Stronger Variants Research Articles

Fair Lotteries for Participatory Budgeting

In pursuit of participatory budgeting (PB) outcomes with broader fairness guarantees, we initiate the study of lotteries over discrete PB outcomes. As the projects have heterogeneous costs, the amount spent may not be equal ex ante and ex post. To address this, we develop a technique to bound the amount by which the ex-post spend differs from the ex-ante spend---the property is termed budget balanced up to one project (BB1). With respect to fairness, we take a best-of-both-worlds perspective, seeking outcomes that are both ex-ante and ex-post fair. Towards this goal, we initiate a study of ex-ante fairness properties in PB, including Individual Fair Share (IFS), Unanimous Fair Share (UFS) and their stronger variants, as well as Group Fair Share (GFS). We show several incompatibility results between these ex-ante fairness notions and existing ex-post concepts based on justified representation. One of our main contributions is a randomized algorithm which simultaneously satisfies ex-ante Strong UFS, ex-post full justified representation (FJR) and ex-post BB1 for PB with binary utilities.

Tree diet: reducing the treewidth to unlock FPT algorithms in RNA bioinformatics

Hard graph problems are ubiquitous in Bioinformatics, inspiring the design of specialized Fixed-Parameter Tractable algorithms, many of which rely on a combination of tree-decomposition and dynamic programming. The time/space complexities of such approaches hinge critically on low values for the treewidth tw of the input graph. In order to extend their scope of applicability, we introduce the Tree-Diet problem, i.e. the removal of a minimal set of edges such that a given tree-decomposition can be slimmed down to a prescribed treewidth tw'. Our rationale is that the time gained thanks to a smaller treewidth in a parameterized algorithm compensates the extra post-processing needed to take deleted edges into account. Our core result is an FPT dynamic programming algorithm for Tree-Diet, using 2^{O(tw)}n time and space. We complement this result with parameterized complexity lower-bounds for stronger variants (e.g., NP-hardness when tw' or tw-tw' is constant). We propose a prototype implementation for our approach which we apply on difficult instances of selected RNA-based problems: RNA design, sequence-structure alignment, and search of pseudoknotted RNAs in genomes, revealing very encouraging results. This work paves the way for a wider adoption of tree-decomposition-based algorithms in Bioinformatics.

Linearly equivalent S-boxes and the division property

Division property is a cryptanalysis method that proves to be very efficient on block ciphers. Computer-aided techniques such as MILP have been widely and successfully used to study various cryptanalysis techniques, and it especially led to many new results for the division property. Nonetheless, we claim that the previous techniques do not consider the full search space. We show that even if the previous techniques fail to find a distinguisher based on the division property over a given function, we can potentially find a relevant distinguisher over a linearly equivalent function. We show that the representation of the block cipher heavily influences the propagation of the division property, and exploiting this, we give an algorithm to efficiently search for such linear mappings. As a result, we exhibit a new distinguisher over 10 rounds of RECTANGLE, while the previous best was over 9 rounds, and rule out such a distinguisher over more than 9 rounds of PRESENT. We also give some insight about the construction of an S-box to strengthen a block cipher against our technique. We prove that using an S-box satisfying a certain criterion is optimal in term of resistance against classical division property. Accordingly, we exhibit stronger variants of RECTANGLE and PRESENT, improving the resistance against division property based distinguishers by 2 rounds.

A Lightweight Defeasible Description Logic in Depth

In this thesis we study KLM-style rational reasoning in defeasible Description Logics. We illustrate that many recent approaches to derive consequences under Rational Closure (and its stronger variants, lexicographic and relevant closure) suffer the fatal drawback of neglecting defeasible information in quantified concepts. We propose novel model-theoretic semantics that are able to derive the missing entailments in two differently strong flavours. Our solution introduces a preference relation to distinguish sets of models in terms of their typicality (amount of defeasible information derivable for quantified concepts). The semantics defined through the most typical (most preferred) sets of models are proven superior to previous approaches in that their entailments properly extend previously derivable consequences, in particular, allowing to derive defeasible consequences for quantified concepts. The dissertation concludes with an algorithmic characterisation of this uniform maximisation of typicality, which accompanies our investigation of the computational complexity for deriving consequences under these new semantics.

Is the comparison of sport to religion justifi ed?

The aim of this paper is to point out certain reasons for which some scholars perceive modern sport as a phenomenon that is signifi cantly similar to or (in stronger variants) identical to religion. Referring to the distinction between substantive and functional defi nitions of religion, I would like to show that this approach is based on the latter and, as such, is burdened with some serious fl aws. In criticizing functional defi nitions of religion I argue for a standpoint that comprises elements of the substantive as well as the functional perspective. In order to illustrate the heuristic merit of this approach, I refer to the analysis which has been put forward by a French anthropologist, Christian Bromberger. Drawing on the conclusions of his studies, I attempt to show that the substantive-functional perspective (a) enables a more detailed description of both sport and religion, which, apart from the similarities, brings out signifi cant diff erences between them, and (b) helps to understand some features of modern Western societies.

Chaos theory from the mathematical point of view

This work is intended as an attempt to survey existingde finitions of chaos for discrete dynamical systems. Discussion is restricted to the settingof topological dynamics, while the measure-theoretic (ergodic theory) and smooth (differentiable dynamical systems) aspects are omitted as exceedingt he scope of this paper. Chaos theory is understood here as a part of topological dynamics, so aforementioned definitions of chaos are just examples of particular dynamical system properties, and are considered inside the framework of the mathematical theory of discrete dynamical systems. It is not the purpose of this article to study chaos theory understood as a new kind of interdisciplinary branch of science devoted to nonlinear phenomena. As for prerequisites, the reader is expected to possess some mathematical maturity, and to be familiar with basic topology of (compact) metric spaces. No preliminary knowledge of the dynamical systems theory is required, however some is recommended. The first two section are devoted to general discussion of the term „chaos” and contains authors opinion on this subject. To facilitate access to the rest of the article some relevant material from the dynamical system theory is briefly repeated in the third section. The next section (Section 4) introduces the notion of topological transitivity along with some stronger variants, namely topological mixing and weak mixing. Section 5 gives a detailed account of the famous Sharkovskii’s Theorem in its full generality. This is required for characterization of chaotic interval maps. Sections 6-13 are devoted to various notions of chaos or related to chaos in dynamical systems. Each section contains an attempt to motivate the notion, historical background and formal definition followed with a review of known properties, relations between various notions of chaos, and some relevant open problems. Section 6 is devoted to a sensitivity to initial conditions – a notion which is accepted as a basic indicator of chaotic behavior. Section 7 introduces a definition of chaos accordingt o Auslander and Yorke. Section 8 examines the notion of Li-Yorke pair and Li-Yorke chaos. Section 9 deals with the definition of chaos introduced in Devaney’s book (Devaney chaos). Section 10 recalls some facts connected with symbolic dynamics, which provides a rich source of examples for various interestingb ehavior, and it is an indispensable tool for exploration of many systems. Section 11 describes the so-called “topological horseshoes”, which are generalizations of the famous example due to Smale. The existence of a horseshoe in a given dynamical system proves the existence of a subsystem with a dynamics similar to some symbolic dynamical system, hence with a very complicated behavior. Section 12 gives a brief exposition of the topological entropy and its relation to chaos. The review of various notions of chaos ends with section 13, containingd escription of distributional chaos.

On the Hofer Geometry Injectivity Radius Conjecture

We verify here some variants of topological and dynamical flavor of the injectivity radius conjecture in Hofer geometry, Lalonde-Savelyev \cite{citeLalondeSavelyevOntheinjectivityradiusinHofergeometry} in the case of $Ham (S^2)$ and $Ham(\Sigma, \omega)$, for $\Sigma$ a closed positive genus surface. In particular we show that any loop in $Ham (S^2)$, respectively $Ham(\Sigma, \omega)$ with $L ^{+}$ Hofer length less than $area(S ^{2} )/2$, respectively any $L ^{+} $ length is contractible through ($L ^{+} $) Hofer shorter loops, in the $C ^{\infty} $ topology. We also prove some stronger variants of this statement on the loop space level. One dynamical type corollary is that there are no smooth, positive Morse index (Ustilovsky) geodesics, in $Ham (S^2)$, respectively in $Ham(\Sigma, \omega)$ with $L ^{+} $ Hofer length less than $area (S ^{2} )/2$, respectively any length. The above condition on the geodesics can be expanded as an explicit and elementary dynamical condition on the associated Hamiltonian flow. We also give some speculations on connections of this later result with curvature properties of the Hamiltonian diffeomorphism group of surfaces.

Best Constrained Approximation in Banach Spaces

In this article, for a real Banach space X and a closed subspace Y, we consider aspects of proximinality, its stronger variants and the notion of centrability, Chebyshev centers, for a class of subspaces that are relatively constrained in a Banach space, in the sense that for x ∉ Y, Y is constrained in span{x, Y}. We show that if X, under the canonical embedding has the strong--ball property in its bidual, then the same is true of Y. We also give applications of these results to proximinality in spaces of Bochner integrable functions. We consider a class of Banach spaces for which a formula due to Smith and Ward on relative Chebyshev centers and radius is valid. We show that any locally constrained subspace of the Grothendieck G-space is a G-space.

Getting Laid and Growing Close: Constructions of Masculinity in Relationship Advice for Heterosexual Men

Despite the growing popularity of men’s self-help products, recent debates surrounding hegemonic masculinity, and attention to the “crisis of masculinity,” research has ignored men’s advice about intimate relationships. Consequently, I examine 30 contemporary relationship advice books and conceptualize their constructions of heterosexual masculinity. Findings demonstrate authors’ overall rejection of hegemonic masculinity, alongside an overarching strategy of “masculinizing” intimacy that promotes two subsidiary gender strategies – relational heroism and tempered ambition – which reframe non-hegemonic behavior as manly. The overarching strategy appears in mild forms in books emphasizing “getting laid” and stronger variants in books that promote “growing close” through intimacy. The strategy promotes a promising departure from the constraints of hegemonic masculinity by broadening men’s acceptable range of talking about and doing masculinity, but continues to emphasize gender difference and enables a reconfiguration of heterosexual masculine intimacy within hegemonic masculinity, thereby limiting its promotion of gender equality.

Isocompactness in the Category of Locales

We study isocompactness in Loc defined, exactly as in Top, by requiring that every countably compact closed sublocale be compact. This is a genuine extension of the same-named topological concept since every Boolean (or, even more emphatically, every paracompact) locale is isocompact. A slightly stronger variant is defined by decreeing that the closure of every complemented countably compact sublocale be compact. Dropping the adjective “complemented” yields a formally even stronger property, which we show to be preserved by finite products. Metrizable locales (or, more generally, perfectly normal locales) do not distinguish between the three variants of isocompactness. Each of the stronger variants of isocompactness travels across a proper map of locales, and in the opposite direction if the map is a surjection in Loc.

Artists in and out of the Caribbean

[First paragraph]Caribbean Art. VEERLE POUPEYE. London: Thames and Hudson, 1998. 224 pp. (Paper US$ 14.95)Transforming the Crown: African, Asian and Caribbean Artists in Britain, 1966-1996. MORA J. BEAUCHAMP-BYRD & M. FRANKLIN SIRMANS (eds.). New York: Caribbean Cultural Center, 1998. 177 pp. (Paper US$ 39.95,£31.95)"Caribbean" (like "Black British") culture is (as a Dutch colleague once said of postmodernism) a bit of a slippery fish. One of the books under review here presents the eclectic artistic productions of professional artists with Caribbean identities of varying sorts - some of them lifelong residents of the region (defined broadly to stretch from Belize and the Bahamas to Curacao and Cayenne), some born in the Caribbean but living elsewhere, and others from far-away parts of the world who have lingered or settled in the Caribbean. The other focuses on artists who trace their cultural heritage variously to Lebanon, France, Malaysia, Spain, China, England, Guyana, India, the Caribbean, the Netherlands, the Philippines, and the whole range of societies in West, East, and Central Africa, all of whom meet under a single ethnic label in galleries in New York and London. Clearly, the principles that vertebrate Caribbean Art and Transforming the Crown are built on the backs of ambiguities, misperceptions, ironies, and ethnocentric logics (not to mention their stronger variants, such as racism). Yet far from invalidating the enterprise, they offer an enlightening inroad to the social, cultural, economic, and political workings of artworlds that reflect globally orchestrated pasts of enormous complexity.

Statistical Metric Spaces Arising from Sets of Random Variables in Euclideann-Space

If $p,q, \cdots $, are random vectors with values from a Euclidean space $E^n $, then the Euclidean distance $d(p,q)$ between p and q is also a random variable. Let $F_{pq} $ be the distribution function of $d(p,q)$. Then the corresponding statistical metric space is defined as the ordered pair $(S,\mathfrak{F})$, where S is the set $\{ p,q, \cdots \} $ and $\mathfrak{F}$ is a collection of ordered pairs $\{ ((p,q),F_{pq} )\} $. In the present work we study the statistical metric spaces which arise when $p,q, \cdots $, are mutually independent random variables with spherically symmetric unimodal densities. It is proven that a weak variant of the generalized Menger triangle inequality is always applicable in these spaces, and in special cases, stronger variants are applicable. Furthermore, the moments of the distribution function $F_{pq} $ are investigated. Suitable powers of these moments define new metrics in the Euclidean space. With respect to each of these metrics, the space is discrete in the small, but is Euclidean in the large (the new distance between p and q as a function of the Euclidean distance between p and q has a positive minimum, and is close to the Euclidean distance when the latter is large).