Supernovae and the Arrow of Time

Supernovae are explosions of stars and are a central problem in astrophysics. Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities develop during the star’s explosion and lead to intense interfacial RT/RM mixing of the star materials. We handle the mathematical challenges of the RT/RM problem based on the group theory approach. We directly link the conservation laws governing RT/RM dynamics to the symmetry-based momentum model, derive the model parameters, and find the analytical solutions and characteristics of RT/RM dynamics with variable accelerations in the linear, nonlinear and mixing regimes. The theory outcomes explain the astrophysical observations and yield the design of laboratory experiments. They suggest that supernova evolution is a non-equilibrium process directed by the arrow of time.     

In Silico Analysis of PORD Mutations on the 3D Structure of P450 Oxidoreductase

Cytochrome P450 oxidoreductase (POR) is a membrane-bound flavoprotein that helps in transferring electrons from its NADPH domain to all cytochrome P450 (CYP450) enzymes. Mutations in the POR gene could severely affect the metabolism of steroid hormones and the development of skeletal muscles, a condition known as Cytochrome P450 oxidoreductase deficiency (PORD). PORD is associated with clinical presentations of disorders of sex development, Antley and Bixler’s syndrome (ABS), as well as an abnormal steroid hormone profile. We have performed an in silico analysis of POR 3D X-ray protein crystal structure to study the effects of reported mutations on the POR enzyme structure. A total of 32 missense mutations were identified, from 170 PORD patients, and mapped on the 3D crystal structure of the POR enzyme. In addition, five of the missense mutations (R457H, A287P, D210G, Y181D and Y607C) were further selected for an in-depth in silico analysis to correlate the observed changes in POR protein structure with the clinical phenotypes observed in PORD patients. Overall, missense mutations found in the binding sites of POR cofactors could lead to a severe form of PORD, emphasizing the importance of POR cofactor binding domains in transferring electrons to the CYP450 enzyme family.     

A Specific HPLC Method to Determine Residual HEPES in [68Ga]Ga-Radiopharmaceuticals: Development and Validation

Background: Nowadays, in Nuclear Medicine, clinically applied radiopharmaceuticals must meet quality release criteria such as high radiochemical purity and radiochemical yield. Many radiopharmaceuticals do not have marketing authorization and have no dedicated monograph within European Pharmacopeia (Ph. Eur.); therefore, general monographs on quality controls (QCs) have to be applied for clinical application. These criteria require standardization and validation in labeling and preparation, including quality controls measurements, according to well defined standard operation procedures. However, QC measurements are often based on detection techniques that are specific to a certain chromatographic system. Several radiosyntheses of [⁶⁸Ga]Ga-radiopharmaceuticals are more efficient and robust when they are performed with 2-[4-(2-hydroxyethyl)piperazin-1-yl] ethanesulfonic acid (HEPES) buffer, which is considered as an impurity to be assessed in the QC procedure, prior to clinical use. Thus, Ph. Eur. has introduced a thin-layer chromatography (TLC) method to quantify the HEPES amount that is present in [⁶⁸Ga]Ga-radiopharmaceuticals. However, this is only qualitative and has proven to be unreliable. Here we develop and validate a new high-performance liquid chromatography (UV-Radio-HPLC) method to quantify the residual amount of HEPES in ⁶⁸Ga-based radiopharmaceuticals. Method: To validate the proposed UV-Radio-HPLC method, a stepwise approach was used, as defined in the guidance document that was adopted by the European Medicines Agency (CMP/ICH/381/95 2014). The assessed parameters are specificity, linearity, precision (repeatability), accuracy, and limit of quantification. A range of concentrations of HEPES (100, 80, 60, 40, 20, 10, 5, 3 μg/mL) were analyzed. Moreover, to test the validity and pertinence of our new HPLC method, we analyzed samples of [⁶⁸Ga]Ga-DOTATOC; [⁶⁸Ga]Ga-PSMA; [⁶⁸Ga]Ga-DOTATATE; [⁶⁸Ga]Ga-Pentixafor; and [⁶⁸Ga]Ga-NODAGA-Exendin-4 from different batches that were prepared for clinical use. Results: In the assessed samples, HEPES could not be detected by the TLC method that was described in Ph. Eur. within 4 min incubation in an iodine-saturated chamber. Our developed HPLC method showed excellent linearity between 3 and 100 μg/mL for HEPES, with a correlation coefficient (R²) for calibration curves that was equal to 0.999, coefficients of variation (CV%) < 2%, and percent deviation value of bias from 100% to 5%, in accordance with acceptance criteria. The intra-day and inter-day precision of our method was statistically confirmed and the limit-of-quantification (LOQ) was 3 μg/mL, confirming the high sensitivity of the method. The amount of HEPES that was detected with our developed HPLC method in the tested [⁶⁸Ga]Ga-radiopharmaceuticals resulted well below the Ph. Eur. limit, especially for [⁶⁸Ga]Ga-NODAGA-Exendin-4. Conclusions: The TLC method that is described in Ph. Eur. to assess residual HEPES in [⁶⁸Ga]-based radiopharmaceuticals may not be sufficiently sensitive and thus unsuitable for QC release. Our new HPLC method was sensitive, quantitative, reproducible, and rapid for QCs, allowing us to exactly determine the residual HEPES amount in [⁶⁸Ga]Ga-radiopharmaceuticals for safe patient administration.     

Age Analysis of Status Updating System with Probabilistic Packet Preemption

The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of a discrete time status updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. We assume that the queue used in the system is Ber/Geo/1/2*/η, which represents that the system size is 2 and the packet in the buffer can be preempted by a fresher packet with probability η. Instead of considering the system’s AoI separately, we use a three-dimensional state vector (n,m,l) to simultaneously track the real-time changes of the AoI, the age of a packet in the server, and the age of a packet waiting in the buffer. We give the explicit expression of the system’s average AoI and show that the average AoI of the system without packet preemption is obtained by letting η=0. When η is set to 1, the mean of the AoI of the system with a Ber/Geo/1/2* queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between the average discrete AoI with the Ber/Geo/1/c queue and the average continuous AoI with the M/M/1/c queue. For each of two extreme cases where η=0 and η=1, we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between the average AoI and the packet preemption probability η, as well as the AoI’s distribution curves in two extreme cases, are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest (EH) node of a wireless sensor network, where the packet in the buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and highlight the merits of considering discrete time systems, in this paper, we provide detailed discussions showing how the results about continuous AoI are derived by analyzing the corresponding discrete time system and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose an idea to analyze the AoI of a system when the service time distribution is arbitrary.     

From Chaos to Ordering: New Studies in the Shannon Entropy of 2D Patterns

Properties of the Voronoi tessellations arising from random 2D distribution points are reported. We applied an iterative procedure to the Voronoi diagrams generated by a set of points randomly placed on the plane. The procedure implied dividing the edges of Voronoi cells into equal or random parts. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of the positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in linear semi-crystalline polymers and metallic glasses. Thus, we can conclude that by applying even a simple set of rules to a random set of seeds, we can introduce order into an initially disordered system. At the same time, the Shannon (Voronoi) entropy showed a tendency to attain values that are typical for completely random patterns; thus, the Shannon (Voronoi) entropy does not distinguish the short-range ordering. The Shannon entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase in the number of iteration steps. The Shannon entropy grew with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Shannon (Voronoi) entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Shannon entropy.     

A Testable Theory for the Emergence of the Classical World

The transition from the quantum to the classical world is not yet understood. Here, we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except on some specific basis. However, we have no established theory for the emergence of a specific basis. Our framework entails the following: (i) Sets of N entangled quantum variables can mutually actualize one another. (ii) Such actualization must occur in only one of the 2^N possible bases. (iii) Mutual actualization progressively breaks symmetry among the 2^N bases. (iv) An emerging “amplitude” for any basis can be amplified by further measurements in that basis, and it can decay between measurements. (v) The emergence of any basis is driven by mutual measurements among the N variables and decoherence with the environment. Quantum Zeno interactions among the N variables mediates the mutual measurements. (vi) As the number of variables, N, increases, the number of Quantum Zeno mediated measurements among the N variables increases. We note that decoherence alone does not yield a specific basis. (vii) Quantum ordered, quantum critical, and quantum chaotic peptides that decohere at nanosecond versus femtosecond time scales can be used as test objects. (viii) By varying the number of amino acids, N, and the use of quantum ordered, critical, or chaotic peptides, the ratio of decoherence to Quantum Zeno effects can be tuned. This enables new means to probe the emergence of one among a set of initially entangled bases via weak measurements after preparing the system in a mixed basis condition. (ix) Use of the three stable isotopes of carbon, oxygen, and nitrogen and the five stable isotopes of sulfur allows any ten atoms in the test protein to be discriminably labeled and the basis of emergence for those labeled atoms can be detected by weak measurements. We present an initial mathematical framework for this theory, and we propose experiments.     

旋光晶体的寻常折射率与左旋光和右旋光折射率的关系

由光的波动方程证明,若介质为旋光物质,则其极化率张量χ一定有非对角对称的共轭虚元素,并导出了旋光晶体的寻常折射率no与左旋光折射率nL和右旋光折射率nR之间的关系.将理论分析结果与实验数据相对照,结果完全吻合.     

晶面指数必互质

通过平面方程证明了晶面指数必无公因子.     

Effect of Poly(methacrylic acid) on the Cytokine Level in an In Vivo Tumor Model

Cancer is a leading cause of mortality globally. Despite remarkable improvements in cancer-treatment approaches, disease recurrence and progression remain major obstacles to therapy. While chemotherapy is still a first-line treatment for a variety of cancers, the focus has shifted to the development and application of new approaches to therapy. Nevertheless, the relationship between immune response, neoplastic diseases and treatment efficiency is not fully understood. Therefore, the aim of the study was to investigate the immunopharmacological effects of methacrylic acid homopolymer in an in vivo tumor model. Materials and methods: Monomeric methacrylic acid was used to synthesize polymers. Methacrylic acid was polymerized in dioxane in the presence of 4-Cyano-4-[(dodecylsulfanylthiocarbonyl)sulfanyl]pentanoic acid. To study the molecular weight characteristics of PMAA by GPC, carboxyl groups were preliminarily methylated with diazomethane. An experimental cancer model was obtained by grafting RMK1 breast cancer cells. The serum levels of IL-6, IL-10, IL-17, transforming growth factor β1 (TGF-β1), and tumor necrosis factor α (TNF-α) were measured by ELISA. Results: The effect of PMAA on the serum concentrations of several cytokines was studied upon its single administration to laboratory animals in early neoplastic process. The IL-6, IL-17 and TGF-β1 concentrations were found to change significantly and reach the level observed in intact rats. The IL-10 concentration tended to normalize. Conclusion: The positive results obtained are the basis for further studies on the effect of methacrylic-acid polymers with different molecular-weight characteristics on the neoplastic process.     

Stochastic calculus for Markov processes associated with non-symmetric Dirichlet forms

Nakao’s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting.It? ’s formula in terms of the extended stochastic integrals is obtained.