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Adobe PDF - MCT-07-0149--Suppl_Data.pdf from Inhibition of the heat shock protein 90 molecular chaperone in vitro and in vivo by novel, synthetic, potent resorcinylic pyrazole/isoxazole amide analogues

Although the heat shock protein 90 (HSP90) inhibitor 17-allylamino-17-demethoxygeldanamycin (17-AAG) shows clinical promise, potential limitations encourage development of alternative chemotypes. We discovered the 3,4-diarylpyrazole resorcinol CCT018159 by high-throughput screening and used structure-based design to generate more potent pyrazole amide analogues, exemplified by VER-49009. Here, we describe the detailed biological properties of VER-49009 and the corresponding isoxazole VER-50589. X-ray crystallography showed a virtually identical HSP90 binding mode. However, the dissociation constant (Kd) of VER-50589 was 4.5 ± 2.2 nmol/L compared with 78.0 ± 10.4 nmol/L for VER-49009, attributable to higher enthalpy for VER-50589 binding. A competitive binding assay gave a lower IC50 of 21 ± 4 nmol/L for VER-50589 compared with 47 ± 9 nmol/L for VER-49009. Cellular uptake of VER-50589 was 4-fold greater than for VER-49009. Mean cellular antiproliferative GI50 values for VER-50589 and VER-49009 for a human cancer cell line panel were 78 ± 15 and 685 ± 119 nmol/L, respectively, showing a 9-fold potency gain for the isoxazole. Unlike 17-AAG, but as with CCT018159, cellular potency of these analogues was independent of NAD(P)H:quinone oxidoreductase 1/DT-diaphorase and P-glycoprotein expression. Consistent with HSP90 inhibition, VER-50589 and VER-49009 caused induction of HSP72 and HSP27 alongside depletion of client proteins, including C-RAF, B-RAF, and survivin, and the protein arginine methyltransferase PRMT5. Both caused cell cycle arrest and apoptosis. Extent and duration of pharmacodynamic changes in an orthotopic human ovarian carcinoma model confirmed the superiority of VER-50589 over VER-49009. VER-50589 accumulated in HCT116 human colon cancer xenografts at levels above the cellular GI50 for 24 h, resulting in 30% growth inhibition. The results indicate the therapeutic potential of the resorcinylic pyrazole/isoxazole amide analogues as HSP90 inhibitors. [Mol Cancer Ther 2007;6(4):1198–211]

The phosphatidylinositide 3-kinase pathway is frequently deregulated in human cancers and inhibitors offer considerable therapeutic potential. We previously described the promising tricyclic pyridofuropyrimidine lead and chemical tool compound PI-103. We now report the properties of the pharmaceutically optimized bicyclic thienopyrimidine derivatives PI-540 and PI-620 and the resulting clinical development candidate GDC-0941. All four compounds inhibited phosphatidylinositide 3-kinase p110α with IC50 ≤ 10 nmol/L. Despite some differences in isoform selectivity, these agents exhibited similar in vitro antiproliferative properties to PI-103 in a panel of human cancer cell lines, with submicromolar potency in PTEN-negative U87MG human glioblastoma cells and comparable phosphatidylinositide 3-kinase pathway modulation. PI-540 and PI-620 exhibited improvements in solubility and metabolism with high tissue distribution in mice. Both compounds gave improved antitumor efficacy over PI-103, following i.p. dosing in U87MG glioblastoma tumor xenografts in athymic mice, with treated/control values of 34% (66% inhibition) and 27% (73% inhibition) for PI-540 (50 mg/kg b.i.d.) and PI-620 (25 mg/kg b.i.d.), respectively. GDC-0941 showed comparable in vitro antitumor activity to PI-103, PI-540, and PI-620 and exhibited 78% oral bioavailability in mice, with tumor exposure above 50% antiproliferative concentrations for >8 hours following 150 mg/kg p.o. and sustained phosphatidylinositide 3-kinase pathway inhibition. These properties led to excellent dose-dependent oral antitumor activity, with daily p.o. dosing at 150 mg/kg achieving 98% and 80% growth inhibition of U87MG glioblastoma and IGROV-1 ovarian cancer xenografts, respectively. Together, these data support the development of GDC-0941 as a potent, orally bioavailable inhibitor of phosphatidylinositide 3-kinase. GDC-0941 has recently entered phase I clinical trials. [Mol Cancer Ther 2009;8(7):1725–38] [Mol Cancer Ther 2009;8(7):1725–38]

Supplementary Figure 1 from Biological properties of potent inhibitors of class I phosphatidylinositide 3-kinases: from PI-103 through PI-540, PI-620 to the oral agent GDC-0941

Supplementary Figure 3C from Biological properties of potent inhibitors of class I phosphatidylinositide 3-kinases: from PI-103 through PI-540, PI-620 to the oral agent GDC-0941

Supplementary Table 1 from Biological properties of potent inhibitors of class I phosphatidylinositide 3-kinases: from PI-103 through PI-540, PI-620 to the oral agent GDC-0941

Supplementary Figure 2 from Biological properties of potent inhibitors of class I phosphatidylinositide 3-kinases: from PI-103 through PI-540, PI-620 to the oral agent GDC-0941

Supplementary Figure 2 from NVP-AUY922: A Novel Heat Shock Protein 90 Inhibitor Active against Xenograft Tumor Growth, Angiogenesis, and Metastasis

Supplementary Figure 5 from A Useful Approach to Identify Novel Small-Molecule Inhibitors of Wnt-Dependent Transcription

Supplementary Figures 1-3 from A Useful Approach to Identify Novel Small-Molecule Inhibitors of Wnt-Dependent Transcription

We describe the biological properties of NVP-AUY922, a novel resorcinylic isoxazole amide heat shock protein 90 (HSP90) inhibitor. NVP-AUY922 potently inhibits HSP90 (Kd = 1.7 nmol/L) and proliferation of human tumor cells with GI50 values of approximately 2 to 40 nmol/L, inducing G1-G2 arrest and apoptosis. Activity is independent of NQO1/DT-diaphorase, maintained in drug-resistant cells and under hypoxic conditions. The molecular signature of HSP90 inhibition, comprising induced HSP72 and depleted client proteins, was readily demonstrable. NVP-AUY922 was glucuronidated less than previously described isoxazoles, yielding higher drug levels in human cancer cells and xenografts. Daily dosing of NVP-AUY922 (50 mg/kg i.p. or i.v.) to athymic mice generated peak tumor levels at least 100-fold above cellular GI50. This produced statistically significant growth inhibition and/or regressions in human tumor xenografts with diverse oncogenic profiles: BT474 breast tumor treated/control, 21%; A2780 ovarian, 11%; U87MG glioblastoma, 7%; PC3 prostate, 37%; and WM266.4 melanoma, 31%. Therapeutic effects were concordant with changes in pharmacodynamic markers, including induction of HSP72 and depletion of ERBB2, CRAF, cyclin-dependent kinase 4, phospho-AKT/total AKT, and hypoxia-inducible factor-1α, determined by Western blot, electrochemiluminescent immunoassay, or immunohistochemistry. NVP-AUY922 also significantly inhibited tumor cell chemotaxis/invasion in vitro, WM266.4 melanoma lung metastases, and lymphatic metastases from orthotopically implanted PC3LN3 prostate carcinoma. NVP-AUY922 inhibited proliferation, chemomigration, and tubular differentiation of human endothelial cells and antiangiogenic activity was reflected in reduced microvessel density in tumor xenografts. Collectively, the data show that NVP-AUY922 is a potent, novel inhibitor of HSP90, acting via several processes (cytostasis, apoptosis, invasion, and angiogenesis) to inhibit tumor growth and metastasis. NVP-AUY922 has entered phase I clinical trials. [Cancer Res 2008;68(8):2850–60]

Supplementary Materials, Table 1 and Figures 1-3 from In vitro Biological Characterization of a Novel, Synthetic Diaryl Pyrazole Resorcinol Class of Heat Shock Protein 90 Inhibitors

Supplementary Figure Legends 1-13, Methods from A Useful Approach to Identify Novel Small-Molecule Inhibitors of Wnt-Dependent Transcription

Supplementary Figure 13 from A Useful Approach to Identify Novel Small-Molecule Inhibitors of Wnt-Dependent Transcription

Supplementary Figure 6 from NVP-AUY922: A Novel Heat Shock Protein 90 Inhibitor Active against Xenograft Tumor Growth, Angiogenesis, and Metastasis

The molecular chaperone heat shock protein 90 (HSP90) has emerged as an exciting molecular target. Derivatives of the natural product geldanamycin, such as 17-allylamino-17-demethoxy-geldanamycin (17-AAG), were the first HSP90 ATPase inhibitors to enter clinical trial. Synthetic small-molecule HSP90 inhibitors have potential advantages. Here, we describe the biological properties of the lead compound of a new class of 3,4-diaryl pyrazole resorcinol HSP90 inhibitor (CCT018159), which we identified by high-throughput screening. CCT018159 inhibited human HSP90β with comparable potency to 17-AAG and with similar ATP-competitive kinetics. X-ray crystallographic structures of the NH2-terminal domain of yeast Hsp90 complexed with CCT018159 or its analogues showed binding properties similar to radicicol. The mean cellular GI50 value of CCT018159 across a panel of human cancer cell lines, including melanoma, was 5.3 μmol/L. Unlike 17-AAG, the in vitro antitumor activity of the pyrazole resorcinol analogues is independent of NQO1/DT-diaphorase and P-glycoprotein expression. The molecular signature of HSP90 inhibition, comprising increased expression of HSP72 protein and depletion of ERBB2, CDK4, C-RAF, and mutant B-RAF, was shown by Western blotting and quantified by time-resolved fluorescent-Cellisa in human cancer cell lines treated with CCT018159. CCT018159 caused cell cytostasis associated with a G1 arrest and induced apoptosis. CCT018159 also inhibited key endothelial and tumor cell functions implicated in invasion and angiogenesis. Overall, we have shown that diaryl pyrazole resorcinols exhibited similar cellular properties to 17-AAG with potential advantages (e.g., aqueous solubility, independence from NQO1 and P-glycoprotein). These compounds form the basis for further structure-based optimization to identify more potent inhibitors suitable for clinical development. [Cancer Res 2007;67(5):2206–16]

Supplementary Figure 3A-B from NVP-AUY922: A Novel Heat Shock Protein 90 Inhibitor Active against Xenograft Tumor Growth, Angiogenesis, and Metastasis

Supplementary Figures 6-9 from A Useful Approach to Identify Novel Small-Molecule Inhibitors of Wnt-Dependent Transcription

Supplementary Figure 5A-B from NVP-AUY922: A Novel Heat Shock Protein 90 Inhibitor Active against Xenograft Tumor Growth, Angiogenesis, and Metastasis

Supplementary Figure 4C-D from NVP-AUY922: A Novel Heat Shock Protein 90 Inhibitor Active against Xenograft Tumor Growth, Angiogenesis, and Metastasis

Supplementary Figure 5C-D from NVP-AUY922: A Novel Heat Shock Protein 90 Inhibitor Active against Xenograft Tumor Growth, Angiogenesis, and Metastasis

Supplementary Figure 4 from A Useful Approach to Identify Novel Small-Molecule Inhibitors of Wnt-Dependent Transcription

The Wnt signaling pathway is frequently deregulated in cancer due to mutations in genes encoding APC, β-catenin, and axin. To identify small-molecule inhibitors of Wnt signaling as potential therapeutics, a diverse chemical library was screened using a transcription factor reporter cell line in which the activity of the pathway was induced at the level of Disheveled protein. A series of deconvolution studies was used to focus on three compound series that selectively killed cancer cell lines with constitutive Wnt signaling. Activities of the compounds included the ability to induce degradation of β-catenin that had been stabilized by a glycogen synthase kinase-3 (GSK-3) inhibitor. This screen illustrates a practical approach to identify small-molecule inhibitors of Wnt signaling that can seed the development of agents suitable to treat patients with Wnt-dependent tumors. Cancer Res; 70(14); 5963–73. ©2010 AACR.

Supplementary Figures 1A-B from NVP-AUY922: A Novel Heat Shock Protein 90 Inhibitor Active against Xenograft Tumor Growth, Angiogenesis, and Metastasis

Supplementary Figure 1C from NVP-AUY922: A Novel Heat Shock Protein 90 Inhibitor Active against Xenograft Tumor Growth, Angiogenesis, and Metastasis

Supplementary Figure 4A-B from NVP-AUY922: A Novel Heat Shock Protein 90 Inhibitor Active against Xenograft Tumor Growth, Angiogenesis, and Metastasis

Let 1 > p > ∞ 1>p>\infty and let n ≥ 1 n\geq 1 . It is proved that a function f : R → C f:\mathbb {R}\to \mathbb {C} is n n -times Fréchet differentiable on S p \mathcal {S}^p at every self-adjoint operator if and only if f f is n n -times differentiable, f ′ , f , … , f ( n ) f’,f,\ldots ,f^{(n)} are bounded and f ( n ) f^{(n)} is uniformly continuous.

We discuss the work of Birman and Solomyak on the singular numbers of integral operators from the point of view of modern approximation theory, in particular, with the use of wavelet techniques. We are able to provide a simple proof of norm estimates for integral operators with kernel in $$B^{1/p-1/2}_{p,p}(\mathbb R,L_2(\mathbb R))$$ . This recovers, extends, and sheds new light on a theorem of Birman and Solomyak. We also use these techniques to provide a simple proof of Schur multiplier bounds for double operator integrals with bounded symbol in $$B^{1/p-1/2}_{2p/(2-p),p}(\mathbb R,L_\infty(\mathbb R))$$ , which extends Birman and Solomyak’s result to symbols without compact domain.

Drawing on a social semiotic framework, this paper sets out to examine two different semiotic systems whose default mode of expression is the human voice – language and music. Through comparing how each system differentially employs the human voice, we can identify both their commonalities and differences, and go some way to treating both equally within de Saussure’s envisaged broader field of “semiology”, avoiding the common trap of “linguistic imperialism”, i.e. taking language as the model for all semiotic systems. Starting by conceptualising the key relationship between the text, or unified instance of meaning-making, and the social contexts in which it functions, the paper then examines the material affordances utilised by each system, and the kinds of social meanings they express.

System identification models relating forearm electromyogram (EMG) signals to phantom wrist radial-ulnar deviation force, pronation-supination moment and/or hand open-close force (EMG-force) are hampered by lack of supervised force/moment output signals in limb-absent subjects. In 12 able-bodied and 7 unilateral transradial limb-absent subjects, we studied three alternative supervised output sources in one degree of freedom (DoF) and 2-DoF target tracking tasks: (1) bilateral tracking with force feedback from the contralateral side (non-dominant for able-bodied/ sound for limb-absent subjects) with the contralateral force as the output, (2) bilateral tracking with force feedback from the contralateral side with the target as the output, and (3) dominant/limb-absent side unilateral target tracking without feedback and the target used as the output. “Best-case” EMG-force errors averaged ~ 10% of maximum voluntary contraction (MVC) when able-bodied subjects’ dominant limb produced unilateral force/moment with feedback. When either bilateral tracking source was used as the model output, statistically larger errors of 12–16 %MVC resulted. The no-feedback alternative produced errors of 25–30 %MVC, which was nearly half the tested force range of ± 30 %MVC. Therefore, the no-feedback model output was not acceptable. We found little performance variation between DoFs. Many subjects struggled to perform 2-DoF target tracking.

We discuss Ando's inequality involving operator monotone functions and demonstrate that a natural strengthening of Ando's result to uniform submajorization holds if and only if the operator monotone function has a very simple rational form.

We study the topic of quantum differentiability on quantum Euclidean $d$-dimensional spaces (otherwise known as Moyal $d$-spaces), and we find conditions that are necessary and sufficient for the singular values of the quantised differential to have decay $O(n^{-\alpha})$ for $0 < \alpha \leq \frac{1}{d}$. This result is substantially more difficult than the analogous problems for Euclidean space and for quantum $d$-tori., Comment: Accepted to Comm. Math. Phys

We introduce the notion of a pre-spectral triple, which is a generalisation of a spectral triple ( A , H , D ) where D is no longer required to be self-adjoint, but closed and symmetric. Despite having weaker assumptions, pre-spectral triples allow us to introduce noncompact noncommutative geometry with boundary. In particular, we derive the Hochschild character theorem in this setting. We give a detailed study of Dirac operators with Dirichlet boundary conditions on domains in R d , d ≥ 2 .

We introduce an abstract theory of the principal symbol mapping for pseudodifferential operators extending the results of Sukochev and Zanin (J Oper Theory, 2019) and providing a simple algebraic approach to the theory of pseudodifferential operators in settings important in noncommutative geometry. We provide a variant of Connes’ trace theorem which applies to certain noncommutative settings, with a minimum of technical preliminaries. Our approach allows us to consider operators with non-smooth symbols, and we demonstrate the power of our approach by extending Connes’ trace theorem to operators with non-smooth symbols in three examples: the Lie group $$\mathrm {SU}(2)$$ , noncommutative tori and Moyal planes.

In this short note we demonstrate that the definition of the density of states of a Schr\"{o}dinger operator with bounded potential in general depends on the choice of the domain undergoing the thermodynamic limit., Comment: 3 pages

In a previous paper we established Cwikel-type estimates on noncommutative tori and used them to get analogues in this setting of the Cwikel-Lieb-Rozenblum (CLR) and Lieb-Thirring inequalities for negative eigenvalues of fractional Schr\"odinger operators. In this paper, we focus on "curved" NC tori, where the role of the usual Laplacian is played by Laplace-Beltrami operators associated with arbitrary Riemannian metrics. The Cwikel-type estimates of our previous paper are extended to pseudodifferential operators and powers of Laplace-Beltrami operators. There are several applications of these estimates. First, we get $L_p$-versions of the usual formula for the trace of \psidos\ on NC tori, i.e., for combinations of \psidos\ with $L_p$-position operators. Next, we get $L_p$-versions of the analogues for NC tori Connes' trace theorem and Connes' integration formula. They give formulas for the NC integrals (a.k.a.\ Dixmier traces) of products of $L_p$-position operators with \psidos\ or powers of the Laplace-Beltrami operators. Moreover, by combining our Cwikel-type estimates with suitable versions of the Birman-Schwinger principle we get versions of the CLR and Lieb-Thirring inequalities for negative eigenvalues of fractional Schr\"odinger operators associated with powers of Laplace-Beltrami operators and $L_p$-potentials. As in the original Euclidean case the Lieb-Thirring inequalities imply a dual Sobolev inequality for orthonormal families. Finally, we discuss spectral asymptotics and semiclassical Weyl's laws for the our classes of operators on curved NC tori. This superseded a previous conjecture in our previous paper., Comment: v2: extra material on Lieb-Thirring and Sobolev inequalities and semiclassical Weyl's law, 38 pages

Background: Failure to address meniscus root tears may place undue loads on anterior cruciate ligament (ACL) reconstructive surgery in the adult population. Because the intraoperative management of lateral meniscus posterior root tears (LMPRTs) may diverge from standard meniscal work and requires specialty items, preoperative diagnosis may be advantageous. Purpose: To evaluate the reliability of radiologist interpretations of preoperative knee magnetic resonance imaging (MRI) scans of lateral meniscus root pathology in a mixed pediatric and adolescent population. Study Design: Cohort study (diagnosis); Level of evidence, 2. Methods: A retrospective review of medical records was performed to identify patients younger than 18 years with an arthroscopically confirmed LMPRT who underwent knee arthroscopy between March 1, 2010, and April 1, 2020. Arthroscopic findings were compared with the reading radiologist’s preoperative MRI interpretations, and patients were stratified into 2 groups: (1) LMPRT diagnosis made preoperatively or (2) diagnosis missed or only mentioned to describe pathology nonspecific to the root. Variables such as body mass index (BMI), open physes, time from injury to MRI, time from MRI to surgery, MRI magnet field strength, musculoskeletal radiologist designation, insurance type, and tear grade were assessed between groups. Results: Overall, 1116 knee arthroscopies were performed, with 49 LMPRTs found; all 49 LMRPTs were found concomitantly with ACL tears (49/535; 9.2%). The average patient age was 15.97 years (range, 11.52-17.97 years). There were 50 MRI scans for 49 patients. An LMPRT was diagnosed based on preoperative MRI scans in 12 of these 50 scans (24%) and mentioned or missed in 38 of the 50 scans (76%). No significant difference was seen between the diagnosis-made versus diagnosis-mentioned/missed groups in BMI, skeletal maturity, time from injury to MRI, time from MRI to surgery, MRI magnet strength, fellowship training of the reading radiologist, tear grade, or insurance type. Conclusion: In 76% of patients, a definitive diagnosis of LMPRT was not made on preoperative MRI scans. Notably, all LMPRTs found intraoperatively were found concomitantly with ACL tears.

In this paper, we establish Cwikel-type estimates for noncommutative tori for any dimension~$n\geq 2$. We use them to derive Cwikel-Lieb-Rozenblum inequalities and and Lieb-Thirring inequalities for the number of negative eigenvalues of fractional Schroedinger operators on noncommutative tori in any dimension~$n\geq 2$. The latter leads to a Sobolev inequality for noncommutative tori. On the way we establish a "borderline version" of the abstract Birman-Schwinger principle for the number of negative eigenvalues of relatively compact form perturbations of a non-negative semi-bounded operator with isolated 0-eigenvalue., v3: major changes. The new version contains new material on Lieb-Thirring inequalities and Sobolev inequality on NC tori + explicit bounds for the best constants for the various inequalities established in the paper. 38 pages

Single-use EMG-force models (i.e., a new model is trained each time the electrodes are donned) are used in various areas, including ergonomics assessment, clinical biomechanics, and motor control research. For one degree of freedom (1-DoF) tasks, input-output (black box) models are common. Recently, black box models have expanded to 2-DoF tasks. To facilitate efficient training, we examined parameters of black box model training methods in 2-DoF force-varying, constant-posture tasks consisting of hand open-close combined with one wrist DoF. We found that approximately 40-60 s of training data is best, with progressively higher EMG-force errors occurring for progressively shorter training durations. Surprisingly, 2-DoF models in which the dynamics were universal across all subjects (only channel gain was trained to each subject) generally performed 15-21% better than models in which the complete dynamics were trained to each subject. In summary, lower error EMG-force models can be formed through diligent attention to optimization of these factors.

We study the class of functions $f$ on $\mathbb{R}$ satisfying a Lipschitz estimate in the Schatten ideal $\mathcal{L}_p$ for $0 < p \leq 1$. The corresponding problem with $p\geq 1$ has been extensively studied, but the quasi-Banach range $0 < p < 1$ is by comparison poorly understood. Using techniques from wavelet analysis, we prove that Lipschitz functions belonging to the homogeneous Besov class $\dot{B}^{\frac{1}{p}}_{\frac{p}{1-p},p}(\mathbb{R})$ obey the estimate $$ \|f(A)-f(B)\|_{p} \leq C_{p}(\|f'\|_{L_{\infty}(\mathbb{R})}+\|f\|_{\dot{B}^{\frac{1}{p}}_{\frac{p}{1-p},p}(\mathbb{R})})\|A-B\|_{p} $$ for all bounded self-adjoint operators $A$ and $B$ with $A-B\in \mathcal{L}_p$. In the case $p=1$, our methods recover and provide a new perspective on a result of Peller that $f \in \dot{B}^1_{\infty,1}$ is sufficient for a function to be Lipschitz in $\mathcal{L}_1$. We also provide related H��lder-type estimates, extending results of Aleksandrov and Peller. In addition, we prove the surprising fact that non-constant periodic functions on $\mathbb{R}$ are not Lipschitz in $\mathcal{L}_p$ for any $0 < p < 1$. This gives counterexamples to a 1991 conjecture of Peller that $f \in \dot{B}^{1/p}_{\infty,p}(\mathbb{R})$ is sufficient for $f$ to be Lipschitz in $\mathcal{L}_p$., 32 pages. To appear in Mathematische Annalen

In the Anglophone sphere, according to popular and most academic understandings, the term “ideograph” is regarded as an unproblematic synonym of 漢字 hànzì ‘Chinese character.’ On graphological grounds, i.e. as applied to writing systems, it can easily be shown that the concept of “ideograph” is both theoretically incoherent and practically unfeasible (McDonald 2016); while historically it is clear that the notion was founded on an imperfect understanding of Chinese characters as a writing system, and grew out of a European obsession with the notion of a “universal character” at a particular historical moment (Mungello 1985; Saussy 2001). Nevertheless the concept has become deeply embedded in European understandings of Chinese language and culture, to the extent that it is, in effect, a valuable conceptual possession of Western modernity (Bush 2010), and promoted alike by those with a detailed knowledge of Chinese writing, such as H. G. Creel (1936), as by those in blissful ignorance of it, like Jacques Derrida (1967/1976). In the Sinophone sphere, while for most practical purposes, as well as in a large proportion of scholarly work, more grounded understandings of Chinese characters as a writing system operate either implicitly or explicitly, the traditional emphasis on characters as a link between civilization and the cosmos (O’Neill 2013), as well as a long tradition of pedagogical “just so stories” about the construction of individual characters (e.g., Zuo 2005), provide a key point of contact with Western notions of the “ideograph” as symbolizing not a word, but an idea or an object. The situation may thus be described involving a type of inversion of the phenomenon of faux amis or “false friends,” where two different words are understood as being more or less synonymous; or alternatively as an example of Lydia Liu’s (2004) notion of a cross-lingual “supersign” where two comparable terms exercise an influence on each other across linguistic and cultural boundaries. This article will attempt to trace the genealogy of these complex and overlapping notions, and see what differing understandings of Chinese characters have to tell us about notions of cultural specificity, cultural production, and cross-cultural (mis-)communication in the contemporary globalized world.

In the eyes of early modern European scholars, Chinese was commonly regarded as a “lacking” language: lacking its own grammatical tradition or “grammatics”; lacking the complex morphology of the classical European languages; even lacking its own “parts of speech” or word classes. In the late 19th century Ma Jianzhong created a grammatics for Chinese by adapting the categories of Latin grammar - and with a good understanding of the similarities and differences between the two languages - but the Chinese grammarians who followed him have struggled with the question of what might be common to all languages and what might be distinctive to Chinese. Ma saw a Chinese grammatics as a way to fill a gap in the country's literacy education, and this applied focus has been shared by most Chinese grammarians since, something which has tended to put restrictions on their description and theorising. A historical perspective is thus absolutely essential for understanding the practical and ideological problems Chinese grammatics continues to face, and can also throw light on the general challenge of extending “European grammar” to non-European languages.

If $c$ is in the main cardioid of the Mandelbrot set, then the Julia set $J$ of the map $\unicode[STIX]{x1D719}_{c}:z\mapsto z^{2}+c$ is a Jordan curve of Hausdorff dimension $p\in [1,2)$. We provide a full proof of a formula for the Hausdorff measure on $J$ in terms of singular traces announced by the first named author in 1996.