Contextual restrictions on cumulativity

This paper revisits the semantic variability of sentences with simple plural (in)definites in English and German, which permit distributive, cumulative and paired-cover construals. I argue that this variability reflects context-dependency rather than LF ambiguity (Schwarzschild 1996) and that the selection of a particular construal in context is driven by the QUD in the same way as the choice between maximal and non-maximal construals of plural definites (Malamud 2012; Križ 2015; Križ & Spector 2020). I then develop a new semantics for plural predication on which non-distributive and non-maximal construals form a natural class. The system extends the idea that non-maximality involves truth-value gaps (e.g. Križ 2015) to non-distributive construals by making use of Schmitt’s (2019) ‘plural projection’ framework, in which plural sentences involve special composition rules.

Insights on the Inhibitory Power of Flavonoids on Tyrosinase Activity: A Survey from 2016 to 2021

Tyrosinase is a multifunctional copper-containing oxidase enzyme that initiates melanin synthesis in humans. Excessive accumulation of melanin pigments or the overexpression of tyrosinase may result in skin-related disorders such as aging spots, wrinkles, melasma, freckles, lentigo, ephelides, nevus, browning and melanoma. Nature expresses itself through the plants as a source of phytochemicals with diverse biological properties. Among these bioactive compounds, flavonoids represent a huge natural class with different categories such as flavones, flavonols, isoflavones, flavan-3-ols, flavanones and chalcones that display antioxidant and tyrosinase inhibitor activities with a diversity of mechanistic approaches. In this review, we explore the role of novel or known flavonoids isolated from different plant species and their participation as tyrosinase inhibitors reported in the last five years from 2016 to 2021. We also discuss the mechanistic approaches through the different studies carried out on these compounds, including in vitro, in vivo and in silico computational research. Information was obtained from Google Scholar, PubMed, and Science Direct. We hope that the updated comprehensive data presented in this review will help researchers to develop new safe, efficacious, and effective drug or skin care products for the prevention of and/or protection against skin-aging disorders.

The Pareto Frontier of Inefficiency in Mechanism Design

We study the trade-off between the price of anarchy (PoA) and the price of stability (PoS) in mechanism design in the prototypical problem of unrelated machine scheduling. We give bounds on the space of feasible mechanisms with respect to these metrics and observe that two fundamental mechanisms, namely the first price (FP) and the second price (SP), lie on the two opposite extrema of this boundary. Furthermore, for the natural class of anonymous task-independent mechanisms, we completely characterize the PoA/PoS Pareto frontier; we design a class of optimal mechanisms [Formula: see text] that lie exactly on this frontier. In particular, these mechanisms range smoothly with respect to parameter [Formula: see text] across the frontier, between the first price ([Formula: see text]) and second price ([Formula: see text]) mechanisms. En route to these results, we also provide a definitive answer to an important question related to the scheduling problem, namely whether nontruthful mechanisms can provide better makespan guarantees in the equilibrium compared with truthful ones. We answer this question in the negative by proving that the price of anarchy of all scheduling mechanisms is at least n, where n is the number of machines.

Tropical fans, scattering equations and amplitudes

We describe a family of tropical fans related to Grassmannian cluster algebras. These fans are related to the kinematic space of massless scattering processes in a number of ways. For each fan associated to the Grassmannian Gr(k, n) there is a notion of a generalised ϕ3 amplitude and an associated set of scattering equations which further generalise the Gr(k, n) scattering equations that have been recently introduced. Here we focus mostly on the cases related to finite Grassmannian cluster algebras and we explain how face variables for the cluster polytopes are simply related to the scattering equations. For the Grassmannians Gr(4, n) the tropical fans we describe are related to the singularities (or symbol letters) of loop amplitudes in planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We show how each choice of tropical fan leads to a natural class of polylogarithms, generalising the notion of cluster adjacency and we describe how the currently known loop data fit into this classification.

Ledrappier–Young formulae for a family of nonlinear attractors

We study a natural class of invariant measures supported on the attractors of a family of nonlinear, non-conformal iterated function systems introduced by Falconer, Fraser and Lee. These are pushforward quasi-Bernoulli measures, a class which includes the well-known class of Gibbs measures for Hölder continuous potentials. We show that these measures are exact dimensional and that their exact dimensions satisfy a Ledrappier–Young formula.

A Logical Characterization of the Preferred Models of Logic Programs with Ordered Disjunction

Logic programs with ordered disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational meaning of ordered disjunction is clear, there exists an important open issue regarding its semantics. In particular, there does not exist a purely model-theoretic approach for determining the most preferred models of an LPOD. At present, the selection of the most preferred models is performed using a technique that is not based exclusively on the models of the program and in certain cases produces counterintuitive results. We provide a novel, model-theoretic semantics for LPODs, which uses an additional truth value in order to identify the most preferred models of a program. We demonstrate that the proposed approach overcomes the shortcomings of the traditional semantics of LPODs. Moreover, the new approach can be used to define the semantics of a natural class of logic programs that can have both ordered and classical disjunctions in the heads of clauses. This allows programs that can express not only strict levels of preferences but also alternatives that are equally preferred.

Pictorial Statistics

This essay discusses Francis Galton’s method of inductive inference where the data are photographs of human faces. His aim of induction was to determine the typical characteristics of the natural class to which the individuals belong by composing the relevant photographs in a specific photographic way. The three populations studied by Galton were people suffering tuberculosis, Jews, and criminals. This essay argues that despite the fact that Galton aimed at mechanical objectivity, subjective judgements nevertheless appear to be a necessary part of this kind of inductive inference. At first sight, this seems very much in the line of Lorraine Daston and Peter Galison’s account of objectivity. They argue that in the twentieth century the awareness arose that mechanical-objective pictures still could contain errors that should be erased by trained judgement. Galton’s case of inductive reasoning, however, departs from this account by showing that the correct composites were achieved by a combination of mechanical procedures and untrained judgements. To arrive at the typical characterizations one first has to familiarize oneself with the data, but the familiarization should be done by someone who is not an expert on the cases under study.

Predicting anti-cancer activity in flavonoids - a graph theoretic approach

In drug design, there are two major causes of drug failure in the clinic. First, the drug has to work, and second, the drug should be safe. Identifying compounds that work for certain ailments require enormous experimental time and, in general, is cost-intensive. In this paper, we are concerned with melanoma, a special type of cancer that affects the skin. In particular, we seek to provide a mathematical model that can predict the ability of flavonoids, a vast and natural class of compounds that are found in plants, in reversing or alleviating melanoma. The basis for our model is the conception of a new graph parameter called, for lack of better terminology, graph activity, which captures melanoma cancer healing properties of the flavonoids. With a superior coefficient of determination, R squared=1, the new model faithfully reproduces anti-cancer activities of some known data sets. We demonstrate that the model can be used to rank the healing abilities of flavonoids which could be a powerful tool in the screening, and identification, of compounds for drug candidates.

Kinematic numerators from the worldsheet: cubic trees from labelled trees

In this note we revisit the problem of explicitly computing tree-level scattering amplitudes in various theories in any dimension from worldsheet formulas. The latter are known to produce cubic-tree expansion of tree amplitudes with kinematic numerators automatically satisfying Jacobi-identities, once any half-integrand on the worldsheet is reduced to logarithmic functions. We review a natural class of worldsheet functions called “Cayley functions”, which are in one-to-one correspondence with labelled trees, and natural expansions of known half-integrands onto them with coefficients that are particularly compact building blocks of kinematic numerators. We present a general formula expressing kinematic numerators of all cubic trees as linear combinations of coefficients of labelled trees, which satisfy Jacobi identities by construction and include the usual combinations in terms of master numerators as a special case. Our results provide an efficient algorithm, which is implemented in a Mathematica package, for computing all tree amplitudes in theories including non-linear sigma model, special Galileon, Yang-Mills-scalar, Einstein-Yang-Mills and Dirac-Born-Infeld.

Dynamic Quantum Games

Quantum games represent the really twenty-first century branch of game theory, tightly linked to the modern development of quantum computing and quantum technologies. The main accent in these developments so far was made on stationary or repeated games. In this paper, we aim at initiating the truly dynamic theory with strategies chosen by players in real time. Since direct continuous observations are known to destroy quantum evolutions (so-called quantum Zeno paradox), the necessary new ingredient for quantum dynamic games must be the theory of non-direct observations and the corresponding quantum filtering. Apart from the technical problems in organizing feedback quantum control in real time, the difficulty in applying this theory for obtaining mathematically amenable control systems is due partially to the fact that it leads usually to rather non-trivial jump-type Markov processes and/or degenerate diffusions on manifolds, for which the corresponding control is very difficult to handle. The starting point for the present research is the remarkable discovery (quite unexpected, at least to the author) that there exists a very natural class of homodyne detections such that the diffusion processes on projective spaces resulting by filtering under such arrangements coincide exactly with the standard Brownian motions (BM) on these spaces. In some cases, one can even reduce the process to the plain BM on Euclidean spaces or tori. The theory of such motions is well studied making it possible to develop a tractable theory of related control and games, which can be at the same time practically implemented on quantum optical devices.