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Herein, we show differences in blood serum of asymptomatic and symptomatic pregnant women infected with COVID-19 and correlate them with laboratory indexes, ATR FTIR and multivariate machine learning methods. We collected the sera of COVID-19 diagnosed pregnant women, in the second trimester (n = 12), third-trimester (n = 7), and second-trimester with severe symptoms (n = 7) compared to the healthy pregnant (n = 11) women, which makes a total of 37 participants. To assign the accuracy of FTIR spectra regions where peak shifts occurred, the Random Forest algorithm, traditional C5.0 single decision tree algorithm and deep neural network approach were used. We verified the correspondence between the FTIR results and the laboratory indexes such as: the count of peripheral blood cells, biochemical parameters, and coagulation indicators of pregnant women. CH 2 scissoring, amide II, amide I vibrations could be used to differentiate the groups. The accuracy calculated by machine learning methods was higher than 90%. We also developed a method based on the dynamics of the absorbance spectra allowing to determine the differences between the spectra of healthy and COVID-19 patients. Laboratory indexes of biochemical parameters associated with COVID-19 validate changes in the total amount of proteins, albumin and lipase.

Early detection of the most common pediatric neoplasm, B-cell precursor lymphoblastic leukemia (BCP-ALL), is challenging and requires invasive bone marrow biopsies. The purpose of this study was to establish new biomarkers for early screening to detect pediatric leukemia. In this small cohort study, Fourier transform infrared (FTIR) spectra were obtained from blood sera of 10 patients with BCP-ALL and were compared with the control samples from 10 children with some conditions other than neoplasm. Using various analytical approaches, including a new physical model, some significant differences were observable. The most important include: the different peak area ratio 2965/1645 cm−1 (p = 0.002); the lower average percentage of both β-sheet and β-turn protein structures in the sera of BCP-ALL patients (p = 0.03); an AdaBoost-based predictive model for classifying healthy vs. BCP-ALL patients with 85% accuracy; and the phase shift of the first derivative in the spectral range 1050–1042 cm−1 correlating with white blood cell (WBC) and blast cell count in BCP-ALL patients contrary to the samples obtained from healthy controls. Although verification in larger groups of patients will be necessary, these promising results suggest that FTIR spectroscopy may have future potential for the early screening of BCP-ALL.

Quantum kinematics of the linear Heisenberg ring, consisting of N crystal nodes, each with spin s, is presented in terms of the Weyl duality between actions of the symmetric and unitary groups in the space of quantum states of the magnet. This space is spanned on magnetic configurations which gives rise to an application of the combinatorial Robinson-SchenstedKnuth algorithm for a unique classification of irreducible basis of the duality of Weyl in terms of a pair of tableaux: a standard Young tableau in the alphabet of nodes, accompanied by a semistandard Weyl tableau in the alphabet of spins. Similarities and distinctions between various group-theoretic and combinatorial objects are discussed within the context of the magnetic interpretation. In particular, the role of the spectrum of Jucys-Murphy operators in the clasification and construction of magnetic eigenstates corresponding to Young tableaux is illustrated. This paper is dedicated to the memory of Professor Brian G. Wybourne, to whom we all owe so much, in learning from his thorough and deep knowledge and in sharing his enthusiasm towards physics.

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The application of the Jucys-Murphy operators, generating a maximal Abelian subalgebra in the group algebra of the symmetric group, in the process of immediate diagonalisation of the one-dimensional Hubbard Hamiltonian is demonstrated. The way of construction of appropriate projection operators of the Young orthogonal basis is pointed out, and the fact that these operators play a role of eigenvectors for Jucys-Murphy operators in the group algebra of the symmetric group is underlined. It is indicated that this operator technique is competitive to the Kostka matrix at the level of bases, which yields matrices of appropriate Clebsh-Gordan coefficients. The permutational symmetry of the lattice chain with N sites occupied by two electrons is discussed in detail.

Abstract:We discuss the one-dimensional Hubbard model, on finite sites spin chain, in context of the action of the direct product of two unitary groups SU(2)×SU(2). The symmetry revealed by this group is applicable in the procedure of exact diagonalization of the Hubbard Hamiltonian. This result combined with the translational symmetry, given as the basis of wavelets of the appropriate Fourier transforms, provides, besides the energy, additional conserved quantities, which are presented in the case of a half-filled, four sites spin chain. Since we are dealing with four elementary excitations, two quasiparticles called "spinons", which carry spin, and two other called "holon" and "antyholon", which carry charge, the usual spin-SU(2) algebra for spinons and the so called pseudospin-SU(2) algebra for holons and antiholons, provide four additional quantum numbers. PACS

In the paper, we proposed a new approach to producing the qubits in electron transport in low-dimensional structures such as double quantum wells or double quantum wires (DQW). The qubit could arise as a result of quantum entanglement of two specific states of electrons in DQW structure. These two specific states are the symmetric and antisymmetric (with respect to inversion symmetry) states arising due to tunneling across the structure, while entanglement could be produced and controlled by means of the source of nonclassical light. We examined the possibility to produce quantum entanglement in the framework of Jaynes-Cummings model and have shown that at least in principle, the entanglement can be achieved due to series of “revivals” and “collapses” in the population inversion due to the interaction of a quantized single-mode EM field with a two-level system.