For decades, discrete choice modelling was practically dominated by only two models: multinomial probit and logit. This paper presents a novel alternative—harmonic choice model. It is qualitatively similar to multinomial probit and logit: if one choice alternative greatly exceeds all (falls below at least one of) other alternatives in terms of utility then it is chosen with probability close to one (zero). Compared to probit and logit, the new model has relatively flat (...) tails and it is steeper in the neighborhood of zero (when all alternatives yield the same utility and the decision maker chooses among them at random). (shrink)

Our aim in this paper was to establish an empirical evaluation for similarity effects modeled by Rubinstein; Azipurua et al.; Leland; and Sileo. These tests are conducted through a sensitivity analysis of two well-known examples of expected utility (EU) independence violations. We found that subjective similarity reported by respondents was explained very well by objective measures suggested in the similarity literature. The empirical results of this analysis also show that: (1) the likelihood of selection for the riskier choice increases (...) as the pair becomes more similar, (2) these choice patterns are consistent with well-known independence violations of expected utility, and (3) a significant proportion of individuals exhibit intransitive choice patterns predicted under similarity effects, but not allowed under generalized expected utility models for risky choice. (shrink)

This note establishes a new identification result for additive random utility discrete choice models. A decision-maker associates a random utility Uj+mj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_{j}+m_{j}$$\end{document} to each alternative in a finite set j∈1,…,J\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$j\in \left\{ 1,\ldots,J\right\} $$\end{document}, where U=U1,…,UJ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {U}=\left\{ U_{1},\ldots,U_{J}\right\} $$\end{document} is unobserved by the researcher and random with an unknown joint distribution, while the (...) perturbation m=m1,…,mJ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {m}=\left $$\end{document} is observed. The decision-maker chooses the alternative that yields the maximum random utility, which leads to a choice probability system m→Pr1|m,…,PrJ|m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf { m\rightarrow }\left,\ldots,\Pr \left \right) $$\end{document}. Previous research has shown that the choice probability system is identified from the observation of the relationship m→Pr1|m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbf {m}\rightarrow \Pr \left $$\end{document}. We show that the complete choice probability system is identified from observation of a relationship m→∑j=1sPrj|m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {m}\rightarrow \sum _{j=1}^{s}\Pr \left $$\end{document}, for any sshrink)

BackgroundNew disease-modifying ways to treat Parkinson’s disease (PD) may soon become a reality with intracerebral transplantation of cell products produced from human embryonic stem cells (hESCs). The aim of this study was to assess what factors influence preferences of patients with PD regarding stem-cell based therapies to treat PD in the future.MethodsPatients with PD were invited to complete a web-based discrete choice experiment to assess the importance of the following attributes: (i) type of treatment, (ii) aim of treatment, (...) (iii) available knowledge of the different types of treatments, (iv) effect on symptoms, and (v) risk for severe side effects. Latent class conditional logistic regression models were used to determine preference estimates and heterogeneity in respondents’ preferences.ResultsA substantial difference in respondents’ preferences was observed in three latent preference patterns (classes). “Effect on symptoms” was the most important attribute in class 1, closely followed by “type of treatment,” with medications as preferred to other treatment alternatives. Effect on symptoms was also the most important attribute in class 2, with treatment with hESCs preferred over other treatment alternatives. Likewise for class 3, that mainly focused on “type of treatment” in the decision-making. Respondents’ class membership was influenced by their experience in treatment, side effects, and advanced treatment therapy as well as religious beliefs.ConclusionsMost of the respondents would accept a treatment with products emanating from hESCs, regardless of views on the moral status of embryos. Preferences of patients with PD may provide guidance in clinical decision-making regarding treatments deriving from stem cells. (shrink)

It is not unusual in real-life that one has to choose among finitely many alternatives when the merit of each alternative is not perfectly known. Instead of observing the actual utilities of the alternatives at hand, one typically observes more or less precise signals that are positively correlated with these utilities. In addition, the decision-maker may, at some cost or disutility of effort, choose to increase the precision of these signals, for example by way of a careful study or the (...) hiring of expertise. We here develop a model of such decision problems. We begin by showing that a version of the monotone likelihood-ratio property is sufficient, and also essentially necessary, for the optimality of the heuristic decision rule to always choose the alternative with the highest signal. Second, we show that it is not always advantageous to face alternatives with higher utilities, a non-monotonicity result that holds even if the decision-maker optimally chooses the signal precision. We finally establish an operational first-order condition for the optimal precision level in a canonical class of decision-problems, and we show that the optimal precision level may be discontinuous in the precision cost. (shrink)

There is a model, for a system of intuitionistic analysis including Brouwer's principle for numbers and Kripke's schema, in which math formula ø-definable discrete sets of choice sequences are subcountable.

Computational modelling has proven to be a valuable approach in developing theories of spoken-word processing. In this paper, we focus on a particular class of theories in which it is assumed that the spoken-word recognition process consists of two consecutive stages, with an `abstract' discrete symbolic representation at the interface between the stages. In evaluating computational models, it is important to bring in independent arguments for the cognitive plausibility of the algorithms that are selected to compute the processes (...) in a theory. This paper discusses the relation between behavioural studies, theories, and computational models of spoken-word recognition. We explain how computational models can be assessed in terms of the goodness of fit with the behavioural data and the cognitive plausibility of the algorithms. An in-depth analysis of several models provides insights into how computational modelling has led to improved theories and to a better understanding of the human spoken-word recognition process. (shrink)

In a remarkable confirmation of OT in an empirical domain for which it was not originally intended, phonological and morphological variation has been successfully modeled by partially ranked categorical constraints (Anttila 1997, 2002). Poetic meter is a good place to extend and test this approach to variation, because there is abundant and diverse quantitative data available for it, and because it is typically governed by a relatively small number of well-understood constraints. I report the results of four such studies here. (...) They confirm that choices among metrical options are governed by the interaction of partially ranked constraints, in each case constraints that are grounded, and motivated independently of variation data by related systems in which they have a fixed rank. The partially ranked constraint systems turned out to predict not only the relative preferences among metrical options, but also their actual frequencies in the corpora, with surprising accuracy. These findings support the partial ranking model of variation, and provide an explanatory benchmark beyond the reach of intrinsically weaker stochastic approaches that posit a statistical component for metrical competence (Hayes & MacEachern 1998). (shrink)

We examined how children’s strategy choices in solving complex subtraction problems are related to grade and to variations in problem complexity. In two studies, third- and fifth-grade children (N≈160 each study) solved multi-digit subtraction problems (e.g., 34 - 18) and described their solution strategies. In the first experiment, strategy selection was investigated by means of a free-choice paradigm, whereas in the second study a discrete-choice approach was implemented. In both experiments, analyses of strategy repertoire indicated that third-grade (...) children were more likely to report less-efficient strategies (i.e., counting) and relied more on the right-to-left solution algorithm compared to fifth-grade children who more often used efficient memory-based retrieval and conceptually-based left-to-right (i.e., decomposition) strategies. Nevertheless, all strategies were reported or selected by both older and younger children and strategy use varied with problem complexity and presentation format for both age groups. These results supported the overlapping waves model of strategy development and provide detailed information about patterns of strategy choice on complex subtraction problems. (shrink)

Discrete choice experiments—selecting the best and/or worst from a set of options—are increasingly used to provide more efficient and valid measurement of attitudes or preferences than conventional methods such as Likert scales. Discrete choice data have traditionally been analyzed with random utility models that have good measurement properties but provide limited insight into cognitive processes. We extend a well-established cognitive model, which has successfully explained both choices and response times for simple decision tasks, to complex, (...) multi-attribute discrete choice data. The fits, and parameters, of the extended model for two sets of choice data (involving patient preferences for dermatology appointments, and consumer attitudes toward mobile phones) agree with those of standard choice models. The extended model also accounts for choice and response time data in a perceptual judgment task designed in a manner analogous to best–worst discrete choice experiments. We conclude that several research fields might benefit from discrete choice experiments, and that the particular accumulator-based models of decision making used in response time research can also provide process-level instantiations for random utility models. (shrink)

Econometric analysis of discrete choice has made considerable use of random utility models to interpret observed choice behavior. Much empirical research concerns choice problems in which persons act with partial knowledge of the utilities of the feasible actions. Economists use random expected utility models to analyze such choice problems. A common practice is to specify fully the expectations that persons hold, in which case choice analysis reduces to inference on preferences alone. However, (...) the expectations assumptions made in empirical research rarely have much foundation. To enable more credible research, this paper considers inference when one specifies a set of expectations that decision makers may plausibly hold. I first pose the idea in abstraction and then specialize to binary response with linear utilities, where the analysis is particularly straightforward. I initially assume that decision makers possess unique subjective probability distributions on the states of nature and make choices that maximize expected utility. I later consider the possibility that persons place only partial probabilistic structure on the states of nature and make undominated choices. (shrink)

The aim of this article is to reveal how care workers in the home-help services handle the process when older people’s relocation to a residential home is under consideration. Since the care workers are engaged daily in defining care receivers’ needs and yet have no formal influence on care decisions in Sweden, the focus is on how they solve this dilemma. In this inductive study, the theoretical framework is based on occupational alliances, relationship-based practice, and discretion. Thirty-three care workers in (...) home-help services are included in open semi-structured interviews. Prominent features in the findings are that the care workers take their stand at the borderland of care management, when they know or try to find out what is right. The conclusions drawn are that care workers find ways to informally influence the decision-making process, quite contrary to the idea of approaches referred to as purchaser/provider models. The implications for social work policy and practice are that a distinction between assessment and intervention may not benefit the field of eldercare and should therefore be regarded as an area in need of thorough reconsideration. (shrink)

The current research explores the women participation in SMEs business by using Probit model. The rapid absorption of women into the labor market has been influenced by several factors. The rapid economic growth was due largely to important growth in the SMEs business, where substantial and proportionally larger increase of female workers has been registered. Among all sectors of the economy, the SMEs have recorded the highest growth rate during the last decade. The increase in the female labor force (...) participation in SMES business may also be attributable to improving economic incentives in employment and policies favoring the employment of women. In addition, the combined effects of increased years of schooling, access to family planning services, improved maternal and child care, leading to arise in the average age at marriage, have allowed women to take advantage of the increased employment opportunities. Survey was conducted from 300 women in SMEs business in rural Sindh by using simple random technique from four districts, Shikarpur, Jacobabad, Kandhkot/Kashmore and Larkana Districts. Questionnaire was the basic tool to find out the major challenges of rural women as an entrepreneur business. It was revealed that there is great potential of rural women I doing the various entrepreneur business like in Kandhkot, Jacobabad, Rali, Ajrak and Sindhi caps they are very much unique and they were generating income from their families. It was further revealed that the rural women is less confident and their husbands were always given them hard time once they are exposing themselves to outside the boundaries of the house. The biggest challenges which they were facing they were doing all business in house, lack of marketing facilities, Karo Kari criminal activities and they were deprived from the basic rights. This study contributes and explores the Rural Women challenges in SMEs business and how these critical unethical problems we can overcome like KARO KARI, and other various social issues growth. (shrink)

This paper attempts to construct a short epistemology of economic models by using as a benchmark a comparison between the methodological issues of contemporary physics and of economics. In particular, the paper focuses on the role of indeterminacy in either sciences. Herein the general claim is that the models of economics fail at dealing with uncertainty as effectively as the models of natural sciences because economists did not manage to overcome the identification problem that is peculiar to (...) economics. In this respect, the paper shows that the models of economics assume an untenable determinism that derives from the notion of rationality of agents. The paper is divided in three sections: the first section deals with the issues related to assumptions in the models of physics and economics; the second section deals with the problem of uncertainty in quantum mechanics and in economics; the third section deals with the problem of causality in both sciences. Eventually, the paper concludes that several methodological problems affect the efficiency of economic models. Most importantly, the paper finds that economic models abstract too much from the reality and, thus, do not provide deep investigations of agents’ discrete choices. This is shown to affect the consistency of models and their explanatory power. Keywords: economics; philosophy of science, epistemology, rationality, uncertainty,. (shrink)

This paper attempts to construct a short epistemology of economic models by using as a benchmark a comparison between the methodological issues of contemporary physics and of economics. In particular, the paper focuses on the role of indeterminacy in either sciences. Herein the general claim is that the models of economics fail at dealing with uncertainty as effectively as the models of natural sciences because economists did not manage to overcome the identification problem that is peculiar to (...) economics. In this respect, the paper shows that the models of economics assume an untenable determinism that derives from the notion of rationality of agents. The paper is divided in three sections: the first section deals with the issues related to assumptions in the models of physics and economics; the second section deals with the problem of uncertainty in quantum mechanics and in economics; the third section deals with the problem of causality in both sciences. Eventually, the paper concludes that several methodological problems affect the efficiency of economic models. Most importantly, the paper finds that economic models abstract too much from the reality and, thus, do not provide deep investigations of agents’ discrete choices. This is shown to affect the consistency of models and their explanatory power. (shrink)

The paper follows the track of a previous paper “Natural cybernetics of time” in relation to history in a research of the ways to be mathematized regardless of being a descriptive humanitarian science withal investigating unique events and thus rejecting any repeatability. The pathway of classical experimental science to be mathematized gradually and smoothly by more and more relevant mathematical models seems to be inapplicable. Anyway quantum mechanics suggests another pathway for mathematization; considering the historical reality as dual or (...) “complimentary” to its model. The historical reality by itself can be seen as mathematical if one considers it in Hegel’s manner as a specific interpretation of the totality being in a permanent self-movement due to being just the totality, i.e. by means of the “speculative dialectics” of history, however realized as a theory both mathematical and empirical and thus falsifiable as by logical contradictions within itself as emprical discrepancies to facts. Not less, a Husserlian kind of “historical phenomenology” is possible along with Hegel’s historical dialectics sharing the postulate of the totality (and thus, that of transcendentalism). One would be to suggest the transcendental counterpart: an “eternal”, i.e. atemporal and aspatial history to the usual, descriptive temporal history, and equating the real course of history as with its alternative, actually happened branches of the regions of the world as with only imaginable, counterfactual histories. That universal and transcendental history is properly mathematical by itself, even in a neo-Pythagorean model. It is only represented on the temporal screen of the standard historiography as a discrete series of unique events. An analogy to the readings of the apparatus in quantum mechanics can be useful. Even more, that analogy is considered rigorously and logically as implied by the mathematical transcendental history and sharing with it the same quantity of information as an invariant to all possible alternative or counterfactual histories. One can involve the hypothetical external viewpoint to history (as if outside of history or from “God’s viewpoint to it), to which all alternative or counterfactual histories can be granted as a class of equivalence sharing the same information (i.e. the number choices, but realized in different sequence or adding redundant ones in each branch) being similar and even mathematically isomorphic to Feynman trajectories in quantum mechanics. Particularly, a fundamental law of mathematical history, the law of least choice of the real historical pathway is deducible from the same approach. Its counterpart in physics is the well-known and confirmed law of least action as far as the quantity of action corresponds equivocally to the quantity of information or that of number elementary historical choices. (shrink)

International borders concentrate opportunities in some societies while limiting them in others. Borders also prevent those in the less favored societies from gaining access to opportunities available in the more favored ones. Both distributive effects of borders are treated here within a comprehensive framework. I argue that each state should have broad discretion under international law to grant or deny entry to immigration seekers; but more favored countries that find themselves under immigration pressure should be legally obligated to fund development (...) assistance for countries that generate immigration pressure. Funding should be subject to conditions of fair and effective use in recipient countries, and should aim at a near-term target of immigration-pressure equilibrium. Equilibrium obtains between two countries when, given appropriate background circumstances, the same proportion of individuals in each manifests a preference to migrate to the other. If meeting the equilibrium target in the short term would be to the long-term disadvantage of the worst-off countries, then a Pareto-superior alternative target supersedes. It mandates development assistance at the level that yields the most favorable human development projections for the worstoff countries. An implementable set of institutions is described that can achieve the equilibrium goal in the long term without unduly sacrificing other important ends, including economic growth, political stability, cultural integrity, the political autonomy of distinct societies, and their proper accountability for policy choices. Key Words: global justice • immigration • borders • development • distributive justice • development assistance • equality • international law • cosmopolitanism. (shrink)

Discrete choice experiments (DCE) are often used to elicit preferences, for instance, in health preference research. However, DCEs only provide binary responses, whilst real-life choices are made with varying degrees of conviction. We aimed to verify whether eliciting self-reported convictions on a 0–100 scale adds meaningful information to the binary choice. Eighty three respondents stated their preferences for health states using DCE and the time trade-off method (TTO). In TTO, utility ranges were also elicited to account for (...) preference imprecision. We verified the properties of the conviction across three areas: (1) response to various choice task modifications (e.g. dominance, increase in complexity, distance from the status quo) and association with rationality violations (e.g. intransitivity); (2) association with test–retest results; (3) relation to the utility difference and imprecision estimated in TTO. Regarding (1), conviction increased in choice tasks with lower complexity, larger relative attractiveness, and lower distance to the status quo. Regarding (2), choices made with above-median conviction were sustained in 90% of the cases, compared to 68% for below-median conviction. Regarding (3), the conviction increases with utility difference and it decreases with utility imprecision; overconfidence seems to prevail: non-zero conviction is reported even for identical utilities. Self-reported conviction in DCE is associated in an intuitive way with the observed choices. It may, therefore, be useful in explaining or predicting behaviour or bridging the gap between the results of various elicitation tasks. (shrink)

The energy domain is still dominated by equilibrium models that underestimate both the dangers and opportunities related to climate change. In reality, climate and energy systems contain tipping points, feedback loops, and exponential developments. This paper describes how to create realistic energy transition management models: quantitative models that can discover profitable pathways from fossil fuels to renewable energy. We review the literature regarding agent-based economics, disruptive innovation, and transition management and determine the following requirements. Actors must be (...) detailed, heterogeneous, interacting, learning, and strategizing. Technology should be represented as a detailed and heterogeneous portfolio that can develop in a bottom-up manner, using endogenous feedback loops. Assumptions about discount rates and the social cost of carbon should be configurable. The model should contain interactions between the global, national, local, and individual level. A review of modelling techniques shows that equilibrium models are unsuitable and that system dynamics and discrete event simulation are too limited. The agent-based approach is found to be uniquely suited for the complex adaptive sociotechnical systems that must be modelled. But the choice for agent-based models does not mean a rejection of other approaches because they can be accommodated within the agent-based framework. We conclude with practical guidelines. (shrink)

We have two main aims: to construct mathematical models for analysing determinism, causality and supervenience; and then to use these to demonstrate the possibility of constructing an ontic construal of the operation of free will - one requiring both the presentation of genuine alternatives to an agent and their selecting between them in a manner that permits the attribution of responsibility. Determinism is modelled using trans-temporal ontic links between discrete juxtaposed universe states and shown to be distinct from (...) predictability. Causality is defined on a temporal sequence of δ-algebras and quantified using a measure. The measure leads to definitions of causal overdetermination and epiphenomena. Proofs are constructed to demonstrate deterministic universes must carry their properties essentially but not necessarily locally. We argue determinism and causality are separate doctrines. These models and results are marshalled to put the case that a counterfactual construal of ontic choice cannot work. In response we propose ‘immanence’ - a modified form of indeterminism whereby a universe can present choices to its denizens. We prove that beings subsumed within a universe cannot pilot their own actions. We then argue these beings can exercise free will only when selecting between choices inhering within immanent relata. A being is responsible for its selections if and only if it is constituted of a temporally evolving deterministic substructure. Our proposal is novel: it avoids injecting indeterminism into the decision process. Topological models for property supervenience are developed and used to reconstruct standard definitions from the literature. These are then used to demonstrate considerations of supervenience do not affect our arguments. We have demonstrated that a model of the exercise of free will involving both genuine choices and responsibility is possible but can only operate within a non-deterministic universe possessing specific traits. (shrink)

Heterocyst spacing in blue -green bacteria is widely assumed to be due to a diffusible inhibitor. The inhibitor, a nitrogen-rich compound, probably glutamine, is produced via the N2-fixing enzymes of the heterocyst and in turn serves to suppress the induction of these enzymes and of the differentiation of vegetative cells to heterocysts. This simple morphogenetic mechanism operating in growing cellular filaments ofAnabaena species is investigated on the basis of a continuous and a discrete cellular model, as well as by (...) cell-by-cell simulation of the inhibitor transport. The resulting distances between heterocysts and kinetics of their production are compared with observations, and the values of physical parameters are estimated from the models. (shrink)

Zusammenfassung Das Ziel der vorliegenden Untersuchung ist es, die Präferenzen deutscher Bürger für die sportlichen Erfolge ihrer einheimischen Athleten und Mannschaften bei Olympischen Sommerspielen zu ermitteln. Hierzu wurde im Juli 2015 mit 159 Personen ein Discrete-Choice-Experiment durchgeführt. In 14 Entscheidungsszenarien standen jeweils zwei Alternativen des Konsums deutschen olympischen Sporterfolges zur Auswahl, die sich in folgenden vier Attributen unterschieden: Sportart, Gesamterfolg, Modus des Konsums und Zahlungsvehikel. Die multivariate Analyse ergab einen signifikanten Einfluss aller vier Attribute auf die Wahlentscheidung. U. (...) a. würden die Befragten 1,26 € im Monat spenden, um olympische Erfolge live im Fernsehen oder Internet miterleben zu können. (shrink)

Incentivising has shown to improve participation in clinical trials. However, ethical concerns suggest that incentives may be coercive, obscure trial risks and encourage individuals to enrol in cli...

Some researchers on binary choice inference have argued that people make inferences based on simple heuristics, such as recognition, fluency, or familiarity. Others have argued that people make inferences based on available knowledge. To examine the boundary between heuristic and knowledge usage, we examine binary choice inference processes in terms of attribute substitution in heuristic use (Kahneman & Frederick, 2005). In this framework, it is predicted that people will rely on heuristic or knowledge‐based inference depending on the subjective (...) difficulty of the inference task. We conducted competitive tests of binary choice inference models representing simple heuristics (fluency and familiarity heuristics) and knowledge‐based inference models. We found that a simple heuristic model (especially a familiarity heuristic model) explained inference patterns for subjectively difficult inference tasks, and that a knowledge‐based inference model explained subjectively easy inference tasks. These results were consistent with the predictions of the attribute substitution framework. Issues on usage of simple heuristics and psychological processes are discussed. (shrink)

This study investigates the literary-historical context of the attempts by late Southern Song critics to periodize Tang poetry. It demonstrates that the primary agenda of these critics was to establish High Tang poetry as the sole correct model. The insistence on the supremacy of the High Tang went in tandem with, and formed part of, the rebuke of contemporary poets for choosing Late Tang poetry as the object of emulation. The focal point of contention was whether Late Tang poetry could (...) or should serve as a useful model, at least for some in the initial stage of their poetic training. In this context, periodizations of Tang poetry functioned as an auxiliary to the discourse on choices of models in the late Southern Song. (shrink)

We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the following properties: it is interpretable in Martin-Löf's type theory. In addition, it is strong enough to prove the Set Compactness theorem and the results in formal topology which make use of this theorem. Moreover, it is stable under the standard constructions from algebraic set theory, namely exact completion, realizability models, forcing as (...) well as more general sheaf extensions. As a result, methods from our earlier work can be applied to show that this extension satisfies various derived rules, such as a derived compactness rule for Cantor space and a derived continuity rule for Baire space. Finally, we show that this extension is robust in the sense that it is also reflected by the model constructions from algebraic set theory just mentioned. (shrink)

We give a new argument supporting a gravitational role in quantum collapse. It is demonstrated that the discreteness of space-time, which results from the proper combination of quantum theory and general relativity, may inevitably result in the dynamical collapse of thewave function. Moreover, the minimum size of discrete space-time yields a plausible collapse criterion consistent with experiments. By assuming that the source to collapse the wave function is the inherent random motion of particles described by the wave function, we (...) further propose a concrete model of wavefunction collapse in the discrete space-time. It is shown that the model is consistent with the existing experiments and macroscopic experiences. (shrink)