Journal articles on the topic 'Taylor expansion diagram'

The absolute visual magnitude as function of the observed color (B-V), also named Hertzsprung-Russell diagram, can be described through five equations; that when calibrated stars are available means eight constants. The developed framework allows to deduce the remaining physical parameters, mass, radius and luminosity. This new technique is applied to the first 10 pc, the first 50 pc, the Hyades and to the determination of the distance of a cluster. The case of the white dwarfs is analyzed assuming the absence of calibrated data: our equation produces a smaller ?2 with respect to the standard color-magnitude calibration when applied to the Villanova Catalog of Spectroscopically Identified White Dwarfs. The theoretical basis of the formulas for the colors and the bolometric correction of the stars is clarified by a Taylor expansion in the temperature of the Planck distribution.

Over the past decade, chaotic systems have found their immense application in different fields, which has led to various generalized, novel, and modified chaotic systems. In this paper, the general jerk equation is combined with a scaled sine map, which has been approximated in terms of a polynomial using Taylor series expansion for exhibiting chaotic behavior. The paper is based on numerical simulation and experimental verification of the system with four control parameters. The proposed system’s chaotic behavior is verified by calculating different chaotic invariants using MATLAB, such as bifurcation diagram, 2-D attractor, Fourier spectra, correlation dimension, and Maximum Lyapunov Exponent. Experimental verification of the system was carried out using Op-Amps with analog multipliers.

It is a common phenomenon in the field of financial research to study the dynamic of financial market and explore the complexity of financial system by using various complex scientific methods. In this paper, the chaotic dynamic properties of financial time series are analyzed. Firstly, the nonlinear characteristics of the data are discussed through the empirical analysis of agriculture index data; the daily agriculture index returns can be decomposed into the different scales based on wavelet analysis. Secondly, the dynamic system of some nonlinear characteristic data is established according to the Taylor series expansion form, and the corresponding dynamic characteristics are analyzed. Finally, the bifurcation diagram of the system shows complicated bifurcation phenomena, which provides a perspective for the analysis of chaotic phenomena of economic data.

The quasi-zero stiffness system has the characteristics of low dynamic stiffness and high static stiffness, which can bring a better driving experience and lower road dynamic load at high speed on irregular roads. This paper studies a type of interconnected quasi-zero stiffness air suspension system, which has two states, namely, the non-interconnected quasi-zero stiffness air suspension and the interconnected quasi-zero stiffness air suspension, to meet the performance requirements under different loads and vehicle speed. First, the mathematical model of the nonlinear system is established based on the basic principles of fluid mechanics and thermodynamics. Then, the stability of the equilibrium point is analyzed using the Lyapunov first method, where the quantitative analysis of the attractive region of the system is conducted through the bifurcation diagram and phase diagram. By using the Taylor series expansion, cell-mapping theory and domain map of attraction, the attractive region of the system is quantitatively analyzed to obtain the parametric feasible domain under stable conditions. Finally, the performance of the quasi-zero stiffness suspension system with the selected parameters under the stability constraint is verified by simulation analysis and experiment. The results show that the system represented in this paper provides higher suspension comfort and stability.

We investigate the properties of QCD at finite isospin chemical potential at zero and non-zero temperatures. This theory is not affected by the sign problem and can be simulated using Monte-Carlo techniques. With increasing isospin chemical potential and temperatures below the deconfinement transition the system changes into a phase where charged pions condense, accompanied by an accumulation of low modes of the Dirac operator. The simulations are enabled by the introduction of a pionic source into the action, acting as an infrared regulator for the theory, and physical results are obtained by removing the regulator via an extrapolation. We present an update of our study concerning the associated phase diagram using 2+1 flavours of staggered fermions with physical quark masses and the comparison to Taylor expansion. We also present first results for our determination of the equation of state at finite isospin chemical potential and give an example for a cosmological application. The results can also be used to gain information about QCD at small baryon chemical potentials using reweighting with respect to the pionic source parameter and the chemical potential and we present first steps in this direction.

This paper proposes a semi-active variable stiffness vibration isolation system based on electromagnetic spring for the low-frequency vibration isolation of mass-varying objects. It is achieved by four straight leaf springs in parallel to an electromagnetic spring system composed of a single electromagnet and a permanent magnet. The equivalent magnetic circuit method is used to compute electromagnetic force of the electromagnetic spring system, and mathematical model of the semi-active vibration isolation system is established according to Maxwell's equations. The nonlinear mathematical model is linearized at the equilibrium point by using the Taylor series expansion theorem to establish linear state-space representation of the system, and then using the traditional PID control method, a double closed-loop feedback control system of the inner current loop and outer location loop is designed. By controlling the current in the coil, the equivalent stiffness and electromagnetic force of the system are variable to achieve semi-active control. Furthermore, the control block diagram of the semi-active vibration isolation system is built based on Simulink software, then make a simulation analysis to the vibration isolation performance of the system and compare the effects of vibration isolation with inner current loop control and without inner current loop control, respectively. Finally, the experiments prove the correctness of the theory. It concludes that this semi-active vibration isolation system is a vibration isolation system with broad application prospects, which has fast current response, high vibration isolation efficiency, and an excellent vibration isolation effect for the low-frequency disturbance of mass-varying objects.

In a recent paper1 a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared, a certain conformal mapping and subsequent resummation by means of Padé approximants. I present numerical examples.

In order to point out the influence of the crystallographic texture on the formability of 2 aluminium alloys, the orientation distribution function (ODF) will be carried out using the series expansion method. Combining the ODF with a Taylor plastic deformation model we are able to calculate the yield loci and to predict the plastic strain ratio which is of high interest in the formability.

The paper addresses the mathematical modelling of the formation of a pointed drop in a four-roller mill, observed by Taylor (1934) in the Cavendish Laboratory. Since the experiments were carried out with drops of small diameter compared to the mill size, the method of matched asymptotic expansions is applicable. A two-dimensional Stokes flow generated by the rotating rollers in the mill but with no drop effect (outer problem) is computed numerically by a boundary-element method. The local expansion of that flow at the centre of the mill, where the drop is to be positioned, is used as a far field for the flow around the drop in unbounded fluid (inner problem). Employing a plane-flow model and using complex-variable techniques, the explicit solutions previously obtained by the author are adapted to the inner problem. It is proved that, with an increasing rotation rate of the rollers, the drop does develop two apparent cusps on the interface, and its shapes have striking similarities with Taylor's experiments. Response diagrams showing the drop distortion versus the elongational strain demonstrate that these are one-to-one function of each other if the drop diameter is greater than a critical value determined by the size of the mill but cease to be one-to-one otherwise. This behaviour is identified with a sudden transition from a rounded drop to a cusped one at a critical strain.

We present several algorithms, executable in a finite number of steps, which have been implemented in the symbolic language maple. The standard form algorithm reduces a system of PDEs to a simplified standard form which has all of its integrability conditions satisfied (i.e. is involutive). The initial data algorithm uses a system's standard form to calculate a set of initial data that uniquely determines a local solution to the system without needing to solve the system. The number of arbitrary constants and arbitrary functions in the general solution to the system is directly calculable from this set. The taylor algorithm uses a system's standard form and initial data set to determine the Taylor series expansion of its solution about any point to any given finite degree. All systems of linear PDEs and many systems of nonlinear PDEs can be reduced to standard form in a finite number of steps. Our algorithms have simple geometric interpretations which are illustrated through the use of diagrams. The standard form algorithm is generally more efficient than the classical methods due to Janet and Cartan for reducing systems of PDEs to involutive form.

The investigation of hyperelastic responses of soft materials and structures is essential for understanding of the mechanical behaviors and for the design of soft systems. In this paper, by considering both the material and geometrical nonlinearities, a new neo-Hookean model for the hyperelastic beam is developed with focus on its nonlinear free vibration with large strain deformations. The neo-Hookean model is employed to capture the large strain deformation of the hyperelastic beam. The governing equations of the hyperelastic beam are derived by using Hamilton’s principle. To avoid expensive calculations for solving the nonlinear governing equations, a simplified Taylor-series expansion model is proposed. The effects of two key system parameters, i.e. the initial displacement amplitude and the slenderness ratio, on the nonlinear free vibrations of the hyperelastic beam are numerically analyzed. The bifurcation diagrams, displacement time traces, phase portraits and power spectral diagrams are presented for the nonlinear free vibrations of the hyperelastic beam. For small initial displacement amplitudes, it is found that the hyperelastic beam will undergo limit cycle oscillations, depending on the initial amplitude employed. For initial displacement amplitudes large enough, interestingly, the free vibration of the hyperelastic beam will become quasi-periodic or chaotic, which were rarely reported for the free vibration of linearly elastic beams. Also observed is the traveling wave feature of oscillating shapes of the hyperelastic beam, indicating that higher-order modes of the beam are excited even for free vibrations. All these new features in the nonlinear free vibrations of hyperelastic beams indicate that the material and geometric nonlinearities play a great role in the dynamic analysis of hyperelastic beams.

A model is presented for viscous flow in a cylindrical cavity (a half-filled annulus lying between horizontal, infinitely long concentric cylinders of radii Ri, Ro rotating with peripheral speeds Ui, Uo). Stokes' approximation is used to formulate a boundary value problem which is solved for the streamfunction, ω, as a function of radius ratio R¯= Ri/Ro and speed ratio S=Ui/Uo.Results show that for S>0 (S<0) the flow domain consists of two (one) large eddies (eddy), each having a stagnation point on the centreline and a potentially rich substructure with separatrices and sub-eddies. The behaviour of the streamfunction solution in the neighbourhood of stagnation points on the centreline is investigated by means of a truncated Taylor expansion. As R¯ and S are varied it is shown that a bifurcation in the flow structure arises in which a centre becomes a saddle stagnation point and vice versa. As R¯→1, a sequence of ‘flow bifurcations’ leads to a flow structure consisting of a set of nested separatrices, and provides the means by which the two-dimensional cavity flow approaches quasi-unidirectional flow in the small gap limit. Control-space diagrams reveal that speed ratio has little effect on the flow structure when S<0 and also when S>0 and aspect ratios are small (except near S=1). For S>0 and moderate to large aspect ratios the bifurcation characteristics of the two large eddies are quite different and depend on both R¯ and S.

AbstractLand degradation (LD) is a complex process affected by both anthropogenic and natural driving variables, and its prevention has become an essential task globally. The aim of the present study was to develop a new quantitative LD mapping approach using machine learning techniques, benchmark models, and human-induced and socio-environmental variables. We employed four machine learning algorithms [Support Vector Machine (SVM), Multivariate Adaptive Regression Splines (MARS), Generalized Linear Model (GLM), and Dragonfly Algorithm (DA)] for LD risk mapping, based on topographic (n = 7), human-induced (n = 5), and geo-environmental (n = 6) variables, and field measurements of degradation in the Pole-Doab watershed, Iran. We assessed the performance of different algorithms using receiver operating characteristic, Kappa index, and Taylor diagram. The results revealed that the main topographic, geoenvironmental, and human-induced variable was slope, geology, and land use change, respectively. Assessments of model performance indicated that DA had the highest accuracy and efficiency, with the greatest learning and prediction power in LD risk mapping. In LD risk maps produced using SVM, GLM, MARS, and DA, 19.16%, 19.29%, 21.76%, and 22.40%, respectively, of total area in the Pole-Doab watershed had a very high degradation risk. The results of this study demonstrate that in LD risk mapping for a region, topographic, and geological factors (static conditions) and human activities (dynamic conditions, e.g., residential and industrial area expansion) should be considered together, for best protection at watershed scale. These findings can help policymakers prioritize land and water conservation efforts.

We study the nonlinear Rayleigh–Taylor instability of the interface between two viscous fluids, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. The fluids are considered to be viscous and incompressible with different kinematic viscosities. The method of multiple expansions has been used for the investigation. In the nonlinear theory, it is shown that the evolution of the amplitude is governed by a Ginzburg–Landau equation. The various stability criteria are discussed both analytically and numerically and stability diagrams are obtained. It has been observed that the heat and mass transfer has stabilizing effect on the stability of the system in the nonlinear analysis.

Abstract In aviation and navigation, complicated parts are milled with high-speed low-feed-per-tooth milling to decrease tool vibration for high quality. Because the nonlinearity of the cutting force coefficient (CFC) is more evident with the relatively smaller instantaneous uncut chip thickness, the stable critical cutting depth and its distribution against different tool postures are affected. Considering the nonlinearity, a nonlinear dynamic CFC model that reveals the effect of the dynamic instantaneous uncut chip thickness on the dynamic cutting force is derived based on the Taylor expansion. A five-axis bull-nose end milling dynamics model is established with the nonlinear dynamic CFC model. The stable critical cutting depth distribution with respect to tool posture is analyzed. The stability results predicted with the dynamic CFC model are compared with those from the static CFC model and the constant CFC model. The effects of tool posture and feed per tooth on stable critical cutting depth were also analyzed, and the proposed model was validated by cutting experiments. The maximal stable critical cutting depths that can be achieved under different tool postures by feed per tooth adjustment were calculated, and corresponding distribution diagrams are proposed for milling parameter optimization.

IntroductionIn his now-seminal book, Pilgrim in the Microworld (1983), David Sudnow details his process of learning to play the game Breakout on the Atari 2600. Sudnow develops an account of his graduation from a novice (having never played a videogame prior, and middle-aged at time of writing) to being able to fluidly perform the various configurative processes involved in an acclimated Breakout player’s repertoire.Sudnow’s account of videogame skill-development is not at odds with common-sense views on the matter: people become competent at videogames by playing them—we get used to how controllers work and feel, and to the timings of the game and those required of our bodies, through exposure. We learn by playing, failing, repeating, and ultimately internalising the game’s rhythms—allowing us to perform requisite actions. While he does not put it in as many words, Sudnow’s account affords parity to various human and nonhuman stakeholders involved in videogame-play: technical, temporal, and corporeal. Essentially, his point is that intertwined technical systems like software and human-interface devices—with their respective temporal rhythms, which coalesce and conflict with those of the human player—require management to play skilfully.The perspective Sudnow develops here is no doubt important, but modes of building competency cannot be strictly fixed around a player-videogame relationship; a relatively noncontroversial view in game studies. Videogame scholars have shown that there is currency in understanding how competencies in gameplay arise from engaging with ancillary objects beyond the thresholds of player-game relations; the literature to date casting a long shadow across a broad spectrum of materials and practices. Pursuing this thread, this article addresses the enterprise (and conceptualisation) of ‘skill building’ in videogames (taken as the ability to ‘beat games’ or cultivate the various competencies to do so) via the invocation of peripheral objects or practices. More precisely, this article develops the perspective that we need to attend to the impacts of ancillary objects on play—positioned as hybrid assemblage, as described in the work of writers like Sudnow. In doing so, I first survey how the intervention of peripheral game material has been researched and theorised in game studies, suggesting that many accounts deal too simply with how players build skill through these means—eliding the fact that play works as an engine of many moving parts. We do not simply become ‘better’ at videogames by engaging peripheral material. Furthering this view, I visit recent literature broadly associated with disciplines like post-phenomenology, which handles the hybridity of play and its extension across bodies, game systems, and other gaming material—attending to how skill building occurs; that is, through the recalibration of perceptual faculties operating in the bodily and temporal dimensions of videogame play. We become ‘better’ at videogames by drawing on peripheral gaming material to augment how we negotiate the rhythms of play.Following on from this, I conclude by mobilising post-phenomenological thinking to further consider skill-building through peripheral material, showing how such approaches can generate insights into important and emerging areas of this practice. Following recent games research, such as the work of James Ash, I adopt Bernard Stiegler’s formulation of technicity—pointing toward the conditioning of play through ancillary gaming objects: focusing particularly on the relationship between game skill, game guides, and embodied processes of memory and perception.In short, this article considers videogame skill-building, through means beyond the game, as a significant recalibration of embodied, temporal, and technical entanglements involved in play. Building Skill: From Guides to BodiesThere is a handsome literature that has sought to conceptualise the influence of ancillary game material, which can be traced to earlier theories of media convergence (Jenkins). More incisive accounts (pointing directly at game-skill) have been developed since, through theoretical rubrics such as paratext and metagaming. A point of congruence is the theme of relation: the idea that the locus of understanding and meaning can be specified through things outside the game. For scholars like Mia Consalvo (who popularised the notion of paratext in game studies), paratexts are a central motor in play. As Consalvo suggests, paratexts are quite often primed to condition how we do things in and around videogames; there is a great instructive potential in material like walkthrough guides, gaming magazines and cheating devices. Subsequent work has since made productive use of the concept to investigate game-skill and peripheral material and practice. Worth noting is Chris Paul’s research on World of Warcraft (WoW). Paul suggests that players disseminate high-level strategies through a practice known as ‘Theorycraft’ in the game’s community: one involving the use of paratextual statistics applications to optimise play—the results then disseminated across Web-forums (see also: Nardi).Metagaming (Salen and Zimmerman 482) is another concept that is often used to position the various extrinsic objects or practices installed in play—a concept deployed by scholars to conceptualise skill building through both games and the things at their thresholds (Donaldson). Moreover, the ability to negotiate out-of-game material has been positioned as a form of skill in its own right (see also: Donaldson). Becoming familiar with paratextual resources and being able to parse this information could then constitute skill-building. Ancillary gaming objects are important, and as some have argued, central in gaming culture (Consalvo). However, critical areas are left unexamined with respect to skill-building, because scholars often fail to place paratexts or metagaming in the contexts in which they operate; that is, amongst the complex technical, embodied and temporal conjunctures of play—such as those described by Sudnow. Conceptually, much of what Sudnow says in Microworld undergirds the post-human, object-oriented, or post-phenomenological literature that has begun to populate game studies (and indeed media studies more broadly). This materially-inflected writing takes seriously the fact that technical objects (like videogames) and human subjects are caught up in the rhythms of each other; digital media exists “as a mode or cluster of operations in consort with matter”, as Anna Munster tells us (330).To return to videogames, Patrick Crogan and Helen Kennedy argue that gameplay is about a “technicity” between human and nonhuman things, irreducible to any sole actor. Play is a confluence of metastable forces and conditions, a network of distributed agencies (see also Taylor, Assemblage). Others like Brendan Keogh forward post-phenomenological approaches (operating under scholars like Don Ihde)—looking past the subject-centred nature of videogame research. Ultimately, these theorists situate play as an ‘exploded diagram’, challenging anthropocentric accounts.This position has proven productive in research on ‘skilled’ or ‘high-level’ play (fertile ground for considering competency-development). Emma Witkowski, T.L. Taylor (Raising), and Todd Harper have suggested that skilled play in games emerges from the management of complex embodied and technical rhythms (echoing the points raised prior by Sudnow).Placing Paratexts in PlayWhile we have these varying accounts of how skill develops within and beyond player-game relationships, these two perspectives are rarely consolidated. That said, I address some of the limited body of work that has sought to place the paratext in the complex and distributed conjunctures of play; building a vocabulary and framework via encounters with what could loosely be called post-phenomenological thinking (not dissimilar to the just surveyed accounts). The strength of this work lies in its development of a more precise view of the operational reality of playing ‘with’ paratexts. The recent work of Darshana Jayemanne, Bjorn Nansen, and Thomas Apperley theorises the outward expansion of games and play, into diverse material, social, and spatial dimensions (147), as an ‘aesthetics of recruitment’. Consideration is given to ‘paratextual’ play and skill. For instance, they provide the example of players invoking the expertise they have witnessed broadcast through Websites like Twitch.tv or YouTube—skill-building operating here across various fronts, and through various modalities (155). Players are ‘recruited’, in different capacities, through expanded interfaces, which ultimately contour phenomenological encounters with games.Ash provides a fine-grained account in research on spatiotemporal perception and videogames—one much more focused on game-skill. Ash examines how high-level communities of players cultivate ‘spatiotemporal sensitivity’ in the game Street Fighter IV through—in Stiegler’s terms—‘exteriorising’ (Fault) game information into various data sets—producing what he calls ‘technicity’. In this way, Ash suggests that these paratextual materials don’t merely ‘influence play’ (Technology 200), but rather direct how players perceive time, and habituate exteriorised temporal rhythms into their embodied facility (a translation of high-level play). By doing so, the game can be played more proficiently. Following the broadly post-phenomenological direction of these works, I develop a brief account of two paratextual practices. Like Ash, I deploy the work of Stiegler (drawing also on Ash’s usage). I utilise Stiegler’s theoretical schema of technicity to roughly sketch how some other areas of skill-building via peripheral material can be placed within the context of play—looking particularly at the conditioning of embodied faculties of player anticipation, memory and perception through play and paratext alike. A Technicity of ParatextThe general premise of Stiegler’s technicity is that the human cannot be thought of independent from their technical supplements—that is, ‘exterior’ technical objects which could include, but are not limited to, technologies (Fault). Stiegler argues that the human, and their fundamental memory structure is finite, and as such is reliant on technical prostheses, which register and transmit experience (Fault 17). This technical supplement is what Stiegler terms ‘tertiary retention’. In short, for Stiegler, technicity can be understood as the interweaving of ‘lived’ consciousness (Cinematic 21) with tertiary retentional apparatus—which is palpably felt in our orientations in and toward time (Fault) and space (including the ‘space’ of our bodies, see New Critique 11).To be more precise, tertiary retention conditions the relationship between perception, anticipation, and subjective memory (or what Stiegler—by way of phenomenologist Edmund Husserl, whose work he renovates—calls primary retention, protention, and secondary retention respectively). As Ash demonstrates (Technology), Stiegler’s framework is rich with potential in investigating the relationship between videogames and their peripheral materials. Invoking technicity, we can rethink—and expand on—commonly encountered forms of paratexts, such as game guides or walkthroughs (an example Consalvo gives in Cheating). Stiegler’s framework provides a means to assess the technical organisation (through both games and paratexts) of embodied and temporal conditions of ‘skilled play’. Following Stiegler, Consalvo’s example of a game guide is a kind of ‘exteriorisation of play’ (to the guide) that adjusts the embodied and temporal conditions of anticipation and memory (which Sudnow would tell us are key in skill-development). To work through an example, if I was playing a hard game (such as Dark Souls [From Software]), the general idea is that I would be playing from memories of the just experienced, and with expectations of what’s to come based on everything that’s happened prior (following Stiegler). There is a technicity in the game’s design here, as Ash would tell us (Technology 190-91). By way of Stiegler (and his reading of Heidegger), Ash argues a popular trend in game design is to force a technologically-mediated interplay between memory, anticipation, and perception by making videogames ‘about’ a “a future outside of present experience” (Technology 191), but hinging this on past-memory. Players then, to be ‘skilful’, and move forward through the game environment without dying, need to manage cognitive and somatic memory (which, in Dark Souls, is conventionally accrued through trial-and-error play; learning through error incentivised through punitive game mechanics, such as item-loss). So, if I was playing against one of the game’s ‘bosses’ (powerful enemies), I would generally only be familiar with the way they manoeuvre, the speed with which they do so, and where and when to attack based on prior encounter. For instance, my past-experience (of having died numerous times) would generally inform me that using a two-handed sword allows me to get in two attacks on a boss before needing to retreat to avoid fatal damage. Following Stiegler, we can understand the inscription of videogame experience in objects like game guides as giving rise to anticipation and memory—albeit based on a “past that I have not lived but rather inherited as tertiary retentions” (Cinematic 60). Tertiary retentions trigger processes of selection in our anticipations, memories, and perceptions. Where videogame technologies are traditionally the tertiary retentions in play (Ash, Technologies), the use of game-guides refracts anticipation, memory, and perception through joint systems of tertiary retention—resulting in the outcome of more efficiently beating a game.To return to my previous example of navigating Dark Souls: where I might have died otherwise, via the guide, I’d be cognisant to the timings within which I can attack the boss without sustaining damage, and when to dodge its crushing blows—allowing me to eventually defeat it and move toward the stage’s end (prompting somatic and cognitive memory shifts, which influence my anticipation in-game). Through ‘neurological’ accounts of technology—such as Stiegler’s technicity—we can think more closely about how playing with a skill-building apparatus (like a game guide) works in practice; allowing us to identify how various situations ingame can be managed via deferring functions of the player (such as memory) to exteriorised objects—shifting conditions of skill building. The prism of technicity is also useful in conceptualising some of the new ways players are building skill beyond the game. In recent years, gaming paratexts have transformed in scope and scale. Gaming has shifted into an age of quantification—with analytics platforms which harvest, aggregate, and present player data gaining significant traction, particularly in competitive and multiplayer videogames. These platforms perform numerous operations that assist players in developing skill—and are marketed as tools for players to improve by reflecting on their own practices and the practices of others (functioning similarly to the previously noted practice of TheoryCraft, but operating at a wider scale). To focus on one example, the WarCraftLogs application in WoW (Image 1) is a highly-sophisticated form of videogame analytics; the perspective of technicity providing insights into its functionality as skill-building apparatus.Image 1: WarCraftLogs. Image credit: Ben Egliston. Following Ash’s use of Stiegler (Technology), quantifying the operations that go into playing WoW can be conceptualised as what Stiegler calls a system of traces (Technology 196). Because of his central thesis of ‘technical existence’, Stiegler maintains that ‘interiority’ is coincident with technical support. As such, there is no calculation, no mental phenomena, that does not arise from internal manipulation of exteriorised symbols (Cinematic 52-54). Following on with his discussion of videogames, Ash suggests that in the exteriorisation of gameplay there is “no opposition between gesture, calculation and the representation of symbols” (Technology 196); the symbols working as an ‘abbreviation’ of gameplay that can be read as such. Drawing influence from this view, I show that ‘Big Data’ analytics platforms like WarCraftLogs similarly allow users to ‘read’ play as a set of exteriorised symbols—with significant outcomes for skill-building; allowing users to exteriorise their own play, examine the exteriorised play of others, and compare exteriorisations of their own play with those of others. Image 2: WarCraftLogs Gameplay Breakdown. Image credit: Ben Egliston.Image 2 shows a screenshot of the WarCraftLogs interface. Here we can see the exteriorisation of gameplay, and how the platform breaks down player inputs and in-game occurrences (written and numeric, like Ash’s game data). The screenshot shows a ‘raid boss’ (where players team up to defeat powerful computer-controlled enemies)—atomising the sequence of inputs a player has made over the course of the encounter. This is an accurate ledger of play—a readout that can speak to mechanical performance (specific ingame events occurred at a specific time), as well as caching and providing parses of somatic inputs and execution (e.g. ability to trace the rates at which players expend in-game resources can provide insights into rapidity of button presses). If information falls outside what is presented, players can work with an Application Programming Interface to develop customised readouts (this is encouraged through other game-data platforms, like OpenDota in Dota 2). Through this system, players can exteriorise their own input and output or view the play of others—both useful in building skill. The first point here—of exteriorising one’s own experience—resonates with Stiegler’s renovation of Husserl's ‘temporal object’—that is, an object that exists in and is formed through time—through temporal fluxes of what appears, what happens and what manifests itself in disappearing (Cinematic 14). Stiegler suggests that tertiary retentional apparatus (e.g. a gramophone) allow us to re-experience a temporal object (e.g. a melody) which would otherwise not be possible due to the finitude of human memory.To elaborate, Stiegler argues that primary memories recede into secondary memory (which is selective reactivation of perception), but through technologies of recording, (such as game-data) we can re-experience these things verbatim. So ultimately, games analytics platforms—as exteriorised technologies of recording—facilitate this after-the-fact interplay between primary and secondary memory where players can ‘audit’ their past performance, reflecting on well-played encounters or revising error. These platforms allow the detailed examination of responses to game mechanics, and provide readouts of the technical and embodied rhythms of play (which can be incorporated into future play via reading the data). Beyond self-reflection, these platforms allow the examination of other’s play. The aggregation and sorting of game-data makes expertise both visible and legible. To elaborate, players are ranked on their performance based on all submitted log-data, offering a view of how expertise ‘works’.Image 3: Top-Ranking Players in WarCraftLogs. Image credit: Ben Egliston.Image 3 shows the top-ranked players on an encounter (the top 10 of over 100,000 logs), which means that these players have performed most competently out of all gameplay parses (the metric being most damage dealt per-second in defeating a boss). Users of the platform can look in detail at the actions performed by top players in that encounter—reading and mobilising data in a similar manner to game-guides; markedly different, however, in terms of the scope (i.e. there are many available logs to draw from) and richness of the data (more detailed and current—with log rankings recalibrated regularly). Conceptually, we can also draw parallels with previous work (see: Ash, Technology)—where the habituation of expert game data can produce new videogame technicities; ways of ‘experiencing’ play as ‘higher-level’ organisation of space and time (Ash, Technology). So, if a player wanted to ‘learn from the experts’ they would restructure their own rhythms of play around high-level logs which provide an ordered readout of various sequences of inputs involved in playing well. Moreover, the platform allows players to compare their logs to those of others—so these various introspective and outward-facing uses can work together, conditioning anticipations with inscriptions of past-play and ‘prosthetic’ memories through other’s log-data. In my experience as a WoW player, I often performed better (or built skill) by comparing and contrasting my own detailed readouts of play to the inputs and outputs of the best players in the world.To summarise, through technicity, I have briefly shown how exteriorising play shifts the conditions of skill-building from recalibrating msnesic and anticipatory processes through ‘firsthand’ play, to reworking these functions through engaging both games and extrinsic objects, like game guides and analytics platforms. Additionally, by reviewing and adopting various usages of technicity, I have pointed out how we might more holistically situate the gaming paratext in skill building. Conclusion There is little doubt—as exemplified through both scholarly and popular interest—that paratextual videogame material reframes modes of building game skill. Following recent work, and by providing a brief account of two paratextual practices (venturing the framework of technicity, via Stiegler and Ash—showing the complication of memory, perception, and anticipation in skill-building), I have contended that videogame-skill building—via paratextual material—can be rendered a process of operating outside of, but still caught up in, the complex assemblages of time, bodies, and technical architectures described by Sudnow at this article’s outset. 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