The word as a unit of internal predictability

A long-standing problem in linguistics is how to define word. Recent research has focused on the incompatibility of diverse definitions, and the challenge of finding a definition that is crosslinguistically applicable. In this study I take a different approach, asking whether one structure is more word-like than another based on the concepts of predictability and information. I hypothesize that word constructions tend to be more “internally predictable” than phrase constructions, where internal predictability is the degree to which the entropy of one constructional element is reduced by mutual information with another element. I illustrate the method with case studies of complex verbs in German and Murrinhpatha, comparing verbs with selectionally restricted elements against those built from free elements. I propose that this method identifies an important mathematical property of many word-like structures, though I do not expect that it will solve all the problems of wordhood.

The word as a unit of internal predictability

A long-standing problem in linguistics is how to define ‘word’. Recent research has focused on the incompatibility of diverse definitions, and the challenge of finding a definition that is cross-linguistically applicable (e.g. Haspelmath 2011; Gijn and Zúñiga 2014; Bickel and Zúñiga 2017; Tallman 2020). In this study I take a different approach, asking whether one structure is more word-like than another based on Shannon’s (1948) concepts of predictability and information. I hypothesise that word constructions tend to be more ‘internally predictable’ than phrase constructions, where internal predictability is the degree to which the entropy of one constructional element is reduced by mutual information with another element. I illustrate the method with case studies of complex verbs in German and Murrinhpatha, comparing verbs with selectionally restricted elements against those built from free elements. I propose that this method identifies an important mathematical property of many word-like structures, though I do not expect that it will solve all the problems of wordhood.

Bell inequalities, counterfactual definiteness and falsifiability

We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical property of Bell’s probabilistic model. Although the amendment does not alter the relevance of the theorem regarding local realism, it brings back Bell theorem from the realm of philosophical discussions about counterfactual conditionals to the concrete experimental arena.

Physical Laws shape up HOX Gene Collinearity

Hox gene collinearity (HGC) is a multiscalar property of many animal phyla particularly important in embryogenesis. It relates entities and events occurring in Hox clusters inside the chromosome DNA and in embryonic tissues. These two entities differ in linear size by more than four orders of magnitude. HGC is observed as spatial collinearity (SC) where the Hox genes are located in the order (Hox1, Hox2, Hox3 …) along the 3’ to 5’ direction of DNA in the genome and a corresponding sequence of ontogenetic units (E1, E2, E3, …) located along the Anterior – Posterior axis of the embyo. Expression of Hox1 occurs in E1. Hox2 in E2, Hox3 in E3… Besides SC, a temporal collinearity (TC) has been also observed in many vertebrates. According to TC first is Hox1 expressed in E1, later is Hox2 expressed in E2, followed by Hox3 in E3,… Lately doubt has been raised whether TC really exists. A biophysical model (BM) was formulated and tested during the last twenty years. According to BM, physical forces are created which pull the Hox genes one after the other driving them to a transcription factory domain where they are transcribed. The existing experiments support this BM description. Symmetry is a physical-mathematical property of Matter that was explored in depth by Noether who formulated a ground-breaking theory that applies to all sizes of Matter. This theory applied to Biology can explain the origin of HGC as applied not only to animals developing along the A/P axis but also to animals with circular symmetry.

The alpha-mixture of survival functions

This paper presents a flexible family which we call the $\alpha$ -mixture of survival functions. This family includes the survival mixture, failure rate mixture, models that are stochastically closer to each of these conventional mixtures, and many other models. The $\alpha$ -mixture is endowed by the stochastic order and uniquely possesses a mathematical property known in economics as the constant elasticity of substitution, which provides an interpretation for $\alpha$ . We study failure rate properties of this family and establish closures under monotone failure rates of the mixture’s components. Examples include potential applications for comparing systems.

Investigating Schema-Free Encoding of Categorical Data Using Prime Numbers in a Geospatial Context

Prime numbers are routinely used in a variety of applications, e.g., cryptography and hashing. A prime number can only be divided by one and the number itself. A semi-prime number is a product of two or more prime numbers (e.g., 5 × 3 = 15) and can only be formed by these numbers (e.g., 3 and 5). Exploiting this mathematical property allows schema-free encoding of geographical data in nominal or ordinal measurement scales for thematic maps. Schema-free encoding becomes increasingly important in the context of data variety. In this paper, I investigate the encoding of categorical thematic map data using prime numbers instead of a sequence of all natural numbers (1, 2, 3, 4, ..., n) as the category identifier. When prime numbers are multiplied, the result as a single value contains the information of more than one location category. I demonstrate how this encoding can be used on three use-cases, (1) a hierarchical legend for one theme (CORINE land use/land cover), (2) a combination of multiple topics in one theme (Köppen-Geiger climate classification), and (3) spatially overlapping regions (tree species distribution). Other applications in the field of geocomputation in general can also benefit from schema-free approaches with dynamic instead of handcrafted encoding of geodata.

Election with Bribe-Effect Uncertainty: A Dichotomy Result

We consider the electoral bribery problem in computational social choice. In this context, extensive studies have been carried out to analyze the computational vulnerability of various voting (or election) rules. However, essentially all prior studies assume a deterministic model where each voter has an associated threshold value, which is used as follows. A voter will take a bribe and vote according to the attacker's (i.e., briber's) preference when the amount of the bribe is above the threshold, and a voter will not take a bribe when the amount of the bribe is not above the threshold (in this case, the voter will vote according to its own preference, rather than the attacker's). In this paper, we initiate the study of a more realistic model where each voter is associated with a willingness function, rather than a fixed threshold value. The willingness function characterizes the likelihood a bribed voter would vote according to the attacker's preference; we call this bribe-effect uncertainty. We characterize the computational complexity of the electoral bribery problem in this new model. In particular, we discover a dichotomy result: a certain mathematical property of the willingness function dictates whether or not the computational hardness can serve as a deterrence to bribery attackers.

Consciousness and integrated energy differences in the brain

To understand consciousness within the framework of natural science we must acknowledge the role of energy in the brain. Many contemporary neuroscientists regard the brain as an information processor. However, evidence from brain imaging experiments demonstrates that the brain is actually a voracious consumer of energy, and that functionality is intimately tied to metabolism. Maintaining a critical level of energy in the brain is required to sustain consciousness, and the organisation of this energy distinguishes conscious from unconscious states. Meanwhile, contemporary physicists often regard energy as an abstract mathematical property. But this view neglects energy's causal efficacy and actuality, as identified by Aristotle and later appreciated by many important biologists, psychologists and physicists. By reconsidering the nature of energy and recasting its role in neural activity, we arrive at a theory of consciousness that is consistent with the laws of physics, chemistry and biology. The argument draws on the integrated information theory (IIT) developed by Tononi et al. but reinterprets their findings from the perspective of energy exchange. In IIT, the conscious state in a system, such as a brain, is defined by the quantity of integrated differences, or information, it contains. According to the approach outlined here, it is in the nature of energy to manifest differences of motion and tension. The level of complexity of the energy differences in a system determines its conscious state. Consciousness occurs because, in Nagel's terminology, there is 'something it is like' to be a sufficiently complex state of energy differences.Consciousness, metabolism, energy, brain, information theory

Does convexity of yield surfaces in plasticity have a physical significance?

Convexity of a function or set is an often needed and important mathematical property. In the case of yield functions [Formula: see text] (or elastic ranges) in terms of stresses, almost all empirical and mechanism-based yield functions have this property. However, requiring positive plastic dissipation does not necessarily exclude non-convex yield functions, which is confirmed by the fact that non-convex yield functions are observed experimentally, although this rarely happens. We therefore ask whether this nice mathematical property reflects a physical material property. This is investigated in an elastic–plastic, small strain, 2D setting. It appears that, at least in this setting, no specific material property can be attributed to the convexity of the yield function.