Superconducting diode effect and interference patterns in kagome CsV3Sb5.

The interplay among frustrated lattice geometry, non-trivial band topology and correlation yields rich quantum states of matter in kagome systems1,2. A series of recent members in this family, AV3Sb5 (A = K, Rb or Cs), exhibit a cascade of symmetry-breaking transitions3, involving the 3Q chiral charge ordering4-8, electronic nematicity9,10, roton pair density wave11 and superconductivity12. The nature of the superconducting order is yet to be resolved. Here we report an indication of dynamic superconducting domains with boundary supercurrents in intrinsic CsV3Sb5 flakes. The magnetic field-free superconducting diode effect is observed with polarity modulated by thermal histories, suggesting that there are dynamic superconducting order domains in a spontaneous time-reversal symmetry-breaking background. Strikingly, the critical current exhibits double-slit superconductivity interference patterns when subjected to an external magnetic field. The characteristics of the patterns are modulated by thermal cycling. These phenomena are proposed as a consequence of periodically modulated supercurrents flowing along certain domain boundaries constrained by fluxoid quantization. Our results imply a time-reversal symmetry-breaking superconducting order, opening a potential for exploring exotic physics, for example, Majorana zero modes, in this intriguing topological kagome system.

Topological Chern vectors in three-dimensional photonic crystals.

The paradigmatic example of a topological phase of matter, the two-dimensional Chern insulator1-5, is characterized by a topological invariant consisting of a single integer, the scalar Chern number. Extending the Chern insulator phase from two to three dimensions requires generalization of the Chern number to a three-vector6,7, similar to the three-dimensional (3D) quantum Hall effect8-13. Such Chern vectors for 3D Chern insulators have never been explored experimentally. Here we use magnetically tunable 3D photonic crystals to achieve the experimental demonstration of Chern vectors and their topological surface states. We demonstrate Chern vector magnitudes of up to six, higher than all scalar Chern numbers previously realized in topological materials. The isofrequency contours formed by the topological surface states in the surface Brillouin zone form torus knots or links, whose characteristic integers are determined by the Chern vectors. We demonstrate a sample with surface states forming a (2, 2) torus link or Hopf link in the surface Brillouin zone, which is topologically distinct from the surface states of other 3D topological phases. These results establish the Chern vector as an intrinsic bulk topological invariant in 3D topological materials, with surface states possessing unique topological characteristics.

Effector-dependent activation and oligomerization of plant NRC class helper NLRs by sensor NLR immune receptors Rpi-amr3 and Rpi-amr1.

Plant pathogens compromise crop yields. Plants have evolved robust innate immunity that depends in part on intracellular Nucleotide-binding, Leucine rich-Repeat (NLR) immune receptors that activate defense responses upon detection of pathogen-derived effectors. Most "sensor" NLRs that detect effectors require the activity of "helper" NLRs, but how helper NLRs support sensor NLR function is poorly understood. Many Solanaceae NLRs require NRC (NLR-Required for Cell death) class of helper NLRs. We show here that Rpi-amr3, a sensor NLR from Solanum americanum, detects AVRamr3 from the potato late blight pathogen, Phytophthora infestans, and activates oligomerization of helper NLRs NRC2 and NRC4 into high-molecular-weight resistosomes. In contrast, recognition of P. infestans effector AVRamr1 by another sensor NLR Rpi-amr1 induces formation of only the NRC2 resistosome. The activated NRC2 oligomer becomes enriched in membrane fractions. ATP-binding motifs of both Rpi-amr3 and NRC2 are required for NRC2 resistosome formation, but not for the interaction of Rpi-amr3 with its cognate effector. NRC2 resistosome can be activated by Rpi-amr3 upon detection of AVRamr3 homologs from other Phytophthora species. Mechanistic understanding of NRC resistosome formation will underpin engineering crops with durable disease resistance.

Metastable precipitation and ion-extractant transport in liquid-liquid separations of trivalent elements.

The extractant-assisted transport of metal ions from aqueous to organic environments by liquid-liquid extraction has been widely used to separate and recover critical elements on an industrial scale. While current efforts focus on designing better extractants and optimizing process conditions, the mechanism that underlies ionic transport remains poorly understood. Here, we report a nonequilibrium process in the bulk aqueous phase that influences interfacial ion transport: the formation of metastable ion-extractant precipitates away from the liquid-liquid interface, separated from it by a depletion region without precipitates. Although the precipitate is soluble in the organic phase, the depletion region separates the two and ions are sequestered in a long-lived metastable state. Since precipitation removes extractants from the aqueous phase, even extractants that are sparingly soluble in water will continue to be withdrawn from the organic phase to feed the aqueous precipitation process. Solute concentrations in both phases and the aqueous pH influence the temporal evolution of the process and ionic partitioning between the precipitate and organic phase. Aqueous ion-extractant precipitation during liquid-liquid extraction provides a reaction path that can influence the extraction kinetics, which plays an important role in designing advanced processes to separate rare earths and other minerals.

Aging and comprehensive molecular profiling in acute myeloid leukemia.

Acute myeloid leukemia (AML) is an aging-related and heterogeneous hematopoietic malignancy. In this study, a total of 1,474 newly diagnosed AML patients with RNA sequencing data were enrolled, and targeted or whole exome sequencing data were obtained in 94% cases. The correlation of aging-related factors including age and clonal hematopoiesis (CH), gender, and genomic/transcriptomic profiles (gene fusions, genetic mutations, and gene expression networks or pathways) was systematically analyzed. Overall, AML patients aged 60 y and older showed an apparently dismal prognosis. Alongside age, the frequency of gene fusions defined in the World Health Organization classification decreased, while the positive rate of gene mutations, especially CH-related ones, increased. Additionally, the number of genetic mutations was higher in gene fusion-negative (GF-) patients than those with GF. Based on the status of CH- and myelodysplastic syndromes (MDS)-related mutations, three mutant subgroups were identified among the GF- AML cohort, namely, CH-AML, CH-MDS-AML, and other GF- AML. Notably, CH-MDS-AML demonstrated a predominance of elderly and male cases, cytopenia, and significantly adverse clinical outcomes. Besides, gene expression networks including HOXA/B, platelet factors, and inflammatory responses were most striking features associated with aging and poor prognosis in AML. Our work has thus unraveled the intricate regulatory circuitry of interactions among different age, gender, and molecular groups of AML.

Trained immunity in recurrent Staphylococcus aureus infection promotes bacterial persistence.

Bacterial persister cells, a sub-population of dormant phenotypic variants highly tolerant to antibiotics, present a significant challenge for infection control. Investigating the mechanisms of antibiotic persistence is crucial for developing effective treatment strategies. Here, we found a significant association between tolerance frequency and previous infection history in bovine mastitis. Previous S. aureus infection led to S. aureus tolerance to killing by rifampicin in subsequent infection in vivo and in vitro. Actually, the activation of trained immunity contributed to rifampicin persistence of S. aureus in secondary infection, where it reduced the effectiveness of antibiotic treatment and increased disease severity. Mechanically, we found that S. aureus persistence was mediated by the accumulation of fumarate provoked by trained immunity. Combination therapy with metformin and rifampicin promoted eradication of persisters and improved the severity of recurrent S. aureus infection. These findings provide mechanistic insight into the relationship between trained immunity and S. aureus persistence, while providing proof of concept that trained immunity is a therapeutic target in recurrent bacterial infections involving persistent pathogens.

LncRNADisease v3.0: an updated database of long non-coding RNA-associated diseases.

Systematic integration of lncRNA-disease associations is of great importance for further understanding their underlying molecular mechanisms and exploring lncRNA-based biomarkers and therapeutics. The database of long non-coding RNA-associated diseases (LncRNADisease) is designed for the above purpose. Here, an updated version (LncRNADisease v3.0) has curated comprehensive lncRNA (including circRNA) and disease associations from the burgeoning literatures. LncRNADisease v3.0 exhibits an over 2-fold increase in experimentally supported associations, with a total of 25440 entries, compared to the last version. Besides, each lncRNA-disease pair is assigned a confidence score based on experimental evidence. Moreover, all associations between lncRNAs/circRNAs and diseases are classified into general associations and causal associations, representing whether lncRNAs or circRNAs can directly lead to the development or progression of corresponding diseases, with 15721 and 9719 entries, respectively. In a case study, we used the data of LncRNADisease v3.0 to calculate the phenotypic similarity between human and mouse lncRNAs. This database will continue to serve as a valuable resource for potential clinical applications related to lncRNAs and circRNAs. LncRNADisease v3.0 is freely available at http://www.rnanut.net/lncrnadisease.

Interfacial Cherenkov radiation from ultralow-energy electrons.

Cherenkov radiation occurs only when a charged particle moves with a velocity exceeding the phase velocity of light in that matter. This radiation mechanism creates directional light emission at a wide range of frequencies and could facilitate the development of on-chip light sources except for the hard-to-satisfy requirement for high-energy particles. Creating Cherenkov radiation from low-energy electrons that has no momentum mismatch with light in free space is still a long-standing challenge. Here, we report a mechanism to overcome this challenge by exploiting a combined effect of interfacial Cherenkov radiation and umklapp scattering, namely the constructive interference of light emission from sequential particle-interface interactions with specially designed (umklapp) momentum-shifts. We find that this combined effect is able to create the interfacial Cherenkov radiation from ultralow-energy electrons, with kinetic energies down to the electron-volt scale. Due to the umklapp scattering for the excited high-momentum Bloch modes, the resulting interfacial Cherenkov radiation is uniquely featured with spatially separated apexes for its wave cone and group cone.

Surface premelting of ice far below the triple point.

Premelting of ice, a quasi-liquid layer (QLL) at the surface below the melting temperature, was first postulated by Michael Faraday 160 y ago. Since then, it has been extensively studied theoretically and experimentally through many techniques. Existing work has been performed predominantly on hexagonal ice, at conditions close to the triple point. Whether the same phenomenon can persist at much lower pressure and temperature, where stacking disordered ice sublimates directly into water vapor, remains unclear. Herein, we report direct observations of surface premelting on ice nanocrystals below the sublimation temperature using transmission electron microscopy (TEM). Similar to what has been reported on hexagonal ice, a QLL is found at the solid-vapor interface. It preferentially decorates certain facets, and its thickness increases as the phase transition temperature is approached. In situ TEM reveals strong diffusion of the QLL, while electron energy loss spectroscopy confirms its amorphous nature. More significantly, the premelting observed in this work is thought to be related to the metastable low-density ultraviscous water, instead of ambient liquid water as in the case of hexagonal ice. This opens a route to understand premelting and grassy liquid state, far away from the normal water triple point.

Deafness causing neuroplastin missense variants fail to promote plasma membrane Ca2+-ATPase levels and Ca2+ transient regulation in brain neurons.

Hearing, the ability to sense sounds, and the processing of auditory information are important for perception of the world. Mice lacking expression of neuroplastin (Np), a type-1 transmembrane glycoprotein, display deafness, multiple cognitive deficiencies, and reduced expression of plasma membrane calcium (Ca2+) ATPases (PMCAs) in cochlear hair cells and brain neurons. In this study, we transferred the deafness causing missense mutations pitch (C315S) and audio-1 (I122N) into human Np (hNp) constructs and investigated their effects at the molecular and cellular levels. Computational molecular dynamics show that loss of the disulfide bridge in hNppitch causes structural destabilization of immunoglobulin-like domain (Ig) III and that the novel asparagine in hNpaudio-1 results in steric constraints and an additional N-glycosylation site in IgII. Additional N-glycosylation of hNpaudio-1 was confirmed by PNGaseF treatment. In comparison to hNpWT, transfection of hNppitch and hNpaudio-1 into HEK293T cells resulted in normal mRNA levels but reduced the Np protein levels and their cell surface expression due to proteasomal/lysosomal degradation. Furthermore, hNppitch and hNpaudio-1 failed to promote exogenous PMCA levels in HEK293T cells. In hippocampal neurons, expression of additional hNppitch or hNpaudio-1 was less efficient than hNpWT to elevate endogenous PMCA levels and to accelerate the restoration of basal Ca2+ levels after electrically evoked Ca2+ transients. We propose that mutations leading to pathological Np variants, as exemplified here by the deafness causing Np mutants, can affect Np-dependent Ca2+ regulatory mechanisms and may potentially cause intellectual and cognitive deficits in humans.

Dihydroartemisinin is an inhibitor of trained immunity through Akt/mTOR/HIF1α signaling pathway.

Trained immunity is mechanistically defined as the metabolically and epigenetically mediated long-term functional adaptation of the innate immune system, characterized by a heightened response to a secondary stimulation. Given appropriate activation, trained immunity represents an attractive anti-infective therapeutic target. Nevertheless, excessive immune response and subsequent inflammatory cascades may contribute to pathological tissue damage, indicating that the negative impacts of trained immunity appear to be significant. In this study, we show that innate immune responses such as the production of extracellular traps, pro-inflammatory cytokines, and autophagy-related proteins were markedly augmented in trained BMDMs. Furthermore, heat-killed C. albicans priming promotes the activation of the AIM2 inflammasome, and AIM2-/- mice exhibit impaired memory response induced by heat-killed C. albicans. Therefore, we establish that the AIM2 inflammasome is involved in trained immunity and emerges as a promising therapeutic target for potentially deleterious effects. Dihydroartemisinin can inhibit the memory response induced by heat-killed C. albicans through modulation of mTOR signaling and the AIM2 inflammasome. The findings suggest that dihydroartemisinin can reduce the induction of trained immunity by heat-killed C. albicans in C57BL/6 mice. Dihydroartemisinin is one such therapeutic intervention that has the potential to treat of diseases characterized by excessive trained immunity.

Using normative modeling to assess pharmacological treatment effect on brain state in patients with schizophrenia.

Quantifying individual differences in neuroimaging metrics is attracting interest in clinical studies with mental disorders. Schizophrenia is diagnosed exclusively based on symptoms, and the biological heterogeneity makes it difficult to accurately assess pharmacological treatment effects on the brain state. Using the Cambridge Centre for Ageing and Neuroscience data set, we built normative models of brain states and mapped the deviations of the brain characteristics of each patient, to test whether deviations were related to symptoms, and further investigated the pharmacological treatment effect on deviation distributions. Specifically, we found that the patients can be divided into 2 groups: the normalized group had a normalization trend and milder symptoms at baseline, and the other group showed a more severe deviation trend. The baseline severity of the depression as well as the overall symptoms could predict the deviation of the static characteristics for the dorsal and ventral attention networks after treatment. In contrast, the positive symptoms could predict the deviations of the dynamic fluctuations for the default mode and dorsal attention networks after treatment. This work evaluates the effect of pharmacological treatment on static and dynamic brain states using an individualized approach, which may assist in understanding the heterogeneity of the illness pathology as well as the treatment response.

LncRNA LUESCC promotes esophageal squamous cell carcinoma by targeting the miR-6785-5p/NRSN2 axis.

Esophageal squamous cell carcinoma (ESCC) is one of the most prevalent gastrointestinal malignancies with high mortality worldwide. Emerging evidence indicates that long noncoding RNAs (lncRNAs) are involved in human cancers, including ESCC. However, the detailed mechanisms of lncRNAs in the regulation of ESCC progression remain incompletely understood. LUESCC was upregulated in ESCC tissues compared with adjacent normal tissues, which was associated with gender, deep invasion, lymph node metastasis, and poor prognosis of ESCC patients. LUESCC was mainly localized in the cytoplasm of ESCC cells. Knockdown of LUESCC inhibited cell proliferation, colony formation, migration, and invasion in vitro and suppressed tumor growth in vivo. Mechanistic investigation indicated that LUESCC functions as a ceRNA by sponging miR-6785-5p to enhance NRSN2 expression, which is critical for the malignant behaviors of ESCC. Furthermore, ASO targeting LUESCC substantially suppressed ESCC both in vitro and in vivo. Collectively, these data demonstrate that LUESCC may exerts its oncogenic role by sponging miR-6785-5p to promote NRSN2 expression in ESCC, providing a potential diagnostic marker and therapeutic target for ESCC patients.

Transcriptome-based molecular subtypes and differentiation hierarchies improve the classification framework of acute myeloid leukemia.

The current classification of acute myeloid leukemia (AML) relies largely on genomic alterations. Robust identification of clinically and biologically relevant molecular subtypes from nongenomic high-throughput sequencing data remains challenging. We established the largest multicenter AML cohort (n = 655) in China, with all patients subjected to RNA sequencing (RNA-Seq) and 619 (94.5%) to targeted or whole-exome sequencing (TES/WES). Based on an enhanced consensus clustering, eight stable gene expression subgroups (G1-G8) with unique clinical and biological significance were identified, including two unreported (G5 and G8) and three redefined ones (G4, G6, and G7). Apart from four well-known low-risk subgroups including PML::RARA (G1), CBFB::MYH11 (G2), RUNX1::RUNX1T1 (G3), biallelic CEBPA mutations or -like (G4), four meta-subgroups with poor outcomes were recognized. The G5 (myelodysplasia-related/-like) subgroup enriched clinical, cytogenetic and genetic features mimicking secondary AML, and hotspot mutations of IKZF1 (p.N159S) (n = 7). In contrast, most NPM1 mutations and KMT2A and NUP98 fusions clustered into G6-G8, showing high expression of HOXA/B genes and diverse differentiation stages, from hematopoietic stem/progenitor cell down to monocyte, namely HOX-primitive (G7), HOX-mixed (G8), and HOX-committed (G6). Through constructing prediction models, the eight gene expression subgroups could be reproduced in the Cancer Genome Atlas (TCGA) and Beat AML cohorts. Each subgroup was associated with distinct prognosis and drug sensitivities, supporting the clinical applicability of this transcriptome-based classification of AML. These molecular subgroups illuminate the complex molecular network of AML, which may promote systematic studies of disease pathogenesis and foster the screening of targeted agents based on omics.

Metal Variance in Multivariate Metal-Organic Frameworks for Boosting Catalytic Conversion of CO2.

Developing efficient, low-cost, MOF catalysts for CO2 conversion at low CO2 concentrations under mild conditions is particularly interesting but remains highly challenging. Herein, we prepared an isostructural series of two-dimensional (2D) multivariate metal-organic frameworks (MTV-MOFs) containing copper- and/or silver-based cyclic trinuclear complexes (Cu-CTC and Ag-CTC). These MTV-MOFs can be used as efficient and reusable heterogeneous catalysts for the cyclization of propargylamine with CO2. The catalytic performance of these MTV-MOFs can be engineered by fine-tuning the Ag/Cu ratio in the framework. Interestingly, the induction of 10% Ag remarkably improved the catalytic efficiency with a turnover frequency (TOF) of 243 h-1, which is 20-fold higher than that of 100% Cu-based MOF (i.e., TOF = 10.8 h-1). More impressively, such a bimetallic MOF still exhibited high catalytic activity even for simulated flue gas with 10% CO2 concentration. Furthermore, the reaction mechanism has been examined through the employment of NMR monitoring experiments and DFT calculations.

Potential causal links of long-term exposure to PM2.5 and its chemical components with the risk of nasopharyngeal carcinoma recurrence: A 10-year cohort study in South China.

There is a lack of evidence from cohort studies on the causal association of long-term exposure to ambient fine particulate matter (PM2.5) and its chemical components with the risk of nasopharyngeal carcinoma (NPC) recurrence. Based on a 10-year prospective cohort of 1184 newly diagnosed NPC patients, we comprehensively evaluated the potential causal links of ambient PM2.5 and its chemical components including black carbon (BC), organic matter (OM), sulfate (SO4 2-), nitrate (NO3 -), and ammonium (NH4 +) with the recurrence risk of NPC using a marginal structural Cox model adjusted with inverse probability weighting. We observed 291 NPC patients experiencing recurrence during the 10-year follow-up and estimated a 33% increased risk of NPC recurrence (hazard ratio [HR]: 1.33, 95% confidence interval [CI]: 1.02-1.74) following each interquartile range (IQR) increase in PM2.5 exposure. Each IQR increment in BC, NH4 +, OM, NO3 -, and SO4 2- was associated with HRs of 1.36 (95%CI: 1.13-1.65), 1.35 (95%CI: 1.07-1.70), 1.33 (95%CI: 1.11-1.59), 1.32 (95%CI: 1.06-1.64), 1.31 (95%CI: 1.08-1.57). The elderly, patients with no family history of cancer, no smoking history, no drinking history, and those with severe conditions may exhibit a greater likelihood of NPC recurrence following exposure to PM2.5 and its chemical components. Additionally, the effect estimates of the five components are greater among patients who were exposed to high concentration than in the full cohort of patients. Our study provides solid evidence for a potential relationship between long-term exposure to PM2.5 and its components and the risk of NPC recurrence.

Comparing genomes of Fructus Amomi-producing species reveals genetic basis of volatile terpenoid divergence.

Wurfbainia longiligularis and Wurfbainia villosa are both rich in volatile terpenoids and are 2 primary plant sources of Fructus Amomi used for curing gastrointestinal diseases. Metabolomic profiling has demonstrated that bornyl diphosphate (BPP)-related terpenoids are more abundant in the W. villosa seeds and have a wider tissue distribution in W. longiligularis. To explore the genetic mechanisms underlying the volatile terpenoid divergence, a high-quality chromosome-level genome of W. longiligularis (2.29 Gb, contig N50 of 80.39 Mb) was assembled. Functional characterization of 17 terpene synthases (WlTPSs) revealed that WlBPPS, along with WlTPS 24/26/28 with bornyl diphosphate synthase (BPPS) activity, contributes to the wider tissue distribution of BPP-related terpenoids in W. longiligularis compared to W. villosa. Furthermore, transgenic Nicotiana tabacum showed that the GCN4-motif element positively regulates seed expression of WvBPPS and thus promotes the enrichment of BPP-related terpenoids in W. villosa seeds. Systematic identification and analysis of candidate TPS in 29 monocot plants from 16 families indicated that substantial expansion of TPS-a and TPS-b subfamily genes in Zingiberaceae may have driven increased diversity and production of volatile terpenoids. Evolutionary analysis and functional identification of BPPS genes showed that BPP-related terpenoids may be distributed only in the Zingiberaceae of monocot plants. This research provides valuable genomic resources for breeding and improving Fructus Amomi with medicinal and edible value and sheds light on the evolution of terpenoid biosynthesis in Zingiberaceae.

Phase retrieval based on deep learning with bandpass filtering in holographic data storage.

A phase retrieval method based on deep learning with bandpass filtering in holographic data storage is proposed. The relationship between the known encoded data pages and their near-field diffraction intensity patterns is established by an end-to-end convolutional neural network, which is used to predict the unknown phase data page. We found the training efficiency of phase retrieval by deep learning is mainly determined by the edge details of the adjacent phase codes, which are the high-frequency components of the phase code. Therefore, we can attenuate the low-frequency components to reduce material consumption. Besides, we also filter out the high-order frequency over twice Nyquist size, which is redundant information with poor anti-noise performance. Compared with full-frequency recording, the consumption of storage media is reduced by 2.94 times, thus improving the storage density.

Polarization evolution on higher and hybrid-order Poincaré spheres with coaxial polarization holograms.

Based on the tensor polarization holography theory, we propose a simple and convenient method in the recording material, phenanthrenequinone-doped polymethylmethacrylate, to generate beams on higher and hybrid-order Poincaré spheres, and realize their polarization evolution on the spheres by combining the recorded phase with the Pancharatnam-Berry phase. By simultaneously adjusting the polarization azimuth angle and relative phase of the recorded waves, independent phase-shifts can be imparted onto two orthogonal circular polarization states in reconstruction process of polarization holography. The beams on basic Poincaré sphere are transformed into that on arbitrary higher or hybrid-order Poincaré spheres. We get the Poincaré spheres' type and polarization distribution of the reconstructed wave by interferometry and polarizer, and the results match well with the theoretical predictions.

Dipolar Huygens-Kerker radiation for surface waves.

Exotic dipolar radiation with zero light emission in one direction but maximal light emission in the opposite direction was envisioned by Huygens in 1690, and it could emerge in vacuum if the ratio between the source's electric and magnetic dipole moments fulfills the Kerker condition as revealed by Kerker in 1983. Due to its intricate connection with both the Huygens principle and Kerker condition, this radiation phenomenon is suggested to be termed as dipolar Huygens-Kerker radiation, and at this moment, the ratio is termed as the Huygens-Kerker ratio. However, the dipolar Huygens-Kerker radiation remains underexplored in non-vacuum matters, inside which the source locates, especially for surface waves. Here we find that the dipolar Huygens-Kerker radiation of surface waves in principle could occur in non-vacuum matters and is essentially featured with the same normalized radiation pattern, which is closely related to the inclination factor that appears in the Fresnel-Kirchhoff diffraction theory. Moreover, the corresponding Huygens-Kerker ratio is intrinsically determined by the phase velocity of excited surface waves. To be specific, the Huygens-Kerker ratio is proportional to the phase velocity for transverse-magnetic surface waves but becomes inversely proportional to the phase velocity for transverse-electric surface waves.