Search

Herpetic geometric glossitis is a unique morphologic variant of HSV (herpes simplex virus) type 1 infection on the dorsum of the tongue that presents as an extremely painful linear central lingual fissure with a branched pattern. in the center of the tongue; there is a branched pattern of fissures that extend bilaterally from the central linear fissure. Herpetic geometric glossitis has been reported in 11 patients; 8 of these individuals were immunocompromised. Medical conditions and immunosuppressive medication treatment (7 patients) or only medical disorders (3 patients) or neither (1 patient) were present. HSV type 1 infection was diagnosed by viral culture in (7 patients), Tzanck preparation (2 patients) or clinically (2 patients). Mucocutaneous HSV infection at non-lingual locations--including the lips, labial mucosa, face and chest--were observed in 5 patients. All patients' symptoms and lesions responded to treatment with oral antiviral therapy: acyclovir (9 patients), famciclovir (1 patient) or valacyclovir (1 patient). The lingual pain and dorsal tongue fissures completely resolved completely within two to 14 days. In summary, herpetic geometric glossitis is a unique HSV type 1 infection, usually in immunocompromised patients, that occurs on the dorsal tongue and responds completely after treatment with orally administered antiviral therapy.

The knife-cut sign is a distinctive manifestation of herpes simplex virus (HSV) type 1 or HSV type 2 infection that has been described in at least 10 immunocompromised patients. It appears as an extremely painful linear erosion or fissure in an intertriginous area such as the body folds beneath the breast, or within the abdomen, or in the inguinal region. Also, concurrent HSV infection at other mucocutaneous sites, or viscera, or both have been observed. The patients had medical conditions (at least 9 patients) and/or immunosuppressive drug therapy (6 patients). The diagnosis of HSV infection was confirmed by viral culture (8 patients), biopsy (4 patients), direct fluorescence antibody testing (3 patients), immunohistochemistry staining (2 patients), polymerase chain reaction (2 patients), or Western blot serologic assay (1 patient). Knife-cut sign-associated HSV infection is potentially fatal; three patients died. However, clinical improvement or complete healing occurred in the patients who received oral valacyclovir (1 patient), or intravenous acyclovir (2 patients), or intravenous acyclovir followed by foscarnet (1 patient). In summary, HSV infection associated with a positive the knife-cut sign is a potentially fatal variant of HSV infection that occurs in the intertriginous areas of immunocompromised patients and usually requires intravenous antiviral therapy.

Chemical analyses of powdered rocks by different laboratories often yield varying results, requiring estimation of the rock's true composition and associated uncertainty. Challenges arise from the peculiar nature of geochemical data. Traditionally, major and trace elements have been measured using different methods, resulting in chemical analyses where the sum of the parts fluctuates around 1 rather than precisely totaling 1. Additionally, all chemical analyses contain an undisclosed mass fraction representing undetected chemical elements. Because of this undisclosed and unknown mass fraction, geochemical data represent a particular kind of compositional data in which closure to unity is not guaranteed. We argue that chemical analyses exist in the hypercube while being sampled from a true composition residing in the simplex. Therefore, we propose an algorithm that generates random chemical analyses by simulating the data acquisition protocol in geochemistry. Using the algorithm's output, we measure the bias and mean squared error (MSE) of various estimators of the true mean composition. Additionally, we explore the impact of missing values on estimator performance. Our findings reveal that the optimized binary log-ratio mean, a new estimator, exhibits the lowest MSE and bias. It performs well even with up to 70% missing values, in contrast to other classical estimators such as the arithmetic mean or the geometric mean. Applying our approach to the GeoPT database, which contains replicate analyses of igneous rocks from numerous geochemical laboratories, we introduce an outlier detection technique based on the Mahalanobis distance between a laboratory's logit coordinates and the optimized mean estimate. This enables a probabilistic ranking of laboratories based on the atypicality of their performance. Finally, we offer an accessible R implementation of our findings through the GitHub repository linked to this paper [subject classification numbers: 10 (compositions) 85 (statistics)]. [ABSTRACT FROM AUTHOR]

We start by an application the of Krein–Milman theorem to the integral representation of completely monotonic functions. Elements of convex optimization are also mentioned. The paper continues with applications of Hahn–Banach-type theorems and polynomial approximation to obtain recent results on the moment problem on the unbounded closed interval [ 0 , + ∞) . Necessary and sufficient conditions for the existence and uniqueness of the solution are pointed out. Operator-valued moment problems and a scalar-valued moment problem are solved. [ABSTRACT FROM AUTHOR]

The rapid development of renewable energy presents challenges to the security and stability of power systems. Aiming at addressing the power system scheduling problem with load demand and wind power uncertainty, this paper proposes the establishment of different error fuzzy sets based on the Wasserstein probability distance to describe the uncertainties of load and wind power separately. Based on these Wasserstein fuzzy sets, a distributed robust chance-constrained scheduling model was established. In addition, the scheduling model was transformed into a linear programming problem through affine transformation and CVaR approximation. The simplex method and an improved differential evolution algorithm were used to solve the model. Finally, the model and algorithm proposed in this paper were applied to model and solve the economic scheduling problem for the IEEE 6-node system with a wind farm. The results show that the proposed method has better optimization performance than the traditional method. [ABSTRACT FROM AUTHOR]

Abstract Background Energy system models based on linear programming have been growing in size with the increasing need to model renewables with high spatial and temporal detail. Larger models lead to high computational requirements. Furthermore, seemingly small changes in a model can lead to drastic differences in runtime. Here, we investigate measures to address this issue. Results We review the mathematical structure of a typical energy system model, and discuss issues of sparsity, degeneracy and large numerical range. We introduce and test a method to automatically scale models to improve numerical range. We test this method as well as tweaks to model formulation and solver preferences, finding that adjustments can have a substantial impact on runtime. In particular, the barrier method without crossover can be very fast, but affects the structure of the resulting optimal solution. Conclusions We conclude with a range of recommendations for energy system modellers: first, on large and difficult models, manually select the barrier method or barrier+crossover method. Second, use appropriate units that minimize the model’s numerical range or apply an automatic scaling procedure like the one we introduce here to derive them automatically. Third, be wary of model formulations with cost-free technologies and dummy costs, as those can dramatically worsen the numerical properties of the model. Finally, as a last resort, know the basic solver tolerance settings for your chosen solver and adjust them if necessary.

Conway established the following geometric fact: If the sides and of a triangle are prolonged beyond the point by the length of the opposite side and the same is done with the vertices and , then the so-constructed 6 points lie on the sole circle whose center coincides with the center of the inscribed circle. V.A. Alexandrov found a spatial analog of the Conway circle. Namely, if in a tetrahedron we mark three points on the prolongations of the edges , , and beyond the vertex at distance from to the half-perimeter of the opposite face and then do the same with the remaining vertices , , and then the so-constructed 12 points lie on the same sphere if and only if is a frame tetrahedron. We address the multidimensional version of the fact for a simplex in the Euclidean space . [ABSTRACT FROM AUTHOR]

The main objective of this article is to develop a way for calculating the volume like element of an -dimensional simplex in non-Euclidean spaces. The volume of a Euclidean tetrahedron can be calculated by this method, which encourages us to apply it in the case of non-Euclidean spaces. Although it can be useful to have an analytical solution to the problem but the solution will be more complicated as the number of dimensions increases. Compared to analytical methods, our methodology is some computational technique that is not only more practical but also very effective. First, we calculate the volume like element for a non-Euclidean tetrahedron (3-simplex) and proceed to dimensions, while specifying the volume like element in terms of the tetrahedron's face angles, circumradii, and inradii. Also, we derive the formulas for the inradii and circumradii of a spherical and hyperbolic triangle of use in calculating the volume like element. Moreover, we suggest a recursive approach to determining the volume like element in an -dimensional non-Euclidean space, avoiding intricate computations in a higher-dimensional space. [ABSTRACT FROM AUTHOR]

An important breakthrough in improving the efficiency of fuel cell systems is the utilization of optimization algorithms to search for operational parameters. In this process, it is crucial to conduct a rational analysis of optimization variables and parameter constraints, along with the use of precision and fast-converging optimization algorithms. In this study, a detailed lumped-parameter fuel cell air supply subsystem model is established and the polarization curve of the fuel cell stack is verified experimentally. Based on which, the coupling relationships among the operational parameters are analyzed and the coupling constraints are derived through simulations. Subsequently, the constrained Nelder–Mead simplex algorithm is used to maximize the system efficiency. Finally, the changes in fuel cell operational parameter after various degrees of degradation are studied. Results show that as the current increases, the optimal oxygen excess ratio decreases, and the optimal cathode inlet pressure increases. Furthermore, the optimization results show that the optimal stack temperature is the lowest constrained temperature that satisfies humidity requirements, which further shrinks the search space of optimization algorithm and transforms a 4-variable optimization problem into a 2-variable optimization problem. Additionally, both the optimal oxygen excess ratio and optimal cathode inlet pressure increase with the increase of degradation time, with the trend becoming more pronounced. The conclusions drawn in this study can serve as guidance for subsequent fuel cell parameters optimization and the selection of operational parameters. • A lumped-parameter model for fuel cell air supply subsystem was established. • The fuel cell operating parameters' constraints were determined. • The constrained simplex method was employed to search for the optimal parameters. • Changes in the optimal parameters were analyzed at different level of degradation. [ABSTRACT FROM AUTHOR]

Background: Energy system models based on linear programming have been growing in size with the increasing need to model renewables with high spatial and temporal detail. Larger models lead to high computational requirements. Furthermore, seemingly small changes in a model can lead to drastic differences in runtime. Here, we investigate measures to address this issue. Results: We review the mathematical structure of a typical energy system model, and discuss issues of sparsity, degeneracy and large numerical range. We introduce and test a method to automatically scale models to improve numerical range. We test this method as well as tweaks to model formulation and solver preferences, finding that adjustments can have a substantial impact on runtime. In particular, the barrier method without crossover can be very fast, but affects the structure of the resulting optimal solution. Conclusions: We conclude with a range of recommendations for energy system modellers: first, on large and difficult models, manually select the barrier method or barrier+crossover method. Second, use appropriate units that minimize the model's numerical range or apply an automatic scaling procedure like the one we introduce here to derive them automatically. Third, be wary of model formulations with cost-free technologies and dummy costs, as those can dramatically worsen the numerical properties of the model. Finally, as a last resort, know the basic solver tolerance settings for your chosen solver and adjust them if necessary. [ABSTRACT FROM AUTHOR]

A spectrophotometric determination of azithromycin was optimized using the simplex model. The approach proved to be accurate and sensitive. The analyte reacted with bromothymol blue (BTB) to form a colored ion pair, which was extracted in chloroform in a buffer medium of pH 4 potassium phthalate. The extracted colored product was assayed at 415 nm, exhibiting a linear quantification range of 1-20 µg/mL. The LOD was 0.671 µg/mL, with a correlation coefficient of 0.9998 and an RSD% of 0.96±0.2. The molar absorptivity was 20253.5 L/mol·cm. The excipients did not interfere with the proposed method for assaying azithromycin in curative formulations. [ABSTRACT FROM AUTHOR]

Compositional data are vectors typically representing proportions of a whole, that is, those whose elements are strictly positive and subject to a unit-sum constraint. The increasing number of fields where this type of data arises makes the development of proper statistical tools an important issue. From a regression perspective, whenever the multivariate response is a compositional vector, a proper model that accounts for the unit-sum constraint is the well-established Dirichlet regression model. However, there are significant drawbacks mainly due to the limited flexibility of the Dirichlet distribution. The aim of this contribution is to introduce a new multivariate regression model for constrained responses, that is based on the extended flexible Dirichlet distribution (which is a structured mixture with Dirichlet distributed components). The new model is obtained by adopting a novel reparameterization which allows for, among other things, the presence of suitably designed cluster-specific regression patterns. It is shown to provide considerably greater flexibility and better performance than the standard Dirichlet regression model. In particular, from theoretical analysis, intensive simulation studies in many challenging scenarios, as well as from a real data application, it emerges that the new regression model can handle several issues affecting the Dirichlet regression, such as the presence of outliers, latent groups, multi-modality, and positive correlations. [ABSTRACT FROM AUTHOR]

MINLO (mixed-integer nonlinear optimization) formulations of the disjunction between the origin and a polytope via a binary indicator variable have broad applicability in nonlinear combinatorial optimization, for modeling a fixed cost c associated with carrying out a set of d activities and a convex variable cost function f associated with the levels of the activities. The perspective relaxation is often used to solve such models to optimality in a branch-and-bound context, especially in the context in which f is univariate (e.g., in Markowitz-style portfolio optimization). But such a relaxation typically requires conic solvers and are typically not compatible with general-purpose NLP software which can accommodate additional classes of constraints. This motivates the study of weaker relaxations to investigate when simpler relaxations may be adequate. Comparing the volume (i.e., Lebesgue measure) of the relaxations as means of comparing them, we lift some of the results related to univariate functions f to the multivariate case. Along the way, we survey, connect and extend relevant results on integration over a simplex, some of which we concretely employ, and others of which can be used for further exploration on our main subject. [ABSTRACT FROM AUTHOR]

Projecting a vector onto a simplex is a well-studied problem that arises in a wide range of optimization problems. Numerous algorithms have been proposed for determining the projection; however, the primary focus of the literature is on serial algorithms. We present a parallel method that decomposes the input vector and distributes it across multiple processors for local projection. Our method is especially effective when the resulting projection is highly sparse, which is the case, for instance, in large-scale problems with independent and identically distributed (i.i.d.) entries. Moreover, the method can be adapted to parallelize a broad range of serial algorithms from the literature. We fill in theoretical gaps in serial algorithm analysis and develop similar results for our parallel analogues. Numerical experiments conducted on a wide range of large-scale instances, both real world and simulated, demonstrate the practical effectiveness of the method. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms—Continuous. Funding: This work was supported by the Office of Naval Research [Grant N00014-23-1-2632]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0328) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0328). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

Using acoustic emission (AE) technique to locate the microcracking of rock samples in the process of rock mechanics test is one of the most effective means to study the spatio-temporal evolution of rock failure. At present, the research on AE source localization method for layered rock considering anisotropic P-wave velocity is insufficient and the location methods are usually two-dimensional. This paper first analyses the characteristics of P-wave velocity of layered rocks, and a method for establishing anisotropic P-wave velocity model of layered rocks is introduced. Then, a three-dimensional AE source localization method for layered rocks is proposed based on the anisotropic P-wave velocity model and simplex algorithm. The influences of iterative initial value, iterative contraction length, number of iterations and P-wave velocity measurement error on the positioning accuracy of this method are studied. And selection methods of those iterative parameters are introduced. Finally, the numerical analysis and true triaxial compression tests for quartz mica schist, quartz schist and black shale are conducted to verify the high location accuracy and efficiency of the proposed method. Numerical tests show that the average absolute distance errors of AE location results are less than 1 mm when the P-wave velocity measurement error is less than 5%, which is much less than that arising from use of the traditional simplex method. And the AE location results are consistent with the failure modes of the true triaxial compression test rock samples. [ABSTRACT FROM AUTHOR]

The method of constructing 47 crystal simplex models using Diamond software and its application in teaching were introduced. [ABSTRACT FROM AUTHOR]

The present paper deals to a family of non-Volterra quadratic stochastic operators depending on a parameter and a permutation and their trajectory behaviours. We find all fixed and periodic points for such non-Volterra quadratic stochastic operator on a finite-dimensional simplex. We proved that the ω- limit set of any trajectory of such non-Volterra quadratic stochastic operator consists of either single point or finite points. [ABSTRACT FROM AUTHOR]

Simplices are the fundamental domain when integrating over convex polytopes. The aim of this work is to establish a novel framework of Monte Carlo integration over simplices, throughout from sampling to variance reduction. Namely, we develop a uniform sampling method on the standard simplex consisting of two independent procedures and construct theories on change of measure on each of the two independent elements in the developed sampling technique with a view towards variance reduction by importance sampling. We provide illustrative figures and numerical results to support our theoretical findings and demonstrate the strong potential of the developed framework for effective implementation and acceleration of Monte Carlo integration over simplices. [ABSTRACT FROM AUTHOR]

We start by an application the of Krein–Milman theorem to the integral representation of completely monotonic functions. Elements of convex optimization are also mentioned. The paper continues with applications of Hahn–Banach-type theorems and polynomial approximation to obtain recent results on the moment problem on the unbounded closed interval [0,+∞). Necessary and sufficient conditions for the existence and uniqueness of the solution are pointed out. Operator-valued moment problems and a scalar-valued moment problem are solved.

The rapid development of renewable energy presents challenges to the security and stability of power systems. Aiming at addressing the power system scheduling problem with load demand and wind power uncertainty, this paper proposes the establishment of different error fuzzy sets based on the Wasserstein probability distance to describe the uncertainties of load and wind power separately. Based on these Wasserstein fuzzy sets, a distributed robust chance-constrained scheduling model was established. In addition, the scheduling model was transformed into a linear programming problem through affine transformation and CVaR approximation. The simplex method and an improved differential evolution algorithm were used to solve the model. Finally, the model and algorithm proposed in this paper were applied to model and solve the economic scheduling problem for the IEEE 6-node system with a wind farm. The results show that the proposed method has better optimization performance than the traditional method.

The formulations of polynomials over a topological simplex combine the elements of topology and algebraic geometry. This paper proposes the formulation of simplicial polynomials and the properties of resulting topological manifolds in two classes, non-degenerate forms and degenerate forms, without imposing the conditions of affine topological spaces. The non-degenerate class maintains the degree preservation principle of the atoms of the polynomials of a topological simplex, which is relaxed in the degenerate class. The concept of hybrid decomposition of a simplicial polynomial in the non-degenerate class is introduced. The decompositions of simplicial polynomial for a large set of simplex vertices generate ideal components from the radical, and the components preserve the topologically isolated origin in all cases within the topological manifolds. Interestingly, the topological manifolds generated by a non-degenerate class of simplicial polynomials do not retain the homeomorphism property under polynomial extension by atom addition if the simplicial condition is violated. However, the topological manifolds generated by the degenerate class always preserve isomorphism with varying rotational orientations. The hybrid decompositions of the non-degenerate class of simplicial polynomials give rise to the formation of simplicial chains. The proposed formulations do not impose strict positivity on simplicial polynomials as a precondition. [ABSTRACT FROM AUTHOR]

In this paper, we propose new proofs of the classical Brunn—Minkowski theorem on the volume of the sum of convex polyhedra P0 and P1 of the same n-dimensional volume in Euclidean space ℝn, n ≥ 2: Vn((1 − t)P0 + tP1) ≥ Vn(P0) = Vn(P1), 0 < t < 1, where the equality holds only if P1 is obtained from P0 by a parallel translation; in other cases, the strict inequality holds. Proofs are based on the sequential partition of the polyhedron P0 into simplexes by hyperplanes. For dimensions n = 2 and n = 3, in the case where P0 is a simplex (a triangle for n = 2), for an arbitrary convex polyhedron P1 ⊂ ℝn, we construct a continuous (in the Hausdorff metric) one-parameter family of convex polyhedra P1(s) ⊂ ℝn, s ∈ [0, 1], P1(0) = P1, for which the function w(s) = Vn((1 − t)P0 + tP1(s)) strictly monotonically decreases, and P1(1) is obtained from P0 by a parallel translation. If P1 is not obtained from P0 by a parallel translation, then, using elementary geometric constructions, we establish the existence of a polyhedron P 1 ′ for which Vn ((1 − t)P0 + tP1) > Vn((1 − t)P0 + t P 1 ′ ). [ABSTRACT FROM AUTHOR]

SCORE was introduced as a spectral approach to network community detection. Since many networks have severe degree heterogeneity, the ordinary spectral clustering (OSC) approach to community detection may perform unsatisfactorily. SCORE alleviates the effect of degree heterogeneity by introducing a new normalization idea in the spectral domain and makes OSC more effective. SCORE is easy to use and computationally fast. It adapts easily to new directions and sees an increasing interest in practice. In this paper, we review the basics of SCORE, the adaption of SCORE to network mixed membership estimation and topic modeling, and the application of SCORE in real data, including two datasets on the publications of statisticians. We also review the theoretical "ideology" underlying SCORE. We show that in the spectral domain, SCORE converts a simplicial cone to a simplex and provides a simple and direct link between the simplex and network memberships. SCORE attains an exponential rate and a sharp phase transition in community detection, and achieves optimal rates in mixed membership estimation and topic modeling. [ABSTRACT FROM AUTHOR]

Abstract The production of eco-efficient cement-based materials is essential to reduce CO2 emissions from the construction industry. A substantial reduction in global CO2 emissions can be achieved by using clinker in mortar and concrete more efficiently and using low-CO2 minerals as partial replacements for Portland cement. However, the proportioning of eco-efficient composites is complex and the reduction in clinker content may affect its properties. This paper aims to optimize the mix design of high-strength mortars containing supplementary cementitious materials (limestone filler, fly ash, metakaolin, silica fume). The compressible packing model associated with a simplex mixture design were used together with chemical parameters, to limit the amount of active SCMs for the model iterations. The results show a significant decrease in the environmental impact of the mortars, which presented compressive strengths between 76 and 118 MPa at 91 days and binder indexes between 10 and 15 kg/m3/MPa. The reactivity of the SCMs (based on the modified Chapelle test) were successfully used to establish the Portland cement substitution (up to 13%), preventing the presence of unreacted SCMs and optimizing the use of limestone filler and sand, which have a lower environmental impact. The high-performance blends reached 8.73 kg CO2e/MPa, up to a 30% reduction in CO2e emissions compared to the mortar with only Portland cement.

Time factor plays an important role in many issues, and the most important of these issues is the issue of transportation, when we need to transport perishable materials such as milk, medicines ,blood,….. etc. or develop war plans to secure the requirements of battle of ammunition - food - and soldiers …..etc., at maximum speed, we need a careful scientific study that enables us to avoid losses, so the researchers studied transport models in the shortest possible time using the values of classic logic and the best solution for such models is a specific value subject to increase or decrease because there is nothing certain in the real reality, all the results of the studies are related to the surrounding conditions of the system under study, due to the sensitivity of these issues had to be reformulated according to a science that takes into account all the cases that the system can go through so that we can take all possible precautions that help us reduce losses and secure the required in the shortest possible time, we have in This research formulates transport models with the shortest time and we presented a special way to solve such models using neutrosophic values, based on the concept of the neutrosophic linear mathematical model, a model that has something of non-determination (indeterminacy) and we reached transport models with the shortest time that are considered a generalization of the existing models because they give us optimal neutrosophic values for time.

Most quantitative magnetization transfer (qMT) imaging methods require acquiring additional quantitative maps (such as T1) for data fitting. A method based on multiple phase-cycled bSSFP was recently proposed to enable high-resolution 3D qMT imaging based on least square fitting without any extra acquisition, and thus has high potential for simplifying the qMT procedure. However, the quantification of qMT parameters with this method was suboptimal, limiting its potential for clinical application despite its simpler protocol and higher spatial resolution. To improve the fitting of qMT data obtained with multiple phase-cycled bSSFP, we propose SIMulation-based Physics-guided Learning of neural network for qMT parameters EXtraction, or SIMPLEX. In contrast to previous deep learning supervised approaches for quantitative MR that require the acquisition of input data and corresponding ground truth for training, we leveraged the MR signal model to generate training samples without expensive data curation. The network was trained exclusively with simulation data by predicting the simulation parameters. The same network was applied directly to in-vivo data without additional training. The approach was verified with both simulation and in-vivo data. SIMPLEX showed a decrease in fitting mean squared error for all simulation data compared to the existing least-square fitting method. The in-vivo experiment revealed that the network performed well with the real in vivo data unseen during training. For all experiments, we observed that SIMPLEX consistently improved the quantification quality of the qMT parameters whilst being more robust to noise compared to the prior technique. The proposed SIMPLEX will expedite the routine clinical application of qMT by providing qMT parameters (exchange rate, pool fraction) as well as T1, T2, and ΔB0 maps simultaneously with high spatial resolution, better reliability, and reduced processing time.

ε Time factor plays an important role in many issues, and the most important of these issues is the issue of transportation, when we need to transport perishable materials such as milk, medicines,blood,….. etc. or develop war plans to secure the requirements of battle of ammunition - food - and soldiers …..etc., at maximum speed, we need a careful scientific study that enables us to avoid losses, so the researchers studied transport models in the shortest possible time using the values of classic logic and the best solution for such models is a specific value subject to increase or decrease because there is nothing certain in the real reality, all the results of the studies are related to the surrounding conditions of the system under study, due to the sensitivity of these issues had to be reformulated according to a science that takes into account all the cases that the system can go through so that we can take all possible precautions that help us reduce losses and secure the required in the shortest possible time, we have in This research formulates transport models with the shortest time and we presented a special way to solve such models using neutrosophic values, based on the concept of the neutrosophic linear mathematical model, a model that has something of non-determination (indeterminacy) and we reached transport models with the shortest time that are considered a generalization of the existing models because they give us optimal neutrosophic values for time, which are unspecified values Nt * = t* ± ε where ε is indeterminism and we will take it in the form then become the matrix of times Nt* = [t * ± ε], where Nt* is any neighborhood of t *, it should be noted that in this research when viewing the example we took some transfer times neutrosophic values of the form Nt ∈ [t1, t2 ] to be able to clarify the main goal of the research. [ABSTRACT FROM AUTHOR]

The standard simplex in |$\mathbb{R}^{n}$|⁠ , also known as the probability simplex, is the set of nonnegative vectors whose entries sum up to 1. It frequently appears as a constraint in optimization problems that arise in machine learning, statistics, data science, operations research and beyond. We convert the standard simplex to the unit sphere and thus transform the corresponding constrained optimization problem into an optimization problem on a simple, smooth manifold. We show that Karush-Kuhn-Tucker points and strict-saddle points of the minimization problem on the standard simplex all correspond to those of the transformed problem, and vice versa. So, solving one problem is equivalent to solving the other problem. Then, we propose several simple, efficient and projection-free algorithms using the manifold structure. The equivalence and the proposed algorithm can be extended to optimization problems with unit simplex, weighted probability simplex or |$\ell _{1}$| -norm sphere constraints. Numerical experiments between the new algorithms and existing ones show the advantages of the new approach. Open source code is available at https://github.com/DanielMckenzie/HadRGD. [ABSTRACT FROM AUTHOR]

Based on the method proposed for solving the so-called -systems of linear equations, it is proved that the orders of homogeneous invariant differential operators of smooth real functions of one variable take values from to , and the dimension of the space of all such operators does not exceed . A classification of invariant differential operators of order is obtained for and for for all orders from 4 to 10. Homogeneous invariant differential operators of the smallest order and the largest order are given, respectively, by the product of the first differentials () and the Wronskian (). The existence of nonzero homogeneous invariant differential operators of order for is proved. [ABSTRACT FROM AUTHOR]

In this paper the results of Radloff and Schwabe (Stat Papers 60:165–177, 2019) will be extended for a special class of symmetrical intensity functions. This includes binary response models with logit and probit link. To evaluate the position and the weights of the two non-degenerated orbits on the k-dimensional ball usually a system of three equations has to be solved. The symmetry allows to reduce this system to a single equation. As a further result, the number of support points can be reduced to the minimal number. These minimally supported designs are highly efficient. The results can be generalized to arbitrary ellipsoidal design regions. [ABSTRACT FROM AUTHOR]

Abstract Ecosystems are complex and sparsely observed making inference and prediction challenging. Empirical dynamic modelling (EDM) circumvents the need for a parametric model and complete observations of all system variables. Classical univariate approaches, which require time‐series observations of only a single focal variable, can produce verifiable out‐of‐sample forecasts; however, they can sometimes require long time series that may be difficult to obtain. More importantly, classical approaches limit the depth of mechanistic understanding that can be gained and the generalizability of forecasts to non‐analogue futures. We review the main ideas of EDM and more recent extensions that expand their capabilities for improving forecasts and understanding mechanism. Algorithms are now available that allow for missing data, unequal sampling intervals and combining short time series, which increase the number of datasets that can be used. Recent extensions of EDM to multivariate time series substantially expand the range of applications and mechanistic questions that can be addressed, including detecting causal coupling, tracking changing interactions in real time, leveraging short time series from information shared in coupled variables, modelling dynamically changing stability, scenario exploration, and management applications involving optimal control.

The risk management business evolves rapidly, so actuaries are faced with the need for new analysis methodologies. However, the use of incorrect methodologies for actuarial modeling can have serious implications for strategic decision making. This study aims to introduce the simplex regression model as a suitable methodology for actuarial modeling of data whose values belong to the unit interval. Using a risk management data set, the linear model with normal distribution and the proposed regression model were compared. The evaluation of the models presented concluded by the quality of the modeling through simplex regression, indicating the quality of this method as a new analysis tool for the actuarial context.

Land use planning involves making an appropriate decision and selecting a use over other alternatives. A step-by-step methodology was developed to evaluate the optimal combination of regional land use technologies and the spatial allocation. For a realistic approach, a case study (specifically Rivadavia department, Salta, Argentina) is considered, which has deforestation problems and the advance of intensive and extractive agriculture. Five management techniques are considered for the area: precision agriculture (T1), advance livestock farming (T2), payment for ecosystem service (T3), traditional agriculture–livestock farming—Criollo (T4), and traditional forest management—Wichi (T5). A land evaluation on a GIS model is carried out to obtain the land suitability for each technique. Analyzing local experts' opinions using the Markowitz portfolio methodology allows us to obtain an optimal combination of techniques. Finally, a Simplex method analysis linked with the GIS is performed to allocate the five techniques over the territory maximizing land suitability and in compliance with percent surface assignments. The result assigns each GIS polygon to a specific technique, reaching optimal land suitability in 92% of the territory. Natural capital and social attributes had a significant and complex impact on technology choice, but objective and optimized approaches in their allocation were possible and provides valuable information to guide public policies. [ABSTRACT FROM AUTHOR]

This paper presents new lower bounds for the lattice covering densities of simplices by studying the Degree-Diameter Problem for abelian Cayley digraphs. In particular, it proves that the density of any lattice covering of a tetrahedron is at least 25/18 and the density of any lattice covering of a four-dimensional simplex is at least 343/264. [ABSTRACT FROM AUTHOR]

In this paper, we consider a quadratic operator on the two-dimensional simplex, which is a convex combination of two quadratic stochastic operators. It is proved that the center of the simplex is a unique fixed point of the operator and this fixed point is an attracting point. [ABSTRACT FROM AUTHOR]

Let Sn be an n -dimensional simplex and Γp(Sn) be the smallest positive number γ such that Sn can be covered by p translates of γSn . We obtain an upper bound of the least positive number β such that −Sn can be covered by two translates of β Sn, which is tight when n = 3 . In addition, we get the exact value of Γn+2(Sn) and an upper bound of Γn+3(Sn) . We also provide the precise value of Γ6(S3), new lower and upper bounds of Γ7(S3), and an upper bound of Γ8(S3) . [ABSTRACT FROM AUTHOR]

Finite elements with polynomial basis functions on the simplex with a symmetric distribution of nodes should have a unique polynomial representation. Unisolvence not only requires that the number of nodes equals the number of independent polynomials spanning a polynomial space of a given degree, but also that the Vandermonde matrix controlling their mapping to the Lagrange interpolating polynomials can be inverted. Here, a necessary condition for unisolvence is presented for polynomial spaces that have non-decreasing degrees when going from the edges and the various faces to the interior of the simplex. It leads to a proof of a conjecture on a necessary condition for unisolvence, requiring the node pattern to be the same as that of the regular simplex. [ABSTRACT FROM AUTHOR]

Purpose of the work is to study the dynamics of the asymptotic behavior of trajectories of discrete Lotka–Volterra dynamical systems with homogeneous tournaments operating in an arbitrary (m − 1)-dimensional simplex. It is known that a dynamic system is an object or a process for which the concept of a state is uniquely defined as a set of certain quantities at a given time, and a law describing the evolution of initial state over time is given. Mainly in questions of population genetics, biology, ecology, epidemiology and economics, systems of nonlinear differential equations describing the evolution of the process under study often arise. Since the Lotka–Volterra equations often arise in life phenomena, the main purpose of the work is to study the trajectories of discrete dynamical Lotka–Volterra systems using elements of graph theory. Methods. In the paper cards of fixed points are constructed for quadratic Lotka–Volterra mappings, that allow describing the dynamics of the systems under consideration. Results. Using cards of fixed points of a discrete dynamical system, criteria for the existence of fixed points with odd nonzero coordinates are given in a particular case, and these results on the location of fixed points of Lotka–Volterra systems are generalized accordingly in the case of an arbitrary simplex. The main results are theorems 5–9, which allow us to describe the dynamics of these systems arising in a number of genetic, epidemiological and ecological models. Conclusion. The results obtained in the paper give a detailed description of the dynamics of the trajectories of Lotka–Volterra maps with homogeneous tournaments. The map of fixed points highlights a specific area in the simplex that is most important and interesting for studying the dynamics of these maps. The results obtained are applicable in environmental problems, for example, to describe and study the cycle of biogens.