Canonical Expressions Research Articles

Orbital and Spin Parts of Angular Momentum Flux Density of Monochromatic Radiation in Nonabsorbing Media with Nonlocal Nonlinear Optical Respons

Using electromagnetic field angular momentum conservation law in a form of balance equation, which relates the angular momentum density, the angular momentum flux density and caused by the anisotropy of the medium torque density in nonabsorbing media, we obtained the formulas for the densities of the orbital and spin parts of the angular momentum and the flux densities of this quantities in case of interaction of monochromatic waves in nonabsorbing medium with spatial dispersion demonstrating n-th order nonlinear optical response to the external light field. In media without spatial and frequency dispersion the obtained expressions coinside with the canonical expressions for the densities and flux densities of the orbital and spin parts of angular momentum. The additional terms to the greatest components among the spin parts of angular momentum and its flux related to nonlinearity of the medium may reach ten percent of their linear parts during self-focusing of the elliptically polarized Gaussian laser beam in isotropic gyrotropic medium near the area of its collapse.

Neuroprotective Effect of Solid Lipid Nanoparticles Loaded with Lepidium sativum (L.) Seed Bioactive Components Enhance Bioavailability and Wnt/β-Catenin/Camk-II Signaling Cascade in SH-SY5Y Neuroblastoma Cells.

The primary pathological hallmark of Alzheimer's disease (AD) is the formation and accumulation of neurofibrillary tangles and plaques, which result from the aggregation of amyloid-β (Aβ) induced by oxidative stress. The effectiveness of Alzheimer's disease (AD) therapeutics significantly hinges on the drug's bioavailability and its ability to penetrate neuronal cells. The current investigation was designed as a first attempt to examine bio-fabricated Lepidium sativum (LS) seed-extract-loaded solid lipid nanoparticles (SLNps) to increase bioavailability and bioefficacy for the prevention of undifferentiated SH-SY5Y neuronal cells from oxidative stress induced by H2O2 and amyloid-β peptide (Aβ,1-42). The SLNps were fabricated using LS extract as a water phase and hyaluronic acid and chia seed fatty acids as a lipid phase, then confirmed and characterized using UV, Zeta size, and SEM methods. The biological safety of synthesized LS-SLNps has been determined using MTT assay and PI staining (nuclear damage) in hMSCs. LS-SLNp-pretreated neuronal cells were induced with oxidative stress and 2 µM of beta-amyloid (Aβ,1-42) fibrils; furthermore, the neuroprotective potential of LS-SLNps was determined through the quenching of oxidative stress, enhancing mitochondrial oxidative capacity, and immunoregulatory potential. Observations found that cells treated with both H2O2 and beta-amyloid (Aβ,1-42) fibrils showed decreased neuronal cell growth, nuclear damage, and mitochondrial membrane potential due to oxidative stress. However, SH-SY5Y cells pretreated with LS-SLNps for 24 h showed an increase in cell proliferation with uniform morphology and increased mitochondrial membrane potential compared to cells pretreated with LS alone. Gene expression analysis found that LS-SLNps increased the expression of Wnt 3a and 5a, which stimulated the canonical, β-catenin, and non-canonical Camk-II expressions of nerve cell growth factors, confirming the molecular-level reversal of neurodegenerative diseases.

Cosmological perturbation theory using generalized Einstein–de Sitter cosmologies

The separable analytical solution in standard perturbation theory for an Einstein--de Sitter (EdS) universe can be generalized to the wider class of such cosmologies (``generalized EdS,'' or gEdS) in which a fraction of the pressureless fluid does not cluster. We derive the corresponding kernels in both Eulerian perturbation theory (EPT) and Lagrangian perturbation theory, generalizing the canonical EdS expressions to a one-parameter family where the parameter can be taken to be the exponent $\ensuremath{\alpha}$ of the growing mode linear amplification $D(a)\ensuremath{\propto}{a}^{\ensuremath{\alpha}}$. For the power spectrum (PS) at one loop in EPT, the contribution additional to standard EdS is given, for each of the ``13'' and ``22'' terms, as a function of two infrared safe integrals. In the second part of the paper we show that the calculation of cosmology-dependent corrections in perturbation theory in standard [e.g., Lambda cold dark matter (LCDM)] models can be simplified, and their magnitude and parameter dependence better understood, by relating them to our analytic results for gEdS models. At second order the time dependent kernels are equivalent to the analytic kernels of the gEdS model with $\ensuremath{\alpha}$ replaced by a single redshift dependent effective growth rate ${\ensuremath{\alpha}}_{2}(z)$. At third order the time evolution can be conveniently parametrized in terms of two additional such effective growth rates. For the PS calculated at one-loop order, the correction to the PS relative to the EdS limit can be expressed in terms of just ${\ensuremath{\alpha}}_{2}(z)$, one additional effective growth rate function, and the four infrared safe integrals of the gEdS limit. This is much simplified compared to expressions in the literature that use six or eight redshift dependent functions and are not explicitly infrared safe. Using the analytic gEdS expression for the PS with $\ensuremath{\alpha}={\ensuremath{\alpha}}_{2}(z)$ gives a good approximation (to $\ensuremath{\sim}25%$) for the exact result.

Stochastic Models for the Fading Channel Success Rate of Sub-6G UWB Systems

This paper presents different stochastic models for entangled UWB fading channels. Closed-form canonical expressions are derived for the statistical distribution of the fading power difference of interfering independent and dependent mixture of flat-fading Rayleigh and Rician channels. The link success probability is derived in terms of the cumulative distribution function of the channel fading power differences. An alternative metric for link success rate (LSR) is developed in terms of the statistical distribution of the ratio of the diffuse powers. Under this alternative formulation, and for the case of 2 independent Rayleigh paths, the LSR statistical distribution was consistent with the heavy-tail Lomax distribution. The scope of future research includes the validation of theoretical and simulated models with real measurements on actual multi-user massive multiple-input-multiple-output (MU-mMIMO) beam-forming sub-6G physical systems.

Almost all Classical Theorems are Intuitionistic

Canonical expressions represent the implicative propositions (i.e., the propositions with only implications) up-to renaming of variables. Using a Monte-Carlo approach, we explore the model of canonical expressions in order to confirm the paradox that says that asymptotically almost all classical theorems are intuitionistic. Actually we found that more than 96.6% of classical theorems are intuitionistic among propositions of size 100.

Asymptotic freedom using a gluon mass as a regulator

Front-Form Hamiltonian dynamics provides a framework in which QCD’s vacuum is simple and states are boost invariant. However, canonical expressions are divergent and must be regulated in order to establish well-defined eigenvalue problems. The Renormalization Group Procedure for Effective Particles (RGPEP) provides a systematic way of finding counterterms and obtaining regulated Hamiltonians. Among its achievements is the description of asymptotic freedom, with a running coupling constant defined as the coefficient in front of the three gluon-vertex operators in the regulated Hamiltonian. However, the obtained results need a deeper understanding, since the coupling exhibits a finite dependence on the regularization functions, at least at the third-order term in the perturbative expansion. Here we present a similar derivation using a different regularization scheme based on massive gluons. The procedure can be extended to incorporate contributions from virtual fermions.

General Equations of Non-Degenerate Conics

Abstract In this article, we present a method to obtain equations of non-degenerate conics in an initial Cartesian frame (xOy), starting from their canonical expressions in another Cartesian frame (x′′Cy′′).

Decoding Neuronal Diversification by Multiplexed Single-cell RNA-Seq.

SummaryCellular reprogramming is driven by a defined set of transcription factors; however, the regulatory logic that underlies cell-type specification and diversification remains elusive. Single-cell RNA-seq provides unprecedented coverage to measure dynamic molecular changes at the single-cell resolution. Here, we multiplex and ectopically express 20 pro-neuronal transcription factors in human dermal fibroblasts and demonstrate a widespread diversification of neurons based on cell morphology and canonical neuronal marker expressions. Single-cell RNA-seq analysis reveals diverse and distinct neuronal subtypes, including reprogramming processes that strongly correlate with the developing brain. Gene mapping of 20 exogenous pro-neuronal transcription factors further unveiled key determinants responsible for neuronal lineage specification and a regulatory logic dictating neuronal diversification, including glutamatergic and cholinergic neurons. The multiplex scRNA-seq approach is a robust and scalable approach to elucidate lineage and cellular specification across various biological systems.

Mean Bit Error Rate Analysis of High Rate IEEE 802.15.3.a UWB Channels

In this work, the performance of ultra-wide band systems (UWB) in high-speed wireless networks is studied. At the physical layer of wireless personal area networks, dual carrier modulation driving multiband orthogonal frequency division multiplexing is implemented for 480 Mbps data rates over 4 classes of UWB scattering channels (CM1, CM2, CM3, CM4) bundeled as per the IEEE 802.15.3a UWB standard. Generalized wireless fading models are presented and canonical expressions for mean bit error rates (MBER) are derived for different modulation and receiver diversity combining schemes. A generating model in terms of the characteristic function of the signal-to-noise ratio is introduced for MBER under general statistical fading conditions, which further develops our previous work. The power density spectral characteristic of the multi-user noise is tuned to a novel generalized innovation-matched filter (GIMF) which is at the core of the UWB receiver. Because of its robustness at also capturing the fading characteristics of the UWB channels, the GIMF detector yields better performance than the classical matched filter and a 10-finger RAKE receiver. The relatively flat CM1 channel is proven to have the best performance, while the highly frequency selective CM4 suffers from the worst performance. CM3 channel slightly outperforms CM4 channel between 0 and 5 dB and exhibits significant improvement over CM4 above 5 dB SNR. CM3 and CM4 channels are proven to have nearly identical performance below 0 dB margins. A comparative analysis was also conducted for the MBER of our model and that of the CF-based model at a 10-finger RAKE receiver developed by Wang et al. It was found that our model outperforms that of the CF-model for CM1 and CM2 channels for a wide dynamic range of SNR values. For CM3 and CM4 channels, our model's performance was superior for SNR values below 8 dB.

MET canonical transcript expression is a predictive biomarker for chemo-sensitivity to MET-inhibitors in hepatocellular carcinoma cell lines.

Long interspersed nuclear element 1 (LINE-1 or L1) is a dominant non-long terminal repeat (non-LTR) retrotransposon in the human genome that has been implicated in the overexpression of MET. Both the canonical MET and L1-MET transcripts are considered to play a role in hepatocellular carcinoma (HCC) development. The aim of this study was to assess the utility of canonical MET, L1-MET, and MET protein expressions as predictive biomarkers for chemo-sensitivity to MET-inhibitors in HCC cell lines in vitro. Additionally, we assessed their expression in tumour tissues from Egyptian HCC patients. MET and L1-MET expressions were assessed by qRT-PCR in six liver cancer cell lines (SNU-387, SNU-475, SK-HEP-1, PLC/PRF/5, SNU-449 and SNU-423) and 47 HCC tumour tissues. MET protein expression was measured by western blot in cell lines and immunohistochemistry in the tumours. Cell proliferation assay was used to assess the effect of crizotinib and tivantinib on the six liver cancer cell lines in correlation with the expression of MET, L1-MET and MET. The antitumor effect of crizotinib and tivantinib correlated with MET gene expression but not with L1-MET transcript or MET protein expressions. No significant difference was observed between HCC tumours and non-tumour samples in MET and L1-MET transcripts expression. There were no significant correlations between the 2-year overall survival rate and the MET, L1-MET transcripts and the MET protein expression. MET RNA expression could be useful biomarker for tivantinib and crizotinib targeted therapy in HCC. The value of assessment of MET protein expression is limited.

Canonical Expressions of Algebraic Curvature Tensors

Algebraic curvature tensors can be expressed in a variety of ways, and it is helpful to develop invariants that can distinguish between them. One potential invariant is the signature of R, which could be defined in a number of ways, similar to the signature of an inner product. This paper shows that any algebraic curvature tensor defined on a vector space V with dim(V) = n can be expressed using only canonical algebraic curvature tensors from forms with rank k or higher for any k in {2,...,n}, and that such an expression is not unique, eliminating some possibilities for what one might define the signature of R to be. We also provide bounds on the minimum number of algebraic curvature tensors of rank k needed to express any given R.

The acceptability judgment of Chinese pseudo-modifiers with and without a sentential context

This paper investigates a particular type of non-canonical construction in Mandarin Chinese displaying an apparent semantics-syntax mismatch. We conducted an acceptability judgment experiment on native Mandarin speakers to evaluate whether such sequences could stand out of context as acceptable fragments. Analyses on experimental results revealed that: both semantic and syntactic acceptability of these sequences were significantly lower than those of canonical nominal classifier phrases; whereas if contextualized, the syntactic acceptability of those sequences became similar to that of canonical nominal phrases. This suggests that the non-canonical sequences are grammatically not on the same footing as canonical expressions; and it is the sentential context that makes these sequences appear structurally well-formed. These findings contribute to general discussions on relationship between constituency and grammaticality by demonstrating the gradient nature of grammaticality, and advocate a dynamic perspective in linguistic analysis that looks at a sequence of words in interaction with other elements in a sentence.

Self-consistent theory of transcriptional control in complex regulatory architectures.

Individual regulatory proteins are typically charged with the simultaneous regulation of a battery of different genes. As a result, when one of these proteins is limiting, competitive effects have a significant impact on the transcriptional response of the regulated genes. Here we present a general framework for the analysis of any generic regulatory architecture that accounts for the competitive effects of the regulatory environment by isolating these effects into an effective concentration parameter. These predictions are formulated using the grand-canonical ensemble of statistical mechanics and the fold-change in gene expression is predicted as a function of the number of transcription factors, the strength of interactions between the transcription factors and their DNA binding sites, and the effective concentration of the transcription factor. The effective concentration is set by the transcription factor interactions with competing binding sites within the cell and is determined self-consistently. Using this approach, we analyze regulatory architectures in the grand-canonical ensemble ranging from simple repression and simple activation to scenarios that include repression mediated by DNA looping of distal regulatory sites. It is demonstrated that all the canonical expressions previously derived in the case of an isolated, non-competing gene, can be generalised by a simple substitution to their grand canonical counterpart, which allows for simple intuitive incorporation of the influence of multiple competing transcription factor binding sites. As an example of the strength of this approach, we build on these results to present an analytical description of transcriptional regulation of the lac operon.

ABCB1 and ABCG2 drug transporters are differentially expressed in non-small cell lung cancers (NSCLC) and expression is modified by cisplatin treatment via altered Wnt signaling

BackgroundLung cancer (LC) is still the most common cause of cancer related deaths worldwide. Non-small cell lung cancer (NSCLC) accounts for 85% of all LC cases but is not a single entity. It is now accepted that, apart from the characteristic driver mutations, the unique molecular signatures of adeno- (AC) and squamous cell carcinomas (SCC), the two most common NSCLC subtypes should be taken into consideration for their management. Therapeutic interventions, however, frequently lead to chemotherapy resistance highlighting the need for in-depth analysis of regulatory mechanisms of multidrug resistance to increase therapeutic efficiency.MethodsNon-canonical Wnt5a and canonical Wnt7b and ABC transporter expressions were tested in primary human LC (n = 90) resections of AC and SCC. To investigate drug transporter activity, a three dimensional (3D) human lung aggregate tissue model was set up using differentiated primary human lung cell types. Following modification of the canonical, beta-catenin dependent Wnt pathway or treatment with cisplatin, drug transporter analysis was performed at mRNA, protein and functional level using qRT-PCR, immunohistochemistry, immune-fluorescent staining and transport function analysis.ResultsNon-canonical Wnt5a is significantly up-regulated in SCC samples making the microenvironment different from AC, where the beta-catenin dependent Wnt7b is more prominent. In primary cancer tissues ABCB1 and ABCG2 expression levels were different in the two NSCLC subtypes. Non-canonical rhWnt5a induced down-regulation of both ABCB1 and ABCG2 transporters in the primary human lung aggregate tissue model recreating the SCC-like transporter pattern. Inhibition of the beta-catenin or canonical Wnt pathway resulted in similar down-regulation of both ABC transporter expression and function. In contrast, cisplatin, the frequently used adjuvant chemotherapeutic agent, activated beta-catenin dependent signaling that lead to up-regulation of both ABCB1 and ABCG2 transporter expression and activity.ConclusionsThe difference in the Wnt microenvironment in AC and SCC leads to variations in ABC transporter expression. Cisplatin via induction of canonical Wnt signaling up-regulates ABCB1 and ABCG2 drug transporters that are not transporters for cisplatin itself but are transporters for drugs that are frequently used in combination therapy with cisplatin modulating drug response.

Molecular control of nitric oxide synthesis through eNOS and caveolin-1 interaction regulates osteogenic differentiation of adipose-derived stem cells by modulation of Wnt/β-catenin signaling.

BackgroundNitric oxide (NO) plays a role in a number of physiological processes including stem cell differentiation and osteogenesis. Endothelial nitric oxide synthase (eNOS), one of three NO-producing enzymes, is located in a close conformation with the caveolin-1 (CAV-1WT) membrane protein which is inhibitory to NO production. Modification of this interaction through mutation of the caveolin scaffold domain can increase NO release. In this study, we genetically modified equine adipose-derived stem cells (eASCs) with eNOS, CAV-1WT, and a CAV-1F92A (CAV-1WT mutant) and assessed NO-mediated osteogenic differentiation and the relationship with the Wnt signaling pathway.MethodsNO production was enhanced by lentiviral vector co-delivery of eNOS and CAV-1F92A to eASCs, and osteogenesis and Wnt signaling was assessed by gene expression analysis and activity of a novel Runx2-GFP reporter. Cells were also exposed to a NO donor (NONOate) and the eNOS inhibitor, l-NAME.ResultsNO production as measured by nitrite was significantly increased in eNOS and CAV-1F92A transduced eASCs +(5.59 ± 0.22 μM) compared to eNOS alone (4.81 ± 0.59 μM) and un-transduced control cells (0.91 ± 0.23 μM) (p < 0.05). During osteogenic differentiation, higher NO correlated with increased calcium deposition, Runx2, and alkaline phosphatase (ALP) gene expression and the activity of a Runx2-eGFP reporter. Co-expression of eNOS and CAV-1WT transgenes resulted in lower NO production. Canonical Wnt signaling pathway-associated Wnt3a and Wnt8a gene expressions were increased in eNOS-CAV-1F92A cells undergoing osteogenesis whilst non-canonical Wnt5a was decreased and similar results were seen with NONOate treatment. Treatment of osteogenic cultures with 2 mM l-NAME resulted in reduced Runx2, ALP, and Wnt3a expressions, whilst Wnt5a expression was increased in eNOS-delivered cells. Co-transduction of eASCs with a Wnt pathway responsive lenti-TCF/LEF-dGFP reporter only showed activity in osteogenic cultures co-transduced with a doxycycline inducible eNOS. Lentiviral vector expression of canonical Wnt3a and non-canonical Wnt5a in eASCs was associated with induced and suppressed osteogenic differentiation, respectively, whilst treatment of eNOS-osteogenic cells with the Wnt inhibitor Dkk-1 significantly reduced expressions of Runx2 and ALP.ConclusionsThis study identifies NO as a regulator of canonical Wnt/β-catenin signaling to promote osteogenesis in eASCs which may contribute to novel bone regeneration strategies.Electronic supplementary materialThe online version of this article (doi:10.1186/s13287-016-0442-9) contains supplementary material, which is available to authorized users.

Spectral-Domain Computation of Fields Radiated by Sources in Non-Birefringent Anisotropic Media

We derive the key expressions to robustly address the eigenfunction expansion-based analysis of electromagnetic (EM) fields produced by current sources within planar non-birefringent anisotropic medium (NBAM) layers. In NBAM, the highly symmetric permeability and permittivity tensors can induce directionally-dependent, but polarization independent, propagation properties supporting "degenerate" characteristic polarizations, i.e. four linearly-independent eigenvectors associated with only two (rather than four) unique, non-defective eigenvalues. We first explain problems that can arise when the source(s) specifically reside within NBAM planar layers when using canonical field expressions. To remedy these problems, we exhibit alternative spectral-domain field expressions, immune to such problems, that form the foundation for a robust eigenfunction expansion-based analysis of time-harmonic EM radiation and scattering within such type of planar-layered media. Numerical results demonstrate the high accuracy and stability achievable using this algorithm.

Marginalization in models generated by compositional expressions

In the framework of models generated by compositional expressions, we solve two topical marginalization problems (namely, the single-marginal problem and the marginal-representation problem) that were solved only for the special class of the so-called “canonical expressions”. We also show that the two problems can be solved “from scratch” with preliminary symbolic computation.

Hamiltonian formalism of minimal massive gravity

We study the three-dimensional Minimal Massive Gravity (MMG) in the Hamiltonian formalism. Canonical expressions for the asymptotic conserved charges are derived by defining the canonical gauge generators. Specifically, the construction of asymptotic structure of MMG requires to introduce suitable boundary conditions. For instance, the application of this procedure is done for the BTZ black hole as a solution to the MMG field equations. The related conserved charges give the energy and angular momentum of the BTZ black hole. We also show that the Poisson bracket algebra of the improved canonical gauge generators produces an asymptotic gauge group which includes two separable versions of Virasoro algebras. Finally, we calculate the entropy of black hole from Cardy formula using the parameters of the boundary conformal field theory and show the result is consistent with the value obtained from Smarr one.

Neural Representations of Emotion Are Organized around Abstract Event Features

Research on emotion attribution has tended to focus on the perception of overt expressions of at most five or six basic emotions. However, our ability to identify others' emotional states is not limited to perception of these canonical expressions. Instead, we make fine-grained inferences about what others feel based on the situations they encounter, relying on knowledge of the eliciting conditions for different emotions. In the present research, we provide convergent behavioral and neural evidence concerning the representations underlying these concepts. First, we find that patterns of activity in mentalizing regions contain information about subtle emotional distinctions conveyed through verbal descriptions of eliciting situations. Second, we identify a space of abstract situation features that well captures the emotion discriminations subjects make behaviorally and show that this feature space outperforms competing models in capturing the similarity space of neural patterns in these regions. Together, the data suggest that our knowledge of others' emotions is abstract and high dimensional, that brain regions selective for mental state reasoning support relatively subtle distinctions between emotion concepts, and that the neural representations in these regions are not reducible to more primitive affective dimensions such as valence and arousal.

Chemical Dynamics Simulations of Benzene Dimer Dissociation.

Classical chemical dynamics simulations were performed to study the intramolecular and unimolecular dissociation dynamics of the benzene dimer, Bz2 → 2 Bz. The dissociation of microcanonical ensembles of Bz2 vibrational states, at energies E corresponding to temperatures T of 700-1500 K, were simulated. For the large Bz2 energies and large number of Bz2 vibrational degrees of freedom, s, the classical microcanonical (RRKM) and canonical (TST) rate constant expressions become identical. The dissociation rate constant for each T is determined from the initial rate dN(t)/dt of Bz2 dissociation, and the k(T) are well-represented by the Arrhenius eq k(T) = A exp(-E(a)/RT). The E(a) of 2.02 kcal/mol agrees well with the Bz2 dissociation energy of 2.32 kcal/mol, and the A-factor of 2.43 × 10(12) s(-1) is of the expected order-of-magnitude. The form of N(t) is nonexponential, resulting from weak coupling between the Bz2 intramolecular and intermolecular modes. With this weak coupling, large Bz2 vibrational excitation, and low Bz2 dissociation energy, most of the trajectories dissociate directly. Simulations, with only the Bz2 intramolecular modes excited at 1000 K, were also performed to study intramolecular vibrational energy redistribution (IVR) between the intramolecular and intermolecular modes. Because of restricted IVR, the initial dissociation is quite slow, but N(t) ultimately becomes exponential, suggesting an IVR time of 20.7 ps.