Control of Overfitting with Physics.

While there are many works on the applications of machine learning, not so many of them are trying to understand the theoretical justifications to explain their efficiency. In this work, overfitting control (or generalization property) in machine learning is explained using analogies from physics and biology. For stochastic gradient Langevin dynamics, we show that the Eyring formula of kinetic theory allows to control overfitting in the algorithmic stability approach-when wide minima of the risk function with low free energy correspond to low overfitting.

Scaling limit of domino tilings on a pentagonal domain.

We consider the six-vertex model at its free-fermion point with domain wall boundary conditions, which is equivalent to random domino tilings of the Aztec diamond. We compute the scaling limit of a particular nonlocal correlation function, essentially equivalent to the partition function for the domino tilings of a pentagon-shaped domain, obtained by cutting away a triangular region from a corner of the initial Aztec diamond. We observe a third-order phase transition when the geometric parameters of the obtained pentagonal domain are tuned to have the fifth side exactly tangent to the arctic ellipse of the corresponding initial model.

Differential Diagnosis of Tuberculosis and Sarcoidosis by Immunological Features Using Machine Learning.

Despite the achievements of modern medicine, tuberculosis remains one of the leading causes of mortality globally. The difficulties in differential diagnosis have particular relevance in the case of suspicion of tuberculosis with other granulomatous diseases. The most similar clinical and radiologic changes are sarcoidosis.

Correction: Morzhin, O.V.; Pechen, A.N. Control of the von Neumann Entropy for an Open Two-Qubit System Using Coherent and Incoherent Drives. 2024, , 36.

In the published article [...

Control of the von Neumann Entropy for an Open Two-Qubit System Using Coherent and Incoherent Drives.

This article is devoted to developing an approach for manipulating the von Neumann entropy S(ρ(t)) of an open two-qubit system with coherent control and incoherent control inducing time-dependent decoherence rates. The following goals are considered: (a) minimizing or maximizing the final entropy S(ρ(T)); (b) steering S(ρ(T)) to a given target value; (c) steering S(ρ(T)) to a target value and satisfying the pointwise state constraint S(ρ(t))≤S¯ for a given S¯; (d) keeping S(ρ(t)) constant at a given time interval. Under the Markovian dynamics determined by a Gorini-Kossakowski-Sudarshan-Lindblad type master equation, which contains coherent and incoherent controls, one- and two-step gradient projection methods and genetic algorithm have been adapted, taking into account the specifics of the objective functionals.

Superoperator Master Equations and Effective Dynamics.

We developed the projection method to derive an analog of the quantum master equation for propagators rather than density matrices themselves. As these propagators are superoperators, we call them superoperator master equations. Furthermore, as the projector maps superoperators to superoperators, we call it a hyperprojector.

Adapted MLP-Mixer network based on crossbar arrays of fast and multilevel switching (Co-Fe-B)(LiNbO) nanocomposite memristors.

MLP-Mixer based on multilayer perceptrons (MLPs) is a novel architecture of a neuromorphic computing system (NCS) introduced for image classification tasks without convolutional layers. Its software realization demonstrates high classification accuracy, although the number of trainable weights is relatively low. One more promising way of improving the NCS performance, especially in terms of power consumption, is its hardware realization using memristors.

Assessment of Comorbidity in Patients with Drug-Resistant Tuberculosis.

A wide range of comorbidities, especially in multidrug-resistant tuberculosis (MDR-TB) and extensively drug-resistant tuberculosis (XDR-TB) patients, markedly complicates selecting effective treatment of tuberculosis (TB) and preventing the development of adverse events. At present, it is impossible to assess the severity of comorbid pathologies and develop indications for the administration of accompanying therapy in TB patients. The aim of this study was to identify the difference in the range of comorbidities between patients with MDR-TB and XDR-TB and assess the impact of comorbidities on TB treatment.

On Geometry of -Adic Coherent States and Mutually Unbiased Bases.

This paper considers coherent states for the representation of Weyl commutation relations over a field of -adic numbers. A geometric object, a lattice in vector space over a field of -adic numbers, corresponds to the family of coherent states. It is proven that the bases of coherent states corresponding to different lattices are mutually unbiased, and that the operators defining the quantization of symplectic dynamics are Hadamard operators.

On Constructing Informationally Complete Covariant Positive Operator-Valued Measures.

We study a projective unitary representation of the product G=G˜×G, where is a locally compact Abelian group and G^ is its dual consisting of characters on . It is proven that the representation is irreducible, which allows us to define a covariant positive operator-valued measure (covariant POVM) generated by orbits of projective unitary representations of G. The quantum tomography associated with the representation is discussed.

The spectrum of [Formula: see text]-soundness.

We study the [Formula: see text]-soundness spectra of theories. Given a recursively enumerable extension [Formula: see text] of [Formula: see text], [Formula: see text] is defined as the set of all 2-ptykes on which [Formula: see text] is correct about well foundedness. This is a measure of how close [Formula: see text] is to being [Formula: see text]-sound.

Learning by Population Genetics and Matrix Riccati Equation.

A model of learning as a generalization of the Eigen's quasispecies model in population genetics is introduced. Eigen's model is considered as a matrix Riccati equation. The error catastrophe in the Eigen's model (when the purifying selection becomes ineffective) is discussed as the divergence of the Perron-Frobenius eigenvalue of the Riccati model in the limit of large matrices.

Efficacy of Tuberculosis Treatment in Patients with Drug-Resistant Tuberculosis with the Use of Bedaquiline: The Experience of the Russian Federation.

Unlabelled: In the conditions of the continued growth of multiple- and extensive drug-resistant tuberculosis, use of the new highly effective anti-tuberculosis drugs in this patient category is of great relevance. The aim of the study was determination the efficacy of treatment in patients with multidrug- and extensive drug-resistant tuberculosis using bedaquiline based on studies published in the Russian Federation.

Materials And Methods: The authors analyzed data published in studies from 2014 to 2022; 41 publications were included in total and 17 articles corresponded to the study design.

nablaDFT: Large-Scale Conformational Energy and Hamiltonian Prediction benchmark and dataset.

Electronic wave function calculation is a fundamental task of computational quantum chemistry. Knowledge of the wave function parameters allows one to compute physical and chemical properties of molecules and materials. Unfortunately, it is infeasible to compute the wave functions analytically even for simple molecules.

Local groups in Delone sets in the Euclidean space.

A Delone (Delaunay) set is a uniformly discrete and relatively dense set of points located in space, and is a natural mathematical model of the set of atomic positions of any solid, whether it is crystalline, quasi-crystalline or amorphous. A Delone set has two positive parameters: r is the packing radius and R is the covering radius. The value 2r can be interpreted as the minimum distance between points of the set.

Effective Gibbs State for Averaged Observables.

We introduce the effective Gibbs state for the observables averaged with respect to fast free dynamics. We prove that the information loss due to the restriction of our measurement capabilities to such averaged observables is non-negative and discuss a thermodynamic role of it. We show that there are a lot of similarities between this effective Hamiltonian and the mean force Hamiltonian, which suggests a generalization of quantum thermodynamics including both cases.

Multipartite Correlations in Quantum Collision Models.

Quantum collision models have proved to be useful for a clear and concise description of many physical phenomena in the field of open quantum systems: thermalization, decoherence, homogenization, nonequilibrium steady state, entanglement generation, simulation of many-body dynamics, and quantum thermometry. A challenge in the standard collision model, where the system and many ancillas are all initially uncorrelated, is how to describe quantum correlations among ancillas induced by successive system-ancilla interactions. Another challenge is how to deal with initially correlated ancillas.

Dynamical Quantum Cherenkov Transition of Fast Impurities in Quantum Liquids.

The challenge of understanding the dynamics of a mobile impurity in an interacting quantum many-body medium comes from the necessity of including entanglement between the impurity and excited states of the environment in a wide range of energy scales. In this Letter, we investigate the motion of a finite mass impurity injected into a three-dimensional quantum Bose fluid as it starts shedding Bogoliubov excitations. We uncover a transition in the dynamics as the impurity's velocity crosses a critical value that depends on the strength of the interaction between the impurity and bosons as well as the impurity's recoil energy.

Hierarchical Structure of Protein Sequence.

Most non-communicable diseases are associated with dysfunction of proteins or protein complexes. The relationship between sequence and structure has been analyzed for a long time, and the analysis of the sequences organization in domains and motifs remains an actual research area. Here, we propose a mathematical method for revealing the hierarchical organization of protein sequences.

Filtration mapping as complete Bell state analyzer for bosonic particles.

In this paper, we present the approach to complete Bell state analysis based on filtering mapping. The key distinctive feature of this appoach is that it avoids complications related to using either hyperentanglement or representation of the Bell states as concatenated Greenber-Horne-Zeilinger (C-GHZ) state to perform discrimination procedure. We describe two techniques developed within the suggested approach and based on two-step algorithms with two different types of filtration mapping which can be called the non-demolition and semi-demolition filtrations.

Patient-specific fluid-structure interaction model of bile flow: comparison between 1-way and 2-way algorithms.

Gallbladder disease is one of the most spread pathologies in the world. Despite the number of operations dealing with biliary surgery increases, the number of postoperative complications is also high. The aim of this study is to show the influence of the biliary system pathology on bile flow character and to numerically assess the effect of surgical operation (cholecystectomy) on the fluid dynamics in the extrahepatic biliary tree, and also to reveal the difference between 1-way and 2-way FSI algorithms on the results.

On the Classical Capacity of General Quantum Gaussian Measurement.

In this paper, we consider the classical capacity problem for Gaussian measurement channels. We establish Gaussianity of the average state of the optimal ensemble in the general case and discuss the Hypothesis of Gaussian Maximizers concerning the structure of the ensemble. Then, we consider the case of one mode in detail, including the dual problem of accessible information of a Gaussian ensemble.

The Influence of Signal Polarization on Quantum Bit Error Rate for Subcarrier Wave Quantum Key Distribution Protocol.

In this paper, we consider the influence of a divergence of polarization of a quantum signal transmitted through an optical fiber channel on the quantum bit error rate of the subcarrier wave quantum key distribution protocol. Firstly, we investigate the dependence of the optical power of the signal on the modulation indices' difference after the second phase modulation of the signal. Then we consider the Liouville equation with regard to relaxation in order to develop expressions of the dynamics of the Stokes parameters.