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Pseudo-inverse learners (PILs) are a kind of feedforward neural network trained with the pseudoinverse learning algorithm, which can be traced back to 1995 originally. PIL is an approach for nongradient descent learning, and its main advantage is the lower computational cost and fast learning procedure, which is especially relevant in the edge computing research field. However, PIL is mostly applied to a deterministic learning problem, while in the real world, the greatest case that is of concern is the uncertainty learning problem. In this work, under the framework of the synergetic learning system (SLS), we introduce an approximated synergetic learning scheme, which can transform uncertainty learning into deterministic learning. We call this new learning framework the Bayesian PIL, and the advantages are also demonstrated in this work.

A new three-dimensional missile guidance law to control the impact vector against a stationary target is proposed. The composite guidance law has two well-known components: Apollo descent guidance and trajectory shaping guidance. These respectively linear and planar guidance laws are combined to achieve a specified impact direction. The main idea is to define an impact plane and to steer the missile onto this plane using Apollo descent guidance while concurrently performing trajectory shaping with reference to the impact plane. The resulting guidance law is expressed by a single equation in vector form, which is straightforward to implement. Because it originates from an optimal formulation, the performance of the proposed technique is expected to be satisfactory. This is confirmed by comparative simulation runs, which also involve the method known as generalized explicit guidance.

By computing the completely bounded norm of the flip map on the Haagerup tensor product $C_0 Y_1\otimes_{C_0 X} C_0 Y_2$ associated to a pair of continuous mappings of locally compact Hausdorff spaces $Y_1\rightarrow X\leftarrow Y_2$, we establish a simple characterisation of the Beck-Chevalley condition for base change of operator modules over commutative $C^*$-algebras, and a descent theorem for continuous fields of Hilbert spaces., Comment: 10 pages. Minor changes to the exposition; corrected an error in Remarks 6 not affecting the rest of the paper

It is known that the conjugate gradient method is still a popular method for many researchers who are focused in solving the large-scale unconstrained optimization problems and nonlinear equations because the method avoids the computation and storage of some matrices so the memory's requirements of the method are very small. In this work, a modified Perry conjugate gradient method which fulfills a global convergence with standard assumptions is shown and analyzed. The idea of new method is based on Perry method by using the equation which is founded via Powell in 1978. The weak Wolfe–Powell search conditions are used to choose the optimal line search, under the line search and suitable conditions, we prove both descent and sufficient descent conditions. In particular, numerical results show that the new conjugate gradient method is more effective and competitive when compared to other of standard conjugate gradient methods including: - CG- Hestenes and Stiefel (H/S) method, CG-Perry method, CG- Dai and Yuan (D/Y) method. The comparison is completed under a group of standard test problems with various dimensions from the CUTEst test library and the comparative performances of the methods are evaluated by total the number of iterations and the total number of function evaluations.

A gradient-based search method (GBSM) is developed to solve multi-objective optimization problems. It uses the multi-objective gradient information to construct descent directions, i.e., Pareto descent directions (PDDs), to accelerate the convergence. In addition, a multi-objective evolutionary algorithm based on decomposition is adopted to improve the diversity. The comparisons between GBSM with several selected multi-objective evolutionary algorithms and gradient based algorithms on benchmark functions indicate that the proposed method performs competitively and effectively.

We generalise sheaf models of intuitionistic logic to univalent type theory over a small category with a Grothendieck topology. We use in a crucial way that we have constructive models of univalence, that can then be relativized to any presheaf models, and these sheaf models are obtained by localisation for a left exact modality. We provide first an abstract notion of descent data which can be thought of as a higher version of the notion of prenucleus on frames, from which can be generated a nucleus (left exact modality) by transfinite iteration. We then provide several examples., Simplified the definition of lex operation, simplified the encoding of the homotopy limit and remark that the homotopy descent data is a lex modality without using higher inductive types

In two pre-registered studies, we leveraged recent advances to disposition theory to examine whether character judgments are relative. We used a Pilot Study to develop a moral continuum of behaviors for a hypothetical television series. We referenced our established moral continuum to create behavioral sequences that represented two characters descending into immorality. We manipulated whether one or both characters were present in the narrative. The simultaneous presence of both characters polarized participants’ moral evaluations of character behavior, categorization of the characters as heroic/villainous, and character liking. Our findings substantiate the systematic effects that character interdependence has on disposition formation. An improved understanding of narrative context can specify when between- and within-character comparisons occur and what effects character interdependence has on disposition theory’s processes. We discuss how narrative schemas, character schemas, and character networks can serve as the elements for explicating the role of narrative context in disposition theory.

Let $\mathcal{P}_s(n)$ denote the $n$th $s$-gonal number. We consider the equation \[\mathcal{P}_s(n) = y^m, \] for integers $n,s,y,$ and $m$. All solutions to this equation are known for $m>2$ and $s \in \{3,5,6,8,20 \}$. We consider the case $s=10$, that of decagonal numbers. Using a descent argument and the modular method, we prove that the only decagonal number $>1$ expressible as a perfect $m$th power with $m>1$ is $\mathcal{P}_{10}(3) = 3^3$., 5 pages. Some typos corrected

Clustering is a common task in data mining for constructing well-separated groups (clusters) from a large set of data points. The balanced minimum sum-of-squares clustering problem is a variant of the classic minimum sum-of-squares clustering (MSSC) problem and arises from broad real-life applications where the cardinalities of any two clusters differ by at most one. This study presents the first memetic algorithm for solving the balanced MSSC problem. The proposed algorithm combines a backbone-based crossover operator for generating offspring solutions and a responsive threshold search that alternates between a threshold-based exploration procedure and a descent-based improvement procedure for improving new offspring solutions. Numerical results on 16 real-life datasets show that the proposed algorithm competes very favorably with several state-of-the-art methods from the literature. Key components of the proposed algorithm are investigated to understand their effects on the performance of the algorithm.

This study aims to discuss the steps of Maudu'i interpretation of the Qur'an. This method has steps in interpreting the Qur'an, and usually responds to the challenges of the times, is more practical, systematic, dynamic and easy to understand in its entirety by the general public. This method is relatively new and is considered actual in interpreting the Qur'an departing from a logical unity and interrelated with one another. The method used in this research is descriptive, a research method that seeks to analyze and describe something, such as existing conditions or relationships, developing opinions, and or ongoing processes. Based on this method, in this study, the author will attempt to reveal experts' understanding regarding the steps of maudu'i interpretation. From this theory, it can be seen that to get a complete understanding of the Qur'an according to a certain theme, we must take certain steps, starting from choosing or determining the topic of the Qur'an in a maudhu`i manner, collecting verses that relating to this problem, coherently compiling the verses according to the chronology of their descent, knowing the correlation (munasabah) of these verses in each letter, arranging the theme of discussion in an appropriate framework, completing the discussion and description with the hadith, and study the verses thematically and thoroughly.

We use descent theoretic methods to solve the homotopy limit problem for Hermitian $K$-theory over quasi-compact and quasi-separated base schemes. As another application of these descent theoretic methods, we compute the cellular Picard group of 2-complete Hermitian $K$-theory over $\mathop{Spec}(\mathbb{C})$, showing that the only invertible cellular spectra are suspensions of the tensor unit., Comment: v4: results made unconditional, assumptions on base scheme weakened. Version to appear in Annals of K-theory

This study aims at describing the concept of al-amwal in the Qur'an which is referred to as treasure. This research focuses more on the concept of property and property ownership in the Qur'an, property as slander (trials), worldly treasures (al-hayah al-dunya), property as a means of doing good. Descriptive research method with qualitative approach is employed in this study. This present study, is a library study using maudhu’i method. Maudhu’i method is a method seeks to find the answer in the Qur'an by collecting ayahs of the Qur'an that have similar purpose, which together discuss a particular topic / title and publish those ayah in accordance with the time of thier descent in accordance with the causes of their descent, then pay attention to the ayahs with explanation, description and relationship with other ayahs. The results show that wealth (wealth) is a primary need for man to support his life in this world. The Qur'an reminds that property must be obtained through lawful manners as stipulated by the shariah law. In fact the Qur'an and the Sunnah clearly explain that property should not be transferred from one person to another through unjustified ways. In stead, it should be transferred based on the sharia, such as through trades or other lawful transactions. The use of property in Islamic teachings must always be in devotion to God and used in the framework of taqqarub (to get closer) to Allah.

The purpose of this paper is to present in linear spaces some results for new notions called A-left (resp., A-right) ascent and A-left (resp., A-right) descent of linear operators (where A is a given operator) which generalize two important notions in operator theory: ascent and descent. Moreover, if A is a positive operator, we obtain several properties of ascent and descent of an operator in semi-Hilbertian spaces. Some basic properties and many results related to the ascent and descent for a linear operator on a linear space Kaashoek (Math Ann 172:105–115, 1967), Taylor (Math Ann 163:18–49, 1966) are extended to these notions. Some stability results under perturbations by compact operators and operators having some finite rank power are also given for these notions.

More attention has been devoted to providing evolutionary accounts of the development of beliefs, or belief-like states, than for desires or preferences. Here I articulate and defend an evolutionar...

We consider relative or subjective optimization problems where the goal function and feasible set are dependent on the current state of the system under consideration. In general, they are formulated as quasi-equilibrium problems, hence finding their solutions may be rather difficult. We describe a rather general class of relative optimization problems in metric spaces, which in addition depend on the starting state. We also utilize quasi-equilibrium type formulations of these problems and show that they admit rather simple descent solution methods. This approach gives suitable trajectories tending to a relatively optimal state. We describe several examples of applications of these problems. Preliminary results of computational experiments confirmed efficiency of the proposed method.

Linear programs (LPs) can be solved by polynomially many moves along the circuit direction improving the objective the most, so-called deepest-descent steps (dd-steps). Computing these steps is NP-hard (De Loera et al. (2019)), a consequence of the hardness of deciding the existence of an optimal circuit-neighbor (OCNP) on LPs with non-unique optima. We prove OCNP is easy under the promise of unique optima, but already O ( n 1 − e ) -approximating dd-steps remains hard even for totally unimodular n -dimensional 0/1-LPs with a unique optimum. We provide a matching n -approximation.

We apply an explicit construction of a simplicial powering in dg-categories, due to Holstein (Properness and simplicial resolutions for the model category dgCat, 2014. arXiv:1403.4381 ) and Arkhipov and Poliakova (Homol Homotopy Appl 22(2):151–162, 2019), as well as our own results on homotopy ends (Arkhipov and Orsted in Homotopy (co)limits via homotopy (co)ends in general combinatorial model categories, 2018. arXiv:1807.03266 ), to obtain an explicit model for the homotopy limit of a cosimplicial system of dg-categories. We apply this to obtain a model for homotopy descent in terms of $$\mathrm {A}_{\infty }$$ -comodules, proving a conjecture by Block et al. (Homol Homotopy Appl 19(2):343–371, 2017) in the process.

In this paper, by linearly combining the numerator and denominator terms of the Dai-Liao (DL) and Bamigbola-Ali-Nwaeze (BAN) conjugate gradient methods (CGMs), a general form of DL-BAN method has been proposed. From this general form, a new hybrid CGM, which was found to possess a sufficient descent property is generated. Numerical experiment was carried out on the new CGM in comparison with four existing CGMs, using some set of large scale unconstrained optimization problems. The result showed a superior performance of new method over majority of the existing methods.

The Spectral conjugate gradient (SCG) methods are among the efficient variants of CG algorithms which are obtained by combining the spectral gradient parameter and CG parameter. The success of SCG methods relies on effective choices of the step-size $\alpha _{k}$ and the search direction $d_{k}$ . This paper presents an SCG method for unconstrained optimization models. The search directions generated by the new method possess sufficient descent property without the restart condition and independent of the line search procedure used. The global convergence of the new method is proved under the weak Wolfe line search. Preliminary numerical results are presented which show that the method is efficient and promising, particularly for large-scale problems. Also, the method was applied to solve the robotic motion control problem and portfolio selection problem.

For the hyperelliptic curve C_p with equation y^2=x(x-2p)(x-p)(x+p)(x+2p) with p a prime number, we discuss bounds for the rank of its Jacobian over Q, find many cases having 2-torsion in the associated Shafarevich-Tate group, and we present some results on rational points of C_p., 17 pages

The article considers the problem of optimal control of an object described by a linear nonstationary system and with a piecewise affine quality functional. The problem is examined in Mayer’s form with both free and partially fixed right endpoints. Piecewise continuous and bounded controls that lie in some parallelepiped at each moment of time are admissible. The standard discretization of the original system and the control parametrization are used, some convergence theorems of the discrete problem solution to the continuous problem solution are presented. Further, for the obtained discrete system, the necessary and sufficient minimum conditions are written out in terms of the codifferential, the method of the modified codifferential descent is applied to it, which guarantees to find the global minimum of this problem in a finite number of steps. The proposed algorithm is illustrated with examples.

This paper engages with a specific image: Darwin's tree of the primates. Although this diagram was sketched in ink on paper in 1868, it did not make it into the publication ofThe Descent of Man(1871). This may seem all the more in need of an explanation because, as Adrian Desmond and James Moore have shown, Darwin strongly relied on the notion of familial genealogy in the development of his theory of organismic evolution, or rather descent. However, Darwin expressed scepticism towards visualizations of phylogenies in correspondence with Ernst Haeckel and in fact also inDescent, considering such representations at once too speculative and too concrete. An abstraction such as a tree diagram left little room to ponder possibilities or demarcate hypotheses from evidence. I thus bring Darwin's primate tree into communication with his view on primate and human phylogeny as formulated inDescent, including his rejection of polygenism. I argue that considering the tree's inherent teleology, as well as its power to suggest species status of human populations and to reify ‘racial’ hierarchies, the absence of the diagram inThe Descent of Manmay be a significant statement.

Let ${\mathcal L}/{\mathcal K}$ be a finite Galois extension and let $X$ be an affine algebraic variety defined over ${\mathcal L}$. Weil's Galois descent theorem provides necessary and sufficient conditions for $X$ to be definable over ${\mathcal K}$, that is, for the existence of an algebraic variety $Y$ defined over ${\mathcal K}$ together with a birational isomorphism $R:X \to Y$ defined over ${\mathcal L}$. Weil's proof does not provide a method to construct the birational isomorphism $R.$ The aim of this paper is to give an explicit construction of $R$., Comment: 11 pages

Most studies of the American reception of Darwin have focused on theOrigin. TheDescent of Man, however, was even more widely read and discussed, especially by those outside the emerging scientific establishment. This essay maps the varied, popular and radical responses to theDescentand suggests that these unauthorized readers helped shape the formation of American scientific institutions (by encouraging scientists to close ranks), as well as ordinary Americans’ perceptions of gender and sex. I argue that the radical – freethinkers, socialists and feminists – embrace of sexual selection theory provides one explanation for naturalists’ scepticism of the theory.

This research is focused on Unconstrained Optimization problems. Among a number of methods that can be used to solve Unconstrained Optimization problems we have worked on Gradient and Coordinate Descent methods. Step size plays an important role for optimization. Here we have performed numerical experiment with Gradient and Coordinate Descent method for several step size choices. Comparison between different variants of Gradient and Coordinate Descent methods and their efficiency are demonstrated by implementing in loss functions minimization problem.

We implement two-cover descent for plane quartics over Q with all 28 bitangents rational and show that on a significant collection of test cases, it resolves the existence of rational points. We also review a classical description of the relevant moduli space and use it to generate examples. We observe that local obstructions are quite rare for such curves, and only seem to occur in practice at primes of good reduction. In particular, having good reduction at 11 implies having no rational points. We also gather numerical data on two-Selmer ranks of Jacobians of these curves, which suggests that these often have non-trivial Tate-Shafarevich groups. We implement two-cover descent for plane quartics over Q with all 28 bitangents rational and show that on a significant collection of test cases, it resolves the existence of rational points. We also review a classical description of the relevant moduli space and use it to generate examples. We observe that local obstructions are quite rare for such curves and only seem to occur in practice at primes of good reduction. In particular, having good reduction at 11 implies having no rational points. We also gather numerical data on two-Selmer ranks of Jacobians of these curves, providing evidence these behave differently from those of general abelian varieties due to the frequent presence of an everywhere locally trivial torsor., 15 pages; Some minor improvements to algorithm and rank data analysis

The article clarifies a well-known man of literature who showed backbone by his tolerance during the hard times of repression in Mongolia. He was the last nobleman descent from the Golden family of Chinggis Khaan. However, he is famous for his literary writings, especially the narrative story 'Soyol Erdene' as his own biography.

This article presents a new and fast indirect method for solving fuel-optimal descent trajectories in the gravitational field of an irregularly-shaped asteroid. The costates associated with a two-impulse descent trajectory are used as approximate costates for the costate initialization of a finite-thrust fuel-optimal trajectory planning problem. The approximate solutions of the initial velocity and mass costates are given in analytical forms. A simple shooting equation is derived to solve the approximate position costates. The two-impulsive descent trajectory is solved by an irregular gravitational Lambert solver. Based on the Lambert solver and approximate costates, an algorithm is proposed for trajectory optimization with varying time of flight. The effectiveness and efficiency of the proposed method are tested through the simulation of landing on the asteroid 433 Eros. Additionally, a computationally efficient approximate model is employed to replace the polyhedral model, which greatly improves the computational speed and enhance the ability to address uncertainties.

This study investigates how family lineage descent groups influence the intergenerational transmission of education for the cohorts of 1940-1989 in the Democratic Republic of Congo (DRC). The study applies both transition matrix and intergenerational persistence (IGP) methods, using the father's years of schooling as a proxy for parental education. The findings suggest a pronounced steady persistence in education for the estimated mean regression coefficient over a period of 49 years. Moreover, results by gender indicate that intergenerational persistence in education has significantly decreased for males in recent cohorts but slightly increased for females. Furthermore, findings suggest that intergenerational persistence has been decreasing in matrilineal descent groups in recent cohorts, while increasing for the patrilineal descent groups. The study gives a good sense of the relationship between family lineage descent and intergenerational transmission of education in DRC. In addition, it indicates that there is both substantial upward and downward intergenerational education mobility in the country.

It is well understood that a supercritical superprocess is equal in law to a discrete Markov branching process whose genealogy is dressed in a Poissonian way with immigration which initiates subcritical superprocesses. The Markov branching process corresponds to the genealogical description ofprolific individuals, that is, individuals who produce eternal genealogical lines of descent, and is often referred to as theskeletonorbackboneof the original superprocess. The Poissonian dressing along the skeleton may be considered to be the remaining non-prolific genealogical mass in the superprocess. Such skeletal decompositions are equally well understood for continuous-state branching processes (CSBP).In a previous article [16] we developed an SDE approach to study the skeletal representation of CSBPs, which provided a common framework for the skeletal decompositions of supercritical and (sub)critical CSBPs. It also helped us to understand how the skeleton thins down onto one infinite line of descent when conditioning on survival until larger and larger times, and eventually forever.Here our main motivation is to show the robustness of the SDE approach by expanding it to the spatial setting of superprocesses. The current article only considers supercritical superprocesses, leaving the subcritical case open.

We give necessary and sufficient conditions for a cdh sheaf to satisfy Milnor excision, following ideas of Bhatt and Mathew. Along the way, we show that the cdh infinity-topos of a quasi-compact quasi-separated scheme of finite valuative dimension is hypercomplete, extending a theorem of Voevodsky to nonnoetherian schemes. As an application, we show that if E is a motivic spectrum over a field k which is n-torsion for some n invertible in k, then the cohomology theory on k-schemes defined by E satisfies Milnor excision., Comment: 28 pages. v3: final version, to appear in Mathematische Annalen; v2: new title and minor corrections

In this paper we consider generalized Leontief model. We show that under certain condition the generalized Leontief model is solvable by iterative descent method based on infeasible interior point algorithm. We prove the convergence of the method from strictly positive starting point. A numerical example is presented to demonstrate the performance of the algorithm

Discussed here is descent theory in the differential context where everything is equipped with a differential operator. To answer a question personally posed by A. Pianzola, we determine all twisted forms of the differential Lie algebras over $\mathbb{C}(t)$ associated with complex simple Lie algebras. Hopf-Galois Theory, a ring-theoretic counterpart of theory of torsors for group schemes, plays a role when we grasp the above-mentioned twisted forms from torsors., Largely revised; in particular, changed the title and added several articles to the References, see the added Remark 2.2

In this study, we focus mainly on the problem of finding the minimum-length path through a set of circular regions by a fixed-wing unmanned aerial vehicle. Such a problem is referred to as the Dubins traveling salesman problem with neighborhoods (DTSPN). Algorithms developed in the literature for solving DTSPN either are computationally demanding or generate low-quality solutions. To achieve a better trade-off between solution quality and computational cost, an efficient gradient-free descent method is designed. The core idea of the descent method is to decompose DTSPN into a series of subproblems, each of which consists of finding the minimum-length path of a Dubins vehicle from a configuration to another configuration via an intermediate circular region. By analyzing the geometric properties of the subproblems, we use a bisection method to solve the subproblems. As a result, the descent method can efficiently address DTSPN by successively solving a series of subproblems. Finally, several numerical experiments are carried out to demonstrate the descent method in comparison with several existing algorithms.

In this paper, we suggest a descent modification of the conjugate gradient method which converges globally provided that the exact minimization condition is satisfied. Preliminary numerical experiments on some benchmark problems show that the method is efficient and promising.

Let $S$ be a finite set of primes. We prove that a form of finite Galois descent obstruction is the only obstruction to the existence of $\mathbb{Z}_{S}$-points on integral models of Hilbert modular varieties, extending a result of D.Helm and F.Voloch about modular curves. Let $L$ be a totally real field. Under (a special case of) the absolute Hodge conjecture and a weak Serre's conjecture for mod $\ell$ representations of the absolute Galois group of $L$, we prove that the same holds also for the $\mathcal{O}_{L,S}$-points., Comment: To appear in Canadian Mathematical Bulletin

Ethnic discrimination has a negative impact on the socioemotional, behavioral, relational, and academic adjustment of adolescents, while belonging with classmates, teachers, heritage, and national group may promote positive socioemotional and academic adjustment. We investigate (1) whether greater discrimination by peers and a lower sense of belonging with classmates, teachers, heritage group, and national group are associated with lower socioemotional and academic adjustment of adolescents of immigrant descent in Germany; and (2) whether a sense of belonging with these different sources acts as a protective factor lowering the negative effects of discrimination on adjustment. Our sample included 439 7th-grade adolescents (51 % female, Mage= 12.4 years) of immigrant descent from 15 Berlin secondary schools. Results showed that higher discrimination was related to greater physiological stress, depressive symptoms, and disruptive school behavior. Higher heritage (but not national) identity, a higher sense of belonging with classmates and with teachers were associated with better socioemotional and academic adjustment. An examination of interaction effects between discrimination and forms of belonging on adjustment revealed that, while the association between discrimination and poorer adjustment weakened for those with higher heritage identity, the association between discrimination and physiological stress increased for those with higher teacher relatedness. We conclude that heritage identity (but not national identity or sense of belonging with classmates) can indeed be a protective factor against the negative effects of discrimination for adolescents of immigrant descent in Germany. Even though belonging with teachers may exacerbate discrimination effects, further investigation with longitudinal data is needed. The findings underline the important role of heritage ties among adolescents of immigrant descent as a source of adjustment, especially in light of discrimination experiences.

The Online Order Batching Problem (OOBP) is a variant of the well-known Order Batching Problem (OBP). As in the OBP, the goal of this problem is to collect all the orders that arrive at a warehouse, following an order batching picking policy, while minimizing a particular objective function. Therefore, orders are grouped in batches, of a maximum predefined capacity, before being collected. Each batch is assigned to a single picker, who collects all the orders within the batch in a single route. Unlike the OBP, this variant presents the peculiarity that the orders considered in each instance are not fully available in the warehouse at the beginning of the day, but they can arrive at the system once the picking process has already begun. Then, batches have to be dynamically updated and, as a consequence, routes must too. In this paper, the maximum turnover time (maximum time that an order remains in the warehouse) and the maximum completion time (total collecting time of all orders received in the warehouse) are minimized. To that aim, we propose an algorithm based in the combination of a Greedy Randomized Adaptive Search Procedure and a Variable Neighborhood Descent. The best variant of our method has been tested over a large set of instances and it has been favorably compared with the best previous approach in the state of the art.

Modern humans are linguistic humans, who acquired the logical properties of phonemes and morae in speech sound to generate an infinite number of word signs and to compose grammatically modulated sentences with complex meanings. 5KA (thousand years ago) they invented characters, which could display individual knowledge and intelligence to be shared and passed on to the following generations. Civilization itself is the linguistic phenomenon where knowledge and thoughts are transferred to subsequent generations via written documents, and very rapid consecutive innovations take place. In the 21st century, we are at the third and final stage of logical linguistic evolution with the interactive search and electric transfer of information via computer networks. It is necessary to clarify the in-brain mechanism for linguistic processing and intelligence to take full advantage of the final stage. The author outlines on the general overview of Digital Linguistics (DL) and identifies the birth of linguistic humans at the time of the laryngeal descent, which provided vowel accented syllables containing logical properties of phonemes and morae, to 66KA on the southern coastline of South Africa at the beginning of Howiesons Poort industry.

Author(s): Chen, L; Hu, X; Wise, SM | Abstract: The full approximation storage (FAS) scheme is a widely used multigrid method for nonlinear problems. In this paper, a new framework to design and analyze FAS-like schemes for convex optimization problems is developed. The new method, the fast subspace descent (FASD) scheme, which generalizes classical FAS, can be recast as an inexact version of nonlinear multigrid methods based on space decomposition and subspace correction. The local problem in each subspace can be simplified to be linear and one gradient descent iteration (with an appropriate step size) is enough to ensure a global linear (geometric) convergence of FASD for convex optimization problems.

Nonlinear least squares iterative solver is considered for real-valued sufficiently smooth functions. The algorithm is based on successive solution of orthogonal projections of the linearized equation on a sequence of appropriately chosen low-dimensional subspaces. The bases of the latter are constructed using only the first-order derivatives of the function. The technique based on the concept of the limiting stepsize along normalized direction (developed earlier by the author) is used to guarantee the monotone decrease of the nonlinear residual norm. Under rather mild conditions, the convergence to zero is proved for the gradient and residual norms. The results of numerical testing are presented, including not only small-sized standard test problems, but also larger and harder examples, such as algebraic problems associated with canonical decomposition of dense and sparse 3D tensors as well as finite-difference discretizations of 2D nonlinear boundary problems for 2nd order partial differential equations.

The notion and the theory of constructing planetary powered descent guidance laws based on fractional polynomials are introduced. Along the way a new perspective to the classical Apollo powered descent guidance designs is gained. As a foundation of this work, a theory is first developed on how to derive an explicit powered descent guidance law by selecting the feedback gains in a unique way in an implicit tracking guidance law. Then by employing a particular profile of the reference thrust acceleration in the tracking law with a special set of gains, a large family of powered descent guidance laws is obtained that offer the flexibility in trajectory shaping and thrust characteristics by two adjustable parameters. An equivalence theory is established to show that each in this family of guidance laws is actually the explicit guidance law from a fractional-polynomial thrust acceleration profile. This insight provides a perfect explanation to the predictable behavior and good targeting performance of these guidance laws. The well-known Apollo lunar descent guidance and E-guidance laws are revealed to be two members of this much broader class of fractional-polynomial powered descent guidance laws.

"Given a Lipschitz and convex objective function of an unconstrained optimization problem, defined on a Banach space, we revisit the class of regular vector fields which was introduced in our previous work on descent methods. We study, in particular, the asymptotic behavior of the sequence of values of the objective function for a certain inexact process generated by a regular vector field when the sequence of computational errors converges to zero and show that this sequence of values converges to the infimum of the given objective function of the unconstrained optimization problem."

This study aims to analyze the k-value on K nearest neighbor classification. k-value is the distance used to find the closest data to label the class from the testing data. Each k-value can produce a different class label against the same testing data. The variants of k-value that we use are k=3, k=5 and k=7 to find the best k-value. There are 2 classes that are used in this research. Both classes are stairs descent and floor classes. The gray level co-occurrence matrix method is used to extract features. The data we use comes from videos obtained from the camera on the smart wheelchair taken by the frame. Refer to the results of our tests, the best k-value is obtained when using k=7 and angle 0° with accuracy is 92.5%. The stairs descent detection system will be implemented in a smart wheelchair

In this paper, according to some suitable features of three-term conjugate gradient methods and excellent theoretical properties of the quasi-Newton methods, a new spectral three-term conjugate gradient is proposed. A modified secant condition is used to compute a suitable spectral parameter. The new search direction ensures the sufficient descent condition without any line search. It is established that the new scheme possesses the global convergence, under the strong Wolfe conditions. Preliminary numerical experiments show the efficiency of the new method, dealing with unconstrained optimization problems.

In this paper we develop a descent theory for morphisms α between a monoid B and a unital magma A in a monoidal category with equalizers and coequalizers. We introduce the category of strong descent data for α and we prove that under faithfully flat conditions this category is equivalent to the one of right B-modules. As an application we prove that the category of strong Hopf modules, introduced by us for Hopf quasigroups and weak Hopf quasigroups, is equivalent to a suitable category of strong descent data.

A variation of the One-to-one Pickup and Delivery Problem (OPDP) in connected graphs, the Split Demand One-to-one Pickup and Delivery Problem with the Shortest-path Transport along Real-life Paths (SDOPDPSTRP) is abstracted from passenger train operation plans based on networks. Unlike the classical OPDP, in the SDOPDPSTRP: the demands can be split and must be transported along the shortest path according to passengers requirements and vehicles should travel along a real-life path. A new kind of integer programming model is formulated for the SDOPDPSTRP based on the connection relationship between pickup-delivery demands (pd-pairs). Two different categories of splitting strategies are proposed to solve the SDOPDPSTRP: split the demands before the calculation and split the demands during the calculation. Two Multi-Start Variable Neighborhood Descent (a MS_VND originating from the other literature and a new MS_VND' IN developed in this article) and seven neighborhood operators are proposed for these two splitting strategies to solve the SDOPDPSTRP. The results show that Approach III outperforms Approach I and Approach II in terms of average solutions with the same algorithm termination conditions and in terms of time efficiency, which has great practical significance for real-life transport organizations.

Given a set of permutations Pi, let S_n(Pi) denote the set of permutations in the symmetric group S_n that avoid every element of Pi in the sense of pattern avoidance. Given a subset S of {1,...,n-1}, let F_S be the fundamental quasisymmetric function indexed by S. Our object of study is the generating function Q_n(Pi) = sum F_{Des sigma} where the sum is over all sigma in S_n(Pi) and Des sigma is the descent set of sigma. We characterize those Pi contained in S_3 such that Q_n(Pi) is symmetric or Schur nonnegative for all n. In the process, we show how each of the resulting Pi can be obtained from a theorem or conjecture involving more general sets of patterns. In particular, we prove results concerning symmetries, shuffles, and Knuth classes, as well as pointing out a relationship with the arc permutations of Elizalde and Roichman. Various conjectures and questions are mentioned throughout., Comment: 3 figures, 28 pages, added some questions