Triple Correlation Research Articles

Triple correlations of Fourier coefficients of cusp forms

We treat an unbalanced shifted convolution sum of Fourier coefficients of cusp forms. As a consequence, we obtain an upper bound for correlation of three Hecke eigenvalues of holomorphic cusp forms \(\sum _{H\le h\le 2H}W\left( \frac{h}{H}\right) \sum _{X\le n\le 2X}\lambda _{1}(n-h)\lambda _{2}(n)\lambda _{3}(n+h)\), which is nontrivial provided that \(H\ge X^{2/3+\varepsilon }\). The result can be viewed as a cuspidal analogue of a recent result of Blomer on triple correlations of divisor functions.

A new technique for measuring single-shot ultrashort laser pulse

A new triple correlation technique for measuring intensity profile of single-shot ultrashort laser pulse is described. The technique uses two consecutive second-order nonlinear interactions of replicas of the pulse for generating a two-coordinate output intensity distribution that corresponds to a third-order correlation function and offers advantages over the previously techniques such as frequency-resolved optical gating, self-referencing spectral phase interferometry for direct field reconstruction because it requires no additional spectral information to profile the pulses. This intensity distribution is recorded, and the pulse profile can be obtained by analytical calculation. Combining the reconstructed intensity profile with its corresponding optical spectrum, the exact phase variation in time can be recovered with Gerchberg-Saxton algorithm through an iterative calculation.

Triple correlations of multiplicative functions

In this paper, we find asymptotic formula for the following sum with explicit error term: \[M_{x}(g_{1}, g_{2}, g_3)=\frac{1}{x}\sum_{n\le x}g_{1}(F_1(n))g_{2}(F_2(n))g_{3} (F_3(n)),\] where $F_1(x), F_2(x)$ and $F_3(x)$ are polynomials with integer coefficients and $g_1,g_2,g_3$ are multilpicative functions with modulus less than or equal to $1.$ Moreover, under some assumption on $g_1,g_2,$ we prove that as $x\rightarrow \infty,$ \[\frac{1}{x}\sum\limits_{n\le x}g_1(n+3)g_2(n+2)\mu(n+1)=o(1)\] and assuming $2$-point Chowla type conjecture we show that as $x\rightarrow \infty,$ \[\frac{1}{x}\sum\limits_{n\le x}g_1(n+3)\mu(n+2)\mu(n+1)=o(1).\]

On triple correlations of divisor functions

We prove an asymptotic formula with power saving error term for a certain triple divisor sum.

Right-handed neutrinos and T-violating, P-conserving interactions

We show that experimental probes of the P-conserving, T-violating triple correlation in polarized neutron or nuclear $\beta$-decay provide a unique probe of possible T-violation at the TeV scale in the presence of right-handed neutrinos. In contrast to other possible sources of semileptonic T-violation involving only left-handed neutrinos, those involving right-handed neutrinos are relatively unconstrained by present limits on the permanent electric dipole moments of the electron, neutral atoms, and the neutron. On the other hand, LHC results for $pp\to e+$ missing transverse energy imply that an order of magnitude of improvement in $D$-coefficient sensitivity would be needed for discovery. Finally, we discuss the interplay with the scale of neutrino mass and naturalness considerations.

Determination of ligand binding modes in weak protein-ligand complexes using sparse NMR data.

We describe a general approach to determine the binding pose of small molecules in weakly bound protein-ligand complexes by deriving distance constraints between the ligand and methyl groups from all methyl-containing residues of the protein. We demonstrate that using a single sample, which can be prepared without the use of expensive precursors, it is possible to generate high-resolution data rapidly and obtain the resonance assignments of Ile, Leu, Val, Ala and Thr methyl groups using triple resonance scalar correlation data. The same sample may be used to obtain Met εCH3 assignments using NOESY-based methods, although the superior sensitivity of NOESY using [U-13C,15N]-labeled protein makes the use of this second sample more efficient. We describe a structural model for a weakly binding ligand bound to its target protein, DsbA, derived from intermolecular methyl-to-ligand nuclear Overhauser enhancements, and demonstrate that the ability to assign all methyl resonances in the spectrum is essential to derive an accurate model of the structure. Once the methyl assignments have been obtained, this approach provides a rapid means to generate structural models for weakly bound protein-ligand complexes. Such weak complexes are often found at the beginning of programs of fragment based drug design and can be challenging to characterize using X-ray crystallography.

F27 - Tumor infiltrating lymphocytes in triple negative breast cancer and correlations with prognosis

Background: Following the development of drugs reactivating the immune system, the need to identify immunological markers that can provide prognostic and predictive information is rapidly increasing. This is mainly relevant in triple negative breast cancers, due to their immunogenic potential. Tumor infiltrating lymphocytes (TILs) have been claimed as possible biomarkers of such immune activation, and we investigated their correlation with prognosis. Material and methods: We retrospectively quantified the stromal TILs in 71 triple negative breast cancer patients (pts) surgically treated. TILs were stained with hematoxylin and eosin and were analyzed according to recommendations of TILs Working Group Consensus. TILs were classified as low if ≤ 10% (L-TILs), as intermediate between 10 and 40% (I-TILs) and as high if > 40% (H-TILs). TILs subsets were correlated with TNM stage, proliferative activity, vascular invasion, adjuvant treatment and disease outcome (DFS and OS). Finally we analyzed the influence of TILs on DFS and OS in 43 TN pts with very bad prognostic factors, defined as pT > 5 cm, pN ≥ 2, presence of vascular invasion and proliferative activity ≥ 70%. Results: Twenty-two pts had L-TILs (31%), 13 pts I-TILs (18.3%) and 36 pts had H-TILs (50.3%). Seventeen pts (23.9%) had disease recurrence, 8 of which at nervous central system. Among TILs subgroups, disease progression occurred more frequently in L-TILs pts (63.6% (mDFS), and in I-TILs (53.8%) than in H-TILs (7.3%). Median DFS was 15.1 mos (95%IC 9.7-20.5) in L-TILs, 56.3 mos (26.5-86.1 mos) in I-TILs and was not reached in H-TILs. Similarly, mOS was 29.3 mos in L-TILs, 74.1 mos in I-TILs and not reached in H-TILs (p < 0.0001). Multivariate analysis showed that TILs subsets constitute an independent prognostic factor for both DFS (HR 0.343, p = 0.006) and OS (HR 0.475, p = 0.009). Also among the 43 TN pts with bad prognostic factors, 66.7% in L-TILs pts showed disease progression, 62.5% in I-TILs pts and 0% in H-TILs pts (p < 0.0001). Conclusions: Our study confirms that stromal TILs subsets, evaluated with hematoxylin and eosin, are independent prognostic factors in triple negative breast cancer patients, with H-TILs subset being associated with a favourable outcome. Moreover, the prognostic value of TILs is maintained even in pts with more unfavorable prognosis, based on classical clinico-pathological features. The adjuvant strategy in TN breast cancer with H-TILs should be re-evaluated.

Erratum: "Experimental observation of triple correlations in fluids" [Condens. Matter Phys., 2013, 16, No. 1, 13003: 1-12; DOI:10.5488/CMP.16.13003

Erratum: "Experimental observation of triple correlations in fluids" [Condens. Matter Phys., 2013, 16, No. 1, 13003: 1-12; DOI:10.5488/CMP.16.13003

The MTV experiment: searching for T-violation in polarized Li-8 at TRIUMF

The MTV experiment (Mott Polarimetry for T-Violation Experiment) is running at TRIUMF, to search for a large T-violating transverse electron-polarization in polarized 8Li β-decay. We aim at reaching precision of 10−4 for the R-correlation, which is defined as a T-violating triple vector correlation in the β-decay rate function. A Mott polarimeter system using a CDC (Cylindrical Drift Chamber) is used to measure the left-right scattering asymmetry in the Mott scattering from a thin metal foil. In the present study, we aim to discuss systematic effects in Mott polarimetry using the CDC.

Blind estimation of pseudo‐random codes in periodic long code direct sequence spread spectrum signals

An estimation method of pseudo-random (PN) codes in the periodic long code direct sequence spread spectrum signals using a pair of spreading code and scrambling code [i.e. long scrambling code direct sequence spread spectrum (LSC-DSSS)] is investigated in this study. Via the investigation of properties of triple correlation function (TCF) of m-sequences, the existence of common peaks in the TCFs of different m-sequences is proved, and the corresponding relationship between common peaks and primitive polynomials is further investigated. Four theorems are proposed as supplements of triple correlation theory and a novel estimation algorithm of the PN codes in LSC-DSSS signals is put forward on the basis of the theorems. With certain carrier frequency and chip rate of spreading code, this algorithm first eliminates the influence of information codes through delay-and-multiply operation. Then the TCF of signal is calculated, and the two PN codes in signal are successfully estimated finally by searching and using the common peak coordinates in the TCF. Simulation results show that the proposed algorithm exhibits excellent performance in estimating PN codes in LSC-DSSS signals.

Analyzing Quantum Correlations Made Simple

AbstractThe understanding of correlations in degenerate nonideal many‐particle systems is complex and theoretically challenging. Using the recently proposed permutation blocking path integral Monte Carlo (PB‐PIMC) scheme, which allows for an exact treatment of many‐body correlations, we study the influence of quantum statistics in a confined few‐particle Coulomb (quantum dot) system. As a versatile tool to gain insight into the internal structure of correlated many‐body systems, the application of triple correlation functions is extended to quantum systems. (© 2016 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors

A nonlinear spectral model in terms of spherically averaged descriptors is derived for the prediction of homogeneous turbulence dynamics in the presence of arbitrary mean-velocity gradients. The governing equations for the tensor $\hat{\unicode[STIX]{x1D619}}_{ij}(\boldsymbol{k},t)$, the Fourier transform of the two-point second-order correlation tensor, are first closed by an anisotropic eddy-damped quasinormal Markovian procedure. This closure is restricted to turbulent flows where linear effects induced by mean-flow gradients have no essential qualitative effects on the dynamics of triple correlations compared with the induced production effects in the equations for second-order correlations. Truncation at the first relevant order of spectral angular dependence allows us to derive from these equations in vector $\boldsymbol{k}$ our final model equations in terms of the wavenumber modulus $k$ only. Analytical spherical integration results in a significant decrease in computational cost. Besides, the model remains consistent with the decomposition in terms of directional anisotropy and polarization anisotropy, with a spherically averaged anisotropic spectral tensor for each contribution. Restriction of anisotropy to spherically averaged descriptors, however, entails a loss of information, and realizability conditions are considered to quantify the upper boundary of anisotropy that can be investigated with the proposed model. Several flow configurations are considered to assess the validity of the present model. Satisfactory agreement with experiments on grid-generated turbulence subjected to successive plane strains is observed, which confirms the capability of the model to account for production of anisotropy by mean-flow gradients. The nonlinear transfer terms of the model are further tested by considering the return to isotropy (RTI) of different turbulent flows. Different RTI rates for directional anisotropy and polarization anisotropy allow us to correctly predict the apparent delayed RTI shown after axisymmetric expansion. The last test case deals with homogeneous turbulence subjected to a constant pure plane shear. The interplay between linear and nonlinear effects is reproduced, yielding the eventual exponential growth of the turbulent kinetic energy.

Core-core and core-valence correlation energy atomic and molecular benchmarks for Li through Ar.

We have established benchmark core-core, core-valence, and valence-valence absolute coupled-cluster single double (triple) correlation energies (±0.1%) for 210 species covering the first- and second-rows of the periodic table. These species provide 194 energy differences (±0.03 mEh) including ionization potentials, electron affinities, and total atomization energies. These results can be used for calibration of less expensive methodologies for practical routine determination of core-core and core-valence correlation energies.

Large low probability of intercept properties of the quaternary sequence with optimal correlation property constructed by legendre sequences

In this paper, we consider the Low Probability of Intercept(LPI) property of the quaternary sequence proposed by Kim, Jang, Kim, and No. We derive the LPI property of the sequence by calculating the triple autocorrelation bound of the sequence. The derived bound is approximately twice square root of the period of sequence that is similar to the triple correlation property of binary Legendre sequence.

Streamwise Evolution of Statistical Events in a Model Wind-Turbine Array

Hot-wire anemometry data, obtained from a wind-tunnel experiment containing a $$3 \times 3$$ model wind-turbine array, are used to conditionally average the Reynolds stresses. Nine profiles at the centreline behind the array are analyzed to characterize the turbulent velocity statistics of the wake flow. Quadrant analysis yields statistical events occurring in the wake of the wind farm where quadrants 2 and 4 produce ejections and sweeps, respectively. The scaled difference between these two events is expressed via the $$\Delta R_{0}$$ parameter and is based on the $$\Delta S_{0}$$ quantity as introduced by M. R. Raupach (J Fluid Mech 108:363–382, 1981). $$\Delta R_{0}$$ attains a maximum value at hub height and changes sign near the top of the rotor. The ratio of quadrant events of upward momentum flux to those of the downward flux, known as the exuberance, is examined and reveals the effect of root vortices persisting to eight rotor diameters downstream. These events are then associated with the triple correlation term present in the turbulent kinetic energy equation of the fluctuations where it is found that ejections play the dual role of entraining mean kinetic energy while convecting turbulent kinetic energy out of the turbine canopy. The development of these various quantities possesses significance in closure models, and is assessed in light of wake remediation, energy transport and power fluctuations, where it is found that the maximum fluctuation is about $$30\%$$ of the mean power produced.

Time-reversal symmetry violation in several Lepton-Flavor-Violating processes

We compute a T-odd triple vector correlation for the $\mu\rightarrow e\gamma $ decay and the $\mu\rightarrow e$ conversion process. We find simple results in terms of the CP violating phases of the effective Hamiltonians. Then we focus on the minimal Left-Right symmetric extension of the Standard Model, which can lead to an appreciable correlation. We show that under rather general assumptions, this correlation can be used to discriminate between Parity or Charge-conjugation as the discrete Left-Right symmetry.

Correlations of heterozygosity with sexual type and sensitivity of Pinus sylvestris L. Trees to the influence of environmental factors

The correlations of genotype heterozygosity with sex and sensitivity of a tree to the influence of ecological factors are considered. A rather close triple correlation between the considered treats is noted. The wave character of correlation of sex and heterozygosity level with sensitivity of trees to growing conditions can testify to the existence of optimal combinations of alleles of homo- and heterozygous loci for the given conditions. They are manifested in the lowering of sensitivity of trees to environmental factors at values of heterozygosity of 0.125 and 0.375. The influence of heterozygosity of trees on the stability of their sexual type in time is revealed. The pines characterized by the greatest hormonal reorganizations in reply to a change in environmental conditions have lower values of heterozygosity.

Nonlinear dielectric response of polar liquids.

The dielectric constant of a polar liquid in a strong electric field changes, in the lowest order, proportionally to the squared field magnitude. The proportionality coefficient (dielectric slope) is traditionally analyzed by mean-field models in terms of the saturation of alignment of individual dipoles as prescribed by the Langevin function. Only a decrease of the dielectric constant induced by the field is allowed by this model, in contrast to observations. Here, the dielectric slope is expressed in terms of the fourth-order cumulant of the liquid dipole moment. The cumulant is in turn separated into the two-particle dipolar correlations, expressed in terms of the Kirkwood factor and the liquid compressibility, and higher, triple and four-particle, dipolar correlations. The model allows both positive and negative dielectric slopes. Two-particle and higher-order correlations largely compensate each other. The analysis of experimental data suggests that dielectric slope gives experimental access to non-trivial triple and four-particle orientational correlations in polar liquids.

Use of triple correlations for the sign determinations of expansion coefficients of symmetric approximations to the diffraction volumes of regular viruses.

An X-ray free electron laser is a new source of x-rays some 10 × 109 times brighter than any previous X-ray source, giving rise to the possibility of structure determination of individual biological particles without crystallization. Some of the earliest samples used in the X-ray free electron laser are viruses because they are about the largest of reproducible bioparticles. We show how common virus near-symmetries can be exploited to find a first approximation to their structures to give a starting point for a perturbation approach to determine their structures.

TOP2A-based prognostication in triple negative breast cancer and correlation with basal phenotype.

1098 Background: Patients with triple-negative breast cancer (TNBC) are ineligible for endocrine and HER2-trageted therapy and remain at high risk for relapse after treatment. Most TNBC are basal-l...