Invariant Expression Research Articles

Moving tubes: the role of walls in a modified Bernoulli equation

Abstract In this paper, standard and introductory examples of fluid dynamics are analyzed from an unusual perspective, choosing reference frames in which the tube carrying the fluid is also moving. In such frames, Bernoulli’s equation is not valid, and to analyze the energy balance one must account for the work exerted by the tube’s wall. This example provides a useful pedagogical bridge between fluid dynamics and mechanics courses, allowing both instructors and curious students to (i) reinforce tools such as the work–energy theorem and (ii) appreciate the special nature of the tube’s rest frame, a point rarely emphasized in textbooks. In addition, it is shown how elementary arguments may be used to construct, for a class of representative examples, a frame invariant expression for the pressure difference.

BTZ and thermal AdS torus partition functions

We rewrite the worldsheet torus partition function of the Thermal AdS CFT by isolating the boundary parameters. Using this, we show that the spectrum of the Euclidean BTZ black hole and Lorentzian AdS3 can be extracted – the latter as a zero temperature limit. A similar procedure recovers the Lorentzian BTZ spectrum proposed in an earlier work. We then use our expression to construct a boundary modular invariant expression as a Poincaré series.

O(9, 25) symmetry of heterotic string theory at orders α′, α′2

In a recent study, we have observed that by imposing a truncated T-duality transformation on the circular reduction of the bosonic couplings in the heterotic theory at four- and six-derivative orders, we can calculate these couplings in a particular YM gauge where the YM potential vanishes but its field strength remains non-zero. Importantly, the coupling constants are independent of the gauge choice, so these results are valid across different YM gauge choices.In this work, we explore the cosmological reduction of these couplings when the YM gauge fields belong to the Cartan subalgebra of SO(32) or E8 × E8. We demonstrate that after applying appropriate one-dimensional field redefinitions and total derivative terms, the couplings can be expressed in a proposed O(9, 25)-invariant canonical form, which is the extension of the canonical O(9, 9)-invariant form for just the NS-NS fields proposed by Hohm and Zwiebach. This O(9, 25)-invariant expression is in terms of the trace of the first time derivative of the generalized metric, which encompasses both the YM field and the NS-NS fields.

Analysis of Deep-Water Low-Frequency Sound Multipath Arrivals and Interference Striation Patterns

The deep-water sound multipath arrivals and interference striation patterns not only vary with range and depth but also with frequency. The first two cases can be solved using a ray-mode method in the high-frequency limit. However, this method may cause unsatisfactory results in treating low-frequency sounds (as low as tens of Hertz) because of the Wentzel-Kramers-Brillouin (WKB) high-frequency approximation assumption. To overcome this problem, the authors exploited phase information to modify the ray parameters, such as the propagation range, the time delay, and the group velocity. Following that, a waveguide invariant (WI) expression was derived to address low-frequency sound interference problems. Numerical investigations demonstrated that the physical mechanism of the frequency dependence of the multipath arrivals and interference striation patterns could be better understood using this modified ray-mode method. In addition, the influence of bottom sound speed on multipath interference structures is also considered.

Relativistic Schrödinger equation and probability currents for free particles

In this work, we start from the problem of quantizing the relativistic Hamiltonian of a free massive particle (rest mass different from 0), a problem exceptionally difficult in the standard approaches to quantum mechanics. In fact, in tempered distribution state space, we find the natural way to define the relativistic Hamiltonian operator and its associated Schrödinger equation The existence of a linear continuous Hermitian operator associated with the Einstein's Hamiltonian of a free particle, defined on the entire tempered distribution space, automatically implies the conservation of Born probability flux (which doesn't mean the conservation of particles number, rather it implies the conservation of the total relativistic energy of the solution wave). We, then, deduce the continuity equation for the Born probability density and study some its different (but equivalent) expressions. We determine some possible forms of probability currents and flux velocity fields associated with the particle evolution. We provide the relativistic invariant expression for both Schrödinger equation and probability flux continuity equations.

Hadrons, superconductor vortices, and cosmological constant

We explore the roles of the trace anomaly in several hadron properties. We derive the scale invariant expression for the pressure from the gravitational form factors (GFF) of QCD which results in consistent results for the mass and rest energy from the GFF and those from the trace and the Hamiltonian of the energy-momentum tensor (EMT) operators. It is shown that the energy-equilibrium correspondence of hadrons infers an equation of state where the trace anomaly matrix element, emerging from the glue condensate in the vacuum, gives a negative constant pressure that leads to confinement, much like the confinement mechanism for the vortices in type II superconductors where the negative constant pressure is due to the cost of depleting the superconducting condensate. We also note that both the trace anomaly in the QCD energy-momentum tensor and the cosmological constant in Einstein's equation are associated with the metric term which contributes to both energy and pressure. Their difference in terms of the role the pressure plays is discussed. Finally, we note that a lattice calculation of the trace anomaly distribution in the pion has addressed a question about the trace anomaly contribution to the pion mass and suggests that there might be a connection between the conformal symmetry breaking and chiral symmetry breaking in this case.

Linguistic Means of Reflection of Characters’ Mimic Gestures in the English Literary Texts of the XIX Century

The complex research of the mimic gestures of characters and their reflection in the English literary texts of the XIX century is carried out. The article reveals common patterns in the functions of nonverbal components of communication that regulate interpersonal relationships and express human emotions in different communicative situations. The national sociocultural and etiquette differences of nonverbal means that were characteristic of stereotypical behavior of the inhabitants of England in the XIX century are substantiated. An invariant (expression of face, smile, look) - variant (semantic and stylistic units) model of organization of means of communication to denote the mimic gestures of characters in the English literary texts of the XIX century is also revealed. Moreover, common patterns and differences in language marking the mimic gestures depending on the positive / negative / neutral reactions of characters in literary communicative situations are identified. Methodological principles of studying kinesics in the paralinguistic aspect are finally determined. Keywords: Communicative Situations, Mimic Gestures, Lexemes, Literary Text, Verbal and Nonverbal Interaction.

Data Normalization of Urine miRNA Profiling from Head and Neck Cancer Patients Treated with Cisplatin.

The microRNA (miRNA) expression profile by qRT-PCR depends directly on the most appropriate normalization strategy adopted; however, currently there is no universally adequate reference gene. Therefore, this study aimed to determine, considering RNA-Seq results, the most adequate endogenous normalizer for use in the relative quantification of urine miRNAs from head and neck cancer patients, treated with cisplatin chemoradiotherapy. The massive sequencing was performed to identify the miRNAs differentially expressed between the group with cisplatin nephrotoxicity (n = 6) and the one without (n = 6). The candidate endogen normalizer was chosen according to four criteria: (1) the miRNA must be expressed in most samples; (2) the miRNA must have a fold change value between 0.99 and 1.01; (3) the miRNA must have a p-value ≥ 0.98; and (4) the miRNA must not be commented on by the final GeneGlobe (Qiagen, Hilden, Germany) analysis. Four miRNAs met all the criteria (hsa-miR-363-5p, hsa-miR-875-5p, hsa-miR-4302, and hsa-miR-6749-5p) and were selected for validation by qRT-PCR in a cohort of 49 patients (including the 12 sequencing participants). Only hsa-miR-875-5p was shown to be an adequate normalizer for the experimental condition under investigation, as it exhibited invariant expression between the two groups.

Primordial black holes and scalar induced gravitational waves from Higgs inflation with noncanonical kinetic term

We resolve the potential-restriction problem in K/G inflation by introducing nonminimal coupling. In this context, Higgs field successfully drives inflation satisfying cosmic microwave background (CMB) observations while enhancing curvature perturbations at small scales, which in turn accounts for primordial black holes (PBHs) and scalar induced gravitational waves (SIGWs). We then uncover the effect of the noncanonical kinetic coupling function in more detail and study its the observational constraint. Besides, we also give the gauge invariant expression for the integral kernel of SIGWs, which is related to terms propagating with the speed of light. Finally, the non-Gaussian effect on PBH abundance and SIGWs is studied. We find that non-Gaussianity makes PBHs form more easily, but its effect on the energy density of SIGWs is negligible.

Autophagy Receptors in the presentation of Viral antigens by MHC-II molecules

CD4+ T lymphocytes play a major role in the establishment and maintenance of antiviral immunity. CD4+ T cells are activated by antigenic peptides, derived from pathogens, presented by MHC-II molecules. It is still widely assumed that CD4+ T cells recognize epitopes derived solely from exogenous viral particles or proteins. However, alternative sources of MHC-II-restricted antigens have been described. We showed that HIV-infected dendritic cells present MHC-II–restricted epitopes derived from newly synthesized proteins to HIV-specific CD4+ T cells. In fact, we confirmed that multiple cellular degradation pathways lead to endogenous presentation of MHC-II-restricted viral antigens, the generation of some viral epitopes being dependent and/or -independent on macroautophagy (herein referred as autophagy). We are charactering further these MHC-II-restricted endogenous presentation pathways. In particular, using RNA silencing, we asked whether autophagy receptors/adaptors that contribute to selective autophagy but also regulate endosome and autophagosome maturation might play a role. Surprisingly, although these receptors share a high structural homology and similar functions, we identified a single autophagy adaptor that strongly influences the presentation of viral antigens by MHC-II molecules. Although silencing of this autophagy adaptor does not impact the expression levels and the recycling of MHC-II molecules, it has a major influence on the ligandome of MHC-II molecules. In the absence of this adaptor, MHC-II molecules accumulate at the proximity of the nucleus in CD63+Lamp1+ acidified compartments. In addition, the lack of this autophagy adaptor has a strong influence on the invariant chain degradation and expression levels, strongly suggesting that it regulates the activation or traffic of vesicles involved in the processing of newly synthesised antigens. Interestingly, some viruses target these autophagy adaptors to favour viral replication. Our work might reveal new escape mechanisms developed by viruses to damper MHC-II restricted antigen presentation and immune responses.

Identification of Human Global, Tissue and Within-Tissue Cell-Specific Stably Expressed Genes at Single-Cell Resolution.

Stably Expressed Genes (SEGs) are a set of genes with invariant expression. Identification of SEGs, especially among both healthy and diseased tissues, is of clinical relevance to enable more accurate data integration, gene expression comparison and biomarker detection. However, it remains unclear how many global SEGs there are, whether there are development-, tissue- or cell-specific SEGs, and whether diseases can influence their expression. In this research, we systematically investigate human SEGs at single-cell level and observe their development-, tissue- and cell-specificity, and expression stability under various diseased states. A hierarchical strategy is proposed to identify a list of 408 spatial-temporal SEGs. Development-specific SEGs are also identified, with adult tissue-specific SEGs enriched with the function of immune processes and fetal tissue-specific SEGs enriched in RNA splicing activities. Cells of the same type within different tissues tend to show similar SEG composition profiles. Diseases or stresses do not show influence on the expression stableness of SEGs in various tissues. In addition to serving as markers and internal references for data normalization and integration, we examine another possible application of SEGs, i.e., being applied for cell decomposition. The deconvolution model could accurately predict the fractions of major immune cells in multiple independent testing datasets of peripheral blood samples. The study provides a reliable list of human SEGs at the single-cell level, facilitates the understanding on the property of SEGs, and extends their possible applications.

Galilean relativity for Brownian dynamics and energetics

We study experimentally the impact of inertial reference frame changes on overdamped Brownian motion. The reference frame changes are implemented by inducing, with a laser, laminar convection flows in a column of fluid where Brownian microspheres are dispersed. The convection flow plays the role of the relative velocity between the laboratory and the fluid comoving frames, and enables us to analyse the consequences of Galilean transformations on Brownian diffusion. We verify in particular how the Brownian dynamics remains ‘weakly’ Galilean invariant, in agreement with recent discussions Cairoli et al (2018 Proc. Natl Acad. Sci. USA 115 5714). We also carefully look at the consequences of Galilean relativity on the Brownian energetics. This leads us to derive a Galilean invariant expression of the stochastic thermodynamic first law, consistent with existing theoretical results Speck et al (2008 Phys. Rev. Lett. 100 178302). We finally discuss a potential ambiguity of the Galilean relativistic features of diffusive systems that has obvious practical implications in the context of force measurements in external flows.

Cross-subject electroencephalogram emotion recognition based on maximum classifier discrepancy

Affective brain-computer interfaces (aBCIs) has important application value in the field of human-computer interaction. Electroencephalogram (EEG) has been widely concerned in the field of emotion recognition due to its advantages in time resolution, reliability and accuracy. However, the non-stationary characteristics and individual differences of EEG limit the generalization of emotion recognition model in different time and different subjects. In this paper, in order to realize the recognition of emotional states across different subjects and sessions, we proposed a new domain adaptation method, the maximum classifier difference for domain adversarial neural networks (MCD_DA). By establishing a neural network emotion recognition model, the shallow feature extractor was used to resist the domain classifier and the emotion classifier, respectively, so that the feature extractor could produce domain invariant expression, and train the decision boundary of classifier learning task specificity while realizing approximate joint distribution adaptation. The experimental results showed that the average classification accuracy of this method was 88.33% compared with 58.23% of the traditional general classifier. It improves the generalization ability of emotion brain-computer interface in practical application, and provides a new method for aBCIs to be used in practice.

Establishment of suitable reference genes for studying relative gene expression during the transition from trophozoites to cyst-like stages and first evidences of stress-induced expression of meiotic genes in Trichomonas vaginalis.

Trichomonas vaginalis is a parasite of the human urogenital tract and the causative agent of trichomoniasis, a sexually transmitted disease of worldwide importance. This parasite is usually found as a motile flagellated trophozoite. However, when subjected to stressful microenvironmental conditions, T. vaginalis trophozoites can differentiate into peculiar cyst-like stages, which exhibit notable physiological resistance to unfavourable conditions. Although well documented in morphological and proteomic terms, patterns of gene expression changes involved in the cellular differentiation into cyst-like stages are mostly unknown. The real-time reverse transcription polymerase chain reaction (RT-qPCR) is recognized as a sensitive and accurate method for quantification of gene expression, providing fluorescence-based data that are proportional to the amount of a target RNA. However, the reliability of relative expression studies depends on the validation of suitable reference genes, which RNAs exhibit a minimum of variation between tested conditions. Here, we attempt to determine suitable reference genes to be used as controls of invariant expression during cold-induced in vitro differentiation of T. vaginalis trophozoites into cyst-like forms. Furthermore, we reveal that the mRNA from the meiotic recombinase Dmc1 is upregulated during this process, indicating that cryptic sexual events may take place in cyst-like stages of T. vaginalis.

Integrating simple genus two string invariants over moduli space

We consider an Sp(4, ℤ) invariant expression involving two factors of the Kawazumi-Zhang (KZ) invariant each of which is a modular graph with one link, and four derivatives on the moduli space of genus two Riemann surfaces. Manipulating it, we show that the integral over moduli space of a linear combination of a modular graph with two links and the square of the KZ invariant reduces to a boundary integral. We also consider an Sp(4, ℤ) invariant expression involving three factors of the KZ invariant and six derivatives on moduli space, from which we deduce that the integral over moduli space of a modular graph with three links reduces to a boundary integral. In both cases, the boundary term is completely determined by the KZ invariant. We show that both the integrals vanish.

The cosmological perturbation theory on the Geodesic Light-Cone background

Inspired by the fully non-linear Geodesic Light-Cone (GLC) gauge, we consider its analogous set of coordinates which describes the unperturbed Universe. Given this starting point, we then build a cosmological perturbation theory on top of it, study the gauge transformation properties related to this new set of perturbations and show the connection with standard cosmological perturbation theory. In particular, we obtain which gauge in standard perturbation theory corresponds to the GLC gauge, and put in evidence how this is a useful alternative to the standard Synchronous Gauge. Moreover, we exploit several viable definitions for gauge invariant combinations. Among others, we build the gauge invariant variables such that their values equal the ones of linearized GLC gauge perturbations. This choice is motivated by two crucial properties of the GLC gauge: i) it admits simple expressions for light-like observables, e.g. redshift and angular distance, at fully non-linear level and ii) the GLC proper time coincides with the one of a free-falling observer. Thanks to the first property, exact expressions can then be easily expanded at linear order to obtain linear gauge invariant expression for the chosen observable. Moreover, the second feature naturally provides gauge invariant expressions for physical observables in terms of the time as measured by such free-falling observer. Finally, we explicitly show all these aspects for the case of the linearized angular distance-redshift relation.

Precise calculation of the decay rate of false vacuum with multi-field bounce

We study the decay rate of a false vacuum in gauge theory at the one-loop level. We pay particular attention to the case where the bounce consists of an arbitrary number of scalar fields. With a multi-field bounce, which has a curved trajectory in the field space, the mixing among the gauge fields and the scalar fields evolves along the path of the bounce in the field space and the one-loop calculation of the vacuum decay rate becomes complicated. We consider the one-loop contribution to the decay rate with an arbitrary choice of the gauge parameter, and obtain a gauge invariant expression of the vacuum decay rate. We also give proper treatments of gauge zero modes and renormalization.

Lewis-Riesenfeld Invariants in Two-level Quantum System Without the Rotating-Wave Approximation

Quantum adiabatic theorem is one of the most important conclusions in quantum mechanics, and is widely used in quantum theory and quantum information technology. However, since quantum adiabatic process is a very slow process, factors such as quantum environmental noise or decoherence will affect the results of quantum adiabatic calculation. Therefore, the shortcut to adiabaticity (STA) theory came into being. In this paper, we study the population inversion in a two-level quantum system within a given time, we propose a Lewis-Riesenfeld invariants technique to realize population transfer for the system without the rotating-wave approximation (RWA). According to the invariant condition, the system time-dependent invariant expression is obtained. The amplitudes of Rabi frequency and detuning in the system could be easily controlled by adjusting control parameters. For population inversion, we can get Rabi frequency and detuning by determining the parameters in the invariant. We analyze the dynamics of the system through invariant operators, therefore, no additional coupling is required. Thereby the high-fidelity population transfer can be implemented in two-level quantum system by our method, and it works even without RWA.

Identification of novel ligands that alter the function of type II NKT cells

Abstract Natural killer T (NKT) cells are distinct innate lymphocytes which recognize lipid antigens in the context of the major histocompatibility complex-like molecule CD1d. When activated, these cells can rapidly produce a variety of cytokines and modulate innate and adaptive immune responses. There are two main subsets of NKT cells, termed type I and type II NKT cells. Type I NKT cells are characterized primarily on the basis of their invariant TCRα expression and reactivity to the glycolipid α-galactosyl ceramide (αGalCer), whereas type II NKT cells express a different and more diverse TCR repertoire than type I NKT cells. Currently, the most widely studied antigen for type II NKT cells is sulfatide. Sulfatide-reactive type II NKT cells are reported to have the immunosuppressive function in autoimmune diseases and cancer. We previously showed a role for sulfatide-reactive type II NKT cells in suppressing tumor immunosurveillance in a murine model of lung metastasis. The activation of type II NKT cells in this model by the injection of sulfatide increased the development of lung metastasis. We synthesized diverse sulfatide-analogues varying in the number of double bonds and hydroxyl groups in the ceramide. In vitro, analogues having a phytosphingosine sphingoid base activated both type II and type I NKT cell hybridomas. On the other hand, the analogue C24:2 with a sphingosine base activated only the type II NKT cell hybridoma. In vivo, the C24:2 analogue significantly reduced the development of lung metastasis, showing distinct and opposite effects from sulfatide. The identification of new ligands inducing altered functional activity of type II NKT cells could be of great interest for developing new anti-tumor immunotherapies.

Invariant expressions for linear complex mechanisms: Single-step substance case

We generalize the results on invariances found for linear two-step mechanisms within our joint kinetics approach. A general invariant expression for any linear complex mechanism with at least two single-step substances is obtained, from corrected ratios of the concentration profiles of single-step substances.The invariant expression consist of the product of three factors of different nature:•A non-thermodynamic factor: the ratio of kinetic coefficients of different chemical reactions.•A thermodynamic factor: the pure or apparent equilibrium constant of a sub-mechanism within the complex mechanism.•An “experimental” factor, defined by the initial conditions of the two experiments needed to determine the invariant expression.The relationship between the structure of the linear complex mechanism and the peculiarities of the invariant expression obtained are presented.A mathematical demonstration of the invariant expression is given. The demonstration is based on an invariant expression from reciprocal experiments, related to Onsager’s reciprocal relations.