Journal articles on the topic 'Quasi concave functions'

By a convex mode of convergence to infinity 〈Ck〉, we mean a sequence of nonempty closed convex subsets of a normed linear space X such that for each k, Ck+1 ⊆ int Ck and and a sequence 〈xn〉 is X is declared convergent to infinity with respect to 〈Ck〉 provided each Ck contains xn eventually. Positive convergence to infinity with respect to a pointed cone with nonempty interior as well as convergence to infinity in a fixed direction fit within this framework. In this paper we study the representation of convex modes of convergence to infinity by quasi-concave functions and associated remetrizations of the space.

In this paper, a new method is proposed for finding an optimal solution to a Quasi-Concave Quadratic Programming Problem with Bounded Variables in which the objective function involves the product of two indefinite factorized linear functions and constraints functions are in the form of linear inequalities. The proposed method is mainly based upon the primal dual simplex method. The Linear Programming with Bounded Variables (LPBV) algorithm is extended to solve quasi-concave Quadratic Programming with Bounded Variables (QPBV). For developing this method, we use programming language MATHEMATICA. We also illustrate numerical examples to demonstrate our method.Dhaka Univ. J. Sci. 63(2):111-117, 2015 (July)

We investigate the stability of isomorphisms acting between interpolation spaces generated by the method of means. We focus on the methods which are determined by balanced sequences for non-degenerate quasi-concave functions. The key point for our investigation is that these methods have orbital description by a single element generated by a special ideal of operators between Banach couples. We prove that if an operator is invertible in one orbit it is also invertible by nearby orbits provided that the corresponding indices of quasi-concave functions generated these orbits are close to each other. In particular, these results apply to the real method of interpolation.

Current neural network architectures have no mechanism for explicitly reasoning about item trade-offs. Such trade-offs are important for popular tasks such as recommendation. The main idea of this work is to give neural networks inductive biases that are inspired by economic theories. To this end, we propose Neural Utility Functions, which directly optimize the gradients of a neural network so that they are more consistent with utility theory, a mathematical framework for modeling choice among items. We demonstrate that Neural Utility Functions can recover theoretical item relationships better than vanilla neural networks, analytically show existing neural networks are not quasi-concave and do not inherently reason about trade-offs, and that augmenting existing models with a utility loss function improves recommendation results. The Neural Utility Functions we propose are theoretically motivated, and yield strong empirical results.

Purpose Severe accuracy loss may occur when finite element comes to the distorted mesh model, and the calculation may fail when element mesh degenerates into concave quadrangle or the element boundary is curved. This is a valuable research topic, and many efforts have been made to develop new finite element models. This paper aims to propose two quasi-conforming membrane elements based on the assumed stress quasi-conforming method and fundamental analytical solutions to overcome the difficulties. Design/methodology/approach First, the fundamental analytical solutions which satisfied both the equilibrium and the compatibility relations of plane stress problem are used as the initial assumed stress of both elements. Then, the stress-function matrices are used as the weighted functions to weaken the strain-displacement equations, which makes only string-net functions on the boundary of the elements are needed in the process of strain integration. Finally, boundary interpolation functions expressed by unknown nodal displacement parameters are adopted to the process of strain integration. Findings The formulations of both elements are simple and concise, and the elements are immune to the distorted mesh, which can be used to the mesh shape degenerates into a triangle or concave quadrangle and curved-side element. The results of the numerical tests have proven that the new models possess high accuracy. Originality/value New formulations of quasi-conforming method are described is detail, and the new strategy exhibits advantages of both analytical and discrete methods.

AbstractLet 0 < p,pi ≤ ∞, 0 < q,qi < ∞ (i = 1, 2) such thatLet E be a quasi-Banach lattice which fails to contain c0 and whose α-convexity constant is equal to 1 for some 0 < α < ∞. Then for every f∈H(E(q)) there exist g∈Hp, 0(E(q0)), h∈Hp1(E(q1)) such thatConsequently, E is q-concave for some finite q if and only if E is uniformly H1-convexifiable in the sense of [24]. Analogous results are also obtained for symmetric spaces of measurable operators. Another result proved in the paper says that if E is a symmetric quasi-Banach function space on (0, ∞) having the analytic Radon–Nikodym property then LE(M, τ) also possesses this property for any semifinite von Neumann algebra (M, τ).

A competitive economic equilibrium model integrated with exchange, consumption, and production is considered. Our goal is to give an existence result when the utility functions are concave, proper, and upper semicontinuous. To this aim we are able to characterize the equilibrium by means of a suitable generalized quasi-variational inequality; then we give the existence of equilibrium by using the variational approach.

In this paper, a new method namely, objective separable method based on Linear Programming with Bounded Variables Algorithm is proposed for finding an optimal solution to a Quasi-Concave Quadratic Programming Problems with Bounded Variables in which the objective function involves the product of two indefinite factorized linear functions and the constraint functions are in the form of linear inequalities. For developing this method, we use programming language MATHEMATICA. We also illustrate numerical examples to demonstrate our method.Dhaka Univ. J. Sci. 64(1): 51-58, 2016 (January)

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

We consider a two-person zero-sum game with two sets of strategic variables which are related by invertible functions. They are denoted by [Formula: see text] and [Formula: see text] for players A and B. The payoff function of Player A is [Formula: see text]. Then, the payoff function of Player B is [Formula: see text]. [Formula: see text] is upper semi-continuous and quasi-concave on [Formula: see text] for each [Formula: see text] (or each [Formula: see text]), upper semi-continuous and quasi-concave on [Formula: see text] for each [Formula: see text] (or each [Formula: see text]), lower semi-continuous and quasi-convex on [Formula: see text] for each [Formula: see text] (or each [Formula: see text], and lower semi-continuous and quasi-convex on [Formula: see text] for each [Formula: see text] (or each [Formula: see text]). We will show that the following four patterns of competition are equivalent, that is, they yield the same outcome. (1) Players A and B choose [Formula: see text] and [Formula: see text] (competition by [Formula: see text]). (2) Players A and B choose [Formula: see text] and [Formula: see text] (competition by [Formula: see text]). (3) Players A and B choose [Formula: see text] and [Formula: see text] (competition by [Formula: see text]). (4) Players A and B choose [Formula: see text] and [Formula: see text] (competition by [Formula: see text]).

Z Utility Theory refers to a class of nonlinear utility functions for solving Risk and Multiple Criteria Decision-Making problems. Z utility functions are hybrids of additive and nonadditive (nonlinear) functions. This paper addresses the concepts and assessment methods for the additive part of Z-utility functions for multiple criteria problems that satisfy the efficiency (nondominancy) principle. We provide a decision paradigm and guidelines on how to approach, formulate, and solve decision-making problems. We, also, overview the modeling of decision process based on four types of decision-making styles. For multi-criteria problems, a new definition of convex efficiency is introduced. Also polyhedral efficiency is developed for presenting multi-criteria efficiency (nondominancy) graphically. New double helix quasi-linear value functions for multi-criteria are developed. Two types of double helix value functions for solving bi-criteria (Advantages versus Disadvantages) and also risk problems are introduced: Food–Fun curves for expected values and Fight-Flight curves for expected risk values. Ordinal/Cardinal Approach (OCA) for assessment of additive utility functions is developed. Simple consistency tests to determine whether the assessed utility function satisfies ordinal and/or cardinal properties are provided. We show that OCA can also be used to solve outranking problems. We provide a critique of Analytic Hierarchy Process (AHP) for assessing additive value functions and show that the developed Ordinal/Cardinal Approach overcomes the shortcomings of AHP. We also develop a unified/integrated approach for simultaneous assessment of nonlinear value and additive (multi-criteria) utility functions. These results in an additive utility function that can be concave, convex, or hybrid concave/convex based on the nonlinear value function. Finally, we show an interactive paired comparisons approach for solving nonadditive and nonlinear utility functions for bi-criteria decision-making problems. Several illustrative examples are provided. The paper provides reliable and robust approaches for modeling the utility preferences of heterogeneous economic agents in macro and micro-economics.

Abstract In this paper, we study games with continuous action spaces and non-linear payoff functions. Our key insight is that Lipschitz continuity of the payoff function allows us to provide algorithms for finding approximate equilibria in these games. We begin by studying Lipschitz games, which encompass, for example, all concave games with Lipschitz continuous payoff functions. We provide an efficient algorithm for computing approximate equilibria in these games. Then we turn our attention to penalty games, which encompass biased games and games in which players take risk into account. Here we show that if the penalty function is Lipschitz continuous, then we can provide a quasi-polynomial time approximation scheme. Finally, we study distance biased games, where we present simple strongly polynomial time algorithms for finding best responses in $$L_1$$ L 1 and $$L_2^2$$ L 2 2 biased games, and then use these algorithms to provide strongly polynomial algorithms that find 2/3 and 5/7 approximate equilibria for these norms, respectively.

The Jensen inequality has been reported as one of the most consequential inequalities that has a lot of applications in diverse fields of science. For this reason, the Jensen inequality has become one of the most discussed developmental inequalities in the current literature on mathematical inequalities. The main intention of this article is to find some novel bounds for the Jensen difference while using some classes of twice differentiable convex functions. We obtain the proposed bounds by utilizing the power mean and Höilder inequalities, the notion of convexity and the prominent Jensen inequality for concave function. We deduce several inequalities for power and quasi-arithmetic means as a consequence of main results. Furthermore, we also establish different improvements for Hölder inequality with the help of obtained results. Moreover, we present some applications of the main results in information theory.

In the era of the fourth industrial revolution, the international community is striving to establish a coordinated system to prevent fatal climate change in a global sense. As a result of such changes in business environments, a new issue, sustainability, has recently presented a paradigm shift and new research opportunity in which the theories and practices in traditional production and operations management are being reinterpreted and reapplied in relation to this emerging issue. Under this research background, we consider an optimal emission-trading problem under a cap-and-trade (CAT) emission regulation when the customers’ demand is given as an arbitrary probability distribution. Such a CAT approach to reduce the amount of emissions is a normative system for the sustainable production of manufacturing firms, which is also closely related to a well-known open innovation in literature of inventory management. Then, we formulate two stochastic inventory optimization models, which can be applied immediately for two famous CAT policies that exist in reality. In particular, our objective is to draw theoretical and practical implications for baseline credit emission regulations, which are innovative and government-led emission regulation policies, with a well-known newsvendor analysis. For our analytical results, we first show that our objective functions are piecewise linear and (quasi)-concave. Thus, it is found that there exists a unique optimal solution to the problem. Second, we successfully obtain the closed-form optimal solutions for the two models considered. Finally, we conduct a sensitivity analysis through a comparative static analysis to examine how the model parameters can affect the optimal solution in each model. All these analytical results and implications are consistent with previous studies in the literature, as well as with our insights for the models.

AbstractVarious Nash equilibrium results for a broad class of aggregative games are presented. The main ones concern equilibrium uniqueness. The setting presupposes that each player has $$\mathbb {R}_+$$ R + as strategy set, makes smoothness assumptions but allows for a discontinuity of stand-alone payoff functions at 0; this possibility is especially important for various contest and oligopolistic games. Conditions are completely in terms of marginal reductions which may be considered as primitives of the game. For many games in the literature they can easily be checked. They automatically imply that conditional payoff functions are strictly quasi-concave. The results are proved by means of the Szidarovszky variant of the Selten–Szidarovszky technique. Their power is illustrated by reproducing quickly and improving upon various results for economic games.

AbstractThe velocity solution of the incompressible Stokes equations is not affected by changes of the right hand side data in form of gradient fields. Most mixed methods do not replicate this property in the discrete formulation due to a relaxation of the divergence constraint which means that they are not pressure-robust. A recent reconstruction approach for classical methods recovers this invariance property for the discrete solution, by mapping discretely divergence-free test functions to exactly divergence-free functions in the sense of $${\varvec{H}}({\text {div}})$$ H ( div ) . Moreover, the Stokes solution has locally singular behavior in three-dimensional domains near concave edges, which degrades the convergence rates on quasi-uniform meshes and makes anisotropic mesh grading reasonable in order to regain optimal convergence characteristics. Finite element error estimates of optimal order on meshes of tensor-product type with appropriate anisotropic grading are shown for the pressure-robust modified Crouzeix–Raviart method using the reconstruction approach. Numerical examples support the theoretical results.

Abstract Since there are still research interests in the physical properties of quasi-binary thermoelectric $${\hbox {Mg}}_{2} {\hbox {X}}_{1-x}{\hbox {Y}}_{x}$$ Mg 2 X 1 - x Y x alloys, with X, Y = Si, Ge, Sn, we present an ab initio analysis that yields the relative formation energy and effective masses of the conduction bands, in the whole compositional range x. We base our calculations on the full-relativistic Korringa, Kohn and Rostocker (KKR) Green’s functions formalism within the coherent potential approximation (CPA). Formation energies, measured relative to the end $${\hbox {Mg}}_{2} \hbox {X}$$ Mg 2 X compounds, show no excess energy for the $${\hbox {Mg}}_{2} \hbox {Si} {-} {\hbox {Mg}}_{2} \hbox {Ge}$$ Mg 2 Si - Mg 2 Ge substitution thus indicating a complete solubility. In contrast, concave and asymmetric formation energies for intermediate compositions in the $${\hbox {Mg}}_{2} \hbox {X} {-} {\hbox {Mg}}_{2} \hbox {Sn}$$ Mg 2 X - Mg 2 Sn alloys manifest a miscibility gap. With this basis, we compute and discuss the crossing of the conduction bands observed in n-type $${\hbox {Mg}}_{2} {\hbox {X}}_{1-x} {\hbox {Sn}}_x$$ Mg 2 X 1 - x Sn x materials. We present direction- and band-dependent effective masses using a generalized single parabolic band effective mass approximation to discuss anisotropic effects, to interpret available experimental and theoretical data, and to predict intermediate and not yet published transport parameters on these alloys.

In una società dove, da più parti, la famiglia è sotto attacco, occorre creare una cultura della famiglia che sia anche per la famiglia. La tendenza a identificare con la famiglia qualsiasi aggregazione di individui, a prescindere dal sesso o dal vincolo che li tiene uniti, produce uno scossone semantico destinato a danneggiare non soltanto la famiglia ma l’intera società. Nonostante i cambiamenti che abbiamo registrato in questi ultimi anni, la famiglia tradizionale continua a essere l’istituzione sociale che più di altre incide sulla formazione delle persone e che più di altre è capace di generare quei capitali individuali e sociali —la fiducia reciproca, il senso del bene comune, la speranza nel futuro, il senso di appartenenza a una catena generazionale, quindi a una tradizione, lo sviluppo di una vera democrazia—, senza i quali è assai difficile immaginare una società degna del nome.In a society where the family suffers attacks from many different sides, a culture of the family is needed that will be also for the family. The tendency of identifying as a family any aggregate of individuals regardless of their sex or of the link that joins them, gives rise to a semantic chaos, which not only hurts the family but society also. In spite of the changes of the last few years, traditional family is still the social institution with more influence on the formation of persons, and the most able to generate individual and social capitals –mutual trust, a shared understanding of common good, hope for the future, the sense of belonging to a generational line or tradition, the development of a true democracy– the lack of which makes it very hard to conceive (the idea of) a society worthy of that name.

So then: That all phenomena in our intermediate state, or quasi-state, represent this one attempt to organise, stabilise, harmonise, individualise -- or to positivise, or to become real: That only to have seeming is to express failure or intermediateness to final failure and final success; That every attempt -- that is observable -- is defeated by Continuity, or by outside forces -- or by the excluded that are continuous with the included: That our whole "existence" is an attempt by the relative to be absolute, or by the local to be the universal. -- Charles Fort, The Book of the Damned (1919) I inspire this essay with outlandish reference from the "Godfather of the paranormal" primarily because upon revision of his seminal, often "disjointed" tome The Book of the Damned, I am immediately struck by the deeply ironic reciprocity his renegade theory of Continuity shares with expansive sociocultural change effected by global communication technologies, specifically, a growing awareness of interconnections -- or links -- between all things. I am swiftly presented, upon making this observation, with Sony's latest TV ad which, rather than attempting to persuade me to buy a Sony product per se, seems considerably more interested in luring me to buy into the digital world the advertisement illustrates, blending it ambiguously into "reality", repetitively informing me that in such an environment, "we are all connected". Following suit, I make the link. But from a strictly Fortean perspective, the link was already there, acknowledged or not, since Fort's ontology of Continuity precludes locality in much the same way as, say, the graphic art of M.C. Escher. Much of what Fort catalogued as "paranormal" phenomena can be seen as signs (in the semiotic sense) of the universe's non-localised nature. Although he did not frame his own perspective in these terms, Fort's writings subtly imply an explanation of "existence" as an assemblage of continuous signs seeking affirmation via exclusion (I am because I am not what I am not), an assemblage read, interpreted and ordered by the exclusive human mind. Mysterious coincidences, apparitions, vanishings, appearances, ESP, telekinesis -- these types of apparently instantaneous phenomena were seen as manifestations of phenomenological connections or mergings where none was believed or known to exist. The role of the Fortean, therefore, has traditionally been both to acknowledge that such phenomena do occur and to elucidate their significance, to explore connections between apparently unconnected phenomena, to make new, illuminating links in an infinitely interlinked universe. Such a role is hardly incompatible, of course, with that of today's average Web surfer. In the virtual environment communication technologies seek to construct, nothing is really local because everything is continuous with, or linked to, everything else. Significantly, these links are of our own making, but were already there, and it is in this sense that the Web is the essence of Forteana electronically virtualised, accounting for cyberspace's prolific production of UFO and conspiracy lore, for example, both traditionally fields of high interest to Forteans. Jodie Dean notes that: With the Internet, conspiracy information has been turned into entertainment ... this is because of the way that the networked society turns all of its citizens into conspiracy theorists: we are all told to search for information and make links. What is interesting about the expansion of conspiracy into mass media is the way that conspiracy thinking comes to define the Zeitgeist, to be synonymous with critical thinking in the networked society. (Pilkington 25) Fortean Continuity has woven itself through much of Western popular culture since Fort's time, obviously underpinning The X-Files and its ilk but surfacing more subtly in Paul Thomas Anderson's Magnolia, for example, where it in fact formed the crux of that film's "confusing" closure: a narratively "unconnected" frog fall, a well-documented but poorly understood phenomenon to which Fort attached considerable significance. Seemingly "unconnected" events like this happen quite often, Fort discovered, and through his study of their social reception (which historically ranges from ignorance to mythic inspiration) reasoned that all phenomena and events are unexplained and unexpected -- are apparently unconnected -- until we are able to establish a context in which they might plausibly "make sense", or be possible, or real. When such a (culturally specific) context is established, often elaborately so in a culture intolerant of randomness, the phenomenon "explained" becomes awash in significance, enriching the entire environment in which it is deemed to occur, reminding us of Continuity and the creative power of explanation. Unless, of course, that explanation is primarily concerned with maintaining a dominant social power structure or paradigmatic worldview which, Fort observed, in the West tends to be interested in downplaying Continuity and promoting fragmentation, or "localisation of the universal". Further, by "excluding" the anomaly altogether (and that includes accepting its presence but maintaining its "otherness"), we only limit the scope of our own observation, leaving the most alluring links unexplored. While all this sounds rather antiquated and mystical (it was Fort's way), I still can't help but think he might have been onto something: upon review Magnolia actually contains numerous clear Fortean references (Coleman 49). Granted a context, the frogs actually make sense. "The message" is that, even if the links seem at first so obscure as to be nonexistent, we are, in a virtual environment, encouraged to make them. In such an environment, the once staunch division between "subjective construction" and "objective observation" becomes largely redundant. The Body as Media Sign This redundancy describes a culture in which the medium has become the message. We are now encouraged to make links by transcending locality via the "technological simulation of consciousness", which McLuhan saw as symptomatic of the "electric age, when our central nervous system is technologically extended to involve us in the whole of mankind and to incorporate the whole of mankind in us..." (4), an age in which media technology essentially elaborates the nonsynthetic interconnective model of biological nature, a model completely inhospitable to notions of "disconnection". When our bodies and their perceptual functions become continuous with the form and information relay of technology, "we" become undeniably continuous, disembodied via the body. Fort's ontology of Continuity (which lead him to conceive the term "teleportation", probably a significant influence on the cosmology of Lovecraft) has become increasingly intrinsic to much horror and science fiction, and especially central to the filmography of Canadian auteur and master of paranoid horror, David Cronenberg. Notably prominent in his first investigation of postmodernity's mediated ontology, Videodrome (1982), the theme of Continuity permeates this often "disjointed" film, which suggests the power of mass media operates not through the message, but through an obscure function of the medium which ultimately renders the "message" redundant as the medium becomes the message. Videodrome, a snuff TV show that seduces Toronto cable station chief Max Renn (James Woods), is encoded with a subliminal signal, which induces a brain tumour that eventually transforms the viewer's reality into video hallucination (and/or vice versa). The nature of the message does not ultimately matter since this subliminal signal can function through any program, even a test pattern. Steven Shaviro notices the psychedelic, McLuhanesque joke: the boundary between "inner bodily excitation and outer objective representation" collapses as the "new regime of the image abolishes the distance required either for disinterested aesthetic contemplation or for stupefied absorption in spectacle" (141). In the addictive cybernetic feedback loop of Videodrome, the distance between the medium and the body eventually collapses -- the body becomes the medium itself, the "New Flesh", and consequently the message: a sign within the hyperreality of an information system in which there are only signs. In such an all-encompassing system of interconnected signs, in which signification becomes incontrovertibly arbitrary, borders don't so much collapse as blend into one another, forming what Cronenberg presents as eXistenZ (1999), an unresolvable "quasi-state" of virtual embodiment. In many ways an elaboration of Videodrome, eXistenZ presents a "different present" style future in which technology, biology, the synthetic, the natural, and the real are completely virtualised with the advent of synthesised, organic virtual reality technology. Consisting of "metaflesh", the game pods/consoles are living tissue requiring a human body as a power source. Connecting directly with the central nervous system via a port at the base of the spine, they become a working part of the biological body, transforming the individual's reality into a narrative game called eXistenZ, so "real" it is ultimately indistinguishable from reality itself, hence its overwhelming appeal. The content of the game is an ambiguous combination of pre-programmed information and the player's own expectations, the objective of the game being to learn why one is playing the game. Progress within the game depends upon saying the right thing to the right person/character, or doing the right thing at the right time, to receive the right information to proceed in the right direction. When progress begins to lag, the player feels an overwhelming urge to do or say something they don't "want" to as their game character temporarily takes over to ensure continuation of the game. Initially felt as artificially induced bodily impulses, these urges eventually become acceptable and naturalised as the player "becomes" their game character, adopting the prescribed attitude and behaviour required for proficiency within the game, allowing them to "do the right thing" more easily, to both "make the links" and reconfigure themselves as links. In this sense eXistenZ is a fitting parable for an increasingly interconnected media culture that equates media transgressions of the body/mind with eventual transcendence from the body/mind into a quasi-corporeal "virtual reality" of cybernetics in which the individual, like everything else that is deemed to exist, is defined as a sign of its own connection to everything else. Existence as game describes existence within a playful culture of desire in which the pursuit of happiness is equated with the pursuit of pleasurable symbols that speak for our selves, and for which a virtual reality becomes a most logical, desirable future, if not a present. Within such an environment we are all characters in the same game, a game called "existence". Our bodies are the game pods which make interaction within existence possible, the vehicular flesh that binds "us" to the gaming environment, their provision of "reality" becoming ever more indistinguishable from the contexts established by increasingly pervasive electronic media. Literality begins to fade schizophrenically in the wake of hypersignificance. As a sign of and within a media age, the body becomes both a medium for a self-reflexive message and a message for a self-reflexive medium. In other words, as eXistenZ suggests, the body is already so incorporated as both media (information system) and media image that there is nothing non-virtual about its reality, or reality in general, for that matter, hence the analogy of existence as interactive simulation, a game. The Fortean Continuity of eXistenZ, I'd suggest, describes the increasingly anarchic power, ebb and flow of signs within a postmodern, virtual environment. Interestingly, Fort ultimately saw existence itself as reliant upon the processional denial of Continuity in the pursuit of the "real", or the Truth, or some kind of localisation of the universal, something that owes no debt to or shares no phenomenological relationship with anything other than itself, something that could only ever be ... self-referential. He argued that, despite our attempts to construct such phenomena, and to define our own lived experience (and our bodies) in these terms, no such phenomena exist in any objective sense because, ultimately, the observer is the observed. Everything is a part of itself, so every attempt to become "real" is doomed to fail, since "real" for Western culture involves some degree of conceptual disconnection, if only of the "real" from the "unreal". Fort didn't miss the irony of Intermediateness, the Truth that could never be, deeply appreciating The amazing paradox of it all: That all things are trying to become the universal by excluding other things. That there is only this one process, and that it does animate all expressions, in all fields of phenomena, of that which we think of as one inter-continuous nexus. (Book of the Damned 9) If then, upon the technological realisation of Continuity, there emerges in Western popular culture a deep obsession with the growing elusiveness of Truth (or "reality") accompanied by a certain degree of "paranoia" -- a veritable Fortean revival -- might this be attributable, at least in part, to the growing inefficacy of Truth and "reality" within the virtual environment of an inherently Fortean media form? References Coleman, Loren. "When Frogs Fall..." Fortean Times 133 (2000): 49. eXistenZ. Dir. David Cronenberg. 1999. Fort, Charles. The Complete Books of Charles Fort. New York: Dover, 1974. McLuhan, Marshall. Understanding Media: The Extensions of Man. London: Routledge, 1964. Pilkington, Mark. "Watching the Watchers." Fortean Times 134 (2000): 24-5. Shaviro, Steven. The Cinematic Body. Minneapolis: U of Minnesota P, 1993. Videodrome. Dir. David Cronenberg. 1982. Citation reference for this article MLA style: Adam Dodd. "The Fortean Continuity of eXistenZ within a Virtual Environment." M/C: A Journal of Media and Culture 3.5 (2000). [your date of access] <http://www.api-network.com/mc/0010/continuity.php>. Chicago style: Adam Dodd, "The Fortean Continuity of eXistenZ within a Virtual Environment," M/C: A Journal of Media and Culture 3, no. 5 (2000), <http://www.api-network.com/mc/0010/continuity.php> ([your date of access]). APA style: Adam Dodd. (2000) The Fortean continuity of eXistenZ within a virtual environment. M/C: A Journal of Media and Culture 3(5). <http://www.api-network.com/mc/0010/continuity.php> ([your date of access]).

Introduction This essay is very much an anxious response to an earlier article, "Controlling Gameplay", that I wrote for M/C about gameplay: the immersive, visceral experience of playing computer and video games. I argued that gameplay concerns the event status of playing computer and video games, and that as such it exceeds the symbolic content of games. Now, I continue to be troubled by the implications of this assertion -- does it not give up too much ground gained by the understanding that social practices such as gaming are socially constructed? Does it not return us to all of the problems associated with claims of access to an essential, authentic experience? In short, it becomes very difficult to contest or question such claims. The term gameplay may well function to depoliticise computer gaming; at least if the domain of the properly sociopolitical is understood as the symbolic field! -- and perhaps we shouldn't concede this point too quickly. In the previous article did I almost against myself end up fetishising the technological through the postulation of this sublime experience? The Fetish & Desire You may well be wondering what any of this has got to do with desire. Well, first let me fill you in on the research context out of which these essays emerge. For the past three years I have been undertaking ethnographic research on computer gaming: first, by participating in online gamer fan activities; and second, in an enterprise ethnographic study of Auran, a computer game development company situated in Brisbane, Australia. "Controlling Gameplay" is clearly marked by my immersion and entanglement in an ethnographic relationship with online gamers. The material on which it is based came from spending up to 25 hours a week online playing and discussing games. The point of these comments is not simply to establish my credentials as a gamer, nor to embarrassingly distance myself from 'going native' by making the appropriate gestures about reflexivity. Rather, I insist on these moments of fetishistic disavowal and illusion as a necessary condition of doing ethnographies. This shifts us from the domain of desire to what Slavoj Zizek, following Lacan, theorises as enjoyment. In the introduction to "Controlling Gameplay" I made the banal point that computer game software is a commodity. Computer games offer an example of the informational commodity circulating through the networks of informational capitalism. This is basically the bottom line of gaming: big business. Zizek carefully outlines that central to the Marxist understanding of commodity fetishism -- the displacement of relations among people onto relations among things -- is a fascination for some kind of mysterious 'content' that is presumed to be hidden by the form of commodities (Sublime Object 16-22). An example of this is the cultural studies academic doing ethnographic research, and believing that his work offers "something more", a potential critical edge, than just the commodification and corporatisation of academic work. It would appear, at least initially, that this is precisely how gameplay is working: the hidden technological sublime behind the empty form of the informational commodity. The problem for critical analysis then becomes that of insisting on asking the question of why this 'content' of gameplay is affirmed in the game's particular status of the commodity form. We are not interested in disclosing "the secret behind the form but the secret of this form itself" (Sublime Object 15). In discussions many gamers would insist on the fact that gameplay is simply the fun factor of playing computer games: nothing more and nothing less. Others would insist on refusing to finally fill in this secret content. After describing gameplay as having something to do with an immersive experience of escapism a gamer would invariably move on to suggest that it perhaps involved the design of a good interface that allows the player to seamlessly participate in the game; or it is to do with quality game-design, a careful balancing of various features that define a particular genre. Or it is a skill developed and honed by many hours of gaming; intense gameplay is an insider's experience that is used to define your belonging as a 'hard-core gamer with cred' -- if it has to be explained and described to you, well, you just won't get it, will you? In the movement of these discussions and exchanges desire is not so much to be found or discovered in the hidden content of an essential, authentic experience that is gameplay, but rather it is right there on the surface, in the work of these displacements. If anything then, unconscious desire is not a deep interior experience of gameplay but in the very form of this movement, in the work that is done to elaborate and produce the effect of a hidden content. And the question arises: what is being avoided or obfuscated in this movement that perhaps has nothing at all to do with an experience of gameplay or even desire for that matter? I will return to this question in a moment. The important step here is not to become overly dazzled by this 'content' of gameplay, but instead to ask the question of why it assumes the form of a commodity. But why this focus on the commodity-form, and the process of fetishistic inversion. After all there is a lot more at stake here than simply the commodity-form or some kind of economic reductionism, essentialism or substantialism. There is also the fascinating power of attraction that this "something more" can exert on academic work. This has to do with the status of a sublime materiality that persists beyond the physical materiality of an object in the networks of business, or even that of an object-cause for intersubjective desire played out in the game of ethnographic research. It is precisely this persistence that is so troubling. But is this interest in fetishistic disavowal, the insistence on "something more", simply a more refined type of traditional ideology critique? That is, is it once more a matter of the illusory knowledge or beliefs of misguided naive gamers which the critical intellectual will come along and tear down, to reveal the true state of affairs -- that there is really nothing there except perhaps a complex, overdetermined effect of socioeconomic processes, a social construction if you like? Is all of this concern with the fetish simply an epistemological and monstrous game played out in the interiority of the thinking subject that has in fact very little, if anything, to do with the effective materiality of the complex assemblage that is computer gaming. Perhaps a shift to the materiality of the processes and objects involved in the production of computer gaming would help us to leave behind the problem of the fetish as some tired epistemological quandary about illusory belief. After all, is not the very idea of commodity fetishism based on a rather tired and limiting opposition between people and things? The Factish In his recent Pandora's Hope: Essays on the Reality of Science Studies, Bruno Latour attacks the notion of the fetish and the modern critical subject that he believes is behind it. Latour's actor-network theory (nicely explained in Sean Aylward Smith's recent article for M/C, "Where Does the Body End?") works to displace the assumed divide between subjects and objects, particularly humans and nonhumans. This is often theorised through richly detailed ethnographic studies that follow the associations between humans and nonhumans that make up the assemblages and collectivities of scientific practice and technological projects. In Pandora's Hope Latour takes aim at the critical gesture of the iconoclast, the modern critic, who seeks to expose the fetish as "something that is nothing in itself, but simply the blank screen onto which we have projected, erroneously, our fancies, our labor, our hopes and passions". A problem for the anti-fetishist is the assumption that people naively believe in the inherent, mysterious qualities of the object in the first place. Anti-fetishism is not so much about the qualities or status of the object and our relations to it, but more a mode of argument: "it is always an accusation. Some person, or some people, are accused of being taken in -- or worse, of cynically manipulating credulous believers -- by someone who is sure of escaping from this illusion and wants to free the others as well: either from naive belief or from being manipulative. But if anti-fetishism is clearly an accusation, it is not a description of what happens with those who believe or are manipulated" (270). Latour argues that the problem of fetishism is all in the mind of the critical thinker. Believing himself disconnected from the realm of things and objects, this monstrous "mind in the vat" "invents the notion of belief and manipulation and projects this notion upon a situation in which the fetish plays an entirely different role" (270). Latour proposes that we shift our attention to the status of the fetish as a quasi-object or factish. The factish has to be fabricated, made, and invented; as such it has a complex and variable ontology in which it is entangled within collective practice. The status of the factish is all about the associations between humans and nonhumans and refuses the disabling opposition between subject and object, epistemology and ontology, internal belief and external world. The modern critic's belief that others believe functions to render invisible the complicated practice through which the categories are mixed and factishes are constructed. To replace all of this Latour suggests that we adopt a heterogeneous ontology in which we externalise belief "among the multiplicity of nonhumans" (284) -- in short that we recognise the ontological content of beliefs, and grant ontology back to nonhuman entities (273-88). By taking up the approach of actor-network theory I could now follow the diverse actors, both human and nonhuman, that make up the network and practices of computer gaming. When the gamers assert that gameplay is this and that and so on, I can take them at their word. They are not telling me, in some hysterical cycle, 'no it's not that, no, not that'. But instead 'yes it is that, and that as well'. They are affirming the multiple and heterogeneous ontology of humans and nonhumans. So I took this toolbox of concepts with me into my fieldwork encounters and interventions at Auran. And not surprisingly it worked really well. I could now quite easily and comfortably follow the entangled materiality of humans and nonhumans; the multiple shifting ontologies of objects such as game engines that function as representations in design reports; key elements in long term corporate business plans; links in relations with other corporations; development tools for game designers; the focus of licensing agreements; and programming problems and challenges for programmers. Game designers, programmers, CEOs, and public relations officers were more than happy to describe and show me the complex entanglements of humans and nonhumans involved in producing computer games. Now, throughout the period of my fieldwork I have been quite anxious and worried about negotiating the conditions of access, about the control exercised by senior Auran management. But at each stage or period of my research I have been amazed by the level of cooperation and access that has been given to me. Nor has Auran management shown much concern about my access to 'problem areas' of the company as it went through various periods of restructuring. I have had open and what I believe to be frank discussions with disgruntled employees who were very uncomfortable and openly critical of various aspects of Auran. And there has been very little effort to control or restrict my use of this material. My impression is that Auran has been more than pleased to put on display for the dazzled gaze of the ethnographer the corporate processes and mechanisms involved in producing computer game software. Initially I was rubbing my hands with glee at this research opportunity. I can see publication potential and career opportunities emerging from this ethnographic entanglement with Auran. The Fetish and Enjoyment But I have become increasingly anxious and worried about how well the fieldwork at Auran has gone, and how well actor-network theory works in explaining the multiple and heterogeneous ontologies of the humans and nonhumans that I have been mixing with for the past two years. And this worry brings me back to the fetish. I think Latour is correct: belief is not something internal, but more a matter of practice, externalised in the relations among humans and nonhumans. But is this not precisely the more useful and correct definition of the fetish, at least under the conditions of informational capitalism? Far from moving us out of the domain of the fetish into the ontological materiality of the factish, Latour is perhaps describing the fetishistic inversion perfectly. It is not at the level of some kind of internal knowledge, belief or deep mysterious unconscious that the misrecognition of the fetishistic inversion takes place. Rather, it is at the properly social level of our acts, what we do, that we overlook the fetishistic 'repressed' social dimension (Sublime Object 20). This nonknowledge of reality is part of the very effectivity of our social acts, "a kind of reality which is possible only on condition that the individuals partaking in it are not aware of its proper logic; that is, a kind of reality whose very ontological consistency implies a certain non-knowledge of its participants" (Sublime Object 21). The further point to recognise, as Zizek points out, is that commodity fetishism is not just the replacement of people with things, or our overlooking the properly social relations between humans behind things. More importantly, it is that this misrecognition occurs precisely at the level of the network of relations among things -- what is a structural effect of this network of relations starts to appear as the immediate property of one of the elements (Sublime Object 23-4). So from all of this the important point for my purposes is that fetishism is not really about what people know. Of course gamers know very well that their software is a commodity, and that capitalist business interests are basically running the show: they talk about the business of gaming all the time. The point is rather the fact that the fetishistic inversion occurs in the very activity of playing. This misrecognition, or illusion if you will, is not about false knowledge: the illusion is structuring reality, our real social activity: "they know very well how things really are, but still they are doing it as if they did not know" (Sublime Object 32). So Latour is quite insightful, belief is radically exterior and as Zizek points out one of the uptakes of this is that things, commodities, end up believing for us -- "it is belief which is radically exterior, embodied in the practical, effective procedure of people" (34). But does not Latour's focus on the complex ontology of objects, and our entanglement with them, at least in some way work to challenge this fetishistic inversion? Is not this obfuscation of the process of production, even if we shift that misrecognition to the relations among things, questioned by the process of exposing or opening the black box of the production mechanism? After all, isn't this precisely what we are trying to do with ethnographies? The difficulty, as Zizek writes in "Fetishism and Its Vicissitudes", is that "far from destroying the 'fetishist' illusion, the insight into the production mechanism in fact even strengthens it". It is the disclosure of the production process itself that "serves as the fetish which fascinates with its presence". And what is being concealed, and persists through all this display of disclosure is "the social mode of production" (102). Zizek warns us "the transparency of the process of production is false in so far as it obfuscates the immaterial virtual order which effectively runs the show ... . Capital functions as the sublime irrepresentable Thing, present only in its effects, in contrast to a commodity, a particular material object which miraculously 'comes to life', starts to move as if endowed with an invisible spirit" (103). Time for me to get back to the question of desire. One of the more fascinating and disturbing uptakes of this approach to the fetish is that the fetishistic misrecognition persists and insists beyond any interpretative intervention. This is the necessary conclusion of the fact that fetishism is not about what we know, but what we do: 'I know all too well that computer games are informational commodities generating profits for capitalist enterprises, but damn, they are fun to play.' The problem with gameplay is not one of explaining it, symbolising it, or even finding the appropriate theoretical vocabulary in which to talk about it. Gamers have come up with a range of different and flexible ways of discussing (dare I say, quite reflexively) the experience of gameplay. The problem is that I can never quite get rid of this problem of gameplay, it insists on sticking and attaching itself to my ethnography. Bruno Latour picks up on this dilemma with the observation that despite all the best efforts of the anti-fetishist critic "somehow the fetish gains in strength ... . The more you want it to be nothing, the more action springs back from it" (270). Even the attempt to generate a kind of critical distance through the process of 'writing up' the dissertation is smeared with the rather disgusting, perverted Enjoyment taken in disclosing and robbing the other of their Enjoyment. It is as if we are compelled, interpellated, by an anonymous superegoic injunction to 'Enjoy our gaming'. As Slavoj Zizek argues in his recent work (including the magnificent The Ticklish Subject: The Absent Centre of Political Ontology) the order of capital no longer functions according to the matrix of desire, a prohibitive injunction that sets in motion the impossibility of satisfying desire that is "reflexively inverted into the desire for nonsatisfaction" (345). Instead we get a corporate "little brother" commanding us to Enjoy ourselves! (The Ticklish Subject 347) Perhaps the only response open to us in these circumstances is in the act of insisting on a bottom line: $. References Banks, John. "Controlling Gameplay." M/C: A Journal of Media and Culture 1.5 (1998). 22 July 1999 <http://www.uq.edu.au/mc/9812/game.php>. Latour, Bruno. Pandora's Hope: Essays on the Reality of Science Studies. Cambridge, Mass.: Harvard UP, 1999. Smith, Sean Aylward. "Where Does the Body End?" M/C: A Journal of Media and Culture 2.3 (1999). 22 July 1999 <http://www.uq.edu.au/mc/9905/end.php>. Zizek, Slavoj. "Fetishism and Its Vicissitudes." The Plague of Fantasies. London: Verso, 1997. 86-126. ---. The Sublime Object of Ideology. London: Verso, 1989. ---. The Ticklish Subject: The Absent Centre of Political Ontology. London: Verso, 1999. Citation reference for this article MLA style: John Banks. "From Fetish to Factish and Back Again." M/C: A Journal of Media and Culture 2.5 (1999). [your date of access] <http://www.uq.edu.au/mc/9907/games.php>. Chicago style: John Banks, "From Fetish to Factish and Back Again," M/C: A Journal of Media and Culture 2, no. 5 (1999), <http://www.uq.edu.au/mc/9907/games.php> ([your date of access]). APA style: John Banks. (1999) From fetish to factish and back again. M/C: A Journal of Media and Culture 2(5). <http://www.uq.edu.au/mc/9907/games.php> ([your date of access]).