Phase diagram and extreme Gibbs measures of the Ising model on a Cayley tree in the presence of competing binary and ternary interactions

One of the main problems of statistical physics is to describe all Gibbs measures corresponding to a given Hamiltonian. It is well known that such measures form a nonempty convex compact subset in the set of all probability measures. The purpose of this article is to investigate phase diagram and extreme Gibbs measures of the Ising model on a Cayley tree in the presence of competing binary and ternary interactions.     

Investigating Bacterial Volatilome for the Classification and Identification of Mycobacterial Species by HS-SPME-GC-MS and Machine Learning

Species of Mycobacteriaceae cause disease in animals and humans, including tuberculosis and leprosy. Individuals infected with organisms in the Mycobacterium tuberculosis complex (MTBC) or non-tuberculous mycobacteria (NTM) may present identical symptoms, however the treatment for each can be different. Although the NTM infection is considered less vital due to the chronicity of the disease and the infrequency of occurrence in healthy populations, diagnosis and differentiation among Mycobacterium species currently require culture isolation, which can take several weeks. The use of volatile organic compounds (VOCs) is a promising approach for species identification and in recent years has shown promise for use in the rapid analysis of both in vitro cultures as well as ex vivo diagnosis using breath or sputum. The aim of this contribution is to analyze VOCs in the culture headspace of seven different species of mycobacteria and to define the volatilome profiles that are discriminant for each species. For the pre-concentration of VOCs, solid-phase micro-extraction (SPME) was employed and samples were subsequently analyzed using gas chromatography–quadrupole mass spectrometry (GC-qMS). A machine learning approach was applied for the selection of the 13 discriminatory features, which might represent clinically translatable bacterial biomarkers.     

Real‐Time Interrogation of Aspirin Reactivity,Biochemistry, and Biodistribution by Hyperpolarized Magnetic Resonance Spectroscopy

Hyperpolarized magnetic resonance spectroscopy enables quantitative, non‐radioactive, real‐time measurement of imaging probe biodistribution and metabolism in vivo. Here, we investigate and report on the development and characterization of hyperpolarized acetylsalicylic acid (aspirin) and its use as a nuclear magnetic resonance (NMR) probe. Aspirin derivatives were synthesized with single‐ and double‐¹³C labels and hyperpolarized by dynamic nuclear polarization with 4.7 % and 3 % polarization, respectively. The longitudinal relaxation constants (T₁) for the labeled acetyl and carboxyl carbonyls were approximately 30 seconds, supporting in vivo imaging and spectroscopy applications. In vitro hydrolysis, transacetylation, and albumin binding of hyperpolarized aspirin were readily monitored in real time by ¹³C‐NMR spectroscopy. Hyperpolarized, double‐labeled aspirin was well tolerated in mice and could be observed by both ¹³C‐MR imaging and ¹³C‐NMR spectroscopy in vivo.     

Real‐Time Interrogation of Aspirin Reactivity,Biochemistry, and Biodistribution by Hyperpolarized Magnetic Resonance Spectroscopy

Hyperpolarized magnetic resonance spectroscopy enables quantitative, non‐radioactive, real‐time measurement of imaging probe biodistribution and metabolism in vivo. Here, we investigate and report on the development and characterization of hyperpolarized acetylsalicylic acid (aspirin) and its use as a nuclear magnetic resonance (NMR) probe. Aspirin derivatives were synthesized with single‐ and double‐¹³C labels and hyperpolarized by dynamic nuclear polarization with 4.7 % and 3 % polarization, respectively. The longitudinal relaxation constants (T₁) for the labeled acetyl and carboxyl carbonyls were approximately 30 seconds, supporting in vivo imaging and spectroscopy applications. In vitro hydrolysis, transacetylation, and albumin binding of hyperpolarized aspirin were readily monitored in real time by ¹³C‐NMR spectroscopy. Hyperpolarized, double‐labeled aspirin was well tolerated in mice and could be observed by both ¹³C‐MR imaging and ¹³C‐NMR spectroscopy in vivo.     

Exact solutions,conservation laws,bifurcation of nonlinear and supernonlinear traveling waves for Sharma–Tasso–Olver equation

In the present work, we observe the dynamical behavior of nonlinear and supernonlinear traveling waves for Sharma–Tasso–Olver (STO) equation. Exact solutions are derived using \({1}/{G^{^{\prime }}}\) expansion and modified Kudryashov methods. The wave transformation is used to transform STO equation into an ordinary differential equation. Combining Runge–Kutta fourth-order and Fourier spectral technique, we use a mixed scheme for the numerical study of STO equation. Since spectral methods expand the solution in trigonometric series resulting into higher-order technique and Runge–Kutta produces improved accuracy, we extract these qualities for a mixed scheme. Results so produced are presented graphically which provide a useful information about the dynamical behavior. Bifurcation behavior of nonlinear and supernonlinear traveling waves of STO equation is studied with the help of bifurcation theory of planar dynamical systems. It is observed that STO equation supports nonlinear solitary wave, periodic wave, shock wave, stable oscillatory wave and most important supernonlinear periodic wave.     

Higher-Order Nonclassical Properties of a Shifted Symmetric Cat State and a One-Dimensional Continuous Superposition of Coherent States

Role of quantum interference in the origin of higher-order nonclassical characteristics of radiation field has been probed vis-à-vis a discrete and a continuous superposition of coherent states. Specifically, the possibilities of observing higher-order nonclassical properties (e.g., higher-order antibunching (HOA), higher-order sub-Poissonian photon statistics (HOSPS), higher-order squeezing (HOS) of Hong-Mandel type and Hillery type) have been investigated using a shifted symmetric cat state that reduces to Yurke-Stoler, even and odd coherent states at various limits. This shifted symmetric cat state which can be viewed as a discrete superposition of coherent states is found to show HOA and HOSPS. Similarly, higher-order nonclassical properties of a one-dimensional continuous superposition of coherent states is also studied here. The investigation has revealed the existence of HOS and HOSPS in the one-dimensional continuous superposition of coherent states studied here. Effect of non-Gaussianity inducing operations (e.g., photon addition and addition followed by subtraction) on these superposition states have also been investigated. Finally, some comparisons have been made between the higher-order nonclassical properties of discrete and continuous superposition of coherent states.     

Optimizing Image Reconstruction in SENSE Using GPU

Parallel magnetic resonance imaging (MRI) (pMRI) uses multiple receiver coils to reduce the MRI scan time. To accelerate the data acquisition process in MRI, less amount of data is acquired from the scanner which leads to artifacts in the reconstructed images. SENSitivity Encoding (SENSE) is a reconstruction algorithm in pMRI to remove aliasing artifacts from the undersampled multi coil data and recovers fully sampled images. The main limitation of SENSE is computing inverse of the encoding matrix. This work proposes the inversion of encoding matrix using Jacobi singular value decomposition (SVD) algorithm for image reconstruction on GPUs to accelerate the reconstruction process. The performance of Jacobi SVD is compared with Gauss–Jordan algorithm. The simulations are performed on two datasets (brain and cardiac) with acceleration factors 2, 4, 6 and 8. The results show that the graphics processing unit (GPU) provides a speed up to 21.6 times as compared to CPU reconstruction. Jacobi SVD algorithm performs better in terms of acceleration in reconstructions on GPUs as compared to Gauss–Jordan method. The proposed algorithm is suitable for any number of coils and acceleration factors for SENSE reconstruction on real time processing systems.     

Effects of f(R) Model on Dynamics of Axial Shear-Free Dissipative Fluids

We present a general analysis on non-static axial system with dissipative shear-free anisotropic fluid using polynomial inflationary f(R) model.We study the effects of dissipation on the dynamics of geodesic matter distribution.This leads the system either to rotation-free or expansion-free but not both simultaneously under geodesic condition.It is found that the system preserves its symmetry in both cases.For the rotation-free case,when there is no dissipation and Ricci scalar is constant,the axial system reduces to FRW universe model.This is exactly the same result obtained in general relativity.