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We show coherent photons with spin and orbital angular momentum have symmetry of special unitary group of degree four, SU(4), both theoretically and experimentally. We show the degree of polarisation could be a measure to characterise the quantum coherency of a spin state, which was significantly affected by the partial trace out of orbital degree of freedom. By changing the amplitudes of the classically entangled state, we observed a crossover from quantum Heisenberg spin to classical Ising spin. We also demonstrated projections of coherent states, which recover the coherency of the spin state, while the SU(4) state is projected to be a simple product state of SU(2)×SU(2). Based on the developed platform, we have explored spin texture of coherent photons, and found a unique spin profile reminiscent of the Bengal cat upon wrapping to a three-dimensional sphere. We have controlled the phase between singlet and triplet states and found the spin texture rotated upon increasing the phase.

Spin is a fundamental degree of freedom, which was discovered by Dirac for an electron in his relativistic quantum mechanics, known as the Dirac equation. The origin of spin for a photon is unclear because Maxwell's equations in a vacuum are Lorentz invariant without introducing the concept of spin. Here, the propagation of coherent rays of photons in a graded-index optical fibre is considered to discuss the origin of polarisation for photons using exact solutions of the Laguerre-Gauss and Hermite-Gauss modes. The energy spectrum is massive, and the effective mass is a function of the confinement and orbital angular momentum. The propagation is described by the one-dimensional (1D) non-relativistic Schrödinger equation, which is equivalent to the 2D space-time Klein-Gordon equation by a unitary transformation. The probabilistic interpretation and the conservation law require the factorisation of the Klein-Gordon equation, leading to the 2D Dirac equation with spin. The spin expectation values of photons correspond to the polarisation state on the Poincaré sphere. As an application of the theory, a polarisation interferometer is proposed, whose energy spectrum shows a Dirac cone in the Stokes parameter space.

Polarisation is described by an SU(2) state due to the coherence of photons emitted from a ubiquitous laser source. We propose a polarisation modulator, called as a Poincaré rotator, which enables dynamic control over a polarisation state by executing an arbitrary rotation on the Poincaré sphere. The Poincaré rotator works as an arbitrary operator in the SU(2) Lie group, combining two U(1) operations to change the phase and the amplitude of the state, respectively. By modulating both the phase and amplitude, we have achieved distinguishable 4×4=16, 8×8=64, and 10×10=100 states on the Poincaré sphere. As a locus of the polarisation states on the sphere, we have successfully drawn the molecular structure of Buckminsterfullerene (C60) and the coastline of the Earth.

Stokes parameters (S) on the Poincaré sphere are very useful values to describe the polarisation state of photons. However, the fundamental principle on the nature of polarisation is not completely understood, yet, because we have no concrete consensus on how to describe spin of photons, quantum-mechanically. Here, we have considered a monochromatic coherent ray of photons, described by a many-body coherent state, and established a fundamental basis to describe the spin state of photons, in connection with a classical description based on Stokes parameters. We show that a spinor description of the coherent state is equivalent to Jones vector for polarisation states, and obtain the spin operators (Ŝ) of all components based on rotators in an SU(2) group theory. Polarisation controllers such as phase-shifters and rotators are also obtained as quantum-mechanical field operators to change the phase of the wavefunction for polarisation states. We show that the Stokes parameters are quantum-mechanical average of the spin operators, S=⟨Ŝ⟩.

The polarization state is described by a quantum mechanical two-level system, which is known as special unitary group of degree 2 [SU(2)]. Polarization is attributed to an internal spin degree of freedom inherent to photons, while photons also possess an orbital degree of freedom. A fundamental understanding of the nature of spin and orbital angular momentum of photons is significant to utilize the degrees of freedom for various applications in optical communications, computations, sensing, and laser-patterning. Here, we show that the orbital angular momentum of coherent photons emitted from a laser diode can be incremented using a vortex lens, and the magnitude of orbital angular momentum increases with an increase in the topological charge inside the mode. The superposition state of the left and right vortices is described by the SU(2) state, similar to polarization; however, the radius of the corresponding Poincaré sphere depends on the topological charge. Consequently, we expect a nested SU(2) structure to describe various states with different magnitudes in orbital angular momentum. We have experimentally developed a simple system to realize an arbitrary SU(2) state of orbital angular momentum by controlling both amplitudes and phases of the left and right vortices using a spin degree of freedom, whose interplays were confirmed by expected far-field images of dipoles and quadruples.

Orbital Angular Momentum (OAM) of photons are ubiquitously used for numerous applications. However, there is a fundamental question whether photonic OAM operators satisfy standard quantum mechanical commutation relationship or not; this also poses a serious concern on the interpretation of an optical vortex as a fundamental quantum degree of freedom. Here, we examined canonical angular momentum operators defined in cylindrical coordinates, and applied them to Laguerre-Gauss (LG) modes in a graded index (GRIN) fibre. We confirmed the validity of commutation relationship for the LG modes and found that ladder operators also work properly with the increment or the decrement in units of the Dirac constant (ℏ). With those operators, we calculated the quantum-mechanical expectation value of the magnitude of angular momentum, which includes contributions from both intrinsic and extrinsic OAM. The obtained results suggest that OAM characterised by the LG modes exhibits a well-defined quantum degree of freedom.

Polarisation states are described by spin expectation values, known as Stokes parameters, the trajectories of which in a rotationally symmetric system form a sphere named after Poincaré. Here, we show that the trajectories of broken rotational symmetric systems can exhibit distinct topological structures in polarisation states. We use a phase-shifter to form a polarisation circle (S1), which interferes with the original input due to the phase change of the output state upon rotation. By rotating the circle using a rotator, the trajectories become a polarisation torus (S1×S1), which was experimentally confirmed in a simple setup using passive optical components together with the Mach–Zehnder interferometer. We also discuss the realisations of other topological features, such as a Möbius strip, a trefoil knot, Hopf links, and topological Dirac bosons, with a bulk-edge correspondence.

Twisted photons with finite orbital angular momentum have a distinct mode profile with topological charge at the center of the mode while propagating in a certain direction. Each mode with different topological charges of m is orthogonal, in the sense that the overlap integral vanishes among modes with different values of m. Here, we theoretically consider a superposition state among three different modes with left and right vortices and a Gaussian mode without a vortex. These three states are considered to be assigned to different quantum states; thus, we employed the su(3) Lie algebra and the associated SU(3) Lie group to classify the photonic states. We calculated expectation values of eight generators of the su(3) Lie algebra, which should be observable, since the generators are Hermite matrices. We proposed to call these parameters Gell-Mann parameters, named after the theoretical physicist Murray Gell-Mann, who established quantum chromodynamics (QCD) for quarks. The Gell-Mann parameters are represented on the eight-dimensional hypersphere with its radius fixed due to the conservation law of the Casimir operator. Thus, we discussed a possibility of exploring photonic QCD in experiments and classified SU(3) states to embed the parameters in SO(6) and SO(5).

The speed of light (c) in a vacuum is independent of the choice of frames to describe the propagation, according to the theory of relativity. We consider how light is characterised in a material, where the speed of light is different from that in a vacuum due to the finite dielectric constant. The phase velocity in a material is smaller than c, such that the speed of a moving frame can be larger than the phase velocity, such that the frame can move faster than the speed of light in a material. Consequently, an unusual Doppler effect is expected, and the wavelength in the moving frame changes from the red-shift to the blue-shift upon increasing the speed of the frame. The corresponding energy of the light also changes sign from positive to negative, while momentum is always positive, leading to the changes of signs for the phase velocity and the helicity. In a graded index fibre, where the exact solution is available, even more complicated phenomena are expected, due to the finite effective mass of photons. Upon the increase of the energy gap, generated by optical confinements and optical orbital angular momentum, the effective mass of photons increases. If the gap is large enough, momentum starts to change the sign upon increasing the frame velocity, while the energy of photons is always positive. In this case, the phase velocity diverges if momentum is in agreement with the fame velocity. Contrary to the unusual behaviours of the phase velocity, the group velocity is always below c. This thought experiment might be useful for considering insight into the polarisation state of light.

Spin angular momentum of a photon corresponds to a polarisation degree of freedom of lights, and such that various polarisation properties are coming from macroscopic manifestation of quantum-mechanical properties of lights. An orbital degree of freedom of lights is also manipulated to form a vortex of lights with orbital angular momentum, which is also quantised. However, it is considered that spin and orbital angular momentum of a photon cannot be split from the total orbital angular momentum in a gauge-invariant way. Here, we revisit this issue for a coherent monochromatic ray from a laser source, propagating in a waveguide. We obtained the helical components of spin and orbital angular momentum by the correspondence with the classical Ponyting vector. By applying a standard quantum field theory using a coherent state, we obtained the gauge-independent expressions of spin and orbital angular momentum operators. During the derivations, it was essential to take a finite cross-sectional area into account, which leads the finite longitudinal component along the direction of the propagation, which allows the splitting. Therefore, the finite mode profile was responsible to justify the splitting, which was not possible as far as we were using plane-wave expansions in a standard theory of quantum-electrodynamics (QED). Our results suggest spin and orbital angular momentum are well-defined quantum-mechanical freedoms at least for coherent photons propagating in a waveguide and in a vacuum with a finite mode profile.

Lie algebra is a hidden mathematical structure behind various quantum systems realised in nature. Here, we consider SU(2) wavefunctions for polarisation states of coherent photons emitted from a laser source, and discuss the relationship to spin expectation values with SO(3) symmetry based on isomorphism theorems. In particular, we found rotated half-wave-plates correspond to mirror reflections in the Poincaré sphere, which do not form a subgroup in the projected O(2) plane due to anti-hermitian property. This could be overcome experimentally by preparing another half-wave-plate to realise a pristine rotator in SU(2), which allows arbitrary rotation angles determined by the physical rotation. By combining another 2 quarter-wave-plates, we could also construct a genuine phase-shifter, thus, realising passive control over the full Poincaré sphere.

AbstractElucidating genotype-by-environment interactions is fundamental for understanding the interplay between genetic and environmental factors that shape complex traits in crops. Genotype-by-environment interactions are of practical importance, as they determine the performance of cultivars grown in different environments, prompting the need for an efficient approach for evaluating genotype-by-environment interactions. Here, we describe a method for genotype-by-environment detection that involves comparing linear mixed models. This method successfully detected genotype-by-environment interactions in rice (Oryza sativa

Abstract Group IV light sources with vertical emission and non-zero orbital-angular momentum (OAM) promise to unlock many novel applications. In this report, we demonstrate cylindrically symmetrical germanium micro-gear cavities, fabricated by etching a grating around the circumference of standard micro-disks, with periods ranging from 14 to 22. Photoluminescence (PL) measurements were done to identify the confined whispering-gallery modes (WGM). Finite-difference time-domain (FDTD) simulations were conducted to map the resonant modes to their modal profiles and characteristics. Vertical emission of WGMs with non-zero OAM was demonstrated, with a clear dependence of the OAM order ( $$\ell$$ ℓ ) on the WGM azimuthal order and the number of micro-gear grating periods. As the chirality, or the direction of rotation, is not controlled in a symmetrical cavity, we propose introducing staircase or triangular-shaped gear periods resulting in an asymmetry. By choosing the diameter, number of periods, and the asymmetrical direction of the gear-teeth, it is possible to generate OAM signals with certain wavelength, OAM order and chirality.

A technique for realizing electrically erasable photonics devices using micro-heaters for localized annealing of lattice defects in silicon is presented. The lattice defects have previously been introduced by ion implantation in order to cause a refractive index change. This technique can be used to fabricate electrically erasable on-chip directional couplers (DCs) and Mach-Zehnder Interferometer (MZI) switches. These devices can be used for wafer scale testing of photonics circuits, allowing testing of individual optical components in a complex photonic integrated circuit, or components for programmable optical circuits, whilst inducing negligible additional optical loss when erased electrically. In this paper, we report the designs and experimental results of fully, rapidly annealing of these devices.

In this paper we demonstrate that by breaking the left/right symmetry in a bi-planar double-silicon on insulator (SOI) photonic crystal (PhC) fin-waveguide, we can couple the conventionally used transverse-electric (TE) polarized mode to the transverse-magnetic (TM) polarization slot-mode. Finite difference time domain (FDTD) simulations indicate that the TE mode couples to the robust TM mode inside the Brillouin zone. Broadband transmission data shows propagation identified with horizontal-slot TM mode within the TE bandgap for fully mismatched fabricated devices. This simultaneously demonstrates TE to TM mode conversion, and the narrowest Si photonics SiO2 slot-mode propagation reported in the literature (10 nm wide slot), which both have many potential telecommunication applications.

A Poincaré sphere is a powerful prescription to describe a polarized state of coherent photons, oscillating along certain directions. The polarized state is described by a vector in the sphere, and various passive optical components, such as polarization plates and quartz rotators are able to rotate the vectorial state by changing the phase and the amplitude among two orthogonal basis states. The polarization is originated from spin of photons, and recently, significant attentions have been made for optical Orbital Angular Momentum (OAM) as another fundamental degree of freedom for photons. The beam shape of photons with OAM is a vortex with a topological charge at the core, and the state of vortexed photons can be described by a hyper-Poincaré sphere. Here, we propose a compact Poincaré rotator, which controls a vortexed state of photons in a silicon photonic platform, based on Finite-Difference Time-Domain (FDTD) simulations. A ring-shaped gear is evanescently coupled to two silicon photonic waveguides, which convert optical momentum to OAM with both left and right vortexed states. By controlling the relative phase and the amplitude of two traveling waves in input ports, we can control the vortexed states in the hyper-Poincaré sphere for photons out of the gear. The impact of the geometrical Pancharatnam-Berry-Guoy's phase and the conservation law of spin and OAM for vortexed photons out of the gear are discussed.

Germanium (Ge) ion implantation into silicon waveguides will induce lattice defects in the silicon, which can eventually change the crystal silicon into amorphous silicon and increase the refractive index from 3.48 to 3.96. A subsequent annealing process, either by using an external laser or integrated thermal heaters can partially or completely remove those lattice defects and gradually change the amorphous silicon back into the crystalline form and, therefore, reduce the material’s refractive index. Utilising this change in optical properties, we successfully demonstrated various erasable photonic devices. Those devices can be used to implement a flexible and commercially viable wafer-scale testing method for a silicon photonics fabrication line, which is a key technology to reduce the cost and increase the yield in production. In addition, Ge ion implantation and annealing are also demonstrated to enable post-fabrication trimming of ring resonators and Mach–Zehnder interferometers and to implement nonvolatile programmable photonic circuits.

The need for hardware random number generators (HRNGs) that can be integrated in a silicon (Si) complementary-metal–oxide–semiconductor (CMOS) platform has become increasingly important in the era of the Internet-of-Things (IoT). Si MOSFETs exhibiting random telegraph signals (RTSs) have been considered as such a candidate for HRNG, though its application has been hindered by RTS’s variability and uncontrollable, unpredictable characteristics. In this paper, we report the generation and randomness evaluation of random numbers from RTSs in a Si single electron pump (SEP) device at room temperature. SEP devices are known to consistently produce RTSs due to a quantum dot electrically defined by multi-layer polycrystalline Si gates. Using RTSs observed in our devices, random numbers were extracted by a classifier supported by supervised learning, where part of data was used to train the classifier before it is applied to the rest to generate random numbers. The random numbers generated from RTSs were used as inputs for the Monte Carlo method to calculate the values of π, and the distribution was compared against the result obtained from the Mersenne Twister, a representative pseudo-random number generator (PRNG), under the same condition. π was estimated more than 80 000 times, and the distribution of the estimated values has a central value of 3.14 with a variance of 0.273, which is only twice as large as the result from PRNG. Our result paves a way to fully electronic CMOS compatible HRNGs that can be integrated in a modern system-on-a-chip in IoT devices.

While the importance of atomic-scale features in silicon-based device for quantum application has been recognized and even the placement of a single atom is now feasible, the role of a dopant in the substrate has not attracted much attention in the context of quantum technology. In this paper, we report random telegraph signals (RTSs) originated from trapping and detrapping of an electron by a donor in the substrate of a p-type metal–oxide–semiconductor field-effect-transistor. RTSs, not seen when the substrate was grounded, were observed when a positive bias was applied to the substrate. The comprehensive study on the signals observed reveals that the nature of the RTSs is discrete threshold voltage variations due to the change in the depletion layer width depending on the charge state of a single dopant, neutral or positively charged.

We show a manipulation of a single electron at room temperature by controlling Random Telegraph Signals (RTSs) by voltage pulses. Our silicon nanowire triple-gate transistor exhibited RTSs when potential barriers were electrically created by two of the three gates. From the statistics of the signals, we optimized the voltage pulse such that a single electron was intentionally captured in the potential well, and the retention time of approximately 10 ms was observed in this memory operation. This study indicates that a single electron effect can be controllable in a form of RTSs at room temperature by electrically defining a potential well.

In a line-defect waveguide of a planer photonic crystal (PhC), we found a new rotational state of polarized light, which exhibits “polarization rotation” on the PhC plane, when a phase mismatch m was added to the air-hole alignment of the waveguide, where mode splitting was simultaneously observed in the dispersion curve. To account for the polarization rotation together with the mode splitting, we propose a two-state model that is constructed from Schrödinger equation obtained from the equation for electromagnetic waves. The proposed two-state model gives an explanation on the relation between the polarization-rotational angle θ and the mismatch m and on its rotational direction (i.e., clockwise or anticlockwise direction) that depends on the mode. Using the two-state model, we also discuss the angular momenta of the polarized light in the PhC waveguide, which are directly related to the Stokes parameters that characterize the polarization rotations.

Carbon allotropes such as diamond, nano-tube, Fullerene, and Graphene were discovered and revolutionised material sciences. These structures have unique translational and rotational symmetries, described by a crystallographic group theory, and the atoms are arranged at specific rigid positions in 3-dimensional ( D ) space. Regardless of these exotic molecular structures, the structures of materials are topologically trivial in a mathematical sense, that their bonds are connected without a link nor a knot. These days, the progress on the synthetic chemistry is significant to make various topologically non-trivial molecular structures. Topological molecules (0 D ) including Trefoil knots, a Hopf-link, a Möbius strip, and Borromean rings, were already realised. However, their potentially exotic electronic properties have not been sufficiently explored. Here, we propose a new 3D carbon allotrope, named Hopfene, which has periodic arrays of Hopf-links to knit horizontal Graphene sheets into vertical ones without connecting by σ bonds. We conducted an ab inito band structure calculation using a Density-Functional-Theory (DFT) for Hopfene, and found that it is well-described by a tight-binding model. We confirmed the original Dirac points of 2 D Graphene were topologically protected upon the introduction of the Hopf links, and low-energy excitations are described by 1 D , 2 D , and 3 D gapless Fermions.

We demonstrate low-loss slot waveguides on silicon-on-insulator (SOI) platform. Waveguides oriented along the (11-2) direction on the Si (110) plane were first fabricated by a standard e-beam lithography and dry etching process. A TMAH based anisotropic wet etching technique was then used to remove any residual side wall roughness. Using this fabrication technique propagation loss as low as 3.7dB/cm was realized in silicon slot waveguide for wavelengths near 1550nm. We also realized low propagation loss of 1dB/cm for silicon strip waveguides.

We have proposed a topological carbon allotrope, named Hopfene, which has three-dimensional (3 D ) arrays of Hopf-links to bind 2 D Graphene layers both horizontally and vertically without forming strong σ bonds between layers. Tight-binding calculations show unique band structures of this crystal, which predicts semi-metal characteristics with the existence of both Weyl and Dirac Fermions depending on the Fermi energy. Here, we have theoretically examined superconductivity of Hopfene based on the attractive Hubbard model. Regardless of its simplicity of the model, we found non-trivial competitions between Hartree–Fock mean-field contributions and Cooper-paring interactions to open semiconductor and superconducting energy gaps, respectively. Consequently, the superconducting order parameters are significantly reduced at every quarterly doping concentration, where the system is in the close vicinity of the quantum critical point, and we found superconductor-insulator transition in the strong coupling limit. Upon doping, we confirmed a classical scenario of a smooth crossover from weak coupling Bardeen-Cooper-Schrieffer (BCS) superconductivity to strong coupling Bose–Einstein Condensation (BEC) of preformed pairs by increasing the interaction strength. We think the proposed Hopfene is a useful platform to investigate the impacts of the topological nature of the Fermi surfaces on the superconductivity and other orders, including charge-density-waves and magnetic orders, and possible quantum phase transitions among them.

Organic–inorganic hybrid molecules constitute analytical tools used in biological systems. Vascular endothelial cells synthesize and secrete proteoglycans, which are macromolecules consisting of a core protein and glycosaminoglycan side chains. Although the expression of endothelial proteoglycans is regulated by several cytokines/growth factors, there may be alternative pathways for proteoglycan synthesis aside from downstream pathways activated by these cytokines/growth factors. Here, we investigated organic–inorganic hybrid molecules to determine a variant capable of analyzing the expression of syndecan-4, a transmembrane heparan-sulfate proteoglycan, and identified 1,10-phenanthroline (o-Phen) with or without zinc (Zn-Phen) or rhodium (Rh-Phen). Bovine aortic endothelial cells in culture were treated with these compounds, and the expression of syndecan-4 mRNA and core proteins was determined by real-time reverse transcription polymerase chain reaction and Western blot analysis, respectively. Our findings indicated that o-Phen and Zn-Phen specifically and strongly induced syndecan-4 expression in cultured vascular endothelial cells through activation of the hypoxia-inducible factor-1α/β pathway via inhibition of prolyl hydroxylase-domain-containing protein 2. These results demonstrated an alternative pathway involved in mediating induction of endothelial syndecan-4 expression and revealed organic–inorganic hybrid molecules as effective tools for analyzing biological systems.

Renin-angiotensin system (RAS) plays a pivotal role in chronic kidney disease (CKD). Angiotensin converting enzyme-related carboxypeptidase 2 (ACE2)/angiotensin (Ang)-(1-7)/Mas receptor axis counteracts the deleterious actions of Ang II. ACE2 exerts its actions by cleaving Ang II into Ang-(1-7) which activates Mas receptor. This study aimed to determine if the expression of Mas receptor is altered in the kidneys of CKD rats, and if indoxyl sulfate (IS), a uremic toxin, affects the expression of Mas receptor in rat kidneys and cultured human proximal tubular cells (HK-2 cells). The expression of Mas receptor was examined in the kidneys of CKD and AST-120-treated CKD rats using immunohistochemistry. Further, the effects of IS on Mas receptor expression in the kidneys of normotensive and hypertensive rats were examined. The effects of IS on the expression of Mas receptor and phosphorylation of endothelial nitric oxide synthase (eNOS) in HK-2 cells were examined using immunoblotting. CKD rats showed reduced renal expression of Mas receptor, while AST-120 restored its expression. Administration of IS downregulated Mas receptor expression in the kidneys of normotensive and hypertensive rats. IS downregulated Mas receptor expression in HK-2 cells in a time- and dose-dependent manner. Knockdown of organic anion transporter 3 (OAT3), aryl hydrocarbon receptor (AhR), and signal transducer and activator of transcription 3 (Stat3) inhibited IS-induced downregulation of Mas receptor and phosphorylated eNOS. N-acetylcysteine, an antioxidant, also inhibited IS-induced downregulation of Mas receptor and phosphorylated eNOS. Ang-(1-7) attenuated IS-induced transforming growth factor-β1 (TGF-β1) expression.Mas receptor expression is reduced in the kidneys of CKD rats. IS downregulates renal expression of Mas receptor via OAT3/AhR/Stat3 pathway in proximal tubular cells. IS-induced downregulation of Mas receptor might be involved in upregulation of TGF-β1 in proximal tubular cells.

Chronic kidney disease (CKD) is associated with an increased risk of cardiovascular disease (CVD). (Pro)renin receptor (PRR) is activated in the kidney of CKD. The present study aimed to determine the role of indoxyl sulfate (IS), a uremic toxin, in PRR activation in rat aorta and human aortic smooth muscle cells (HASMCs). We examined the expression of PRR and renin/prorenin in rat aorta using immunohistochemistry. Both CKD rats and IS-administrated rats showed elevated expression of PRR and renin/prorenin in aorta compared with normal rats. IS upregulated the expression of PRR and prorenin in HASMCs. N-acetylcysteine, an antioxidant, and diphenyleneiodonium, an inhibitor of nicotinamide adenine dinucleotide phosphate oxidase, suppressed IS-induced expression of PRR and prorenin in HASMCs. Knock down of organic anion transporter 3 (OAT3), aryl hydrocarbon receptor (AhR) and nuclear factor-κB p65 (NF-κB p65) with small interfering RNAs inhibited IS-induced expression of PRR and prorenin in HASMCs. Knock down of PRR inhibited cell proliferation and tissue factor expression induced by not only prorenin but also IS in HASMCs.IS stimulates aortic expression of PRR and renin/prorenin through OAT3-mediated uptake, production of reactive oxygen species, and activation of AhR and NF-κB p65 in vascular smooth muscle cells. IS-induced activation of PRR promotes cell proliferation and tissue factor expression in vascular smooth muscle cells.