BackgroundConventionally, transcranial direct current stimulation (tDCS) aims to focalize the current reaching the target region-of-interest (ROI). The focality can be quantified by the dose-target-determination-index (DTDI). Despite having a uniform tDCS setup, some individuals receive focal stimulation (high DTDI) while others show reduced focality (“non-focal”). The volume of cerebrospinal fluid (CSF), gray matter (GM), and white matter (WM) underlying each ROI govern the tDCS current distribution inside the brain, thereby regulating focality.AimTo determine the regional volume parameters that differentiate the focal and (...) non-focal groups.MethodsT1-weighted images of the brain from 300 age-sex matched adults were divided into three equal groups- (a) Young (20 ≤ × < 40 years), (b) Middle (40 ≤ × < 60 years), and (c) Older (60 ≤ × < 80 years). For each group, inter and intra-hemispheric montages with electrodes at (1) F3 and right supraorbital region (F3-RSO), and (2) CP5 and Cz (CP5-Cz) were simulated, targeting the left- Dorsolateral Prefrontal Cortex (DLPFC) and -Inferior Parietal Lobule (IPL), respectively. Both montages were simulated for two current doses (1 and 2 mA). For each individual head simulated for a tDCS configuration (montage and dose), the current density at each region-of-interest (ROI) and their DTDI were calculated. The individuals were categorized into two groups- (1) Focal (DTDI ≥ 0.75), and (2) Non-focal (DTDI < 0.75). The regional volume of CSF, GM, and WM of all the ROIs was determined. For each tDCS configuration and ROI, three 3-way analysis of variance was performed considering- (i) GM, (ii) WM, and (iii) CSF as the dependent variable (DV). The age group, sex, and focality group were the between-subject factors. For a given ROI, if any of the 3 DV’s showed a significant main effect or interaction involving the focality group, then that ROI was classified as a “focal ROI.”ResultsRegional CSF was the principal determinant of focality. For interhemispheric F3-RSO montage, interaction effect (p < 0.05) of age and focality was observed at Left Caudate Nucleus, with the focal group exhibiting higher CSF volume. The CSF volume of focal ROI correlated positively (r ∼ 0.16, p < 0.05) with the current density at the target ROI (DLPFC). For intrahemispheric CP5-Cz montage, a significant (p < 0.05) main effect was observed at the left pre- and post-central gyrus, with the focal group showing lower CSF volume. The CSF volume correlated negatively (r ∼ –0.16, p < 0.05) with current density at left IPL. The results were consistent for both current doses.ConclusionThe CSF channels the flow of tDCS current between electrodes with focal ROIs acting like reservoirs of current. The position of focal ROI in the channel determines the stimulation intensity at the target ROI. For focal stimulation in interhemispheric F3-RSO, the proximity of focal ROI reserves the current density at the target ROI (DLPFC). In contrast, for intrahemispheric montage (CP5-Cz), the far-end location of focal ROI reduces the current density at the target (IPL). (shrink)

This seventh volume of Collected Papers includes 70 papers comprising 974 pages on (theoretic and applied) neutrosophics, written between 2013-2021 by the author alone or in collaboration with the following 122 co-authors from 22 countries: Mohamed Abdel-Basset, Abdel-Nasser Hussian, C. Alexander, Mumtaz Ali, Yaman Akbulut, Amir Abdullah, Amira S. Ashour, Assia Bakali, Kousik Bhattacharya, Kainat Bibi, R. N. Boyd, Ümit Budak, Lulu Cai, Cenap Özel, Chang Su Kim, Victor Christianto, Chunlai Du, Chunxin Bo, Rituparna Chutia, Cu Nguyen Giap, Dao The (...) Son, Vinayak Devvrat, Arindam Dey, Partha Pratim Dey, Fahad Alsharari, Feng Yongfei, S. Ganesan, Shivam Ghildiyal, Bibhas C. Giri, Masooma Raza Hashmi, Ahmed Refaat Hawas, Hoang Viet Long, Le Hoang Son, Hongbo Wang, Hongnian Yu, Mihaiela Iliescu, Saeid Jafari, Temitope Gbolahan Jaiyeola, Naeem Jan, R. Jeevitha, Jun Ye, Anup Khan, Madad Khan, Salma Khan, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Kifayat Ullah, Kishore Kumar P.K., Sujit Kumar De, Prasun Kumar Nayak, Malayalan Lathamaheswari, Luong Thi Hong Lan, Anam Luqman, Luu Quoc Dat, Tahir Mahmood, Hafsa M. Malik, Nivetha Martin, Mai Mohamed, Parimala Mani, Mingcong Deng, Mohammed A. Al Shumrani, Mohammad Hamidi, Mohamed Talea, Kalyan Mondal, Muhammad Akram, Muhammad Gulistan, Farshid Mofidnakhaei, Muhammad Shoaib, Muhammad Riaz, Karthika Muthusamy, Nabeela Ishfaq, Deivanayagampillai Nagarajan, Sumera Naz, Nguyen Dinh Hoa, Nguyen Tho Thong, Nguyen Xuan Thao, Noor ul Amin, Dragan Pamučar, Gabrijela Popović, S. Krishna Prabha, Surapati Pramanik, Priya R, Qiaoyan Li, Yaser Saber, Said Broumi, Saima Anis, Saleem Abdullah, Ganeshsree Selvachandran, Abdulkadir Sengür, Seyed Ahmad Edalatpanah, Shahbaz Ali, Shahzaib Ashraf, Shouzhen Zeng, Shio Gai Quek, Shuangwu Zhu, Shumaiza, Sidra Sayed, Sohail Iqbal, Songtao Shao, Sundas Shahzadi, Dragiša Stanujkić, Željko Stević, Udhayakumar Ramalingam, Zunaira Rashid, Hossein Rashmanlou, Rajkumar Verma, Luige Vlădăreanu, Victor Vlădăreanu, Desmond Jun Yi Tey, Selçuk Topal, Naveed Yaqoob, Yanhui Guo, Yee Fei Gan, Yingcang Ma, Young Bae Jun, Yuping Lai, Hafiz Abdul Wahab, Wei Yang, Xiaohong Zhang, Edmundas Kazimieras Zavadskas, Lemnaouar Zedam. (shrink)

This eighth volume of Collected Papers includes 75 papers comprising 973 pages on (theoretic and applied) neutrosophics, written between 2010-2022 by the author alone or in collaboration with the following 102 co-authors (alphabetically ordered) from 24 countries: Mohamed Abdel-Basset, Abduallah Gamal, Firoz Ahmad, Ahmad Yusuf Adhami, Ahmed B. Al-Nafee, Ali Hassan, Mumtaz Ali, Akbar Rezaei, Assia Bakali, Ayoub Bahnasse, Azeddine Elhassouny, Durga Banerjee, Romualdas Bausys, Mircea Boșcoianu, Traian Alexandru Buda, Bui Cong Cuong, Emilia Calefariu, Ahmet Çevik, Chang Su Kim, Victor (...) Christianto, Dae Wan Kim, Daud Ahmad, Arindam Dey, Partha Pratim Dey, Mamouni Dhar, H. A. Elagamy, Ahmed K. Essa, Sudipta Gayen, Bibhas C. Giri, Daniela Gîfu, Noel Batista Hernández, Hojjatollah Farahani, Huda E. Khalid, Irfan Deli, Saeid Jafari, Tèmítópé Gbóláhàn Jaíyéolá, Sripati Jha, Sudan Jha, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, M. Karthika, Kawther F. Alhasan, Giruta Kazakeviciute-Januskeviciene, Qaisar Khan, Kishore Kumar P K, Prem Kumar Singh, Ranjan Kumar, Maikel Leyva-Vázquez, Mahmoud Ismail, Tahir Mahmood, Hafsa Masood Malik, Mohammad Abobala, Mai Mohamed, Gunasekaran Manogaran, Seema Mehra, Kalyan Mondal, Mohamed Talea, Mullai Murugappan, Muhammad Akram, Muhammad Aslam Malik, Muhammad Khalid Mahmood, Nivetha Martin, Durga Nagarajan, Nguyen Van Dinh, Nguyen Xuan Thao, Lewis Nkenyereya, Jagan M. Obbineni, M. Parimala, S. K. Patro, Peide Liu, Pham Hong Phong, Surapati Pramanik, Gyanendra Prasad Joshi, Quek Shio Gai, R. Radha, A.A. Salama, S. Satham Hussain, Mehmet Șahin, Said Broumi, Ganeshsree Selvachandran, Selvaraj Ganesan, Shahbaz Ali, Shouzhen Zeng, Manjeet Singh, A. Stanis Arul Mary, Dragiša Stanujkić, Yusuf Șubaș, Rui-Pu Tan, Mirela Teodorescu, Selçuk Topal, Zenonas Turskis, Vakkas Uluçay, Norberto Valcárcel Izquierdo, V. Venkateswara Rao, Volkan Duran, Ying Li, Young Bae Jun, Wadei F. Al-Omeri, Jian-qiang Wang, Lihshing Leigh Wang, Edmundas Kazimieras Zavadskas. (shrink)

Most commonly, the scientific realism debate is seen as dividing those who do and do not think that the striking empirical and practical successes of at least our best scientific theories indicate with high probability that those theories are ‘approximately true’. But I want to suggest that this characterization of the debate has far outlived its usefulness. Not only does it obscure the central differences between two profoundly different types of contemporary scientific realist, but even more importantly it serves to (...) disguise the most substantial points of actual disagreement between these two kinds of realists and those who instead think the historical record of scientific inquiry itself reveals that such realism is untenable in either form. (shrink)

We analyse the extent of possible computations following Hogarth ([2004]) conducted in Malament–Hogarth (MH) spacetimes, and Etesi and Németi ([2002]) in the special subclass containing rotating Kerr black holes. Hogarth ([1994]) had shown that any arithmetic statement could be resolved in a suitable MH spacetime. Etesi and Németi ([2002]) had shown that some relations on natural numbers that are neither universal nor co-universal, can be decided in Kerr spacetimes, and had asked specifically as to the extent of computational limits there. (...) The purpose of this note is to address this question, and further show that MH spacetimes can compute far beyond the arithmetic: effectively Borel statements (so hyperarithmetic in second-order number theory, or the structure of analysis) can likewise be resolved: Theorem A. If H is any hyperarithmetic predicate on integers, then there is an MH spacetime in which any query ? n H ? can be computed. In one sense this is best possible, as there is an upper bound to computational ability in any spacetime, which is thus a universal constant of that spacetime. Theorem C. Assuming the (modest and standard) requirement that spacetime manifolds be paracompact and Hausdorff, for any spacetime there will be a countable ordinal upper bound, , on the complexity of questions in the Borel hierarchy computable in it. Introduction 1.1 History and preliminaries Hyperarithmetic Computations in MH Spacetimes 2.1 Generalising SADn regions 2.2 The complexity of questions decidable in Kerr spacetimes An Upper Bound on Computational Complexity for Each Spacetime CiteULike Connotea Del.icio.us What's this? (shrink)

We show how in the hierarchies${F_\alpha }$of Fieldian truth sets, and Herzberger’s${H_\alpha }$revision sequence starting from any hypothesis for${F_0}$ that essentially each${H_\alpha }$ carries within it a history of the whole prior revision process.As applications we provide a precise representation for, and a calculation of the length of, possiblepath independent determinateness hierarchiesof Field’s construction with a binary conditional operator. We demonstrate the existence of generalized liar sentences, that can be considered as diagonalizing past the determinateness hierarchies definable in Field’s recent (...) models. The ‘defectiveness’ of such diagonal sentences necessarily cannot be classified by any of the determinateness predicates of the model. They are ‘ineffable liars’. We may consider them a response to the claim of Field that ‘the conditional can be used to show that the theory is not subject to “revenge problems”.’. (shrink)

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

Aron Gurwitsch claims that the field of consciousness is invariantly organized in a theme, thematic field, margin pattern. However, at least two perceptual presentations, chaos and boundlessness, are not ordered in accordance with this pattern. The question this study poses then is the following: given Gurwitsch's field-theory of experiential organization, what is the structure, status, and function of chaos and boundlessness in the field of consciousness? ;Using Gurwitsch's field-theory organization as a base, the structure of thematic chaos and then of (...) thematic boundlessness is articulated: the first by contrasting the field-theories of Gurwitsch and James, the second by contrasting Gurwitsch and Kant. It is concluded that in both cases no thematic Gestalt-coherence and no thematic field as relevant context is presented. ;In terms of status and function, chaos and boundlessness are interpreted as necessary limits. These "limit cases" are not "ideal limits" since they are possible perceptual presentations. Also, limit is taken to mean a two-edged presentation, one that is both an ending and a beginning. Interpreting Gurwitsch, we conclude that both cases are epistemological endings, since they represent a necessary end to the ordinary perception of things. Interpreting James, we conclude that it is possible that thematic chaos is also a metaphysical beginning in experience, since it is that experience in which reality is presented as underived and original. Interpreting Kant, we conclude that it is possible that boundlessness is also an ethical beginning in experience, since it is that experience in which the most original feeling of our sense of humanity is presented. ;We show that chaos and boundlessness each have their own unique field-organization, that they function as two-edged limits involving epistemological concerns on the one hand and metaphysical and ethical concerns respectively on the other, and that their structure and status as limits in the field of consciousness are not contingent but necessary. (shrink)

This paper examines Hume’s ‘Title Principle’ and its role in a response to one of the ‘manifest contradictions’ he identifies in the conclusion to Book I of A Treatise on Human Nature. This ‘contradiction’ is a tension between two ‘equally natural and necessary’ principles of the imagination, our causal inferences and our propensity to believe in the continued and distinct existence of objects. The problem is that the consistent application of causal reason undercuts any grounds with have for the belief (...) in continued and distinct existence, and yet that belief is as ‘natural and necessary’ as our propensity to infer effects from causes. The TP appears to offer a way to resolve this ‘contradiction’. It statesWhere reason is lively, and mixes itself with some propensity, it ought to be assented to. Where it does not, it never can have any title to operate upon us.’ In brief, if it can be shown that the causal inferences that undermine the belief in external world are not ‘lively’ nor mixed with some propensity’ then we have grounds for think that they have no normative authority. This is in part a response to another ‘manifest contradiction’, namely the apparently self-undermining nature of reason. In this paper I examine the nature and grounds of the TP and its relation to these ‘manifest contradictions’. (shrink)

We look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta’s theory of truth over arithmetic using \emph{fully varied revision} sequences yields a complete \Pi13 set of integers; (iii) the set of \emph{stably categorical} sentences using their revision operator ψ is similarly \Pi13 and which (...) is complete in Gödel’s universe of constructible sets L; (iv) give an alternative account of a theory of truth—realistic variance that simplifies full variance, whilst at the same time arriving at Kripkean fixed points. (shrink)

The figure of Peter the Tomb, various aspects of his life and activity, as well as the era called by his name, have long been the subject of study by numerous scholars, comprehensive and meticulous research. It is enough to mention the works of M.Grushevsky, A.Zhukovsky, V.Klimov, A.Kolodny, V.Nichik, O.Sarapin, L.Filipovich and V.Shevchenko, in which the phenomenon of the metropolitan, his spiritual and religious dominant, is thoroughly and thoroughly explained, the influence of P. Mogila's heritage on the past and present. (...) And yet it is impossible to talk about the exhaustiveness of this topic, because such inexhaustibility is dictated by the very universe of its multidimensional activity. This is what determines the relevance of the proposed article. And this, in turn, gives rise to reflections on the need for scientific innovative understanding of religious philosophy as a constant basis of thinking of Petro Mohyla, which, in particular, was reflected in his "Notebook", which is still a little-studied phenomenon of Ukrainian spiritual culture, for the first time it saw the world only in 1995, more than 60 years after its invention by M. Grushevsky. This work, like all narratives on the spiritual and religious themes that make up it, is an integral part of the metropolitan's religious and philosophical heritage. (shrink)

Evolutionary fitness threats and rewards are associated with subjectively unpleasant and pleasant sensations, respectively. Initially, these correlations appear explainable via adaptation by natural selection. But here I analyse the major metaphysical perspectives on consciousness – physicalism, dualism, and panpsychism – and conclude that none help to understand the adaptive-seeming correlations via adaptation. I also argue that a recently proposed explanation, the phenomenal powers view, has major problems that mean it cannot explain the adaptive-seeming correlations via adaptation either. So the mystery (...) – call it the evolutionary paradox of consciousness – remains. Some have used this mystery to argue for non-naturalistic (e.g. theistic) explanations. But I propose a naturalistic, non-adaptive explanation of the adaptive-seeming correlations: namely, ‘sensational associative learning’ during development. In this perspective, pairing of particular sensations with unconditioned stimuli – fitness rewards or threats – cause the sensations themselves to come to be interpreted as good or bad, respectively. Sensations, like colours, that are not reliably paired with either fitness rewards or threats remain largely unvalenced. Sensational associative learning also provides explanations for adaptive-seeming structural aspects of sensations, such as the observation that sounds of different pitch are experienced as ordinal in correspondence to their wavelengths while the same is not true of colours of different hue. The sensational associative learning perspective appears compatible with physicalism, panpsychism, and dualism (though not epiphenomenalism). (shrink)

Problem: Ernst von Glasersfeld’s radical constructivism has been highly influential in the fields of mathematics and science education. However, its relevance is typically limited to analyses of classroom interactions and students’ reasoning. Methods: A project that aims to support improvements in the quality of mathematics instruction across four large urban districts is framed as a case with which to illustrate the far-reaching consequences of von Glasersfeld’s constructivism for mathematics and science educators. Results: Von Glasersfeld’s constructivism orients us to question the (...) standard view of policy implementation as a process of travel down through a system and to conceptualize it instead as the situated reorganization of practice at multiple levels of a system. In addition, von Glasersfeld’s constructivism orients us to understand rather than merely evaluate policies by viewing the actions of the targets of policies as reasonable from their point of view. Implications: The potential contributions of von Glasersfeld’s constructivism to mathematics and science education have been significantly underestimated by restricting the focus to classroom actions and interactions. The illustrative case of research on the application of these ideas also indicates the relevance of constructivism to researchers in educational policy and educational leadership. (shrink)