Notion Of Weight Research Articles

What Does a Notion of Weight Mean to Chimpanzees?

How to best understand how animals think about the world? Considering that cognition develops in interactions with the outside world, we need to compare the cognitive performance of individuals of the same species living under different ecological conditions. I propose here to compare the notion of weight studied in captive chimpanzees to the ones observed in a wild chimpanzee population that is using hammers of different weights to crack nuts during many months of the year. Detailing different situations where the chimpanzees have to select a hammer for cracking two species of nuts of different hardness, my colleagues and I could illustrate the flexibility of the causal reasoning performed by the chimpanzees, including stable anticipation of weight, combining weight with density and transport distance, and the gradual shift of selection criteria with increasing transport distance. Combined with results from captive studies on the notion of weight in chimpanzees, this suggests that when individuals face specific ecological challenges, they may acquire sophisticated causal reasoning generalized over different contexts. The evolution of cognition in chimpanzees suggests a complex interplay with ecology, memory demands, individual differences, and technical challenges important to the population.

$$\mathrm{K}$$-weight bounds for $$\gamma $$-hyperelliptic semigroups

In this note, we show that \(\gamma \)-hyperelliptic numerical semigroups of genus \(g \gg \gamma \) satisfy a refinement of a well-known characteristic weight inequality due to Torres. The refinement arises from substituting the usual notion of weight by an alternative version, the K-weight, which we previously introduced in the course of our study of unibranch curve singularities.

The weight of the world

This article is an extract from the Practical Pre-School book, Developing Early Maths Skills Outdoors; it explores the notion of weight in relation to physical development and a child's mathematical knowledge.

Weight, Density and Space in the Norwegian Reindeer Crisis–Notes Towards a Critique

For decades now, the dominant narrative about indigenous reindeer pastoralism in northern Norway has been that there is a crisis of excess: an oversized reindeer population, poorly held in check by poorly governed herders, is overgrazing the tundra, degrading the pasture grounds, spilling over into urban spaces and precipitating moral crises by starving to death “out there,” on the tundra. Set against the background of this ongoing crisis, the present paper focuses on a set of particularly dense conceptual intersections that cluster around the notion of weight , and the manner in which weight functions both as a crisis indicator and a metric for assessment in contemporary Norwegian pastoral governance. Tracing the work and structure of the weight concept as applied to reindeer–against a dominant government narrative that parses numerical indicators as neutral, objective and apolitical–the paper outlines some of the erasures that the weight metric simultaneously carries out and occludes. The aim of the exercise is to specify and critically reframe certain core issues in the current management of Norwegian pastoralism, by problematising the supposedly neutral, scientific operation of quantitative metrics and assessment practices.

Strict independence

We investigate the notions of strict independence and strict non-forking, and establish basic properties and connections between the two. In particular, it follows from our investigation that in resilient theories strict non-forking is symmetric. Based on this study, we develop notions of weight which characterize NTP2, dependence and strong dependence. Many of our proofs rely on careful analysis of sequences that witness dividing. We prove simple characterizations of such sequences in resilient theories, as well as of Morley sequences which are witnesses. As a by-product we obtain information on types co-dominated by generically stable types in dependent theories. For example, we prove that every Morley sequence in such a type is a witness.

On simple modules over twisted finite category algebras

The purpose of this note is to show that the recent proof, by Ganyushkin, Mazorchuk and Steinberg, of the parametrisation of simple modules over finite semigroup algebras due to Clifford, Munn and Ponizovski˘i carries over to twisted finite category algebras. We observe that the parametrisations of simple modules over Brauer algebras, Temperley-Lieb algebras, and Jones algebras due to Graham and Lehrer, can be obtained as special cases of our main result. We further note that the notion of weights in the context of Alperin’s weight conjecture extends to twisted finite category algebras.

Weight structures vs.t-structures; weight filtrations, spectral sequences, and complexes (for motives and in general)

AbstractIn this paper we introduce a new notion ofweight structure (w)for a triangulated categoryC; this notion is an important natural counterpart of the notion oft-structure. It allows extending several results of the preceding paper [Bon09] to a large class of triangulated categories and functors.Theheartofwis an additive categoryHw⊂C. We prove that a weight structure yields Postnikov towers for anyX∈ObjC(whose 'factors'Xi∈ObjHw). For any (co)homological functorH:C→A(Ais abelian) such a tower yields aweight spectral sequenceT : H(Xi[j]) ⇒H(X[i + j]); Tis canonical and functorial inXstarting fromE2.Tspecializes to the usual (Deligne) weight spectral sequences for 'classical' realizations of Voevodsky's motivesDMeffgm(if we considerw = wChowwithHw=Choweff) and to Atiyah-Hirzebruch spectral sequences in topology.We prove that there often exists an exact conservative weight complex functorC→K(Hw). This is a generalization of the functort:DMeffgm→Kb(Choweff) constructed in [Bon09] (which is an extension of the weight complex of Gillet and Soulé). We prove thatK0(C) ≅K0(Hw) under certain restrictions.We also introduce the concept of adjacent structures: at-structure isadjacenttowif their negative parts coincide. This is the case for the Postnikovt-structure for the stable homotopy categorySH(of topological spectra) and a certain weight structure for it that corresponds to the cellular filtration. We also define a new (Chow)t-structuretChowforDMeff_⊃DMeffgmwhich is adjacent to the Chow weight structure. We haveHtChow≅ AddFun(Choweffop,Ab);tChowis related to unramified cohomology. Functors left adjoint to those that aret-exact with respect to somet-structures are weight-exact with respect to the corresponding adjacent weight structures, and vice versa. Adjacent structures identify two spectral sequences converging toC(X,Y): the one that comes from weight truncations ofXwith the one coming fromt-truncations ofY(forX,Y∈ObjC). Moreover, the philosophy of adjacent structures allows expressing torsion motivic cohomology of certain motives in terms of the étale cohomology of their 'submotives'. This is an extension of the calculation of E2of coniveau spectral sequences (by Bloch and Ogus).

Klazar trees and perfect matchings

Martin Klazar computed the total weight of ordered trees under 12 different notions of weight. The last and perhaps the most interesting of these weights, w 12 , led to a recurrence relation and an identity for which he requested combinatorial explanations. Here we provide such explanations. To do so, we introduce the notion of a “Klazar violator” vertex in an increasing ordered tree and observe that w 12 counts what we call Klazar trees—increasing ordered trees with no Klazar violators. A highlight of the paper is a bijection from n -edge increasing ordered trees to perfect matchings of [ 2 n ] = { 1 , 2 , … , 2 n } that sends Klazar violators to even numbers matched to a larger odd number. We find the distribution of the latter matches and, in particular, establish the one-summation explicit formula ∑ k = 1 ⌊ n / 2 ⌋ ( 2 k − 1 ) ! ! 2 { n + 1 2 k + 1 } for the number of perfect matchings of [ 2 n ] with no even-to-larger-odd matches. The proofs are mostly bijective.

Negative asymptotic topological dimension, a new condensate, and their relation to the quantized Zipf law

We introduce the notion of weight for the asymptotic topological dimension. Planck’s formula for black-body radiation is refined. We introduce the notion of negative asymptotic topological dimension (of hole dimension). The condensate in the hole dimension is applied to the quantized Zipf law for frequency dictionaries (obtained earlier by the author).

Do things weigh more or less in the mountains?

The notion of weight can be associated with three distinct physical quantities: the force ofgravity due to the Earth; the resultant of this gravitational force and the centrifugal forcearising from the Earth’s rotation; and the ‘apparent weight in air’, i.e., what is measuredby a scale located in the Earth’s atmosphere. Starting from a real life student–teacherexchange, this article sets out the variety of meanings that students and teachers mayattribute to the term ‘weight’. It then explores how the weight and apparent weight of anobject vary with mountain altitude. The effects of the mass of the mountain and thebuoyant force of the air are considered and calculated. The question of whether apparentweight increases or decreases with increasing elevation is addressed in detail.

Lattice of fuzzy subalgebras in universal algebra

We prove that the (quasi-) identities in the lattice of subuniverses definable by lattice terms hold also in the lattice of fuzzy subalgebras for an arbitrary algebra. This means that the set of (quasi-) identities true in the lattice of subuniverses is equal to the set of those true in the lattice of fuzzy subalgebras for any given algebra. Moreover, we mention the case when there occur infinitary join operations. For this purpose, we define the notion of weights over an abstract algebra, and show that there is a canonical one-to-one correspondence between the lattice of fuzzy subalgebras and the lattice of weights. By using the notion of weights, we give a concrete description of the fuzzy subalgebra generated by an arbitrary fuzzy subset.

Semisimple Lie Algebras of Differential Operators

Starting from the commutation relations in a complex semisimple Lie algebra $${\mathfrak{g}}$$ , one may obtain a space $${\hat {\mathfrak{g}}}$$ of vector fields on Euclidean space such that $${\mathfrak{g}}$$ and $${\hat {\mathfrak{g}}}$$ are isomorphic when $${\hat {\mathfrak{g}}}$$ is equipped with the usual Lie bracket between vector fields and the isotropy subalgebra of $${\hat {\mathfrak{g}}}$$ is a Borel subalgebra $${\mathfrak{b}}$$ . Furthermore, one may adjoin to the vector fields in $${\hat {\mathfrak{g}}}$$ multiplication operators to obtain an $$\mathfrak{h}*$$ -parameter family of distinct presentations of $$\mathfrak{g}$$ as spaces of differential operators, where $$\mathfrak{h}*$$ is the dual of a Cartan subalgebra. Some of these presentations will preserve a space of polynomials on Euclidean space, and, in fact, all the finite-dimensional representations of $$\mathfrak{g}$$ can be presented in this way. All of this is carried out explicitly for arbitrary $$\mathfrak{g}$$ . In doing so, one discovers there is a Lie group of diffeomorphisms of the unipotent subgroup N complementary to B which acts on these presentations and preserves a certain notion of weight.

Admissibility of Weights on Non-normed $*$-Algebras

The notion of weights on (topological) $*$-algebras is defined and studied. The primary purpose is to define the notions of admissibility and approximate admissibility of weights, and to investigate when a weight is admissible or approximately admissible. The results obtained are applied to vector weights and tracial weight on unbounded operator algebras, as well as to weights on smooth subalgebras of a C$^*$-algebra.

Weights on Partial *-Algebras

The notion of weight, familiar for C*- and W*-algebras, is extended, in two different ways, to partial *-algebras, and the corresponding Gel′fand-Naimark-Segal representation is constructed (leading in one case to operators on a partial inner product space). Physically relevant examples are presented in the case of a graded partial *-algebra.

Weight sequences versus gap sequences at singular points of Gorenstein curves

After some foundational material concerning the so-calledWronskian k-forms, the fundamental notion ofweight sequence at a pointP of a Gorenstein curve (singular or not) is introduced. Thanks to this definition it is possible to extend the notion ofWeierstras gaps sequence (WGS) at a singular point of a Gorenstein curve. The latter reduces to the classical one for points of smooth curves. In Sections 6 and 7, some geometrical interpretations and discussions of previous results of Widland and Lax are given, showing the naturality of the definition of WGS at a singular point.

A simple characterization of fuzzy subgroups

We introduce here the notion of weights over an arbitrary group. We have shown that all fuzzy subgroups can be characterized by making use of weights. Furthermore, we have given a concrete description of the fuzzy subgroups of a wide variety of groups, using the notion of weights.

Weak radix representation and cyclic codes over euclidean domains

Here we show that to some extent the two theories cyclic arithmetic coding and cyclic polynomial coding can be subsumed under a “unified” theory based on a more or less arbitrary Euclidean domain. In particular, we show that Hamming weight (for cyclic polynomial codes) and arithmetic weight (for cyclic arithmetic codes) are special cases of a more general notion of weight defined for Euclidean rings. of fundamental importance in this development is a general-ization of the notion of radix representation for integers which we call a weak radix representation. For several specific Euclidean rings we prove the existence of certain unique canonical weak radix representations for all ring elements. We show, for example, that every Gaussian integer has a unique representation of the form (1) each aj is zero or a unit, and whenever aj≠0 , then aj+1 = aj+2 = 0 This is analogous to a known result of Reitwiesner that each rational integer has a unique representation of the form (1) where r - 2, each aj. is 0 or ± 1...