt; and &lt;i&gt;T. b. gambiense&lt;/i&gt; are able to resist lysis by TLF. There are two distinct sub-groups of &lt;i&gt;T. b. gambiense&lt;/i&gt; that differ genetically and by human serum resistance phenotypes. Group 1 &lt;i&gt;T. b. gambiense&lt;/i&gt; have an invariant phenotype whereas group 2 show variable resistance. Previous data indicated that group 1 &lt;i&gt;T. b. gambiense&lt;/i&gt; are resistant to TLF-1 due in-part to reduced uptake of TLF-1 mediated by reduced expression of the TLF-1 receptor (the haptoglobin-hemoglobin receptor (&lt;i&gt;HpHbR&lt;/i&gt;)) gene. Here we investigate if this is also true in group 2 parasites.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Methodology:&lt;/b&gt; Isogenic resistant and sensitive group 2 &lt;i&gt;T. b. gambiense&lt;/i&gt; were derived and compared to other T. brucei parasites. Both resistant and sensitive lines express the &lt;i&gt;HpHbR&lt;/i&gt; gene at similar levels and internalized fluorescently labeled TLF-1 similar fashion to &lt;i&gt;T. b. brucei&lt;/i&gt;. Both resistant and sensitive group 2, as well as group 1 &lt;i&gt;T. b. gambiense&lt;/i&gt;, internalize recombinant APOL1, but only sensitive group 2 parasites are lysed.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Conclusions:&lt;/b&gt; Our data indicate that, despite group 1 &lt;i&gt;T. b. gambiense&lt;/i&gt; avoiding TLF-1, it is resistant to the main lytic component, APOL1. Similarly group 2 &lt;i&gt;T. b. gambiense&lt;/i&gt; is innately resistant to APOL1, which could be based on the same mechanism. However, group 2 &lt;i&gt;T. b. gambiense&lt;/i&gt; variably displays this phenotype and expression does not appear to correlate with a change in expression site or expression of &lt;i&gt;HpHbR&lt;/i&gt;. Thus there are differences in the mechanism of human serum resistance between &lt;i&gt;T. b. gambiense&lt;/i&gt; groups 1 and 2.&lt;/p&gt

The TgsGP gene is essential for resistance to human serum in Trypanosoma brucei gambiense

Trypanosoma brucei gambiense causes 97% of all cases of African sleeping sickness, a fatal disease of sub-Saharan Africa. Most species of trypanosome, such as T. b. brucei, are unable to infect humans due to the trypanolytic serum protein apolipoprotein-L1 (APOL1) delivered via two trypanosome lytic factors (TLF-1 and TLF-2). Understanding how T. b. gambiense overcomes these factors and infects humans is of major importance in the fight against this disease. Previous work indicated that a failure to take up TLF-1 in T. b. gambiense contributes to resistance to TLF-1, although another mechanism is required to overcome TLF-2. Here, we have examined a T. b. gambiense specific gene, TgsGP, which had previously been suggested, but not shown, to be involved in serum resistance. We show that TgsGP is essential for resistance to lysis as deletion of TgsGP in T. b. gambiense renders the parasites sensitive to human serum and recombinant APOL1. Deletion of TgsGP in T. b. gambiense modified to uptake TLF-1 showed sensitivity to TLF-1, APOL1 and human serum. Reintroducing TgsGP into knockout parasite lines restored resistance. We conclude that TgsGP is essential for human serum resistance in T. b. gambiense

Generalized Thue-Morse words and palindromic richness

We prove that the generalized Thue-Morse word $\mathbf{t}_{b,m}$ defined for $b \geq 2$ and $m \geq 1$ as $\mathbf{t}_{b,m} = (s_b(n) \mod m)_{n=0}^{+\infty}$, where $s_b(n)$ denotes the sum of digits in the base-$b$ representation of the integer $n$, has its language closed under all elements of a group $D_m$ isomorphic to the dihedral group of order $2m$ consisting of morphisms and antimorphisms. Considering simultaneously antimorphisms $\Theta \in D_m$, we show that $\mathbf{t}_{b,m}$ is saturated by $\Theta$-palindromes up to the highest possible level. Using the terminology generalizing the notion of palindromic richness for more antimorphisms recently introduced by the author and E. Pelantov\'a, we show that $\mathbf{t}_{b,m}$ is $D_m$-rich. We also calculate the factor complexity of $\mathbf{t}_{b,m}$.Comment: 11 page

T/B scaling without quasiparticle mass divergence: YbCo2Ge4

YbCo$_2$Ge$_4$ is a clean paramagnetic Kondo lattice which displays non-Fermi liquid behavior. We report a detailed investigation of the specific heat, magnetic Gr\"uneisen parameter ($\Gamma_{\rm mag}$) and temperature derivative of the magnetization ($M$) on a high-quality single crystal at temperatures down to $0.1$~K and magnetic fields up to 7~T. $\Gamma_{\rm mag}$ and $dM/dT$ display a divergence upon cooling and obey $T/B$ scaling. Similar behavior has previously been found in several other Yb-based Kondo lattices and related to a zero-field quantum critical point without fine tuning of pressure or composition. However, in the approach of $B\rightarrow 0$ the electronic heat capacity coefficient of YbCo$_2$Ge$_4$ saturates at low $T$, excluding ferromagnetic quantum criticality. This indicates that $T/B$ scaling is insufficient to prove a zero-field quantum critical point.Comment: 6 pages, 6 figures (including supplemental material

Homogeneous explosion and shock initiation for a three-step chain-branching reaction model

The role of chain-branching cross-over temperatures in shock-induced ignition of reactive materials is studied by numerical simulation, using a three-step chainbranching reaction model. In order to provide insight into shock initiation, the simpler problem of a spatially homogeneous explosion is first considered. It is shown that for ratios of the cross-over temperature to the initial temperature, T-B, sufficiently less than unity, the homogeneous explosion can be quantitatively described by a widely used two-step model, while for T-B sufficiently above unity the homogeneous explosion can be effectively described by the standard one-step model. From the matchings between these homogeneous-explosion solutions, the parameters of the reduced models are identified in terms of those of the three-step model. When T-B is close to unity, all the reactions of the three-step model have a leading role, and hence in this case the model cannot be reduced further. In the case of shock initiation, for T-B (which is now the ratio of the cross-over temperature to the initial shock temperature) sufficiently below unity, the three-step solutions are qualitatively described by those of the matched two-step model, but there are quantitative differences due to the assumption in the reduced model that a purely chain-branching explosion occurs instantaneously. For T-B sufficiently above unity, the matched one-step model is found to effectively describe the way in which the heat release and fluid dynamics couple. For T-B close to unity, the competition between chain branching and chain termination is important from the outset. In these cases the speed at which the forward moving explosion wave that emerges from the piston is sensitive to T-B, and changes from supersonic to subsonic for a value of T-B just below unity