In this paper we present the measurement of charged pion two-particle femtoscopic correlation functions in $\sqrt{S_{NN}}$= 200 GeV Au+Au collisions, in 31 average transverse mass bins, separately for positive and negative pion pairs. Lévy-shaped source distributions yield a statistically acceptable description of the measured correlation functions, with three physical parameters: correlation strength parameter λ , Lévy index α and Lévy scale parameter R. The transverse mass dependence of these Lévy parameters is then investigated. Their physical interpretation is also discussed, and the appearance of a new scaling variable is observed.

Globalized in 1995 through the TRIPs Agreement, humanity’s dominant mechanism for encouraging innovations involves 20-year product patents, whose monopoly features enable innovators to reap large markups or licensing fees from early users. Exclusive reliance on this reward mechanism in the pharmaceutical sector is morally problematic for two main reasons. First, it imposes a great burden on poor people who cannot afford to buy patented treatments at monopoly prices and whose specific health problems are therefore neglected by pharmacological research. Second, it discourages pharmaceutical firms from fighting diseases at the population level with the aim of slashing their incidence. These problems can be much alleviated by establishing a supplementary alternative reward mechanism that would enable pharmaceutical innovators to exchange their monopoly privileges on a patented product for impact rewards based on the actual health gains achieved with this product. Such an international Health Impact Fund (HIF) would create powerful new incentives to develop remedies against diseases concentrated among the poor, rapidly to provide such remedies with ample care at very low prices, and to deploy them strategically to contain, suppress, and ideally to eradicate the target disease. By promoting innovations and their diffusion together, the HIF would greatly enlarge the benefits, and thereby also the cost-effectiveness, of the pharmaceutical sector, in favor of the world’s poor especially.

Transcriptional regulations have been widely studied as one of the main bridges between biology and other basic sciences as well as medicine. The traffic across it has been mostly unidirectional: chemistry and physics provided a lot of tools for biology, although the supply is now saturating. The traffic in opposite direction, the supply of subjects to develop chemistry and physics, has been only a little. However, if there are any, the supply will be at least from transcription, because the notion of chemical reaction is the strongest. This topic is aimed to increase the opposite traffic by introducing the forefront of physicochemical studies of transcription.

Hemoconcentration membranes used in cardiopulmonary bypass require a pore structure design with high pure water permeability, and which does not allow protein adsorption and useful protein loss. However, studies on hemoconcentration membranes have not been conducted yet. The purpose of this study was to analyze three-dimensional pore structures and protein fouling before and after blood contact with capillary membranes using the tortuous pore diffusion model and a scanning probe microscope system. We examined two commercially available capillary membranes of similar polymer composition that are successfully used in hemoconcentration clinically. Assuming the conditions of actual use in cardiopulmonary bypass, we perfused these membranes with bovine blood. Pure water permeability before and after bovine blood perfusion was measured using the dead-end filtration. The scanning probe microscopy system was used for analysis. High-resolution three-dimensional pore structures on the inner surface of the membranes were observed before blood contact. On the other hand, pore structures after blood contact could not be observed due to protein fouling. The pore diameters calculated by the tortuous pore diffusion model and scanning probe microscopy were mostly similar and could be validated reciprocally. Achievable pure water permeabilities showed no difference despite protein fouling, leading to low values of albumin SC. This is due to the mechanism that protein fouling occurs on the membrane surface, while there is little internal pore blocking. Therefore, controlling the fouling is essential for membranes in medical use. These characteristics of the hemoconcentration membranes examined in this study are suitable for clinical use.

Electrolysis stands as a pivotal method for environmentally sustainable hydrogen production. However, the formation of gas bubbles during the electrolysis process poses significant challenges by impeding the electrochemical reactions, diminishing cell efficiency, and dramatically increasing energy consumption. Furthermore, the inherent difficulty in detecting these bubbles arises from the non-transparency of the wall of electrolysis cells. Additionally, these gas bubbles induce alterations in the conductivity of the electrolyte, leading to corresponding fluctuations in the magnetic flux density outside of the electrolysis cell, which can be measured by externally placed magnetic sensors. By solving the inverse problem of the Biot-Savart Law, we can estimate the conductivity distribution as well as the void fraction within the cell. In this work, we study different approaches to solve the inverse problem including Invertible Neural Networks (INNs) and Tikhonov regularization. Our experiments demonstrate that INNs are much more robust to solving the inverse problem than Tikhonov regularization when the level of noise in the magnetic flux density measurements is not known or changes over space and time.

Acute encephalopathy with biphasic seizures and reduced diffusion (AESD) is characterized by biphasic seizures following febrile viral infections and delayed reduced diffusion of the cerebral white matter on magnetic resonance imaging (MRI) diffusion-weighted imaging (DWI) (bright tree appearance, BTA). However, hypoxic encephalopathy with biphasic seizures and AESD-mimicking imaging findings has not been reported. Herein, we report an case of hypoxic encephalopathy due to suffocation with concomitant biphasic seizures and BTA, mimicking AESD. On day 1, a 5-month-old female was found face down with breathing cessation and deteriorating consciousness level. The electroencephalography (EEG) revealed periodic epileptic discharges, suggesting possible nonconvulsive status epilepticus. Despite the improvements in consciousness level and EEG abnormalities on day 2, her consciousness level deteriorated again with generalized tonic-clonic seizures on day 3, and head MRI-DWI revealed restricted diffusion predominantly in the subcortical areas, suggesting BTA. Treatment for acute encephalopathy resolved clinical sei-zures and EEG abnormalities. The persistence of abnormal EEG, reflecting abnormal excitation and accumulation of neurotoxic substances caused by hypoxia, may have contributed to the devel-opment of AESD-like findings. As hypoxic encephalopathy causes AESD-like biphasic seizures, monitoring the consciousness level, seizure occurrence, and EEG abnormalities even after acute symptoms have temporarily improved following hypoxia is essential.

Urination on carpet and subflooring can develop into persistent and challenging to mitigate odor. Very little or no information is published on how these VOCs change over time when urine is deposited on the carpet covering a plywood-type subflooring. This research has investigated the VOCs emitted from carpet+subflooring (control), carpet+subflooring sprayed with water (control with moisture), and cat urine-contaminated carpet+subflooring (treatment) over time (day 0 and 15). In addition, the effect of popular cleaning products on VOCs emitted and evaluated their efficacy in eliminating those indoor odors over time (day 0 and 15). Carpet-subflooring with all treatments were also contaminated with Micrococcus luteus, nonmotile obligate aerobe commonly found in household dust, to observe the impact of the aerobe on carpet-subflooring VOCs emission. VOCs emitted from carpet+subflooring receiving different treatments were collected from headspace using solid-phase microextraction (SPME). The VOCs were analyzed using a multidimensional gas chromatography-mass spectrometer attached to an olfactometry (GC-MS-O). Many common VOCs were released from the carpet on day one and day fifteen, specifically from urine contamination. Cleaning products were effective in masking several potent odors of cat urine contaminated carpet VOCs on day one but unable to remove the odor appeared on day 15 in most cases.

The biophysical consequences of nanoscale curvature have been challenging to resolve due to size-dependent membrane behavior and the experimental resolution limits imposed by optical diffraction. Recent advances in nanoengineering and super-resolution techniques have enabled new capabilities for creating and observing curvature. In particular, draping supported lipid bilayers over lithographically patterned substrates provides a model system for endocytic pits. The experiments and simulations presented below describe the possible detection of membrane curvature through fluorescence recovery after photobleaching (FRAP), fluorescence correlation spectroscopy (FCS), single particle tracking (SPT), and polarized localization microscopy (PLM). FRAP and FCS depend on diffraction-limited illumination and detection. In particular, a simulation of FRAP shows no effects on lipids diffusion due to a 50 nm diameter membrane bud at any stage in the budding process. Simulated FCS demonstrated small effects due to a 50 nm radius membrane bud that was amplified with curvature-dependent lipid mobility changes. However, PLM and SPT achieve sub-diffraction-limited resolution of membrane budding and lipid mobility through the identification of the single-lipid positions with ≤15 nm spatial and ≤20 ms temporal resolution. By mapping the single-lipid step lengths to locations on the membrane, the effects of curvature on lipid behavior have been resolved.

Despite being small and simple structured in comparison to their victims, virus particles have the potential to harm severly and even kill highly developed species such as humans. To face upcoming virus pandemics, detailed quantitative biophysical understanding of intracellular virus replication mechanisms is inevitable. Unveiling the relationship of form and function might allow to determine putative attack points relevant for the systematic development of direct antiviral agents (DAA) and potent vaccines. Biophysical investigations of spatio-temporal dynamics of intracellular virus replication so far are rare. We are developing a framework to allow for fully spatio-temporal resolved virus replication dynamics simulations based on partial differential equations models (PDE) and evaluated with advanced numerical mathematical methods on leading supercomputers. This study presents an advanced highly nonlinear model of the genome replication cycle of a specific RNA virus, the Hepatitis C virus (HCV). The diffusion-reaction model mimics the interplay of the major components of the viral RNA (vRNA) cycle, namely non structural viral proteins (NSP), vRNA and a generic host factor. Technically, we couple surface PDEs (sufPDEs) on the 3D embedded 2D Endoplasmatic Reticulum (ER) manifold with PDEs in the 3D membranous web (MW) and cytosol volume. (The MWs are the replication factories growing on the ER induced by NSPs.) The sufPDE/PDE model is evaluated at realistic reconstructed cell geometries which are based on experimental data. The simulations couple the effects of NSPs which are restricted to the ER surface with effects appearing in the volume. The volume effects include the host factor supply from the cytosol and the MW dynamics. Special emphasis is put to the exchange of components between ER surface, MWs and cytosol volume. As the vRNA spatial properties are not fully understood so far in experiment, the model allows for vRNA both restricted to the ER and moving in the cytosol. The visualization of the simulation resembles a look into some sort of fully 3D resolved “in silico microscopes” to mirror and complement in vitro / in vivo experiments for the intracellular vRNA cycle dynamics. The output data are quantitatively consistent with experimental data and provoke advanced experimental studies to validate the model.

Dam breaches have catastrophic consequences, causing severe property damage, life loss, and environmental impact. The Kulekhani reservoir rockfill dam break was studied to evaluate the downstream impact. The appropriate breaching parameter of MacDonald and Langridge (1984) regression equations was selected based on the sixteen observed dam failure cases and cross-sectional geometry of the existing dam of Kulekhani. The 2D Diffusion Wave and Full Dynamic Wave Equation were applied for downstream flood assessment, Full Dynamic Wave was able to capture the physical flow phenomena like river bend effects resulting in higher flow velocity at the outer bend, and formation of eddies considering losses. The application of a Full Dynamic Equation was found to be appropriate for rapidly varying unsteady flow considering steep slopes, and sudden changes in channel geometry. Flood mapping of water depth, flow velocity, flood intensity, and arrival time were carried out for flood hazard assessment classified by the American Society of Civil Engineers (ASCE). Flow depth and extension of the flow area were compared to identify the affected area, higher flow depth and larger extension were observed using a Full Dynamic Wave Equation as a result of less flow velocity considering the losses. Almost 17 minutes of the arrival time of peak difference at the Bagmati River confluence was evaluated between the models which plays an important role in decision-making for selection of the flood model. Flood mitigation with river diversion works through a hydraulic measure of Levee was suggested to protect the highly affected households of Ranche, Nagmar, Khanikhet, and Debaltar towns. Most of the household was found to be safe after the construction of the Levee except for eleven houses that lie along the river below flood elevation of 1269.6 m.a.s.l. This signifies the importance of room for the rivers and the human settlement near the river might be life-threatening.

Our investigations show that electrochemical corrosion of copper is faster than electrochemical corrosion of aluminium at temperatures below 100oC. Literature data analysis shows that the Al atoms diffuse faster than the Cu atoms at temperatures higher than 475oC, Al rich intermetallic compounds (IMCs) are formed faster in the Cu-Al system, and the Kirkendall plane shifts toward Al side. Electrochemical corrosion occurs due to electric current and due to diffusion. An electronic devise working time, for example, depends on initial copper cover thickness on aluminium wire, connected to the electronic devise, temperature, and volume and dislocation pipe diffusion coefficients, so copper, iron, and aluminium electrochemical corrosion rates are investigated experimentally at room temperature and at temperature 100oC. Intrinsic diffusivities ratios of copper and aluminium at different temperatures and diffusion activation energies in the Cu-Al system are calculated by proposed here methods using literature experimental data. Dislocation pipe and volume diffusion activation energies of pure iron are calculated separately by earlier proposed method using literature experimental data. Aluminium dissolved into NaCl solution as the Al3+ ions at room temperature and at temperature 100oC, iron dissolved into NaCl solution as the Fe2+ (not Fe3+) ions at room temperature and at temperature 100oC, copper dissolved into NaCl solution as the Cu+ ions at room temperature and as the Cu+ and the Cu2+ ions at temperature 100oC. It is founded experimentally that copper corrosion is higher than aluminium corrosion, and ratio of electrochemical corrosion rates, kCu/kAl>1, decreases with temperature increasing, although iron electrochemical corrosion rate doesn’t depend on temperature below 100oC. It is obvious, because melting point of iron is more higher then melting point of copper or aluminium. It is calculated that copper electrochemical corrosion rate is approximately equal to aluminium electrochemical corrosion at temperature about 300oC, so copper can dissolve into NaCl solution mostly as the Cu2+ ions at temperature about 300oC. Ratio of intrinsic diffusivities, DCu/DAl <1, increases with temperature increasing, and intrinsic diffusivity of aluminium could be approximately equal to intrinsic diffusivity of copper at temperature about 460oC.

Magnetic nanoparticles are met across many biological species ranging from magnetosensitive bacteria, fishes, bees, bats, rats, birds, to humans. They can be both of biogenetic origin and due to environmental contamination, being either in paramagnetic or ferromagnetic state. The energy of such naturally occurring single-domain magnetic nanoparticles can reach up to 10-20 room k_BT in the magnetic field of the Earth, which naturally led to supposition that they can serve as sensory elements in various animals. This work explores within a stochastic modeling framework a fascinating hypothesis of magnetosensitive ion channels with magnetic nanoparticles serving as sensory elements, especially, how realistic it is given a highly dissipative viscoelastic interior of living cells and typical sizes of nanoparticles possibly involved.

Evaporating liquid sessile drop deposited on horizontal surface is an important object of applications (printing technologies, electronics, sensorics, medical diagnostics, hydrophobic coatings, etc.) and theoretical investigations (microfluidics, self-assembly of nanoparticle, crystallization of the solute, etc.). The arsenal of formulas for calculating the slow evaporation of an axisymmetric drop of capillary dimensions deposited on a flat solid surface is reviewed. Such characteristics as vapor density, evaporation flux density, total evaporation rate are considered. Exact solutions obtained in the framework of the Maxwellian model, in which the evaporation process of the drop is limited by vapor diffusion from the drop surface to the surrounding air, are presented. The summary covers both well-known results obtained during the last decades and new results published by us in the last few years, but practically unknown to the wide scientific community. The newest formulas, not yet published in refereed publications, concerning exact solutions for a number of specific contact angles are also presented. In addition, new approximate solutions are presented for the first time (total evaporation rate and mass loss per unit surface area per unit time in the whole range of contact angles ), which can be used in modeling without requiring significant computational resources.

In this perspective article, we ponder topographical enhancements of artificial neural networks. In our recent paper in JMLR, we proved a quasi-equivalence between the network width and depth and also discussed the power of intra-links, which can be viewed as network height. In 1982, Hopfield published a network to model human associative memory, which contains many loops for dynamic evolution toward fixed points. Based on noising-denoising loops, diffusion models are recently developed to enable Bayesian modeling and inference with big data. Furthermore, we envision development of multi-AI-agent systems through “netware” engineering as a quantum leap of software engineering for emergent behaviors and autonomous AI at individual and population levels. We believe that the novel use of links and loops in space and time via multi-scale coupling would catalyze the next-generation neural networks.

One of the most important problems in the presence of epidemics and pandemics is an accurate prediction and preparedness. Scholars and experts argue that future pandemics and/or epidemics are almost inevitable events and is not whether next pandemics will happen, but when a new heath emergency will emerge. Epidemiologic models for prediction of Coronavirus Disease 2019 (COVID-19) have shown many limitations because of unpredictable dynamics of the new viral agent SARS-CoV-2 in environment and society. The main goals of this study are twofold: first, the analysis of anthropogenic activities and factors that may trigger pandemic threats; second, the planning of new directions for strategies to reduce risks that a pandemic threat emerges and/or in the initial phase to reduce vast diffusion and negative impact of new viral agents that can generate hazards and problems in public health, environment and socioeconomic systems. In particular, the investigation and understanding of sources and driving factors concerning the emergence and diffusion of new pandemics have critical aspects for strategic actions of forecast, prevention and preparation of effective policy responses to cope with next pandemic crises and health emergencies. Insights here endeavor, whenever possible, to clarify these problems to increase the knowledge of the sources and factor determining the emergence of new viral agents in order to design optimal response policies to face next pandemic diseases similar to COVID-19. .

In this work we identify combinations of technological activities that signal the presence local capabilities in a country to successfully export a product. We use country-level patent and trade data to generate a multi-layer network, and we apply maximization of entropy to generate synthetic data to effectively divide signal from noise. We show that in several sectors the signal far exceed the noise. Our exercise provides robust evidence of the presence of synergies between technologies to explain trade performances in specific markets. This can be highly useful for policy makers, to inform industrial and innovation policies.

The transmission of light is one of the key optical processes in the terrestrial environment (the atmosphere and underlying surfaces). The dependence of light transmittance on the illumination/observation conditions and optical properties of the atmosphere–underlying system can be studied using the integro-differential radiative transfer equation. However, for numerous applications a set of analytical equations is needed to describe the transmitted light intensity and flux. In this paper, we describe various analytical techniques to study light transmittance through light scattering and absorbing media. A physical significance and improved mathematical accuracy of approximations are provided using the analytical models for the diffusion exponent, average cosine of the light field, spherical and plane albedos. The accuracy of various approximations is studied using exact radiative transfer calculations with various scattering phase functions, single-scattering albedos, observational conditions, and optical depths.

Due to the complexity, high-risk, and conservative character of construction companies, advanced digital technologies do not become widely adopted in the short term, while vendors make determined efforts to overcome this and disseminate their technologies. This paper presents the methods of an investigation addressing the extremely complex issues related to the current practices of digital technology adoption in construction. It discusses how construction companies follow a specific logical process linked to need, project objectives, characteristics of the adopting organization, and the characteristics of the new technology to be adopted. The study aims to demonstrate a novel method of data collection and analysis including data and methodological triangulation techniques including the use of NVivo and AHP to explore how companies make the decision to uptake a new technology (e.g. advanced crane, tunnel boring machine or drones) by focusing on customer and vendor activities, their interactions, contributing factors, and people involved in the process. The major original contribution of this paper is to develop an innovative methodological Cube for investigating the Construction Technology Adoption Process (CTAP) covering technology adoption, acceptance, diffusion and implementation concepts. CTAP is a framework that delineates the phases of the process that customer organizations use when deciding to adopt a new digital technology and the parallel vendor activities. The significance of these contributions is that they enable vendors to understand how to match their strategies with customer expectations in each phase of the CTAP. It also provides a benchmark for new construction companies to use the current best practice of decision making. Future research is warranted to more clearly delineate any differences with developing nations or related industries such as mining and property management.

: Broad-spectrum antifungal drug deployed for topical therapy, specific for onychomycosis, Itraconazole was used as the active pharmaceutical ingredient in a nail lacquer formulation1. The objective of the study was to optimize an antifungal nail lacquer, which when applied topically onto the dorsal surface of the nail plate would facilitate the transungual penetration of the drug. Itraconazole hydrochloride was synthesized to aid the formulation of the lacquers. The optimization involved comparing four different formulations of 1%w/w Itraconazole nail lacquers containing combinations of penetration enhancers (Urea, Salicylic acid, and Papain) based on their ability to facilitate diffusion of the drug through the nail plate over five days. The drug uptake was quantified by extracting the drug from the nail clippings and analyzing it. The tests conducted to account for the quality of the optimized formulation were drug content, spreadability, check for precipitation, and accelerated stability. The results demonstrated that the optimized 1%w/w Itraconazole nail lacquer contained 5%w/w Salicylic acid, 5 %w/w Papain, and 2.8% w/w Urea. The drug uptake from nail clippings was higher than the MIC90 for T. Rubrum strain, and the quality of the optimized lacquer was not compromised throughout three weeks2. The hypothesis stated that the inclusion of Salicylic acid, Papain, and Urea in an Itraconazole (1%w/w) nail lacquer would have the highest transungual penetration on application to the nail plate. In conclusion, the hypothesis was accepted, and the optimized lacquer passed the drug uptake evaluation and all quality control tests.

In this paper, the author utilizes Saddle Theorem and variational methods to deduce existence of at least six stationary solutions for reaction-diffusion Gilpin-Ayala competition model (RDGACM). To obtain the global stabilization of the positive stationary solution of the RDGACM, the author designs a suitable impulsive event triggered mechanism (IETM) to derive the global exponential stability of the the positive stationary solution. It is worth mentioning that the new mechanism can exclude Zeno behavior and effectively reduce the cost of impulse control through event triggering mechanism. Besides, compared with existing literature, the restrictions on the parameters of the RDGACM are relaxed so that the methods used in existing literature can not be applied to the relaxed case of this paper, and so the author makes comprehensive use of Saddle Theorem, orthogonal decomposition of Sobolev space $H_0^1(\Omega)$ and variational methods to overcome the mathematical difficulty. Numerical examples show the effectiveness of the methods proposed in this paper.

This study presents the interaction with human host metabolism of SARS-CoV-2 ORF7b protein (43 aa), using a Protein-Protein-Interaction Networks analysis. After pruning, we selected from BioGRID the 51 most significant proteins among 2,753 proven interactions and 1,708 interactors, specific to ORF7b. We used these proteins as functional seeds and we got a significant network of 551 nodes via STRING. We performed topological analysis and calculated topological distributions by Cytoscape. Seven high ranked proteins as hub and seven as bottleneck following a hub-and-spoke network-architectural-model were found. Through this interaction model, we identified significant GO-processes (5,057 terms in 15 categories) induced in human metabolism by ORF7b. High statistical significance processes of dysregulated molecular cell mechanisms by the action of ORF7b were discovered. We detected disease-related human proteins and their involvement in metabolic roles, how they relate in a distorted way to signaling and/or functional systems, in particular intra- and inter-cellular signaling systems and the molecular mechanisms that supervise to programmed cell death, with mechanisms similar to that of cancer metastasis diffusion. A cluster analysis showed 10 compact and significant functional clusters, where two of them overlap in a Giant-Connected-Components core of 206 total nodes. These two clusters contain most of the high-rank nodes. ORF7b mainly acts through these two clusters, inducing most of the metabolic dysregulation. We conducted a co-regulation, transcriptional analysis by hub and bottleneck proteins. This analysis allowed us to define the transcription factors and miRNAs that control the high-ranking proteins and the dysregulated processes, within the limits of the poor knowledge that these sectors still impose.

This feature study attempts on setting a granules involving mesoscopic matter-aggregation context as a problem of passing locally by the matter-aggregating system from classical stochastic (mesoscopic limit) to a quantum description (nanoscale quantum-size effect limit). A d-dimensional entropy-production aggregation of the granules-involving matter is considered in terms of a (sub)diffusive realization. It turns out that when taking a full d-dimensional pathway of the aggregation toward the nanoscale, one is capable of disclosing a Heisenberg type (diffusional) relation, setting up an upper uncertainty bound for the (sub)diffusive very slow granules-including environment that matches the quantum limit of h/2pm (m– average mass of a granule; h – the Planck’s constant) for the diffusion coefficient of the aggregation, likely first proposed by Fürth in 1933, and qualitatively foreseen by Schrödinger some years before, both in the context of a diffusing particle cluster. The classical-quantum passage uncovered here, also termed insightfully the quantum-size effect (as borrowed from the quantum dots’ parlance), works properly for the three-dimensional (d=3) case, making use of a substantial physical fact that the (nano)granules interact readily via their surfaces with the also granular surroundings in which they are immersed. This natural observation is embodied in the basic averaging construction of the diffusion coefficient of the aggregation of interest. Certain, possibly biomedical, applications of the model can also be viewed by prospective inspection of tiny inhomogeneities in nanofibrillar and/or lamellar matter for which certain numerical realizations are plausible to prepare based on thorough nanoscale experiments.

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. \ref{GROWTH2}. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with $p$-branches leaving each vertex. Such trees are endowed with algebraic structure, the $p$-adic number fields. We apply theory of the $p$-adic diffusion equation to describe coronavirus' spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling {\it dynamics on energy landscapes.} To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider {\it linearly increasing barriers.} This structure matches with mild regulations in Sweden. The virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the covid-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. We present socio-medical specialties of the covid-19 epidemic supporting our purely diffusional model.

Chronoamperometric curves of the oxidation of a ferrocenyl derivative by the potential step showed diffusion controlled-like currents less than the Cottrell's equation at a platinum wire electrode. The lower deviation cannot be explained by the Butler-Volmer heterogeneous kinetics, but was ascribed to the negatively capacitive current associated with the redox reaction. The deviation at the fully oxidized potential corresponds to the non-zero concentration at the electrode surface, which cannot be predicted from the Nernst equation. The Nernst equation expresses the relationship of the potential with the activity at the electrode surface rather than the concentration. The diffusion equation provides the relation of the current with the surface concentration rather than the activity. The negative capacitance or the non-zero concentration may arise from structure formation on the electrode owing to the dipole-dipole interaction, which is similar to the generation of the double layer capacitance including frequency dispersion. On this concept, we derive here expressions for the lowered diffusion-controlled current and the time-dependent surface concentration. The negatively capacitive current shows the time-dependence of t-0.9, which is similar to the decay of the double layer capacitive currents. The surface concentration decays with the t-0.4-dependence.

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long–range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long–range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations and agent–based models. Reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first–passage time distributions. Research has lead us to question whether the observed long–range memory is a result of actual long–range memory process or just a consequence of non–linearity of Markov processes. As our most recent result we discuss the long–range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the ARFIMA sample series. Our newly obtained results seem indicate that new estimators of self–similarity and long–range memory for analyzing systems with non–Gaussian distributions have to be developed.

In CNS drug discovery, estimation of brain exposure of lead compounds is critical for their optimization. Compounds need to cross the blood-brain barrier (BBB) to reach the pharmacological targets in the CNS. The BBB is a complex system involving passive and active mechanisms of transport and efflux transporters such as P-glycoproteins (P-gp) and breast cancer resistance protein (BCRP), which play an essential role in CNS penetration of small molecules. Several in vivo, in vitro and in silico methods are available to estimate human brain penetration. Preclinical species are used as in vivo models to understand the unbound brain exposure by deriving the Kp,uu parameter, the brain/plasma ratio of exposure corrected with the plasma and brain free fraction. MDCK-mdr1 (Madin Darby canine kidney cells transfected with the MDR1 gene encoding for the human P-gp) assay is the most commonly used in vitro assay to estimate compound permeability and human efflux. The in silico methods to predict brain exposure, such as CNS MPO, CNS BBB scores and various Machine Learning models, help save costs and speed up compound discovery and optimization at all stages. These methods enable the screening of virtual compounds and building of a CNS penetrable compounds library as well as optimization of lead molecules for CNS penetration. Therefore, it is crucial to understand these methods' reliability and ability to predict CNS penetration. We review the in silico, in vitro and in vivo data and their correlation with each other and assess published in silico approaches to predict the BBB penetrability of compounds.

In advanced world stroke is one of the disabling cause of death that can be managed with thrombolysis if presents early despite further risk of intracerebral haemorrhage. Secondary prevention is an important objective in ischaemic stroke where recurrence is very high with subsequent stroke. Carotid End Arterectomy impact a definitive and effective role for both symptomatic and asymptomatic carotid stenosis for secondary stroke prevention in selective cases. Thrombolysis is a potential primary management for certain group whereas carotid surgery employs secondary preventative measure in a specified ischaemic stroke group.