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We investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods. We find that even a single effective topological neighbour suffices for significant order in a system with non-local topological interactions. We also explore topological information flow patterns and clustering dynamics using Hodge spectral entropy and mean Forman-Ricci curvature.

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To assess the excess mortality burden of Covid-19 in the United States, we estimated sex, age and race stratified all-cause excess deaths in each county of the US during 2020 and 2021. Using spatial Bayesian models trained on all recorded deaths between 2003-2019, we estimated 463,187 (95% uncertainty interval (UI): 426,139 - 497,526) excess deaths during 2020, and 544,105 (95% UI: 492,202 - 592,959) excess deaths during 2021 nationally, with considerable geographical heterogeneity. Excess mortality rate (EMR) nearly doubled for each 10-year increase in age and was consistently higher among men than women. EMR in the Black population was 1.5 times that of the White population nationally and as high as 3.8 times in some states. Among the 25-54 year population excess mortality was highest in the American Indian/Alaskan Native (AI/AN) population among the four racial groups studied, and in a few states was as high as 6 times that of the White population. Strong association of EMR with county-level social vulnerability was estimated, including positive associations with prevalence of disability (standardized effect: 40.6 excess deaths per 100,000), older population (37.6), poverty (23.6), and unemployment (18.5), whereas population density (-50), higher education (-38.6), and income (-35.4) were protective. Together, these estimates provide a more reliable and comprehensive understanding of the mortality burden of the pandemic in the US thus far. They suggest that Covid-19 amplified social and racial disparities. Short-term measures to protect more vulnerable groups in future Covid-19 waves and systemic corrective steps to address long-term societal inequities are necessary.

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BACKGROUND: Aneurysm morphology has been correlated with rupture. Previous reports identified several morphologic indices that predict rupture status, but they measure only specific qualities of the morphology of an aneurysm in a semiquantitative fashion. Fractal analysis is a geometric technique whereby the overall complexity of a shape is quantified through the calculation of a fractal dimension (FD). By progressively altering the scale of measurement of a shape and determining the number of segments required to incorporate the entire shape, a noninteger value for the dimension of the shape is derived. We present a proof-of-concept study to calculate the FD of an aneurysm for a small cohort of patients with aneurysms in 2 specific locations to determine whether FD is associated with aneurysm rupture status. METHODS: Twenty-nine aneurysms of the posterior communicating and middle cerebral arteries were segmented from computed tomography angiograms in 29 patients. FD was calculated using a standard box-counting algorithm extended for use with three-dimensional shapes. Nonsphericity index and undulation index (UI) were used to validate the data against previously reported parameters associated with rupture status. RESULTS: Nineteen ruptured and 10 unruptured aneurysms were analyzed. Through logistic regression analysis, lower FD was found to be significantly associated with rupture status (P = 0.035; odds ratio, 0.64; 95% confidence interval, 0.42-0.97 per FD increment of 0.05). CONCLUSIONS: In this proof-of-concept study, we present a novel approach to quantify the geometric complexity of intracranial aneurysms through FD. These data suggest an association between FD and patient-specific aneurysm rupture status.

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The paper is based on a hitherto unexplored document (audiotape of an interview accompanied by a German transcript) from 1953, located in the Freud Papers at the Library of Congress. It contributes to a better understanding of the impact of Freud and of Psychoanalysis on personalities from the exact sciences, here represented by the noted applied mathematicians Richard von Mises and Hilda Geiringer from Vienna. The detailed discussion of the interview sheds some new light on the different roles of Kraus and Freud in the Vienna culture, on the Vienna Jugendkulturbewegung (youth culture movement) during WWI in which Geiringer was involved, on Freud's and Siegfried Bernfeld's standing around 1930 among German philosophers and psychologists, and on Wilhelm Fließ' theory of periodicity, which von Mises-based on his attitude as an applied mathematician-defended against superficial accusations. Finally, new biographical material is provided for von Mises and the remotely related Freud family, and for Geiringer's and von Mises' early lives. The interview, which was taken during the Cold War, also allows conclusions as to how politics influenced the memories and views of the participants. Part of the aim of the paper is historical documentation of unknown material (letters by Karl Kraus and Wolfgang Köhler, one book review by Wilhelm Ostwald, a file on R. Pfennig), including some correction of erroneous information in the literature.

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INTRODUCTION: At the present time, much attention has been focused on new types of solar cells, called perovskite solar cells. They are highly efficient devices with more than 25% power conversion efficiency. However, perovskite solar cell performance has not yet been fully explored. OBJECTIVES: We aimed to mathematically investigate the analytical modeling of current-voltage curves of planar heterojunction perovskite solar cells using Perovich Special Trans Function Theory (STFT). Furthermore, we proposed novel analytical closed-form solutions for short-circuit current and open-circuit voltage of these cells in terms of STFT. We evaluated the safety for laying the theoretical foundation by comparing the accuracy of the proposed expressions by the known methods. METHODS: A novel hybrid metaheuristic algorithm, called particle swarm optimization (PSO) - evaporation rate water cycle algorithm (ERWCA), is proposed to determine equivalent circuit parameters of the perovskite solar cell. A novel objective function is introduced for estimating the parameters for that purpose too. RESULTS: It was shown that STFT is very applicable and efficient for representing current-voltage expressions of perovskite solar cells. STFT provides a more accurate solution and requires fewer order members than the solutions provided by the conventional Taylor series. Based on these expressions and numerical calculations, it is verified that the characteristic values ​​of variables (short-circuit current, no-load voltage, efficiency, and fill factor) were not accurately calculated in the literature. Also, parameters of equivalent circuits of these cells were not accurately estimated. The equivalent circuit parameters were determined using the algorithm proposed in this work, which fit the verified values ​​of characteristic quantities much better than the literature. CONCLUSION: This work lays the foundation for developing the planar-structured perovskite solar cell models, in which the proposed estimation method and expressions are highly effective and provide excellent results.

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Glioblastoma multiforme (GBM) is one of the most deadly forms of cancer. Methods of characterizing these tumours are valuable for improving predictions of their progression and response to treatment. A mathematical model called the proliferation-invasion (PI) model has been used extensively in the literature to model the growth of these tumours, though it relies on known values of two key parameters: the tumour cell diffusivity and proliferation rate. Unfortunately, these parameters are difficult to estimate in a patient-specific manner, making personalized tumour forecasting challenging. In this paper, we develop and apply a deep learning model capable of making accurate estimates of these key GBM-characterizing parameters while simultaneously producing a full prediction of the tumour progression curve. Our method uses two sets of multi sequence MRI in order to produce estimations and relies on a preprocessing pipeline which includes brain tumour segmentation and conversion to tumour cellularity. We first apply our deep learning model to synthetic tumours to showcase the model's capabilities and identify situations where prediction errors are likely to occur. We then apply our model to a clinical dataset consisting of five patients diagnosed with GBM. For all patients, we derive evidence-based estimates for each of the PI model parameters and predictions for the future progression of the tumour, along with estimates of the parameter uncertainties. Our work provides a new, easily generalizable method for the estimation of patient-specific tumour parameters, which can be built upon to aid physicians in designing personalized treatments.

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Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority of frameworks assessing infectious disease risk consider only epistemic uncertainty. We only ever observe a single epidemic, and therefore cannot empirically determine aleatoric uncertainty. Here, we characterise both epistemic and aleatoric uncertainty using a time-varying general branching process. Our framework explicitly decomposes aleatoric variance into mechanistic components, quantifying the contribution to uncertainty produced by each factor in the epidemic process, and how these contributions vary over time. The aleatoric variance of an outbreak is itself a renewal equation where past variance affects future variance. We find that, superspreading is not necessary for substantial uncertainty, and profound variation in outbreak size can occur even without overdispersion in the offspring distribution (i.e. the distribution of the number of secondary infections an infected person produces). Aleatoric forecasting uncertainty grows dynamically and rapidly, and so forecasting using only epistemic uncertainty is a significant underestimate. Therefore, failure to account for aleatoric uncertainty will ensure that policymakers are misled about the substantially higher true extent of potential risk. We demonstrate our method, and the extent to which potential risk is underestimated, using two historical examples.

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External beam radiation therapy is a key part of modern cancer treatments which uses high doses of radiation to destroy tumour cells. Despite its widespread usage and extensive study in theoretical, experimental, and clinical works, many questions still remain about how best to administer it. Many mathematical studies have examined optimal scheduling of radiotherapy, and most come to similar conclusions. Importantly though, these studies generally assume intratumoral homogeneity. But in recent years, it has become clear that tumours are not homogeneous masses of cancerous cells, but wildly heterogeneous masses with various subpopulations which grow and respond to treatment differently. One subpopulation of particular importance is cancer stem cells (CSCs) which are known to exhibit higher radioresistence compared with non-CSCs. Knowledge of these differences between cell types could theoretically lead to changes in optimal treatment scheduling. Only a few studies have examined this question, and interestingly, they arrive at apparent conflicting results. However, an understanding of their assumptions reveals a key difference which leads to their differing conclusions. In this paper, we generalize the problem of temporal optimization of dose distribution of radiation therapy to a two cell type model. We do so by creating a mathematical model and a numerical optimization algorithm to find the distribution of dose which leads to optimal cell kill. We then create a data set of optimization solutions and use data analysis tools to learn the relationships between model parameters and the qualitative behaviour of optimization results. Analysis of the model and discussion of biological importance are provided throughout. We find that the key factor in predicting the behaviour of the optimal distribution of radiation is the ratio between the radiosensitivities of the present cell types. These results can provide guidance for treatment in cases where clinicians have knowledge of tumour heterogeneity and of the abundance of CSCs.

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Stochastic-based optimization algorithms are effective approaches to addressing optimization challenges. In this article, a new optimization algorithm called the Election-Based Optimization Algorithm (EBOA) was developed that mimics the voting process to select the leader. The fundamental inspiration of EBOA was the voting process, the selection of the leader, and the impact of the public awareness level on the selection of the leader. The EBOA population is guided by the search space under the guidance of the elected leader. EBOA's process is mathematically modeled in two phases: exploration and exploitation. The efficiency of EBOA has been investigated in solving thirty-three objective functions of a variety of unimodal, high-dimensional multimodal, fixed-dimensional multimodal, and CEC 2019 types. The implementation results of the EBOA on the objective functions show its high exploration ability in global search, its exploitation ability in local search, as well as the ability to strike the proper balance between global search and local search, which has led to the effective efficiency of the proposed EBOA approach in optimizing and providing appropriate solutions. Our analysis shows that EBOA provides an appropriate balance between exploration and exploitation and, therefore, has better and more competitive performance than the ten other algorithms to which it was compared.

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Although anonymous data are not considered personal data, recent research has shown how individuals can often be re-identified. Scholars have argued that previous findings apply only to small-scale datasets and that privacy is preserved in large-scale datasets. Using 3 months of location data, we (1) show the risk of re-identification to decrease slowly with dataset size, (2) approximate this decrease with a simple model taking into account three population-wide marginal distributions, and (3) prove that unicity is convex and obtain a linear lower bound. Our estimates show that 93% of people would be uniquely identified in a dataset of 60M people using four points of auxiliary information, with a lower bound at 22%. This lower bound increases to 87% when five points are available. Taken together, our results show how the privacy of individuals is very unlikely to be preserved even in country-scale location datasets.

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In a series of lectures given in 2003, soon after receiving the Fields Medal for his results in the Algebraic Geometry, Vladimir Voevodsky (1966-2017) identifies two strategic goals for mathematics, which he plans to pursue in his further research. The first goal is to develop a ''computerised library of mathematical knowledge,'' which supports an automated proof-verification. The second goal is to ''bridge pure and applied mathematics.'' Voevodsky's research towards the first goal brought about the new Univalent foundations of mathematics. In view of the second goal Voevodsky in 2004 started to develop a mathematical theory of Population Dynamics, which involved the Categorical Probability theory. This latter project did not bring published results and was abandoned by Voevodsky in 2009 when he decided to focus his efforts on the Univalent foundations and closely related topics. In the present paper, which is based on Voevodsky's archival sources, I present Voevodsky's views of mathematics and its relationships with natural sciences, critically discuss these views, and suggest how Voevodsky's ideas and approaches in the applied mathematics can be further developed and pursued. A special attention is given to Voevodsky's original strategy to bridge the persisting gap between pure and applied mathematics where computers and the computer-assisted mathematics play a major role.

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Language is an integral part of society which enables communication among its members. To shed light on how words gain their meaning and how their meaning evolves over time, color naming is often used as a case study. The color domain can be defined by a physical space, making it a useful concept for studying denotation of meaning. Though humans can distinguish millions of colors, language provides us with a small, manageable set of terms for categorizing the space. Partitions of the color space vary across different language groups and evolve over time (e.g. new color terms may enter a language). Investigating universal patterns in color naming provides insight into the mechanisms that give rise to the observed data. Recently, computational techniques have been utilized to study this phenomenon. Here, we develop a methodology for transforming a color naming data set-namely, the World Color Survey-which is based on constraints imposed by the stimulus space. This transformed data is used to initialize a nonparametric Bayesian machine learning model in order to implement a culture and theory-independent study of universal color naming patterns across different language groups. All of the methods described are executed by our Python software package called ColorBBDP. • Data from the World Color Survey is transformed from its original format into binary features vectors which can be given as input to the Beta-Bernoulli Dirichlet Process Mixture Model. • This paper provides a specific application of Variational Inference on the Beta-Bernoulli Dirichlet Process Mixture Model towards a color naming data set. • New mathematical measures for performing post-cluster analyses are also detailed in this paper.

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The Kimberley Process Certification Scheme (KPCS) was established in 2000 as a means of controlling the flow of conflict diamonds, mostly, from the African continent. In 2013, the KPCS imposed an embargo on diamonds from the Central African Republic (CAR). Since then the embargo has been lifted in certain prefectures of the country, however, smuggling is suspected from non-compliant areas. Three parcels of diamonds suspected to have mining origins in the CAR, were analysed. These diamonds were investigated for their morphological and chemical characteristics, to establish a diamond fingerprint and to determine if these diamonds had the same fingerprint as previously analysed diamonds from CAR or the Democratic Republic of the Congo (DRC). The analyses of these diamonds were included in the already established diamond database of rough diamonds from the African continent. The morphological characteristics identified included the mass (ct), colour, surface coatings, dominant, secondary and tertiary form, shape, breakage, inclusions, abrasion and surface features that are specific to octahedral, dodecahedral and cubic shapes. The morphological characteristics determined from the diamonds revealed that morphology alone cannot be used as a discriminatory method for diamond fingerprinting. Fourier transform infrared spectroscopy (FTIR) identified the nitrogen concentration and aggregation state of that N. This allowed for the typing of the diamonds as Type I (containing N) and Type II (containing no measureable N). The concentration of N in the three parcels is less than 600 ppm. Further classification of Type I diamonds was performed according to the N aggregation state as single, double or four-fold. The vast majority of diamonds show a combination of nitrogen aggregation states while few were classified as Type II. Fourier transform IR showed no discernible trends between the current study and the established database. Laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) was used as a means of determining the trace element concentrations of 69Ga, 88Sr, 89Y, 90Zr, 93Nb, 133Cs, 137Ba, 139La, 140Ce, 141Pr, 146Nd, 147Sm, 153Eu, 157Gd, 159Tb, 163Dy, 165Ho, 166Er, 169Tm, 172Yb, 175Lu, 178Hf, 181Ta, 232Th and 238U. Laser ablation ICP-MS determined that not all elements produce statistically viable data, however, the data could still be used to discern trace element differences and trends among the parcels. In the current set of diamonds, laser ablation ICP-MS data for parcels A and B showed an excellent agreement with each other as well as those from diamonds previously analysed from CAR. None of the three parcels showed any similarity to data from Bria River or the DRC. It is concluded that the diamonds from parcels A and B are very likely to have mining origins in the same area in the CAR, whereas parcel C is distinct and of possible mixed origin.

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The paper presents the problem of modeling and simulation of thermal energy generation in a batch-fired straw boiler combined with a buffer tank. The batch-fired straw boiler in concern have a combustion chamber and a water jacket. During the combustion process, the combustion chamber heats up and from it the water jacket. Within the boiler, water circulates between the water jacket and the buffer tank. The author proposes a thermal model of the heating installation and a method of identifying the parameters of this model. This model has been simulated in the MATLAB/Simulink environment and presented as an electric analogue. The model of the system has been validated, which means that system parameters have been identified. This identification was based on the results of measurements of the straw combustion processes which were conducted using a laboratory installation. Finally, a model consistent with actual experiments was obtained. The presented model allows for the observation of changes in heating power consumption variations occurring during the straw feed combustion, which depend on the operating parameters of the system. The results of the model can be applied in the optimization of the configuration of the installation.

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The main intension of this paper is to extract new and further general analytical wave solutions to the (2 + 1)-dimensional fractional Ablowitz-Kaup-Newell-Segur (AKNS) equation in the sense of conformable derivative by implementing the advanced exp ( - ϕ ( ξ ) ) -expansion method. This method is a particular invention of the generalized exp ( - ϕ ( ξ ) ) -expansion method. By the virtue of the advanced exp ( - ϕ ( ξ ) ) -expansion method, a series of kink, singular kink, soliton, combined soliton, and periodic wave solutions are constructed to our preferred space time-fractional (2 + 1)- dimensional AKNS equation. An extensive class of new exact traveling wave solutions are transpired in terms of, hyperbolic, trigonometric, and rational functions. To express the underlying propagated features, some attained solutions are exhibited by making their three-dimensional (3D), two-dimensional (2D) combined, and 2D line plot with the help of computational packages MATLAB. All plots are given to show the proper wave features through the founded solutions to the studied equation with particular preferring of the selected parameters. Moreover, it may conclude that the attained solutions and their physical features might be helpful to comprehend the water wave propagation in water wave mechanics.

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BACKGROUND: To understand the impact and volume of coronavirus (COVID-19) crisis, univariate analysis is tedious for describing the datasets reported daily. However, to capture the full picture and be able to compare situations and consequences for different countries, multivariate analytical models are suggested in order to visualize and compare the situation of different countries more accurately and precisely. AIMS: We aimed to utilize data analysis tools that display the relative positions of data points in fewer dimensions while keeping the variation of the original data set as much as possible, and cluster countries according to their scores on the formed dimensions. METHODS: Principal component analysis (PCA) and Partitioning around medoids (PAM) clustering algorithms were used to analyze data of 56 countries, 82 countries and 91 countries with COVID-19 at three time points, eligible countries included in the analysis are those with total cases of 500 or more with no missing data. RESULTS: After performing PCA, we generated two scores: Disease Magnitude score that represents total cases, total deaths, total actives cases, and critically ill cases, and Mortality Recovery Ratio score that represents the ratio between total deaths to total recoveries in any given country. CONCLUSION: Accurate multivariate analyses can be of great value as they can simplify difficult concepts, explore and communicate findings from health datasets, and support the decision-making process.

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The Wiener-Granger causality test is used to predict future experimental results from past observations in a purely mathematical way. For instance, in many scientific papers this test has been used to study the causality relations in the case of neuronal activities. Albeit some papers reported repeatedly about problems or open questions related to the application of the Granger causality test on biological systems, these criticisms were always related to some kind of assumptions to be made before the test's application. In our paper instead we investigate the Granger method itself, making use exclusively of fundamental mathematical tools like Fourier transformation and differential calculus. We find that the ARMA method reconstructs any time series from any time series, regardless of their properties, and that the quality of the reconstruction is given by the properties of the Fourier transform. In literature several definitions of "causality" have been proposed in order to maintain the idea that the Granger test might be able to predict future events and prove causality between time series. We find instead that not even the most fundamental requirement underlying any possible definition of causality is met by the Granger causality test. No matter of the details, any definition of causality should refer to the prediction of the future from the past; instead by inverting the time series we find that Granger also allows one to "predict" the past from the future.

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From Jan. 6, 2019 to Feb. 18, 2019, OSIRIS-REx observed asteroid (101955) Bennu ejecting 11 plumes of dust, of which part is escaping and another part is re-captured by the asteroid. The relative magnitudes of the typical forces acting on the emitted dust are quite different from the environments of the planets and other minor planets in the solar system. Here we show that ejected dust grains from the surface of Bennu can be caught in the gravitational field of Bennu. To this end, we calculated numerically the trajectories of dust grains of various sizes, from the 0.1µm to the ten millimeter range. The shape and the fate of an emitted cloud of particles depend on the size of the grains: smaller grains form a more narrowly confined dust trail while trails formed by larger grains disperse more rapidly. Four different fates are possible for ejected dust. All grains with radius less than 1.0µm, directly re-impact on Bennu or they escape directly. In contrast, a fraction of grains with a radius larger than 10.0 µm will impact or escape only after performing a number of non-Keplerian revolutions around Bennu. Our findings show how dust grains may populate the vicinity of Bennu and other active asteroids and that they can reach interplanetary space and other celestial bodies, implying that organic matter can be transported from carbonaceous asteroids to other celestial bodies, including Earth.

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The present article reports the combined effects of radiation and heat origination on the electro-kinetically induced hydromagnetic squeezed flow of a pseudoplastic fluid. The fluid is passing over a microcantilever sensor surface positioned in the superficial free stream. Microcantiliver sensor can detect the flow rate and the variance in the temperature of the fluid. The thermal conductivity and fluid viscosity are assumed as a function of temperature. Boundary layer approximations are considered to construct a pseudoplastic fluid flow model. The governing system is then resolved into a non-dimensional form with the assistance of an appropriate set of control parameters. The solution to these non-dimensional equations has calculated with the assistance of familiar numerical techniques i.e. Shooting technique. The results specify that flow of fluid, temperature, and velocity profiles are remarkably influenced by the radiation parameter, fluid parameter, heat generation parameter, thermal relaxation parameter, magnetic parameter, and the squeezing number. A comprehensive graphical and tabular study is constructed to check the convergence of the obtained results. One can detect that the temperature curve is changing slightly for the Christov-Cattaneo heat transfer model as compared to classical Fourier's law of heat transfer. Further, the physical quantities, i.e. free stream velocity, variable viscosity, thermal conductivity, Weissenberg number, and Prandtl number have strong impacts on the boundary layer flow equations. It is perceived that the fluid velocity profile rises for the growing value of the magnetic parameter, but reduces for squashed flow index b. Also, a positive variation is found in the temperature profile for rising values of ß and Q .

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Vector-born disease models are extensively used for surveillance and control processes. The most simple and generally use model (SEIR-SEI model) cannot explain a variety of phenomena involved in these diseases spread and development. In order to obtain a wider insight of the vector-born disease models (and the dynamics involved in them), this work focuses into analyse the classical model, a modified versions of it, and 8 their parameters. The modified version includes host mobility, 9 environmental, re-susceptibility, and mosquito life cycle considerations. As results it is observed that there are a limiting number of parameters that play the most important roles in the dynamics (those related to mortality rates, recovery rate from infectious, and pathogen transmission probabilities). Therefore, parameters determination should focus primarily into estimate these values. Stronger effects of the environmental variables are observed and expected by using different parameters and/or the use of multiple environmental variable at the same time.