Quantification as reference: Evidence from Q-verbs

Formal semantics has so far focused on three categories of quantifiers, to wit, Q-determiners (e.g. 'every'), Q-adverbs (e.g. 'always'), and Q-auxiliaries (e.g. 'would'). All three can be analyzed in terms of tripartite logical forms (LF). This paper presents evidence from verbs with distributive affixes (Q-verbs), in Kalaallisut, Polish, and Bininj Gun-wok, which cannot be analyzed in terms of tripartite LFs. It is argued that a Q-verb involves discourse reference to a distributive verbal dependency, i.e. an episode-valued function that sends different semantic objects in a contextually salient plural domain to different episodes

Edge-aware Multi-task Network for Integrating Quantification Segmentation and Uncertainty Prediction of Liver Tumor on Multi-modality Non-contrast MRI

Simultaneous multi-index quantification, segmentation, and uncertainty estimation of liver tumors on multi-modality non-contrast magnetic resonance imaging (NCMRI) are crucial for accurate diagnosis. However, existing methods lack an effective mechanism for multi-modality NCMRI fusion and accurate boundary information capture, making these tasks challenging. To address these issues, this paper proposes a unified framework, namely edge-aware multi-task network (EaMtNet), to associate multi-index quantification, segmentation, and uncertainty of liver tumors on the multi-modality NCMRI. The EaMtNet employs two parallel CNN encoders and the Sobel filters to extract local features and edge maps, respectively. The newly designed edge-aware feature aggregation module (EaFA) is used for feature fusion and selection, making the network edge-aware by capturing long-range dependency between feature and edge maps. Multi-tasking leverages prediction discrepancy to estimate uncertainty and improve segmentation and quantification performance. Extensive experiments are performed on multi-modality NCMRI with 250 clinical subjects. The proposed model outperforms the state-of-the-art by a large margin, achieving a dice similarity coefficient of 90.01$\pm$1.23 and a mean absolute error of 2.72$\pm$0.58 mm for MD. The results demonstrate the potential of EaMtNet as a reliable clinical-aided tool for medical image analysis

First-order Goedel logics

First-order Goedel logics are a family of infinite-valued logics where the sets of truth values V are closed subsets of [0, 1] containing both 0 and 1. Different such sets V in general determine different Goedel logics G_V (sets of those formulas which evaluate to 1 in every interpretation into V). It is shown that G_V is axiomatizable iff V is finite, V is uncountable with 0 isolated in V, or every neighborhood of 0 in V is uncountable. Complete axiomatizations for each of these cases are given. The r.e. prenex, negation-free, and existential fragments of all first-order Goedel logics are also characterized.Comment: 37 page

Zero-one laws with respect to models of provability logic and two Grzegorczyk logics

It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. Therefore, many properties of models, such as having an even number of elements, cannot be expressed in the language of first-order logic. Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5 and for frames corresponding to S4 and S5. In this paper, we prove zero-one laws for provability logic and its two siblings Grzegorczyk logic and weak Grzegorczyk logic, with respect to model validity. Moreover, we axiomatize validity in almost all relevant finite models, leading to three different axiom systems

A 3D cell death assay to quantitatively determine ferroptosis in spheroids

The failure of drug efficacy in clinical trials remains a big issue in cancer research. This is largely due to the limitations of two-dimensional (2D) cell cultures, the most used tool in drug screening. Nowadays, three-dimensional (3D) cultures, including spheroids, are acknowledged to be a better model of the in vivo environment, but detailed cell death assays for 3D cultures (including those for ferroptosis) are scarce. In this work, we show that a new cell death analysis method, named 3D Cell Death Assay (3DELTA), can efficiently determine different cell death types including ferroptosis and quantitatively assess cell death in tumour spheroids. Our method uses Sytox dyes as a cell death marker and Triton X-100, which efficiently permeabilizes all cells in spheroids, was used to establish 100% cell death. After optimization of Sytox concentration, Triton X-100 concentration and timing, we showed that the 3DELTA method was able to detect signals from all cells without the need to disaggregate spheroids. Moreover, in this work we demonstrated that 2D experiments cannot be extrapolated to 3D cultures as 3D cultures are less sensitive to cell death induction. In conclusion, 3DELTA is a more cost-effective way to identify and measure cell death type in 3D cultures, including spheroids.</jats:p