A decision maker using the Analytic Hierarchy Process (AHP) could be consistent, and still provide no information in the resulting vector of priorities. An extreme example would be a pairwise comparison judgment matrix filled with 1s which is totally consistent under the various definitions of consistency, but has provided no information about the prioritization of alternatives resulting from the decision maker's judgments. In this paper, the quality of a consistent decision maker's judgments using the Analytic Hierarchy Process is placed (...) in the context of the entropy of the resulting vector of priorities. Indeed, it is the purpose of this paper to provide a formal definition of this notion ofentropy of a priority vector, and to provide a framework for a quantitative measurement of the information content of consistent pairwise comparison judgment matrices of a decision maker who is using the Analytic Hierarchy Process. We will prove that the entropy of the vector of priorities for consistent matrices follows a normal distribution and discuss some general considerations of this result. (shrink)

Psychoanalysis and Christianity hold forth the promise of genuinely radical change, transforming a person so substantially such that ‘nothing remains the same’; even if the objective conditions of one’s existence stay fixed, the very lens with which the ‘born again’ subject views the world would have undergone so traumatic an upheaval that values, priorities and everything previously deemed essential would have been reimagined. It is, quite truly, a new beginning. This paper aims to insinuate a close proximity between Žižekian concepts (...) of the traumatically emergent and new vis-à-vis Biblical ideas of salvation, vocation and agape love. I also wish to demonstrate how even the Christian sacraments of baptism and the eucharist point to death and dying as their constitutive elements, with the result that sacrifice for the world becomes the main political role the Church must play. (shrink)

Within the domain of public health, vector-borne diseases are among the most vehemently discussed issues. Recent scientific breakthroughs in genome editing technology provided a solution to this issue in the form of a gene drive that might decrease and even eradicate vector-borne diseases. Gene drives are engineered, and designed genes that can break typical inheritance rules and be passed to almost all of the carrier’s offspring. This genome editing and gene drive technology has become a powerful tool for (...) ecological and environmental engineering, through which man can manipulate his surroundings, adjusting it to himself and directly mastering evolution and the ecosystem. Although the gene drive technology has been perceived as promising in the public health domain, ecological implications of its use are not to be underestimated. The primary aim of this paper is to overcome the ongoing discussion which mostly focuses on whether priority should be given to the environment or to public health, and to find an adequate answer and solution. In this quest to find the proper answer and solution, Pierre Teilhard de Chardin’s thought might be useful, especially his concepts of the biosphere and the noosphere which may provide some clarifications as to why we are at the moment so cautious with gene drive technology and how we need to move towards a better common future on earth. (shrink)

Policies for the allocation of COVID-19 vaccine were implemented in early 2021 as soon as vaccine became available. Those responsible for the planning and execution of COVID-19 vaccination had to make choices about who received vaccination first while numerous authors offered their own recommendations. This paper provides an account of how such decisions should be made by focusing on the specifics of the situation at hand. In that light, I offer an argument for prioritising those who are likely vectors of (...) the disease and a criticism of the victim-focused priority proposals put forward by the US Centers for Disease Control and Prevention, the National Academies of Sciences, Engineering, and Medicine, the UK National Health Service, and others. I also offer thoughts on how those authors may have gone astray. (shrink)

The release of over 6,000 genetically modified mosquitoes (GMM) into uninhabited Malaysian forests in 2010 was a frantic step on the part of the Malaysian government to combat the spread of dengue fever. The field trial was designed to control and reduce the dengue vector by producing offspring that die in the early developmental stage, thus decreasing the local Aedes aegypti population below the dengue transmission threshold. However, the GMM trials were discontinued in Malaysia despite being technologically feasible. The (...) lack of systematic studies in terms of cost-benefit analysis, questionable research efficacy and safety-related concerns might have contributed to the termination of the field trial. Hence, this research aims to evaluate the feasibility of GMM release in Malaysia by using a holistic approach based on an Islamic ethical-legal assessment under the maslahah-mafsadah (benefit-risk) concept. Three main strategies based on the maslahah-mafsadah concept approach have been applied: 1) an evidence-based approach, 2) an impact-based approach and, 3) a priority approach. The analysis concluded that GMM could be categorised as zanniyyah (probable). GMM is a promising alternative for dengue control, but many issues must be addressed before its widespread adoption. (shrink)

The article is devoted to how stable the forms of government are, as well as what are the main directions of their evolution in the context of the modernization of the state and civil society. The purpose of the study is to establish the specifics of modernization of modern forms of government in the conditions of political transformation. The significance of systemic and non-systemic political forces, their value and ideological and doctrinal settings in the context of stability or instability of (...) the form of state government is characterized. It was emphasized that socio-economic processes also program approaches to the modernization of the form of state government. The balance of relations between the central and local authorities is analyzed as one of the serious factors in the formation of the agenda of reforms of the form of government. The European priorities and the vector of the development of Ukrainian statehood, which require bringing the constitutional and legal base into compliance with the functioning of supranational institutions, are revealed. The ratio of the mechanisms of separation of powers, which regulate the power functionality of each institutional branch, in order to prevent one branch from performing the main functions of another, has been clarified. It is revealed that constitutional changes aimed at unifying the institutional design of decision-making are an integral process of European integration. It is proved that the attitude towards the constitution as an unchanging document and a necessary value begins to change due to the new needs of state formation. It has been established that criticism of constitutional changes aimed at changing the form of government is becoming more and more widespread due to the politicization of specific proposals. It is assumed that the expediency of modernizing the fundamental principles of forms of state government is especially problematic during the Russian war in Ukraine. It was established that the presence of non-public rules for the distribution of powers and influence within the political and institutional design of modern Ukraine actualizes the need for transparency in approaches to the transformation of the form of government. It has been found that ascertaining the crisis of the constitutional and legal foundations of the political design of Ukrainian democracy requires proposals to overcome the crisis. It was concluded that in the conditions of political transformations there is a vector of unmotivated changes to the constitutions that regulate the balance of interaction between the branches of government. (shrink)

The article is devoted to defining the essence of security, particularly national security, its interpretation, main features, structure, and factors. The research focuses on the main concepts of the modern understanding of national security and defines national security according to recent research. The authors have performed a structural and functional analysis of the system of national security of Ukraine, which would be an adequate counteraction to threats to vital national interests. The article examines the multi-vector interpretation and representation of (...) the security phenomenon with an increased focus on the axiological paradigm of postmodern society analysis. The cardinal role of postmodernism is considered as a manifestation of postmodern culture in the value dimension of social-political existence. Postmodernism, on the one hand, enabled new vectors of analytical understanding and perception of the security phenomenon. On the other hand, it introduced an imbalance and determined the crisis factor in the space of classical perception of security guarantors due to violating the established foundations and traditions. The rejection factor is seen as a core feature of postmodern social-political reality. The emphasis is given to the problem of the security standard in the security studies and the idea of the mutual determination of both national interests and national values. The article states the importance and priority of historical memory and the phenomenon of mentality in the context of future analytical discourses in the scope of Ukrainian security studies. (shrink)

This is the second of two papers responding (somewhat belatedly) to ‘recent’ commentary on various aspects of hyperplane dependence (HD) by several authors. In this paper I focus on the issues of the general need for HD dynamical variables, the identification of physically meaningful localizable properties, the basis vectors representing such properties and the relationship between the concepts of ‘localizable within’ and ‘measureable within’. The authors responded to here are de Koning, Halvorson, Clifton and Wallace. In the first paper of (...) this set (Fleming 2003b) I focused on the issues of the relations of HD to state reduction and unitary evolution and addressed comments of Maudlin and Myrvold. The central conclusion argued for in this second paper (§§ 5, 7) is the non-existence of strictly localizable objects or measurement processes and the consequent undermining of the principle of universal microcausality. This contrasts with the existence of strictly localizable properties and results in the consequent priority of the concept of ‘localizable within’ over ‘measureable within’. The paper opens with discussions of the need for and status of HD dynamical variables which are responses to anonymous queries. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Crushing Pressures and Radical IdeasJohn Z. Sadler, MD (bio)Back in 2011, I wrote a paper for the Journal of Bioethical Inquiry, an Australian journal, for a special issue dedicated to ethical issues associated with psychiatric genetics research. The editor was particularly excited by the recent findings of the 5-HTT allele in psychiatric illness. I had different ideas about what I wanted to write about, and the editor, Michael Robertson, (...) graciously considered them and ultimately published the paper. At the time I was interested in the colossal investment of National Institutes of Mental Health (NIMH) research dollars in psychiatric genetic research; at the time I was troubled at the lack of on-the-ground clinical implications of this research investment, and figured an Australian journal and referees would be more generous to a critical paper on U.S. funding priorities. I dug into the National Institutes of Health (NIH), NIMH, and National Science Foundation websites and found some crude dollar evidence of respective expenditures for research funding in various disorders and focus areas, and compared these investments to psychiatric genetic research funding commitments. I will not go into details (Sadler, 2011), but the gist was that the psychiatric genetics research enterprise was and had been an extraordinarily expensive enterprise, when other research questions that could be immediately implementable into clinical care improvements remained marginally funded at best. The paper was not read widely and other than a couple of annoyed responses from psychiatric genetic researchers, not much came of it.This concern about funding priorities was one of the reasons why I was pleased to see this paper by Turkheimer and Greer which explores the long term results of the Spit for Science (S4S) initiative, which was launched grandly the same year as my paper’s whisper from down under. I hope this Philosophical Case Conference explores the many dimensions of interest for this paper, which is extraordinarily careful and even handed in its attitude, while at the same time being incisive in its analysis.My focus here is not in the science per se, which is beyond my competence. I’m interested in Turkheimer and Greer’s (T&G) conceptual overview of this research program. More specifically, I focus on T&G’s highlighting of the extraordinary willingness of the S4S authors to interpret prevailingly negative results in the most generous, even misleading, degree possible. I try to provide some possible ways of understanding this kind of research rhetoric exhibited by a cohort of highly respected, very successful scientists.I acknowledge the well-described varieties of interpretive bias that all of us are subject to. First on the list must be confirmation bias, our tendency to interpret situations in terms consistent [End Page 447] with our preconceived notions—in this case, the idea that genetics has something important to do with addictive disorders. Another might be epistemic overconfidence—the tendency to fail at interpretive skepticism in favor of one’s preferred conclusion. Related to this may also be interpretive momentum, the tendency to maintain a conviction about the correctness of one’s expectations and disregard inconsistent findings over the course of a research program—in this case, the multiple S4S studies (O’Sullivan & Schofeld, 2018). However, these kinds of biases tend to “blame” the individual authors’ thinking styles. I opine, though, that other vectors shaping the declaring-success rhetoric are more important.These sources have to do with the state of practice in doing biomedical science research in universities and particularly academic medical centers (AMCs) today. I identify several causal vectors that compel, however subtly, researchers to declare success in the face of failure. I have only picked three, and in no order of importance: 1) funding caps for NIH grants, 2) the overleveraging of university budgets and ballooning dependence on soft money, and 3) the incentivizing of intellectual property development within AMCs.Funding Caps for NIH GrantsIf you are a university or AMC, one way you hold onto your most productive scientists (e.g., grants, publications, discoveries, and status) is by paying them well. Single NIH grants today commonly amount to millions of dollars, and often tens of millions. These bring... (shrink)

When describing motion along both the horizontal and vertical axes, languages from different families express the elements encoding verticality before those coding for horizontality (e.g., going up right instead of right up). In light of the motor grounding of language, the present study investigated whether the prevalence of verticality in Path expression also governs the trajectory of arm biological movements. Using a 3D virtual-reality setting, we tracked the kinematics of hand pointing movements in five spatial directions, two of which implied (...) the vertical and horizontal vectors equally (i.e., up right +45° and bottom right −45°). Movement onset could be prompted by visual or auditory verbal cues, the latter being canonical in French (“en haut à droite”/up right) or not (“à droite en haut”/right up). In two experiments, analyses of the index finger kinematics revealed a significant effect of gravity, with earlier acceleration, velocity, and deceleration peaks for upward (+45°) than downward (−45°) movements, irrespective of the instructions. Remarkably, confirming the linguistic observations, we found that vertical kinematic parameters occurred earlier than horizontal ones for upward movements, both for visual and congruent verbal cues. Non-canonical verbal instructions significantly affected this temporal dynamic: for upward movements, the horizontal and vertical components temporally aligned, while they reversed for downward movements where the kinematics of the vertical axis was delayed with respect to that of the horizontal one. This temporal dynamic is so deeply anchored that non-canonical verbal instructions allowed for horizontality to precede verticality only for movements that do not fight against gravity. Altogether, our findings provide new insights into the embodiment of language by revealing that linguistic path may reflect the organization of biological movements, giving priority to the vertical axis. (shrink)

Hospitality industry plays a crucial role in the development of tourism. Predicting the future demand of a hotel is a key step in the process of hotel revenue management. Hotel passenger flow prediction plays an important role in guiding the formulation of hotel pricing and operating strategies. On the one hand, hotel passenger flow prediction can provide decision support for hotel managers and effectively avoid the waste of hotel resources and loss of revenue caused by the loss of customers. On (...) the other hand, it is the guarantee of the priority occupation of business opportunities by hotel enterprises, which can help hotel enterprises adjust their operation strategies reasonably to better adapt to the market situation. In addition, hotel passenger flow prediction is helpful to judge the overall operating condition of the hotel industry and assess the risk level of the hotel project to be built. Hotel passenger flow is affected by many factors, such as weather, environment, season, holidays, economy, and emergencies, and has the characteristics of complex nonlinear fluctuation. The existing demand predicting methods include linear methods and nonlinear methods. The linear prediction methods rely on the stability of environment and time series, so they cannot completely simulate the complex nonlinear fluctuations characteristics of hotel passenger flow. Traditional nonlinear prediction methods need to improve the prediction accuracy, and they are difficult to deal with the increasing data of hotel passenger flow. Based on the above analysis, this paper constructs a deep learning prediction model based on Long Short-Term Memory to predict the number of actual monthly arrival bookings. The number of actual monthly arrival bookings can reflect the actual monthly passenger flow of a hotel. The prediction model can effectively reduce the loss caused by cancellation or nonarrival of bookings due to various reasons and improve the hotel revenue. The experimental part of this paper is based on the booking demand dataset of a resort hotel in Portugal from July 1, 2015, to August 31, 2017. Artificial neural network and support vector regression are built as benchmark models to predict the number of actual monthly arrival bookings of this hotel. The experimental results show that, compared with the benchmark models, the LSTM model can effectively improve the prediction ability and provide necessary reference for the hotel's future pricing decision and operation mode arrangement. (shrink)

The paper examines a concept of the Balto-Black Sea Union, which ideas were translated into reality during the Kievan Rus and Grand Duchy of Lithuania period. In the 10th-11th centuries the road from the North to the South, from the East-country to the Black Sea ran through the territory of Ukraine. The way 'from the Varangians to the Greeks' integrated two regions, the Baltic and the Black Sea, and was to the advantage of all those involved. This conceptual idea was (...) again looked into by Ukrainian politicians and researchers in the early 20th century, it was explored and proposed by Mykhailo Grushevskyi, Yuriy Lypa and Stepan Rudnytskyi. The idea of the 'inter-sea area' became a subject for active discussion in Polish, Ukrainian, Belorussian and Lithuanian political quarters in the late 1980s. This plot deserves attention of contemporary Ukrainian politicians in the current dynamic geopolitical context as an efficient and timely anti-Russian international project which will underpin the security of Ukraine. This idea was partially implemented in the form of the GUAM, the Black Sea Organization for Economic Cooperation and the Community of Democratic Choice. The natural vector 'North - South' of communicative and transit transport flows is not used in full measure by Ukraine. The Balto-Black Sea Union offers a significant security component which is of interest to the USA and the European Union. The emergence of such new world economic centers as the USA, the EU and China imparts a new focus to foreign policy priorities of Ukraine. (shrink)

The article is a philosophical attempt to solve the problem of quantum space. The problem has not been solved by experiment nor by arithmetical formalism so that the author makes use of analogy. The starting-point is the electromagnetic wave (EM). Hitherto, our ideas about the EM wave are the result of macroscopic mathematical operations. The EM wave should be subjected to logical analysis and abstraction if we wish to grasp its essential features. The essential features may be considered as: 1. (...) the dualism of the energie natures E and H, 2. the perpendicular relation E ┴ H, 3. the impossibility of determining the priority of E or H (electromagnetic unidentifity), 4. the most generally accepted symmetry E = h (E = not H) and H = Ē (H = not E), 5. the passage is made from E to H and from H to E by reflection and turning in another plane, 6. the passage is made through „electromagnetic zero“, 7. an element of the EM wave is E ┴ W ┴ H, where W is the vector of propagation, 8. an element of the EM wave realizes tetradic geometry, generally quadrupol (fig. 1 and 2).The elementary unit of space also probably realizes tetradic geometry. We shall continue to call the hypothetical quantum of electromagnetic space a magnel (abbrev. mgl.). It corresponds to a quadrupol. The author analyses the constructive geometry of a tetrahedron. Two polar sections, perpendicular to each other, at a distance W, give the tetrahedron of forces, in other words the quadrupol. The construction of a tetrahedron is an example of the passage from one dimension to space.What type of geometry is there in matter? For the appraisal of crystalline bodies the right tetrahedron is generally accepted (fig. 3). In certain conditions matter is always crystalline. Many crystalochemical substances have a tetradic configuration (table 1). At least 90% of matter has tetradic geometry. The spaces between the maximum close — packing of atoms are also tetrahedrons (fig. 4).Within the atomic nucleus we find tetradic geometry on the basis of the quadrupol electric moment. Complete atoms also give out quadrupol radiation. The form of the system is concluded from the radiation. Matter in quantities increasing from the atomic nucleus up to the crystalochemical groups, uses tetradic geometry. Similarly it can be assumed that the same geometry is in force within the scale of a quantum of space — a magnel — just as on a megascopic scale. A ray of light does not go round the Universe on the inner side of a sphere, as Einstein held, but on the inner plane of a tetrahedron (fig. 5) and thus in a closed system of 3 hyperbola.The arisal of a photon depends on the zero movement of a vacuum (the interior movement of a magnel). It polarizes neighbouring magnels. In view of the symmetry of matter and the tetradic geometry of matter, there ought to exist magnels (fig. 6a) and antimagnels (fig. 6b). The antimagnel is an ideal figure of infinitely thin walls separating 4 negative hyperboidal planes. Polarisation is transferred as a fluctuation of the vacuum. With interference and superposition of fluctuation energetic condensation may arise. The springy deformation of the magnel gives the quantum of radiation EM. The photon moves like the recombination wave of the magnel. The return to the normal granularity of space is linked with the emission of the photon. The laws of condensation of energy and geometrical contraction are general laws of matter from the magnel through elementary particles (the arisal of pairs and annihilation), atomic nuclei, atoms, to nebulae inclusive. The effect is the same — the emission of a quantum of light.The author discusses the method of analogy which he has used. It is based on three principles: abstraction, proper analogy, interpolation. By abstraction essential elements, in this case the EM wave, are comprehended. By analogy, the results of abstraction are applied to matter of another order of size. Interpolation fills in the missing elements in some level (fig. 7). A philosophical method so conceived, for investigating physical phenomena, may be useful in cases where it is not possible to use the experimental method, or where a formal method is missing. (shrink)

Livestock are important assets in Africa, helping improve the nutritional status of their owners, and contributing to economic growth. Can these roles continue and can livestock production systems be further developed so that they will be sustainable? A key feature of livestock in Africa is that they fulfill multiple roles, ranging from draught power, to providing manure, milk, and meat. Constraints to increasing productivity include both physical and institutional. In the former category, constraints to adopting draught power include insufficient numbers (...) at the individual household level. Lack of adequate pasture is probably the most important constraint. Diseases are also notable constraints to improving productivity, particularly those categorized as Group I (highly contagious — e.g., rinderpest) or Group II (vector-borne parasitic and viral—e.g., trypanosomiasis). Institutional constraints include lack of research and market distortions. To improve productivity, at the macroeconomic level, governments must continue or start policies aimed at liberalizing markets and revaluing exchange rates. Also, research institutions need an increase in funding for periods of ten or more years. Research and other livestock institutions may be able to leverage limited resources by forming more collaborative relationships at the regional level. Research priorities include breeding on specific aspects, such as increased milk production. However, it must be realized that breeding programs have an inherent problem in disseminating improved breeds in a rapid and equitable manner. Quality of pasture may be improved by further research on more accurately calculating stocking rates and on developing mechanisms to control numbers on pastures (e.g., community controlled grazing schemes). Other research priorities include new technologies to improve animal health, funding of micro-enterprises to add value to livestock products, and market information systems for small-scale farmers. Schemes to increase livestock production in Africa will only occur if innovations closely match the local sets of circumstances. Given the multiple roles of livestock, research into innovations that local communities will readily adopt must take a systems approach. (shrink)

The remarkable performance of large language models (LLMs) on complex linguistic tasks has sparked debate about their capabilities. Unlike humans, these models learn language solely from textual data without directly interacting with the world. Yet they generate seemingly meaningful text on diverse topics. This achievement has renewed interest in the classical `Symbol Grounding Problem' -- the question of whether the internal representations and outputs of symbolic AI systems can possess intrinsic meaning that is not parasitic on external interpretation. Although modern (...) LLMs compute over vectors rather than symbols, an analogous problem arises for these systems, which we call the Vector Grounding Problem. This paper has two main goals. First, we distinguish five main notions of grounding that are often conflated in the literature, and argue that only one of them, which we call referential grounding, is relevant to the Vector Grounding Problem. Second, drawing on philosophical theories of representational content, we provide two arguments for the claim that LLMs and related systems can achieve referential grounding: (1) through preference fine-tuning methods that explicitly establish world-involving functions, and (2) through pre-training alone, which in limited domains may select for internal states with world-involving content, as mechanistic interpretability research suggests. Through these pathways, LLMs can establish connections to the world sufficient for intrinsic meaning. One potentially surprising implication of our discussion is that that multimodality and embodiment are neither necessary nor sufficient to overcome the Grounding Problem. *Note: this is an updated and improved version of the preprint originally made available on ArXiv in 2023.*. (shrink)

Vector models of language are based on the contextual aspects of language, the distributions of words and how they co-occur in text. Truth conditional models focus on the logical aspects of language, compositional properties of words and how they compose to form sentences. In the truth conditional approach, the denotation of a sentence determines its truth conditions, which can be taken to be a truth value, a set of possible worlds, a context change potential, or similar. In the (...) class='Hi'>vector models, the degree of co-occurrence of words in context determines how similar the meanings of words are. In this paper, we put these two models together and develop a vector semantics for language based on the simply typed lambda calculus models of natural language. We provide two types of vector semantics: a static one that uses techniques familiar from the truth conditional tradition and a dynamic one based on a form of dynamic interpretation inspired by Heim’s context change potentials. We show how the dynamic model can be applied to entailment between a corpus and a sentence and provide examples. (shrink)

We show that vector space semantics and functional semantics in two-sorted first order logic are equivalent for pregroup grammars. We present an algorithm that translates functional expressions to vector expressions and vice-versa. The semantics is compositional, variable free and invariant under change of order or multiplicity. It includes the semantic vector models of Information Retrieval Systems and has an interior logic admitting a comprehension schema. A sentence is true in the interior logic if and only if the (...) ‘usual’ first order formula translating the sentence holds. The examples include negation, universal quantifiers and relative pronouns. (shrink)

The paper contains a discussion on two kinds of coincidence experiments. First, a standard two-photon coincidence experiment is considered and it is shown that its outcomes are incompatible with any classical radiation theory because of the role of the state vector reduction phenomenon in such an experiment. In the second part of the paper a proposed new kind of photon coincidence experiment is discussed. The classical and quantum predictions for the outcomes of this experiment differ dramatically and therefore the (...) experiment should constitute a new limitation to the classical radiation theories. The proposed experiment should also yield information about the kinematics of the reduction of the state vector process. (shrink)

We investigate the deductive strength of statements concerning vector spaces over specific fields in the hierarchy of various choice principles.

This paper uncovers the basic reason for the mysterious change of sign from plus to minus in the fourth coordinate of nature's Pythagorean law, usually accepted on empirical grounds, although it destroys the rational basis of a Riemannian geometry. Here we assume a genuine, positive-definite Riemannian space and an action principle which is quadratic in the curvature quantities (and thus scale invariant). The constant σ between the two basic invariants is equated to1/2. Then the matter tensor has the trace zero. (...) In consequence of the constancy of the scalar curvature and the divergence identity of the matter tensor, the perturbation metric has to satisfy a scalar and a vector condition, with a negative sign in the fourth coordinate. These conditions lead to the Lorentz condition and the wave equation for the vector potential. Thus the entire Maxwell-Lorentz type of electrodynamics becomes logically derivable, making no concession to any irrationality. (shrink)

This paper proves a homomorphism between extensional formal semantics and distributional vector space semantics, demonstrating structural compatibility. Formal semantics models meaning as reference, using logical structures to map linguistic expressions to truth conditions, while distributional semantics represents meaning through word vectors derived from contextual usage. By constructing injective mappings that preserve semantic relationships, we show that every semantic function in an extensional model corresponds to a compatible vector space operation. This result respects compositionality and extends to function compositions, (...) constant interpretations, and n-ary relations. Rather than pursuing unification, we highlight a mathematical foundation for hybrid cognitive models that integrate symbolic and sub-symbolic reasoning and semantics. These findings support multimodal language processing, aligning ‘meaning as reference’ (Frege, Tarski) with ‘meaning as use’ (Wittgenstein, Firth). (shrink)

We show that the assertion that every vector space is a projective module implies the axiom of multiple choice and that the reverse implication does not hold in set theory weakened to permit the existence of atoms.

This paper introduces a compositional semantics of locativeprepositional phrases which is based on a vector space ontology.Model-theoretic properties of prepositions like monotonicity andconservativity are defined in this system in a straightforward way.These notions are shown to describe central inferences with spatialexpressions and to account for the grammaticality of prepositionmodification. Model-theoretic constraints on the set of possibleprepositions in natural language are specified, similar to the semanticuniversals of Generalized Quantifier Theory.

The vector product method developed in previous articles for space rotations and Lorentz transformations is extended to the cases of four-vectors, anti-symmetric tensors, and their transformations in Minkowski space. The electromagnetic fields are expressed in “six-vector” form using the notationH +iE, and this vector form is shown to be relativistically invariant. The wave equations of electromagnetism are derived using these vector products. The following three equations are deduced, which summarize electrodynamics in a compact form: (1) Maxwell's (...) four equations expressed as one, (2) the scalar and vector potential wave equations combined into one relation, and (3) the wave equations for the electric and magnetic fields and the continuity equation combined together. Space inversion, time reversal, and magnetic monopoles are also treated. (shrink)

Critics of reliability theories of epistemic justificationoften claim that the `generality problem' is an insurmountabledifficulty for such theories. The generality problem is theproblem of specifying the level of generality at which abelief-forming process is to be described for the purposeof assessing its reliability. This problem is not asintractable as it seems. There are illuminating solutionsto analogous problems in the ethics literature. Reliabilistsought to attend to utilitarian approaches to choices betweeninfinite utility streams; they also ought to attend towelfarist approaches to social (...) choice situations that donot demand full aggregation of individual welfares.These analogies suggest that the traditional `single number'approach to reliability is misguided. I argue that a newapproach – the `vector reliability' approach – is preferable.Vector reliability theories associate target beliefs withreliability vectors – that is, structured collections ofreliability numbers – and construct criteria of epistemicjustification that appeal to these vectors. The bulk of thetheoretical labor involved in a reliability account of epistemicjustification is thus transferred from picking a uniquereliability number to constructing a plausible criterionof epistemic justification. (shrink)

Vector spaces over unspecified fields can be axiomatized as one-sorted structures, namely, abelian groups with the relation of parallelism. Parallelism is binary linear dependence. When equipped with the n-ary relation of linear dependence for some positive integer n, a vector-space is existentially closed if and only if it is n-dimensional over an algebraically closed field. In the signature with an n-ary predicate for linear dependence for each positive integer n, the theory of infinite-dimensional vector spaces over algebraically (...) closed fields is the model-completion of the theory of vector spaces. (shrink)

Large language models (LLMs) produce seemingly meaningful outputs, yet they are trained on text alone without direct interaction with the world. This leads to a modern variant of the classical symbol grounding problem in AI: can LLMs' internal states and outputs be about extra-linguistic reality, independently of the meaning human interpreters project onto them? We argue that they can. We first distinguish referential grounding—the connection between a representation and its worldly referent—from other forms of grounding and argue it is the (...) only kind essential to solving the problem. We contend that referential grounding is achieved when a system's internal states satisfy two conditions derived from teleosemantic theories of representation: (1) they stand in appropriate causal-informational relations to the world, and (2) they have a history of selection that has endowed them with the function of carrying this information. We argue that LLMs can meet both conditions, even without multimodality or embodiment. (shrink)

Vector logic is a mathematical model of the propositional calculus in which the logical variables are represented by vectors and the logical operations by matrices. In this framework, many tautologies of classical logic are intrinsic identities between operators and, consequently, they are valid beyond the bivalued domain. The operators can be expressed as Kronecker polynomials. These polynomials allow us to show that many important tautologies of classical logic are generated from basic operators via the operations called Type I and (...) Type II products. Finally, it is described a matrix version of the Fredkin gate that extends its properties to the many-valued domain, and it is proved that the filtered Fredkin operators are second degree Kronecker polynomials that cannot be generated by Type I or Type II products. (shrink)

I defend the extremist position that the fundamental ontology of the world consists of a vector in Hilbert space evolving according to the Schrödinger equation. The laws of physics are determined solely by the energy eigenspectrum of the Hamiltonian. The structure of our observed world, including space and fields living within it, should arise as a higher-level emergent description. I sketch how this might come about, although much work remains to be done.

Neuron diagrams are heavily employed in academic discussions of causation. Stephen Mumford and Rani Lill Anjum, however, offer an alternative approach employing vector diagrams, which this paper attempts to develop further. I identify three ways in which dispositionalists have taken the activities of powers to be related: stimulation, mutual manifestation, and contribution combination. While Mumford and Anjum do provide resources for representing contribution combination, which might be sufficient for their particular brand of dispositionalism, I argue that those resources are (...) not flexible enough to further accommodate either stimulation or mutual manifestation. Representational tools are provided to address these limitations, improving the general value of the vector model for dispositionalist approaches to causation. (shrink)

Programming artificial intelligence to make fairness assessments of texts through top-down rules, bottom-up training, or hybrid approaches, has presented the challenge of defining cross-cultural fairness. In this paper a simple method is presented which uses vectors to discover if a verb is unfair or fair. It uses already existing relational social ontologies inherent in Word Embeddings and thus requires no training. The plausibility of the approach rests on two premises. That individuals consider fair acts those that they would be willing (...) to accept if done to themselves. Secondly, that such a construal is ontologically reflected in Word Embeddings, by virtue of their ability to reflect the dimensions of such a perception. These dimensions being: responsibility vs. irresponsibility, gain vs. loss, reward vs. sanction, joy vs. pain, all as a single vector. The paper finds it possible to quantify and qualify a verb as fair or unfair by calculating the cosine similarity of the said verb’s embedding vector against FairVec—which represents the above dimensions. We apply this to Glove and Word2Vec embeddings. Testing on a list of verbs produces an F1 score of 95.7, which is improved to 97.0. Lastly, a demonstration of the method’s applicability to sentence measurement is carried out. (shrink)

The Anthropocene, a concept to describe the planetary consequences of human culture, demands that we imagine the earth itself as an image-recording medium. It is a concept that confronts the entangled histories of industrialization and abstraction, revealing the thoroughly mediated circumstances from which perceptions of ‘nature’ emerge. This article considers an accelerated form of abstraction induced by technological capitalism, a form with thoroughly material consequences described by McKenzie Wark as ‘vectoral’. If the age of the human is recorded on the (...) earth, the vector is the tool of its stratigraphic inscription. Taking Tom McCarthy’s novel Satin Island (2015) as an example, this article speculates on a photographic practice immanent to the vector. In Satin Island (2015), photographic images do not reinforce a human world but instead provoke a growing awareness of otherworldliness. These images confront the more radical and paradoxical consequences of the Anthropocene, an era that in fact names the end of the very category of human. (shrink)

We study the theory of K-vector spaces with a predicate for the union X of an infinite family of independent subspaces. We show that if K is infinite then the theory is complete and admits quantifier elimination in the language of K-vector spaces with predicates for the n-fold sums of X with itself. If K is finite this is no longer true, but we still have that a natural completion is near-model-complete.

Scenes filled with moving objects are often hierarchically organized: the motion of a migrating goose is nested within the flight pattern of its flock, the motion of a car is nested within the traffic pattern of other cars on the road, the motion of body parts are nested in the motion of the body. Humans perceive hierarchical structure even in stimuli with two or three moving dots. An influential theory of hierarchical motion perception holds that the visual system performs a (...) “vector analysis” of moving objects, decomposing them into common and relative motions. However, this theory does not specify how to resolve ambiguity when a scene admits more than one vector analysis. We describe a Bayesian theory of vector analysis and show that it can account for classic results from dot motion experiments. Our theory takes a step towards understanding how moving scenes are parsed into objects. (shrink)

Although great progress in neuroanatomy and physiology has occurred lately, we still cannot go directly to those levels to discover the neural mechanisms of higher cognition and consciousness. But we can use neurocomputational methods based on these details to push this project forward. Here we describe vector subtraction as an operation that computes sequential paths through high-dimensional vector spaces. Vector-space interpretations of network activity patterns are a fruitful resource in recent computational neuroscience. Vector subtraction also appears (...) to be implemented neurally in primate frontal eye field activity, which computes dimensions of saccadic eye movements. We use this apparent neural implementation as a model and construct from it a general neurocomputational account of an important type of sequential cognitive and conscious process. We defend the biological plausibility of all components of the general model and show that it yields testable anatomical and physiological predictions. We close by suggesting some interesting consequences for consciousness if our model characterizes correctly the neural mechanisms producing a common type of episode in our conscious streams. (shrink)

Apoptosis proteins have a central role in the development and homeostasis of an organism. These proteins are very important for understanding the mechanism of programmed cell death, and their function is related to their types. According to the classification scheme by Zhou and Doctor (2003), the apoptosis proteins are categorized into the following four types: (1) cytoplasmic protein; (2) plasma membrane-bound protein; (3) mitochondrial inner and outer proteins; (4) other proteins. A powerful learning machine, the Support Vector Machine, is (...) applied for predicting the type of a given apoptosis protein by incorporating the sqrt-amino acid composition effect. High success rates were obtained by the re-substitute test (98/98 = 100 %) and the jackknife test (89/98 = 90.8%). (shrink)

A passive brain–computer interface based upon functional near-infrared spectroscopy brain signals is used for earlier detection of human drowsiness during driving tasks. This BCI modality acquired hemodynamic signals of 13 healthy subjects from the right dorsolateral prefrontal cortex of the brain. Drowsiness activity is recorded using a continuous-wave fNIRS system and eight channels over the right DPFC. During the experiment, sleep-deprived subjects drove a vehicle in a driving simulator while their cerebral oxygen regulation state was continuously measured. Vector phase (...) analysis was used as a classifier to detect drowsiness state along with sleep stage-based threshold criteria. Extensive training and testing with various feature sets and classifiers are done to justify the adaptation of threshold criteria for any subject without requiring recalibration. Three statistical features along with six VPA features were used. The average accuracies for the five classifiers are 90.9% for discriminant analysis, 92.5% for support vector machines, 92.3% for nearest neighbors, 92.4% for both decision trees, and ensembles over all subjects’ data. Trajectory slopes of CORE vector magnitude and angle: m and m are the best-performing features, along with ensemble classifier with the highest accuracy of 95.3% and minimum computation time of 40 ms. The statistical significance of the results is validated with a p-value of less than 0.05. The proposed passive BCI scheme demonstrates a promising technique for online drowsiness detection using VPA along with sleep stage classification. (shrink)

Professor Oleksandr Kyryliuk's monograph "Universals of Culture and Semiotics of Discourse. Fairy Tale and Ritual", the idea of which is based on the basic formula "life-death-immortality" proposed and substantiated by him, certainly became a "new word" in the structural study of the fairy tale.This idea was picked up and adopted by other well-known specialists, as evidenced by the fact that despite its rather "respectable" age, the monograph continues to be among the most cited works of the scientist. The main significance (...) of this fundamental work lies in the substantiation Prof. O. Kyryliuk's position that the identical structuring of fairy tales and rituals is due not to direct borrowing, but to common cultural universals. In general, the fairy tale research of this author can be classified as a consideration of the transformation of later versions of fairy tales compared to their early versions, which allows restoring the already lost meaning of the latter. In other cases, O. Kyryliuk, through a return to the archaic prototype of a modern fairy tale, in which its folklore and ritual basis still remains transparent, reconstructs the already lost meaning of a later fairy tale. The third direction of this author's fairy tale research is a review of the usual interpretation of the fairy tale and its reinterpretation, which, in his opinion, does not distort, but rather reproduces its authentic content. The fourth vector of the professor's fairy tale studies is an appeal to the problem of creating literary fairy tales or other literary works based on folklore. The fifth direction of the fairy tale researcher's study is the consideration of analytical and descriptive languages of describing fairy tale narratives. That is, along with the substantive analysis of folklore and fairy tale material, O. Kyryliuk resorted to a certain "methodological reflection", when his attention was attracted not by the material itself, but by the scientific languages of its description. At the same time, a number of such languages of description, in particular V. Propp, he subjected to constructive criticism on the basis of the ideas of K. Popper. No less important for him was the desire to offer his own versions of solving the problem of classifying fairy tale material, in particular, the creation of an index of fairy tale motifs on universal-cultural principles. This is the sixth vector of the scientist's fairy tale research. An important feature of all these studies is the conceptual integrity of the applied methods of analysis, which is based on the author's idea of categories of boundary grounds and worldview codes as universals of culture, which has acquired and continues to have wide implementation in various fields of scientific knowledge and is developing in the works of famous scientists. This article is devoted to a general overview of the many years of work of Prof. O. Kyryliuk in fairy tale studies, which has been reflected in authoritative publications. (shrink)

We show that the axiom of choice AC is equivalent to the Vector Space Kinna-Wagner Principle, i.e., the assertion: “For every family [MATHEMATICAL SCRIPT CAPITAL V]= {Vi : i ∈ k} of non trivial vector spaces there is a family ℱ = {Fi : i ∈ k} such that for each i ∈ k, Fiis a non empty independent subset of Vi”. We also show that the statement “every vector space over ℚ has a basis” implies that (...) every infinite well ordered set of pairs has an infinite subset with a choice set, a fact which is known not to be a consequence of the axiom of multiple choice MC. (shrink)

Einstein's linear Lagrangian is replaced by a Lagrangian which is quadratic in the curvature quantities (gauge invariance). The hypothesis is made that the basic metrical field is highly agitated (due to periodic boundary conditions) thus establishing a submicroscopic basic lattice structure of the space-time world which, however, is macroscopically isotropic. All consequences follow from these assumptions. The “free vector” of Einstein's theory (void of physical significance and used for the normalization of the reference system) is no longer free but (...) of physical significance. It becomes subject to the wave equation and the Lorentz condition. It can thus be identified with the electromagnetic vector potential. Although the present investigation does not go beyond the linear approximation, the contours of auniverse of maxium rationality emerge. (shrink)

This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. It is a sequel to my Linear and Geometric Algebra. That text is a prerequisite for this one. -/- Linear algebra and vector calculus have provided the basic vocabulary of mathematics in dimensions greater than one for the past one hundred years. Just as geometric algebra generalizes linear algebra in powerful ways, geometric calculus generalizes vector calculus in powerful ways.

Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been (...) shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass $m$ and bivector spin $S$ has been derived in the form $\varvec{\sigma }_3 mc^2{\mathcal {J}}_{\pm } =\lambda \Omega _{\mathbf{s}} \cdot \mathrm{{S}} {\mathcal {J}}_{\pm }$ . Where, $\Omega _{s}$ is the angular velocity bivector of complex rotations, $c$ is the velocity of light. The unit vector $\varvec{\sigma }_3$ acts as an operator on the idempotents ${\mathcal {J}}_{+}$ and ${\mathcal {J}}_{-}$ to give the eigen values $\lambda =\pm 1.$ The constant $\lambda $ represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed. (shrink)

We define rational Hermite interpolants to vector-valued functions and show that, in the context of Clifford algebras, the numerator and denominator polynomials belong to a complex extension of the Lipschitz group. We also discuss the problem of constructing an algebraic representation for the generalized inverse of a vector, which is at the heart of the usual development of vector rational approximation.

Generalizing the work of Einstein and Mayer, it is assumed that at each point of space-time there exists a vector-spinor space with Nv vector dimensions and Ns spinor dimensions, where Nv=2k and Ns=2 k, k⩾3. This space is decomposed into a tangent space with4 vector and4 spinor dimensions and an internal space with Nv−4 vector and Ns−4 spinor dimension. A variational principle leads to field equations for geometric quantities which can be identified with physical fields such (...) as the electromagnetic field, Yang-Mills gauge fields, and wave functions of bosons and fermions. (shrink)

Edelman suggests that any shape is encoded by an excitation vector with components corresponding to excitations of corresponding neuronal modules. This results in discrimination of stimuli in a shape space of low dimensionality. Similar vector encoding is present in color vision. Red-green, blue-yellow, bright and dark neurons are modules that represent a number of different color stimuli in color space of low dimensionality. Vector encoding allows effective computation of color differences and color similarities. Such a neuronal (...) class='Hi'>vector-encoding approach has also been applied to the perception of visual movement, line orientation, and stereopsis. (shrink)

Quantum theory has the property of “local tomography”: the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We consider in this paper a class of theories more holistic than quantum theory in that they are constrained only by “bilocal tomography”: the state of any composite system is determined by the statistics of measurements on pairs of components. Under a few auxiliary assumptions, (...) we derive certain general features of such theories. In particular, we show how the number of state parameters can depend on the number of perfectly distinguishable states. We also show that real-vector-space quantum theory, while not locally tomographic, is bilocally tomographic. (shrink)

We consider maximal almost disjoint families of block subspaces of countable vector spaces, focusing on questions of their size and definability. We prove that the minimum infinite cardinality of such a family cannot be decided in ZFC and that the “spectrum” of cardinalities of mad families of subspaces can be made arbitrarily large, in analogy to results for mad families on ω. We apply the author’s local Ramsey theory for vector spaces [32] to give partial results concerning their (...) definability. (shrink)