We use the category of presheaves over PTIME-functions in order to show that Cook and Urquhart's higher-order function algebra PV ω defines exactly the PTIME-functions. As a byproduct we obtain a syntax-free generalisation of PTIME-computability to higher types. By restricting to sheaves for a suitable topology we obtain a model for intuitionistic predicate logic with ∑ 1 b -induction over PV ω and use this to re-establish that the provably total functions in this system are polynomial time computable. Finally, we (...) apply the category-theoretic approach to a new higher-order extension of Bellantoni-Cook's system BC of safe recursion. (shrink)

The space CS(R) has a unique “Borel structure” in the following sense. Note that there is a natural mapping from R¥ onto CS(R}; namely, taking ranges. We can combine this with any Borel bijection from R onto R¥ in order to get a “preferred” surjection F:R ® CS(R).

Executive functions represent higher order top-down mechanisms regulating information processing. While suboptimal EF have been studied in various patient groups, their impact on successful behavior is still not well described. Previously, it has been suggested that design fluency —a test including several simultaneous EF components mainly related to fluency, cognitive flexibility, and creativity—predicts successful behavior in a quickly changing environment where fast and dynamic adaptions are required, such as ball sports. We hypothesized that similar behaviors are of importance in the (...) selection process of elite police force applicants. To test this hypothesis, we compared elite police force applicants with a control group of police officer trainees. Although both groups were better than the norm, the elite police force applicants had a significantly better performance in DF total correct when adjusting for sex and age [F = 18.98, p < 0.001]. To understand how this capacity was altered by stress and tiredness, we re-tested the elite police force applicants several days during an extreme field assessment lasting 10 days. The results suggested that there was a lower than expected improvement in DF total correct and a decline in the DF3-subtest that includes a larger component of cognitive flexibility than the other subtests. Although there was a positive correlation between the baseline session and the re-test in DF3 [r = 0.49, p = 0.001], the applicants having the highest scores in the baseline test also displayed the largest percentage decline in the re-test [r = −0.46, p = 0.003]. In conclusion, our result suggests that higher order EF that include cognitive flexibility and creativity are of importance in the application for becoming an elite police officer but relatively compromised in a stressful situation. Moreover, as the decline is different between the individuals, the results suggest that applicants should be tested during baseline conditions and during stressful conditions to describe their cognitive capacity fully. (shrink)

This article discusses ethical questions in neurosurgery as falling into two categories, namely those surrounding what neurosurgeons are currently doing, i.e. their current practices, and those surrounding what neurosurgeons will, theoretically, be capable of doing in the future, i.e. their future practices. It reveals the current and emerging applications of functional neurosurgery as well as the future controversies that will stem from them. It focuses on psychosurgery, enhancement and the brain–machine interface, in order to illustrate the pertinent ethical challenges (...) and the role of the neurosurgeon in helping to address them. These three applications represent natural extensions of each other, as an exploration of the underlying mechanisms of psychopathology will ultimately provide insight into normal brain function. Concerns about the future of implantable technology, and the neurosurgeon's role in installing it, need to be addressed. (shrink)

Background: Patients prescribed with medication that treats mental health conditions benefit the most compared to those prescribed with other types of medication. However, they are also the most difficult to adhere. The development of mobile health (mHealth) applications (‘apps’) to help patients monitor their adherence is fast growing but with limited evidence on their efficacy. There is no evidence on the content of these apps for patients taking psychotropic medication. The aim of this study is to identify and evaluate the (...) aims and functioning of available apps that are aiming to help and educate patients to adhere to medication that treats mental health conditions. Method: Three platform descriptions (Apple, Google and Microsoft) were searched between October 2015 and February 2016. Included apps need to focus on adherence to medication that treats mental health conditions and use at least a reinforcement strategy. Descriptive information was extracted and apps evaluated on a number of assessment criteria using content analysis. Results: Sixteen apps were identified. All apps included self-monitoring properties like reminders and psycho-educational properties like mood logs. It was unclear how the latter were used or how adherence was measured. Major barriers to medication adherence like patients’ illness and medication beliefs and attitudes were not considered nor where information to patients about mediation side effects. Very few apps were tailored and none was developed based on established theories explaining the processes for successful medication adherence like cognitions and beliefs. Reported information on app development and validation was poor. Discussion: A variety of apps with different properties that tackle both intentional and unintentional non-adherence from a different perspective are identified. An evidence-based approach and co-creation with patients is needed. This will ensure that the apps increase the possibility to impact on non-adherence. Theories like social cognition models can be useful in ensuring that patients’ education, motivation, skills, beliefs and type of adherence are taken into consideration when developing the apps. Findings from this study can help clinicians and patients make informed choices and pursue policy-makers to integrate evidence when developing future apps. Quality-assurance tools are needed to ensure the apps are systematically evaluated. (shrink)

A review of extent business ethics research uncovered well over 200 published articles that investigated the role of job functions within a business organization as an explanatory factor of ethical or unethical behavior. While an important body of work, ethical breaches are often found to cut across job functions and involve multiple disciplines embedded in a business organization. This research seeks to explore a crossfunctional explanation for ethical reasoning by using an instrument new to business ethics research, the Wason selection (...) task, but well-grounded and validated in cognitive research and evolutionary psychology, to assess an individual's ability to detect rule-based social contract violations. A sample of 276 full-time business practitioners, enrolled in part-time M.B.A. programs, from the accounting, finance, information technology, marketing, supply chain, and human resource management job functions were compared on their ability to detect rule violators across a series of production scenarios in the Wason selection task. Rates of cheater detection were calculated to determine if substantive differences existed across job functions. This was followed by a series of pairwise comparisons of percentages of cheater detection across the job functions using z-tests for assessing statistical significance. The data analysis showed differences in cheater detection, with most of the variance due to the marketing job function group. Insights from this study for scholars, educators, and practitioners in the business ethics field are discussed. (shrink)

The objective of this paper is to present a new theory of synaptic function in the nervous system. The basis for this theory is the experimental demonstration that a nerve impulse assumes five different forms as it advances through the synaptic region, and that five basic mathematical operations have been identified as being involved in the transformation of one form into another form. As a result of these data, the synaptic region is regarded as a functional unit where information (...) coming to it is unpacked, processed, stored, and retrieved for transit to another synaptic region or effector site. The data also suggests that a nerve impulse is a bolus of energy, therefore, without substance; that it contains information coded in its shape or form; that it is precisely described mathematically. Furthermore, the data suggests synaptic regions process these nerve impulses by applying mathematical operations to them; that function in the synaptic region is highly stereotyped (programmed); that chemical substances are associated with the mathematical operations. The basic approach of this theory is to regard a significant portion of the nervous system as an interface between the external universe and man himself. As an interface, the nervous system receives and processes information from both the external universe and man himself in a programmed manner. The interface functions by converting the information it receives into a bolus of energy, the nerve impulse, then processes the bolus by converting it into numbers or functions and applying mathematical operation to it. (shrink)

Aphasia is a language disorder that occurs after a stroke and impairs listening, speaking, reading, writing, and calculation skills. Patients with post-stroke aphasia in Japan are increasing due to population aging and the advancement of medical treatment. Opportunities for adequate speech therapy in chronic stroke are limited due to time constraints. Recent studies have reported that intensive speech therapy for a short period of time or continuous speech therapy using high-tech equipment, including speech applications (apps, can improve aphasia even in (...) the chronic stage. However, its underlying mechanism for improving language function and its effect on other cognitive functions remains unclear. In the present study, we investigated whether intensive speech therapy using a newly developed speech support app could improve aphasia and other cognitive functions in patients with chronic stroke. Furthermore, we examined whether it can alter the brain network related to language and other cortical areas. Thus, we conducted a prospective, single-comparison study to examine the effects of a new speech support app on language and cognitive functions and used resting state functional MRI (rs-fMRI) regions of interest (ROI) to ROI analysis to determine changes in the related brain network. Two patients with chronic stroke participated in this study. They used the independent speech therapy system to perform eight sets of 20 randomly presented words/time (taking approximately 20 min), for 8 consecutive weeks. Their language, higher cognitive functions including attention function, and rs-fMRI, were evaluated before and after the rehabilitation intervention using the speech support app. Both patients had improved pronunciation, daily conversational situations, and attention. The rs-fMRI analysis showed increased functional connectivity of brain regions associated with language and attention related areas. Our results show that intensive speech therapy using this speech support app can improve language and attention functions even in the chronic stage of stroke, and may be a useful tool for patients with aphasia. In the future, we will conduct longitudinal studies with larger numbers of patients, which we hope will continue the trends seen in the current study, and provide even stronger evidence for the usefulness of this new speech support app. (shrink)

In the context of propositional logics, we apply semantics modulo satisfiability—a restricted semantics which comprehends only valuations that satisfy some specific set of formulas—with the aim to efficiently solve some computational tasks. Three possible such applications are developed.We begin by studying the possibility of implicitly representing rational McNaughton functions in Łukasiewicz Infinitely-valued Logic through semantics modulo satisfiability. We theoretically investigate some approaches to such representation concept, called representation modulo satisfiability, and describe a polynomial algorithm that builds representations in the newly (...) introduced system. An implementation of the algorithm, test results and ways to randomly generate rational McNaughton functions for testing are presented. Moreover, we propose an application of such representations to the formal verification of properties of neural networks by means of the reasoning framework of Łukasiewicz Infinitely-valued Logic.Then, we move to the investigation of the satisfiability of joint probabilistic assignments to formulas of Łukasiewicz Infinitely-valued Logic, which is known to be an NP-complete problem. We provide an exact decision algorithm derived from the combination of linear algebraic methods with semantics modulo satisfiability. Also, we provide an implementation for such algorithm for which the phenomenon of phase transition is empirically detected.Lastly, we study the game theory situation of observable games, which are games that are known to reach a Nash equilibrium, however, an external observer does not know what is the exact profile of actions that occur in a specific instance; thus, such observer assigns subjective probabilities to players actions. We study the decision problem of determining if a set of these probabilistic constraints is coherent by reducing it to the problems of satisfiability of probabilistic assignments to logical formulas both in Classical Propositional Logic and Łukasiewicz Infinitely-valued Logic depending on whether only pure equilibria or also mixed equilibria are allowed. Such reductions rely upon the properties of semantics modulo satisfiability. We provide complexity and algorithmic discussion for the coherence problem and, also, for the problem of computing maximal and minimal probabilistic constraints on actions that preserves coherence.prepared by Sandro Márcio da Silva Preto.E-mail: [email protected]:https://doi.org/10.11606/T.45.2021.tde-17062021-163257. (shrink)

The equations of motion for a particle in a classical gauge field are derived from the invariance identities 2 and basic assumptions about the Lagrangian. They are found to be consistent with the equations of some other approaches to classical gauge-field theory, and are expressed in terms of a set of undetermined functions Eα. The functions Eα are found to satisfy a system of differential equations which has the same formal structure as a system of equations from Yang-Mills theory. 3 (...) These results are obtained by a new method which applies techniques from the theory of functional equations to deduce the way in which the arguments of the Lagrangian must combine. The method constitutes an aid for obtaining the equations of motion when a non-gauge-invariant Lagrangian is chosen, and it is assumed that the equations of motion can be written in a gauge-invariant manner. (shrink)

To improve the safety and the performance of operators involved in risky and demanding missions, human-machine cooperation should be dynamically adapted, in terms of dialogue or function allocation. To support this reconfigurable cooperation, a crucial point is to assess online the operator’s ability to keep performing the mission. The article explores the concept of Operator Functional State, then it proposes to operationalize this concept on the specific activity of drone swarm monitoring, carried out by 22 participants on simulator SUSIE. (...) With the aid of supervised learning methods, physiological and contextual are classified into three classes, corresponding to different levels of OFS. This classification would help for adapting the countermeasures to the situation faced by operators. (shrink)

Compared to constraint-based causal discovery, causal discovery based on functional causal models is able to identify the whole causal model under appropriate assumptions [Shimizu et al. 2006; Hoyer et al. 2009; Zhang and Hyvärinen 2009b]. Functional causal models represent the effect as a function of the direct causes together with an independent noise term. Examples include the linear non-Gaussian acyclic model, nonlinear additive noise model, and post-nonlinear model. Currently, there are two ways to estimate the parameters in the (...) models: dependence minimization and maximum likelihood. In this article, we show that for any acyclic functional causal model, minimizing the mutual information between the hypothetical cause and the noise term is equivalent to maximizing the data likelihood with a flexible model for the distribution of the noise term. We then focus on estimation of the PNL causal model and propose to estimate it with the warped Gaussian process with the noise modeled by the mixture of Gaussians. As a Bayesian nonparametric approach, it outperforms the previous one based on mutual information minimization with nonlinear functions represented by multilayer perceptrons; we also show that unlike the ordinary regression, estimation results of the PNL causal model are sensitive to the assumption on the noise distribution. Experimental results on both synthetic and real data support our theoretical claims. (shrink)

In the first place, we present the definition and fundamental properties of information functions — functions which establish a correspondence between sets of formulas and the information contained in them. The intuitions for the notion of information stem from the conception of Bar-Hillel and Carnap in [3]. In § 2 we will briefly show how those notions can be applied to the logic of theory change. In § 3 we will use them for proving two theorems about the lattices of (...) classical subtheories and their content. (shrink)

In this paper, we first introduce the incomplete extended Gamma and Beta functions with matrix parameters; then, we establish some different properties for these new extensions. Furthermore, we give a specific application for the incomplete Bessel matrix function by using incomplete extended Gamma and Beta functions; at last, we construct the relation between the incomplete confluent hypergeometric matrix functions and incomplete Bessel matrix function.

The famous advaitic expressions -/- Brahma sat jagat mithya jivo brahma eva na apraha and Asti bhaati priyam namam roopamcheti amsa panchakam AAdya trayam brahma roopam tato dwayam jagat roopam -/- will be analyzed through physics and electronics and interpreted. -/- Four phases of mind, four modes of language acquisition and communication and seven cognitive states of mind participating in human cognitive and language acquisition and communication processes will be identified and discussed. -/- Implications and application of such an (...) identification and analysis to the fields of cognitive sciences, mind-machine modeling, natural language comprehension field of artificial intelligence and physiological psychology will be hinted. A comprehensive modern scientific understanding of human consciousness, mind and mental functions will be presented. (shrink)

In both theoretical and applied modeling in behavioral sciences, it is common to choose a mathematical specification of functional form and distribution of unobservables on grounds of analytic convenience without support from explicit theoretical postulates. This article discusses the issue of deriving particular qualitative hypotheses about functional form restrictions in structural models from intuitive theoretical axioms. In particular, we focus on a family of postulates known as dimensional invariance. Subsequently, we discuss how specific qualitative postulates can be reformulated (...) so as to allow for conventional statistical hypothesis testing, and we also derive details of a particular likelihood ratio test procedure. An empirical application of the testing procedure is carried out, based on data from a Stated Preference survey. (shrink)

We present two applications of forcing with finite sequences of models as side conditions, adding objects of size \. The first involves adding a \ sequence and variants of such sequences. The second involves adding partial weak specializing functions for trees of height \.

The pipeline framework for identifying ethical issues in machine learning healthcare applications outlined by Char et al. is a very useful starting point for the systematic consideration...

Development of decision-support and intelligent agent systems necessitates mathematical descriptions of uncertainty and fuzziness in order to model vagueness. This paper seeks to present an outline of Peirce’s triadic logic as a practical new way to model vagueness in the context of artificial intelligence. Charles Sanders Peirce was an American scientist–philosopher and a great logician whose triadic logic is a culmination of the study of semiotics and the mathematical study of anti-Cantorean model of continuity and infinitesimals. After presenting Peircean semiotics (...) within AI perspective, a mathematical formulation of a Peircean triadic set is given in relationship with classical and fuzzy sets. Using basic logical operators, all possible respective implication operators, bi-equivalence operators, valid rules of inference, and associative, distributive and commutative logical properties are derived and verified through the truth function approach. In order to suggest practical directions, aggregation operators for Peirce’s triadic logic have been formulated. A mathematical formulation of a medical diagnostic problem and ER diagram of a library management system using Peirce’s triadic relation show potential for further applications of the proposed triadic set and triadic logic. Alongside, a classical AI game—The Wumpus World—is implemented to show practical efficacy in comparison with binary implementation. Besides giving some preliminary formulations for trichotomous set theory and definition of finite automaton, development of hybrid architectures for intelligent agents and evolutionary computations are discussed as potential practical avenues for Peirce’s triadic logic. (shrink)