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Detecting out-of-distribution (OOD) samples for trusted medical image segmentation remains a significant challenge. The critical issue here is the lack of a strict definition of abnormal data, which often results in artificial problem settings without measurable clinical impact. In this paper, we redesign the OOD detection problem according to the specifics of volumetric medical imaging and related downstream tasks (e.g., segmentation). We propose using the downstream model's performance as a pseudometric between images to define abnormal samples. This approach enables us to weigh different samples based on their performance impact without an explicit ID/OOD distinction. We incorporate this weighting in a new metric called Expected Performance Drop (EPD). EPD is our core contribution to the new problem design, allowing us to rank methods based on their clinical impact. We demonstrate the effectiveness of EPD-based evaluation in 11 CT and MRI OOD detection challenges.

Deep Learning models perform unreliably when the data comes from a distribution different from the training one. In critical applications such as medical imaging, out-of-distribution (OOD) detection methods help to identify such data samples, preventing erroneous predictions. In this paper, we further investigate the OOD detection effectiveness when applied to 3D medical image segmentation. We design several OOD challenges representing clinically occurring cases and show that none of these methods achieve acceptable performance. Methods not dedicated to segmentation severely fail to perform in the designed setups; their best mean false positive rate at 95% true positive rate (FPR) is 0.59. Segmentation-dedicated ones still achieve suboptimal performance, with the best mean FPR of 0.31 (lower is better). To indicate this suboptimality, we develop a simple method called Intensity Histogram Features (IHF), which performs comparable or better in the same challenges, with a mean FPR of 0.25. Our findings highlight the limitations of the existing OOD detection methods on 3D medical images and present a promising avenue for improving them. To facilitate research in this area, we release the designed challenges as a publicly available benchmark and formulate practical criteria to test the OOD detection generalization beyond the suggested benchmark. We also propose IHF as a solid baseline to contest the emerging methods., Comment: This work has been submitted to the IEEE for possible publication. 10 pages, 5 figures, 5 tables

We examine the effect of a jet transversal structure from magnetohydrodynamic semi-analytical modelling on the total intensity profiles of relativistic jets from active galactic nuclei. In order to determine the conditions for forming double- and triple-peaked transverse intensity profiles, we calculate the radiative transfer for synchrotron emission with self-absorption from the jets described by the models with a constant angular velocity and with a total electric current closed inside a jet. We show that double-peaked profiles appear either in the models with high maximal Lorentz factors or in optically thick conditions. We show that triple-peaked profiles in radio galaxies constrain the fraction of the emitting particles in a jet. We introduce the possible conditions for triple-peaked profiles under the assumptions that nonthermal electrons are preferably located at the jet edges or are distributed according to Ohmic heating., Comment: 22 pages, 11 figures, accepted by MNRAS

Deep Learning (DL) models tend to perform poorly when the data comes from a distribution different from the training one. In critical applications such as medical imaging, out-of-distribution (OOD) detection helps to identify such data samples, increasing the model's reliability. Recent works have developed DL-based OOD detection that achieves promising results on 2D medical images. However, scaling most of these approaches on 3D images is computationally intractable. Furthermore, the current 3D solutions struggle to achieve acceptable results in detecting even synthetic OOD samples. Such limited performance might indicate that DL often inefficiently embeds large volumetric images. We argue that using the intensity histogram of the original CT or MRI scan as embedding is descriptive enough to run OOD detection. Therefore, we propose a histogram-based method that requires no DL and achieves almost perfect results in this domain. Our proposal is supported two-fold. We evaluate the performance on the publicly available datasets, where our method scores 1.0 AUROC in most setups. And we score second in the Medical Out-of-Distribution challenge without fine-tuning and exploiting task-specific knowledge. Carefully discussing the limitations, we conclude that our method solves the sample-level OOD detection on 3D medical images in the current setting., Comment: We had made a mistake in the proposed algorithm's code (IHF), which led to a biased evaluation -- the reported AUROC scores (Tab. 1) are higher than they should be. It led to a false conclusion and the primary paper's message

When applying a Deep Learning model to medical images, it is crucial to estimate the model uncertainty. Voxel-wise uncertainty is a useful visual marker for human experts and could be used to improve the model's voxel-wise output, such as segmentation. Moreover, uncertainty provides a solid foundation for out-of-distribution (OOD) detection, improving the model performance on the image-wise level. However, one of the frequent tasks in medical imaging is the segmentation of distinct, local structures such as tumors or lesions. Here, the structure-wise uncertainty allows more precise operations than image-wise and more semantic-aware than voxel-wise. The way to produce uncertainty for individual structures remains poorly explored. We propose a framework to measure the structure-wise uncertainty and evaluate the impact of OOD data on the model performance. Thus, we identify the best UE method to improve the segmentation quality. The proposed framework is tested on three datasets with the tumor segmentation task: LIDC-IDRI, LiTS, and a private one with multiple brain metastases cases.

To propose a mathematical model of consciousness and will, we first simulated the inverted qualia with a toy model of a neural network. As a result, we confirmed that there can be an inverted qualia on the neural network. In other words, the qualia were individual-dependent and considered difficult as an indicator of consciousness and will. To solve that difficulty, we introduce a probability space and a random variable into a set of qualia and define a public language for events. Based on this idea of public language, consciousness and will are modeled. In this proposal, future actions are randomly selected from the comparison between "recognition of events" by external observation and past episodic memory, and the actual "recognition of actions" is regarded as the occurrence of consciousness. The basic formula is also derived. This proposal is compared with other past philosophical discussions., Comment: 21 pages, 4 figures, 4 tables

(Abridged) Modern studies and industrial applications related to the design, radiation protection, and reliability of nuclear facilities, medical applications, as well as space research and exploration are relying on extensive simulations and modeling. Computer codes realizing semi-classical and quantum molecular dynamics (QMD) approaches are often employed to make up for the lack of accelerator data on many nuclear reactions at intermediate and high energies (>10s of MeV/n) and are in high demand. This contribution focuses on the methodology of generating reliable proton-induced cross sections in the energy range below 1 GeV. We developed a problem-oriented computer framework based on MCNPX and CASCADE/INPE codes to calculate activation cross section data at intermediate and high energies. Goodness of the fits of nucleon-nucleus interaction models to the existing data is evaluated based on elaborated algorithms. The method is based on the analysis of a large set of data and calculated cross sections for different targets and residual nuclei in a wide range of proton energies using numerous criteria. In practice, this could be done by tuning the model parameters and algorithms to fit required experimental data subset, or through achieving unification and consistency of fundamental parameters for all considered reactions. The presented framework is pursuing the latter approach. We use proton-induced reactions on Si and Fe nuclei to illustrate the application of the developed multi-criteria algorithm, where we use all data below 1 GeV available from the EXFOR data library and the IAEA CRP "Benchmark of Spallation Models." We show that the analysis of the predictive power of various intermediate and high-energy models based on the multi-criteria algorithm allows more sophisticated selection of appropriate models in a given energy range and residual nuclei domain., Comment: A poster E1.16-0085-21 presented at an event E1.16 "Origin of Cosmic Rays," 43th COSPAR Scientific Assembly (hybrid), 28 Jan - 4 Feb 2021, Sydney, Australia. For a full agenda of the event E1.16, see https://www.cospar-assembly.org/admin/session_cospar.php?session=903

We prove the local well-posedness for a two phase problem of magnetohydrodynamics with a sharp interface. The solution is obtained in the maximal regularity space: $H^1_p((0, T), L_q) \cap L_p((0, T), H^2_q)$ with $1 < p, q < \infty$ and 2/p + N/q < 1$, where $N$ is the space dimension

We prove some anologues for algebras of recent group-theoretic results (due to Khukhro, Klyachko, Makarenko, Milentyeva, and Shumyatsky) on large characteristic subgroups satisfying a given property.

We describe a graph parametrization of rational quadratic differentials with presence of a simple pole, whose critical trajectories form a network depending on parameters focusing on the network topological jumps. Obtained bifurcation diagrams are associated with the Stasheff polytopes., Comment: 14 pages, 8 figures

The paper presents two new results concerning the varieties of Leibnitz algebras. In the case of prime characteristic p of the base field constructed example not nilpotent variety of Leibnitz algebras satisfying an Engel condition order p. In the case of zero characteristic obtained new results concerning the space of multilinear elements variety of left nilpotent of the class not more than 3 Leibnitz algebras., Comment: 9 pages

We establish some estimates of the the angular derivatives from below for holomorphic self-maps of the unit disk at one and two fixed points of the unit circle provided there is no fixed point inside the unit disk. The results complement Cowen-Pommerenke and Anderson-Vasil'ev type estimates in the case of univalent functions. We use the method of extremal length and propose a new semigroup approach to deriving inequalities for holomorphic self-maps of the disk which are not necessarily univalent using known inequalities for univalent functions. This approach allowed us to receive a new Ossermans type estimate as well as inequalities for holomorphic self-maps which images do not separate the origin and the boundary.

An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for solving multi-dimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a tree of trees data structure. The mesh in r-space is automatically generated around embedded boundaries and dynamically adapted to local solution properties. The mesh in v-space is created on-the-fly for each cell in r-space. Mappings between neighboring v-space trees implemented for the advection operator in configuration space. We have developed new algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive mesh in velocity space: importance sampling, multi-point projection method, and the variance reduction method. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions in a Lorentz gas. New AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce computational cost and memory usage for solving challenging kinetic problems.

The current-voltage and spectral characteristics of a flux flow oscillator (FFO), based on a long Josephson junction, are studied. The investigations are performed in the range of small bias currents and magnetic fields, where the FFO radiates a quasi-chaotic signal with extremely large radiation linewidth, and the displaced linear slope (DLS) is observed at the current-voltage characteristic. By direct numerical simulation of the sine-Gordon equation it is demonstrated that for large lengths of the Josephson junction or in the case of finite matching of the FFO with external waveguide system, the DLS with extremely large linewidth is transformed into Fiske steps with very narrow linewidth. While there is the common belief that the chaotic regime of the FFO is due to excitation of the internal oscillation modes in the "soft" fluxon chain, it is demonstrated that this regime is inspired by multiple reflections of the traveling waves from junction ends., Comment: 4 pages, 7 figures

In this work we study the dynamics of free 3D relativistic Gaussian wave packets with different spin polarization. We analyze the connection between the symmetry of initial state and the dynamical characteristics of moving particle. The corresponding solutions of Dirac equation having different types of symmetry were evaluated analytically and numerically and after that the electron probability densities, as well as, the spin densities were visualized. The average values of velocity of the packet center and the average spin were calculated analytically, and the parameters of transient Zitterbewegung in different directions were obtained. These results can be useful for the interpretation of future experiments with trapped ions., Comment: 10 pages, 7 figures

For hole systems with an effective spin 3/2 we analyzed analytically and numerically the evolution of wave packets with the different initial polarizations. The dynamics of such systems is determined by the $4\times 4$ Luttinger Hamiltonian. We work in the space of arbitrary superposition of light- and heavy-hole states of the "one-particle system". For 2D packets we obtained the analytical solution for the components of wave function and analyzed the space-time dependence of probability densities as well as angular momentum densities. Depending on the value of the parameter $a=k_0d$ ($k_0$ is the average momentum vector and $d$ is the packet width) two scenarios of evolution are realized. For $a>>1$ the initial wave packet splits into two parts and the coordinates of packet center experience the transient oscillations or {\it Zitterbewegung} (ZB) as for other two-band systems. In the case when $a<<1$ the distribution of probability density at $t>0$ remains almost cylindrically symmetric and the ripples arise at the circumference of wave packet. The ZB in this case is absent. We evaluated and visualized for different values of parameter $a$ the space-time dependence of angular momentum densities, which have the multipole structure. It was shown that the average momentum components can precess in the absence of external or effective magnetic fields due to the interference of the light- and heavy hole states. For localized initial states this precession has a transient character., Comment: 9 pages, 8 gigure

The dynamics of charge particles described by Gaussian wave packet in monolayer graphene is studied analytically and numerically. We demonstrate that the shape of wave packet at arbitrary time depends on correlation between the initial electron amplitudes $\psi_1(\vec r,0)$ and $\psi_2(\vec r,0)$ on the sublattices $A$ and $B$ correspondingly (i.e. pseudospin polarization). For the transverse pseudospin polarization the motion of the center of wave packet occurs in the direction perpendicular to the average momentum $ {\vec p_0}=\hbar \vec{k_0}$. Moreover, in this case the initial wave packet splits into two parts moving with opposite velocities along $ {\vec p_0}$. If the initial direction of pseudospin coincides with average momentum the splitting is absent and the center of wave packet is displaced at $t>0$ along the same direction. The results of our calculations show that all types of motion experience {\it zitterbewegung}. Besides, depending on initial polarization the velocity of the packet center may have the constant component $v_c=uf(a)$, where $u\approx 10^8 cm/s$ is the Fermi velocity and $f(a)$ is a function of the parameter $a=k_0d$ ($d$ is the initial width of wave packet). As a result, the direction of the packet motion is determined not only by the orientation of the average momentum, but mainly by the phase difference between the up- and low- components of the wave functions. Similar peculiarities of the dynamics of 2D electron wave packet connected with initial spin polarization should take place in the semiconductor quantum well under the influence of the Rashba spin-orbit coupling., Comment: 7 pages, 8 figures, to be published in Phys. Rev. B

We study the effect of splitting and zitterbewegung of 1D and 2D electron wave packets in the semiconductor quantum well under the influence of the Rashba spin orbit coupling. Results of our investigations show that the spin orbit interaction induces dramatic qualitative changes in the evolution of spin polarized wave packet. The initial wave packet splits into two parts with different spin polarization propagating with unequal group velocity. This splitting appears due to the presence of two branches of electron spectrum corresponding to the stationary states with different chirality. It is demonstrated also that in the presence of external magnetic field B$ perpendicular to the electron gas plane the wave packet splits into two parts which rotates with different cyclotron frequencies. It was shown that after some periods the electron density distributes around cyclotron orbit and the motion acquire an irregular character. Our calculations were made for both cases of weak and strong spin orbit coupling., Comment: 11 pages, 6 figures

An analysis of experimental heat capacity at $T>T_{c}$ is presented for series of samples $(R)Ba_2Cu_3O_{6+x}$ (with $x$ close to optimal). For all samples the anomaly was discovered which occurred steadily in the interval 250-290 K (anomaly $T_{h}$). The anomaly $T_{h}$ looks like a phase transition anomaly. It was shown that the anomaly $T_{h}$ correlates with superconducting anomaly $T_c$, temperatures $T_{h}$ and $T_{c}$ being connected by the ratio $T_{h}\approx 3T_c$. The anomaly $T_{h}$ is interpreted as the origination of pairing the charge carriers. Anomalies at $T\approx 3T_c$ were also detected in heat capacity of low temperature superconductors $Hg$ and $Nb_3Ge$., Comment: 6 pages, 10 figures, revtex4

Investigations of dynamic and thermodynamic properties for a molecular crystal tris-hexafluoroacetylacetonate-iron $Fe(O_2C_5HF_6)_3$ are presented. Heat capacity $C_p(T)$ has been measured by adiabatic calorimetry method in the temperature range $4.8-321 K$. An anomaly with a maximum at $T_c = 44.6 K$ has been discovered. Intermolecular vibrations spectrum was calculated by lattice dynamics method in quasiharmonic approximation. Intramolecular frequencies are found by solving the Schr\"odinger equation in approach of small harmonic oscillations. In the frequency interval $\approx 30-70 cm^{-1}$ overlapping the spectrums intra- and intermolecular oscillations has been found. The good agreement for calculated and experimental $C_p(T)$ occurred to be possible for two sets of the force constants. These sets describe two phases above and below $T_c$. The difference between phases is connected with freezing of rotation $CF_3$ groups. It has been concluded that the interaction between different modes leads to phase transition and anomaly in heat capacity., Comment: 5 pages, 5 figures, revtex4

The temperature dependence of heat capacity for the samples of 90 K phase of YBa_2Cu_3O_{6+x} with x = 0.85, 0.90 and 0.95 was investigated above T_c. For separating the heat capacity into regular and anomalous contributions the special technique was used. For all the samples the anomalies in intervals 100-200 K (T_{low}), 205-230 K (T_m) and 260-290 K (T_h) were detected. At T = 3T_c the temperature "echo" from superconducting phase transition was discovered. This "echo" is connected with the anomaly T_h, which is believed to mark the rise of pairing carriers of charge without phase coherence. We connect the anomaly T_m with the Neel point of magnetic subsystem which has antiferromagnetism coexisting with superconductivity. The x - dependence of entropy S_h points out that T_h - process probably exists only in the frameworks of 90 K phase. The curves S_m(x) and S_h(x) intersect each other at the optimal doping. The discovered anomalies mark new lines on the phase diagram of YBa_2Cu_3O_{6+x} - compounds., Comment: 4 pages, RevTex4, 5 EPS figures, submitted to Phys.Rev.Lett

Two narrow anomalies with peaks at $\sim 30 K$ and $\sim 60 K$ and a wide diffuse anomaly within the range 110-240 K have been found in a low temperature heat capacity of chromium tris-acetylacetonate Cr(AA)_3. Besides, the reversible change in color has been discovered when cooling the crystals to liquid nitrogen temperature (thermochromism). To clear up the nature of these effects the static magnetic susceptibility was measured within the temperature range 2-300 K, the ESR-spectra on the Cr^{3+} ion and the transmission spectra in visible region were recorded at 78 K and 300 K, the Raman spectra were measured within the range 5-220 K. It has been ascertained that the reversible effect of thermochromism is observed in most of $\beta$-diketonates of the transition metals. Some tentative considerations concerning the origin of discovered effects are put forward., Comment: 8 pages, latex, 5 eps figures

The process of manufacturing grids, the peculiarities of the structural design, the fittings, the requirements on the tools and work area are discussed.