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For three specific singular perturbed three-component reaction–diffusion systems that admit N-spike solutions in one of the components on a finite domain, we present a detailed analysis for the dynamics of temporal oscillations in the spike positions. The onset of these oscillations is induced by N Hopf bifurcations with respect to the translation modes that are excited nearly simultaneously. To understand the dynamics of N spikes in the vicinity of Hopf bifurcations, we combine the center manifold reduction and the matched asymptotic method to derive a set of ordinary differential equations (ODEs) of dimension 2N describing the spikes’ locations and velocities, which can be recognized as normal forms of multiple Hopf bifurcations. The reduced ODE system then is represented in the form of linear oscillators with weakly nonlinear damping. By applying the multiple-time method, the leading order of the oscillation amplitudes is further characterized by an N-dimensional ODE system of the Stuart–Landau type. Although the leading order dynamics of these three systems are different, they have the same form after a suitable transformation. On the basis of the reduced systems for the oscillation amplitudes, we prove that there are at most ⌊ N / 2 ⌋ + 1 stable equilibria, corresponding to ⌊ N / 2 ⌋ + 1 types of different oscillations. This resolves an open problem proposed by Xie et al. (Nonlinearity 34(8):5708–5743, 2021) for a three-component Schnakenberg system and generalizes the results to two other classic systems. Numerical simulations are presented to verify the analytic results. [ABSTRACT FROM AUTHOR]

Population migration within spatial structures significantly influences disease spread. Given the typically uneven environment, individuals randomly interact with various others, facilitating disease transmission over time. Complex networks are integrated into infectious disease models and effectively capture these contact dynamics. In this paper, we propose a two-delay networked SIR epidemic model featuring a Crowley-Martin type incidence rate and Holling III type treatment rate. The stability of three equilibria of the model is proved by analyzing the distribution of characteristic roots. When two delays change at the same time, the stable region of the equilibrium on delays plane and the existence of Hopf bifurcation are obtained by the method of stability switching curves. Furthermore, we calculate the normal form of Hopf bifurcation to obtain the direction of Hopf bifurcation and the stability of bifurcation periodic solutions. Finally, numerical simulation on a small-world Watts-Strogatz network is performed to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

A diffusive Lotka–Volterra competition system with memory-based diffusion is analyzed. The stability of the boundary steady states depends on memory-based self-diffusion but is independent of memory-based cross-diffusion. However, memory-based cross-diffusion induces instability in the constant coexistence state, increasing the complexity of the spatiotemporal dynamics of the system. We establish the critical conditions under which the constant coexistence state loses its stability through Turing bifurcation, Hopf bifurcation, and double-Hopf bifurcation. The normal form of the double-Hopf bifurcation is also derived. This allows us to prove the existence of an unstable spatially inhomogeneous quasi-periodic solution, and the coexistence of two types of stable spatially inhomogeneous periodic solutions with different wave numbers. In particular, a repulsive memory-based diffusion induces competing species to coexist in spatially segregated steady-state patterns, and an attractive memory-based diffusion can induce competing species to coexist in spatially segregated time-periodic patterns. [ABSTRACT FROM AUTHOR]

This study establishes a novel time-delay fractional SEIHR infectious disease model to investigate the effects of saturated incidence rates and time delays on different populations, including susceptibles, infected individuals, recovered individuals, and latent infected individuals. First, the existence and boundedness of the model's solutions are verified, confirming its well-posedness. Subsequently, the existence of equilibria is analyzed, and the impact of parameter variations on the system is explored by examining the equilibria ϵ 0 and ϵ ∗ , as well as the basic reproduction number R 0 . Additionally, the global dynamics of the equilibria are further analyzed using the Lyapunov method, while Hopf bifurcation theory is applied to explore the conditions under which the system shifts from stability to oscillatory behavior. Numerical simulations further validate the theoretical analysis, showing that time-delay effects significantly influence the system's responsiveness and the rate of disease transmission. Moreover, when the time delay τ crosses the critical threshold τ 0 , the system exhibits periodic oscillations. By predicting periodic fluctuations and incorporating memory effects and persistent influences, we can better control epidemics, emphasizing the importance of time-delay adjustments and enhancing the system's biological realism. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of n-valued groups and studies their algebraic and topological properties. We explore a number of examples. An important class consists of those that we call n-coset groups; they arise as orbit spaces of groups G modulo a group of automorphisms with n elements. However, there are many examples that do not arise from this construction. We see that the theory of n-valued groups is distinct from that of groups with a given automorphism group. There are natural concepts of the action of an n-valued group on a space and of a representation in an algebra of operators. We introduce the (purely algebraic) notion of an n-Hopf algebra and show that the ring of functions on an n-valued group and, in the topological case, the cohomology has an n-Hopf algebra structure. The cohomology algebra of the classifying space of a compact Lie group admits the structure of an n-Hopf algebra, where n is the order of the Weyl group; the homology with dual structure is also an n-Hopf algebra. In general the group ring of an n-valued group is not an n-Hopf algebra but it is for an n-coset group constructed from an abelian group. Using the properties of n-Hopf algebras we show that certain spaces do not admit the structure of an n-valued group and that certain commutative n-valued groups do not arise by applying the n-coset construction to any commutative group. [ABSTRACT FROM AUTHOR]

We prove that the R-matrix and Drinfeld presentations of the Yangian double in type A are isomorphic. The central elements of the completed Yangian double in type A at the critical level are constructed. The images of these elements under a Harish-Chandra-type homomorphism are calculated by applying a version of the Poincaré-Birkhoff-Witt theorem for the R-matrix presentation. These images coincide with the eigenvalues of the central elements in the Wakimoto modules. [ABSTRACT FROM AUTHOR]

Protein language models (PLMs) play a dominant role in protein representation learning. Most existing PLMs regard proteins as sequences of 20 natural amino acids. The problem with this representation method is that it simply divides the protein sequence into sequences of individual amino acids, ignoring the fact that certain residues often occur together. Therefore, it is inappropriate to view amino acids as isolated tokens. Instead, the PLMs should recognize the frequently occurring combinations of amino acids as a single token. In this study, we use the byte-pair-encoding algorithm and unigram to construct advanced residue vocabularies for protein sequence tokenization, and we have shown that PLMs pre-trained using these advanced vocabularies exhibit superior performance on downstream tasks when compared to those trained with simple vocabularies. Furthermore, we introduce PETA, a comprehensive benchmark for systematically evaluating PLMs. We find that vocabularies comprising 50 and 200 elements achieve optimal performance. Our code, model weights, and datasets are available at https://github.com/ginnm/ProteinPretraining. Scientific contribution: This study introduces advanced protein sequence tokenization analysis, leveraging the byte-pair-encoding algorithm and unigram. By recognizing frequently occurring combinations of amino acids as single tokens, our proposed method enhances the performance of PLMs on downstream tasks. Additionally, we present PETA, a new comprehensive benchmark for the systematic evaluation of PLMs, demonstrating that vocabularies of 50 and 200 elements offer optimal performance. [ABSTRACT FROM AUTHOR]

Teacher immediacy and classroom communication apprehension have been well researched in the United States. Instructional communication research in Brazil is limited, and several topics still demand investigation among the population of Brazil. This study extends current research on teacher immediacy and classroom communication apprehension to the Brazilian population. We should extend the analysis to the Brazilian context instead of relying on previous investigations from other regions as the basis for cross-cultural theorizing. A total of 221 students participated in the survey. This study reports four significant findings: (1) Brazilian students' perceptions of teacher immediacy are greater than American students' perceptions of teacher immediacy; (2) American students have higher levels of Classroom Communication Apprehension than Brazilian students; (3) Classroom communication apprehension is negatively correlated with American students' perceptions of teacher immediacy; and (4) Classroom communication apprehension is not significantly correlated with Brazilian students' perceptions of teacher immediacy. Highly immediate teachers will have less apprehensive students. [ABSTRACT FROM AUTHOR]

Esophageal pressure (Peso) is one of the most common and minimally invasive methods used to assess the respiratory and lung mechanics in patients receiving mechanical ventilation. However, the Peso measurement is contaminated by cardiogenic oscillations (CGOs), which cannot be easily eliminated in real-time. The field of study dealing with the elimination of CGO from Peso signals is still in the early stages of its development. In this study, we present an adaptive filtering-based method by constructing a reference signal based on the heart rate and sine function to remove CGOs in real-time. The proposed technique is tested using clinical data acquired from 20 patients admitted to the intensive care unit. Lung compliance (QUOTE) and esophageal pressure swings (△Pes) are used to evaluate the performance and efficiency of the proposed technique. The CGO can be efficiently suppressed when the constructional reference signal contains the fundamental, and second and third harmonic frequencies of the heart rate signal. The analysis of the data of 8 patients with controlled mechanical ventilation reveals that the standard deviation/mean of the QUOTE is reduced by 28.4–79.2% without changing the QUOTE and the △Pes measurement is more accurate, with the use of our proposed technique. The proposed technique can effectively eliminate the CGOs from the measured Peso signals in real-time without requiring additional equipment to collect the reference signal. [ABSTRACT FROM AUTHOR]

Whole-brain models have proven to be useful to understand the emergence of collective activity among neural populations or brain regions. These models combine connectivity matrices, or connectomes, with local node dynamics, noise, and, eventually, transmission delays. Multiple choices for the local dynamics have been proposed. Among them, nonlinear oscillators corresponding to a supercritical Hopf bifurcation have been used to link brain connectivity and collective phase and amplitude dynamics in different brain states. Here, we studied the linear fluctuations of this model to estimate its stationary statistics, i.e., the instantaneous and lagged covariances and the power spectral densities. This linear approximation—that holds in the case of heterogeneous parameters and time-delays—allows analytical estimation of the statistics and it can be used for fast parameter explorations to study changes in brain state, changes in brain activity due to alterations in structural connectivity, and modulations of parameter due to non-equilibrium dynamics. [ABSTRACT FROM AUTHOR]

In this work, the influences of nonlocal interactions on the growing inclusion are studied which are embedded in an elastic wave metamaterial with local resonators. The nonlocal interactions between main resonators are considered as linear springs connected to the second nearest neighboring ones. In addition, the inclusion is supposed that particle masses change along a straight line. Based on the Wiener–Hopf method, the ratio of the tip to end displacements of the inclusion is derived. Furthermore, the dynamic effective mass and stop band frequency are discussed. Numerical results show that in comparison with the system without nonlocal interactions, the new periodic structure can make the displacement ratio tend to the case of homogeneous lattices for high-speed regions. It indicates that more powerful resistance can be created by nonlocal springs during the inclusion growth. [ABSTRACT FROM AUTHOR]

Various approaches have used neural networks as probabilistic models for the design of protein sequences. These "inverse folding" models employ different objective functions, which come with trade-offs that have not been assessed in detail before. This study introduces probabilistic definitions of protein stability and conformational specificity and demonstrates the relationship between these chemical properties and the p (structure | seq) Boltzmann probability objective. This links the Boltzmann probability objective function to experimentally verifiable outcomes. We propose a novel sequence decoding algorithm, referred to as "BayesDesign", that leverages Bayes' Rule to maximize the p (structure | seq) objective instead of the p (seq | structure) objective common in inverse folding models. The efficacy of BayesDesign is evaluated in the context of two protein model systems, the NanoLuc enzyme and the WW structural motif. Both BayesDesign and the baseline ProteinMPNN algorithm increase the thermostability of NanoLuc and increase the conformational specificity of WW. The possible sources of error in the model are analyzed. [ABSTRACT FROM AUTHOR]

The method of characteristics is extended to set-valued Hamilton-Jacobi equations. This problem arises from a calculus of variations’ problem with a multicriteria Lagrangian function: through an embedding into a set-valued framework, a set-valued Hamilton-Jacobi equation is derived, where the Hamiltonian function is the Fenchel conjugate of the Lagrangian function. In this paper a method of characteristics is described and some results are given for the Fenchel conjugate. [ABSTRACT FROM AUTHOR]

With the rapid growth in artificial intelligence, designing high-speed and low-power semiconducting materials is of utmost importance. This investigation provides a theoretical basis to access covalently bonded transition metal-graphene nanoribbon (TM-GNR) hybrid semiconductors whose DFT-computed bandgaps were much narrower than the commonly used pentacene. Systematic optimization of substrates containing remotely placed boryl groups and the transition metals produced the zwitterions via ionic Bergman cyclization (i-BC) and unlocked the polymerization of metal-substituted polyenynes. Aside from i-BC, the subsequent steps were barrierless, which involved structureless transition regions. Multivariate analysis revealed the strong dependence of activation energy and the cyclization mode on the electronic nature of boron and Au(I). Consequently, three regions corresponding to radical Bergman (r-BC), ionic Bergman (i-BC), and ionic Schreiner-Pascal (i-SP) cyclizations were identified. The boundaries between these regions corresponded to the mechanistic shift induced by the three-center-three-electron (3c-3e) hydrogen bond, three-center-four-electron (3c-4e) hydrogen bond, and vacant p-orbital on boron. The ideal combination for cascade polymerization was observed near the boundary between i-BC and i-SP. Transition-metal-graphene nanoribbons (TM-GNR) exhibit unusual optoelectronic properties, however, synthetic access to such materials remains highly challenging. Here, the authors report a quantum chemical substrate design via DFT to access TM-GNR hybrid semiconductors using zwitterionic Bergman cyclization-triggered cascade polymerization. [ABSTRACT FROM AUTHOR]

Background: Veno-arterial extracorporeal membrane oxygenation (V-A ECMO) requires a large amount of economic and human resources. The presence of bystander cardiopulmonary resuscitation (CPR) was focused on selecting appropriate V-A ECMO candidates. Result: This study retrospectively enrolled 39 patients with V-A ECMO due to out-of-hospital cardiac arrest (CA) between January 2010 and March 2019. The introduction criteria of V-A ECMO included the following: (1) < 75 years old, (2) CA on arrival, (3) < 40 min from CA to hospital arrival, (4) shockable rhythm, and (5) good activity of daily living (ADL). The prescribed introduction criteria were not met by 14 patients, but they were introduced to V-A ECMO at the discretion of their attending physicians and were also included in the analysis. Neurological prognosis at discharge was defined using The Glasgow-Pittsburgh Cerebral Performance and Overall Performance Categories of Brain Function (CPC). Patients were divided into good or poor neurological prognosis (CPC ≤ 2 or ≥ 3) groups (8 vs. 31 patients). The good prognosis group had a significantly larger number of patients who received bystander CPR (p = 0.04). The mean CPC at discharge was compared based on the combination with the presence of bystander CPR and all five original criteria. Patients who received bystander CPR and met all original five criteria showed significantly better CPC than patients who did not receive bystander CPR and did not meet some of the original five criteria (p = 0.046). Conclusion: Considering the presence of bystander CPR help in selecting the appropriate candidate of V-A ECMO among out-of-hospital CA cases. [ABSTRACT FROM AUTHOR]

Bisphenol A (BPA) is mainly used to produce polycarbonate consumer products. However, the occurrence of BPA and other bisphenol analogues (BPs) in polystyrene-made plastic products, such as white foam take-out containers (WFTOCs), has not been well investigated. In this study, occurrence of 20 BPs in WFTOC samples collected from China, Canada, and Poland were investigated with a sample size of 152. Results showed that 11 out of 20 BPs have been detected at least in one WFTOC sample. Among them, BPA was the most frequently detected BP, followed by bisphenol S (BPS) and bisphenol AF, while BPF was the least detected BP. Very high concentrations of BPA and BPS were detected in WFTOCs from China (mean 2694 and 552 ng/g), compared with Canada (81 and 45 ng/g, respectively) and Poland (95 and 16 ng/g). Other BPs, such as bisphenol TMC (BPTMC; detection frequency 65%, range < LOQ − 224 ng/g), bisphenol G (17%, < LOQ − 11 ng/g), and bisphenol BP (11%, < LOQ − 1.6 ng/g), were also detected in Chinese WFTOC samples. The mean partitioning coefficients of BPA, BPS, bisphenol AP, and BPTMC between WFTOCs and tap water, 10% ethanol, 50% ethanol, corn oil, or steamed rice were 0.22 − 2.9%, 0.16 − 5.1%, 0.11 − 7.5%, 2.3 − 6.5%, or 0.19 − 0.36%, respectively. The estimated daily intake of BPA, BPS, and BPTMC through using WFTOCs were 0.50 − 547, 0.054 − 229, and < 0.66 ng/kg bw/day, respectively, for general population in China, Canada, and Poland. Overall, this study first reveals the unexpected presence of BPs in WFTOCs made of polystyrene, which contributes to the better understanding of the sources of human exposure to BPs. [ABSTRACT FROM AUTHOR]

In the present paper, a spatially discretized diffusive Brusselator model with zero-flux boundary conditions is considered. Firstly, the global existence and uniqueness of the positive solution are proved. Then the local stability of the unique spatially homogeneous steady state is considered by analyzing the relevant eigenvalue problem with the aid of decoupling method. Hence, the occurrence conditions of Turing bifurcation and Hopf bifurcation for the model at this steady state are obtained. Meanwhile, the comparative simulations on the stability regions of the steady state between the spatially discretized diffusive Brusselator model and its counterpart in continuous space are given. Furthermore, the approximate expressions of the bifurcating periodic solutions are derived according to Hopf bifurcation theorem. The bifurcating spatially nonhomogeneous periodic solutions show the formation of a special kind of periodic structures for this model. Finally, numerical simulations are given to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

In budding yeast Saccharomyces cerevisiae, the switch from aerobic fermentation to respiratory growth is separated by a period of growth arrest, known as the diauxic shift, accompanied by a significant metabolic rewiring, including the derepression of gluconeogenesis and the establishment of mitochondrial respiration. Previous studies reported hundreds of proteins and tens of metabolites accumulating differentially across the diauxic shift transition. To assess the differences in the protein–protein (PPIs) and protein–metabolite interactions (PMIs) yeast samples harvested in the glucose-utilizing, fermentative phase, ethanol-utilizing and early stationary respiratory phases were analysed using isothermal shift assay (iTSA) and a co-fractionation mass spectrometry approach, PROMIS. Whereas iTSA monitors changes in protein stability and is informative towards protein interaction status, PROMIS uses co-elution to delineate putative PPIs and PMIs. The resulting dataset comprises 1627 proteins and 247 metabolites, hundreds of proteins and tens of metabolites characterized by differential thermal stability and/or fractionation profile, constituting a novel resource to be mined for the regulatory PPIs and PMIs. The examples discussed here include (i) dissociation of the core and regulatory particle of the proteasome in the early stationary phase, (ii) the differential binding of a co-factor pyridoxal phosphate to the enzymes of amino acid metabolism and (iii) the putative, phase-specific interactions between proline-containing dipeptides and enzymes of central carbon metabolism. [ABSTRACT FROM AUTHOR]

The presence of endocrine-disrupting chemicals in our daily life is increasing every day and, by extension, human exposure and the consequences thereof. Among these substances are bisphenols and parabens. Urine is used to analyze the exposure. The determination of 12 bisphenol homologues and 6 parabens is proposed. A procedure based on a method previously developed by our research group in 2014 is improved. The extraction yield is higher, because the new protocol is 5 times more efficient. Also, a comparison between calibration with pure standards and matrix calibration, to calculate the matrix effect, was also made. A high grade of matrix effect for all analytes was observed. In terms of validation, the limits of detection (LOD) were between 0.03 and 0.3 ng mL−1 and limits of quantification (LOQ) 0.1 to 1.0 ng mL−1, respectively, and the recovery is higher than 86.4% and lower than 113.6%, with a RSD lower than 13.5% in all cases. A methodology for accurate and sensitive quantification of bisphenol homologues together with parabens in human urine using UHPLC-MS/MS was developed. The method was successfully applied to 30 urine samples from children. [ABSTRACT FROM AUTHOR]

Our kidneys receive about one-fifth of the cardiac output at rest and have a low oxygen extraction ratio, but may sustain, under some conditions, hypoxic injuries that might lead to chronic kidney disease. This is due to large regional variations in renal blood flow and oxygenation, which are the prerequisite for some and the consequence of other kidney functions. The concurrent operation of these functions is reliant on a multitude of neuro-hormonal signaling cascades and feedback loops that also include the regulation of renal blood flow and tissue oxygenation. Starting with open questions on regulatory processes and disease mechanisms, we review herein the literature on renal blood flow and oxygenation. We assess the current understanding of renal blood flow regulation, reasons for disparities in oxygen delivery and consumption, and the consequences of disbalance between O2 delivery, consumption, and removal. We further consider methods for measuring and computing blood velocity, flow rate, oxygen partial pressure, and related parameters and point out how limitations of these methods constitute important hurdles in this area of research. We conclude that to obtain an integrated understanding of the relation between renal function and renal blood flow and oxygenation, combined experimental and computational modeling studies will be needed. [ABSTRACT FROM AUTHOR]

Directional deep brain stimulation (dDBS) provides multiple programming options. Knowledge of the spatial lead orientation is useful for time-efficient programming. Recent studies demonstrated deviations of up to 90° from the intended orientation angle. We examined the deviation of dDBS-lead orientation for leads from two different manufacturers using intraoperative stereotactic (STX) X-ray images. Intraoperative 2D-X-ray images were acquired after implantation of the first lead (TP1) and the second lead (TP2) enabling the estimation of the spatial position of the first lead at TP1 and TP2 and of changes of the orientation for a defined time period. Two investigators retrospectively estimated the orientation of the directional marker for 64 patients. The mean deviation from intended spatial orientation was 40.8° ± 46.1° for all examined leads. The spatial orientation of the first lead did not significantly change within a period of approximately 1 h. The degree of deviation did not differ significantly between two lead manufacturers but depended on the lead fixation technique. Our results showed deviations from the intended orientation angle immediately after the insertion of dDBS leads. The initial spatial orientation remained stable for approximately 1 h and was not caused by technical properties of the implanted lead. Hence, it was most probably the result of unintended mechanical torsion during insertion and/or fixation. Because precise determination of the lead orientation is mandatory for target-oriented dDBS programming, the use of additional imaging suitable for precise 3D visualization of lead contacts and/or the positioning marker is recommended. [ABSTRACT FROM AUTHOR]

Hypoxia is a key prognostic indicator in most solid tumors, as it is correlated to tumor angiogenesis, metastasis, recurrence, and response to therapy. Accurate measurement and mapping of tumor oxygenation profile and changes upon intervention could facilitate disease progression assessment and assist in treatment planning. Currently, no gold standard exists for non-invasive spatiotemporal measurement of hypoxia. Magnetic resonance imaging (MRI) represents an attractive option as it is a clinically available and non-ionizing imaging modality. Specifically, perfluorocarbon (PFC) beacons can be externally introduced into the tumor tissue and the linear dependence of their spin-lattice relaxation rate (R1) on the local partial pressure of oxygen (pO2) exploited for real-time tissue oxygenation monitoring in vivo. In this review, we will focus on early studies and recent developments of fluorine-19 MRI and spectroscopy (MRS) for evaluation of tumor oximetry and response to therapy. [ABSTRACT FROM AUTHOR]

Background: Magnetic resonance spectroscopy (MRS) provides non-invasive information about metabolic features in different regions of the brain affected by mesial temporal sclerosis (MTS). Purpose: To review articles analyzing the most common alterations in biochemical parameters in MTS and the applications of MRS in presurgical assessment. Methods: We undertook a systematic literature search for MRS in MTS in PubMed, SCOPUS, and Cochrane based on the MESH terms ""Magnetic Resonance Spectroscopy", "Proton Magnetic Resonance Spectroscopy", "Carbon-13 Magnetic Resonance Spectroscopy", "1H-MRS", "31P-MRS", "mesial temporal sclerosis", "hippocampal sclerosis", "mesial temporal seizure", and "mesial temporal epilepsy". Results: Of the initial 134 articles found, 30 were selected after the exclusion process. Of these, 13 detected a decrease in N-acetylaspartate (NAA), 9 showed a decreased in the ratio NAA/Cho+Cr, and 8 demonstrated a decreased in the ratio NAA/Cr, all of them in the ipsilateral hippocampus. Nine studies also found reduced NAA levels in extrahippocampal regions. Conclusions: The main findings were a decrease in NAA in the ipsilateral hippocampus. In addition, NAA levels were low outside the hippocampus so MTS could be a more extensive disease. Patients without MTS also presented a decrease in NAA in the ipsilateral hippocampus although NAA was even lower in the MTS patients. Thus, MRS could be useful in the presurgical evaluation to locate the epileptogenic focus, but not specific for the diagnosis of MTS. [ABSTRACT FROM AUTHOR]

Recent studies by the authors developing the theory and applications of block elements in problems of mechanics and physics have unexpectedly resulted in the possibility of interpretation of one more feature of these mechanical and mathematical objects. Following the idea of Benoit Mandelbrot on fractality, i.e., self-similarity in nature, the investigation of block elements as objects with fractal properties is carried out. It is shown that known natural phenomena, processes, and objects described by boundary-value problems for partial differential equations and sets of such equations have self-similar packed block elements as solutions. Moreover, the special role of packed block elements generated by the boundary-value problems for the simplest wave equations, or Helmholtz equations, is highlighted. In the multitude of packed block elements for the boundary-value problems of natural processes, they are objects of a discrete topological space and have the maximum topology representing all the other block elements of the multitude by their unions. At the same time, the wave equation or the Helmholtz equation are analogues of the Schrödinger equation, which is the basis of quantum mechanics. The Schrödinger equation describes the states of elementary particles in quantum mechanics. In this regard, a situation arises in which the fundamental principle of both the quantum world and the specified natural processes are self-similar named equations, which accomplish their functions on the corresponding scales. The packed block elements generated by the boundary-value problems for the same equations as for the Schrödinger equation implement their functions in a continuous medium, and the states of elementary particles are described by similar equations in quantum mechanics. [ABSTRACT FROM AUTHOR]

According to both trial and clinical data on direct oral anticoagulants (DOACs) elderly patients are at greatest risk of bleeding. It is unclear whether age intrinsically affects anticoagulation response. To investigate the age-related sensitivity to DOACs, we compared the pharmacological activity of the direct factor Xa inhibitor, rivaroxaban, between young and elderly subjects ex-vivo. 36 fit elderly and 30 fit young subjects [median (IQR) age: 83(75–87) vs 30(26–38) years] provided a blood sample. Clotting parameters were measured in the resultant plasma samples incubated with rivaroxaban (100–500 ng/ml). Parametric, non-parametric tests and regression lines adjusted for rivaroxaban concentration and baseline values were used to compare data. Rivaroxaban produced a greater prolongation of both Prothrombin Time (PT) and modified Prothrombin Time (mPT) (both p < 0.001) in the elderly compared to young subjects (with difference in mean PT increasing from 1.6 to 6.1s and for mPT from 23.5 to 71.1s at 100 ng/ml and 500 ng/ml plasma rivaroxaban concentration, respectively). Factor X and factor II activity was significantly lower in the elderly in the presence of rivaroxaban (p < 0.001 for both). Rivaroxaban prolonged time-based parameters and suppressed the amount of thrombin generation to a significantly greater extent in the elderly compared to young subjects [%change from baseline for Endogenous Thrombin Potential (ETP): − 35.0 ± 4.4 vs − 29.8 ± 7.4 nM*min; p = 0.002]. The use of validated DOAC assays will be of considerable benefit for monitoring elderly patients who, because of their increased sensitivity to rivaroxaban, may require lower doses of the drug for therapeutic anticoagulation. [ABSTRACT FROM AUTHOR]

(B) Graphical representations of protein stability (thermal profile heat map) and protein structural features (structural barcodes) for each protein measured in TPP and LiP-MS experiments. Biophysical proteomics methods are also suitable to study protein-protein interactions based on the simple rationale that protein-forming complexes have often similar thermal stabilities, thus co-aggregate or are in general more protected from proteolysis. To this end, proteomics approaches have been frequently used to map protein expression in multiple experimental conditions and to identify protein-protein interactions. While informative, protein amounts and physical protein associations do not provide a full picture of protein function. [Extracted from the article]

Motion groups of links in the three sphere S 3 are generalizations of the braid groups, which are motion groups of points in the disk D 2 . Representations of motion groups can be used to model statistics of extended objects such as closed strings in physics. Each 1-extended (3 + 1) -topological quantum field theory (TQFT) will provide representations of motion groups, but it is difficult to compute such representations explicitly in general. In this paper, we compute representations of the motion groups of links in S 3 with generalized axes from Dijkgraaf–Witten (DW) TQFTs inspired by dimension reduction. A succinct way to state our result is as a step toward a twisted generalization (Conjecture 1) of a conjecture for DW theories of dimension reduction from (3 + 1) to (2 + 1) : DW G 3 + 1 ≅ ⊕ [ g ] ∈ [ G ] DW C (g) 2 + 1 , where the sum runs over all conjugacy classes [ g ] ∈ [ G ] of G and C(g) the centralizer of any element g ∈ [ g ] . We prove a version of Conjecture 1 for the mapping class groups of closed manifolds and the case of torus links labeled by pure fluxes. [ABSTRACT FROM AUTHOR]

Let X ε : S 2 n - 1 → T S 2 n - 1 be a smooth perturbation of X 0 , the vector field associated to the dynamical system defined by n identical uncoupled harmonic oscillators constrained to their 1-energy level. We are dealing with the case when any orbit of every X ε is closed: while in general is false that the vector fields of the perturbation are orbitally equivalent to the unperturbed X 0 (Villarini in Ergod Theory Dyn Syst 39:1–32, 2019), we prove that this rigidity behaviour is indeed true if each X ε restricted to a codimension 2 sphere in S 2 n - 1 is orbitally conjugated to a subsystem of X 0 made by n - 1 harmonic oscillators. In other words: to have a non-rigid, or truly non-linear, perturbation of X 0 at least two harmonic oscillators must be destroyed by the perturbation. We use this rigidity result to prove a linearization theorem for real analytic multicentres. Finally we give an example of a real analytic perturbation of X 0 showing discontinuous changing of integer invariants of the vector fields of the perturbation. [ABSTRACT FROM AUTHOR]

Summary: The pandemic from the SARS-CoV‑2 virus is currently challenging healthcare systems all over the world. Maintaining appropriate staffing and resources in healthcare facilities is essential to guarantee a safe working environment for healthcare personnel and safe patient care. Extracorporeal membrane oxygenation (ECMO) represents a valuable therapeutic option in patients with severe heart or lung failure. Although only a limited proportion of COVID-19 patients develop respiratory or circulatory failure that is refractory to conventional treatment, it is of utmost importance to clearly define criteria for the use of ECMO in this steadily growing patient population. The ECMO working group of the Medical University of Vienna has established the following recommendations for ECMO support in COVID-19 patients. [ABSTRACT FROM AUTHOR]

In this paper, we study the number of equilibria of the replicator–mutator dynamics for both deterministic and random multi-player two-strategy evolutionary games. For deterministic games, using Descartes' rule of signs, we provide a formula to compute the number of equilibria in multi-player games via the number of change of signs in the coefficients of a polynomial. For two-player social dilemmas (namely the Prisoner's Dilemma, Snow Drift, Stag Hunt and Harmony), we characterize (stable) equilibrium points and analytically calculate the probability of having a certain number of equilibria when the payoff entries are uniformly distributed. For multi-player random games whose pay-offs are independently distributed according to a normal distribution, by employing techniques from random polynomial theory, we compute the expected or average number of internal equilibria. In addition, we perform extensive simulations by sampling and averaging over a large number of possible payoff matrices to compare with and illustrate analytical results. Numerical simulations also suggest several interesting behaviours of the average number of equilibria when the number of players is sufficiently large or when the mutation is sufficiently small. In general, we observe that introducing mutation results in a larger average number of internal equilibria than when mutation is absent, implying that mutation leads to larger behavioural diversity in dynamical systems. Interestingly, this number is largest when mutation is rare rather than when it is frequent. [ABSTRACT FROM AUTHOR]

As an extension of the discrete Sommerfeld problems on lattices, the scattering of a time-harmonic wave is considered on an infinite square lattice when there exists a pair of semi-infinite cracks or rigid constraints. Due to the presence of stagger, also called offset, in the alignment of the defect edges the asymmetry in the problem leads to a matrix Wiener–Hopf kernel that cannot be reduced to scalar Wiener–Hopf in any known way. In the corresponding continuum model the same problem is a well-known formidable one which possesses certain special structure with exponentially growing elements on the diagonal of kernel. From this viewpoint the present paper tackles a discrete analog of the same by reformulating the Wiener–Hopf problem and reducing it to a finite set of linear algebraic equations; the coefficients of which can be found by an application of the scalar Wiener–Hopf factorization. The considered discrete paradigm involving lattice waves is relevant for modern applications of mechanics and physics at small length scales. [ABSTRACT FROM AUTHOR]

We propose new and original mathematical connections between Hamilton–Jacobi (HJ) partial differential equations (PDEs) with initial data and neural network architectures. Specifically, we prove that some classes of neural networks correspond to representation formulas of HJ PDE solutions whose Hamiltonians and initial data are obtained from the parameters of the neural networks. These results do not rely on universal approximation properties of neural networks; rather, our results show that some classes of neural network architectures naturally encode the physics contained in some HJ PDEs. Our results naturally yield efficient neural network-based methods for evaluating solutions of some HJ PDEs in high dimension without using grids or numerical approximations. We also present some numerical results for solving some inverse problems involving HJ PDEs using our proposed architectures. [ABSTRACT FROM AUTHOR]

For a smooth projective quadric X, Alexander Vishik introduced the notion of connections. He discovered connections arising from the splitting pattern of X as well as the so-called excellent connections. Recently, Victor Petrov and Nikita Semenov found new connections arising from the J-invariantJ(X), which is a layer of the elementary discrete invariant E D (X) , both further Vishik's inventions. In this note, we give a new proof for Peterov–Semenov's connections and extend them to the remaining layers of E D (X) . Also, we briefly discuss connections on nonsmooth quadrics. [ABSTRACT FROM AUTHOR]

Scalar wave propagation across a semi-infinite step or step-like discontinuity on any one boundary of the square lattice waveguides is considered within nearest-neighbour interaction approximation. An application of the Wiener–Hopf method does yield an exact solution of the discrete scattering problem, using which, as the main result of the paper, the transmission coefficients for energy flux are obtained. It is assumed that a wave mode is incident from either side of the step and the question addressed is what fraction of incident energy is transmitted across the atomic step discontinuity. A total of ten configurations are presented that arise due to various placements of discrete Dirichlet and Neumann boundary conditions on the waveguide. Numerical illustrations of a measure of ‘conductance’ are provided. [ABSTRACT FROM AUTHOR]

Bursting oscillations in systems with multi-frequency slow excitations reflect multi-timescale dynamics. As there exist many kinds of multiple periodic excitations in actual dynamical systems, the analysis of dynamical behavior of such systems has received much attention. In this article, we first investigate the bursting in Sprott B system with a single excitation. We show that Hopf bifurcation delay may exhibit due to the effect of slow passage through the supercritical Hopf bifurcation. Interestingly, such delay behavior leads to a pinched "Hopf/Hopf"-hysteresis bursting when delay time is long enough. Then, we focus on the effects of the additional excitation β 2 cos (ω 2 t) on the zero-crossing pinched "Hopf/Hopf"-hysteresis bursting. We find that, under the effects of β 2 cos (ω 2 t) , "Hopf/Hopf"-bifurcation-delay-induced hysteresis behaviors may exhibit very interesting dynamical characteristics. In particular, each equilibrium branch may become the one with twists and turns. Then, the novel bursting pattern, turnover-of-zero-crossing pinched-"Hopf/Hopf"-hysteresis-induced bursting, is disclosed accordingly. In addition, we show that the equilibrium branches may cross each other spirally, leading to multiple intersection points under certain parameter conditions. There are two Hopf bifurcation points perching separately upon either side of the intersection points. This creates multiple delay-induced hysteresis behavior, and the other novel bursting pattern, cascaded pinched "Hopf/Hopf"-hysteresis bursting, is thus created. Finally, we investigate the complex amplitude-modulated bursting (CAMB) rhythms in Sprott B system with multi-frequency slow excitations. [ABSTRACT FROM AUTHOR]

We prove the equivalence of two presentations of the Yangian Y(g) of a simple Lie algebra g, and we also show the equivalence with a third presentation when g is either an orthogonal or a symplectic Lie algebra. As an application, we obtain an explicit correspondence between two versions of the classification theorem of finite-dimensional irreducible modules for orthogonal and symplectic Yangians. [ABSTRACT FROM AUTHOR]

We introduce a new family of thermostat flows on the unit tangent bundle of an oriented Riemannian two-manifold. Suitably reparametrised, these flows include the geodesic flow of metrics of negative Gauss curvature and the geodesic flow induced by the Hilbert metric on the quotient surface of divisible convex sets. We show that the family of flows can be parametrised in terms of certain weighted holomorphic differentials and investigate their properties. In particular, we prove that they admit a dominated splitting and we identify special cases in which the flows are Anosov. In the latter case, we study when they admit an invariant measure in the Lebesgue class and the regularity of the weak foliations. [ABSTRACT FROM AUTHOR]

In this work, we provide the first generalized and critical analysis of data on the chemistry of malononitrile dimer (2-aminopropene-1,1,3-tricarbonitrile) - a multifunctional reagent that is widely used for the preparation of diverse heterocyclic systems. The majority of references are from the last 20-25 years. [ABSTRACT FROM AUTHOR]

We introduce two Hopf algebroids associated to a proper and holomorphic Lie group action on a complex manifold. We prove that the cyclic cohomology of each Hopf algebroid is equal to the Dolbeault cohomology of invariant differential forms. When the action is cocompact, we develop a generalized complex Hodge theory for the Dolbeault cohomology of invariant differential forms. We prove that every cyclic cohomology class of these two Hopf algebroids can be represented by a generalized harmonic form. This implies that the space of cyclic cohomology of each Hopf algebroid is finite dimensional. As an application of the techniques developed in this paper, we generalize the Serre duality and prove a Kodaira type vanishing theorem. [ABSTRACT FROM AUTHOR]

We provide a very brief review of the description of colored invariants for the Hopf link in terms of characters, which need to be taken at a peculiar deformation of the topological locus, depending on one of the two representations associated with the two components of the link. Most important, we extend the description of this locus to conjugate and, generically, to composite representations and also define the “adjoint” Schur functions emerging in the dual description. [ABSTRACT FROM AUTHOR]

When the so-called eek effect emerges while shifting a vehicle shift gearbox, car drivers perceive audible noise and vibrations of drivetrain components. Some physical approaches have been provided in order to explain the effect as well as to search for countermeasures. In Jehle and Fidlin (ZAMM J Appl Math Mech 94(11):911-916 (2014), the interaction of sliding clutch disk and gears is addressed in a rigid body model. The clutch disk’s non-conservative follower forces in combination with geometric coupling in gears imply the action of non-symmetric restoring- and velocity-proportional forces. The desired motion of gearbox components can therefore undergo a mode-coupling flutter instability, out of which vibrations emerge with exponentially growing amplitudes. As the contacts in clutch and gears hold non-smooth transitions such as the possibility of sticking and opening, dynamic solutions are both limited and complex. In this contribution, first of all model details concerning the gear formulation are revised: rigid and viscoelastic normal contact are compared, which imply differences in the nature of the solution and method of stability analysis. Nevertheless the two approaches are shown to converge. Finally, the dynamics behind the loss of stability of the desired motion is investigated. [ABSTRACT FROM AUTHOR]

Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincaré-Weyl generators or $$\mathfrak {gl}(n)$$ generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) $$\kappa $$ -Minkowski spaces and (iii) $$\kappa $$ -Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed. [ABSTRACT FROM AUTHOR]

Background: Non-vitamin K dependent oral anticoagulants (NOACs) significantly decrease overall major bleeding rates compared with vitamin K antagonists (VKAs) but there is conflicting evidence regarding the relative risk of gastrointestinal bleeding. Since data regarding the types, the management, and the outcome of NOAC-associated gastrointestinal bleeding are scarce, we aimed to fill this gap by comparing cases of gastrointestinal bleeding associated with NOAC, VKA, or antiplatelet therapy.Methods: All major gastrointestinal bleeding events documented in the prospective Dresden NOAC registry were identified, and bleeding location, lesion type, endoscopic treatment, use of blood and coagulation factor transfusion, length of stay, and in-hospital mortality were compared with historical data from a large cohort of consecutive gastrointestinal bleeding patients.Results: In the 143 NOAC therapy cases, upper gastrointestinal tract bleeding was seen in 44.1%, lower gastrointestinal tract bleeding was seen in 42.0%, and no lesion could be identified in the remaining 14.0%. In contrast, upper gastrointestinal tract bleeding was commoner in the 185 VKA therapy cases (53.0%) and in the 711 antiplatelet therapy cases (68.1%). Among cases with upper gastrointestinal tract bleeding during VKA or antiplatelet therapy, 54.1% and 61.4% respectively presented with ulcers, compared with 27.0% for NOAC therapy. In contrast, hemorrhoid bleeding was the predominant lesion type for lower gastrointestinal tract bleeding with NOAC therapy, with a rate of 33.3%, compared with 10.6% with VKA therapy and 8.7% with antiplatelet therapy. NOAC-associated gastrointestinal bleeding resulted in comparatively low resource consumption, shorter hospitalization, and low in-hospital mortality (1.6%) compared with gastrointestinal bleeding historically seen with use of VKAs (in-hospital mortality 5.6%) or antiplatelet agents (in-hospital mortality 11.9%).Conclusions: Gastrointestinal bleeding in NOAC recipients is different from that seen with VKA or antiplatelet therapy and has a better short-term prognosis. [ABSTRACT FROM AUTHOR]

We introduce Hopf polyads in order to unify Hopf monads and group actions on monoidal categories. A polyad is a lax functor from a small category (its source) to the bicategory of categories, and a Hopf polyad is a comonoidal polyad whose fusion operators are invertible. The main result states that the normalization of a Hopf polyad is a strong (co)monoidal action-type polyad (or strong monoidal pseudofunctor). The normalization of a polyad is a new polyad having simpler structure but the same category of modules. We show that, under certain assumptions, a Hopf polyad can be 'wrapped up' into a Hopf monad. This generalizes the fact that finite group actions on tensor categories can be seen as Hopf monads. Hopf categories in the sense of Batista, Caenepeel and Vercruysse can be viewed as Hopf polyads in a braided setting via the notion of Hopf polyalgebras. As a special case of the main theorem, we generalize a description of the center of graded fusion category due to Turaev and Virelizier to tensor categories: if $\mathcal {C}$ is a G-graded (locally bounded) tensor category, then G acts on the relative center of $\mathcal {C}$ with respect to the degree one part $\mathcal {C}_{1}$ , and the equivariantization of this action is the center of $\mathcal {C}$ . [ABSTRACT FROM AUTHOR]

We introduce the generalized twisted $$\Gamma \times \mathbb {T}^{n}$$ -equivariant degree with n free parameters, where $$\Gamma $$ is a nonabelian finite group, present a computational formulae based on the reduction to $$\mathbb {T}^{n}$$ -equivariant maps and reduction of parameters techniques. This twisted equivariant degree can be effectively applied to study Hopf bifurcation with symmetries from relative equilibria. We give an example of such bifurcation in a system of ODEs. [ABSTRACT FROM AUTHOR]

The present study examines the hydrogen peroxide scavenging, anticoagulant and thrombolytic activities of silver nanoparticles (AgNPs) that were biosynthesized using extracts obtained from spider cobweb (CB), pod (KP), seed (KS) and seed shell (KSS) of kolanut ( Cola nitida). The nearly spherical shaped AgNPs, with surface plasmon resonance of 431.5-457.5 nm, were polydispersed having sizes of 3-50, 12-80, 8-50, and 5-40 nm for CB, KP, KS and KSS-AgNPs respectively. Hydrogen peroxide scavenging activities of 77-99.8% were obtained using 1-20 µg/ml of AgNPs. The particles prevented the coagulation of blood, and also showed thrombolytic activities of 55.76-89.83%, with KSS-AgNPs having the highest activity. Microscopic examination of the lyzed blood clot supported the thrombolytic activities. On the other hand, silver nitrate solution showed negligible activity of 1.92%, while thrombolysis of 7.55, 8.70, 8.93 and 30.19% were obtained for the extracts of KSS, CB, KS and KP respectively. The results herein presented showed potential biomedical applications of the biosynthesized AgNPs to scavenge free radicals and for the management of blood coagulation disorders and thrombotic diseases. [ABSTRACT FROM AUTHOR]