Search

The IL-17 pathway displays remarkably diverse functional modes between different subphyla, classes, and even orders, yet its driving factors remains elusive. Here, we demonstrate that the IL-17 pathway originated through domain shuffling between a Toll-like receptor (TLR)/IL-1R pathway and a neurotrophin-RTK (receptor-tyrosine-kinase) pathway (a Trunk-Torso pathway). Unlike other new pathways that evolve independently, the IL-17 pathway remains intertwined with its donor pathways throughout later evolution. This intertwining not only influenced the gains and losses of domains and components in the pathway but also drove the diversification of the pathway's functional modes among animal lineages. For instance, we reveal that the crustacean female sex hormone, a neurotrophin inducing sex differentiation, could interact with IL-17Rs and thus be classified as true IL-17s. Additionally, the insect prothoracicotropic hormone, a neurotrophin initiating ecdysis in Drosophila by binding to Torso, could bind to IL-17Rs in other insects. Furthermore, IL-17R and TLR/IL-1R pathways maintain crosstalk in amphioxus and zebrafish. Moreover, the loss of the Death domain in the pathway adaptor connection to IκB kinase and stress-activated protein kinase (CIKSs) dramatically reduced their abilities to activate nuclear factor-kappaB (NF-κB) and activator protein 1 (AP-1) in amphioxus and zebrafish. Reinstating this Death domain not only enhanced NF-κB/ AP-1 activation but also strengthened anti-bacterial immunity in zebrafish larvae. This could explain why the mammalian IL-17 pathway, whose CIKS also lacks Death, is considered a weak signaling activator, relying on synergies with other pathways. Our findings provide insights into the functional diversity of the IL-17 pathway and unveil evolutionary principles that could govern the pathway and be used to redesign and manipulate it. [ABSTRACT FROM AUTHOR]

In this article, we propose to study a general notion of a down‐up Markov chain for multifurcating trees with n$$ n $$ labeled leaves. We study in detail down‐up chains associated with the (α,γ)$$ \left(\alpha, \gamma \right) $$‐model of Chen et al. (Electron. J. Probab. 14 (2009), 400–430.), generalizing and further developing previous work by Forman et al. (arXiv:1802.00862, 2018; arXiv:1804.01205, 2018; arXiv:1809.07756, 2018; Random Struct. Algoritm. 54 (2020), 745–769; Electron. J. Probab. 25 (2020), 1–46.) in the binary special cases. The technique we deploy utilizes the construction of a growth process and a down‐up Markov chain on trees with planar structure. Our construction ensures that natural projections of the down‐up chain are Markov chains in their own right. We establish label dynamics that at the same time preserve the labeled alpha‐gamma distribution and keep the branch points between the k$$ k $$ smallest labels for order n2$$ {n}^2 $$ time steps for all k≥2$$ k\ge 2 $$. We conjecture the existence of diffusive scaling limits generalizing the "Aldous diffusion" by Forman et al. (arXiv:1802.00862, 2018; arXiv:1804.01205, 2018; arXiv:1809.07756, 2018.) as a continuum‐tree‐valued process and the "algebraic α$$ \alpha $$‐Ford tree evolution" by Löhr et al. (Ann. Probab. 48 (2020), 2565–2590.) and by Nussbaumer and Winter (arXiv:2006.09316, 2020.) as a process in a space of algebraic trees. [ABSTRACT FROM AUTHOR]

In life, it is common for almost every kind of organism to interact with one another. In the human realm, such interactions are at the basis of joint actions, when two or more agents syntonize their actions to achieve a common goal. Shared intentionality is the theoretical construct referring to the suite of abilities that enable such coordinated and collaborative interactions. While shared intentionality has become an important concept in research on social cognition, there is controversy surrounding its evolutionary origins. An aspect still unexplored but promising to bring new insights into this open debate is the study of aneural organisms. To fill this gap, here we investigate whether climbing plants can act jointly to achieve a common goal, i.e. reaching the light. We examined Pisum Sativum plants growing intertwined when there is a need to climb but a potential support is not present in the environment. Three-dimensional kinematic analysis of their movement revealed a coordinated and complementary behaviour. They tend to coordinate their movement in time and space to achieve a joint climbing. By deliberately extending the context in which a joint action takes place, we pay tribute to the complex nature of this social phenomenon. The next challenge for the field of joint action is to generate a perspective that links coordination mechanisms to an evolutionary framework across taxa. [ABSTRACT FROM AUTHOR]

We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces. [ABSTRACT FROM AUTHOR]

We show that for pairs (Q, R) and (S, T) of disjoint subsets of vertices of a graph G, if G is sufficiently large, then there exists a vertex v in V (G) - (Q \cup R \cup S \cup T) such that there are two ways to reduce G by a vertex-minor operation that removes v while preserving the connectivity between Q and R and the connectivity between S and T. Our theorem implies an analogous theorem of Chen and Whittle (SIAM J. Discrete Math., 28 (2014), pp. 1402--1404) for matroids restricted to binary matroids. [ABSTRACT FROM AUTHOR]

Copyright of Zeitschrift für Gerontologie und Geriatrie is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Following Beurling's theorem the natural compressions of the multiplication operator in the classical L 2 space are compressions to model spaces and to their orthogonal complements. Here, two possibly different model spaces are considered, hence asymmetric truncated Toeplitz and asymmetric dual truncated Toeplitz operators are investigated. The main purpose of the paper is to characterize operators which intertwine compressions of the unilateral shift. [ABSTRACT FROM AUTHOR]

We construct a generalisation of Bakry–Émery curvature to prove twisted intertwining relations for Markov semigroups. These relations are applied to Brascamp–Lieb type inequalities and spectral gap results. It extends the method of Arnaudon, Bonnefont and Joulin, to Riemannian manifolds and to a wider class of twists. These results are illustrated with several examples. [ABSTRACT FROM AUTHOR]

For a family of multidimensional gambler models we provide formulas for the winning probabilities in terms of parameters of the system and for the distribution of a game duration in terms of eigenvalues of underlying one-dimensional games. These formulas were known for the one-dimensional case - initially proofs were purely analytical, recently probabilistic constructions have been given. Concerning the game duration, in many cases our approach yields sample-path constructions. We heavily exploit intertwining between (not necessarily) stochastic matrices (for game duration results), a notion of Siegmund duality (for winning/ruin probabilities), and a notion of Kronecker products. [ABSTRACT FROM AUTHOR]

Given k ∈ N , a nonnegative function f ∈ C r [ a , b ] , r ≥ 0 , an arbitrary finite collection of points { α i } i ∈ J ⊂ [ a , b ] , and a corresponding collection of nonnegative integers { m i } i ∈ J with 0 ≤ m i ≤ r , i ∈ J , is it true that, for sufficiently large n ∈ N , there exists a polynomial P n of degree n such that (i) | f (x) − P n (x) | ≤ c ρ n r (x) ω k (f (r) , ρ n (x) ; [ a , b ]) , x ∈ [ a , b ] , where ρ n (x) ≔ n − 1 1 − x 2 + n − 2 and ω k is the classical k th modulus of smoothness. (ii) P (ν) (α i) = f (ν) (α i) , for all 0 ≤ ν ≤ m i and all i ∈ J , and (iii) either P ≥ f on [ a , b ] (onesided approximation), or P ≥ 0 on [ a , b ] (positive approximation)? We provide precise answers not only to this question, but also to similar questions for more general intertwining and copositive polynomial approximation. It turns out that many of these answers are quite unexpected. We also show that, in general, similar questions for q -monotone approximation with q ≥ 1 have negative answers, i.e., q -monotone approximation with general interpolatory constraints is impossible if q ≥ 1. [ABSTRACT FROM AUTHOR]

Across the world, researchers have always been keen to understand the link between language, nature, and culture. They are also interested in finding out the effects that nature-culture relationship have created on people and their surroundings. The interconnectedness of ecology and language depends on how humans treat each other and how the natural world and the language influence human thoughts, concepts, ideas, ideologies, and world views. Literature has always been considered a medium that portrays the interconnectedness between environment and human culture. "The Vegetarian," a novel written by the South Korean novelist Han Kang, reflects upon the two selves of human beings; one being greed and the other being responsibility toward family and society and the adherence to social norms and values. The interconnectedness of man with nature is read through the perspective of Ecolinguistics. Ecolinguistics, a paradigm of linguistic research, discusses not only the ecological aspect of language but also analyses the social and ecological context in which societies are embedded. The term "nature" as used in the article, refers to the general realm of living plants and animals whereas, the term "culture" alludes to a set of customs, traditions, values, or specific practices within society. The entwined relationship of nature and culture formulates the cultural background of human thoughts, nature's influence on human deeds and its role in the cultural artefacts of language, social norms, heritage and rituals among people. The objective of this article is to analyze the intertwining of nature and culture in "The Vegetarian." It also focuses on the concept of "back-to-nature" as followed by South Korean society. [ABSTRACT FROM AUTHOR]

Applications in remote inspection and medicine have motivated the recent development of innovative thin, flexible-backboned robots. However, such robots often experience difficulties in maintaining their intended posture under gravitational and other external loadings. Thin-stemmed climbing plants face many of the same problems. One highly effective solution adopted by such plants features the use of tendrils and tendril-like structures, or the intertwining of several individual stems to form braid-like structures. In this paper, we present new plant-inspired robotic tendril-bearing and intertwining stem hardware and corresponding novel attachment strategies for thin continuum robots. These contributions to robotics are motivated by new insights into plant tendril and intertwining mechanics and behavior. The practical applications of the resulting GrowBots is discussed in the context of space exploration and mining operations.

"Chiasm, Flesh and Nature. Merleau-Ponty and the Problem of Mediality". The notion of flesh, belonging to the last stage of Merleau-Ponty's thought, occupies a decisive place in specialized research on the author. However, few publications highlight the immense influence of the latter in current thought, especially in the post-humanist and materialist currents of contemporary philosophy. We propose, in the pages that follow, to analyze this category from the point of view of a philosophy of relationship, interpreting it from the figure of mediality or relating them to a notion of medium. For this, in the first part, we will elucidate the notion of medium used in Phenomenology of Perception and the postulation of experience as a starting point. In the second part, we will specify the multiple dimensions in which the notion of flesh unfolds in the late philosophy of the author. Once the epistemological, phenomenological and ontological aspects of the ontology of the flesh have been addressed, its philosophical potential will be analyzed, projecting the treatments for the problems of nature, an issue that we consider of vital importance for current philosophical reflections. [ABSTRACT FROM AUTHOR]

The present paper forms the fourth and final paper in a series of papers concerning "inter-universal Teichmüller theory". In the first three papers of the series, we introduced and studied the theory surrounding the log-theta-lattice, a highly noncommutative two-dimensional diagram of "miniature models of conventional scheme theory", called Θ±ellNF-Hodge theaters, that were associated, in the first paper of the series, to certain data, called initial Θ-data. This data includes an elliptic curve EFEF over a number field FF, together with a prime number l≥5. Consideration of various properties of the log-theta-lattice led naturally to the establishment, in the third paper of the series, of multiradial algorithms for constructing "splitting monoids of LGP-monoids". Here, we recall that "multiradial algorithms" are algorithms that make sense from the point of view of an "alien arithmetic holomorphic structure", i.e., the ring/scheme structure of a Θ±ellNF-Hodge theater related to a given Θ±ellNF-Hodge theater by means of a non-ring/scheme-theoretic horizontal arrow of the log-theta-lattice. In the present paper, estimates arising from these multiradial algorithms for splitting monoids of LGP-monoids are applied to verify various diophantine results which imply, for instance, the so-called Vojta Conjecture for hyperbolic curves, the ABC Conjecture, and the Szpiro Conjecture for elliptic curves. Finally, we examine - albeit from an extremely naive/non-expert point of view! - the foundational/set-theoretic issues surrounding the vertical and horizontal arrows of the log-theta-lattice by introducing and studying the basic properties of the notion of a "species", which may be thought of as a sort of formalization, via set-theoretic formulas, of the intuitive notion of a "type of mathematical object". These foundational issues are closely related to the central role played in the present series of papers by various results from absolute anabelian geometry, as well as to the idea of gluing together distinct models of conventional scheme theory, i.e., in a fashion that lies outside the framework of conventional scheme theory. Moreover, it is precisely these foundational issues surrounding the vertical and horizontal arrows of the log-theta-lattice that led naturally to the introduction of the term "inter-universal". [ABSTRACT FROM AUTHOR]

The present paper constitutes the third paper in a series of four papers and may be regarded as the culmination of the abstract conceptual portion of the theory developed in the series. In the present paper, we study the theory surrounding the log-theta-lattice, a highly noncommutative two-dimensional diagram of "miniature models of conventional scheme theory", called Θ±ellNF-Hodge theaters. Here, we recall that Θ±ellNF-Hodge theaters were associated, in the first paper of the series, to certain data, called initial Θ-data, that includes an elliptic curve EFEF over a number field FF, together with a prime number l≥5. Each arrow of the log-theta-lattice corresponds to a certain gluing operation between the Θ±ellNF-Hodge theaters in the domain and codomain of the arrow. The horizontal arrows of the log-theta-lattice are defined as certain versions of the "Θ-link" that was constructed, in the second paper of the series, by applying the theory of Hodge-Arakelov-theoretic evaluation - i.e., evaluation in the style of the scheme-theoretic Hodge-Arakelov theory established by the author in previous papers - of the [reciprocal of the l-th root of the] theta function at l-torsion points. In the present paper, we focus on the theory surrounding the log-link between Θ±ellNF-Hodge theaters. The log-link is obtained, roughly speaking, by applying, at each [say, for simplicity, nonarchimedean] valuation of the number field under consideration, the local p-adic logarithm. The significance of the log-link lies in the fact that it allows one to construct log-shells, i.e., roughly speaking, slightly adjusted forms of the image of the local units at the valuation under consideration via the local p-adic logarithm. The theory of log-shells was studied extensively in a previous paper by the author. The vertical arrows of the log-theta-lattice are given by the log-link. Consideration of various properties of the log-theta-lattice leads naturally to the establishment of multiradial algorithms for constructing "splitting monoids of logarithmic Gaussian procession monoids". Here, we recall that "multiradial algorithms" are algorithms that make sense from the point of view of an "alien arithmetic holomorphic structure", i.e., the ring/scheme structure of a Θ±ellNF-Hodge theater related to a given Θ±ellNF-Hodge theater by means of a non-ring/scheme-theoretic horizontal arrow of the log-theta-lattice. These logarithmic Gaussian procession monoids, or LGP-monoids, for short, may be thought of as the log-shell-theoretic versions of the Gaussian monoids that were studied in the second paper of the series. Finally, by applying these multiradial algorithms for splitting monoids of LGP-monoids, we obtain estimates for the log-volume of these LGP-monoids. Explicit computations of these estimates will be applied, in the fourth paper of the series, to derive various diophantine results. [ABSTRACT FROM AUTHOR]

Consider the Aldous Markov chain on the space of rooted binary trees with n labeled leaves in which at each transition a uniform random leaf is deleted and reattached to a uniform random edge. Now, fix 1 ≤ k

The aim of this paper is to offer an original and comprehensive spectral theoretical approach to the study of convergence to equilibrium, and in particular of the hypocoercivity phenomenon, for contraction semigroups in Hilbert spaces. Our approach rests on a commutation relationship for linear operators known as intertwining, and we utilize this identity to transfer spectral information from a known, reference semigroup ˜P = (e−tÃ)t⩾0 to a target semigroup PP which is the object of study. This allows us to obtain conditions under which PP satisfies a hypocoercive estimate with exponential decay rate given by the spectral gap of Ã. Along the way we also develop a functional calculus involving the non-self-adjoint resolution of identity induced by the intertwining relations. We apply these results in a general Hilbert space setting to two cases: degenerate, hypoelliptic Ornstein-Uhlenbeck semigroups on Rd, and non-local Jacobi semigroups on [0,1]d, which have been introduced and studied for d = 1 in [12]. In both cases we obtain hypocoercive estimates and are able to explicitly identify the hypocoercive constants. [ABSTRACT FROM AUTHOR]

We propose a new method for performing multiscale analysis of functions defined on the vertices of a finite connected weighted graph. Our approach relies on a random spanning forest to downsample the set of vertices, and on approximate solutions of Markov intertwining relation to provide a subgraph structure and a filter bank leading to a wavelet basis of the set of functions. Our construction involves two parameters q and q ′. The first one controls the mean number of kept vertices in the downsampling, while the second one is a tuning parameter between space localization and frequency localization. We provide an explicit reconstruction formula, bounds on the reconstruction operator norm and on the error in the intertwining relation, and a Jackson-like inequality. These bounds lead to recommend a way to choose the parameters q and q ′. We illustrate the method by numerical experiments. [ABSTRACT FROM AUTHOR]

In speaking of the social dimensions of human experience, we inevitably become involved in the debate regarding how they are to be studied. Should we embrace the first-person perspective, which is that of the phenomenologists, and begin with the experiences composing our directly experienced lifeworld? Alternately, should we follow the lead of natural scientists and take up the third-person perspective? This is the perspective that asserts that we must begin with what is true for everyone, i.e., with what is available to both me and Others (the “they” that forms the grammatical third person). Both perspectives are one sided in that each presupposes the other for its intelligibility. The third-person perspective is Cartesian and, as I show, privileges space, while the first-person perspective is social in Levinas’s sense and presupposes time. Our reality, I argue, embraces both perspectives and is, in fact, set by their intertwining.

This paper links genderlects and mixed languages. Both may have their roots in a gender dichotomy, where two distinct populations come together and blend into a new one, with different linguistic consequences. Mixed languages are generally assumed to be the result of deliberate or conscious language change and often come about as the result of an act of identity, connected to the birth of a new social or ethnic group. Societies or ethnic groups that are the result of mixed marriages may develop a mixed language or a genderlect. I show that there is a connection between the two, as proven in one specific case: a mixed language developed into a genderlect over several centuries. Typically, mixed languages combine elements from two languages with results that are so unusual that they are clearly not the result of normal language change, i.e. they are not outcomes of regular transmission between generations. Certain combinations found in genderlects show parallel patterns, for example in having personal pronouns or deictic elements that derive from other languages. Comparative evidence based on structural parallels suggests that some such genderlects (though not necessarily all) derive from deliberate changes by earlier generations. In this paper, I also investigate whether there is a link between societies with socially quite different roles for men and women, and societies with a genderlect, and find that such a link does not seem to exist. [ABSTRACT FROM AUTHOR]

In life, it is common for almost every kind of organism to interact with one another. In the human realm, such interactions are at the basis of joint actions, when two or more agents syntonize their actions to achieve a common goal. Shared intentionality is the theoretical construct referring to the suite of abilities that enable such coordinated and collaborative interactions. While shared intentionality has become an important concept in research on social cognition, there is controversy surrounding its evolutionary origins. An aspect still unexplored but promising to bring new insights into this open debate is the study of aneural organisms. To fill this gap, here we investigate whether climbing plants can act jointly to achieve a common goal, i.e. reaching the light. We examined Pisum Sativum plants growing intertwined when there is a need to climb but a potential support is not present in the environment. Three-dimensional kinematic analysis of their movement revealed a coordinated and complementary behaviour. They tend to coordinate their movement in time and space to achieve a joint climbing. By deliberately extending the context in which a joint action takes place, we pay tribute to the complex nature of this social phenomenon. The next challenge for the field of joint action is to generate a perspective that links coordination mechanisms to an evolutionary framework across taxa., Competing Interests: The authors declare that they have no conflicts of interest in this work., (© The Author(s) 2023. Published by Oxford University Press on behalf of the Annals of Botany Company.)

The traditional quantification of free motions on Euclidean spaces into the Laplacian is revisited as a complex intertwining obtained through Doob transforms with respect to complex eigenvectors. This approach can be applied to free motions on finitely generated discrete Abelian groups: ℤm, with m ∈ ℕ, finite tori and their products. It leads to a proposition of Markov quantification. It is a first attempt to give a probability-oriented interpretation of exp(ξL), when L is a (finite) Markov generator and ξ is a complex number of modulus 1. [ABSTRACT FROM AUTHOR]

Jean Améry's memoir of his imprisonment and torture by the Nazis links the loss of "trust in the world" to the violence he experienced. The loss of trust makes him feel homeless. He can no longer find a place in the intersubjective world, the world for everyone. What is this "trust in the world" (Weltvertrauen)? How does violence destroy it? In this article, I use Améry's remarks as guide for understanding the relation of violence, trust, and homelessness. Trust, I argue, is crucial to the constitution of the intersubjective world. Violence, by undermining trust in Others, destroys the sense that this world is "for everyone." In excluding the victim from its "for everyone," it enforces a homelessness that transforms the victim's very being-in-the-world. [ABSTRACT FROM AUTHOR]

Wilson (Proceedings of the twenty-eight annual acm symposium on the theory of computing, pp. 296-303, 1996) in the 1990s described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a powerful tool in analyzing structures on networks and along this line of thinking, in recent works (Avena and Gaudillière in A proof of the transfer-current theorem in absence of reversibility, in Stat. Probab. Lett. 142, 17-22 (2018); Avena and Gaudillière in J Theor Probab, 2017. 10.1007/s10959-017-0771-3; Avena et al. in Approximate and exact solutions of intertwining equations though random spanning forests, 2017. arXiv:1702.05992v1; Avena et al. in Intertwining wavelets or multiresolution analysis on graphs through random forests, 2017. arXiv:1707.04616, to appear in ACHA (2018)) we focused on applications of spanning rooted forests on finite graphs. The resulting main conclusions are reviewed in this paper by collecting related theorems, algorithms, heuristics and numerical experiments. A first foundational part on determinantal structures and efficient sampling procedures is followed by four main applications: (1) a random-walk-based notion of well-distributed points in a graph, (2) a framework to describe metastable-like dynamics in finite settings by means of Markov intertwining dualities, (3) coarse graining schemes for networks and associated processes, (4) wavelets-like pyramidal algorithms for graph signals. [ABSTRACT FROM AUTHOR]

We find all self-duality functions of the form D(ξ,η)=∏xd(ξx,ηx)for a class of interacting particle systems. We call these duality functions of simple factorized form. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion processes, as well as duality and self-duality functions for their continuous counterparts. The approach is based on, firstly, a general relation between factorized duality functions and stationary product measures and, secondly, an intertwining relation provided by generating functions. For the interacting particle systems, these self-duality and duality functions turn out to be generalizations of those previously obtained in Giardinà et al. (J Stat Phys 135:25-55, 2009) and, more recently, in Franceschini and Giardinà (Preprint, arXiv:1701.09115, 2016). Thus, we discover that only these two families of dualities cover all possible cases. Moreover, the same method discloses all simple factorized self-duality functions for interacting diffusion systems such as the Brownian energy process, where both the process and its dual are in continuous variables. [ABSTRACT FROM AUTHOR]

The overall aim of this paper is to defend the value of the arts as uniquely instructive regarding philosophical questions. Specifically, I aim to achieve two things: firstly, to show that through the phenomenological challenge to dualist and monist ontologies the key debate in aesthetics regarding subjective response and objective judgment is reconfigured and resolved. I argue that Merleau-Ponty's analyses complement and complete Kant's project. Secondly, I propose that through Merleau-Ponty's phenomenological interrogations of the creative process the broader issue of the viability of his relational nondualist ontology is defended against accusations that it has not gone beyond dualism or that it has collapsed into a monism. [ABSTRACT FROM AUTHOR]

We continue our investigation of the intertwining relations for Markov semigroups and extend our previous results to multi-dimensional diffusions. In particular these formulae entail new functional inequalities of Brascamp-Lieb type for log-concave distributions and beyond. Our results are illustrated by some classical and less classical examples. [ABSTRACT FROM AUTHOR]

In this paper, we find the relationships between the order of constrained approximation by a polynomials which is copositive with a function (f), by modulus of smoothness τk-1 , to the function f ,which is multiply by Jc , and between the best approximation to the pairs of "intertwining splines of a polynomials" in I = [-b, b] , and the same of relationships but by the modulus of smoothness ωk-1φ to the function f multiply by n-1 |Jc | . Also we find the order of constrained approximation to the pairs of intertwining polynomials in (IiUi+1 ) . [ABSTRACT FROM AUTHOR]

It is now generally accepted that human beings are naturally, possibly even essentially, intersubjective. This chapter offers a robust defence of an enhanced and extended intersubjectivity, criticising the paucity of individuating notions of agency and emphasising the community and reciprocity of our affective co-existence with other living organisms and things. I refer to this modified intersubjectivity, which most closely expresses the implicit intricacy of our pre-reflective neuro-muscular experiential entanglement, as 'enkinaesthesia'. The community and reciprocity of this entanglement is characterised as dialogical, and in this dialogue, as part of our anticipatory preparedness, we have a capacity for intentional transgression, feeling our way with our world but, more particularly, co-feeling our way with the mind and intentions of the other. Thus we are, not so much 'mind'-reading, as 'mind'-feeling, and it is through this enkinaesthetic 'mind'-feeling dialogue that values-realising activity originates and we uncover the deep roots of morality. [ABSTRACT FROM AUTHOR]

The essay discusses selected poems from Thomas Hardy's vast body of poetry, focusing on representations of the self and the world. Employing Maurice Merleau-Ponty's concepts such as the body-subject, wild being, flesh and reversibility, the essay offers an analysis of Hardy's poems in the light of phenomenological philosophy. It argues that far from demonstrating 'cosmic indifference', Hardy's poetry offers a sympathetic vision of interrelations governing the universe. The attunement with voices of the Earth foregrounded in the poems enables the self's entanglement in the flesh of the world, a chiasmatic intertwining of beings inserted between the leaves of the world. The relation of the self with the world is established through the act of perception, mainly visual and aural, when the body becomes intertwined with the world, thus resulting in a powerful welding. Such moments of vision are brief and elusive, which enhances a sense of transitoriness and, yet, they are also timeless as the self becomes immersed in the experience. As time is a recurrent theme in Hardy's poetry, this essay discusses it in the context of dwelling, the provisionality of which is demonstrated in the prevalent sense of temporality, marked by seasons and birdsong, which underline the rhythms of the world. [ABSTRACT FROM AUTHOR]

The claim of this article is that the perpetrators of violence are “liminal” figures, being inside and yet outside of the world in which they act. It is this liminality, this existing on the border, that makes their violence senseless. Because of it, their actions can be understood in terms neither of the actual reality of their victims nor of the imagined reality that the perpetrators placed them in. Sense, here, fails, for the lack of a common frame. Liminality exists in a number of forms: economic, religious, and political—each with its potential for violence. What distinguishes political liminality is the scale of its violence. As Carl Schmitt shows, the liminal sovereign or ruler is both inside and outside the state, employing its means for violence even as he is unconstrained by its laws. I contend that this sovereign exists in a continuum with the practitioners of terrorist violence, who are also liminal figures. To analyze this liminality, I explore the intertwining between the self and the world that sets up the common frame that gives sense to actions. I then examine the causes of its breakdown. [ABSTRACT FROM AUTHOR]

LetRbe any associative ring and let. By making use of the bicommutant comm, Koliha and Patrício [Elements of rings with equal spectral idempotents. J Aust Math Soc. 2002;72:137–152], Wang and Chen [Pseudo Drazin inverses in associative rings and Banach algebras. Linear Algebra Appl. 2012;437:1332–1345], and Drazin [Generalized inverses: uniqueness proofs and three new classes. Linear Algebra Appl. 2014;449:402–416] have found three ways to define a unique idempotentpassociated withafor increasingly generala. In this article it is shown that one can associate withaunique ‘left’ and ‘right’ idempotentspandqunder much weaker conditions ona. For any semigroupSand any given, in 2012 [Drazin MP. A class of outer generalized inverses. Linear Algebra Appl. 2012;436:1909–1923] the author definedas being a (b, c)-inverseofaif,and, which hypotheses are satisfied, for suitablebandc, by essentially every known outer generalized inversey. Here it is shown that ifbandcare equivalent under J.A. Green’s equivalence relation(or, in particular, if, as holds for the Moore–Penrose inverse, for the pseudo-inverseand for the Bott-Duffin inverse), thenand. This leads to weaker alternative conditions ona, b, cstill sufficient for the existence of unique corresponding left and right idempotentsp, q. Beyondcomm, etc., a more general version is established which replaces ordinary commutativity by an intertwining property. [ABSTRACT FROM AUTHOR]

A necessary and sufficient condition is obtained for the existence of strong stationary times for ergodic one-dimensional diffusions, whatever the initial distribution. The strong stationary times are constructed through intertwinings with dual processes, in the Diaconis-Fill sense, taking values in the set of segments of the extended line ℝ ∪{-∞, +∞}. They can be seen as natural Doob transforms of the extensions to the diffusion framework of the evolving sets of Morris-Peres. Starting from a singleton set, the dual process begins by evolving into true segments in the same way a Bessel process of dimension 3 escapes from 0. The strong stationary time corresponds to the first time the full segment [-∞, +∞] is reached. The benchmark Ornstein-Uhlenbeck process cannot be treated in this way; it will nevertheless be seen how to use other strong times to recover its optimal exponential rate of convergence to equilibrium in the total variation sense. [ABSTRACT FROM AUTHOR]

This article aims to show that La Vérité, jusqu’à la faute by Jean-Paul Michel presents a poetics of interlace. That implies the intertwining of perspectives and viewpoints that enables them to increase in complexity from both literary and philosophical viewpoints.

Even a quick look at the history of religions leaves one impressed with how often the animal has been taken as a manifestation of the sacred. Another feature, frequently found, is the emphasis on the transcendence of the divine. Its radical alterity is such that we cannot directly encounter it. What is the alterity, the transcendence that conjoins these features? In this article, I argue that this alterity is that of the unconscious. Two types of impulses spring from it: impulses that we symbolically project as the Eros rooted in our animal, embodied existence and impulses that we project as springing from the divine. The only way that we can form a stable representation of ourselves is through the intertwining of both of them. Such an intertwining can be accounted for by means of Merleau-Ponty's model of reversibility and mutual disclosure. [ABSTRACT FROM AUTHOR]

This article examines a way to define left and right versions of the large class of “ ( b , c ) -inverses” introduced by the writer in (2012) [6] : Given any semigroup S and any a , b , c ∈ S , then a is called left ( b , c ) - invertible if b ∈ S c a b , and x ∈ S is called a left ( b , c ) - inverse of a if x ∈ S c and x a b = b , and dually c ∈ c a b S , z ∈ S b and c a z = z for right ( b , c ) -inverses z of a . It is shown that left and right ( b , c ) -invertibility of a together imply ( b , c ) -invertibility, in which case every left ( b , c ) -inverse of a is also a right ( b , c ) -inverse, and conversely, and then all left or right ( b , c ) -inverses of a coincide. When b = c (e.g. for the Moore-Penrose inverse or for the pseudo-inverse of the author) left ( b , b ) -invertibility coincides with right ( b , b ) -invertibility in every strongly π -regular semigroup. A fundamental result of Vaserstein and Goodearl, which guarantees the left-right symmetry of Bass's property of stable range 1, is extended from two-sided inverses to left or right inverses, and, for central b , to left or right ( b , b ) -inverses. [ABSTRACT FROM AUTHOR]